diff options
95 files changed, 26080 insertions, 32551 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 580f35bf..4931d673 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,12 @@ +2008-11-20 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/coerce.spad.pamphlet (CoercibleFrom): New. + (ConvertibleFrom): Likewise. + (RetractableTo): Use it. + * algebra/Makefile.pamphlet (axiom_algebra_layer_0): Include + KRCFROM and KVTFROM. + * share/algebra/: Update databases. + 2008-11-18 Gabriel Dos Reis <gdr@cs.tamu.edu> * interp/sys-utility.boot (loadExports): New. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 7d0e7223..0e9b9f99 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -356,6 +356,7 @@ axiom_algebra_bootstrap_objects = \ axiom_algebra_layer_0 = \ AHYP ATTREG CFCAT ELTAB KOERCE KONVERT \ + KRCFROM KVTFROM \ MSYSCMD OM OMCONN OMDEV OUT \ PRIMCAT PRINT PTRANFN SPFCAT TYPE UTYPE \ PROPERTY BASTYPE BASTYPE- CATEGORY LMODULE \ diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index f6156809..28f9ad4e 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -185,6 +185,7 @@ system.spad.pamphlet (MSYSCMD) axiom_algebra_layer_0 = \ AHYP ATTREG CFCAT ELTAB KOERCE KONVERT \ + KRCFROM KVTFROM \ MSYSCMD OM OMCONN OMDEV OUT \ PRIMCAT PRINT PTRANFN SPFCAT TYPE UTYPE \ PROPERTY BASTYPE BASTYPE- CATEGORY LMODULE \ diff --git a/src/algebra/coerce.spad.pamphlet b/src/algebra/coerce.spad.pamphlet index f270bba6..8176377a 100644 --- a/src/algebra/coerce.spad.pamphlet +++ b/src/algebra/coerce.spad.pamphlet @@ -1,15 +1,20 @@ \documentclass{article} \usepackage{axiom} -\begin{document} + \title{\$SPAD/src/algebra coerce.spad} \author{Richard Jenks, Manuel Bronstein, Gabriel Dos Reis} + + +\begin{document} + \maketitle \begin{abstract} \end{abstract} -\eject \tableofcontents \eject + \section{category TYPE Type} + <<category TYPE Type>>= )abbrev category TYPE Type ++ The new fundamental Type (keeping Object for 1.5 as well) @@ -39,6 +44,7 @@ UnionType(): Category == with nil \section{category KOERCE CoercibleTo} + <<category KOERCE CoercibleTo>>= )abbrev category KOERCE CoercibleTo ++ Category for coerce @@ -53,7 +59,28 @@ CoercibleTo(S:Type): Category == with ++ coerce(a) transforms a into an element of S. @ + +\section{category KRCFROM CoercibleFrom} + +<<category KRCFROM CoercibleFrom>>= +)abbrev category KRCFROM CoercibleFrom +++ Author: Gabriel Dos Reis +++ Date Create: November 19, 2008 +++ Date Last Modified: November 19, 2008 +++ See Also: CoercibleTo +++ Description: +++ A is coercible from B iff any element of domain B can be +++ automically converted into an element of domain B. In symbols +++ A has CoercibleFrom B <=> B has CoercibleTo A +CoercibleFrom(S: Type): Category == with + coerce: S -> % + ++ coerce(s) transforms `s' into an element of `%'. + +@ + + \section{category KONVERT ConvertibleTo} + <<category KONVERT ConvertibleTo>>= )abbrev category KONVERT ConvertibleTo ++ Category for convert @@ -69,20 +96,43 @@ ConvertibleTo(S:Type): Category == with ++ convert(a) transforms a into an element of S. @ + +\section{category KVTFROM ConvertibleFrom} + +<<category KVTFROM ConvertibleFrom>>= +)abbrev category KVTFROM ConvertibleFrom +++ Author: Gabriel Dos Reis +++ Date Create: November 19, 2008 +++ Date Last Modified: November 19, 2008 +++ See Also: ConvertibleTo +++ Description: +++ A is convertible from B iff any element of domain B can be +++ explicitly converted into an element of domain B. In symbols +++ A has ConvertibleFrom B <=> B has ConvertibleTo A +ConvertibleFrom(S: Type): Category == with + convert: S -> % + ++ convert(s) transforms `s' into an element of `%'. + +@ + + + + + \section{category RETRACT RetractableTo} + <<category RETRACT RetractableTo>>= )abbrev category RETRACT RetractableTo ++ Category for retract ++ Author: ??? ++ Date Created: ??? -++ Date Last Updated: 14 May 1991 +++ Date Last Updated: November 19, 2008 +++ Related Constructor: CoercibleFrom ++ Description: ++ A is retractable to B means that some elementsif A can be converted ++ into elements of B and any element of B can be converted into an ++ element of A. -RetractableTo(S: Type): Category == with - coerce: S -> % - ++ coerce(a) transforms a into an element of %. +RetractableTo(S: Type): Category == CoercibleFrom S with retractIfCan: % -> Union(S,"failed") ++ retractIfCan(a) transforms a into an element of S if possible. ++ Returns "failed" if a cannot be made into an element of S. @@ -95,10 +145,14 @@ RetractableTo(S: Type): Category == with u @ + \section{License} + <<license>>= --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 @@ -134,7 +188,9 @@ RetractableTo(S: Type): Category == with <<category TYPE Type>> <<category UTYPE UnionType>> <<category KOERCE CoercibleTo>> +<<category KRCFROM CoercibleFrom>> <<category KONVERT ConvertibleTo>> +<<category KVTFROM ConvertibleFrom>> <<category RETRACT RetractableTo>> @ \eject diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index 4b434a9d..f0cf420e 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -603,6 +603,7 @@ (|CancellationAbelianMonoid| . CABMON) (|CharacteristicNonZero| . CHARNZ) (|CharacteristicZero| . CHARZ) + (|CoercibleFrom| . KRCFROM) (|CoercibleTo| . KOERCE) (|Collection| . CLAGG) (|CombinatorialFunctionCategory| . CFCAT) @@ -610,6 +611,7 @@ (|CommutativeRing| . COMRING) (|ComplexCategory| . COMPCAT) (|Conduit| . CONDUIT) + (|ConvertibleFrom| . KVTFROM) (|ConvertibleTo| . KONVERT) (|DequeueAggregate| . DQAGG) (|Dictionary| . DIAGG) diff --git a/src/algebra/strap/ABELGRP-.lsp b/src/algebra/strap/ABELGRP-.lsp index 2fdeec9b..dc10e8f6 100644 --- a/src/algebra/strap/ABELGRP-.lsp +++ b/src/algebra/strap/ABELGRP-.lsp @@ -68,38 +68,3 @@ 0 0 13 0 21 2 0 11 0 0 12 2 0 0 0 0 9 2 0 0 13 0 21 2 0 0 15 0 16))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|AbelianGroup&| '|isFunctor| - '(((* ($ (|Integer|) $)) T (ELT $ 21)) - ((- ($ $ $)) T (ELT $ 9)) ((- ($ $)) T (ELT $ NIL)) - ((|subtractIfCan| ((|Union| $ "failed") $ $)) T - (ELT $ 12)) - ((* ($ (|NonNegativeInteger|) $)) T (ELT $ 16)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ NIL))) - (|addModemap| '|AbelianGroup&| '(|AbelianGroup&| |#1|) - '((CATEGORY |domain| - (SIGNATURE * (|#1| (|Integer|) |#1|)) - (SIGNATURE - (|#1| |#1| |#1|)) - (SIGNATURE - (|#1| |#1|)) - (SIGNATURE |subtractIfCan| - ((|Union| |#1| "failed") |#1| |#1|)) - (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) - (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) - (|AbelianGroup|)) - T '|AbelianGroup&| - (|put| '|AbelianGroup&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE * (|#1| (|Integer|) |#1|)) - (SIGNATURE - (|#1| |#1| |#1|)) - (SIGNATURE - (|#1| |#1|)) - (SIGNATURE |subtractIfCan| - ((|Union| |#1| "failed") |#1| - |#1|)) - (SIGNATURE * - (|#1| (|NonNegativeInteger|) |#1|)) - (SIGNATURE * - (|#1| (|PositiveInteger|) |#1|))) - (|AbelianGroup|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/ABELGRP.lsp b/src/algebra/strap/ABELGRP.lsp index dd8da1ef..e2f7daf4 100644 --- a/src/algebra/strap/ABELGRP.lsp +++ b/src/algebra/strap/ABELGRP.lsp @@ -13,7 +13,7 @@ ((* ($ (|Integer|) $)) T)) NIL '((|Integer|)) NIL)) |AbelianGroup|) - (SETELT #0# 0 '(|AbelianGroup|)))))) + (|setShellEntry| #0# 0 '(|AbelianGroup|)))))) (DEFUN |AbelianGroup| () (LET () @@ -21,9 +21,4 @@ (|AbelianGroup;AL|) (T (SETQ |AbelianGroup;AL| (|AbelianGroup;|)))))) -(SETQ |$CategoryFrame| - (|put| '|AbelianGroup| '|isCategory| T - (|addModemap| '|AbelianGroup| '(|AbelianGroup|) - '((|Category|)) T '|AbelianGroup| |$CategoryFrame|))) - (MAKEPROP '|AbelianGroup| 'NILADIC T) diff --git a/src/algebra/strap/ABELMON-.lsp b/src/algebra/strap/ABELMON-.lsp index 1c1cdd43..bfdc7eee 100644 --- a/src/algebra/strap/ABELMON-.lsp +++ b/src/algebra/strap/ABELMON-.lsp @@ -61,29 +61,3 @@ 16 6 13 6 17 2 0 0 11 0 18 1 0 8 0 10 0 0 0 15 2 0 0 11 0 18 2 0 0 13 0 14))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|AbelianMonoid&| '|isFunctor| - '(((* ($ (|NonNegativeInteger|) $)) T (ELT $ 18)) - ((|zero?| ((|Boolean|) $)) T (ELT $ 10)) - ((|sample| ($)) T (ELT $ 15)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ 14))) - (|addModemap| '|AbelianMonoid&| '(|AbelianMonoid&| |#1|) - '((CATEGORY |domain| - (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) - (SIGNATURE |zero?| ((|Boolean|) |#1|)) - (SIGNATURE |sample| (|#1|)) - (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) - (|AbelianMonoid|)) - T '|AbelianMonoid&| - (|put| '|AbelianMonoid&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE * - (|#1| (|NonNegativeInteger|) |#1|)) - (SIGNATURE |zero?| ((|Boolean|) |#1|)) - (SIGNATURE |sample| (|#1|)) - (SIGNATURE * - (|#1| (|PositiveInteger|) |#1|))) - (|AbelianMonoid|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/ABELMON.lsp b/src/algebra/strap/ABELMON.lsp index f0eaa266..af28662b 100644 --- a/src/algebra/strap/ABELMON.lsp +++ b/src/algebra/strap/ABELMON.lsp @@ -17,7 +17,7 @@ '((|NonNegativeInteger|) (|Boolean|)) NIL)) |AbelianMonoid|) - (SETELT #0# 0 '(|AbelianMonoid|)))))) + (|setShellEntry| #0# 0 '(|AbelianMonoid|)))))) (DEFUN |AbelianMonoid| () (LET () @@ -25,9 +25,4 @@ (|AbelianMonoid;AL|) (T (SETQ |AbelianMonoid;AL| (|AbelianMonoid;|)))))) -(SETQ |$CategoryFrame| - (|put| '|AbelianMonoid| '|isCategory| T - (|addModemap| '|AbelianMonoid| '(|AbelianMonoid|) - '((|Category|)) T '|AbelianMonoid| |$CategoryFrame|))) - (MAKEPROP '|AbelianMonoid| 'NILADIC T) diff --git a/src/algebra/strap/ABELSG-.lsp b/src/algebra/strap/ABELSG-.lsp index a248d398..9391dd77 100644 --- a/src/algebra/strap/ABELSG-.lsp +++ b/src/algebra/strap/ABELSG-.lsp @@ -38,20 +38,3 @@ '(2 8 6 7 6 9 2 0 0 7 0 10 2 0 0 7 0 10))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|AbelianSemiGroup&| '|isFunctor| - '(((* ($ (|PositiveInteger|) $)) T (ELT $ 10))) - (|addModemap| '|AbelianSemiGroup&| - '(|AbelianSemiGroup&| |#1|) - '((CATEGORY |domain| - (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) - (|AbelianSemiGroup|)) - T '|AbelianSemiGroup&| - (|put| '|AbelianSemiGroup&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE * - (|#1| (|PositiveInteger|) |#1|))) - (|AbelianSemiGroup|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/ABELSG.lsp b/src/algebra/strap/ABELSG.lsp index 7c2a2a7d..062071e2 100644 --- a/src/algebra/strap/ABELSG.lsp +++ b/src/algebra/strap/ABELSG.lsp @@ -13,7 +13,7 @@ ((* ($ (|PositiveInteger|) $)) T)) NIL '((|PositiveInteger|)) NIL)) |AbelianSemiGroup|) - (SETELT #0# 0 '(|AbelianSemiGroup|)))))) + (|setShellEntry| #0# 0 '(|AbelianSemiGroup|)))))) (DEFUN |AbelianSemiGroup| () (LET () @@ -21,10 +21,4 @@ (|AbelianSemiGroup;AL|) (T (SETQ |AbelianSemiGroup;AL| (|AbelianSemiGroup;|)))))) -(SETQ |$CategoryFrame| - (|put| '|AbelianSemiGroup| '|isCategory| T - (|addModemap| '|AbelianSemiGroup| '(|AbelianSemiGroup|) - '((|Category|)) T '|AbelianSemiGroup| - |$CategoryFrame|))) - (MAKEPROP '|AbelianSemiGroup| 'NILADIC T) diff --git a/src/algebra/strap/ALAGG.lsp b/src/algebra/strap/ALAGG.lsp index 16c80bd0..8d0f1fea 100644 --- a/src/algebra/strap/ALAGG.lsp +++ b/src/algebra/strap/ALAGG.lsp @@ -34,9 +34,9 @@ T)) NIL 'NIL NIL)) . #2=(|AssociationListAggregate|)))))) . #2#) - (SETELT #0# 0 - (LIST '|AssociationListAggregate| (|devaluate| |t#1|) - (|devaluate| |t#2|))))))) + (|setShellEntry| #0# 0 + (LIST '|AssociationListAggregate| (|devaluate| |t#1|) + (|devaluate| |t#2|))))))) (DEFUN |AssociationListAggregate| (&REST #0=#:G1402 &AUX #1=#:G1400) (DSETQ #1# #0#) @@ -53,10 +53,3 @@ #'|AssociationListAggregate;| #1#))) |AssociationListAggregate;AL|)) #2#)))) - -(SETQ |$CategoryFrame| - (|put| '|AssociationListAggregate| '|isCategory| T - (|addModemap| '|AssociationListAggregate| - '(|AssociationListAggregate| |#1| |#2|) - '((|Category|) (|SetCategory|) (|SetCategory|)) T - '|AssociationListAggregate| |$CategoryFrame|))) diff --git a/src/algebra/strap/BOOLEAN.lsp b/src/algebra/strap/BOOLEAN.lsp index 693fc054..1e367244 100644 --- a/src/algebra/strap/BOOLEAN.lsp +++ b/src/algebra/strap/BOOLEAN.lsp @@ -220,62 +220,4 @@ 0 0 1 2 0 18 0 0 22 2 0 0 0 0 12))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|Boolean| '|isFunctor| - '(((|test| ($ $)) T (ELT $ 6)) - ((|nor| ($ $ $)) T (ELT $ 16)) - ((|nand| ($ $ $)) T (ELT $ 17)) - ((|xor| ($ $ $)) T (ELT $ 15)) - ((|false| ($)) T (CONST $ 8)) - ((|true| ($)) T (CONST $ 7)) - ((|convert| ((|InputForm|) $)) T (ELT $ 36)) - ((|not| ($ $)) T (ELT $ 9)) - ((|and| ($ $ $)) T (ELT $ 11)) - ((|or| ($ $ $)) T (ELT $ 13)) - ((|implies| ($ $ $)) T (ELT $ 20)) - ((|equiv| ($ $ $)) T (ELT $ 21)) - ((~ ($ $)) T (ELT $ 10)) ((|/\\| ($ $ $)) T (ELT $ 12)) - ((|\\/| ($ $ $)) T (ELT $ 14)) - ((|size| ((|NonNegativeInteger|))) T (ELT $ 24)) - ((|index| ($ (|PositiveInteger|))) T (ELT $ 28)) - ((|lookup| ((|PositiveInteger|) $)) T (ELT $ 29)) - ((|random| ($)) T (ELT $ 30)) - ((|min| ($ $ $)) T (ELT $ NIL)) - ((|max| ($ $ $)) T (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ 22)) - ((|latex| ((|String|) $)) T (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ 39)) - ((= ((|Boolean|) $ $)) T (ELT $ 19)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|Boolean| '(|Boolean|) - '((|Join| (|OrderedFinite|) (|Logic|) - (|PropositionalLogic|) - (|ConvertibleTo| (|InputForm|)) - (CATEGORY |domain| - (SIGNATURE |true| ($) |constant|) - (SIGNATURE |false| ($) |constant|) - (SIGNATURE |xor| ($ $ $)) - (SIGNATURE |nand| ($ $ $)) - (SIGNATURE |nor| ($ $ $)) - (SIGNATURE |test| ($ $))))) - T '|Boolean| - (|put| '|Boolean| '|mode| - '(|Mapping| - (|Join| (|OrderedFinite|) (|Logic|) - (|PropositionalLogic|) - (|ConvertibleTo| (|InputForm|)) - (CATEGORY |domain| - (SIGNATURE |true| ($) |constant|) - (SIGNATURE |false| ($) - |constant|) - (SIGNATURE |xor| ($ $ $)) - (SIGNATURE |nand| ($ $ $)) - (SIGNATURE |nor| ($ $ $)) - (SIGNATURE |test| ($ $))))) - |$CategoryFrame|)))) - (MAKEPROP '|Boolean| 'NILADIC T) diff --git a/src/algebra/strap/CABMON.lsp b/src/algebra/strap/CABMON.lsp index a95397c0..11a8f26a 100644 --- a/src/algebra/strap/CABMON.lsp +++ b/src/algebra/strap/CABMON.lsp @@ -14,7 +14,7 @@ T)) NIL 'NIL NIL)) |CancellationAbelianMonoid|) - (SETELT #0# 0 '(|CancellationAbelianMonoid|)))))) + (|setShellEntry| #0# 0 '(|CancellationAbelianMonoid|)))))) (DEFUN |CancellationAbelianMonoid| () (LET () @@ -23,10 +23,4 @@ (T (SETQ |CancellationAbelianMonoid;AL| (|CancellationAbelianMonoid;|)))))) -(SETQ |$CategoryFrame| - (|put| '|CancellationAbelianMonoid| '|isCategory| T - (|addModemap| '|CancellationAbelianMonoid| - '(|CancellationAbelianMonoid|) '((|Category|)) T - '|CancellationAbelianMonoid| |$CategoryFrame|))) - (MAKEPROP '|CancellationAbelianMonoid| 'NILADIC T) diff --git a/src/algebra/strap/CHAR.lsp b/src/algebra/strap/CHAR.lsp index f6d4583e..b04e065f 100644 --- a/src/algebra/strap/CHAR.lsp +++ b/src/algebra/strap/CHAR.lsp @@ -236,85 +236,4 @@ 0 1 2 0 6 0 0 8))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|Character| '|isFunctor| - '(((|alphanumeric?| ((|Boolean|) $)) T (ELT $ 36)) - ((|lowerCase?| ((|Boolean|) $)) T (ELT $ 32)) - ((|upperCase?| ((|Boolean|) $)) T (ELT $ 30)) - ((|alphabetic?| ((|Boolean|) $)) T (ELT $ 34)) - ((|hexDigit?| ((|Boolean|) $)) T (ELT $ 28)) - ((|digit?| ((|Boolean|) $)) T (ELT $ 26)) - ((|lowerCase| ($ $)) T (ELT $ 44)) - ((|upperCase| ($ $)) T (ELT $ 43)) - ((|escape| ($)) T (ELT $ 19)) - ((|quote| ($)) T (ELT $ 18)) - ((|space| ($)) T (ELT $ 17)) - ((|char| ($ (|String|))) T (ELT $ 42)) - ((|char| ($ (|NonNegativeInteger|))) T (ELT $ 11)) - ((|ord| ((|NonNegativeInteger|) $)) T (ELT $ 14)) - ((|size| ((|NonNegativeInteger|))) T (ELT $ 10)) - ((|index| ($ (|PositiveInteger|))) T (ELT $ 13)) - ((|lookup| ((|PositiveInteger|) $)) T (ELT $ 15)) - ((|random| ($)) T (ELT $ 16)) - ((|min| ($ $ $)) T (ELT $ NIL)) - ((|max| ($ $ $)) T (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ 8)) - ((|latex| ((|String|) $)) T (ELT $ 38)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ 21)) - ((= ((|Boolean|) $ $)) T (ELT $ 7)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|Character| '(|Character|) - '((|Join| (|OrderedFinite|) - (CATEGORY |domain| - (SIGNATURE |ord| - ((|NonNegativeInteger|) $)) - (SIGNATURE |char| - ($ (|NonNegativeInteger|))) - (SIGNATURE |char| ($ (|String|))) - (SIGNATURE |space| ($)) - (SIGNATURE |quote| ($)) - (SIGNATURE |escape| ($)) - (SIGNATURE |upperCase| ($ $)) - (SIGNATURE |lowerCase| ($ $)) - (SIGNATURE |digit?| ((|Boolean|) $)) - (SIGNATURE |hexDigit?| ((|Boolean|) $)) - (SIGNATURE |alphabetic?| - ((|Boolean|) $)) - (SIGNATURE |upperCase?| ((|Boolean|) $)) - (SIGNATURE |lowerCase?| ((|Boolean|) $)) - (SIGNATURE |alphanumeric?| - ((|Boolean|) $))))) - T '|Character| - (|put| '|Character| '|mode| - '(|Mapping| - (|Join| (|OrderedFinite|) - (CATEGORY |domain| - (SIGNATURE |ord| - ((|NonNegativeInteger|) $)) - (SIGNATURE |char| - ($ (|NonNegativeInteger|))) - (SIGNATURE |char| ($ (|String|))) - (SIGNATURE |space| ($)) - (SIGNATURE |quote| ($)) - (SIGNATURE |escape| ($)) - (SIGNATURE |upperCase| ($ $)) - (SIGNATURE |lowerCase| ($ $)) - (SIGNATURE |digit?| - ((|Boolean|) $)) - (SIGNATURE |hexDigit?| - ((|Boolean|) $)) - (SIGNATURE |alphabetic?| - ((|Boolean|) $)) - (SIGNATURE |upperCase?| - ((|Boolean|) $)) - (SIGNATURE |lowerCase?| - ((|Boolean|) $)) - (SIGNATURE |alphanumeric?| - ((|Boolean|) $))))) - |$CategoryFrame|)))) - (MAKEPROP '|Character| 'NILADIC T) diff --git a/src/algebra/strap/CLAGG-.lsp b/src/algebra/strap/CLAGG-.lsp index 4b61a7db..09d47ce4 100644 --- a/src/algebra/strap/CLAGG-.lsp +++ b/src/algebra/strap/CLAGG-.lsp @@ -268,107 +268,3 @@ 13 0 16 2 0 10 13 0 14 2 0 12 13 0 15 1 0 10 0 11))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|Collection&| '|isFunctor| - '(((|removeDuplicates| ($ $)) T (ELT $ 36)) - ((|remove| ($ |#2| $)) T (ELT $ 32)) - ((|reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|)) - T (ELT $ 34)) - ((|select| ($ (|Mapping| (|Boolean|) |#2|) $)) T - (ELT $ 29)) - ((|remove| ($ (|Mapping| (|Boolean|) |#2|) $)) T - (ELT $ 27)) - ((|reduce| (|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|)) T - (ELT $ 24)) - ((|reduce| (|#2| (|Mapping| |#2| |#2| |#2|) $)) T - (ELT $ 22)) - ((|find| ((|Union| |#2| "failed") - (|Mapping| (|Boolean|) |#2|) $)) - T (ELT $ 19)) - ((|count| ((|NonNegativeInteger|) |#2| $)) T - (ELT $ NIL)) - ((|count| ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#2|) $)) - T (ELT $ 14)) - ((|every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) $)) - T (ELT $ 16)) - ((|any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) $)) T - (ELT $ 15)) - ((|#| ((|NonNegativeInteger|) $)) T (ELT $ 11))) - (|addModemap| '|Collection&| '(|Collection&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE |removeDuplicates| (|#1| |#1|)) - (SIGNATURE |remove| (|#1| |#2| |#1|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| - |#2|)) - (SIGNATURE |select| - (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |remove| - (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) - (SIGNATURE |find| - ((|Union| |#2| "failed") - (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) |#2| |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |every?| - ((|Boolean|) (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |any?| - ((|Boolean|) (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) - (|Collection| |#2|) (|Type|)) - T '|Collection&| - (|put| '|Collection&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |removeDuplicates| - (|#1| |#1|)) - (SIGNATURE |remove| (|#1| |#2| |#1|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) - |#1| |#2| |#2|)) - (SIGNATURE |select| - (|#1| (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |remove| - (|#1| (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) - |#1| |#2|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) - |#1|)) - (SIGNATURE |find| - ((|Union| |#2| "failed") - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) |#2| |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |every?| - ((|Boolean|) - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |any?| - ((|Boolean|) - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |#| - ((|NonNegativeInteger|) |#1|))) - (|Collection| |#2|) (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/CLAGG.lsp b/src/algebra/strap/CLAGG.lsp index 6ec49d46..a7cff743 100644 --- a/src/algebra/strap/CLAGG.lsp +++ b/src/algebra/strap/CLAGG.lsp @@ -90,7 +90,8 @@ (|InputForm|))))) '((|List| |t#1|)) NIL)) . #1=(|Collection|))))) . #1#) - (SETELT #0# 0 (LIST '|Collection| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|Collection| (|devaluate| |t#1|))))))) (DEFUN |Collection| (#0=#:G1398) (LET (#1=#:G1399) @@ -102,9 +103,3 @@ (SETQ #1# (|Collection;| #0#))) |Collection;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|Collection| '|isCategory| T - (|addModemap| '|Collection| '(|Collection| |#1|) - '((|Category|) (|Type|)) T '|Collection| - |$CategoryFrame|))) diff --git a/src/algebra/strap/COMRING.lsp b/src/algebra/strap/COMRING.lsp index 6bf0118a..01ad8233 100644 --- a/src/algebra/strap/COMRING.lsp +++ b/src/algebra/strap/COMRING.lsp @@ -11,7 +11,7 @@ (|mkCategory| '|package| NIL '(((|commutative| "*") T)) 'NIL NIL)) |CommutativeRing|) - (SETELT #0# 0 '(|CommutativeRing|)))))) + (|setShellEntry| #0# 0 '(|CommutativeRing|)))))) (DEFUN |CommutativeRing| () (LET () @@ -19,9 +19,4 @@ (|CommutativeRing;AL|) (T (SETQ |CommutativeRing;AL| (|CommutativeRing;|)))))) -(SETQ |$CategoryFrame| - (|put| '|CommutativeRing| '|isCategory| T - (|addModemap| '|CommutativeRing| '(|CommutativeRing|) - '((|Category|)) T '|CommutativeRing| |$CategoryFrame|))) - (MAKEPROP '|CommutativeRing| 'NILADIC T) diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp index 1123d4d0..57f96e29 100644 --- a/src/algebra/strap/DFLOAT.lsp +++ b/src/algebra/strap/DFLOAT.lsp @@ -696,9 +696,8 @@ (GO #0#)))) (LETT |me| (MANEXP |x|) |DFLOAT;manexp|) (LETT |two53| - (SPADCALL (FLOAT-RADIX 0.0) - (FLOAT-DIGITS 0.0) - (|getShellEntry| $ 117)) + (EXPT (FLOAT-RADIX 0.0) + (FLOAT-DIGITS 0.0)) |DFLOAT;manexp|) (EXIT (CONS (* |s| (FIX (* |two53| (QCAR |me|)))) @@ -706,9 +705,9 @@ #0# (EXIT #0#))))) (DEFUN |DFLOAT;rationalApproximation;$2NniF;83| (|f| |d| |b| $) - (PROG (|#G102| |nu| |ex| BASE #0=#:G1525 |de| |tol| |#G103| |q| |r| - |p2| |q2| #1=#:G1541 |#G104| |#G105| |p0| |p1| |#G106| - |#G107| |q0| |q1| |#G108| |#G109| |s| |t| #2=#:G1539) + (PROG (|#G102| |nu| |ex| BASE #0=#:G1526 |de| |tol| |#G103| |q| |r| + |p2| |q2| #1=#:G1544 |#G104| |#G105| |p0| |p1| |#G106| + |#G107| |q0| |q1| |#G108| |#G109| |s| |t| #2=#:G1542) (RETURN (SEQ (EXIT (SEQ (PROGN (LETT |#G102| (|DFLOAT;manexp| |f| $) @@ -776,14 +775,14 @@ (- (* |nu| |q2|) (* |de| |p2|))) (|getShellEntry| $ - 120)) + 119)) (* |de| (ABS |p2|)))) (EXIT (PROGN (LETT #1# (SPADCALL |p2| |q2| (|getShellEntry| $ - 119)) + 118)) |DFLOAT;rationalApproximation;$2NniF;83|) (GO #1#))))) (PROGN @@ -825,36 +824,36 @@ |DFLOAT;rationalApproximation;$2NniF;83|) (|check-subtype| (>= #2# 0) '(|NonNegativeInteger|) #2#)))) - (|getShellEntry| $ 121))))))) + (|getShellEntry| $ 120))))))) #1# (EXIT #1#))))) (DEFUN |DFLOAT;**;$F$;84| (|x| |r| $) - (PROG (|n| |d| #0=#:G1550) + (PROG (|n| |d| #0=#:G1553) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (COND - ((SPADCALL |r| (|getShellEntry| $ 122)) + ((SPADCALL |r| (|getShellEntry| $ 121)) (|error| "0**0 is undefined")) - ((SPADCALL |r| (|getShellEntry| $ 123)) + ((SPADCALL |r| (|getShellEntry| $ 122)) (|error| "division by 0")) ('T 0.0))) - ((OR (SPADCALL |r| (|getShellEntry| $ 122)) + ((OR (SPADCALL |r| (|getShellEntry| $ 121)) (= |x| 1.0)) 1.0) ('T (COND - ((SPADCALL |r| (|spadConstant| $ 124) - (|getShellEntry| $ 125)) + ((SPADCALL |r| (|spadConstant| $ 123) + (|getShellEntry| $ 124)) |x|) ('T (SEQ (LETT |n| (SPADCALL |r| - (|getShellEntry| $ 126)) + (|getShellEntry| $ 125)) |DFLOAT;**;$F$;84|) (LETT |d| (SPADCALL |r| - (|getShellEntry| $ 127)) + (|getShellEntry| $ 126)) |DFLOAT;**;$F$;84|) (EXIT (COND ((MINUSP |x|) @@ -893,7 +892,7 @@ (DEFUN |DoubleFloat| () (PROG () (RETURN - (PROG (#0=#:G1563) + (PROG (#0=#:G1566) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| '|DoubleFloat|) @@ -914,7 +913,7 @@ (RETURN (PROGN (LETT |dv$| '(|DoubleFloat|) . #0=(|DoubleFloat|)) - (LETT $ (|newShell| 141) . #0#) + (LETT $ (|newShell| 140) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -975,45 +974,45 @@ (|Union| 104 '"failed") |DFLOAT;retractIfCan;$U;77| |DFLOAT;retract;$I;78| (|Union| 24 '"failed") |DFLOAT;retractIfCan;$U;79| |DFLOAT;sign;$I;80| - |DFLOAT;abs;2$;81| (63 . **) (69 . |Zero|) (73 . /) - (79 . *) (85 . |coerce|) (90 . |zero?|) (95 . |negative?|) - (100 . |One|) (104 . =) (110 . |numer|) (115 . |denom|) + |DFLOAT;abs;2$;81| (63 . |Zero|) (67 . /) (73 . *) + (79 . |coerce|) (84 . |zero?|) (89 . |negative?|) + (94 . |One|) (98 . =) (104 . |numer|) (109 . |denom|) |DFLOAT;**;$F$;84| (|PatternMatchResult| 101 $) (|Pattern| 101) (|Factored| $) (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 132 '"failed") (|List| $) (|Union| 134 '"failed") + (|Union| 131 '"failed") (|List| $) (|Union| 133 '"failed") (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) (|Record| (|:| |quotient| $) (|:| |remainder| $)) (|SparseUnivariatePolynomial| $) - (|Record| (|:| |coef| 134) (|:| |generator| $)) + (|Record| (|:| |coef| 133) (|:| |generator| $)) (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $))) - '#(~= 120 |zero?| 126 |wholePart| 131 |unitNormal| 136 - |unitCanonical| 141 |unit?| 146 |truncate| 151 |tanh| 156 - |tan| 161 |subtractIfCan| 166 |squareFreePart| 172 - |squareFree| 177 |sqrt| 182 |sizeLess?| 187 |sinh| 193 - |sin| 198 |sign| 203 |sech| 208 |sec| 213 |sample| 218 - |round| 222 |retractIfCan| 227 |retract| 237 |rem| 247 - |recip| 253 |rationalApproximation| 258 |quo| 271 - |principalIdeal| 277 |prime?| 282 |precision| 287 - |positive?| 291 |pi| 296 |patternMatch| 300 |order| 307 - |one?| 312 |nthRoot| 317 |norm| 323 |negative?| 328 - |multiEuclidean| 333 |min| 339 |max| 349 |mantissa| 359 - |log2| 364 |log10| 369 |log| 374 |lcm| 379 |latex| 390 - |inv| 395 |hash| 400 |gcdPolynomial| 405 |gcd| 411 - |fractionPart| 422 |floor| 427 |float| 432 |factor| 445 - |extendedEuclidean| 450 |exquo| 463 |expressIdealMember| - 469 |exponent| 475 |exp1| 480 |exp| 484 |euclideanSize| - 489 |divide| 494 |digits| 500 |differentiate| 504 |csch| - 515 |csc| 520 |coth| 525 |cot| 530 |cosh| 535 |cos| 540 - |convert| 545 |coerce| 565 |characteristic| 595 |ceiling| - 599 |bits| 604 |base| 608 |atanh| 612 |atan| 617 - |associates?| 628 |asinh| 634 |asin| 639 |asech| 644 - |asec| 649 |acsch| 654 |acsc| 659 |acoth| 664 |acot| 669 - |acosh| 674 |acos| 679 |abs| 684 |Zero| 689 |One| 693 - |OMwrite| 697 |Gamma| 721 D 726 |Beta| 737 >= 743 > 749 = - 755 <= 761 < 767 / 773 - 785 + 796 ** 802 * 832) + '#(~= 114 |zero?| 120 |wholePart| 125 |unitNormal| 130 + |unitCanonical| 135 |unit?| 140 |truncate| 145 |tanh| 150 + |tan| 155 |subtractIfCan| 160 |squareFreePart| 166 + |squareFree| 171 |sqrt| 176 |sizeLess?| 181 |sinh| 187 + |sin| 192 |sign| 197 |sech| 202 |sec| 207 |sample| 212 + |round| 216 |retractIfCan| 221 |retract| 231 |rem| 241 + |recip| 247 |rationalApproximation| 252 |quo| 265 + |principalIdeal| 271 |prime?| 276 |precision| 281 + |positive?| 285 |pi| 290 |patternMatch| 294 |order| 301 + |one?| 306 |nthRoot| 311 |norm| 317 |negative?| 322 + |multiEuclidean| 327 |min| 333 |max| 343 |mantissa| 353 + |log2| 358 |log10| 363 |log| 368 |lcm| 373 |latex| 384 + |inv| 389 |hash| 394 |gcdPolynomial| 399 |gcd| 405 + |fractionPart| 416 |floor| 421 |float| 426 |factor| 439 + |extendedEuclidean| 444 |exquo| 457 |expressIdealMember| + 463 |exponent| 469 |exp1| 474 |exp| 478 |euclideanSize| + 483 |divide| 488 |digits| 494 |differentiate| 498 |csch| + 509 |csc| 514 |coth| 519 |cot| 524 |cosh| 529 |cos| 534 + |convert| 539 |coerce| 559 |characteristic| 589 |ceiling| + 593 |bits| 598 |base| 602 |atanh| 606 |atan| 611 + |associates?| 622 |asinh| 628 |asin| 633 |asech| 638 + |asec| 643 |acsch| 648 |acsc| 653 |acoth| 658 |acot| 663 + |acosh| 668 |acos| 673 |abs| 678 |Zero| 683 |One| 687 + |OMwrite| 691 |Gamma| 715 D 720 |Beta| 731 >= 737 > 743 = + 749 <= 755 < 761 / 767 - 779 + 790 ** 796 * 826) '((|approximate| . 0) (|canonicalsClosed| . 0) (|canonicalUnitNormal| . 0) (|noZeroDivisors| . 0) ((|commutative| "*") . 0) (|rightUnitary| . 0) @@ -1021,7 +1020,7 @@ (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - 0 0 0 0 0 0)) + 0 0 0 0 0 0 0 0)) (CONS '#(|FloatingPointSystem&| |RealNumberSystem&| |Field&| |EuclideanDomain&| NIL |UniqueFactorizationDomain&| |GcdDomain&| @@ -1038,8 +1037,8 @@ |HyperbolicFunctionCategory&| |ArcTrigonometricFunctionCategory&| |TrigonometricFunctionCategory&| NIL NIL - |RadicalCategory&| |RetractableTo&| - |RetractableTo&| NIL NIL |BasicType&| NIL) + |RadicalCategory&| |RetractableTo&| NIL + |RetractableTo&| NIL NIL NIL |BasicType&| NIL) (CONS '#((|FloatingPointSystem|) (|RealNumberSystem|) (|Field|) (|EuclideanDomain|) @@ -1072,321 +1071,71 @@ (|HyperbolicFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|TrigonometricFunctionCategory|) - (|OpenMath|) (|ConvertibleTo| 130) + (|OpenMath|) (|ConvertibleTo| 129) (|RadicalCategory|) (|RetractableTo| 104) + (|CoercibleFrom| 104) (|RetractableTo| 24) + (|CoercibleFrom| 24) (|ConvertibleTo| 101) (|ConvertibleTo| 13) (|BasicType|) (|CoercibleTo| 38)) - (|makeByteWordVec2| 140 + (|makeByteWordVec2| 139 '(0 6 0 7 2 9 0 8 6 10 1 9 11 0 12 2 9 11 0 13 14 1 9 11 0 15 1 9 11 0 16 2 0 0 22 0 29 1 38 0 13 39 1 41 0 13 42 1 93 13 13 94 2 93 13 13 13 96 1 101 - 0 13 102 2 24 0 0 22 117 0 104 0 118 - 2 104 0 24 24 119 2 24 0 105 0 120 1 - 104 0 24 121 1 104 18 0 122 1 104 18 - 0 123 0 104 0 124 2 104 18 0 0 125 1 - 104 24 0 126 1 104 24 0 127 2 0 18 0 - 0 1 1 0 18 0 87 1 0 24 0 98 1 0 140 0 - 1 1 0 0 0 1 1 0 18 0 1 1 0 0 0 1 1 0 - 0 0 75 1 0 0 0 63 2 0 90 0 0 1 1 0 0 - 0 1 1 0 131 0 1 1 0 0 0 54 2 0 18 0 0 - 1 1 0 0 0 73 1 0 0 0 61 1 0 24 0 115 - 1 0 0 0 78 1 0 0 0 65 0 0 0 1 1 0 0 0 - 1 1 0 110 0 111 1 0 113 0 114 1 0 104 - 0 109 1 0 24 0 112 2 0 0 0 0 1 1 0 90 - 0 91 2 0 104 0 105 107 3 0 104 0 105 - 105 106 2 0 0 0 0 1 1 0 139 134 1 1 0 - 18 0 1 0 0 22 27 1 0 18 0 1 0 0 0 37 - 3 0 129 0 130 129 1 1 0 24 0 33 1 0 - 18 0 1 2 0 0 0 24 1 1 0 0 0 1 1 0 18 - 0 86 2 0 135 134 0 1 0 0 0 32 2 0 0 0 - 0 51 0 0 0 31 2 0 0 0 0 50 1 0 24 0 - 25 1 0 0 0 28 1 0 0 0 55 1 0 0 0 60 2 - 0 0 0 0 1 1 0 0 134 1 1 0 8 0 1 1 0 0 - 0 1 1 0 88 0 89 2 0 138 138 138 1 1 0 - 0 134 1 2 0 0 0 0 1 1 0 0 0 1 1 0 0 0 - 1 3 0 0 24 24 22 99 2 0 0 24 24 1 1 0 - 131 0 1 3 0 133 0 0 0 1 2 0 136 0 0 1 - 2 0 90 0 0 1 2 0 135 134 0 1 1 0 24 0 - 26 0 0 0 36 1 0 0 0 59 1 0 105 0 1 2 - 0 137 0 0 1 0 0 22 1 1 0 0 0 92 2 0 0 - 0 105 1 1 0 0 0 76 1 0 0 0 66 1 0 0 0 - 77 1 0 0 0 64 1 0 0 0 74 1 0 0 0 62 1 - 0 41 0 43 1 0 130 0 1 1 0 101 0 103 1 - 0 13 0 100 1 0 0 104 1 1 0 0 24 58 1 - 0 0 104 1 1 0 0 24 58 1 0 0 0 1 1 0 - 38 0 40 0 0 105 1 1 0 0 0 1 0 0 22 30 - 0 0 22 23 1 0 0 0 81 2 0 0 0 0 108 1 - 0 0 0 69 2 0 18 0 0 1 1 0 0 0 79 1 0 - 0 0 67 1 0 0 0 84 1 0 0 0 72 1 0 0 0 - 82 1 0 0 0 70 1 0 0 0 83 1 0 0 0 71 1 - 0 0 0 80 1 0 0 0 68 1 0 0 0 116 0 0 0 - 34 0 0 0 35 2 0 11 9 0 20 3 0 11 9 0 - 18 21 1 0 8 0 17 2 0 8 0 18 19 1 0 0 - 0 95 1 0 0 0 1 2 0 0 0 105 1 2 0 0 0 - 0 97 2 0 18 0 0 1 2 0 18 0 0 1 2 0 18 - 0 0 52 2 0 18 0 0 1 2 0 18 0 0 44 2 0 - 0 0 24 53 2 0 0 0 0 85 2 0 0 0 0 47 1 - 0 0 0 45 2 0 0 0 0 46 2 0 0 0 0 57 2 - 0 0 0 104 128 2 0 0 0 24 56 2 0 0 0 - 105 1 2 0 0 0 22 1 2 0 0 104 0 1 2 0 - 0 0 104 1 2 0 0 0 0 48 2 0 0 24 0 49 - 2 0 0 105 0 1 2 0 0 22 0 29))))) + 0 13 102 0 104 0 117 2 104 0 24 24 + 118 2 24 0 105 0 119 1 104 0 24 120 1 + 104 18 0 121 1 104 18 0 122 0 104 0 + 123 2 104 18 0 0 124 1 104 24 0 125 1 + 104 24 0 126 2 0 18 0 0 1 1 0 18 0 87 + 1 0 24 0 98 1 0 139 0 1 1 0 0 0 1 1 0 + 18 0 1 1 0 0 0 1 1 0 0 0 75 1 0 0 0 + 63 2 0 90 0 0 1 1 0 0 0 1 1 0 130 0 1 + 1 0 0 0 54 2 0 18 0 0 1 1 0 0 0 73 1 + 0 0 0 61 1 0 24 0 115 1 0 0 0 78 1 0 + 0 0 65 0 0 0 1 1 0 0 0 1 1 0 110 0 + 111 1 0 113 0 114 1 0 104 0 109 1 0 + 24 0 112 2 0 0 0 0 1 1 0 90 0 91 2 0 + 104 0 105 107 3 0 104 0 105 105 106 2 + 0 0 0 0 1 1 0 138 133 1 1 0 18 0 1 0 + 0 22 27 1 0 18 0 1 0 0 0 37 3 0 128 0 + 129 128 1 1 0 24 0 33 1 0 18 0 1 2 0 + 0 0 24 1 1 0 0 0 1 1 0 18 0 86 2 0 + 134 133 0 1 0 0 0 32 2 0 0 0 0 51 0 0 + 0 31 2 0 0 0 0 50 1 0 24 0 25 1 0 0 0 + 28 1 0 0 0 55 1 0 0 0 60 2 0 0 0 0 1 + 1 0 0 133 1 1 0 8 0 1 1 0 0 0 1 1 0 + 88 0 89 2 0 137 137 137 1 1 0 0 133 1 + 2 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 3 0 0 + 24 24 22 99 2 0 0 24 24 1 1 0 130 0 1 + 3 0 132 0 0 0 1 2 0 135 0 0 1 2 0 90 + 0 0 1 2 0 134 133 0 1 1 0 24 0 26 0 0 + 0 36 1 0 0 0 59 1 0 105 0 1 2 0 136 0 + 0 1 0 0 22 1 1 0 0 0 92 2 0 0 0 105 1 + 1 0 0 0 76 1 0 0 0 66 1 0 0 0 77 1 0 + 0 0 64 1 0 0 0 74 1 0 0 0 62 1 0 41 0 + 43 1 0 129 0 1 1 0 101 0 103 1 0 13 0 + 100 1 0 0 104 1 1 0 0 24 58 1 0 0 104 + 1 1 0 0 24 58 1 0 0 0 1 1 0 38 0 40 0 + 0 105 1 1 0 0 0 1 0 0 22 30 0 0 22 23 + 1 0 0 0 81 2 0 0 0 0 108 1 0 0 0 69 2 + 0 18 0 0 1 1 0 0 0 79 1 0 0 0 67 1 0 + 0 0 84 1 0 0 0 72 1 0 0 0 82 1 0 0 0 + 70 1 0 0 0 83 1 0 0 0 71 1 0 0 0 80 1 + 0 0 0 68 1 0 0 0 116 0 0 0 34 0 0 0 + 35 2 0 11 9 0 20 3 0 11 9 0 18 21 1 0 + 8 0 17 2 0 8 0 18 19 1 0 0 0 95 1 0 0 + 0 1 2 0 0 0 105 1 2 0 0 0 0 97 2 0 18 + 0 0 1 2 0 18 0 0 1 2 0 18 0 0 52 2 0 + 18 0 0 1 2 0 18 0 0 44 2 0 0 0 24 53 + 2 0 0 0 0 85 2 0 0 0 0 47 1 0 0 0 45 + 2 0 0 0 0 46 2 0 0 0 0 57 2 0 0 0 104 + 127 2 0 0 0 24 56 2 0 0 0 105 1 2 0 0 + 0 22 1 2 0 0 104 0 1 2 0 0 0 104 1 2 + 0 0 0 0 48 2 0 0 24 0 49 2 0 0 105 0 + 1 2 0 0 22 0 29))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|DoubleFloat| '|isFunctor| - '(((|rationalApproximation| - ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) - (|NonNegativeInteger|))) - T (ELT $ 106)) - ((|rationalApproximation| - ((|Fraction| (|Integer|)) $ (|NonNegativeInteger|))) - T (ELT $ 107)) - ((|Beta| ($ $ $)) T (ELT $ 97)) - ((|Gamma| ($ $)) T (ELT $ 95)) - ((|atan| ($ $ $)) T (ELT $ 108)) - ((|log10| ($ $)) T (ELT $ 55)) - ((|log2| ($ $)) T (ELT $ 28)) - ((|exp1| ($)) T (ELT $ 36)) - ((/ ($ $ (|Integer|))) T (ELT $ 53)) - ((|convert| ((|InputForm|) $)) T (ELT $ 43)) - ((|tan| ($ $)) T (ELT $ 63)) - ((|sin| ($ $)) T (ELT $ 61)) - ((|sec| ($ $)) T (ELT $ 65)) - ((|csc| ($ $)) T (ELT $ 66)) - ((|cot| ($ $)) T (ELT $ 64)) - ((|cos| ($ $)) T (ELT $ 62)) - ((|acos| ($ $)) T (ELT $ 68)) - ((|acot| ($ $)) T (ELT $ 71)) - ((|acsc| ($ $)) T (ELT $ 70)) - ((|asec| ($ $)) T (ELT $ 72)) - ((|asin| ($ $)) T (ELT $ 67)) - ((|atan| ($ $)) T (ELT $ 69)) - ((|cosh| ($ $)) T (ELT $ 74)) - ((|coth| ($ $)) T (ELT $ 77)) - ((|csch| ($ $)) T (ELT $ 76)) - ((|sech| ($ $)) T (ELT $ 78)) - ((|sinh| ($ $)) T (ELT $ 73)) - ((|tanh| ($ $)) T (ELT $ 75)) - ((|acosh| ($ $)) T (ELT $ 80)) - ((|acoth| ($ $)) T (ELT $ 83)) - ((|acsch| ($ $)) T (ELT $ 82)) - ((|asech| ($ $)) T (ELT $ 84)) - ((|asinh| ($ $)) T (ELT $ 79)) - ((|atanh| ($ $)) T (ELT $ 81)) - ((|log| ($ $)) T (ELT $ 60)) - ((|exp| ($ $)) T (ELT $ 59)) ((** ($ $ $)) T (ELT $ 57)) - ((|pi| ($)) T (ELT $ 37)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $ (|Boolean|))) - T (ELT $ 21)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $)) T - (ELT $ 20)) - ((|OMwrite| ((|String|) $ (|Boolean|))) T (ELT $ 19)) - ((|OMwrite| ((|String|) $)) T (ELT $ 17)) - ((|differentiate| ($ $)) T (ELT $ 92)) - ((D ($ $)) T (ELT $ NIL)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((D ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|max| ($)) - (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) - (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) - (ELT $ 31)) - ((|min| ($)) - (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) - (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|)))) - (ELT $ 32)) - ((|decreasePrecision| ((|PositiveInteger|) (|Integer|))) - (|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL)) - ((|increasePrecision| ((|PositiveInteger|) (|Integer|))) - (|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL)) - ((|precision| ((|PositiveInteger|) (|PositiveInteger|))) - (|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL)) - ((|digits| ((|PositiveInteger|) (|PositiveInteger|))) - (|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL)) - ((|bits| ((|PositiveInteger|) (|PositiveInteger|))) - (|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL)) - ((|precision| ((|PositiveInteger|))) T (ELT $ 27)) - ((|digits| ((|PositiveInteger|))) T (ELT $ NIL)) - ((|bits| ((|PositiveInteger|))) T (ELT $ 30)) - ((|mantissa| ((|Integer|) $)) T (ELT $ 25)) - ((|exponent| ((|Integer|) $)) T (ELT $ 26)) - ((|base| ((|PositiveInteger|))) T (ELT $ 23)) - ((|order| ((|Integer|) $)) T (ELT $ 33)) - ((|float| ($ (|Integer|) (|Integer|) - (|PositiveInteger|))) - T (ELT $ 99)) - ((|float| ($ (|Integer|) (|Integer|))) T (ELT $ NIL)) - ((|round| ($ $)) T (ELT $ NIL)) - ((|truncate| ($ $)) T (ELT $ NIL)) - ((|fractionPart| ($ $)) T (ELT $ NIL)) - ((|wholePart| ((|Integer|) $)) T (ELT $ 98)) - ((|floor| ($ $)) T (ELT $ NIL)) - ((|ceiling| ($ $)) T (ELT $ NIL)) - ((|norm| ($ $)) T (ELT $ NIL)) - ((|patternMatch| - ((|PatternMatchResult| (|Float|) $) $ - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) $))) - T (ELT $ NIL)) - ((|convert| ((|Pattern| (|Float|)) $)) T (ELT $ NIL)) - ((** ($ $ (|Fraction| (|Integer|)))) T (ELT $ 128)) - ((|nthRoot| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|sqrt| ($ $)) T (ELT $ 54)) - ((|retract| ((|Fraction| (|Integer|)) $)) T (ELT $ 109)) - ((|retractIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") $)) - T (ELT $ 111)) - ((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ NIL)) - ((|retract| ((|Integer|) $)) T (ELT $ 112)) - ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T - (ELT $ 114)) - ((|coerce| ($ (|Integer|))) T (ELT $ 58)) - ((|convert| ((|DoubleFloat|) $)) T (ELT $ 100)) - ((|convert| ((|Float|) $)) T (ELT $ 103)) - ((< ((|Boolean|) $ $)) T (ELT $ 44)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|max| ($ $ $)) T (ELT $ 50)) - ((|min| ($ $ $)) T (ELT $ 51)) - ((|positive?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|negative?| ((|Boolean|) $)) T (ELT $ 86)) - ((|sign| ((|Integer|) $)) T (ELT $ 115)) - ((|abs| ($ $)) T (ELT $ 116)) ((/ ($ $ $)) T (ELT $ 85)) - ((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ NIL)) - ((* ($ (|Fraction| (|Integer|)) $)) T (ELT $ NIL)) - ((* ($ $ (|Fraction| (|Integer|)))) T (ELT $ NIL)) - ((** ($ $ (|Integer|))) T (ELT $ 56)) - ((|inv| ($ $)) T (ELT $ NIL)) - ((|prime?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|squareFree| ((|Factored| $) $)) T (ELT $ NIL)) - ((|squareFreePart| ($ $)) T (ELT $ NIL)) - ((|factor| ((|Factored| $) $)) T (ELT $ NIL)) - ((|multiEuclidean| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ NIL)) - ((|extendedEuclidean| - ((|Union| (|Record| (|:| |coef1| $) - (|:| |coef2| $)) - "failed") - $ $ $)) - T (ELT $ NIL)) - ((|extendedEuclidean| - ((|Record| (|:| |coef1| $) (|:| |coef2| $) - (|:| |generator| $)) - $ $)) - T (ELT $ NIL)) - ((|rem| ($ $ $)) T (ELT $ NIL)) - ((|quo| ($ $ $)) T (ELT $ NIL)) - ((|divide| - ((|Record| (|:| |quotient| $) (|:| |remainder| $)) - $ $)) - T (ELT $ NIL)) - ((|euclideanSize| ((|NonNegativeInteger|) $)) T - (ELT $ NIL)) - ((|sizeLess?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|expressIdealMember| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ NIL)) - ((|principalIdeal| - ((|Record| (|:| |coef| (|List| $)) - (|:| |generator| $)) - (|List| $))) - T (ELT $ NIL)) - ((|gcdPolynomial| - ((|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $))) - T (ELT $ NIL)) - ((|lcm| ($ (|List| $))) T (ELT $ NIL)) - ((|lcm| ($ $ $)) T (ELT $ NIL)) - ((|gcd| ($ (|List| $))) T (ELT $ NIL)) - ((|gcd| ($ $ $)) T (ELT $ NIL)) - ((|unit?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|associates?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|unitCanonical| ($ $)) T (ELT $ NIL)) - ((|unitNormal| - ((|Record| (|:| |unit| $) (|:| |canonical| $) - (|:| |associate| $)) - $)) - T (ELT $ NIL)) - ((|exquo| ((|Union| $ "failed") $ $)) T (ELT $ NIL)) - ((|coerce| ($ $)) T (ELT $ NIL)) - ((|coerce| ($ (|Integer|))) T (ELT $ 58)) - ((|characteristic| ((|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|One| ($)) T (CONST $ 35)) - ((|one?| ((|Boolean|) $)) T (ELT $ NIL)) - ((** ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|recip| ((|Union| $ "failed") $)) T (ELT $ 91)) - ((* ($ $ $)) T (ELT $ 48)) - ((** ($ $ (|PositiveInteger|))) T (ELT $ NIL)) - ((* ($ (|Integer|) $)) T (ELT $ 49)) - ((- ($ $ $)) T (ELT $ 47)) ((- ($ $)) T (ELT $ 45)) - ((|subtractIfCan| ((|Union| $ "failed") $ $)) T - (ELT $ NIL)) - ((* ($ (|NonNegativeInteger|) $)) T (ELT $ NIL)) - ((|zero?| ((|Boolean|) $)) T (ELT $ 87)) - ((|sample| ($)) T (CONST $ NIL)) - ((|Zero| ($)) T (CONST $ 34)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ 29)) - ((+ ($ $ $)) T (ELT $ 46)) - ((|latex| ((|String|) $)) T (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ 89)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ 40)) - ((= ((|Boolean|) $ $)) T (ELT $ 52)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|DoubleFloat| '(|DoubleFloat|) - '((|Join| (|FloatingPointSystem|) (|DifferentialRing|) - (|OpenMath|) - (|TranscendentalFunctionCategory|) - (|ConvertibleTo| (|InputForm|)) - (CATEGORY |domain| - (SIGNATURE / ($ $ (|Integer|))) - (SIGNATURE ** ($ $ $)) - (SIGNATURE |exp1| ($)) - (SIGNATURE |log2| ($ $)) - (SIGNATURE |log10| ($ $)) - (SIGNATURE |atan| ($ $ $)) - (SIGNATURE |Gamma| ($ $)) - (SIGNATURE |Beta| ($ $ $)) - (SIGNATURE |rationalApproximation| - ((|Fraction| (|Integer|)) $ - (|NonNegativeInteger|))) - (SIGNATURE |rationalApproximation| - ((|Fraction| (|Integer|)) $ - (|NonNegativeInteger|) - (|NonNegativeInteger|)))))) - T '|DoubleFloat| - (|put| '|DoubleFloat| '|mode| - '(|Mapping| - (|Join| (|FloatingPointSystem|) - (|DifferentialRing|) (|OpenMath|) - (|TranscendentalFunctionCategory|) - (|ConvertibleTo| (|InputForm|)) - (CATEGORY |domain| - (SIGNATURE / ($ $ (|Integer|))) - (SIGNATURE ** ($ $ $)) - (SIGNATURE |exp1| ($)) - (SIGNATURE |log2| ($ $)) - (SIGNATURE |log10| ($ $)) - (SIGNATURE |atan| ($ $ $)) - (SIGNATURE |Gamma| ($ $)) - (SIGNATURE |Beta| ($ $ $)) - (SIGNATURE - |rationalApproximation| - ((|Fraction| (|Integer|)) $ - (|NonNegativeInteger|))) - (SIGNATURE - |rationalApproximation| - ((|Fraction| (|Integer|)) $ - (|NonNegativeInteger|) - (|NonNegativeInteger|)))))) - |$CategoryFrame|)))) - (MAKEPROP '|DoubleFloat| 'NILADIC T) diff --git a/src/algebra/strap/DIFRING-.lsp b/src/algebra/strap/DIFRING-.lsp index 0c2afaf6..1c9f8444 100644 --- a/src/algebra/strap/DIFRING-.lsp +++ b/src/algebra/strap/DIFRING-.lsp @@ -57,33 +57,3 @@ '(1 6 0 0 7 2 6 0 0 9 11 2 0 0 0 9 10 2 0 0 0 9 12 1 0 0 0 8))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|DifferentialRing&| '|isFunctor| - '(((D ($ $ (|NonNegativeInteger|))) T (ELT $ 12)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ 10)) - ((D ($ $)) T (ELT $ 8)) - ((|differentiate| ($ $)) T (ELT $ NIL))) - (|addModemap| '|DifferentialRing&| - '(|DifferentialRing&| |#1|) - '((CATEGORY |domain| - (SIGNATURE D (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE D (|#1| |#1|)) - (SIGNATURE |differentiate| (|#1| |#1|))) - (|DifferentialRing|)) - T '|DifferentialRing&| - (|put| '|DifferentialRing&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE D - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE D (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1|))) - (|DifferentialRing|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/DIFRING.lsp b/src/algebra/strap/DIFRING.lsp index 63e3b4fd..89e91f31 100644 --- a/src/algebra/strap/DIFRING.lsp +++ b/src/algebra/strap/DIFRING.lsp @@ -17,7 +17,7 @@ ((D ($ $ (|NonNegativeInteger|))) T)) NIL '((|NonNegativeInteger|)) NIL)) |DifferentialRing|) - (SETELT #0# 0 '(|DifferentialRing|)))))) + (|setShellEntry| #0# 0 '(|DifferentialRing|)))))) (DEFUN |DifferentialRing| () (LET () @@ -25,10 +25,4 @@ (|DifferentialRing;AL|) (T (SETQ |DifferentialRing;AL| (|DifferentialRing;|)))))) -(SETQ |$CategoryFrame| - (|put| '|DifferentialRing| '|isCategory| T - (|addModemap| '|DifferentialRing| '(|DifferentialRing|) - '((|Category|)) T '|DifferentialRing| - |$CategoryFrame|))) - (MAKEPROP '|DifferentialRing| 'NILADIC T) diff --git a/src/algebra/strap/DIVRING-.lsp b/src/algebra/strap/DIVRING-.lsp index b8b219ec..4a61885c 100644 --- a/src/algebra/strap/DIVRING-.lsp +++ b/src/algebra/strap/DIVRING-.lsp @@ -58,53 +58,3 @@ 19 1 6 0 15 20 2 6 0 15 0 21 2 6 0 0 0 22 2 0 0 0 15 16 2 0 0 17 0 23))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|DivisionRing&| '|isFunctor| - '(((** ($ $ (|Integer|))) T (ELT $ 16)) - ((* ($ $ (|Fraction| (|Integer|)))) T (ELT $ NIL)) - ((* ($ (|Fraction| (|Integer|)) $)) T (ELT $ 23)) - ((** ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((* ($ $ $)) T (ELT $ NIL)) - ((** ($ $ (|PositiveInteger|))) T (ELT $ NIL)) - ((* ($ (|Integer|) $)) T (ELT $ NIL)) - ((* ($ (|NonNegativeInteger|) $)) T (ELT $ NIL)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ NIL))) - (|addModemap| '|DivisionRing&| '(|DivisionRing&| |#1|) - '((CATEGORY |domain| - (SIGNATURE ** (|#1| |#1| (|Integer|))) - (SIGNATURE * - (|#1| |#1| (|Fraction| (|Integer|)))) - (SIGNATURE * - (|#1| (|Fraction| (|Integer|)) |#1|)) - (SIGNATURE ** - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE * (|#1| |#1| |#1|)) - (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) - (SIGNATURE * (|#1| (|Integer|) |#1|)) - (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) - (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) - (|DivisionRing|)) - T '|DivisionRing&| - (|put| '|DivisionRing&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE ** (|#1| |#1| (|Integer|))) - (SIGNATURE * - (|#1| |#1| - (|Fraction| (|Integer|)))) - (SIGNATURE * - (|#1| (|Fraction| (|Integer|)) - |#1|)) - (SIGNATURE ** - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE * (|#1| |#1| |#1|)) - (SIGNATURE ** - (|#1| |#1| (|PositiveInteger|))) - (SIGNATURE * (|#1| (|Integer|) |#1|)) - (SIGNATURE * - (|#1| (|NonNegativeInteger|) |#1|)) - (SIGNATURE * - (|#1| (|PositiveInteger|) |#1|))) - (|DivisionRing|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/DIVRING.lsp b/src/algebra/strap/DIVRING.lsp index e72ef347..ce6499f5 100644 --- a/src/algebra/strap/DIVRING.lsp +++ b/src/algebra/strap/DIVRING.lsp @@ -16,7 +16,7 @@ ((|inv| ($ $)) T)) NIL '((|Integer|)) NIL))) |DivisionRing|) - (SETELT #0# 0 '(|DivisionRing|)))))) + (|setShellEntry| #0# 0 '(|DivisionRing|)))))) (DEFUN |DivisionRing| () (LET () @@ -24,9 +24,4 @@ (|DivisionRing;AL|) (T (SETQ |DivisionRing;AL| (|DivisionRing;|)))))) -(SETQ |$CategoryFrame| - (|put| '|DivisionRing| '|isCategory| T - (|addModemap| '|DivisionRing| '(|DivisionRing|) - '((|Category|)) T '|DivisionRing| |$CategoryFrame|))) - (MAKEPROP '|DivisionRing| 'NILADIC T) diff --git a/src/algebra/strap/ENTIRER.lsp b/src/algebra/strap/ENTIRER.lsp index 9b89cfc9..d82918d3 100644 --- a/src/algebra/strap/ENTIRER.lsp +++ b/src/algebra/strap/ENTIRER.lsp @@ -11,7 +11,7 @@ (|mkCategory| '|package| NIL '((|noZeroDivisors| T)) 'NIL NIL)) |EntireRing|) - (SETELT #0# 0 '(|EntireRing|)))))) + (|setShellEntry| #0# 0 '(|EntireRing|)))))) (DEFUN |EntireRing| () (LET () @@ -19,9 +19,4 @@ (|EntireRing;AL|) (T (SETQ |EntireRing;AL| (|EntireRing;|)))))) -(SETQ |$CategoryFrame| - (|put| '|EntireRing| '|isCategory| T - (|addModemap| '|EntireRing| '(|EntireRing|) - '((|Category|)) T '|EntireRing| |$CategoryFrame|))) - (MAKEPROP '|EntireRing| 'NILADIC T) diff --git a/src/algebra/strap/ES-.lsp b/src/algebra/strap/ES-.lsp index 15d5ab4d..d17b7e1b 100644 --- a/src/algebra/strap/ES-.lsp +++ b/src/algebra/strap/ES-.lsp @@ -934,282 +934,3 @@ 53 1 0 0 15 55 1 0 0 0 17 1 0 20 10 22))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|ExpressionSpace&| '|isFunctor| - '(((|odd?| ((|Boolean|) $)) T (ELT $ 131)) - ((|even?| ((|Boolean|) $)) T (ELT $ 129)) - ((|eval| ($ $ (|BasicOperator|) (|Mapping| $ $))) T - (ELT $ 77)) - ((|eval| ($ $ (|BasicOperator|) - (|Mapping| $ (|List| $)))) - T (ELT $ 71)) - ((|eval| ($ $ (|List| (|BasicOperator|)) - (|List| (|Mapping| $ (|List| $))))) - T (ELT $ 85)) - ((|eval| ($ $ (|List| (|BasicOperator|)) - (|List| (|Mapping| $ $)))) - T (ELT $ 83)) - ((|eval| ($ $ (|Symbol|) (|Mapping| $ $))) T (ELT $ 75)) - ((|eval| ($ $ (|Symbol|) (|Mapping| $ (|List| $)))) T - (ELT $ 69)) - ((|eval| ($ $ (|List| (|Symbol|)) - (|List| (|Mapping| $ (|List| $))))) - T (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Symbol|)) - (|List| (|Mapping| $ $)))) - T (ELT $ 84)) - ((|freeOf?| ((|Boolean|) $ (|Symbol|))) T (ELT $ 51)) - ((|freeOf?| ((|Boolean|) $ $)) T (ELT $ 59)) - ((|map| ($ (|Mapping| $ $) (|Kernel| $))) T (ELT $ 89)) - ((|kernel| ($ (|BasicOperator|) (|List| $))) T - (ELT $ 100)) - ((|kernel| ($ (|BasicOperator|) $)) T (ELT $ 61)) - ((|is?| ((|Boolean|) $ (|Symbol|))) T (ELT $ 116)) - ((|is?| ((|Boolean|) $ (|BasicOperator|))) T - (ELT $ 117)) - ((|belong?| ((|Boolean|) (|BasicOperator|))) T - (ELT $ 22)) - ((|operator| ((|BasicOperator|) (|BasicOperator|))) T - (ELT $ 91)) - ((|operators| ((|List| (|BasicOperator|)) $)) T - (ELT $ 38)) - ((|tower| ((|List| (|Kernel| $)) $)) T (ELT $ 30)) - ((|mainKernel| ((|Union| (|Kernel| $) "failed") $)) T - (ELT $ 93)) - ((|height| ((|NonNegativeInteger|) $)) T (ELT $ 46)) - ((|distribute| ($ $ $)) T (ELT $ 119)) - ((|distribute| ($ $)) T (ELT $ 53)) - ((|paren| ($ (|List| $))) T (ELT $ 56)) - ((|paren| ($ $)) T (ELT $ 19)) - ((|box| ($ (|List| $))) T (ELT $ 55)) - ((|box| ($ $)) T (ELT $ 17)) - ((|subst| ($ $ (|List| (|Kernel| $)) (|List| $))) T - (ELT $ NIL)) - ((|subst| ($ $ (|List| (|Equation| $)))) T (ELT $ 123)) - ((|subst| ($ $ (|Equation| $))) T (ELT $ 81)) - ((|elt| ($ (|BasicOperator|) (|List| $))) T (ELT $ 109)) - ((|elt| ($ (|BasicOperator|) $ $ $ $)) T (ELT $ 65)) - ((|elt| ($ (|BasicOperator|) $ $ $)) T (ELT $ 64)) - ((|elt| ($ (|BasicOperator|) $ $)) T (ELT $ 63)) - ((|elt| ($ (|BasicOperator|) $)) T (ELT $ 62)) - ((|eval| ($ $ (|List| $) (|List| $))) T (ELT $ NIL)) - ((|eval| ($ $ $ $)) T (ELT $ NIL)) - ((|eval| ($ $ (|Equation| $))) T (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| $)))) T (ELT $ 121)) - ((|eval| ($ $ (|List| (|Kernel| $)) (|List| $))) T - (ELT $ NIL)) - ((|eval| ($ $ (|Kernel| $) $)) T (ELT $ NIL)) - ((|retract| ((|Kernel| $) $)) T (ELT $ 112)) - ((|retractIfCan| ((|Union| (|Kernel| $) "failed") $)) T - (ELT $ 113))) - (|addModemap| '|ExpressionSpace&| - '(|ExpressionSpace&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |odd?| ((|Boolean|) |#1|)) - (SIGNATURE |even?| ((|Boolean|) |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|BasicOperator|) - (|Mapping| |#1| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|BasicOperator|) - (|Mapping| |#1| (|List| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|BasicOperator|)) - (|List| (|Mapping| |#1| (|List| |#1|))))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|BasicOperator|)) - (|List| (|Mapping| |#1| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| (|Symbol|) (|Mapping| |#1| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|Symbol|) - (|Mapping| |#1| (|List| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Symbol|)) - (|List| (|Mapping| |#1| (|List| |#1|))))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Symbol|)) - (|List| (|Mapping| |#1| |#1|)))) - (SIGNATURE |freeOf?| - ((|Boolean|) |#1| (|Symbol|))) - (SIGNATURE |freeOf?| ((|Boolean|) |#1| |#1|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#1| |#1|) (|Kernel| |#1|))) - (SIGNATURE |kernel| - (|#1| (|BasicOperator|) (|List| |#1|))) - (SIGNATURE |kernel| - (|#1| (|BasicOperator|) |#1|)) - (SIGNATURE |is?| ((|Boolean|) |#1| (|Symbol|))) - (SIGNATURE |is?| - ((|Boolean|) |#1| (|BasicOperator|))) - (SIGNATURE |belong?| - ((|Boolean|) (|BasicOperator|))) - (SIGNATURE |operator| - ((|BasicOperator|) (|BasicOperator|))) - (SIGNATURE |operators| - ((|List| (|BasicOperator|)) |#1|)) - (SIGNATURE |tower| - ((|List| (|Kernel| |#1|)) |#1|)) - (SIGNATURE |mainKernel| - ((|Union| (|Kernel| |#1|) "failed") |#1|)) - (SIGNATURE |height| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |distribute| (|#1| |#1| |#1|)) - (SIGNATURE |distribute| (|#1| |#1|)) - (SIGNATURE |paren| (|#1| (|List| |#1|))) - (SIGNATURE |paren| (|#1| |#1|)) - (SIGNATURE |box| (|#1| (|List| |#1|))) - (SIGNATURE |box| (|#1| |#1|)) - (SIGNATURE |subst| - (|#1| |#1| (|List| (|Kernel| |#1|)) - (|List| |#1|))) - (SIGNATURE |subst| - (|#1| |#1| (|List| (|Equation| |#1|)))) - (SIGNATURE |subst| - (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) (|List| |#1|))) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) |#1| |#1| |#1| |#1|)) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) |#1| |#1| - |#1|)) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) |#1| |#1|)) - (SIGNATURE |elt| (|#1| (|BasicOperator|) |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#1|) (|List| |#1|))) - (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) - (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Equation| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Kernel| |#1|)) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|Kernel| |#1|) |#1|)) - (SIGNATURE |retract| ((|Kernel| |#1|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Kernel| |#1|) "failed") |#1|))) - (|ExpressionSpace|)) - T '|ExpressionSpace&| - (|put| '|ExpressionSpace&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |odd?| ((|Boolean|) |#1|)) - (SIGNATURE |even?| ((|Boolean|) |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|BasicOperator|) - (|Mapping| |#1| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|BasicOperator|) - (|Mapping| |#1| (|List| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|BasicOperator|)) - (|List| - (|Mapping| |#1| (|List| |#1|))))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|BasicOperator|)) - (|List| (|Mapping| |#1| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| (|Symbol|) - (|Mapping| |#1| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|Symbol|) - (|Mapping| |#1| (|List| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Symbol|)) - (|List| - (|Mapping| |#1| (|List| |#1|))))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Symbol|)) - (|List| (|Mapping| |#1| |#1|)))) - (SIGNATURE |freeOf?| - ((|Boolean|) |#1| (|Symbol|))) - (SIGNATURE |freeOf?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#1| |#1|) - (|Kernel| |#1|))) - (SIGNATURE |kernel| - (|#1| (|BasicOperator|) - (|List| |#1|))) - (SIGNATURE |kernel| - (|#1| (|BasicOperator|) |#1|)) - (SIGNATURE |is?| - ((|Boolean|) |#1| (|Symbol|))) - (SIGNATURE |is?| - ((|Boolean|) |#1| - (|BasicOperator|))) - (SIGNATURE |belong?| - ((|Boolean|) (|BasicOperator|))) - (SIGNATURE |operator| - ((|BasicOperator|) - (|BasicOperator|))) - (SIGNATURE |operators| - ((|List| (|BasicOperator|)) |#1|)) - (SIGNATURE |tower| - ((|List| (|Kernel| |#1|)) |#1|)) - (SIGNATURE |mainKernel| - ((|Union| (|Kernel| |#1|) - "failed") - |#1|)) - (SIGNATURE |height| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |distribute| - (|#1| |#1| |#1|)) - (SIGNATURE |distribute| (|#1| |#1|)) - (SIGNATURE |paren| - (|#1| (|List| |#1|))) - (SIGNATURE |paren| (|#1| |#1|)) - (SIGNATURE |box| (|#1| (|List| |#1|))) - (SIGNATURE |box| (|#1| |#1|)) - (SIGNATURE |subst| - (|#1| |#1| - (|List| (|Kernel| |#1|)) - (|List| |#1|))) - (SIGNATURE |subst| - (|#1| |#1| - (|List| (|Equation| |#1|)))) - (SIGNATURE |subst| - (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) - (|List| |#1|))) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) |#1| |#1| - |#1| |#1|)) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) |#1| |#1| - |#1|)) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) |#1| |#1|)) - (SIGNATURE |elt| - (|#1| (|BasicOperator|) |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#1|) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| |#1| |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|Equation| |#1|)))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|Kernel| |#1|)) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|Kernel| |#1|) |#1|)) - (SIGNATURE |retract| - ((|Kernel| |#1|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Kernel| |#1|) - "failed") - |#1|))) - (|ExpressionSpace|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/ES.lsp b/src/algebra/strap/ES.lsp index 757ce9e6..5199b94c 100644 --- a/src/algebra/strap/ES.lsp +++ b/src/algebra/strap/ES.lsp @@ -144,7 +144,7 @@ (|Equation| $)) NIL))) |ExpressionSpace|) - (SETELT #0# 0 '(|ExpressionSpace|)))))) + (|setShellEntry| #0# 0 '(|ExpressionSpace|)))))) (DEFUN |ExpressionSpace| () (LET () @@ -152,9 +152,4 @@ (|ExpressionSpace;AL|) (T (SETQ |ExpressionSpace;AL| (|ExpressionSpace;|)))))) -(SETQ |$CategoryFrame| - (|put| '|ExpressionSpace| '|isCategory| T - (|addModemap| '|ExpressionSpace| '(|ExpressionSpace|) - '((|Category|)) T '|ExpressionSpace| |$CategoryFrame|))) - (MAKEPROP '|ExpressionSpace| 'NILADIC T) diff --git a/src/algebra/strap/EUCDOM-.lsp b/src/algebra/strap/EUCDOM-.lsp index f354c167..405da119 100644 --- a/src/algebra/strap/EUCDOM-.lsp +++ b/src/algebra/strap/EUCDOM-.lsp @@ -550,102 +550,3 @@ 0 0 0 0 21 3 0 36 0 0 0 37 2 0 31 0 0 32 2 0 16 0 0 17 2 0 45 41 0 46))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|EuclideanDomain&| '|isFunctor| - '(((|multiEuclidean| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ 53)) - ((|extendedEuclidean| - ((|Union| (|Record| (|:| |coef1| $) - (|:| |coef2| $)) - "failed") - $ $ $)) - T (ELT $ 37)) - ((|extendedEuclidean| - ((|Record| (|:| |coef1| $) (|:| |coef2| $) - (|:| |generator| $)) - $ $)) - T (ELT $ 32)) - ((|rem| ($ $ $)) T (ELT $ 15)) - ((|quo| ($ $ $)) T (ELT $ 14)) - ((|sizeLess?| ((|Boolean|) $ $)) T (ELT $ 11)) - ((|expressIdealMember| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ 46)) - ((|principalIdeal| - ((|Record| (|:| |coef| (|List| $)) - (|:| |generator| $)) - (|List| $))) - T (ELT $ 44)) - ((|gcd| ($ (|List| $))) T (ELT $ NIL)) - ((|gcd| ($ $ $)) T (ELT $ 21)) - ((|exquo| ((|Union| $ "failed") $ $)) T (ELT $ 17))) - (|addModemap| '|EuclideanDomain&| - '(|EuclideanDomain&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |multiEuclidean| - ((|Union| (|List| |#1|) "failed") - (|List| |#1|) |#1|)) - (SIGNATURE |extendedEuclidean| - ((|Union| (|Record| (|:| |coef1| |#1|) - (|:| |coef2| |#1|)) - "failed") - |#1| |#1| |#1|)) - (SIGNATURE |extendedEuclidean| - ((|Record| (|:| |coef1| |#1|) - (|:| |coef2| |#1|) - (|:| |generator| |#1|)) - |#1| |#1|)) - (SIGNATURE |rem| (|#1| |#1| |#1|)) - (SIGNATURE |quo| (|#1| |#1| |#1|)) - (SIGNATURE |sizeLess?| ((|Boolean|) |#1| |#1|)) - (SIGNATURE |expressIdealMember| - ((|Union| (|List| |#1|) "failed") - (|List| |#1|) |#1|)) - (SIGNATURE |principalIdeal| - ((|Record| (|:| |coef| (|List| |#1|)) - (|:| |generator| |#1|)) - (|List| |#1|))) - (SIGNATURE |gcd| (|#1| (|List| |#1|))) - (SIGNATURE |gcd| (|#1| |#1| |#1|)) - (SIGNATURE |exquo| - ((|Union| |#1| "failed") |#1| |#1|))) - (|EuclideanDomain|)) - T '|EuclideanDomain&| - (|put| '|EuclideanDomain&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |multiEuclidean| - ((|Union| (|List| |#1|) "failed") - (|List| |#1|) |#1|)) - (SIGNATURE |extendedEuclidean| - ((|Union| - (|Record| (|:| |coef1| |#1|) - (|:| |coef2| |#1|)) - "failed") - |#1| |#1| |#1|)) - (SIGNATURE |extendedEuclidean| - ((|Record| (|:| |coef1| |#1|) - (|:| |coef2| |#1|) - (|:| |generator| |#1|)) - |#1| |#1|)) - (SIGNATURE |rem| (|#1| |#1| |#1|)) - (SIGNATURE |quo| (|#1| |#1| |#1|)) - (SIGNATURE |sizeLess?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |expressIdealMember| - ((|Union| (|List| |#1|) "failed") - (|List| |#1|) |#1|)) - (SIGNATURE |principalIdeal| - ((|Record| - (|:| |coef| (|List| |#1|)) - (|:| |generator| |#1|)) - (|List| |#1|))) - (SIGNATURE |gcd| (|#1| (|List| |#1|))) - (SIGNATURE |gcd| (|#1| |#1| |#1|)) - (SIGNATURE |exquo| - ((|Union| |#1| "failed") |#1| - |#1|))) - (|EuclideanDomain|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/EUCDOM.lsp b/src/algebra/strap/EUCDOM.lsp index 7c101f7e..3c060c32 100644 --- a/src/algebra/strap/EUCDOM.lsp +++ b/src/algebra/strap/EUCDOM.lsp @@ -42,7 +42,7 @@ (|Boolean|)) NIL)) |EuclideanDomain|) - (SETELT #0# 0 '(|EuclideanDomain|)))))) + (|setShellEntry| #0# 0 '(|EuclideanDomain|)))))) (DEFUN |EuclideanDomain| () (LET () @@ -50,9 +50,4 @@ (|EuclideanDomain;AL|) (T (SETQ |EuclideanDomain;AL| (|EuclideanDomain;|)))))) -(SETQ |$CategoryFrame| - (|put| '|EuclideanDomain| '|isCategory| T - (|addModemap| '|EuclideanDomain| '(|EuclideanDomain|) - '((|Category|)) T '|EuclideanDomain| |$CategoryFrame|))) - (MAKEPROP '|EuclideanDomain| 'NILADIC T) diff --git a/src/algebra/strap/FFIELDC-.lsp b/src/algebra/strap/FFIELDC-.lsp index d0a70454..0f649439 100644 --- a/src/algebra/strap/FFIELDC-.lsp +++ b/src/algebra/strap/FFIELDC-.lsp @@ -650,105 +650,3 @@ 44 1 0 32 33 34 1 0 0 0 37 1 0 15 0 38))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|FiniteFieldCategory&| '|isFunctor| - '(((|order| ((|PositiveInteger|) $)) T (ELT $ 52)) - ((|discreteLog| ((|NonNegativeInteger|) $)) T - (ELT $ 60)) - ((|primitive?| ((|Boolean|) $)) T (ELT $ 51)) - ((|createPrimitiveElement| ($)) T (ELT $ 44)) - ((|conditionP| - ((|Union| (|Vector| $) "failed") (|Matrix| $))) - T (ELT $ 34)) - ((|charthRoot| ($ $)) T (ELT $ 37)) - ((|differentiate| ($ $)) T (ELT $ 8)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|init| ($)) T (ELT $ 9)) - ((|nextItem| ((|Union| $ "failed") $)) T (ELT $ 16)) - ((|discreteLog| - ((|Union| (|NonNegativeInteger|) "failed") $ $)) - T (ELT $ 71)) - ((|order| ((|OnePointCompletion| (|PositiveInteger|)) $)) - T (ELT $ 21)) - ((|charthRoot| ((|Union| $ "failed") $)) T (ELT $ 38)) - ((|gcdPolynomial| - ((|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 93))) - (|addModemap| '|FiniteFieldCategory&| - '(|FiniteFieldCategory&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |order| ((|PositiveInteger|) |#1|)) - (SIGNATURE |discreteLog| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |primitive?| ((|Boolean|) |#1|)) - (SIGNATURE |createPrimitiveElement| (|#1|)) - (SIGNATURE |conditionP| - ((|Union| (|Vector| |#1|) "failed") - (|Matrix| |#1|))) - (SIGNATURE |charthRoot| (|#1| |#1|)) - (SIGNATURE |differentiate| (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |init| (|#1|)) - (SIGNATURE |nextItem| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |discreteLog| - ((|Union| (|NonNegativeInteger|) "failed") - |#1| |#1|)) - (SIGNATURE |order| - ((|OnePointCompletion| (|PositiveInteger|)) - |#1|)) - (SIGNATURE |charthRoot| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |gcdPolynomial| - ((|SparseUnivariatePolynomial| |#1|) - (|SparseUnivariatePolynomial| |#1|) - (|SparseUnivariatePolynomial| |#1|)))) - (|FiniteFieldCategory|)) - T '|FiniteFieldCategory&| - (|put| '|FiniteFieldCategory&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |order| - ((|PositiveInteger|) |#1|)) - (SIGNATURE |discreteLog| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |primitive?| - ((|Boolean|) |#1|)) - (SIGNATURE |createPrimitiveElement| - (|#1|)) - (SIGNATURE |conditionP| - ((|Union| (|Vector| |#1|) - "failed") - (|Matrix| |#1|))) - (SIGNATURE |charthRoot| (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |init| (|#1|)) - (SIGNATURE |nextItem| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |discreteLog| - ((|Union| (|NonNegativeInteger|) - "failed") - |#1| |#1|)) - (SIGNATURE |order| - ((|OnePointCompletion| - (|PositiveInteger|)) - |#1|)) - (SIGNATURE |charthRoot| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |gcdPolynomial| - ((|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|)))) - (|FiniteFieldCategory|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/FFIELDC.lsp b/src/algebra/strap/FFIELDC.lsp index 4bc08870..9f7cef9b 100644 --- a/src/algebra/strap/FFIELDC.lsp +++ b/src/algebra/strap/FFIELDC.lsp @@ -49,7 +49,7 @@ (|Matrix| $)) NIL)) |FiniteFieldCategory|) - (SETELT #0# 0 '(|FiniteFieldCategory|)))))) + (|setShellEntry| #0# 0 '(|FiniteFieldCategory|)))))) (DEFUN |FiniteFieldCategory| () (LET () @@ -57,10 +57,4 @@ (|FiniteFieldCategory;AL|) (T (SETQ |FiniteFieldCategory;AL| (|FiniteFieldCategory;|)))))) -(SETQ |$CategoryFrame| - (|put| '|FiniteFieldCategory| '|isCategory| T - (|addModemap| '|FiniteFieldCategory| - '(|FiniteFieldCategory|) '((|Category|)) T - '|FiniteFieldCategory| |$CategoryFrame|))) - (MAKEPROP '|FiniteFieldCategory| 'NILADIC T) diff --git a/src/algebra/strap/FPS-.lsp b/src/algebra/strap/FPS-.lsp index 312a0bbc..6cbb70df 100644 --- a/src/algebra/strap/FPS-.lsp +++ b/src/algebra/strap/FPS-.lsp @@ -55,41 +55,3 @@ 13 2 9 0 7 0 14 0 6 0 15 2 0 0 9 9 11 0 0 7 16))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|FloatingPointSystem&| '|isFunctor| - '(((|digits| ((|PositiveInteger|) (|PositiveInteger|))) T - (ELT $ NIL)) - ((|digits| ((|PositiveInteger|))) T (ELT $ 16)) - ((|float| ($ (|Integer|) (|Integer|) - (|PositiveInteger|))) - T (ELT $ NIL)) - ((|float| ($ (|Integer|) (|Integer|))) T (ELT $ 11))) - (|addModemap| '|FloatingPointSystem&| - '(|FloatingPointSystem&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |digits| - ((|PositiveInteger|) (|PositiveInteger|))) - (SIGNATURE |digits| ((|PositiveInteger|))) - (SIGNATURE |float| - (|#1| (|Integer|) (|Integer|) - (|PositiveInteger|))) - (SIGNATURE |float| - (|#1| (|Integer|) (|Integer|)))) - (|FloatingPointSystem|)) - T '|FloatingPointSystem&| - (|put| '|FloatingPointSystem&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |digits| - ((|PositiveInteger|) - (|PositiveInteger|))) - (SIGNATURE |digits| - ((|PositiveInteger|))) - (SIGNATURE |float| - (|#1| (|Integer|) (|Integer|) - (|PositiveInteger|))) - (SIGNATURE |float| - (|#1| (|Integer|) (|Integer|)))) - (|FloatingPointSystem|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/FPS.lsp b/src/algebra/strap/FPS.lsp index f3935aa4..313baa93 100644 --- a/src/algebra/strap/FPS.lsp +++ b/src/algebra/strap/FPS.lsp @@ -70,7 +70,7 @@ '((|approximate| T)) '((|PositiveInteger|) (|Integer|)) NIL)) |FloatingPointSystem|) - (SETELT #0# 0 '(|FloatingPointSystem|)))))) + (|setShellEntry| #0# 0 '(|FloatingPointSystem|)))))) (DEFUN |FloatingPointSystem| () (LET () @@ -78,10 +78,4 @@ (|FloatingPointSystem;AL|) (T (SETQ |FloatingPointSystem;AL| (|FloatingPointSystem;|)))))) -(SETQ |$CategoryFrame| - (|put| '|FloatingPointSystem| '|isCategory| T - (|addModemap| '|FloatingPointSystem| - '(|FloatingPointSystem|) '((|Category|)) T - '|FloatingPointSystem| |$CategoryFrame|))) - (MAKEPROP '|FloatingPointSystem| 'NILADIC T) diff --git a/src/algebra/strap/GCDDOM-.lsp b/src/algebra/strap/GCDDOM-.lsp index 8e9a0e77..b3a3bbc5 100644 --- a/src/algebra/strap/GCDDOM-.lsp +++ b/src/algebra/strap/GCDDOM-.lsp @@ -233,43 +233,3 @@ 20 21 2 0 0 0 0 14 2 0 40 40 40 41 1 0 0 20 22))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|GcdDomain&| '|isFunctor| - '(((|gcdPolynomial| - ((|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 41)) - ((|lcm| ($ (|List| $))) T (ELT $ 21)) - ((|lcm| ($ $ $)) T (ELT $ 14)) - ((|gcd| ($ (|List| $))) T (ELT $ 22)) - ((|gcd| ($ $ $)) T (ELT $ NIL))) - (|addModemap| '|GcdDomain&| '(|GcdDomain&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |gcdPolynomial| - ((|SparseUnivariatePolynomial| |#1|) - (|SparseUnivariatePolynomial| |#1|) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |lcm| (|#1| (|List| |#1|))) - (SIGNATURE |lcm| (|#1| |#1| |#1|)) - (SIGNATURE |gcd| (|#1| (|List| |#1|))) - (SIGNATURE |gcd| (|#1| |#1| |#1|))) - (|GcdDomain|)) - T '|GcdDomain&| - (|put| '|GcdDomain&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |gcdPolynomial| - ((|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE |lcm| (|#1| (|List| |#1|))) - (SIGNATURE |lcm| (|#1| |#1| |#1|)) - (SIGNATURE |gcd| (|#1| (|List| |#1|))) - (SIGNATURE |gcd| (|#1| |#1| |#1|))) - (|GcdDomain|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/GCDDOM.lsp b/src/algebra/strap/GCDDOM.lsp index 313add96..8f4675a6 100644 --- a/src/algebra/strap/GCDDOM.lsp +++ b/src/algebra/strap/GCDDOM.lsp @@ -23,15 +23,10 @@ (|List| $)) NIL)) |GcdDomain|) - (SETELT #0# 0 '(|GcdDomain|)))))) + (|setShellEntry| #0# 0 '(|GcdDomain|)))))) (DEFUN |GcdDomain| () (LET () (COND (|GcdDomain;AL|) (T (SETQ |GcdDomain;AL| (|GcdDomain;|)))))) -(SETQ |$CategoryFrame| - (|put| '|GcdDomain| '|isCategory| T - (|addModemap| '|GcdDomain| '(|GcdDomain|) '((|Category|)) - T '|GcdDomain| |$CategoryFrame|))) - (MAKEPROP '|GcdDomain| 'NILADIC T) diff --git a/src/algebra/strap/HOAGG-.lsp b/src/algebra/strap/HOAGG-.lsp index 21abe57d..b1b57cdc 100644 --- a/src/algebra/strap/HOAGG-.lsp +++ b/src/algebra/strap/HOAGG-.lsp @@ -324,89 +324,3 @@ 0 32 0 37 2 0 18 19 0 20 2 0 18 0 0 31 1 0 16 0 17))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|HomogeneousAggregate&| '|isFunctor| - '(((|coerce| ((|OutputForm|) $)) T (ELT $ 37)) - ((= ((|Boolean|) $ $)) T (ELT $ 31)) - ((|eval| ($ $ (|List| |#2|) (|List| |#2|))) T - (ELT $ NIL)) - ((|eval| ($ $ |#2| |#2|)) T (ELT $ NIL)) - ((|eval| ($ $ (|Equation| |#2|))) T (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| |#2|)))) T (ELT $ 13)) - ((|member?| ((|Boolean|) |#2| $)) T (ELT $ 28)) - ((|count| ((|NonNegativeInteger|) |#2| $)) T (ELT $ 26)) - ((|members| ((|List| |#2|) $)) T (ELT $ 23)) - ((|count| ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#2|) $)) - T (ELT $ 22)) - ((|every?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) $)) - T (ELT $ 21)) - ((|any?| ((|Boolean|) (|Mapping| (|Boolean|) |#2|) $)) T - (ELT $ 20)) - ((|#| ((|NonNegativeInteger|) $)) T (ELT $ 17))) - (|addModemap| '|HomogeneousAggregate&| - '(|HomogeneousAggregate&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE |coerce| ((|OutputForm|) |#1|)) - (SIGNATURE = ((|Boolean|) |#1| |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#2|) (|List| |#2|))) - (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) - (SIGNATURE |eval| (|#1| |#1| (|Equation| |#2|))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Equation| |#2|)))) - (SIGNATURE |member?| ((|Boolean|) |#2| |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) |#2| |#1|)) - (SIGNATURE |members| ((|List| |#2|) |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |every?| - ((|Boolean|) (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |any?| - ((|Boolean|) (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |#| ((|NonNegativeInteger|) |#1|))) - (|HomogeneousAggregate| |#2|) (|Type|)) - T '|HomogeneousAggregate&| - (|put| '|HomogeneousAggregate&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |coerce| - ((|OutputForm|) |#1|)) - (SIGNATURE = ((|Boolean|) |#1| |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#2|) - (|List| |#2|))) - (SIGNATURE |eval| - (|#1| |#1| |#2| |#2|)) - (SIGNATURE |eval| - (|#1| |#1| (|Equation| |#2|))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|Equation| |#2|)))) - (SIGNATURE |member?| - ((|Boolean|) |#2| |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) |#2| |#1|)) - (SIGNATURE |members| - ((|List| |#2|) |#1|)) - (SIGNATURE |count| - ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |every?| - ((|Boolean|) - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |any?| - ((|Boolean|) - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |#| - ((|NonNegativeInteger|) |#1|))) - (|HomogeneousAggregate| |#2|) (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/HOAGG.lsp b/src/algebra/strap/HOAGG.lsp index baccec79..7e2bb119 100644 --- a/src/algebra/strap/HOAGG.lsp +++ b/src/algebra/strap/HOAGG.lsp @@ -97,8 +97,8 @@ (|List| |t#1|)) NIL)) . #1=(|HomogeneousAggregate|))))) . #1#) - (SETELT #0# 0 - (LIST '|HomogeneousAggregate| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|HomogeneousAggregate| (|devaluate| |t#1|))))))) (DEFUN |HomogeneousAggregate| (#0=#:G1399) (LET (#1=#:G1400) @@ -110,10 +110,3 @@ (SETQ #1# (|HomogeneousAggregate;| #0#))) |HomogeneousAggregate;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|HomogeneousAggregate| '|isCategory| T - (|addModemap| '|HomogeneousAggregate| - '(|HomogeneousAggregate| |#1|) - '((|Category|) (|Type|)) T '|HomogeneousAggregate| - |$CategoryFrame|))) diff --git a/src/algebra/strap/ILIST.lsp b/src/algebra/strap/ILIST.lsp index 3bf0bc8d..39658b69 100644 --- a/src/algebra/strap/ILIST.lsp +++ b/src/algebra/strap/ILIST.lsp @@ -716,255 +716,3 @@ 0 0 1 2 5 11 0 0 1 2 7 11 0 0 48 2 5 11 0 0 1 2 5 11 0 0 1 1 0 8 0 9))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|IndexedList| '|isFunctor| - '(((|coerce| ((|OutputForm|) $)) - (|has| |#1| (|CoercibleTo| (|OutputForm|))) (ELT $ 46)) - ((~= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ 48)) - ((|hash| ((|SingleInteger|) $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|latex| ((|String|) $)) (|has| |#1| (|SetCategory|)) - (ELT $ 51)) - ((|list| ($ |#1|)) T (ELT $ NIL)) - ((|concat!| ($ $ |#1|)) T (ELT $ NIL)) - ((|concat!| ($ $ $)) T (ELT $ 54)) - ((|delete!| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|delete!| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|remove!| ($ (|Mapping| (|Boolean|) |#1|) $)) T - (ELT $ NIL)) - ((|insert!| ($ |#1| $ (|Integer|))) T (ELT $ NIL)) - ((|insert!| ($ $ $ (|Integer|))) T (ELT $ NIL)) - ((|merge!| ($ (|Mapping| (|Boolean|) |#1| |#1|) $ $)) T - (ELT $ 58)) - ((|select!| ($ (|Mapping| (|Boolean|) |#1|) $)) T - (ELT $ NIL)) - ((|remove!| ($ |#1| $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|removeDuplicates!| ($ $)) - (|has| |#1| (|SetCategory|)) (ELT $ 55)) - ((|merge!| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|merge| ($ (|Mapping| (|Boolean|) |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|reverse| ($ $)) T (ELT $ 29)) - ((|sort| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) T - (ELT $ NIL)) - ((|sorted?| - ((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $)) - T (ELT $ NIL)) - ((|position| - ((|Integer|) (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $ (|Integer|))) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|merge| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|sort| ($ $)) (|has| |#1| (|OrderedSet|)) (ELT $ NIL)) - ((|sorted?| ((|Boolean|) $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|copyInto!| ($ $ $ (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|reverse!| ($ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 28)) - ((|sort!| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 57)) - ((|sort!| ($ $)) - (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) - (|has| |#1| (|OrderedSet|))) - (ELT $ NIL)) - ((|min| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|max| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((> ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((< ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|possiblyInfinite?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|explicitlyFinite?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|qsetelt!| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|qelt| (|#1| $ (|Integer|))) T (ELT $ NIL)) - ((|elt| (|#1| $ (|Integer|) |#1|)) T (ELT $ NIL)) - ((|elt| (|#1| $ (|Integer|))) T (ELT $ NIL)) - ((|entries| ((|List| |#1|) $)) T (ELT $ NIL)) - ((|index?| ((|Boolean|) (|Integer|) $)) T (ELT $ NIL)) - ((|indices| ((|List| (|Integer|)) $)) T (ELT $ NIL)) - ((|entry?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|maxIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ NIL)) - ((|minIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ 31)) - ((|fill!| ($ $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|swap!| ((|Void|) $ (|Integer|) (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|convert| ((|InputForm|) $)) - (|has| |#1| (|ConvertibleTo| (|InputForm|))) - (ELT $ NIL)) - ((|removeDuplicates| ($ $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|remove| ($ |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|reduce| - (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|select| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|remove| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|find| ((|Union| |#1| "failed") - (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|construct| ($ (|List| |#1|))) T (ELT $ 26)) - ((|new| ($ (|NonNegativeInteger|) |#1|)) T (ELT $ NIL)) - ((|concat| ($ $ |#1|)) T (ELT $ NIL)) - ((|concat| ($ (|List| $))) T (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|elt| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|delete| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|delete| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|insert| ($ |#1| $ (|Integer|))) T (ELT $ NIL)) - ((|insert| ($ $ $ (|Integer|))) T (ELT $ NIL)) - ((|setelt| - (|#1| $ (|UniversalSegment| (|Integer|)) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|split!| ($ $ (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 59)) - ((|setelt| (|#1| $ "last" |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setlast!| (|#1| $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| ($ $ "rest" $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 24)) - ((|setrest!| ($ $ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 23)) - ((|setelt| (|#1| $ "first" |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 22)) - ((|setfirst!| (|#1| $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 21)) - ((|cycleSplit!| ($ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|cycleTail| ($ $)) T (ELT $ NIL)) - ((|cycleLength| ((|NonNegativeInteger|) $)) T - (ELT $ NIL)) - ((|cycleEntry| ($ $)) T (ELT $ 36)) - ((|third| (|#1| $)) T (ELT $ NIL)) - ((|second| (|#1| $)) T (ELT $ NIL)) - ((|tail| ($ $)) T (ELT $ NIL)) - ((|last| ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|elt| (|#1| $ "last")) T (ELT $ NIL)) - ((|last| (|#1| $)) T (ELT $ NIL)) - ((|rest| ($ $ (|NonNegativeInteger|))) T (ELT $ 32)) - ((|elt| ($ $ "rest")) T (ELT $ 20)) - ((|rest| ($ $)) T (ELT $ 18)) - ((|first| ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|elt| (|#1| $ "first")) T (ELT $ 15)) - ((|first| (|#1| $)) T (ELT $ 13)) - ((|concat| ($ |#1| $)) T (ELT $ 10)) - ((|concat| ($ $ $)) T (ELT $ NIL)) - ((|setvalue!| (|#1| $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| (|#1| $ "value" |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setchildren!| ($ $ (|List| $))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|node?| ((|Boolean|) $ $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|child?| ((|Boolean|) $ $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|distance| ((|Integer|) $ $)) T (ELT $ NIL)) - ((|leaves| ((|List| |#1|) $)) T (ELT $ NIL)) - ((|cyclic?| ((|Boolean|) $)) T (ELT $ 34)) - ((|elt| (|#1| $ "value")) T (ELT $ NIL)) - ((|value| (|#1| $)) T (ELT $ NIL)) - ((|leaf?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|nodes| ((|List| $) $)) T (ELT $ NIL)) - ((|children| ((|List| $) $)) T (ELT $ NIL)) - ((|eval| ($ $ (|List| |#1|) (|List| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ |#1| |#1|)) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|Equation| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| |#1|)))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|member?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ 53)) - ((|count| ((|NonNegativeInteger|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|members| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|parts| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ 27)) - ((|count| ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|map!| ($ (|Mapping| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1|) $)) T (ELT $ NIL)) - ((|#| ((|NonNegativeInteger|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ 9)) - ((|sample| ($)) T (CONST $ NIL)) - ((|size?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|more?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|less?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|empty?| ((|Boolean|) $)) T (ELT $ 17)) - ((|empty| ($)) T (ELT $ 16)) - ((|copy| ($ $)) T (ELT $ 35)) - ((|eq?| ((|Boolean|) $ $)) T (ELT $ 12))) - (|addModemap| '|IndexedList| '(|IndexedList| |#1| |#2|) - '((|ListAggregate| |#1|) (|Type|) (|Integer|)) T - '|IndexedList| - (|put| '|IndexedList| '|mode| - '(|Mapping| (|ListAggregate| |#1|) (|Type|) - (|Integer|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/INS-.lsp b/src/algebra/strap/INS-.lsp index b16fd75f..229a04fa 100644 --- a/src/algebra/strap/INS-.lsp +++ b/src/algebra/strap/INS-.lsp @@ -415,164 +415,3 @@ 36 0 0 7 8 2 0 11 0 0 20 2 0 0 0 0 55))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|IntegerNumberSystem&| '|isFunctor| - '(((|invmod| ($ $ $)) T (ELT $ 84)) - ((|powmod| ($ $ $ $)) T (ELT $ 86)) - ((|mask| ($ $)) T (ELT $ 23)) - ((|copy| ($ $)) T (ELT $ 17)) - ((|rationalIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") $)) - T (ELT $ 74)) - ((|rational| ((|Fraction| (|Integer|)) $)) T (ELT $ 72)) - ((|rational?| ((|Boolean|) $)) T (ELT $ 24)) - ((|symmetricRemainder| ($ $ $)) T (ELT $ 79)) - ((|bit?| ((|Boolean|) $ $)) T (ELT $ 20)) - ((|even?| ((|Boolean|) $)) T (ELT $ 14)) - ((|init| ($)) T (ELT $ 60)) - ((|nextItem| ((|Union| $ "failed") $)) T (ELT $ 64)) - ((|convert| ((|DoubleFloat|) $)) T (ELT $ 33)) - ((|convert| ((|Float|) $)) T (ELT $ 31)) - ((|permutation| ($ $ $)) T (ELT $ 57)) - ((|factorial| ($ $)) T (ELT $ 53)) - ((|binomial| ($ $ $)) T (ELT $ 55)) - ((|patternMatch| - ((|PatternMatchResult| (|Integer|) $) $ - (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) $))) - T (ELT $ 69)) - ((|convert| ((|Pattern| (|Integer|)) $)) T (ELT $ 40)) - ((|convert| ((|InputForm|) $)) T (ELT $ 36)) - ((|retract| ((|Integer|) $)) T (ELT $ 37)) - ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T - (ELT $ 59)) - ((|convert| ((|Integer|) $)) T (ELT $ NIL)) - ((|differentiate| ($ $)) T (ELT $ 10)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|positive?| ((|Boolean|) $)) T (ELT $ 16)) - ((|euclideanSize| ((|NonNegativeInteger|) $)) T - (ELT $ 28)) - ((|factor| ((|Factored| $) $)) T (ELT $ 45)) - ((|squareFree| ((|Factored| $) $)) T (ELT $ 47)) - ((|prime?| ((|Boolean|) $)) T (ELT $ 50)) - ((|characteristic| ((|NonNegativeInteger|))) T - (ELT $ 8))) - (|addModemap| '|IntegerNumberSystem&| - '(|IntegerNumberSystem&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |invmod| (|#1| |#1| |#1|)) - (SIGNATURE |powmod| (|#1| |#1| |#1| |#1|)) - (SIGNATURE |mask| (|#1| |#1|)) - (SIGNATURE |copy| (|#1| |#1|)) - (SIGNATURE |rationalIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") - |#1|)) - (SIGNATURE |rational| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |rational?| ((|Boolean|) |#1|)) - (SIGNATURE |symmetricRemainder| - (|#1| |#1| |#1|)) - (SIGNATURE |bit?| ((|Boolean|) |#1| |#1|)) - (SIGNATURE |even?| ((|Boolean|) |#1|)) - (SIGNATURE |init| (|#1|)) - (SIGNATURE |nextItem| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) - (SIGNATURE |convert| ((|Float|) |#1|)) - (SIGNATURE |permutation| (|#1| |#1| |#1|)) - (SIGNATURE |factorial| (|#1| |#1|)) - (SIGNATURE |binomial| (|#1| |#1| |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Integer|) |#1|) - |#1| (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) |#1|))) - (SIGNATURE |convert| - ((|Pattern| (|Integer|)) |#1|)) - (SIGNATURE |convert| ((|InputForm|) |#1|)) - (SIGNATURE |retract| ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") |#1|)) - (SIGNATURE |convert| ((|Integer|) |#1|)) - (SIGNATURE |differentiate| (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |positive?| ((|Boolean|) |#1|)) - (SIGNATURE |euclideanSize| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) - (SIGNATURE |squareFree| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |prime?| ((|Boolean|) |#1|)) - (SIGNATURE |characteristic| - ((|NonNegativeInteger|)))) - (|IntegerNumberSystem|)) - T '|IntegerNumberSystem&| - (|put| '|IntegerNumberSystem&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |invmod| (|#1| |#1| |#1|)) - (SIGNATURE |powmod| - (|#1| |#1| |#1| |#1|)) - (SIGNATURE |mask| (|#1| |#1|)) - (SIGNATURE |copy| (|#1| |#1|)) - (SIGNATURE |rationalIfCan| - ((|Union| (|Fraction| (|Integer|)) - "failed") - |#1|)) - (SIGNATURE |rational| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |rational?| - ((|Boolean|) |#1|)) - (SIGNATURE |symmetricRemainder| - (|#1| |#1| |#1|)) - (SIGNATURE |bit?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |even?| ((|Boolean|) |#1|)) - (SIGNATURE |init| (|#1|)) - (SIGNATURE |nextItem| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |convert| - ((|DoubleFloat|) |#1|)) - (SIGNATURE |convert| ((|Float|) |#1|)) - (SIGNATURE |permutation| - (|#1| |#1| |#1|)) - (SIGNATURE |factorial| (|#1| |#1|)) - (SIGNATURE |binomial| - (|#1| |#1| |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Integer|) - |#1|) - |#1| (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) - |#1|))) - (SIGNATURE |convert| - ((|Pattern| (|Integer|)) |#1|)) - (SIGNATURE |convert| - ((|InputForm|) |#1|)) - (SIGNATURE |retract| - ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") - |#1|)) - (SIGNATURE |convert| - ((|Integer|) |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |positive?| - ((|Boolean|) |#1|)) - (SIGNATURE |euclideanSize| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |factor| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |squareFree| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |prime?| - ((|Boolean|) |#1|)) - (SIGNATURE |characteristic| - ((|NonNegativeInteger|)))) - (|IntegerNumberSystem|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/INS.lsp b/src/algebra/strap/INS.lsp index af5969d3..ef6261ca 100644 --- a/src/algebra/strap/INS.lsp +++ b/src/algebra/strap/INS.lsp @@ -63,7 +63,7 @@ (|Boolean|)) NIL))) |IntegerNumberSystem|) - (SETELT #0# 0 '(|IntegerNumberSystem|)))))) + (|setShellEntry| #0# 0 '(|IntegerNumberSystem|)))))) (DEFUN |IntegerNumberSystem| () (LET () @@ -71,10 +71,4 @@ (|IntegerNumberSystem;AL|) (T (SETQ |IntegerNumberSystem;AL| (|IntegerNumberSystem;|)))))) -(SETQ |$CategoryFrame| - (|put| '|IntegerNumberSystem| '|isCategory| T - (|addModemap| '|IntegerNumberSystem| - '(|IntegerNumberSystem|) '((|Category|)) T - '|IntegerNumberSystem| |$CategoryFrame|))) - (MAKEPROP '|IntegerNumberSystem| 'NILADIC T) diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp index 7fa42593..0e57fde8 100644 --- a/src/algebra/strap/INT.lsp +++ b/src/algebra/strap/INT.lsp @@ -628,7 +628,7 @@ (|unitsKnown| . 0)) (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)) + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)) (CONS '#(|IntegerNumberSystem&| |EuclideanDomain&| |UniqueFactorizationDomain&| NIL NIL |GcdDomain&| |IntegralDomain&| |Algebra&| NIL @@ -638,7 +638,7 @@ |Monoid&| NIL NIL |OrderedSet&| |AbelianSemiGroup&| |SemiGroup&| NIL |SetCategory&| NIL NIL NIL NIL NIL NIL NIL - |RetractableTo&| NIL |BasicType&| NIL) + |RetractableTo&| NIL NIL |BasicType&| NIL) (CONS '#((|IntegerNumberSystem|) (|EuclideanDomain|) (|UniqueFactorizationDomain|) @@ -669,6 +669,7 @@ (|ConvertibleTo| 123) (|ConvertibleTo| 50) (|RetractableTo| 11) + (|CoercibleFrom| 11) (|ConvertibleTo| 11) (|BasicType|) (|CoercibleTo| 36)) (|makeByteWordVec2| 131 @@ -719,180 +720,4 @@ 2 0 0 131 0 1))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|Integer| '|isFunctor| - '(((|OMwrite| ((|Void|) (|OpenMathDevice|) $ (|Boolean|))) - T (ELT $ 24)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $)) T - (ELT $ 23)) - ((|OMwrite| ((|String|) $ (|Boolean|))) T (ELT $ 22)) - ((|OMwrite| ((|String|) $)) T (ELT $ 20)) - ((|convert| ((|String|) $)) T (ELT $ 53)) - ((|invmod| ($ $ $)) T (ELT $ NIL)) - ((|powmod| ($ $ $ $)) T (ELT $ NIL)) - ((|mulmod| ($ $ $ $)) T (ELT $ 44)) - ((|submod| ($ $ $ $)) T (ELT $ 43)) - ((|addmod| ($ $ $ $)) T (ELT $ 42)) - ((|mask| ($ $)) T (ELT $ NIL)) - ((|dec| ($ $)) T (ELT $ 32)) - ((|inc| ($ $)) T (ELT $ 31)) - ((|copy| ($ $)) T (ELT $ 30)) - ((|random| ($ $)) T (ELT $ 65)) - ((|random| ($)) T (ELT $ 64)) - ((|rationalIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") $)) - T (ELT $ NIL)) - ((|rational| ((|Fraction| (|Integer|)) $)) T - (ELT $ NIL)) - ((|rational?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|symmetricRemainder| ($ $ $)) T (ELT $ NIL)) - ((|positiveRemainder| ($ $ $)) T (ELT $ 55)) - ((|bit?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|shift| ($ $ $)) T (ELT $ 82)) - ((|length| ($ $)) T (ELT $ 41)) - ((|base| ($)) T (ELT $ 29)) - ((|even?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|odd?| ((|Boolean|) $)) T (ELT $ 75)) - ((|init| ($)) T (CONST $ NIL)) - ((|nextItem| ((|Union| $ "failed") $)) T (ELT $ NIL)) - ((|convert| ((|DoubleFloat|) $)) T (ELT $ 49)) - ((|convert| ((|Float|) $)) T (ELT $ 47)) - ((|permutation| ($ $ $)) T (ELT $ NIL)) - ((|factorial| ($ $)) T (ELT $ NIL)) - ((|binomial| ($ $ $)) T (ELT $ NIL)) - ((|patternMatch| - ((|PatternMatchResult| (|Integer|) $) $ - (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) $))) - T (ELT $ NIL)) - ((|convert| ((|Pattern| (|Integer|)) $)) T (ELT $ NIL)) - ((|convert| ((|InputForm|) $)) T (ELT $ 52)) - ((|reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| $))) - T (ELT $ 58)) - ((|reducedSystem| - ((|Record| (|:| |mat| (|Matrix| (|Integer|))) - (|:| |vec| (|Vector| (|Integer|)))) - (|Matrix| $) (|Vector| $))) - T (ELT $ 62)) - ((|retract| ((|Integer|) $)) T (ELT $ NIL)) - ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T - (ELT $ NIL)) - ((|coerce| ($ (|Integer|))) T (ELT $ 39)) - ((|convert| ((|Integer|) $)) T (ELT $ 40)) - ((|differentiate| ($ $)) T (ELT $ NIL)) - ((D ($ $)) T (ELT $ NIL)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((D ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|abs| ($ $)) T (ELT $ 63)) - ((|sign| ((|Integer|) $)) T (ELT $ NIL)) - ((|negative?| ((|Boolean|) $)) T (ELT $ 35)) - ((|positive?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|min| ($ $ $)) T (ELT $ 77)) - ((|max| ($ $ $)) T (ELT $ 76)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ 67)) - ((|principalIdeal| - ((|Record| (|:| |coef| (|List| $)) - (|:| |generator| $)) - (|List| $))) - T (ELT $ NIL)) - ((|expressIdealMember| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ NIL)) - ((|sizeLess?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|euclideanSize| ((|NonNegativeInteger|) $)) T - (ELT $ NIL)) - ((|divide| - ((|Record| (|:| |quotient| $) (|:| |remainder| $)) - $ $)) - T (ELT $ 79)) - ((|quo| ($ $ $)) T (ELT $ 80)) - ((|rem| ($ $ $)) T (ELT $ 81)) - ((|extendedEuclidean| - ((|Record| (|:| |coef1| $) (|:| |coef2| $) - (|:| |generator| $)) - $ $)) - T (ELT $ NIL)) - ((|extendedEuclidean| - ((|Union| (|Record| (|:| |coef1| $) - (|:| |coef2| $)) - "failed") - $ $ $)) - T (ELT $ NIL)) - ((|multiEuclidean| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ NIL)) - ((|factor| ((|Factored| $) $)) T (ELT $ 105)) - ((|squareFreePart| ($ $)) T (ELT $ NIL)) - ((|squareFree| ((|Factored| $) $)) T (ELT $ NIL)) - ((|prime?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|gcdPolynomial| - ((|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 119)) - ((|lcm| ($ (|List| $))) T (ELT $ NIL)) - ((|lcm| ($ $ $)) T (ELT $ NIL)) - ((|gcd| ($ (|List| $))) T (ELT $ NIL)) - ((|gcd| ($ $ $)) T (ELT $ 86)) - ((|unit?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|associates?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|unitCanonical| ($ $)) T (ELT $ 89)) - ((|unitNormal| - ((|Record| (|:| |unit| $) (|:| |canonical| $) - (|:| |associate| $)) - $)) - T (ELT $ 88)) - ((|exquo| ((|Union| $ "failed") $ $)) T (ELT $ 84)) - ((|coerce| ($ $)) T (ELT $ NIL)) - ((|coerce| ($ (|Integer|))) T (ELT $ 39)) - ((|characteristic| ((|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|One| ($)) T (CONST $ 28)) - ((|one?| ((|Boolean|) $)) T (ELT $ 26)) - ((** ($ $ (|NonNegativeInteger|))) T (ELT $ 74)) - ((|recip| ((|Union| $ "failed") $)) T (ELT $ 85)) - ((* ($ $ $)) T (ELT $ 71)) - ((** ($ $ (|PositiveInteger|))) T (ELT $ NIL)) - ((* ($ (|Integer|) $)) T (ELT $ 72)) - ((- ($ $ $)) T (ELT $ 70)) ((- ($ $)) T (ELT $ 68)) - ((|subtractIfCan| ((|Union| $ "failed") $ $)) T - (ELT $ NIL)) - ((* ($ (|NonNegativeInteger|) $)) T (ELT $ NIL)) - ((|zero?| ((|Boolean|) $)) T (ELT $ 25)) - ((|sample| ($)) T (CONST $ NIL)) - ((|Zero| ($)) T (CONST $ 27)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ NIL)) - ((+ ($ $ $)) T (ELT $ 69)) - ((|latex| ((|String|) $)) T (ELT $ 54)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ 34)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ 38)) - ((= ((|Boolean|) $ $)) T (ELT $ 66)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|Integer| '(|Integer|) - '((|Join| (|IntegerNumberSystem|) - (|ConvertibleTo| (|String|)) (|OpenMath|) - (CATEGORY |domain| - (SIGNATURE |random| ($ $)) - (ATTRIBUTE |canonical|) - (ATTRIBUTE |canonicalsClosed|) - (ATTRIBUTE |noetherian|) - (ATTRIBUTE |infinite|)))) - T '|Integer| - (|put| '|Integer| '|mode| - '(|Mapping| - (|Join| (|IntegerNumberSystem|) - (|ConvertibleTo| (|String|)) - (|OpenMath|) - (CATEGORY |domain| - (SIGNATURE |random| ($ $)) - (ATTRIBUTE |canonical|) - (ATTRIBUTE |canonicalsClosed|) - (ATTRIBUTE |noetherian|) - (ATTRIBUTE |infinite|)))) - |$CategoryFrame|)))) - (MAKEPROP '|Integer| 'NILADIC T) diff --git a/src/algebra/strap/INTDOM-.lsp b/src/algebra/strap/INTDOM-.lsp index a8b6e221..b44a7d0d 100644 --- a/src/algebra/strap/INTDOM-.lsp +++ b/src/algebra/strap/INTDOM-.lsp @@ -100,47 +100,3 @@ 11 1 0 12 0 18 1 0 14 0 16 2 0 12 0 0 20))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|IntegralDomain&| '|isFunctor| - '(((|unit?| ((|Boolean|) $)) T (ELT $ 18)) - ((|associates?| ((|Boolean|) $ $)) T (ELT $ 20)) - ((|unitCanonical| ($ $)) T (ELT $ 11)) - ((|unitNormal| - ((|Record| (|:| |unit| $) (|:| |canonical| $) - (|:| |associate| $)) - $)) - T (ELT $ 9)) - ((|recip| ((|Union| $ "failed") $)) T (ELT $ 16))) - (|addModemap| '|IntegralDomain&| '(|IntegralDomain&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |unit?| ((|Boolean|) |#1|)) - (SIGNATURE |associates?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |unitCanonical| (|#1| |#1|)) - (SIGNATURE |unitNormal| - ((|Record| (|:| |unit| |#1|) - (|:| |canonical| |#1|) - (|:| |associate| |#1|)) - |#1|)) - (SIGNATURE |recip| - ((|Union| |#1| "failed") |#1|))) - (|IntegralDomain|)) - T '|IntegralDomain&| - (|put| '|IntegralDomain&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |unit?| ((|Boolean|) |#1|)) - (SIGNATURE |associates?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |unitCanonical| - (|#1| |#1|)) - (SIGNATURE |unitNormal| - ((|Record| (|:| |unit| |#1|) - (|:| |canonical| |#1|) - (|:| |associate| |#1|)) - |#1|)) - (SIGNATURE |recip| - ((|Union| |#1| "failed") |#1|))) - (|IntegralDomain|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/INTDOM.lsp b/src/algebra/strap/INTDOM.lsp index fc558f82..a452bca6 100644 --- a/src/algebra/strap/INTDOM.lsp +++ b/src/algebra/strap/INTDOM.lsp @@ -23,7 +23,7 @@ ((|unit?| ((|Boolean|) $)) T)) NIL '((|Boolean|)) NIL)) |IntegralDomain|) - (SETELT #0# 0 '(|IntegralDomain|)))))) + (|setShellEntry| #0# 0 '(|IntegralDomain|)))))) (DEFUN |IntegralDomain| () (LET () @@ -31,9 +31,4 @@ (|IntegralDomain;AL|) (T (SETQ |IntegralDomain;AL| (|IntegralDomain;|)))))) -(SETQ |$CategoryFrame| - (|put| '|IntegralDomain| '|isCategory| T - (|addModemap| '|IntegralDomain| '(|IntegralDomain|) - '((|Category|)) T '|IntegralDomain| |$CategoryFrame|))) - (MAKEPROP '|IntegralDomain| 'NILADIC T) diff --git a/src/algebra/strap/ISTRING.lsp b/src/algebra/strap/ISTRING.lsp index 3dd2bb09..20b18b16 100644 --- a/src/algebra/strap/ISTRING.lsp +++ b/src/algebra/strap/ISTRING.lsp @@ -1041,258 +1041,3 @@ 14 2 5 11 0 0 1 2 5 11 0 0 15 1 0 7 0 13))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|IndexedString| '|isFunctor| - '(((~= ((|Boolean|) $ $)) - (|has| (|Character|) (|SetCategory|)) (ELT $ NIL)) - ((= ((|Boolean|) $ $)) - (|has| (|Character|) (|SetCategory|)) (ELT $ 14)) - ((|coerce| ((|OutputForm|) $)) - (|has| (|Character|) (|CoercibleTo| (|OutputForm|))) - (ELT $ 27)) - ((|hash| ((|SingleInteger|) $)) - (|has| (|Character|) (|SetCategory|)) (ELT $ NIL)) - ((|latex| ((|String|) $)) - (|has| (|Character|) (|SetCategory|)) (ELT $ 38)) - ((|hash| ((|Integer|) $)) T (ELT $ 69)) - ((|elt| ($ $ $)) T (ELT $ NIL)) - ((|rightTrim| ($ $ (|CharacterClass|))) T (ELT $ 65)) - ((|rightTrim| ($ $ (|Character|))) T (ELT $ 64)) - ((|leftTrim| ($ $ (|CharacterClass|))) T (ELT $ 63)) - ((|leftTrim| ($ $ (|Character|))) T (ELT $ 62)) - ((|trim| ($ $ (|CharacterClass|))) T (ELT $ NIL)) - ((|trim| ($ $ (|Character|))) T (ELT $ NIL)) - ((|split| ((|List| $) $ (|CharacterClass|))) T - (ELT $ 61)) - ((|split| ((|List| $) $ (|Character|))) T (ELT $ 60)) - ((|coerce| ($ (|Character|))) T (ELT $ NIL)) - ((|position| - ((|Integer|) (|CharacterClass|) $ (|Integer|))) - T (ELT $ 50)) - ((|position| ((|Integer|) $ $ (|Integer|))) T - (ELT $ 47)) - ((|replace| ($ $ (|UniversalSegment| (|Integer|)) $)) T - (ELT $ 44)) - ((|match?| ((|Boolean|) $ $ (|Character|))) T - (ELT $ 73)) - ((|match| ((|NonNegativeInteger|) $ $ (|Character|))) T - (ELT $ 70)) - ((|substring?| ((|Boolean|) $ $ (|Integer|))) T - (ELT $ 46)) - ((|suffix?| ((|Boolean|) $ $)) T (ELT $ 51)) - ((|prefix?| ((|Boolean|) $ $)) T (ELT $ 72)) - ((|upperCase!| ($ $)) T (ELT $ 34)) - ((|upperCase| ($ $)) T (ELT $ NIL)) - ((|lowerCase!| ($ $)) T (ELT $ 37)) - ((|lowerCase| ($ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) - (|has| (|Character|) (|OrderedSet|)) (ELT $ 15)) - ((> ((|Boolean|) $ $)) - (|has| (|Character|) (|OrderedSet|)) (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) - (|has| (|Character|) (|OrderedSet|)) (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) - (|has| (|Character|) (|OrderedSet|)) (ELT $ NIL)) - ((|max| ($ $ $)) (|has| (|Character|) (|OrderedSet|)) - (ELT $ NIL)) - ((|min| ($ $ $)) (|has| (|Character|) (|OrderedSet|)) - (ELT $ NIL)) - ((|sort!| ($ $)) - (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) - (|has| (|Character|) (|OrderedSet|))) - (ELT $ NIL)) - ((|sort!| ($ (|Mapping| (|Boolean|) (|Character|) - (|Character|)) - $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|reverse!| ($ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|copyInto!| ($ $ $ (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 66)) - ((|sorted?| ((|Boolean|) $)) - (|has| (|Character|) (|OrderedSet|)) (ELT $ NIL)) - ((|sort| ($ $)) (|has| (|Character|) (|OrderedSet|)) - (ELT $ NIL)) - ((|merge| ($ $ $)) (|has| (|Character|) (|OrderedSet|)) - (ELT $ NIL)) - ((|position| ((|Integer|) (|Character|) $ (|Integer|))) - (|has| (|Character|) (|SetCategory|)) (ELT $ 48)) - ((|position| ((|Integer|) (|Character|) $)) - (|has| (|Character|) (|SetCategory|)) (ELT $ NIL)) - ((|position| - ((|Integer|) (|Mapping| (|Boolean|) (|Character|)) - $)) - T (ELT $ NIL)) - ((|sorted?| - ((|Boolean|) - (|Mapping| (|Boolean|) (|Character|) - (|Character|)) - $)) - T (ELT $ NIL)) - ((|sort| ($ (|Mapping| (|Boolean|) (|Character|) - (|Character|)) - $)) - T (ELT $ NIL)) - ((|reverse| ($ $)) T (ELT $ NIL)) - ((|merge| ($ (|Mapping| (|Boolean|) (|Character|) - (|Character|)) - $ $)) - T (ELT $ NIL)) - ((|setelt| - ((|Character|) $ (|UniversalSegment| (|Integer|)) - (|Character|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|insert| ($ $ $ (|Integer|))) T (ELT $ 23)) - ((|insert| ($ (|Character|) $ (|Integer|))) T - (ELT $ NIL)) - ((|delete| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|delete| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|elt| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ 21)) - ((|map| ($ (|Mapping| (|Character|) (|Character|) - (|Character|)) - $ $)) - T (ELT $ NIL)) - ((|concat| ($ (|List| $))) T (ELT $ 67)) - ((|concat| ($ $ $)) T (ELT $ 16)) - ((|concat| ($ (|Character|) $)) T (ELT $ NIL)) - ((|concat| ($ $ (|Character|))) T (ELT $ NIL)) - ((|new| ($ (|NonNegativeInteger|) (|Character|))) T - (ELT $ 9)) - ((|construct| ($ (|List| (|Character|)))) T (ELT $ NIL)) - ((|find| ((|Union| (|Character|) "failed") - (|Mapping| (|Boolean|) (|Character|)) $)) - T (ELT $ NIL)) - ((|reduce| - ((|Character|) - (|Mapping| (|Character|) (|Character|) - (|Character|)) - $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| - ((|Character|) - (|Mapping| (|Character|) (|Character|) - (|Character|)) - $ (|Character|))) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|remove| ($ (|Mapping| (|Boolean|) (|Character|)) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|select| ($ (|Mapping| (|Boolean|) (|Character|)) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| - ((|Character|) - (|Mapping| (|Character|) (|Character|) - (|Character|)) - $ (|Character|) (|Character|))) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|remove| ($ (|Character|) $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|removeDuplicates| ($ $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|convert| ((|InputForm|) $)) - (|has| (|Character|) (|ConvertibleTo| (|InputForm|))) - (ELT $ NIL)) - ((|swap!| ((|Void|) $ (|Integer|) (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|fill!| ($ $ (|Character|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|first| ((|Character|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ NIL)) - ((|minIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ 28)) - ((|maxIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ 42)) - ((|entry?| ((|Boolean|) (|Character|) $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|indices| ((|List| (|Integer|)) $)) T (ELT $ NIL)) - ((|index?| ((|Boolean|) (|Integer|) $)) T (ELT $ NIL)) - ((|entries| ((|List| (|Character|)) $)) T (ELT $ NIL)) - ((|elt| ((|Character|) $ (|Integer|))) T (ELT $ 52)) - ((|elt| ((|Character|) $ (|Integer|) (|Character|))) T - (ELT $ NIL)) - ((|qelt| ((|Character|) $ (|Integer|))) T (ELT $ NIL)) - ((|setelt| ((|Character|) $ (|Integer|) (|Character|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 45)) - ((|qsetelt!| - ((|Character|) $ (|Integer|) (|Character|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Character|)) - (|List| (|Character|)))) - (AND (|has| (|Character|) (|Evalable| (|Character|))) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|Character|) (|Character|))) - (AND (|has| (|Character|) (|Evalable| (|Character|))) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|Equation| (|Character|)))) - (AND (|has| (|Character|) (|Evalable| (|Character|))) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| (|Character|))))) - (AND (|has| (|Character|) (|Evalable| (|Character|))) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|member?| ((|Boolean|) (|Character|) $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|count| ((|NonNegativeInteger|) (|Character|) $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| (|Character|) (|SetCategory|))) - (ELT $ NIL)) - ((|members| ((|List| (|Character|)) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|parts| ((|List| (|Character|)) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|count| ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) (|Character|)) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|every?| - ((|Boolean|) (|Mapping| (|Boolean|) (|Character|)) - $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|any?| ((|Boolean|) - (|Mapping| (|Boolean|) (|Character|)) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|map!| ($ (|Mapping| (|Character|) (|Character|)) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 33)) - ((|map| ($ (|Mapping| (|Character|) (|Character|)) $)) T - (ELT $ NIL)) - ((|#| ((|NonNegativeInteger|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ 13)) - ((|sample| ($)) T (CONST $ NIL)) - ((|size?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|more?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|less?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|empty?| ((|Boolean|) $)) T (ELT $ 12)) - ((|empty| ($)) T (ELT $ 10)) - ((|copy| ($ $)) T (ELT $ 17)) - ((|eq?| ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|IndexedString| '(|IndexedString| |#1|) - '((|Join| (|StringAggregate|) - (CATEGORY |domain| - (SIGNATURE |hash| ((|Integer|) $)))) - (|Integer|)) - T '|IndexedString| - (|put| '|IndexedString| '|mode| - '(|Mapping| - (|Join| (|StringAggregate|) - (CATEGORY |domain| - (SIGNATURE |hash| - ((|Integer|) $)))) - (|Integer|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/LIST.lsp b/src/algebra/strap/LIST.lsp index e43d4ed3..949f0960 100644 --- a/src/algebra/strap/LIST.lsp +++ b/src/algebra/strap/LIST.lsp @@ -353,308 +353,3 @@ 0 0 11 3 6 12 13 0 8 29 2 6 12 13 0 28 1 6 15 0 26 2 6 15 0 8 27))))) '|lookupIncomplete|)) - -(SETQ |$CategoryFrame| - (|put| '|List| '|isFunctor| - '(((~= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) - (|has| |#1| (|CoercibleTo| (|OutputForm|))) - (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|latex| ((|String|) $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $ (|Boolean|))) - (|has| |#1| (|OpenMath|)) (ELT $ 29)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $)) - (|has| |#1| (|OpenMath|)) (ELT $ 28)) - ((|OMwrite| ((|String|) $ (|Boolean|))) - (|has| |#1| (|OpenMath|)) (ELT $ 27)) - ((|OMwrite| ((|String|) $)) (|has| |#1| (|OpenMath|)) - (ELT $ 26)) - ((|setDifference| ($ $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ 37)) - ((|setIntersection| ($ $ $)) - (|has| |#1| (|SetCategory|)) (ELT $ 34)) - ((|setUnion| ($ $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ 32)) - ((|append| ($ $ $)) T (ELT $ 11)) - ((|cons| ($ |#1| $)) T (ELT $ 10)) - ((|null| ((|Boolean|) $)) T (ELT $ 9)) - ((|nil| ($)) T (ELT $ 7)) - ((|list| ($ |#1|)) T (ELT $ NIL)) - ((|concat!| ($ $ |#1|)) T (ELT $ NIL)) - ((|concat!| ($ $ $)) T (ELT $ NIL)) - ((|delete!| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|delete!| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|remove!| ($ (|Mapping| (|Boolean|) |#1|) $)) T - (ELT $ NIL)) - ((|insert!| ($ |#1| $ (|Integer|))) T (ELT $ NIL)) - ((|insert!| ($ $ $ (|Integer|))) T (ELT $ NIL)) - ((|merge!| ($ (|Mapping| (|Boolean|) |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|select!| ($ (|Mapping| (|Boolean|) |#1|) $)) T - (ELT $ NIL)) - ((|remove!| ($ |#1| $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|removeDuplicates!| ($ $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|merge!| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|merge| ($ (|Mapping| (|Boolean|) |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|reverse| ($ $)) T (ELT $ NIL)) - ((|sort| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) T - (ELT $ NIL)) - ((|sorted?| - ((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $)) - T (ELT $ NIL)) - ((|position| - ((|Integer|) (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $ (|Integer|))) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|merge| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|sort| ($ $)) (|has| |#1| (|OrderedSet|)) (ELT $ NIL)) - ((|sorted?| ((|Boolean|) $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|copyInto!| ($ $ $ (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|reverse!| ($ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|sort!| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|sort!| ($ $)) - (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) - (|has| |#1| (|OrderedSet|))) - (ELT $ NIL)) - ((|min| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|max| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((> ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((< ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|possiblyInfinite?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|explicitlyFinite?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|qsetelt!| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|qelt| (|#1| $ (|Integer|))) T (ELT $ NIL)) - ((|elt| (|#1| $ (|Integer|) |#1|)) T (ELT $ NIL)) - ((|elt| (|#1| $ (|Integer|))) T (ELT $ 36)) - ((|entries| ((|List| |#1|) $)) T (ELT $ NIL)) - ((|index?| ((|Boolean|) (|Integer|) $)) T (ELT $ NIL)) - ((|indices| ((|List| (|Integer|)) $)) T (ELT $ NIL)) - ((|entry?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|maxIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ NIL)) - ((|minIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ NIL)) - ((|fill!| ($ $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|swap!| ((|Void|) $ (|Integer|) (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|convert| ((|InputForm|) $)) - (|has| |#1| (|ConvertibleTo| (|InputForm|))) - (ELT $ 45)) - ((|removeDuplicates| ($ $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ 31)) - ((|remove| ($ |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|reduce| - (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|select| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|remove| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|find| ((|Union| |#1| "failed") - (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|construct| ($ (|List| |#1|))) T (ELT $ NIL)) - ((|new| ($ (|NonNegativeInteger|) |#1|)) T (ELT $ NIL)) - ((|concat| ($ $ |#1|)) T (ELT $ NIL)) - ((|concat| ($ (|List| $))) T (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|elt| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|delete| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|delete| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|insert| ($ |#1| $ (|Integer|))) T (ELT $ NIL)) - ((|insert| ($ $ $ (|Integer|))) T (ELT $ NIL)) - ((|setelt| - (|#1| $ (|UniversalSegment| (|Integer|)) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|split!| ($ $ (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| (|#1| $ "last" |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setlast!| (|#1| $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| ($ $ "rest" $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setrest!| ($ $ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| (|#1| $ "first" |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setfirst!| (|#1| $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|cycleSplit!| ($ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|cycleTail| ($ $)) T (ELT $ NIL)) - ((|cycleLength| ((|NonNegativeInteger|) $)) T - (ELT $ NIL)) - ((|cycleEntry| ($ $)) T (ELT $ NIL)) - ((|third| (|#1| $)) T (ELT $ NIL)) - ((|second| (|#1| $)) T (ELT $ NIL)) - ((|tail| ($ $)) T (ELT $ NIL)) - ((|last| ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|elt| (|#1| $ "last")) T (ELT $ NIL)) - ((|last| (|#1| $)) T (ELT $ NIL)) - ((|rest| ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|elt| ($ $ "rest")) T (ELT $ NIL)) - ((|rest| ($ $)) T (ELT $ NIL)) - ((|first| ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|elt| (|#1| $ "first")) T (ELT $ NIL)) - ((|first| (|#1| $)) T (ELT $ NIL)) - ((|concat| ($ |#1| $)) T (ELT $ NIL)) - ((|concat| ($ $ $)) T (ELT $ 30)) - ((|setvalue!| (|#1| $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setelt| (|#1| $ "value" |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|setchildren!| ($ $ (|List| $))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|node?| ((|Boolean|) $ $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|child?| ((|Boolean|) $ $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|distance| ((|Integer|) $ $)) T (ELT $ NIL)) - ((|leaves| ((|List| |#1|) $)) T (ELT $ NIL)) - ((|cyclic?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|elt| (|#1| $ "value")) T (ELT $ NIL)) - ((|value| (|#1| $)) T (ELT $ NIL)) - ((|leaf?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|nodes| ((|List| $) $)) T (ELT $ NIL)) - ((|children| ((|List| $) $)) T (ELT $ NIL)) - ((|eval| ($ $ (|List| |#1|) (|List| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ |#1| |#1|)) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|Equation| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| |#1|)))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|member?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ 33)) - ((|count| ((|NonNegativeInteger|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|members| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|parts| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|count| ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|map!| ($ (|Mapping| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1|) $)) T (ELT $ NIL)) - ((|#| ((|NonNegativeInteger|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|sample| ($)) T (CONST $ NIL)) - ((|size?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|more?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|less?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|empty?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|empty| ($)) T (ELT $ NIL)) - ((|copy| ($ $)) T (ELT $ NIL)) - ((|eq?| ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|List| '(|List| |#1|) - '((|Join| (|ListAggregate| |#1|) - (CATEGORY |domain| (SIGNATURE |nil| ($)) - (SIGNATURE |null| ((|Boolean|) $)) - (SIGNATURE |cons| ($ |#1| $)) - (SIGNATURE |append| ($ $ $)) - (IF (|has| |#1| (|SetCategory|)) - (PROGN - (SIGNATURE |setUnion| ($ $ $)) - (SIGNATURE |setIntersection| - ($ $ $)) - (SIGNATURE |setDifference| - ($ $ $))) - |%noBranch|) - (IF (|has| |#1| (|OpenMath|)) - (ATTRIBUTE (|OpenMath|)) - |%noBranch|))) - (|Type|)) - T '|List| - (|put| '|List| '|mode| - '(|Mapping| - (|Join| (|ListAggregate| |#1|) - (CATEGORY |domain| - (SIGNATURE |nil| ($)) - (SIGNATURE |null| - ((|Boolean|) $)) - (SIGNATURE |cons| ($ |#1| $)) - (SIGNATURE |append| ($ $ $)) - (IF (|has| |#1| (|SetCategory|)) - (PROGN - (SIGNATURE |setUnion| ($ $ $)) - (SIGNATURE |setIntersection| - ($ $ $)) - (SIGNATURE |setDifference| - ($ $ $))) - |%noBranch|) - (IF (|has| |#1| (|OpenMath|)) - (ATTRIBUTE (|OpenMath|)) - |%noBranch|))) - (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/LNAGG-.lsp b/src/algebra/strap/LNAGG-.lsp index 8fb55dad..b997b6b1 100644 --- a/src/algebra/strap/LNAGG-.lsp +++ b/src/algebra/strap/LNAGG-.lsp @@ -102,53 +102,3 @@ 0 7 0 8 22 1 0 11 0 12 2 0 13 8 0 15 2 0 0 0 7 19 2 0 0 7 0 20))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|LinearAggregate&| '|isFunctor| - '(((|insert| ($ $ $ (|Integer|))) T (ELT $ NIL)) - ((|insert| ($ |#2| $ (|Integer|))) T (ELT $ 22)) - ((|concat| ($ (|List| $))) T (ELT $ NIL)) - ((|concat| ($ $ $)) T (ELT $ NIL)) - ((|concat| ($ |#2| $)) T (ELT $ 20)) - ((|concat| ($ $ |#2|)) T (ELT $ 19)) - ((|maxIndex| ((|Integer|) $)) T (ELT $ 24)) - ((|indices| ((|List| (|Integer|)) $)) T (ELT $ 12)) - ((|index?| ((|Boolean|) (|Integer|) $)) T (ELT $ 15))) - (|addModemap| '|LinearAggregate&| - '(|LinearAggregate&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE |insert| - (|#1| |#1| |#1| (|Integer|))) - (SIGNATURE |insert| - (|#1| |#2| |#1| (|Integer|))) - (SIGNATURE |concat| (|#1| (|List| |#1|))) - (SIGNATURE |concat| (|#1| |#1| |#1|)) - (SIGNATURE |concat| (|#1| |#2| |#1|)) - (SIGNATURE |concat| (|#1| |#1| |#2|)) - (SIGNATURE |maxIndex| ((|Integer|) |#1|)) - (SIGNATURE |indices| - ((|List| (|Integer|)) |#1|)) - (SIGNATURE |index?| - ((|Boolean|) (|Integer|) |#1|))) - (|LinearAggregate| |#2|) (|Type|)) - T '|LinearAggregate&| - (|put| '|LinearAggregate&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |insert| - (|#1| |#1| |#1| (|Integer|))) - (SIGNATURE |insert| - (|#1| |#2| |#1| (|Integer|))) - (SIGNATURE |concat| - (|#1| (|List| |#1|))) - (SIGNATURE |concat| (|#1| |#1| |#1|)) - (SIGNATURE |concat| (|#1| |#2| |#1|)) - (SIGNATURE |concat| (|#1| |#1| |#2|)) - (SIGNATURE |maxIndex| - ((|Integer|) |#1|)) - (SIGNATURE |indices| - ((|List| (|Integer|)) |#1|)) - (SIGNATURE |index?| - ((|Boolean|) (|Integer|) |#1|))) - (|LinearAggregate| |#2|) (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/LNAGG.lsp b/src/algebra/strap/LNAGG.lsp index 98805faf..39b44e3c 100644 --- a/src/algebra/strap/LNAGG.lsp +++ b/src/algebra/strap/LNAGG.lsp @@ -67,7 +67,8 @@ (|NonNegativeInteger|)) NIL)) . #2=(|LinearAggregate|)))))) . #2#) - (SETELT #0# 0 (LIST '|LinearAggregate| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|LinearAggregate| (|devaluate| |t#1|))))))) (DEFUN |LinearAggregate| (#0=#:G1400) (LET (#1=#:G1401) @@ -79,9 +80,3 @@ (SETQ #1# (|LinearAggregate;| #0#))) |LinearAggregate;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|LinearAggregate| '|isCategory| T - (|addModemap| '|LinearAggregate| '(|LinearAggregate| |#1|) - '((|Category|) (|Type|)) T '|LinearAggregate| - |$CategoryFrame|))) diff --git a/src/algebra/strap/LSAGG-.lsp b/src/algebra/strap/LSAGG-.lsp index 4823fd5b..504a9575 100644 --- a/src/algebra/strap/LSAGG-.lsp +++ b/src/algebra/strap/LSAGG-.lsp @@ -959,195 +959,3 @@ 31 38 3 0 0 0 0 31 60 1 0 0 0 58 2 0 10 0 0 66))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|ListAggregate&| '|isFunctor| - '(((|list| ($ |#2|)) T (ELT $ 15)) - ((|delete!| ($ $ (|Integer|))) T (ELT $ 38)) - ((|delete!| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ 44)) - ((|remove!| ($ (|Mapping| (|Boolean|) |#2|) $)) T - (ELT $ 37)) - ((|insert!| ($ |#2| $ (|Integer|))) T (ELT $ 34)) - ((|insert!| ($ $ $ (|Integer|))) T (ELT $ 36)) - ((|merge!| ($ (|Mapping| (|Boolean|) |#2| |#2|) $ $)) T - (ELT $ 30)) - ((|select!| ($ (|Mapping| (|Boolean|) |#2|) $)) T - (ELT $ 28)) - ((|remove!| ($ |#2| $)) T (ELT $ NIL)) - ((|removeDuplicates!| ($ $)) T (ELT $ 64)) - ((|merge!| ($ $ $)) T (ELT $ NIL)) - ((|merge| ($ (|Mapping| (|Boolean|) |#2| |#2|) $ $)) T - (ELT $ 24)) - ((|sorted?| - ((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $)) - T (ELT $ 50)) - ((|position| - ((|Integer|) (|Mapping| (|Boolean|) |#2|) $)) - T (ELT $ 47)) - ((|position| ((|Integer|) |#2| $)) T (ELT $ NIL)) - ((|position| ((|Integer|) |#2| $ (|Integer|))) T - (ELT $ 61)) - ((|merge| ($ $ $)) T (ELT $ NIL)) - ((|sorted?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|copyInto!| ($ $ $ (|Integer|))) T (ELT $ 60)) - ((|reverse!| ($ $)) T (ELT $ 56)) - ((|sort!| ($ (|Mapping| (|Boolean|) |#2| |#2|) $)) T - (ELT $ 12)) - ((|sort!| ($ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ 66)) - ((|reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|)) - T (ELT $ 53)) - ((|reduce| (|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|)) T - (ELT $ 51)) - ((|reduce| (|#2| (|Mapping| |#2| |#2| |#2|) $)) T - (ELT $ 21)) - ((|find| ((|Union| |#2| "failed") - (|Mapping| (|Boolean|) |#2|) $)) - T (ELT $ 46)) - ((|new| ($ (|NonNegativeInteger|) |#2|)) T (ELT $ 54)) - ((|map| ($ (|Mapping| |#2| |#2| |#2|) $ $)) T - (ELT $ 55)) - ((|map| ($ (|Mapping| |#2| |#2|) $)) T (ELT $ NIL)) - ((|copy| ($ $)) T (ELT $ 58))) - (|addModemap| '|ListAggregate&| - '(|ListAggregate&| |#1| |#2|) - '((CATEGORY |domain| (SIGNATURE |list| (|#1| |#2|)) - (SIGNATURE |delete!| (|#1| |#1| (|Integer|))) - (SIGNATURE |delete!| - (|#1| |#1| (|UniversalSegment| (|Integer|)))) - (SIGNATURE |remove!| - (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |insert!| - (|#1| |#2| |#1| (|Integer|))) - (SIGNATURE |insert!| - (|#1| |#1| |#1| (|Integer|))) - (SIGNATURE |merge!| - (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| - |#1|)) - (SIGNATURE |select!| - (|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |remove!| (|#1| |#2| |#1|)) - (SIGNATURE |removeDuplicates!| (|#1| |#1|)) - (SIGNATURE |merge!| (|#1| |#1| |#1|)) - (SIGNATURE |merge| - (|#1| (|Mapping| (|Boolean|) |#2| |#2|) |#1| - |#1|)) - (SIGNATURE |sorted?| - ((|Boolean|) - (|Mapping| (|Boolean|) |#2| |#2|) |#1|)) - (SIGNATURE |position| - ((|Integer|) (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |position| ((|Integer|) |#2| |#1|)) - (SIGNATURE |position| - ((|Integer|) |#2| |#1| (|Integer|))) - (SIGNATURE |merge| (|#1| |#1| |#1|)) - (SIGNATURE |sorted?| ((|Boolean|) |#1|)) - (SIGNATURE |copyInto!| - (|#1| |#1| |#1| (|Integer|))) - (SIGNATURE |reverse!| (|#1| |#1|)) - (SIGNATURE |sort!| - (|#1| (|Mapping| (|Boolean|) |#2| |#2|) - |#1|)) - (SIGNATURE |sort!| (|#1| |#1|)) - (SIGNATURE < ((|Boolean|) |#1| |#1|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2| - |#2|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#2|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) |#1|)) - (SIGNATURE |find| - ((|Union| |#2| "failed") - (|Mapping| (|Boolean|) |#2|) |#1|)) - (SIGNATURE |new| - (|#1| (|NonNegativeInteger|) |#2|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#2| |#2| |#2|) |#1| |#1|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#2| |#2|) |#1|)) - (SIGNATURE |copy| (|#1| |#1|))) - (|ListAggregate| |#2|) (|Type|)) - T '|ListAggregate&| - (|put| '|ListAggregate&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |list| (|#1| |#2|)) - (SIGNATURE |delete!| - (|#1| |#1| (|Integer|))) - (SIGNATURE |delete!| - (|#1| |#1| - (|UniversalSegment| (|Integer|)))) - (SIGNATURE |remove!| - (|#1| (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |insert!| - (|#1| |#2| |#1| (|Integer|))) - (SIGNATURE |insert!| - (|#1| |#1| |#1| (|Integer|))) - (SIGNATURE |merge!| - (|#1| - (|Mapping| (|Boolean|) |#2| |#2|) - |#1| |#1|)) - (SIGNATURE |select!| - (|#1| (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |remove!| (|#1| |#2| |#1|)) - (SIGNATURE |removeDuplicates!| - (|#1| |#1|)) - (SIGNATURE |merge!| (|#1| |#1| |#1|)) - (SIGNATURE |merge| - (|#1| - (|Mapping| (|Boolean|) |#2| |#2|) - |#1| |#1|)) - (SIGNATURE |sorted?| - ((|Boolean|) - (|Mapping| (|Boolean|) |#2| |#2|) - |#1|)) - (SIGNATURE |position| - ((|Integer|) - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |position| - ((|Integer|) |#2| |#1|)) - (SIGNATURE |position| - ((|Integer|) |#2| |#1| - (|Integer|))) - (SIGNATURE |merge| (|#1| |#1| |#1|)) - (SIGNATURE |sorted?| - ((|Boolean|) |#1|)) - (SIGNATURE |copyInto!| - (|#1| |#1| |#1| (|Integer|))) - (SIGNATURE |reverse!| (|#1| |#1|)) - (SIGNATURE |sort!| - (|#1| - (|Mapping| (|Boolean|) |#2| |#2|) - |#1|)) - (SIGNATURE |sort!| (|#1| |#1|)) - (SIGNATURE < ((|Boolean|) |#1| |#1|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) - |#1| |#2| |#2|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) - |#1| |#2|)) - (SIGNATURE |reduce| - (|#2| (|Mapping| |#2| |#2| |#2|) - |#1|)) - (SIGNATURE |find| - ((|Union| |#2| "failed") - (|Mapping| (|Boolean|) |#2|) - |#1|)) - (SIGNATURE |new| - (|#1| (|NonNegativeInteger|) |#2|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#2| |#2| |#2|) - |#1| |#1|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#2| |#2|) |#1|)) - (SIGNATURE |copy| (|#1| |#1|))) - (|ListAggregate| |#2|) (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/LSAGG.lsp b/src/algebra/strap/LSAGG.lsp index 924ec233..bfe188ac 100644 --- a/src/algebra/strap/LSAGG.lsp +++ b/src/algebra/strap/LSAGG.lsp @@ -24,7 +24,8 @@ '(((|list| ($ |t#1|)) T)) NIL 'NIL NIL)) . #1=(|ListAggregate|))))) . #1#) - (SETELT #0# 0 (LIST '|ListAggregate| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|ListAggregate| (|devaluate| |t#1|))))))) (DEFUN |ListAggregate| (#0=#:G1431) (LET (#1=#:G1432) @@ -36,9 +37,3 @@ (SETQ #1# (|ListAggregate;| #0#))) |ListAggregate;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|ListAggregate| '|isCategory| T - (|addModemap| '|ListAggregate| '(|ListAggregate| |#1|) - '((|Category|) (|Type|)) T '|ListAggregate| - |$CategoryFrame|))) diff --git a/src/algebra/strap/MONOID-.lsp b/src/algebra/strap/MONOID-.lsp index 6673562a..b3cf1042 100644 --- a/src/algebra/strap/MONOID-.lsp +++ b/src/algebra/strap/MONOID-.lsp @@ -59,35 +59,3 @@ 0 0 11 1 0 12 0 13 1 0 8 0 10 2 0 0 0 17 18))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|Monoid&| '|isFunctor| - '(((|recip| ((|Union| $ "failed") $)) T (ELT $ 13)) - ((** ($ $ (|NonNegativeInteger|))) T (ELT $ 18)) - ((|one?| ((|Boolean|) $)) T (ELT $ 10)) - ((|sample| ($)) T (ELT $ 11)) - ((** ($ $ (|PositiveInteger|))) T (ELT $ NIL))) - (|addModemap| '|Monoid&| '(|Monoid&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |recip| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE ** - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |one?| ((|Boolean|) |#1|)) - (SIGNATURE |sample| (|#1|)) - (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) - (|Monoid|)) - T '|Monoid&| - (|put| '|Monoid&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |recip| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE ** - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |one?| ((|Boolean|) |#1|)) - (SIGNATURE |sample| (|#1|)) - (SIGNATURE ** - (|#1| |#1| (|PositiveInteger|)))) - (|Monoid|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/MONOID.lsp b/src/algebra/strap/MONOID.lsp index 43b52fd0..538e9b0e 100644 --- a/src/algebra/strap/MONOID.lsp +++ b/src/algebra/strap/MONOID.lsp @@ -18,14 +18,9 @@ '((|NonNegativeInteger|) (|Boolean|)) NIL)) |Monoid|) - (SETELT #0# 0 '(|Monoid|)))))) + (|setShellEntry| #0# 0 '(|Monoid|)))))) (DEFUN |Monoid| () (LET () (COND (|Monoid;AL|) (T (SETQ |Monoid;AL| (|Monoid;|)))))) -(SETQ |$CategoryFrame| - (|put| '|Monoid| '|isCategory| T - (|addModemap| '|Monoid| '(|Monoid|) '((|Category|)) T - '|Monoid| |$CategoryFrame|))) - (MAKEPROP '|Monoid| 'NILADIC T) diff --git a/src/algebra/strap/MTSCAT.lsp b/src/algebra/strap/MTSCAT.lsp index ecc72ee2..443b2d5f 100644 --- a/src/algebra/strap/MTSCAT.lsp +++ b/src/algebra/strap/MTSCAT.lsp @@ -84,9 +84,9 @@ (|List| (|NonNegativeInteger|))) NIL)) . #2=(|MultivariateTaylorSeriesCategory|)))))) . #2#) - (SETELT #0# 0 - (LIST '|MultivariateTaylorSeriesCategory| - (|devaluate| |t#1|) (|devaluate| |t#2|))))))) + (|setShellEntry| #0# 0 + (LIST '|MultivariateTaylorSeriesCategory| + (|devaluate| |t#1|) (|devaluate| |t#2|))))))) (DEFUN |MultivariateTaylorSeriesCategory| (&REST #0=#:G1402 &AUX #1=#:G1400) @@ -105,10 +105,3 @@ #1#))) |MultivariateTaylorSeriesCategory;AL|)) #2#)))) - -(SETQ |$CategoryFrame| - (|put| '|MultivariateTaylorSeriesCategory| '|isCategory| T - (|addModemap| '|MultivariateTaylorSeriesCategory| - '(|MultivariateTaylorSeriesCategory| |#1| |#2|) - '((|Category|) (|Ring|) (|OrderedSet|)) T - '|MultivariateTaylorSeriesCategory| |$CategoryFrame|))) diff --git a/src/algebra/strap/NNI.lsp b/src/algebra/strap/NNI.lsp index 2d3fe6a9..329200c6 100644 --- a/src/algebra/strap/NNI.lsp +++ b/src/algebra/strap/NNI.lsp @@ -120,78 +120,4 @@ 0 0 0 0 1 2 0 0 12 0 1 2 0 0 11 0 1))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|NonNegativeInteger| '|isFunctor| - '(((|random| ($ $)) T (ELT $ NIL)) - ((|shift| ($ $ (|Integer|))) T (ELT $ 7)) - ((|exquo| ((|Union| $ "failed") $ $)) T (ELT $ NIL)) - ((|divide| - ((|Record| (|:| |quotient| $) (|:| |remainder| $)) - $ $)) - T (ELT $ NIL)) - ((|gcd| ($ $ $)) T (ELT $ NIL)) - ((|rem| ($ $ $)) T (ELT $ NIL)) - ((|quo| ($ $ $)) T (ELT $ NIL)) - ((* ($ $ $)) T (ELT $ NIL)) - ((** ($ $ (|PositiveInteger|))) T (ELT $ NIL)) - ((|One| ($)) T (CONST $ NIL)) - ((|one?| ((|Boolean|) $)) T (ELT $ NIL)) - ((** ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|recip| ((|Union| $ "failed") $)) T (ELT $ NIL)) - ((|sup| ($ $ $)) T (ELT $ 6)) - ((|subtractIfCan| ((|Union| $ "failed") $ $)) T - (ELT $ 9)) - ((|Zero| ($)) T (CONST $ NIL)) - ((|sample| ($)) T (CONST $ NIL)) - ((|zero?| ((|Boolean|) $)) T (ELT $ NIL)) - ((* ($ (|NonNegativeInteger|) $)) T (ELT $ NIL)) - ((+ ($ $ $)) T (ELT $ NIL)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ NIL)) - ((|min| ($ $ $)) T (ELT $ NIL)) - ((|max| ($ $ $)) T (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|latex| ((|String|) $)) T (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ NIL)) - ((= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|NonNegativeInteger| - '(|NonNegativeInteger|) - '((|Join| (|OrderedAbelianMonoidSup|) (|Monoid|) - (CATEGORY |domain| (SIGNATURE |quo| ($ $ $)) - (SIGNATURE |rem| ($ $ $)) - (SIGNATURE |gcd| ($ $ $)) - (SIGNATURE |divide| - ((|Record| (|:| |quotient| $) - (|:| |remainder| $)) - $ $)) - (SIGNATURE |exquo| - ((|Union| $ "failed") $ $)) - (SIGNATURE |shift| ($ $ (|Integer|))) - (SIGNATURE |random| ($ $)) - (ATTRIBUTE (|commutative| "*"))))) - T '|NonNegativeInteger| - (|put| '|NonNegativeInteger| '|mode| - '(|Mapping| - (|Join| (|OrderedAbelianMonoidSup|) - (|Monoid|) - (CATEGORY |domain| - (SIGNATURE |quo| ($ $ $)) - (SIGNATURE |rem| ($ $ $)) - (SIGNATURE |gcd| ($ $ $)) - (SIGNATURE |divide| - ((|Record| (|:| |quotient| $) - (|:| |remainder| $)) - $ $)) - (SIGNATURE |exquo| - ((|Union| $ "failed") $ $)) - (SIGNATURE |shift| - ($ $ (|Integer|))) - (SIGNATURE |random| ($ $)) - (ATTRIBUTE (|commutative| "*"))))) - |$CategoryFrame|)))) - (MAKEPROP '|NonNegativeInteger| 'NILADIC T) diff --git a/src/algebra/strap/OINTDOM.lsp b/src/algebra/strap/OINTDOM.lsp index c68598c8..e03dfea0 100644 --- a/src/algebra/strap/OINTDOM.lsp +++ b/src/algebra/strap/OINTDOM.lsp @@ -8,7 +8,7 @@ (RETURN (PROG1 (LETT #0# (|Join| (|IntegralDomain|) (|OrderedRing|)) |OrderedIntegralDomain|) - (SETELT #0# 0 '(|OrderedIntegralDomain|)))))) + (|setShellEntry| #0# 0 '(|OrderedIntegralDomain|)))))) (DEFUN |OrderedIntegralDomain| () (LET () @@ -16,10 +16,4 @@ (|OrderedIntegralDomain;AL|) (T (SETQ |OrderedIntegralDomain;AL| (|OrderedIntegralDomain;|)))))) -(SETQ |$CategoryFrame| - (|put| '|OrderedIntegralDomain| '|isCategory| T - (|addModemap| '|OrderedIntegralDomain| - '(|OrderedIntegralDomain|) '((|Category|)) T - '|OrderedIntegralDomain| |$CategoryFrame|))) - (MAKEPROP '|OrderedIntegralDomain| 'NILADIC T) diff --git a/src/algebra/strap/ORDRING-.lsp b/src/algebra/strap/ORDRING-.lsp index 9b433619..c5eb9558 100644 --- a/src/algebra/strap/ORDRING-.lsp +++ b/src/algebra/strap/ORDRING-.lsp @@ -64,28 +64,3 @@ 0 16 0 17 1 0 8 0 10 1 0 8 0 11 1 0 0 0 19))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|OrderedRing&| '|isFunctor| - '(((|abs| ($ $)) T (ELT $ 19)) - ((|sign| ((|Integer|) $)) T (ELT $ 17)) - ((|negative?| ((|Boolean|) $)) T (ELT $ 11)) - ((|positive?| ((|Boolean|) $)) T (ELT $ 10))) - (|addModemap| '|OrderedRing&| '(|OrderedRing&| |#1|) - '((CATEGORY |domain| (SIGNATURE |abs| (|#1| |#1|)) - (SIGNATURE |sign| ((|Integer|) |#1|)) - (SIGNATURE |negative?| ((|Boolean|) |#1|)) - (SIGNATURE |positive?| ((|Boolean|) |#1|))) - (|OrderedRing|)) - T '|OrderedRing&| - (|put| '|OrderedRing&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |abs| (|#1| |#1|)) - (SIGNATURE |sign| ((|Integer|) |#1|)) - (SIGNATURE |negative?| - ((|Boolean|) |#1|)) - (SIGNATURE |positive?| - ((|Boolean|) |#1|))) - (|OrderedRing|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/ORDRING.lsp b/src/algebra/strap/ORDRING.lsp index a15e19b1..a4ded68e 100644 --- a/src/algebra/strap/ORDRING.lsp +++ b/src/algebra/strap/ORDRING.lsp @@ -15,7 +15,7 @@ ((|abs| ($ $)) T)) NIL '((|Integer|) (|Boolean|)) NIL)) |OrderedRing|) - (SETELT #0# 0 '(|OrderedRing|)))))) + (|setShellEntry| #0# 0 '(|OrderedRing|)))))) (DEFUN |OrderedRing| () (LET () @@ -23,9 +23,4 @@ (|OrderedRing;AL|) (T (SETQ |OrderedRing;AL| (|OrderedRing;|)))))) -(SETQ |$CategoryFrame| - (|put| '|OrderedRing| '|isCategory| T - (|addModemap| '|OrderedRing| '(|OrderedRing|) - '((|Category|)) T '|OrderedRing| |$CategoryFrame|))) - (MAKEPROP '|OrderedRing| 'NILADIC T) diff --git a/src/algebra/strap/OUTFORM.lsp b/src/algebra/strap/OUTFORM.lsp index dead66e8..97591c7a 100644 --- a/src/algebra/strap/OUTFORM.lsp +++ b/src/algebra/strap/OUTFORM.lsp @@ -969,365 +969,4 @@ 0 0 0 0 85))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|OutputForm| '|isFunctor| - '(((SEGMENT ($ $)) T (ELT $ 96)) - ((SEGMENT ($ $ $)) T (ELT $ 95)) - ((|not| ($ $)) T (ELT $ 94)) - ((|or| ($ $ $)) T (ELT $ 93)) - ((|and| ($ $ $)) T (ELT $ 92)) - ((|exquo| ($ $ $)) T (ELT $ 91)) - ((|quo| ($ $ $)) T (ELT $ 90)) - ((|rem| ($ $ $)) T (ELT $ 89)) - ((|div| ($ $ $)) T (ELT $ 88)) - ((** ($ $ $)) T (ELT $ 87)) ((/ ($ $ $)) T (ELT $ 86)) - ((* ($ $ $)) T (ELT $ 85)) ((- ($ $)) T (ELT $ 84)) - ((- ($ $ $)) T (ELT $ 83)) ((+ ($ $ $)) T (ELT $ 82)) - ((>= ($ $ $)) T (ELT $ 81)) ((<= ($ $ $)) T (ELT $ 80)) - ((> ($ $ $)) T (ELT $ 79)) ((< ($ $ $)) T (ELT $ 78)) - ((~= ($ $ $)) T (ELT $ 77)) ((= ($ $ $)) T (ELT $ 17)) - ((|blankSeparate| ($ (|List| $))) T (ELT $ 57)) - ((|semicolonSeparate| ($ (|List| $))) T (ELT $ 53)) - ((|commaSeparate| ($ (|List| $))) T (ELT $ 52)) - ((|pile| ($ (|List| $))) T (ELT $ 51)) - ((|paren| ($ (|List| $))) T (ELT $ 63)) - ((|paren| ($ $)) T (ELT $ 62)) - ((|bracket| ($ (|List| $))) T (ELT $ 61)) - ((|bracket| ($ $)) T (ELT $ 60)) - ((|brace| ($ (|List| $))) T (ELT $ 59)) - ((|brace| ($ $)) T (ELT $ 58)) - ((|int| ($ $ $ $)) T (ELT $ 135)) - ((|int| ($ $ $)) T (ELT $ 134)) - ((|int| ($ $)) T (ELT $ 133)) - ((|prod| ($ $ $ $)) T (ELT $ 132)) - ((|prod| ($ $ $)) T (ELT $ 131)) - ((|prod| ($ $)) T (ELT $ 130)) - ((|sum| ($ $ $ $)) T (ELT $ 129)) - ((|sum| ($ $ $)) T (ELT $ 128)) - ((|sum| ($ $)) T (ELT $ 127)) - ((|overlabel| ($ $ $)) T (ELT $ 112)) - ((|overbar| ($ $)) T (ELT $ 106)) - ((|prime| ($ $ (|NonNegativeInteger|))) T (ELT $ 111)) - ((|prime| ($ $)) T (ELT $ 108)) - ((|dot| ($ $ (|NonNegativeInteger|))) T (ELT $ 110)) - ((|dot| ($ $)) T (ELT $ 107)) - ((|quote| ($ $)) T (ELT $ 105)) - ((|supersub| ($ $ (|List| $))) T (ELT $ 74)) - ((|scripts| ($ $ (|List| $))) T (ELT $ 71)) - ((|presuper| ($ $ $)) T (ELT $ 67)) - ((|presub| ($ $ $)) T (ELT $ 66)) - ((|super| ($ $ $)) T (ELT $ 65)) - ((|sub| ($ $ $)) T (ELT $ 64)) - ((|binomial| ($ $ $)) T (ELT $ 97)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ 126)) - ((|rarrow| ($ $ $)) T (ELT $ 121)) - ((|assign| ($ $ $)) T (ELT $ 119)) - ((|slash| ($ $ $)) T (ELT $ 118)) - ((|over| ($ $ $)) T (ELT $ 117)) - ((|root| ($ $ $)) T (ELT $ 116)) - ((|root| ($ $)) T (ELT $ 115)) - ((|zag| ($ $ $)) T (ELT $ 114)) - ((|matrix| ($ (|List| (|List| $)))) T (ELT $ 50)) - ((|box| ($ $)) T (ELT $ 113)) - ((|label| ($ $ $)) T (ELT $ 120)) - ((|string| ($ $)) T (ELT $ 104)) - ((|elt| ($ $ (|List| $))) T (ELT $ 99)) - ((|infix?| ((|Boolean|) $)) T (ELT $ 98)) - ((|postfix| ($ $ $)) T (ELT $ 103)) - ((|infix| ($ $ $ $)) T (ELT $ 102)) - ((|infix| ($ $ (|List| $))) T (ELT $ 101)) - ((|prefix| ($ $ (|List| $))) T (ELT $ 100)) - ((|vconcat| ($ (|List| $))) T (ELT $ 76)) - ((|hconcat| ($ (|List| $))) T (ELT $ 75)) - ((|vconcat| ($ $ $)) T (ELT $ 46)) - ((|hconcat| ($ $ $)) T (ELT $ 38)) - ((|center| ($ $)) T (ELT $ 42)) - ((|right| ($ $)) T (ELT $ 44)) - ((|left| ($ $)) T (ELT $ 43)) - ((|center| ($ $ (|Integer|))) T (ELT $ 39)) - ((|right| ($ $ (|Integer|))) T (ELT $ 41)) - ((|left| ($ $ (|Integer|))) T (ELT $ 40)) - ((|rspace| ($ (|Integer|) (|Integer|))) T (ELT $ 47)) - ((|vspace| ($ (|Integer|))) T (ELT $ 45)) - ((|hspace| ($ (|Integer|))) T (ELT $ 37)) - ((|superHeight| ((|Integer|) $)) T (ELT $ 34)) - ((|subHeight| ((|Integer|) $)) T (ELT $ 33)) - ((|height| ((|Integer|))) T (ELT $ 35)) - ((|width| ((|Integer|))) T (ELT $ 36)) - ((|height| ((|Integer|) $)) T (ELT $ 32)) - ((|width| ((|Integer|) $)) T (ELT $ 31)) - ((|doubleFloatFormat| ((|String|) (|String|))) T - (ELT $ 8)) - ((|empty| ($)) T (ELT $ 13)) - ((|outputForm| ($ (|DoubleFloat|))) T (ELT $ 25)) - ((|outputForm| ($ (|String|))) T (ELT $ 30)) - ((|outputForm| ($ (|Symbol|))) T (ELT $ 23)) - ((|outputForm| ($ (|Integer|))) T (ELT $ 21)) - ((|messagePrint| ((|Void|) (|String|))) T (ELT $ 15)) - ((|message| ($ (|String|))) T (ELT $ 14)) - ((|print| ((|Void|) $)) T (ELT $ 10)) - ((|latex| ((|String|) $)) T (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ 19)) - ((= ((|Boolean|) $ $)) T (ELT $ 16)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|OutputForm| '(|OutputForm|) - '((|Join| (|SetCategory|) - (CATEGORY |domain| - (SIGNATURE |print| ((|Void|) $)) - (SIGNATURE |message| ($ (|String|))) - (SIGNATURE |messagePrint| - ((|Void|) (|String|))) - (SIGNATURE |outputForm| ($ (|Integer|))) - (SIGNATURE |outputForm| ($ (|Symbol|))) - (SIGNATURE |outputForm| ($ (|String|))) - (SIGNATURE |outputForm| - ($ (|DoubleFloat|))) - (SIGNATURE |empty| ($)) - (SIGNATURE |doubleFloatFormat| - ((|String|) (|String|))) - (SIGNATURE |width| ((|Integer|) $)) - (SIGNATURE |height| ((|Integer|) $)) - (SIGNATURE |width| ((|Integer|))) - (SIGNATURE |height| ((|Integer|))) - (SIGNATURE |subHeight| ((|Integer|) $)) - (SIGNATURE |superHeight| - ((|Integer|) $)) - (SIGNATURE |hspace| ($ (|Integer|))) - (SIGNATURE |vspace| ($ (|Integer|))) - (SIGNATURE |rspace| - ($ (|Integer|) (|Integer|))) - (SIGNATURE |left| ($ $ (|Integer|))) - (SIGNATURE |right| ($ $ (|Integer|))) - (SIGNATURE |center| ($ $ (|Integer|))) - (SIGNATURE |left| ($ $)) - (SIGNATURE |right| ($ $)) - (SIGNATURE |center| ($ $)) - (SIGNATURE |hconcat| ($ $ $)) - (SIGNATURE |vconcat| ($ $ $)) - (SIGNATURE |hconcat| ($ (|List| $))) - (SIGNATURE |vconcat| ($ (|List| $))) - (SIGNATURE |prefix| ($ $ (|List| $))) - (SIGNATURE |infix| ($ $ (|List| $))) - (SIGNATURE |infix| ($ $ $ $)) - (SIGNATURE |postfix| ($ $ $)) - (SIGNATURE |infix?| ((|Boolean|) $)) - (SIGNATURE |elt| ($ $ (|List| $))) - (SIGNATURE |string| ($ $)) - (SIGNATURE |label| ($ $ $)) - (SIGNATURE |box| ($ $)) - (SIGNATURE |matrix| - ($ (|List| (|List| $)))) - (SIGNATURE |zag| ($ $ $)) - (SIGNATURE |root| ($ $)) - (SIGNATURE |root| ($ $ $)) - (SIGNATURE |over| ($ $ $)) - (SIGNATURE |slash| ($ $ $)) - (SIGNATURE |assign| ($ $ $)) - (SIGNATURE |rarrow| ($ $ $)) - (SIGNATURE |differentiate| - ($ $ (|NonNegativeInteger|))) - (SIGNATURE |binomial| ($ $ $)) - (SIGNATURE |sub| ($ $ $)) - (SIGNATURE |super| ($ $ $)) - (SIGNATURE |presub| ($ $ $)) - (SIGNATURE |presuper| ($ $ $)) - (SIGNATURE |scripts| ($ $ (|List| $))) - (SIGNATURE |supersub| ($ $ (|List| $))) - (SIGNATURE |quote| ($ $)) - (SIGNATURE |dot| ($ $)) - (SIGNATURE |dot| - ($ $ (|NonNegativeInteger|))) - (SIGNATURE |prime| ($ $)) - (SIGNATURE |prime| - ($ $ (|NonNegativeInteger|))) - (SIGNATURE |overbar| ($ $)) - (SIGNATURE |overlabel| ($ $ $)) - (SIGNATURE |sum| ($ $)) - (SIGNATURE |sum| ($ $ $)) - (SIGNATURE |sum| ($ $ $ $)) - (SIGNATURE |prod| ($ $)) - (SIGNATURE |prod| ($ $ $)) - (SIGNATURE |prod| ($ $ $ $)) - (SIGNATURE |int| ($ $)) - (SIGNATURE |int| ($ $ $)) - (SIGNATURE |int| ($ $ $ $)) - (SIGNATURE |brace| ($ $)) - (SIGNATURE |brace| ($ (|List| $))) - (SIGNATURE |bracket| ($ $)) - (SIGNATURE |bracket| ($ (|List| $))) - (SIGNATURE |paren| ($ $)) - (SIGNATURE |paren| ($ (|List| $))) - (SIGNATURE |pile| ($ (|List| $))) - (SIGNATURE |commaSeparate| - ($ (|List| $))) - (SIGNATURE |semicolonSeparate| - ($ (|List| $))) - (SIGNATURE |blankSeparate| - ($ (|List| $))) - (SIGNATURE = ($ $ $)) - (SIGNATURE ~= ($ $ $)) - (SIGNATURE < ($ $ $)) - (SIGNATURE > ($ $ $)) - (SIGNATURE <= ($ $ $)) - (SIGNATURE >= ($ $ $)) - (SIGNATURE + ($ $ $)) - (SIGNATURE - ($ $ $)) - (SIGNATURE - ($ $)) - (SIGNATURE * ($ $ $)) - (SIGNATURE / ($ $ $)) - (SIGNATURE ** ($ $ $)) - (SIGNATURE |div| ($ $ $)) - (SIGNATURE |rem| ($ $ $)) - (SIGNATURE |quo| ($ $ $)) - (SIGNATURE |exquo| ($ $ $)) - (SIGNATURE |and| ($ $ $)) - (SIGNATURE |or| ($ $ $)) - (SIGNATURE |not| ($ $)) - (SIGNATURE SEGMENT ($ $ $)) - (SIGNATURE SEGMENT ($ $))))) - T '|OutputForm| - (|put| '|OutputForm| '|mode| - '(|Mapping| - (|Join| (|SetCategory|) - (CATEGORY |domain| - (SIGNATURE |print| ((|Void|) $)) - (SIGNATURE |message| - ($ (|String|))) - (SIGNATURE |messagePrint| - ((|Void|) (|String|))) - (SIGNATURE |outputForm| - ($ (|Integer|))) - (SIGNATURE |outputForm| - ($ (|Symbol|))) - (SIGNATURE |outputForm| - ($ (|String|))) - (SIGNATURE |outputForm| - ($ (|DoubleFloat|))) - (SIGNATURE |empty| ($)) - (SIGNATURE |doubleFloatFormat| - ((|String|) (|String|))) - (SIGNATURE |width| - ((|Integer|) $)) - (SIGNATURE |height| - ((|Integer|) $)) - (SIGNATURE |width| ((|Integer|))) - (SIGNATURE |height| - ((|Integer|))) - (SIGNATURE |subHeight| - ((|Integer|) $)) - (SIGNATURE |superHeight| - ((|Integer|) $)) - (SIGNATURE |hspace| - ($ (|Integer|))) - (SIGNATURE |vspace| - ($ (|Integer|))) - (SIGNATURE |rspace| - ($ (|Integer|) (|Integer|))) - (SIGNATURE |left| - ($ $ (|Integer|))) - (SIGNATURE |right| - ($ $ (|Integer|))) - (SIGNATURE |center| - ($ $ (|Integer|))) - (SIGNATURE |left| ($ $)) - (SIGNATURE |right| ($ $)) - (SIGNATURE |center| ($ $)) - (SIGNATURE |hconcat| ($ $ $)) - (SIGNATURE |vconcat| ($ $ $)) - (SIGNATURE |hconcat| - ($ (|List| $))) - (SIGNATURE |vconcat| - ($ (|List| $))) - (SIGNATURE |prefix| - ($ $ (|List| $))) - (SIGNATURE |infix| - ($ $ (|List| $))) - (SIGNATURE |infix| ($ $ $ $)) - (SIGNATURE |postfix| ($ $ $)) - (SIGNATURE |infix?| - ((|Boolean|) $)) - (SIGNATURE |elt| - ($ $ (|List| $))) - (SIGNATURE |string| ($ $)) - (SIGNATURE |label| ($ $ $)) - (SIGNATURE |box| ($ $)) - (SIGNATURE |matrix| - ($ (|List| (|List| $)))) - (SIGNATURE |zag| ($ $ $)) - (SIGNATURE |root| ($ $)) - (SIGNATURE |root| ($ $ $)) - (SIGNATURE |over| ($ $ $)) - (SIGNATURE |slash| ($ $ $)) - (SIGNATURE |assign| ($ $ $)) - (SIGNATURE |rarrow| ($ $ $)) - (SIGNATURE |differentiate| - ($ $ (|NonNegativeInteger|))) - (SIGNATURE |binomial| ($ $ $)) - (SIGNATURE |sub| ($ $ $)) - (SIGNATURE |super| ($ $ $)) - (SIGNATURE |presub| ($ $ $)) - (SIGNATURE |presuper| ($ $ $)) - (SIGNATURE |scripts| - ($ $ (|List| $))) - (SIGNATURE |supersub| - ($ $ (|List| $))) - (SIGNATURE |quote| ($ $)) - (SIGNATURE |dot| ($ $)) - (SIGNATURE |dot| - ($ $ (|NonNegativeInteger|))) - (SIGNATURE |prime| ($ $)) - (SIGNATURE |prime| - ($ $ (|NonNegativeInteger|))) - (SIGNATURE |overbar| ($ $)) - (SIGNATURE |overlabel| ($ $ $)) - (SIGNATURE |sum| ($ $)) - (SIGNATURE |sum| ($ $ $)) - (SIGNATURE |sum| ($ $ $ $)) - (SIGNATURE |prod| ($ $)) - (SIGNATURE |prod| ($ $ $)) - (SIGNATURE |prod| ($ $ $ $)) - (SIGNATURE |int| ($ $)) - (SIGNATURE |int| ($ $ $)) - (SIGNATURE |int| ($ $ $ $)) - (SIGNATURE |brace| ($ $)) - (SIGNATURE |brace| - ($ (|List| $))) - (SIGNATURE |bracket| ($ $)) - (SIGNATURE |bracket| - ($ (|List| $))) - (SIGNATURE |paren| ($ $)) - (SIGNATURE |paren| - ($ (|List| $))) - (SIGNATURE |pile| ($ (|List| $))) - (SIGNATURE |commaSeparate| - ($ (|List| $))) - (SIGNATURE |semicolonSeparate| - ($ (|List| $))) - (SIGNATURE |blankSeparate| - ($ (|List| $))) - (SIGNATURE = ($ $ $)) - (SIGNATURE ~= ($ $ $)) - (SIGNATURE < ($ $ $)) - (SIGNATURE > ($ $ $)) - (SIGNATURE <= ($ $ $)) - (SIGNATURE >= ($ $ $)) - (SIGNATURE + ($ $ $)) - (SIGNATURE - ($ $ $)) - (SIGNATURE - ($ $)) - (SIGNATURE * ($ $ $)) - (SIGNATURE / ($ $ $)) - (SIGNATURE ** ($ $ $)) - (SIGNATURE |div| ($ $ $)) - (SIGNATURE |rem| ($ $ $)) - (SIGNATURE |quo| ($ $ $)) - (SIGNATURE |exquo| ($ $ $)) - (SIGNATURE |and| ($ $ $)) - (SIGNATURE |or| ($ $ $)) - (SIGNATURE |not| ($ $)) - (SIGNATURE SEGMENT ($ $ $)) - (SIGNATURE SEGMENT ($ $))))) - |$CategoryFrame|)))) - (MAKEPROP '|OutputForm| 'NILADIC T) diff --git a/src/algebra/strap/PI.lsp b/src/algebra/strap/PI.lsp index 3503efb1..2cf0e75e 100644 --- a/src/algebra/strap/PI.lsp +++ b/src/algebra/strap/PI.lsp @@ -72,41 +72,4 @@ 0 0 6 0 1))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|PositiveInteger| '|isFunctor| - '(((|gcd| ($ $ $)) T (ELT $ NIL)) - ((* ($ $ $)) T (ELT $ NIL)) - ((** ($ $ (|PositiveInteger|))) T (ELT $ NIL)) - ((|One| ($)) T (CONST $ NIL)) - ((|sample| ($)) T (CONST $ NIL)) - ((|one?| ((|Boolean|) $)) T (ELT $ NIL)) - ((** ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|recip| ((|Union| $ "failed") $)) T (ELT $ NIL)) - ((+ ($ $ $)) T (ELT $ NIL)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ NIL)) - ((|min| ($ $ $)) T (ELT $ NIL)) - ((|max| ($ $ $)) T (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|latex| ((|String|) $)) T (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ NIL)) - ((= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|PositiveInteger| '(|PositiveInteger|) - '((|Join| (|OrderedAbelianSemiGroup|) (|Monoid|) - (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) - (ATTRIBUTE (|commutative| "*"))))) - T '|PositiveInteger| - (|put| '|PositiveInteger| '|mode| - '(|Mapping| - (|Join| (|OrderedAbelianSemiGroup|) - (|Monoid|) - (CATEGORY |domain| - (SIGNATURE |gcd| ($ $ $)) - (ATTRIBUTE (|commutative| "*"))))) - |$CategoryFrame|)))) - (MAKEPROP '|PositiveInteger| 'NILADIC T) diff --git a/src/algebra/strap/POLYCAT-.lsp b/src/algebra/strap/POLYCAT-.lsp index c33191ee..f081f580 100644 --- a/src/algebra/strap/POLYCAT-.lsp +++ b/src/algebra/strap/POLYCAT-.lsp @@ -142,8 +142,8 @@ |POLYCAT-;convert;SIf;43|)) (DEFUN |POLYCAT-;eval;SLS;1| (|p| |l| $) - (PROG (#0=#:G1686 #1=#:G1426 #2=#:G1687 #3=#:G1688 |lvar| #4=#:G1689 - |e| #5=#:G1690) + (PROG (#0=#:G1688 #1=#:G1426 #2=#:G1689 #3=#:G1690 |lvar| #4=#:G1691 + |e| #5=#:G1692) (RETURN (SEQ (COND ((NULL |l|) |p|) @@ -261,7 +261,7 @@ ('T (CONS 0 |l|)))))) (DEFUN |POLYCAT-;isTimes;SU;4| (|p| $) - (PROG (|lv| #0=#:G1691 |v| #1=#:G1692 |l| |r|) + (PROG (|lv| #0=#:G1693 |v| #1=#:G1694 |l| |r|) (RETURN (SEQ (COND ((OR (NULL (LETT |lv| @@ -402,7 +402,7 @@ (|getShellEntry| $ 62))) (DEFUN |POLYCAT-;primitiveMonomials;SL;12| (|p| $) - (PROG (#0=#:G1693 |q| #1=#:G1694) + (PROG (#0=#:G1695 |q| #1=#:G1696) (RETURN (SEQ (PROGN (LETT #0# NIL |POLYCAT-;primitiveMonomials;SL;12|) @@ -522,7 +522,7 @@ (|getShellEntry| $ 77))) (DEFUN |POLYCAT-;allMonoms| (|l| $) - (PROG (#0=#:G1695 |p| #1=#:G1696) + (PROG (#0=#:G1697 |p| #1=#:G1698) (RETURN (SEQ (SPADCALL (SPADCALL @@ -549,7 +549,7 @@ (|getShellEntry| $ 82)))))) (DEFUN |POLYCAT-;P2R| (|p| |b| |n| $) - (PROG (|w| |bj| #0=#:G1698 |i| #1=#:G1697) + (PROG (|w| |bj| #0=#:G1700 |i| #1=#:G1699) (RETURN (SEQ (LETT |w| (SPADCALL |n| (|spadConstant| $ 23) @@ -578,7 +578,7 @@ (EXIT |w|))))) (DEFUN |POLYCAT-;eq2R| (|l| |b| $) - (PROG (#0=#:G1699 |bj| #1=#:G1700 #2=#:G1701 |p| #3=#:G1702) + (PROG (#0=#:G1701 |bj| #1=#:G1702 #2=#:G1703 |p| #3=#:G1704) (RETURN (SEQ (SPADCALL (PROGN @@ -628,7 +628,7 @@ (|getShellEntry| $ 92)))))) (DEFUN |POLYCAT-;reducedSystem;MM;20| (|m| $) - (PROG (#0=#:G1703 |r| #1=#:G1704 |b| #2=#:G1705 |bj| #3=#:G1706 |d| + (PROG (#0=#:G1705 |r| #1=#:G1706 |b| #2=#:G1707 |bj| #3=#:G1708 |d| |mm| |l|) (RETURN (SEQ (LETT |l| (SPADCALL |m| (|getShellEntry| $ 95)) @@ -705,7 +705,7 @@ (EXIT |mm|))))) (DEFUN |POLYCAT-;reducedSystem;MVR;21| (|m| |v| $) - (PROG (#0=#:G1707 |s| #1=#:G1708 |b| #2=#:G1709 |bj| #3=#:G1710 |d| + (PROG (#0=#:G1709 |s| #1=#:G1710 |b| #2=#:G1711 |bj| #3=#:G1712 |d| |n| |mm| |w| |l| |r|) (RETURN (SEQ (LETT |l| (SPADCALL |m| (|getShellEntry| $ 95)) @@ -812,8 +812,8 @@ (SPADCALL |pp| (|getShellEntry| $ 121))) (DEFUN |POLYCAT-;factor;SF;26| (|p| $) - (PROG (|v| |ansR| #0=#:G1711 |w| #1=#:G1712 |up| |ansSUP| #2=#:G1713 - |ww| #3=#:G1714) + (PROG (|v| |ansR| #0=#:G1713 |w| #1=#:G1714 |up| |ansSUP| #2=#:G1715 + |ww| #3=#:G1716) (RETURN (SEQ (LETT |v| (SPADCALL |p| (|getShellEntry| $ 43)) |POLYCAT-;factor;SF;26|) @@ -912,13 +912,13 @@ (|getShellEntry| $ 134))))))))))) (DEFUN |POLYCAT-;conditionP;MU;27| (|mat| $) - (PROG (|ll| #0=#:G1715 |z| #1=#:G1716 |ch| |l| #2=#:G1717 #3=#:G1718 - #4=#:G1580 #5=#:G1578 #6=#:G1579 #7=#:G1719 |vars| |degs| - #8=#:G1720 |d| #9=#:G1721 |nd| #10=#:G1607 #11=#:G1587 - |deg1| |redmons| #12=#:G1722 |v| #13=#:G1724 |u| - #14=#:G1723 |llR| |monslist| |ans| #15=#:G1725 - #16=#:G1726 |mons| #17=#:G1727 |m| #18=#:G1728 |i| - #19=#:G1603 #20=#:G1601 #21=#:G1602) + (PROG (|ll| #0=#:G1717 |z| #1=#:G1718 |ch| |l| #2=#:G1719 #3=#:G1720 + #4=#:G1582 #5=#:G1580 #6=#:G1581 #7=#:G1721 |vars| |degs| + #8=#:G1722 |d| #9=#:G1723 |nd| #10=#:G1609 #11=#:G1589 + |deg1| |redmons| #12=#:G1724 |v| #13=#:G1726 |u| + #14=#:G1725 |llR| |monslist| |ans| #15=#:G1727 + #16=#:G1728 |mons| #17=#:G1729 |m| #18=#:G1730 |i| + #19=#:G1605 #20=#:G1603 #21=#:G1604) (RETURN (SEQ (EXIT (SEQ (LETT |ll| (SPADCALL @@ -1281,7 +1281,7 @@ $)))))))))) (DEFUN |POLYCAT-;charthRootlv| (|p| |vars| |ch| $) - (PROG (|v| |dd| |cp| |d| #0=#:G1628 |ans| |ansx| #1=#:G1635) + (PROG (|v| |dd| |cp| |d| #0=#:G1630 |ans| |ansx| #1=#:G1637) (RETURN (SEQ (EXIT (COND ((NULL |vars|) @@ -1410,7 +1410,7 @@ (SPADCALL |p| (|getShellEntry| $ 167))) (DEFUN |POLYCAT-;squareFreePart;2S;34| (|p| $) - (PROG (|s| |f| #0=#:G1729 #1=#:G1649 #2=#:G1647 #3=#:G1648) + (PROG (|s| |f| #0=#:G1731 #1=#:G1651 #2=#:G1649 #3=#:G1650) (RETURN (SEQ (SPADCALL (SPADCALL @@ -1456,7 +1456,7 @@ (|getShellEntry| $ 174))) (DEFUN |POLYCAT-;primitivePart;2S;36| (|p| $) - (PROG (#0=#:G1653) + (PROG (#0=#:G1655) (RETURN (QVELT (SPADCALL (PROG2 (LETT #0# @@ -1472,7 +1472,7 @@ 1)))) (DEFUN |POLYCAT-;primitivePart;SVarSetS;37| (|p| |v| $) - (PROG (#0=#:G1659) + (PROG (#0=#:G1661) (RETURN (QVELT (SPADCALL (PROG2 (LETT #0# @@ -1895,425 +1895,3 @@ 149 98 154 3 0 0 0 16 53 55 3 0 0 0 9 36 52 1 0 145 0 156 2 0 24 0 0 186))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|PolynomialCategory&| '|isFunctor| - '(((|gcdPolynomial| - ((|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 109)) - ((|squareFree| ((|Factored| $) $)) T (ELT $ 165)) - ((|squareFreePart| ($ $)) T (ELT $ 173)) - ((|charthRoot| ((|Union| $ "failed") $)) T (ELT $ 156)) - ((< ((|Boolean|) $ $)) T (ELT $ 186)) - ((|convert| ((|InputForm|) $)) T (ELT $ 221)) - ((|convert| ((|Pattern| (|Integer|)) $)) T (ELT $ 206)) - ((|convert| ((|Pattern| (|Float|)) $)) T (ELT $ 213)) - ((|patternMatch| - ((|PatternMatchResult| (|Integer|) $) $ - (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) $))) - T (ELT $ 192)) - ((|patternMatch| - ((|PatternMatchResult| (|Float|) $) $ - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) $))) - T (ELT $ 199)) - ((|factor| ((|Factored| $) $)) T (ELT $ 140)) - ((|factorPolynomial| - ((|Factored| (|SparseUnivariatePolynomial| $)) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 120)) - ((|factorSquareFreePolynomial| - ((|Factored| (|SparseUnivariatePolynomial| $)) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 122)) - ((|solveLinearPolynomialEquation| - ((|Union| (|List| (|SparseUnivariatePolynomial| $)) - "failed") - (|List| (|SparseUnivariatePolynomial| $)) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 116)) - ((|conditionP| - ((|Union| (|Vector| $) "failed") (|Matrix| $))) - T (ELT $ 154)) - ((|primitivePart| ($ $ |#4|)) T (ELT $ 183)) - ((|content| ($ $ |#4|)) T (ELT $ 175)) - ((|discriminant| ($ $ |#4|)) T (ELT $ 78)) - ((|resultant| ($ $ $ |#4|)) T (ELT $ 76)) - ((|primitiveMonomials| ((|List| $) $)) T (ELT $ 63)) - ((|totalDegree| - ((|NonNegativeInteger|) $ (|List| |#4|))) - T (ELT $ 74)) - ((|totalDegree| ((|NonNegativeInteger|) $)) T - (ELT $ 71)) - ((|isExpt| - ((|Union| (|Record| (|:| |var| |#4|) - (|:| |exponent| - (|NonNegativeInteger|))) - "failed") - $)) - T (ELT $ 47)) - ((|isTimes| ((|Union| (|List| $) "failed") $)) T - (ELT $ 42)) - ((|isPlus| ((|Union| (|List| $) "failed") $)) T - (ELT $ 31)) - ((|monomial| - ($ $ (|List| |#4|) (|List| (|NonNegativeInteger|)))) - T (ELT $ 57)) - ((|monomial| ($ $ |#4| (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|monicDivide| - ((|Record| (|:| |quotient| $) (|:| |remainder| $)) - $ $ |#4|)) - T (ELT $ 162)) - ((|monomials| ((|List| $) $)) T (ELT $ 28)) - ((|coefficient| - ($ $ (|List| |#4|) (|List| (|NonNegativeInteger|)))) - T (ELT $ 55)) - ((|coefficient| ($ $ |#4| (|NonNegativeInteger|))) T - (ELT $ 52)) - ((|reducedSystem| ((|Matrix| |#2|) (|Matrix| $))) T - (ELT $ 99)) - ((|reducedSystem| - ((|Record| (|:| |mat| (|Matrix| |#2|)) - (|:| |vec| (|Vector| |#2|))) - (|Matrix| $) (|Vector| $))) - T (ELT $ 106)) - ((|reducedSystem| - ((|Record| (|:| |mat| (|Matrix| (|Integer|))) - (|:| |vec| (|Vector| (|Integer|)))) - (|Matrix| $) (|Vector| $))) - T (ELT $ NIL)) - ((|reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| $))) - T (ELT $ NIL)) - ((|retract| (|#4| $)) T (ELT $ 59)) - ((|retractIfCan| ((|Union| |#4| "failed") $)) T - (ELT $ 60)) - ((|eval| ($ $ (|List| |#4|) (|List| $))) T (ELT $ NIL)) - ((|eval| ($ $ |#4| $)) T (ELT $ NIL)) - ((|eval| ($ $ (|List| |#4|) (|List| |#2|))) T - (ELT $ NIL)) - ((|eval| ($ $ |#4| |#2|)) T (ELT $ NIL)) - ((|eval| ($ $ (|List| $) (|List| $))) T (ELT $ NIL)) - ((|eval| ($ $ $ $)) T (ELT $ NIL)) - ((|eval| ($ $ (|Equation| $))) T (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| $)))) T (ELT $ 21)) - ((|monomial| ($ |#2| |#3|)) T (ELT $ NIL)) - ((|coefficient| (|#2| $ |#3|)) T (ELT $ NIL)) - ((|retract| ((|Integer|) $)) T (ELT $ NIL)) - ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T - (ELT $ NIL)) - ((|retract| ((|Fraction| (|Integer|)) $)) T (ELT $ NIL)) - ((|retractIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") $)) - T (ELT $ NIL)) - ((|retractIfCan| ((|Union| |#2| "failed") $)) T - (ELT $ NIL)) - ((|retract| (|#2| $)) T (ELT $ NIL)) - ((|content| (|#2| $)) T (ELT $ NIL)) - ((|primitivePart| ($ $)) T (ELT $ 180))) - (|addModemap| '|PolynomialCategory&| - '(|PolynomialCategory&| |#1| |#2| |#3| |#4|) - '((CATEGORY |domain| - (SIGNATURE |gcdPolynomial| - ((|SparseUnivariatePolynomial| |#1|) - (|SparseUnivariatePolynomial| |#1|) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |squareFree| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |squareFreePart| (|#1| |#1|)) - (SIGNATURE |charthRoot| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE < ((|Boolean|) |#1| |#1|)) - (SIGNATURE |convert| ((|InputForm|) |#1|)) - (SIGNATURE |convert| - ((|Pattern| (|Integer|)) |#1|)) - (SIGNATURE |convert| - ((|Pattern| (|Float|)) |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Integer|) |#1|) - |#1| (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) |#1|))) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Float|) |#1|) |#1| - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) |#1|))) - (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) - (SIGNATURE |factorPolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| |#1|)) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |factorSquareFreePolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| |#1|)) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |solveLinearPolynomialEquation| - ((|Union| (|List| - (|SparseUnivariatePolynomial| - |#1|)) - "failed") - (|List| (|SparseUnivariatePolynomial| |#1|)) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |conditionP| - ((|Union| (|Vector| |#1|) "failed") - (|Matrix| |#1|))) - (SIGNATURE |primitivePart| (|#1| |#1| |#4|)) - (SIGNATURE |content| (|#1| |#1| |#4|)) - (SIGNATURE |discriminant| (|#1| |#1| |#4|)) - (SIGNATURE |resultant| (|#1| |#1| |#1| |#4|)) - (SIGNATURE |primitiveMonomials| - ((|List| |#1|) |#1|)) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1| (|List| |#4|))) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |isExpt| - ((|Union| (|Record| (|:| |var| |#4|) - (|:| |exponent| - (|NonNegativeInteger|))) - "failed") - |#1|)) - (SIGNATURE |isTimes| - ((|Union| (|List| |#1|) "failed") |#1|)) - (SIGNATURE |isPlus| - ((|Union| (|List| |#1|) "failed") |#1|)) - (SIGNATURE |monomial| - (|#1| |#1| (|List| |#4|) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |monomial| - (|#1| |#1| |#4| (|NonNegativeInteger|))) - (SIGNATURE |monicDivide| - ((|Record| (|:| |quotient| |#1|) - (|:| |remainder| |#1|)) - |#1| |#1| |#4|)) - (SIGNATURE |monomials| ((|List| |#1|) |#1|)) - (SIGNATURE |coefficient| - (|#1| |#1| (|List| |#4|) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |coefficient| - (|#1| |#1| |#4| (|NonNegativeInteger|))) - (SIGNATURE |reducedSystem| - ((|Matrix| |#2|) (|Matrix| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| (|:| |mat| (|Matrix| |#2|)) - (|:| |vec| (|Vector| |#2|))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| (|:| |mat| - (|Matrix| (|Integer|))) - (|:| |vec| - (|Vector| (|Integer|)))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Matrix| (|Integer|)) (|Matrix| |#1|))) - (SIGNATURE |retract| (|#4| |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#4| "failed") |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#4|) (|List| |#1|))) - (SIGNATURE |eval| (|#1| |#1| |#4| |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#4|) (|List| |#2|))) - (SIGNATURE |eval| (|#1| |#1| |#4| |#2|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#1|) (|List| |#1|))) - (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) - (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Equation| |#1|)))) - (SIGNATURE |monomial| (|#1| |#2| |#3|)) - (SIGNATURE |coefficient| (|#2| |#1| |#3|)) - (SIGNATURE |retract| ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") |#1|)) - (SIGNATURE |retract| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") - |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#2| "failed") |#1|)) - (SIGNATURE |retract| (|#2| |#1|)) - (SIGNATURE |content| (|#2| |#1|)) - (SIGNATURE |primitivePart| (|#1| |#1|))) - (|PolynomialCategory| |#2| |#3| |#4|) (|Ring|) - (|OrderedAbelianMonoidSup|) (|OrderedSet|)) - T '|PolynomialCategory&| - (|put| '|PolynomialCategory&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |gcdPolynomial| - ((|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE |squareFree| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |squareFreePart| - (|#1| |#1|)) - (SIGNATURE |charthRoot| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE < ((|Boolean|) |#1| |#1|)) - (SIGNATURE |convert| - ((|InputForm|) |#1|)) - (SIGNATURE |convert| - ((|Pattern| (|Integer|)) |#1|)) - (SIGNATURE |convert| - ((|Pattern| (|Float|)) |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Integer|) - |#1|) - |#1| (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) - |#1|))) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Float|) - |#1|) - |#1| (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) - |#1|))) - (SIGNATURE |factor| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |factorPolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| - |#1|)) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE - |factorSquareFreePolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| - |#1|)) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE - |solveLinearPolynomialEquation| - ((|Union| - (|List| - (|SparseUnivariatePolynomial| - |#1|)) - "failed") - (|List| - (|SparseUnivariatePolynomial| - |#1|)) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE |conditionP| - ((|Union| (|Vector| |#1|) - "failed") - (|Matrix| |#1|))) - (SIGNATURE |primitivePart| - (|#1| |#1| |#4|)) - (SIGNATURE |content| (|#1| |#1| |#4|)) - (SIGNATURE |discriminant| - (|#1| |#1| |#4|)) - (SIGNATURE |resultant| - (|#1| |#1| |#1| |#4|)) - (SIGNATURE |primitiveMonomials| - ((|List| |#1|) |#1|)) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1| - (|List| |#4|))) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |isExpt| - ((|Union| - (|Record| (|:| |var| |#4|) - (|:| |exponent| - (|NonNegativeInteger|))) - "failed") - |#1|)) - (SIGNATURE |isTimes| - ((|Union| (|List| |#1|) "failed") - |#1|)) - (SIGNATURE |isPlus| - ((|Union| (|List| |#1|) "failed") - |#1|)) - (SIGNATURE |monomial| - (|#1| |#1| (|List| |#4|) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |monomial| - (|#1| |#1| |#4| - (|NonNegativeInteger|))) - (SIGNATURE |monicDivide| - ((|Record| (|:| |quotient| |#1|) - (|:| |remainder| |#1|)) - |#1| |#1| |#4|)) - (SIGNATURE |monomials| - ((|List| |#1|) |#1|)) - (SIGNATURE |coefficient| - (|#1| |#1| (|List| |#4|) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |coefficient| - (|#1| |#1| |#4| - (|NonNegativeInteger|))) - (SIGNATURE |reducedSystem| - ((|Matrix| |#2|) (|Matrix| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| - (|:| |mat| (|Matrix| |#2|)) - (|:| |vec| (|Vector| |#2|))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| - (|:| |mat| - (|Matrix| (|Integer|))) - (|:| |vec| - (|Vector| (|Integer|)))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Matrix| (|Integer|)) - (|Matrix| |#1|))) - (SIGNATURE |retract| (|#4| |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#4| "failed") |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#4|) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| |#4| |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#4|) - (|List| |#2|))) - (SIGNATURE |eval| - (|#1| |#1| |#4| |#2|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#1|) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| |#1| |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|Equation| |#1|)))) - (SIGNATURE |monomial| - (|#1| |#2| |#3|)) - (SIGNATURE |coefficient| - (|#2| |#1| |#3|)) - (SIGNATURE |retract| - ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") - |#1|)) - (SIGNATURE |retract| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Fraction| (|Integer|)) - "failed") - |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#2| "failed") |#1|)) - (SIGNATURE |retract| (|#2| |#1|)) - (SIGNATURE |content| (|#2| |#1|)) - (SIGNATURE |primitivePart| - (|#1| |#1|))) - (|PolynomialCategory| |#2| |#3| |#4|) - (|Ring|) (|OrderedAbelianMonoidSup|) - (|OrderedSet|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/POLYCAT.lsp b/src/algebra/strap/POLYCAT.lsp index 69b15a81..f2e8f11b 100644 --- a/src/algebra/strap/POLYCAT.lsp +++ b/src/algebra/strap/POLYCAT.lsp @@ -219,9 +219,9 @@ (|NonNegativeInteger|))) NIL)) . #1=(|PolynomialCategory|))))) . #1#) - (SETELT #0# 0 - (LIST '|PolynomialCategory| (|devaluate| |t#1|) - (|devaluate| |t#2|) (|devaluate| |t#3|))))))) + (|setShellEntry| #0# 0 + (LIST '|PolynomialCategory| (|devaluate| |t#1|) + (|devaluate| |t#2|) (|devaluate| |t#3|))))))) (DEFUN |PolynomialCategory| (&REST #0=#:G1418 &AUX #1=#:G1416) (DSETQ #1# #0#) @@ -236,11 +236,3 @@ (APPLY #'|PolynomialCategory;| #1#))) |PolynomialCategory;AL|)) #2#)))) - -(SETQ |$CategoryFrame| - (|put| '|PolynomialCategory| '|isCategory| T - (|addModemap| '|PolynomialCategory| - '(|PolynomialCategory| |#1| |#2| |#3|) - '((|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) - (|OrderedSet|)) - T '|PolynomialCategory| |$CategoryFrame|))) diff --git a/src/algebra/strap/PRIMARR.lsp b/src/algebra/strap/PRIMARR.lsp index 9aa4b635..b9f73fa8 100644 --- a/src/algebra/strap/PRIMARR.lsp +++ b/src/algebra/strap/PRIMARR.lsp @@ -233,187 +233,3 @@ 1 2 5 19 0 0 1 2 5 19 0 0 1 1 0 7 0 8))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|PrimitiveArray| '|isFunctor| - '(((~= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) - (|has| |#1| (|CoercibleTo| (|OutputForm|))) - (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|latex| ((|String|) $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((< ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((> ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|max| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|min| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|sort!| ($ $)) - (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) - (|has| |#1| (|OrderedSet|))) - (ELT $ NIL)) - ((|sort!| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|reverse!| ($ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|copyInto!| ($ $ $ (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|sorted?| ((|Boolean|) $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|sort| ($ $)) (|has| |#1| (|OrderedSet|)) (ELT $ NIL)) - ((|merge| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $ (|Integer|))) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|position| - ((|Integer|) (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|sorted?| - ((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $)) - T (ELT $ NIL)) - ((|sort| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) T - (ELT $ NIL)) - ((|reverse| ($ $)) T (ELT $ NIL)) - ((|merge| ($ (|Mapping| (|Boolean|) |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|setelt| - (|#1| $ (|UniversalSegment| (|Integer|)) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|insert| ($ $ $ (|Integer|))) T (ELT $ NIL)) - ((|insert| ($ |#1| $ (|Integer|))) T (ELT $ NIL)) - ((|delete| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|delete| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|elt| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|concat| ($ (|List| $))) T (ELT $ NIL)) - ((|concat| ($ $ $)) T (ELT $ NIL)) - ((|concat| ($ |#1| $)) T (ELT $ NIL)) - ((|concat| ($ $ |#1|)) T (ELT $ NIL)) - ((|new| ($ (|NonNegativeInteger|) |#1|)) T (ELT $ 12)) - ((|construct| ($ (|List| |#1|))) T (ELT $ NIL)) - ((|find| ((|Union| |#1| "failed") - (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|remove| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|select| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| - (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|remove| ($ |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|removeDuplicates| ($ $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|convert| ((|InputForm|) $)) - (|has| |#1| (|ConvertibleTo| (|InputForm|))) - (ELT $ NIL)) - ((|swap!| ((|Void|) $ (|Integer|) (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|fill!| ($ $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 17)) - ((|first| (|#1| $)) (|has| (|Integer|) (|OrderedSet|)) - (ELT $ NIL)) - ((|minIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ 10)) - ((|maxIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ NIL)) - ((|entry?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|indices| ((|List| (|Integer|)) $)) T (ELT $ NIL)) - ((|index?| ((|Boolean|) (|Integer|) $)) T (ELT $ NIL)) - ((|entries| ((|List| |#1|) $)) T (ELT $ NIL)) - ((|elt| (|#1| $ (|Integer|))) T (ELT $ 14)) - ((|elt| (|#1| $ (|Integer|) |#1|)) T (ELT $ NIL)) - ((|qelt| (|#1| $ (|Integer|))) T (ELT $ 13)) - ((|setelt| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 16)) - ((|qsetelt!| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ 15)) - ((|eval| ($ $ (|List| |#1|) (|List| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ |#1| |#1|)) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|Equation| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| |#1|)))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|member?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|count| ((|NonNegativeInteger|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|members| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|parts| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|count| ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|map!| ($ (|Mapping| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1|) $)) T (ELT $ NIL)) - ((|#| ((|NonNegativeInteger|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ 8)) - ((|sample| ($)) T (CONST $ NIL)) - ((|size?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|more?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|less?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|empty?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|empty| ($)) T (ELT $ 11)) - ((|copy| ($ $)) T (ELT $ NIL)) - ((|eq?| ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|PrimitiveArray| '(|PrimitiveArray| |#1|) - '((|OneDimensionalArrayAggregate| |#1|) (|Type|)) T - '|PrimitiveArray| - (|put| '|PrimitiveArray| '|mode| - '(|Mapping| - (|OneDimensionalArrayAggregate| |#1|) - (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/PSETCAT-.lsp b/src/algebra/strap/PSETCAT-.lsp index f0aa0b4c..a216f16e 100644 --- a/src/algebra/strap/PSETCAT-.lsp +++ b/src/algebra/strap/PSETCAT-.lsp @@ -961,130 +961,3 @@ 0 0 0 9 32 2 0 0 0 9 34 2 0 15 0 0 40))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|PolynomialSetCategory&| '|isFunctor| - '(((|triangular?| ((|Boolean|) $)) T (ELT $ 47)) - ((|rewriteIdealWithRemainder| - ((|List| |#5|) (|List| |#5|) $)) - T (ELT $ 90)) - ((|rewriteIdealWithHeadRemainder| - ((|List| |#5|) (|List| |#5|) $)) - T (ELT $ 87)) - ((|remainder| - ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) - (|:| |den| |#2|)) - |#5| $)) - T (ELT $ 81)) - ((|headRemainder| - ((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| - $)) - T (ELT $ 73)) - ((|roughUnitIdeal?| ((|Boolean|) $)) T (ELT $ 49)) - ((|roughEqualIdeals?| ((|Boolean|) $ $)) T (ELT $ 58)) - ((|roughSubIdeal?| ((|Boolean|) $ $)) T (ELT $ 55)) - ((|roughBase?| ((|Boolean|) $)) T (ELT $ 53)) - ((|trivialIdeal?| ((|Boolean|) $)) T (ELT $ 48)) - ((|sort| ((|Record| (|:| |under| $) (|:| |floor| $) - (|:| |upper| $)) - $ |#4|)) - T (ELT $ 36)) - ((|collectUpper| ($ $ |#4|)) T (ELT $ 33)) - ((|collect| ($ $ |#4|)) T (ELT $ 34)) - ((|collectUnder| ($ $ |#4|)) T (ELT $ 32)) - ((|mainVariable?| ((|Boolean|) |#4| $)) T (ELT $ 30)) - ((|mainVariables| ((|List| |#4|) $)) T (ELT $ 27)) - ((|variables| ((|List| |#4|) $)) T (ELT $ 23)) - ((= ((|Boolean|) $ $)) T (ELT $ 40))) - (|addModemap| '|PolynomialSetCategory&| - '(|PolynomialSetCategory&| |#1| |#2| |#3| |#4| |#5|) - '((CATEGORY |domain| - (SIGNATURE |triangular?| ((|Boolean|) |#1|)) - (SIGNATURE |rewriteIdealWithRemainder| - ((|List| |#5|) (|List| |#5|) |#1|)) - (SIGNATURE |rewriteIdealWithHeadRemainder| - ((|List| |#5|) (|List| |#5|) |#1|)) - (SIGNATURE |remainder| - ((|Record| (|:| |rnum| |#2|) - (|:| |polnum| |#5|) (|:| |den| |#2|)) - |#5| |#1|)) - (SIGNATURE |headRemainder| - ((|Record| (|:| |num| |#5|) - (|:| |den| |#2|)) - |#5| |#1|)) - (SIGNATURE |roughUnitIdeal?| ((|Boolean|) |#1|)) - (SIGNATURE |roughEqualIdeals?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |roughSubIdeal?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |roughBase?| ((|Boolean|) |#1|)) - (SIGNATURE |trivialIdeal?| ((|Boolean|) |#1|)) - (SIGNATURE |sort| - ((|Record| (|:| |under| |#1|) - (|:| |floor| |#1|) (|:| |upper| |#1|)) - |#1| |#4|)) - (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) - (SIGNATURE |collect| (|#1| |#1| |#4|)) - (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) - (SIGNATURE |mainVariable?| - ((|Boolean|) |#4| |#1|)) - (SIGNATURE |mainVariables| ((|List| |#4|) |#1|)) - (SIGNATURE |variables| ((|List| |#4|) |#1|)) - (SIGNATURE = ((|Boolean|) |#1| |#1|))) - (|PolynomialSetCategory| |#2| |#3| |#4| |#5|) - (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) - (|RecursivePolynomialCategory| |#2| |#3| |#4|)) - T '|PolynomialSetCategory&| - (|put| '|PolynomialSetCategory&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |triangular?| - ((|Boolean|) |#1|)) - (SIGNATURE |rewriteIdealWithRemainder| - ((|List| |#5|) (|List| |#5|) |#1|)) - (SIGNATURE - |rewriteIdealWithHeadRemainder| - ((|List| |#5|) (|List| |#5|) |#1|)) - (SIGNATURE |remainder| - ((|Record| (|:| |rnum| |#2|) - (|:| |polnum| |#5|) - (|:| |den| |#2|)) - |#5| |#1|)) - (SIGNATURE |headRemainder| - ((|Record| (|:| |num| |#5|) - (|:| |den| |#2|)) - |#5| |#1|)) - (SIGNATURE |roughUnitIdeal?| - ((|Boolean|) |#1|)) - (SIGNATURE |roughEqualIdeals?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |roughSubIdeal?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |roughBase?| - ((|Boolean|) |#1|)) - (SIGNATURE |trivialIdeal?| - ((|Boolean|) |#1|)) - (SIGNATURE |sort| - ((|Record| (|:| |under| |#1|) - (|:| |floor| |#1|) - (|:| |upper| |#1|)) - |#1| |#4|)) - (SIGNATURE |collectUpper| - (|#1| |#1| |#4|)) - (SIGNATURE |collect| (|#1| |#1| |#4|)) - (SIGNATURE |collectUnder| - (|#1| |#1| |#4|)) - (SIGNATURE |mainVariable?| - ((|Boolean|) |#4| |#1|)) - (SIGNATURE |mainVariables| - ((|List| |#4|) |#1|)) - (SIGNATURE |variables| - ((|List| |#4|) |#1|)) - (SIGNATURE = ((|Boolean|) |#1| |#1|))) - (|PolynomialSetCategory| |#2| |#3| |#4| - |#5|) - (|Ring|) (|OrderedAbelianMonoidSup|) - (|OrderedSet|) - (|RecursivePolynomialCategory| |#2| |#3| - |#4|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/PSETCAT.lsp b/src/algebra/strap/PSETCAT.lsp index e5b90b16..4db40c2c 100644 --- a/src/algebra/strap/PSETCAT.lsp +++ b/src/algebra/strap/PSETCAT.lsp @@ -102,10 +102,10 @@ (|List| |t#3|)) NIL)) . #2=(|PolynomialSetCategory|)))))) . #2#) - (SETELT #0# 0 - (LIST '|PolynomialSetCategory| (|devaluate| |t#1|) - (|devaluate| |t#2|) (|devaluate| |t#3|) - (|devaluate| |t#4|))))))) + (|setShellEntry| #0# 0 + (LIST '|PolynomialSetCategory| (|devaluate| |t#1|) + (|devaluate| |t#2|) (|devaluate| |t#3|) + (|devaluate| |t#4|))))))) (DEFUN |PolynomialSetCategory| (&REST #0=#:G1434 &AUX #1=#:G1432) (DSETQ #1# #0#) @@ -121,12 +121,3 @@ #1#))) |PolynomialSetCategory;AL|)) #2#)))) - -(SETQ |$CategoryFrame| - (|put| '|PolynomialSetCategory| '|isCategory| T - (|addModemap| '|PolynomialSetCategory| - '(|PolynomialSetCategory| |#1| |#2| |#3| |#4|) - '((|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) - (|OrderedSet|) - (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) - T '|PolynomialSetCategory| |$CategoryFrame|))) diff --git a/src/algebra/strap/QFCAT-.lsp b/src/algebra/strap/QFCAT-.lsp index 00304cb1..78512ea8 100644 --- a/src/algebra/strap/QFCAT-.lsp +++ b/src/algebra/strap/QFCAT-.lsp @@ -519,269 +519,3 @@ 67 0 70 1 0 76 0 79 1 0 0 55 57 1 0 0 85 90 0 0 29 31 2 0 48 0 0 50))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|QuotientFieldCategory&| '|isFunctor| - '(((< ((|Boolean|) $ $)) T (ELT $ 50)) - ((|init| ($)) T (ELT $ 16)) - ((|nextItem| ((|Union| $ "failed") $)) T (ELT $ 20)) - ((|retract| ((|Integer|) $)) T (ELT $ 92)) - ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T - (ELT $ 95)) - ((|retract| ((|Fraction| (|Integer|)) $)) T (ELT $ NIL)) - ((|retractIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") $)) - T (ELT $ NIL)) - ((|convert| ((|DoubleFloat|) $)) T (ELT $ 47)) - ((|convert| ((|Float|) $)) T (ELT $ 44)) - ((|convert| ((|InputForm|) $)) T (ELT $ 40)) - ((|retract| ((|Symbol|) $)) T (ELT $ 60)) - ((|retractIfCan| ((|Union| (|Symbol|) "failed") $)) T - (ELT $ 65)) - ((|coerce| ($ (|Symbol|))) T (ELT $ 57)) - ((|random| ($)) T (ELT $ 98)) - ((|fractionPart| ($ $)) T (ELT $ 54)) - ((|denominator| ($ $)) T (ELT $ 12)) - ((|numerator| ($ $)) T (ELT $ 10)) - ((|patternMatch| - ((|PatternMatchResult| (|Float|) $) $ - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) $))) - T (ELT $ 84)) - ((|patternMatch| - ((|PatternMatchResult| (|Integer|) $) $ - (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) $))) - T (ELT $ 75)) - ((|convert| ((|Pattern| (|Float|)) $)) T (ELT $ 79)) - ((|convert| ((|Pattern| (|Integer|)) $)) T (ELT $ 70)) - ((|reducedSystem| ((|Matrix| |#2|) (|Matrix| $))) T - (ELT $ 28)) - ((|reducedSystem| - ((|Record| (|:| |mat| (|Matrix| |#2|)) - (|:| |vec| (|Vector| |#2|))) - (|Matrix| $) (|Vector| $))) - T (ELT $ 112)) - ((|reducedSystem| - ((|Record| (|:| |mat| (|Matrix| (|Integer|))) - (|:| |vec| (|Vector| (|Integer|)))) - (|Matrix| $) (|Vector| $))) - T (ELT $ NIL)) - ((|reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| $))) - T (ELT $ NIL)) - ((|differentiate| ($ $ (|Mapping| |#2| |#2|))) T - (ELT $ 36)) - ((|differentiate| - ($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) - T (ELT $ NIL)) - ((|differentiate| - ($ $ (|List| (|Symbol|)) - (|List| (|NonNegativeInteger|)))) - T (ELT $ NIL)) - ((|differentiate| - ($ $ (|Symbol|) (|NonNegativeInteger|))) - T (ELT $ NIL)) - ((|differentiate| ($ $ (|List| (|Symbol|)))) T - (ELT $ NIL)) - ((|differentiate| ($ $ (|Symbol|))) T (ELT $ NIL)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|differentiate| ($ $)) T (ELT $ NIL)) - ((|map| ($ (|Mapping| |#2| |#2|) $)) T (ELT $ 22)) - ((|retract| (|#2| $)) T (ELT $ NIL)) - ((|retractIfCan| ((|Union| |#2| "failed") $)) T - (ELT $ NIL)) - ((|coerce| ($ |#2|)) T (ELT $ NIL)) - ((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ 90)) - ((|coerce| ($ $)) T (ELT $ NIL)) - ((|coerce| ($ (|Integer|))) T (ELT $ NIL)) - ((|characteristic| ((|NonNegativeInteger|))) T - (ELT $ 31)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ NIL))) - (|addModemap| '|QuotientFieldCategory&| - '(|QuotientFieldCategory&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE < ((|Boolean|) |#1| |#1|)) - (SIGNATURE |init| (|#1|)) - (SIGNATURE |nextItem| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |retract| ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") |#1|)) - (SIGNATURE |retract| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") - |#1|)) - (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) - (SIGNATURE |convert| ((|Float|) |#1|)) - (SIGNATURE |convert| ((|InputForm|) |#1|)) - (SIGNATURE |retract| ((|Symbol|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Symbol|) "failed") |#1|)) - (SIGNATURE |coerce| (|#1| (|Symbol|))) - (SIGNATURE |random| (|#1|)) - (SIGNATURE |fractionPart| (|#1| |#1|)) - (SIGNATURE |denominator| (|#1| |#1|)) - (SIGNATURE |numerator| (|#1| |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Float|) |#1|) |#1| - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) |#1|))) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Integer|) |#1|) - |#1| (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) |#1|))) - (SIGNATURE |convert| - ((|Pattern| (|Float|)) |#1|)) - (SIGNATURE |convert| - ((|Pattern| (|Integer|)) |#1|)) - (SIGNATURE |reducedSystem| - ((|Matrix| |#2|) (|Matrix| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| (|:| |mat| (|Matrix| |#2|)) - (|:| |vec| (|Vector| |#2|))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| - (|:| |mat| (|Matrix| (|Integer|))) - (|:| |vec| (|Vector| (|Integer|)))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Matrix| (|Integer|)) (|Matrix| |#1|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |differentiate| (|#1| |#1|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#2| |#2|) |#1|)) - (SIGNATURE |retract| (|#2| |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#2| "failed") |#1|)) - (SIGNATURE |coerce| (|#1| |#2|)) - (SIGNATURE |coerce| - (|#1| (|Fraction| (|Integer|)))) - (SIGNATURE |coerce| (|#1| |#1|)) - (SIGNATURE |coerce| (|#1| (|Integer|))) - (SIGNATURE |characteristic| - ((|NonNegativeInteger|))) - (SIGNATURE |coerce| ((|OutputForm|) |#1|))) - (|QuotientFieldCategory| |#2|) (|IntegralDomain|)) - T '|QuotientFieldCategory&| - (|put| '|QuotientFieldCategory&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE < ((|Boolean|) |#1| |#1|)) - (SIGNATURE |init| (|#1|)) - (SIGNATURE |nextItem| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |retract| - ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") - |#1|)) - (SIGNATURE |retract| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Fraction| (|Integer|)) - "failed") - |#1|)) - (SIGNATURE |convert| - ((|DoubleFloat|) |#1|)) - (SIGNATURE |convert| ((|Float|) |#1|)) - (SIGNATURE |convert| - ((|InputForm|) |#1|)) - (SIGNATURE |retract| - ((|Symbol|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Symbol|) "failed") - |#1|)) - (SIGNATURE |coerce| (|#1| (|Symbol|))) - (SIGNATURE |random| (|#1|)) - (SIGNATURE |fractionPart| (|#1| |#1|)) - (SIGNATURE |denominator| (|#1| |#1|)) - (SIGNATURE |numerator| (|#1| |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Float|) - |#1|) - |#1| (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) - |#1|))) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Integer|) - |#1|) - |#1| (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) - |#1|))) - (SIGNATURE |convert| - ((|Pattern| (|Float|)) |#1|)) - (SIGNATURE |convert| - ((|Pattern| (|Integer|)) |#1|)) - (SIGNATURE |reducedSystem| - ((|Matrix| |#2|) (|Matrix| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| - (|:| |mat| (|Matrix| |#2|)) - (|:| |vec| (|Vector| |#2|))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Record| - (|:| |mat| - (|Matrix| (|Integer|))) - (|:| |vec| - (|Vector| (|Integer|)))) - (|Matrix| |#1|) (|Vector| |#1|))) - (SIGNATURE |reducedSystem| - ((|Matrix| (|Integer|)) - (|Matrix| |#1|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1|)) - (SIGNATURE |map| - (|#1| (|Mapping| |#2| |#2|) |#1|)) - (SIGNATURE |retract| (|#2| |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#2| "failed") |#1|)) - (SIGNATURE |coerce| (|#1| |#2|)) - (SIGNATURE |coerce| - (|#1| (|Fraction| (|Integer|)))) - (SIGNATURE |coerce| (|#1| |#1|)) - (SIGNATURE |coerce| - (|#1| (|Integer|))) - (SIGNATURE |characteristic| - ((|NonNegativeInteger|))) - (SIGNATURE |coerce| - ((|OutputForm|) |#1|))) - (|QuotientFieldCategory| |#2|) - (|IntegralDomain|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/QFCAT.lsp b/src/algebra/strap/QFCAT.lsp index be400de3..dd721698 100644 --- a/src/algebra/strap/QFCAT.lsp +++ b/src/algebra/strap/QFCAT.lsp @@ -89,8 +89,8 @@ (|PolynomialFactorizationExplicit|)))) 'NIL NIL)) . #1=(|QuotientFieldCategory|))))) . #1#) - (SETELT #0# 0 - (LIST '|QuotientFieldCategory| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|QuotientFieldCategory| (|devaluate| |t#1|))))))) (DEFUN |QuotientFieldCategory| (#0=#:G1400) (LET (#1=#:G1401) @@ -103,10 +103,3 @@ (SETQ #1# (|QuotientFieldCategory;| #0#))) |QuotientFieldCategory;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|QuotientFieldCategory| '|isCategory| T - (|addModemap| '|QuotientFieldCategory| - '(|QuotientFieldCategory| |#1|) - '((|Category|) (|IntegralDomain|)) T - '|QuotientFieldCategory| |$CategoryFrame|))) diff --git a/src/algebra/strap/RCAGG-.lsp b/src/algebra/strap/RCAGG-.lsp index 599cc1a2..e10fc5da 100644 --- a/src/algebra/strap/RCAGG-.lsp +++ b/src/algebra/strap/RCAGG-.lsp @@ -64,27 +64,3 @@ 18 3 0 7 0 9 7 12 2 0 7 0 9 10 2 0 15 0 0 18))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|RecursiveAggregate&| '|isFunctor| - '(((|setelt| (|#2| $ "value" |#2|)) T (ELT $ 12)) - ((|child?| ((|Boolean|) $ $)) T (ELT $ 18)) - ((|elt| (|#2| $ "value")) T (ELT $ 10))) - (|addModemap| '|RecursiveAggregate&| - '(|RecursiveAggregate&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) - (SIGNATURE |child?| ((|Boolean|) |#1| |#1|)) - (SIGNATURE |elt| (|#2| |#1| "value"))) - (|RecursiveAggregate| |#2|) (|Type|)) - T '|RecursiveAggregate&| - (|put| '|RecursiveAggregate&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |setelt| - (|#2| |#1| "value" |#2|)) - (SIGNATURE |child?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |elt| (|#2| |#1| "value"))) - (|RecursiveAggregate| |#2|) (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/RCAGG.lsp b/src/algebra/strap/RCAGG.lsp index c03c9f27..46649f33 100644 --- a/src/algebra/strap/RCAGG.lsp +++ b/src/algebra/strap/RCAGG.lsp @@ -60,7 +60,8 @@ (|Integer|) (|List| |t#1|)) NIL)) . #1=(|RecursiveAggregate|))))) . #1#) - (SETELT #0# 0 (LIST '|RecursiveAggregate| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|RecursiveAggregate| (|devaluate| |t#1|))))))) (DEFUN |RecursiveAggregate| (#0=#:G1398) (LET (#1=#:G1399) @@ -72,9 +73,3 @@ (SETQ #1# (|RecursiveAggregate;| #0#))) |RecursiveAggregate;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|RecursiveAggregate| '|isCategory| T - (|addModemap| '|RecursiveAggregate| - '(|RecursiveAggregate| |#1|) '((|Category|) (|Type|)) - T '|RecursiveAggregate| |$CategoryFrame|))) diff --git a/src/algebra/strap/REF.lsp b/src/algebra/strap/REF.lsp index 30394145..0142338b 100644 --- a/src/algebra/strap/REF.lsp +++ b/src/algebra/strap/REF.lsp @@ -109,51 +109,3 @@ 1 1 22 0 1 1 0 6 0 11 1 0 6 0 13 1 1 16 0 21 2 0 8 0 0 9))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|Reference| '|isFunctor| - '(((~= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) - (|has| |#1| (|SetCategory|)) (ELT $ 21)) - ((|hash| ((|SingleInteger|) $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|latex| ((|String|) $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((= ((|Boolean|) $ $)) T (ELT $ 9)) - ((|setref| (|#1| $ |#1|)) T (ELT $ 14)) - ((|deref| (|#1| $)) T (ELT $ 13)) - ((|setelt| (|#1| $ |#1|)) T (ELT $ 12)) - ((|elt| (|#1| $)) T (ELT $ 11)) - ((|ref| ($ |#1|)) T (ELT $ 10))) - (|addModemap| '|Reference| '(|Reference| |#1|) - '((|Join| (|Type|) - (CATEGORY |domain| - (SIGNATURE |ref| ($ |#1|)) - (SIGNATURE |elt| (|#1| $)) - (SIGNATURE |setelt| (|#1| $ |#1|)) - (SIGNATURE |deref| (|#1| $)) - (SIGNATURE |setref| (|#1| $ |#1|)) - (SIGNATURE = ((|Boolean|) $ $)) - (IF (|has| |#1| (|SetCategory|)) - (ATTRIBUTE (|SetCategory|)) - |%noBranch|))) - (|Type|)) - T '|Reference| - (|put| '|Reference| '|mode| - '(|Mapping| - (|Join| (|Type|) - (CATEGORY |domain| - (SIGNATURE |ref| ($ |#1|)) - (SIGNATURE |elt| (|#1| $)) - (SIGNATURE |setelt| - (|#1| $ |#1|)) - (SIGNATURE |deref| (|#1| $)) - (SIGNATURE |setref| - (|#1| $ |#1|)) - (SIGNATURE = ((|Boolean|) $ $)) - (IF (|has| |#1| (|SetCategory|)) - (ATTRIBUTE (|SetCategory|)) - |%noBranch|))) - (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/RING-.lsp b/src/algebra/strap/RING-.lsp index 3ce200ae..f5a4504a 100644 --- a/src/algebra/strap/RING-.lsp +++ b/src/algebra/strap/RING-.lsp @@ -31,23 +31,3 @@ (|makeByteWordVec2| 10 '(0 6 0 7 2 6 0 8 0 9 1 0 0 8 10))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|Ring&| '|isFunctor| - '(((|coerce| ($ (|Integer|))) T (ELT $ 10)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ NIL))) - (|addModemap| '|Ring&| '(|Ring&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |coerce| (|#1| (|Integer|))) - (SIGNATURE |coerce| ((|OutputForm|) |#1|))) - (|Ring|)) - T '|Ring&| - (|put| '|Ring&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |coerce| - (|#1| (|Integer|))) - (SIGNATURE |coerce| - ((|OutputForm|) |#1|))) - (|Ring|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/RING.lsp b/src/algebra/strap/RING.lsp index 016a3ee0..7b61ea0f 100644 --- a/src/algebra/strap/RING.lsp +++ b/src/algebra/strap/RING.lsp @@ -17,14 +17,9 @@ '((|Integer|) (|NonNegativeInteger|)) NIL)) |Ring|) - (SETELT #0# 0 '(|Ring|)))))) + (|setShellEntry| #0# 0 '(|Ring|)))))) (DEFUN |Ring| () (LET () (COND (|Ring;AL|) (T (SETQ |Ring;AL| (|Ring;|)))))) -(SETQ |$CategoryFrame| - (|put| '|Ring| '|isCategory| T - (|addModemap| '|Ring| '(|Ring|) '((|Category|)) T '|Ring| - |$CategoryFrame|))) - (MAKEPROP '|Ring| 'NILADIC T) diff --git a/src/algebra/strap/RNG.lsp b/src/algebra/strap/RNG.lsp index 6a2f53a5..7e7bf619 100644 --- a/src/algebra/strap/RNG.lsp +++ b/src/algebra/strap/RNG.lsp @@ -7,14 +7,9 @@ (PROG (#0=#:G1397) (RETURN (PROG1 (LETT #0# (|Join| (|AbelianGroup|) (|SemiGroup|)) |Rng|) - (SETELT #0# 0 '(|Rng|)))))) + (|setShellEntry| #0# 0 '(|Rng|)))))) (DEFUN |Rng| () (LET () (COND (|Rng;AL|) (T (SETQ |Rng;AL| (|Rng;|)))))) -(SETQ |$CategoryFrame| - (|put| '|Rng| '|isCategory| T - (|addModemap| '|Rng| '(|Rng|) '((|Category|)) T '|Rng| - |$CategoryFrame|))) - (MAKEPROP '|Rng| 'NILADIC T) diff --git a/src/algebra/strap/RNS-.lsp b/src/algebra/strap/RNS-.lsp index ef8a5ed3..042d128b 100644 --- a/src/algebra/strap/RNS-.lsp +++ b/src/algebra/strap/RNS-.lsp @@ -187,91 +187,3 @@ 0 33 1 0 0 25 28 1 0 0 25 28 0 0 7 8 1 0 0 0 39))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|RealNumberSystem&| '|isFunctor| - '(((|round| ($ $)) T (ELT $ 22)) - ((|truncate| ($ $)) T (ELT $ 16)) - ((|fractionPart| ($ $)) T (ELT $ 11)) - ((|floor| ($ $)) T (ELT $ 38)) - ((|ceiling| ($ $)) T (ELT $ 39)) - ((|norm| ($ $)) T (ELT $ 24)) - ((|patternMatch| - ((|PatternMatchResult| (|Float|) $) $ - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) $))) - T (ELT $ 49)) - ((|convert| ((|Pattern| (|Float|)) $)) T (ELT $ 33)) - ((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ 28)) - ((|coerce| ($ (|Integer|))) T (ELT $ NIL)) - ((|convert| ((|DoubleFloat|) $)) T (ELT $ NIL)) - ((|convert| ((|Float|) $)) T (ELT $ NIL)) - ((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ 28)) - ((|coerce| ($ $)) T (ELT $ NIL)) - ((|coerce| ($ (|Integer|))) T (ELT $ NIL)) - ((|characteristic| ((|NonNegativeInteger|))) T - (ELT $ 8)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ NIL))) - (|addModemap| '|RealNumberSystem&| - '(|RealNumberSystem&| |#1|) - '((CATEGORY |domain| (SIGNATURE |round| (|#1| |#1|)) - (SIGNATURE |truncate| (|#1| |#1|)) - (SIGNATURE |fractionPart| (|#1| |#1|)) - (SIGNATURE |floor| (|#1| |#1|)) - (SIGNATURE |ceiling| (|#1| |#1|)) - (SIGNATURE |norm| (|#1| |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Float|) |#1|) |#1| - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) |#1|))) - (SIGNATURE |convert| - ((|Pattern| (|Float|)) |#1|)) - (SIGNATURE |coerce| - (|#1| (|Fraction| (|Integer|)))) - (SIGNATURE |coerce| (|#1| (|Integer|))) - (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) - (SIGNATURE |convert| ((|Float|) |#1|)) - (SIGNATURE |coerce| - (|#1| (|Fraction| (|Integer|)))) - (SIGNATURE |coerce| (|#1| |#1|)) - (SIGNATURE |coerce| (|#1| (|Integer|))) - (SIGNATURE |characteristic| - ((|NonNegativeInteger|))) - (SIGNATURE |coerce| ((|OutputForm|) |#1|))) - (|RealNumberSystem|)) - T '|RealNumberSystem&| - (|put| '|RealNumberSystem&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |round| (|#1| |#1|)) - (SIGNATURE |truncate| (|#1| |#1|)) - (SIGNATURE |fractionPart| (|#1| |#1|)) - (SIGNATURE |floor| (|#1| |#1|)) - (SIGNATURE |ceiling| (|#1| |#1|)) - (SIGNATURE |norm| (|#1| |#1|)) - (SIGNATURE |patternMatch| - ((|PatternMatchResult| (|Float|) - |#1|) - |#1| (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) - |#1|))) - (SIGNATURE |convert| - ((|Pattern| (|Float|)) |#1|)) - (SIGNATURE |coerce| - (|#1| (|Fraction| (|Integer|)))) - (SIGNATURE |coerce| - (|#1| (|Integer|))) - (SIGNATURE |convert| - ((|DoubleFloat|) |#1|)) - (SIGNATURE |convert| ((|Float|) |#1|)) - (SIGNATURE |coerce| - (|#1| (|Fraction| (|Integer|)))) - (SIGNATURE |coerce| (|#1| |#1|)) - (SIGNATURE |coerce| - (|#1| (|Integer|))) - (SIGNATURE |characteristic| - ((|NonNegativeInteger|))) - (SIGNATURE |coerce| - ((|OutputForm|) |#1|))) - (|RealNumberSystem|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/RNS.lsp b/src/algebra/strap/RNS.lsp index 2ece00ea..f9641660 100644 --- a/src/algebra/strap/RNS.lsp +++ b/src/algebra/strap/RNS.lsp @@ -31,7 +31,7 @@ ((|abs| ($ $)) T)) NIL '((|Integer|)) NIL))) |RealNumberSystem|) - (SETELT #0# 0 '(|RealNumberSystem|)))))) + (|setShellEntry| #0# 0 '(|RealNumberSystem|)))))) (DEFUN |RealNumberSystem| () (LET () @@ -39,10 +39,4 @@ (|RealNumberSystem;AL|) (T (SETQ |RealNumberSystem;AL| (|RealNumberSystem;|)))))) -(SETQ |$CategoryFrame| - (|put| '|RealNumberSystem| '|isCategory| T - (|addModemap| '|RealNumberSystem| '(|RealNumberSystem|) - '((|Category|)) T '|RealNumberSystem| - |$CategoryFrame|))) - (MAKEPROP '|RealNumberSystem| 'NILADIC T) diff --git a/src/algebra/strap/SETAGG-.lsp b/src/algebra/strap/SETAGG-.lsp index 103e4819..a9253081 100644 --- a/src/algebra/strap/SETAGG-.lsp +++ b/src/algebra/strap/SETAGG-.lsp @@ -60,38 +60,3 @@ 0 0 7 0 14 2 0 0 0 7 13 2 0 0 0 0 10 2 0 0 0 7 15))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|SetAggregate&| '|isFunctor| - '(((|union| ($ |#2| $)) T (ELT $ 14)) - ((|union| ($ $ |#2|)) T (ELT $ 13)) - ((|union| ($ $ $)) T (ELT $ NIL)) - ((|symmetricDifference| ($ $ $)) T (ELT $ 10)) - ((|difference| ($ $ |#2|)) T (ELT $ 15)) - ((|difference| ($ $ $)) T (ELT $ NIL))) - (|addModemap| '|SetAggregate&| - '(|SetAggregate&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE |union| (|#1| |#2| |#1|)) - (SIGNATURE |union| (|#1| |#1| |#2|)) - (SIGNATURE |union| (|#1| |#1| |#1|)) - (SIGNATURE |symmetricDifference| - (|#1| |#1| |#1|)) - (SIGNATURE |difference| (|#1| |#1| |#2|)) - (SIGNATURE |difference| (|#1| |#1| |#1|))) - (|SetAggregate| |#2|) (|SetCategory|)) - T '|SetAggregate&| - (|put| '|SetAggregate&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |union| (|#1| |#2| |#1|)) - (SIGNATURE |union| (|#1| |#1| |#2|)) - (SIGNATURE |union| (|#1| |#1| |#1|)) - (SIGNATURE |symmetricDifference| - (|#1| |#1| |#1|)) - (SIGNATURE |difference| - (|#1| |#1| |#2|)) - (SIGNATURE |difference| - (|#1| |#1| |#1|))) - (|SetAggregate| |#2|) (|SetCategory|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/SETAGG.lsp b/src/algebra/strap/SETAGG.lsp index 37a253ed..d40ba5ab 100644 --- a/src/algebra/strap/SETAGG.lsp +++ b/src/algebra/strap/SETAGG.lsp @@ -44,7 +44,8 @@ '((|Boolean|) (|List| |t#1|)) NIL)) . #1=(|SetAggregate|))))) . #1#) - (SETELT #0# 0 (LIST '|SetAggregate| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|SetAggregate| (|devaluate| |t#1|))))))) (DEFUN |SetAggregate| (#0=#:G1398) (LET (#1=#:G1399) @@ -56,9 +57,3 @@ (SETQ #1# (|SetAggregate;| #0#))) |SetAggregate;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|SetAggregate| '|isCategory| T - (|addModemap| '|SetAggregate| '(|SetAggregate| |#1|) - '((|Category|) (|SetCategory|)) T '|SetAggregate| - |$CategoryFrame|))) diff --git a/src/algebra/strap/SETCAT-.lsp b/src/algebra/strap/SETCAT-.lsp index a84a276e..30703707 100644 --- a/src/algebra/strap/SETCAT-.lsp +++ b/src/algebra/strap/SETCAT-.lsp @@ -42,22 +42,3 @@ (|makeByteWordVec2| 10 '(1 0 9 0 10 1 0 7 0 8))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|SetCategory&| '|isFunctor| - '(((|latex| ((|String|) $)) T (ELT $ 10)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ 8))) - (|addModemap| '|SetCategory&| '(|SetCategory&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |latex| ((|String|) |#1|)) - (SIGNATURE |hash| ((|SingleInteger|) |#1|))) - (|SetCategory|)) - T '|SetCategory&| - (|put| '|SetCategory&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |latex| ((|String|) |#1|)) - (SIGNATURE |hash| - ((|SingleInteger|) |#1|))) - (|SetCategory|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/SETCAT.lsp b/src/algebra/strap/SETCAT.lsp index 2ea735a4..22ad6fd5 100644 --- a/src/algebra/strap/SETCAT.lsp +++ b/src/algebra/strap/SETCAT.lsp @@ -16,7 +16,7 @@ NIL '((|String|) (|SingleInteger|)) NIL))) |SetCategory|) - (SETELT #0# 0 '(|SetCategory|)))))) + (|setShellEntry| #0# 0 '(|SetCategory|)))))) (DEFUN |SetCategory| () (LET () @@ -24,9 +24,4 @@ (|SetCategory;AL|) (T (SETQ |SetCategory;AL| (|SetCategory;|)))))) -(SETQ |$CategoryFrame| - (|put| '|SetCategory| '|isCategory| T - (|addModemap| '|SetCategory| '(|SetCategory|) - '((|Category|)) T '|SetCategory| |$CategoryFrame|))) - (MAKEPROP '|SetCategory| 'NILADIC T) diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp index f1c1c5f9..2da14713 100644 --- a/src/algebra/strap/SINT.lsp +++ b/src/algebra/strap/SINT.lsp @@ -572,7 +572,7 @@ (|leftUnitary| . 0) (|unitsKnown| . 0)) (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)) + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)) (CONS '#(|IntegerNumberSystem&| |EuclideanDomain&| |UniqueFactorizationDomain&| NIL NIL |GcdDomain&| |IntegralDomain&| |Algebra&| NIL @@ -582,7 +582,7 @@ |Monoid&| NIL NIL |OrderedSet&| |AbelianSemiGroup&| |SemiGroup&| |Logic&| NIL |SetCategory&| NIL NIL NIL NIL NIL NIL - |RetractableTo&| NIL |BasicType&| NIL) + |RetractableTo&| NIL NIL |BasicType&| NIL) (CONS '#((|IntegerNumberSystem|) (|EuclideanDomain|) (|UniqueFactorizationDomain|) @@ -613,6 +613,7 @@ (|ConvertibleTo| 92) (|ConvertibleTo| 94) (|RetractableTo| 12) + (|CoercibleFrom| 12) (|ConvertibleTo| 12) (|BasicType|) (|CoercibleTo| 29)) (|makeByteWordVec2| 104 @@ -659,201 +660,4 @@ 0 56 0 1 2 0 0 104 0 1))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|SingleInteger| '|isFunctor| - '(((|Or| ($ $ $)) T (ELT $ 47)) - ((|And| ($ $ $)) T (ELT $ 46)) - ((|Not| ($ $)) T (ELT $ 45)) - ((|xor| ($ $ $)) T (ELT $ 48)) - ((|not| ($ $)) T (ELT $ 42)) ((|min| ($)) T (ELT $ 39)) - ((|max| ($)) T (ELT $ 38)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $ (|Boolean|))) - T (ELT $ 25)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $)) T - (ELT $ 24)) - ((|OMwrite| ((|String|) $ (|Boolean|))) T (ELT $ 23)) - ((|OMwrite| ((|String|) $)) T (ELT $ 21)) - ((~ ($ $)) T (ELT $ 41)) ((|/\\| ($ $ $)) T (ELT $ 43)) - ((|\\/| ($ $ $)) T (ELT $ 44)) - ((|invmod| ($ $ $)) T (ELT $ NIL)) - ((|powmod| ($ $ $ $)) T (ELT $ NIL)) - ((|mulmod| ($ $ $ $)) T (ELT $ 73)) - ((|submod| ($ $ $ $)) T (ELT $ 75)) - ((|addmod| ($ $ $ $)) T (ELT $ 74)) - ((|mask| ($ $)) T (ELT $ NIL)) - ((|dec| ($ $)) T (ELT $ 51)) - ((|inc| ($ $)) T (ELT $ 50)) - ((|copy| ($ $)) T (ELT $ NIL)) - ((|random| ($ $)) T (ELT $ 84)) - ((|random| ($)) T (ELT $ 83)) - ((|rationalIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") $)) - T (ELT $ NIL)) - ((|rational| ((|Fraction| (|Integer|)) $)) T - (ELT $ NIL)) - ((|rational?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|symmetricRemainder| ($ $ $)) T (ELT $ NIL)) - ((|positiveRemainder| ($ $ $)) T (ELT $ 81)) - ((|bit?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|shift| ($ $ $)) T (ELT $ 72)) - ((|length| ($ $)) T (ELT $ 71)) - ((|base| ($)) T (ELT $ 37)) - ((|even?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|odd?| ((|Boolean|) $)) T (ELT $ 64)) - ((|init| ($)) T (CONST $ NIL)) - ((|nextItem| ((|Union| $ "failed") $)) T (ELT $ NIL)) - ((|convert| ((|DoubleFloat|) $)) T (ELT $ NIL)) - ((|convert| ((|Float|) $)) T (ELT $ NIL)) - ((|permutation| ($ $ $)) T (ELT $ NIL)) - ((|factorial| ($ $)) T (ELT $ NIL)) - ((|binomial| ($ $ $)) T (ELT $ NIL)) - ((|patternMatch| - ((|PatternMatchResult| (|Integer|) $) $ - (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) $))) - T (ELT $ NIL)) - ((|convert| ((|Pattern| (|Integer|)) $)) T (ELT $ NIL)) - ((|convert| ((|InputForm|) $)) T (ELT $ NIL)) - ((|reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| $))) - T (ELT $ 28)) - ((|reducedSystem| - ((|Record| (|:| |mat| (|Matrix| (|Integer|))) - (|:| |vec| (|Vector| (|Integer|)))) - (|Matrix| $) (|Vector| $))) - T (ELT $ 80)) - ((|retract| ((|Integer|) $)) T (ELT $ NIL)) - ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T - (ELT $ NIL)) - ((|coerce| ($ (|Integer|))) T (ELT $ 82)) - ((|convert| ((|Integer|) $)) T (ELT $ 32)) - ((|differentiate| ($ $)) T (ELT $ NIL)) - ((D ($ $)) T (ELT $ NIL)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((D ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) - ((|abs| ($ $)) T (ELT $ 63)) - ((|sign| ((|Integer|) $)) T (ELT $ NIL)) - ((|negative?| ((|Boolean|) $)) T (ELT $ 76)) - ((|positive?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|min| ($ $ $)) T (ELT $ 68)) - ((|max| ($ $ $)) T (ELT $ 67)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ 49)) - ((|principalIdeal| - ((|Record| (|:| |coef| (|List| $)) - (|:| |generator| $)) - (|List| $))) - T (ELT $ NIL)) - ((|expressIdealMember| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ NIL)) - ((|sizeLess?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|euclideanSize| ((|NonNegativeInteger|) $)) T - (ELT $ NIL)) - ((|divide| - ((|Record| (|:| |quotient| $) (|:| |remainder| $)) - $ $)) - T (ELT $ 61)) - ((|quo| ($ $ $)) T (ELT $ 58)) - ((|rem| ($ $ $)) T (ELT $ 59)) - ((|extendedEuclidean| - ((|Record| (|:| |coef1| $) (|:| |coef2| $) - (|:| |generator| $)) - $ $)) - T (ELT $ NIL)) - ((|extendedEuclidean| - ((|Union| (|Record| (|:| |coef1| $) - (|:| |coef2| $)) - "failed") - $ $ $)) - T (ELT $ NIL)) - ((|multiEuclidean| - ((|Union| (|List| $) "failed") (|List| $) $)) - T (ELT $ NIL)) - ((|factor| ((|Factored| $) $)) T (ELT $ NIL)) - ((|squareFreePart| ($ $)) T (ELT $ NIL)) - ((|squareFree| ((|Factored| $) $)) T (ELT $ NIL)) - ((|prime?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|gcdPolynomial| - ((|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $))) - T (ELT $ NIL)) - ((|lcm| ($ (|List| $))) T (ELT $ NIL)) - ((|lcm| ($ $ $)) T (ELT $ NIL)) - ((|gcd| ($ (|List| $))) T (ELT $ NIL)) - ((|gcd| ($ $ $)) T (ELT $ 62)) - ((|unit?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|associates?| ((|Boolean|) $ $)) T (ELT $ NIL)) - ((|unitCanonical| ($ $)) T (ELT $ NIL)) - ((|unitNormal| - ((|Record| (|:| |unit| $) (|:| |canonical| $) - (|:| |associate| $)) - $)) - T (ELT $ 86)) - ((|exquo| ((|Union| $ "failed") $ $)) T (ELT $ NIL)) - ((|coerce| ($ $)) T (ELT $ NIL)) - ((|coerce| ($ (|Integer|))) T (ELT $ 82)) - ((|characteristic| ((|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|One| ($)) T (CONST $ 36)) - ((|one?| ((|Boolean|) $)) T (ELT $ 66)) - ((** ($ $ (|NonNegativeInteger|))) T (ELT $ 57)) - ((|recip| ((|Union| $ "failed") $)) T (ELT $ NIL)) - ((* ($ $ $)) T (ELT $ 55)) - ((** ($ $ (|PositiveInteger|))) T (ELT $ NIL)) - ((* ($ (|Integer|) $)) T (ELT $ 34)) - ((- ($ $ $)) T (ELT $ 54)) ((- ($ $)) T (ELT $ 52)) - ((|subtractIfCan| ((|Union| $ "failed") $ $)) T - (ELT $ NIL)) - ((* ($ (|NonNegativeInteger|) $)) T (ELT $ NIL)) - ((|zero?| ((|Boolean|) $)) T (ELT $ 65)) - ((|sample| ($)) T (CONST $ NIL)) - ((|Zero| ($)) T (CONST $ 35)) - ((* ($ (|PositiveInteger|) $)) T (ELT $ NIL)) - ((+ ($ $ $)) T (ELT $ 53)) - ((|latex| ((|String|) $)) T (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ 70)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ 31)) - ((= ((|Boolean|) $ $)) T (ELT $ 40)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|SingleInteger| '(|SingleInteger|) - '((|Join| (|IntegerNumberSystem|) (|Logic|) - (|OpenMath|) - (CATEGORY |domain| (ATTRIBUTE |canonical|) - (ATTRIBUTE |canonicalsClosed|) - (ATTRIBUTE |noetherian|) - (SIGNATURE |max| ($)) - (SIGNATURE |min| ($)) - (SIGNATURE |not| ($ $)) - (SIGNATURE ~ ($ $)) - (SIGNATURE |/\\| ($ $ $)) - (SIGNATURE |\\/| ($ $ $)) - (SIGNATURE |xor| ($ $ $)) - (SIGNATURE |Not| ($ $)) - (SIGNATURE |And| ($ $ $)) - (SIGNATURE |Or| ($ $ $))))) - T '|SingleInteger| - (|put| '|SingleInteger| '|mode| - '(|Mapping| - (|Join| (|IntegerNumberSystem|) (|Logic|) - (|OpenMath|) - (CATEGORY |domain| - (ATTRIBUTE |canonical|) - (ATTRIBUTE |canonicalsClosed|) - (ATTRIBUTE |noetherian|) - (SIGNATURE |max| ($)) - (SIGNATURE |min| ($)) - (SIGNATURE |not| ($ $)) - (SIGNATURE ~ ($ $)) - (SIGNATURE |/\\| ($ $ $)) - (SIGNATURE |\\/| ($ $ $)) - (SIGNATURE |xor| ($ $ $)) - (SIGNATURE |Not| ($ $)) - (SIGNATURE |And| ($ $ $)) - (SIGNATURE |Or| ($ $ $))))) - |$CategoryFrame|)))) - (MAKEPROP '|SingleInteger| 'NILADIC T) diff --git a/src/algebra/strap/STAGG-.lsp b/src/algebra/strap/STAGG-.lsp index 58ab78db..830a8636 100644 --- a/src/algebra/strap/STAGG-.lsp +++ b/src/algebra/strap/STAGG-.lsp @@ -351,119 +351,3 @@ 20 23 2 0 0 0 24 31 2 0 0 0 0 47 1 0 0 34 36 2 0 0 0 0 33))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|StreamAggregate&| '|isFunctor| - '(((|possiblyInfinite?| ((|Boolean|) $)) T (ELT $ 12)) - ((|explicitlyFinite?| ((|Boolean|) $)) T (ELT $ 11)) - ((|setelt| (|#2| $ (|Integer|) |#2|)) T (ELT $ 41)) - ((|elt| (|#2| $ (|Integer|) |#2|)) T (ELT $ NIL)) - ((|elt| (|#2| $ (|Integer|))) T (ELT $ 23)) - ((|fill!| ($ $ |#2|)) T (ELT $ 40)) - ((|concat| ($ $ |#2|)) T (ELT $ NIL)) - ((|concat| ($ (|List| $))) T (ELT $ 36)) - ((|elt| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ 31)) - ((|setelt| - (|#2| $ (|UniversalSegment| (|Integer|)) |#2|)) - T (ELT $ 44)) - ((|setelt| (|#2| $ "last" |#2|)) T (ELT $ NIL)) - ((|setelt| ($ $ "rest" $)) T (ELT $ NIL)) - ((|setelt| (|#2| $ "first" |#2|)) T (ELT $ NIL)) - ((|concat!| ($ $ |#2|)) T (ELT $ NIL)) - ((|concat!| ($ $ $)) T (ELT $ 47)) - ((|elt| (|#2| $ "last")) T (ELT $ NIL)) - ((|elt| ($ $ "rest")) T (ELT $ NIL)) - ((|first| ($ $ (|NonNegativeInteger|))) T (ELT $ 17)) - ((|elt| (|#2| $ "first")) T (ELT $ NIL)) - ((|first| (|#2| $)) T (ELT $ NIL)) - ((|concat| ($ |#2| $)) T (ELT $ NIL)) - ((|concat| ($ $ $)) T (ELT $ 33)) - ((|setelt| (|#2| $ "value" |#2|)) T (ELT $ NIL)) - ((|elt| (|#2| $ "value")) T (ELT $ NIL)) - ((|map!| ($ (|Mapping| |#2| |#2|) $)) T (ELT $ 39))) - (|addModemap| '|StreamAggregate&| - '(|StreamAggregate&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE |possiblyInfinite?| - ((|Boolean|) |#1|)) - (SIGNATURE |explicitlyFinite?| - ((|Boolean|) |#1|)) - (SIGNATURE |setelt| - (|#2| |#1| (|Integer|) |#2|)) - (SIGNATURE |elt| (|#2| |#1| (|Integer|) |#2|)) - (SIGNATURE |elt| (|#2| |#1| (|Integer|))) - (SIGNATURE |fill!| (|#1| |#1| |#2|)) - (SIGNATURE |concat| (|#1| |#1| |#2|)) - (SIGNATURE |concat| (|#1| (|List| |#1|))) - (SIGNATURE |elt| - (|#1| |#1| (|UniversalSegment| (|Integer|)))) - (SIGNATURE |setelt| - (|#2| |#1| (|UniversalSegment| (|Integer|)) - |#2|)) - (SIGNATURE |setelt| (|#2| |#1| "last" |#2|)) - (SIGNATURE |setelt| (|#1| |#1| "rest" |#1|)) - (SIGNATURE |setelt| (|#2| |#1| "first" |#2|)) - (SIGNATURE |concat!| (|#1| |#1| |#2|)) - (SIGNATURE |concat!| (|#1| |#1| |#1|)) - (SIGNATURE |elt| (|#2| |#1| "last")) - (SIGNATURE |elt| (|#1| |#1| "rest")) - (SIGNATURE |first| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |elt| (|#2| |#1| "first")) - (SIGNATURE |first| (|#2| |#1|)) - (SIGNATURE |concat| (|#1| |#2| |#1|)) - (SIGNATURE |concat| (|#1| |#1| |#1|)) - (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) - (SIGNATURE |elt| (|#2| |#1| "value")) - (SIGNATURE |map!| - (|#1| (|Mapping| |#2| |#2|) |#1|))) - (|StreamAggregate| |#2|) (|Type|)) - T '|StreamAggregate&| - (|put| '|StreamAggregate&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |possiblyInfinite?| - ((|Boolean|) |#1|)) - (SIGNATURE |explicitlyFinite?| - ((|Boolean|) |#1|)) - (SIGNATURE |setelt| - (|#2| |#1| (|Integer|) |#2|)) - (SIGNATURE |elt| - (|#2| |#1| (|Integer|) |#2|)) - (SIGNATURE |elt| - (|#2| |#1| (|Integer|))) - (SIGNATURE |fill!| (|#1| |#1| |#2|)) - (SIGNATURE |concat| (|#1| |#1| |#2|)) - (SIGNATURE |concat| - (|#1| (|List| |#1|))) - (SIGNATURE |elt| - (|#1| |#1| - (|UniversalSegment| (|Integer|)))) - (SIGNATURE |setelt| - (|#2| |#1| - (|UniversalSegment| (|Integer|)) - |#2|)) - (SIGNATURE |setelt| - (|#2| |#1| "last" |#2|)) - (SIGNATURE |setelt| - (|#1| |#1| "rest" |#1|)) - (SIGNATURE |setelt| - (|#2| |#1| "first" |#2|)) - (SIGNATURE |concat!| (|#1| |#1| |#2|)) - (SIGNATURE |concat!| (|#1| |#1| |#1|)) - (SIGNATURE |elt| (|#2| |#1| "last")) - (SIGNATURE |elt| (|#1| |#1| "rest")) - (SIGNATURE |first| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |elt| (|#2| |#1| "first")) - (SIGNATURE |first| (|#2| |#1|)) - (SIGNATURE |concat| (|#1| |#2| |#1|)) - (SIGNATURE |concat| (|#1| |#1| |#1|)) - (SIGNATURE |setelt| - (|#2| |#1| "value" |#2|)) - (SIGNATURE |elt| (|#2| |#1| "value")) - (SIGNATURE |map!| - (|#1| (|Mapping| |#2| |#2|) |#1|))) - (|StreamAggregate| |#2|) (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/STAGG.lsp b/src/algebra/strap/STAGG.lsp index 01d3f13a..03bb692d 100644 --- a/src/algebra/strap/STAGG.lsp +++ b/src/algebra/strap/STAGG.lsp @@ -27,7 +27,8 @@ T)) NIL '((|Boolean|)) NIL)) . #1=(|StreamAggregate|))))) . #1#) - (SETELT #0# 0 (LIST '|StreamAggregate| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|StreamAggregate| (|devaluate| |t#1|))))))) (DEFUN |StreamAggregate| (#0=#:G1405) (LET (#1=#:G1406) @@ -39,9 +40,3 @@ (SETQ #1# (|StreamAggregate;| #0#))) |StreamAggregate;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|StreamAggregate| '|isCategory| T - (|addModemap| '|StreamAggregate| '(|StreamAggregate| |#1|) - '((|Category|) (|Type|)) T '|StreamAggregate| - |$CategoryFrame|))) diff --git a/src/algebra/strap/SYMBOL.lsp b/src/algebra/strap/SYMBOL.lsp index 8f641a49..f19cf4da 100644 --- a/src/algebra/strap/SYMBOL.lsp +++ b/src/algebra/strap/SYMBOL.lsp @@ -915,191 +915,4 @@ 1 2 0 21 0 0 50))))) '|lookupComplete|)) -(SETQ |$CategoryFrame| - (|put| '|Symbol| '|isFunctor| - '(((|sample| ($)) T (CONST $ 124)) - ((|list| ((|List| $) $)) T (ELT $ 107)) - ((|string| ((|String|) $)) T (ELT $ 84)) - ((|elt| ($ $ (|List| (|OutputForm|)))) T (ELT $ 58)) - ((|argscript| ($ $ (|List| (|OutputForm|)))) T - (ELT $ 60)) - ((|superscript| ($ $ (|List| (|OutputForm|)))) T - (ELT $ 59)) - ((|subscript| ($ $ (|List| (|OutputForm|)))) T - (ELT $ 57)) - ((|script| - ($ $ - (|Record| (|:| |sub| (|List| (|OutputForm|))) - (|:| |sup| (|List| (|OutputForm|))) - (|:| |presup| (|List| (|OutputForm|))) - (|:| |presub| (|List| (|OutputForm|))) - (|:| |args| (|List| (|OutputForm|)))))) - T (ELT $ 82)) - ((|script| ($ $ (|List| (|List| (|OutputForm|))))) T - (ELT $ 56)) - ((|scripts| - ((|Record| (|:| |sub| (|List| (|OutputForm|))) - (|:| |sup| (|List| (|OutputForm|))) - (|:| |presup| (|List| (|OutputForm|))) - (|:| |presub| (|List| (|OutputForm|))) - (|:| |args| (|List| (|OutputForm|)))) - $)) - T (ELT $ 87)) - ((|scripted?| ((|Boolean|) $)) T (ELT $ 22)) - ((|name| ($ $)) T (ELT $ 83)) - ((|coerce| ($ (|String|))) T (ELT $ 48)) - ((|resetNew| ((|Void|))) T (ELT $ 106)) - ((|new| ($ $)) T (ELT $ 101)) ((|new| ($)) T (ELT $ 95)) - ((|patternMatch| - ((|PatternMatchResult| (|Float|) $) $ - (|Pattern| (|Float|)) - (|PatternMatchResult| (|Float|) $))) - T (ELT $ 73)) - ((|patternMatch| - ((|PatternMatchResult| (|Integer|) $) $ - (|Pattern| (|Integer|)) - (|PatternMatchResult| (|Integer|) $))) - T (ELT $ 66)) - ((|convert| ((|Pattern| (|Float|)) $)) T (ELT $ 75)) - ((|convert| ((|Pattern| (|Integer|)) $)) T (ELT $ 77)) - ((|convert| ((|Symbol|) $)) T (ELT $ 47)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $ (|Boolean|))) - T (ELT $ 36)) - ((|OMwrite| ((|Void|) (|OpenMathDevice|) $)) T - (ELT $ 35)) - ((|OMwrite| ((|String|) $ (|Boolean|))) T (ELT $ 34)) - ((|OMwrite| ((|String|) $)) T (ELT $ 33)) - ((|convert| ((|InputForm|) $)) T (ELT $ 46)) - ((|min| ($ $ $)) T (ELT $ NIL)) - ((|max| ($ $ $)) T (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) T (ELT $ NIL)) - ((> ((|Boolean|) $ $)) T (ELT $ NIL)) - ((< ((|Boolean|) $ $)) T (ELT $ 50)) - ((|latex| ((|String|) $)) T (ELT $ 90)) - ((|hash| ((|SingleInteger|) $)) T (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ 53)) - ((= ((|Boolean|) $ $)) T (ELT $ 49)) - ((~= ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|Symbol| '(|Symbol|) - '((|Join| (|OrderedSet|) - (|ConvertibleTo| (|InputForm|)) (|OpenMath|) - (|ConvertibleTo| (|Symbol|)) - (|ConvertibleTo| (|Pattern| (|Integer|))) - (|ConvertibleTo| (|Pattern| (|Float|))) - (|PatternMatchable| (|Integer|)) - (|PatternMatchable| (|Float|)) - (CATEGORY |domain| (SIGNATURE |new| ($)) - (SIGNATURE |new| ($ $)) - (SIGNATURE |resetNew| ((|Void|))) - (SIGNATURE |coerce| ($ (|String|))) - (SIGNATURE |name| ($ $)) - (SIGNATURE |scripted?| ((|Boolean|) $)) - (SIGNATURE |scripts| - ((|Record| - (|:| |sub| - (|List| (|OutputForm|))) - (|:| |sup| - (|List| (|OutputForm|))) - (|:| |presup| - (|List| (|OutputForm|))) - (|:| |presub| - (|List| (|OutputForm|))) - (|:| |args| - (|List| (|OutputForm|)))) - $)) - (SIGNATURE |script| - ($ $ - (|List| (|List| (|OutputForm|))))) - (SIGNATURE |script| - ($ $ - (|Record| - (|:| |sub| - (|List| (|OutputForm|))) - (|:| |sup| - (|List| (|OutputForm|))) - (|:| |presup| - (|List| (|OutputForm|))) - (|:| |presub| - (|List| (|OutputForm|))) - (|:| |args| - (|List| (|OutputForm|)))))) - (SIGNATURE |subscript| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |superscript| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |argscript| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |elt| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |string| ((|String|) $)) - (SIGNATURE |list| ((|List| $) $)) - (SIGNATURE |sample| ($) |constant|)))) - T '|Symbol| - (|put| '|Symbol| '|mode| - '(|Mapping| - (|Join| (|OrderedSet|) - (|ConvertibleTo| (|InputForm|)) - (|OpenMath|) - (|ConvertibleTo| (|Symbol|)) - (|ConvertibleTo| - (|Pattern| (|Integer|))) - (|ConvertibleTo| - (|Pattern| (|Float|))) - (|PatternMatchable| (|Integer|)) - (|PatternMatchable| (|Float|)) - (CATEGORY |domain| - (SIGNATURE |new| ($)) - (SIGNATURE |new| ($ $)) - (SIGNATURE |resetNew| ((|Void|))) - (SIGNATURE |coerce| - ($ (|String|))) - (SIGNATURE |name| ($ $)) - (SIGNATURE |scripted?| - ((|Boolean|) $)) - (SIGNATURE |scripts| - ((|Record| - (|:| |sub| - (|List| (|OutputForm|))) - (|:| |sup| - (|List| (|OutputForm|))) - (|:| |presup| - (|List| (|OutputForm|))) - (|:| |presub| - (|List| (|OutputForm|))) - (|:| |args| - (|List| (|OutputForm|)))) - $)) - (SIGNATURE |script| - ($ $ - (|List| - (|List| (|OutputForm|))))) - (SIGNATURE |script| - ($ $ - (|Record| - (|:| |sub| - (|List| (|OutputForm|))) - (|:| |sup| - (|List| (|OutputForm|))) - (|:| |presup| - (|List| (|OutputForm|))) - (|:| |presub| - (|List| (|OutputForm|))) - (|:| |args| - (|List| (|OutputForm|)))))) - (SIGNATURE |subscript| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |superscript| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |argscript| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |elt| - ($ $ (|List| (|OutputForm|)))) - (SIGNATURE |string| - ((|String|) $)) - (SIGNATURE |list| ((|List| $) $)) - (SIGNATURE |sample| ($) - |constant|)))) - |$CategoryFrame|)))) - (MAKEPROP '|Symbol| 'NILADIC T) diff --git a/src/algebra/strap/TSETCAT-.lsp b/src/algebra/strap/TSETCAT-.lsp index da0e9e85..10ae2d9c 100644 --- a/src/algebra/strap/TSETCAT-.lsp +++ b/src/algebra/strap/TSETCAT-.lsp @@ -1150,302 +1150,3 @@ 43 2 0 11 0 99 100 1 0 114 0 115 2 0 11 9 0 118 2 0 11 0 0 19))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|TriangularSetCategory&| '|isFunctor| - '(((|coHeight| ((|NonNegativeInteger|) $)) T (ELT $ 130)) - ((|extend| ($ $ |#5|)) T (ELT $ 127)) - ((|select| ((|Union| |#5| "failed") $ |#4|)) T - (ELT $ 119)) - ((|algebraic?| ((|Boolean|) |#4| $)) T (ELT $ 118)) - ((|algebraicVariables| ((|List| |#4|) $)) T (ELT $ 115)) - ((|rest| ((|Union| $ "failed") $)) T (ELT $ 112)) - ((|last| ((|Union| |#5| "failed") $)) T (ELT $ 110)) - ((|first| ((|Union| |#5| "failed") $)) T (ELT $ 109)) - ((|reduceByQuasiMonic| (|#5| |#5| $)) T (ELT $ 98)) - ((|collectQuasiMonic| ($ $)) T (ELT $ 120)) - ((|removeZero| (|#5| |#5| $)) T (ELT $ 94)) - ((|initiallyReduce| (|#5| |#5| $)) T (ELT $ 81)) - ((|headReduce| (|#5| |#5| $)) T (ELT $ 78)) - ((|stronglyReduce| (|#5| |#5| $)) T (ELT $ 75)) - ((|rewriteSetWithReduction| - ((|List| |#5|) (|List| |#5|) $ - (|Mapping| |#5| |#5| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - T (ELT $ 73)) - ((|reduce| - (|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - T (ELT $ 69)) - ((|initiallyReduced?| ((|Boolean|) $)) T (ELT $ 107)) - ((|headReduced?| ((|Boolean|) $)) T (ELT $ 105)) - ((|stronglyReduced?| ((|Boolean|) $)) T (ELT $ 102)) - ((|autoReduced?| - ((|Boolean|) $ - (|Mapping| (|Boolean|) |#5| (|List| |#5|)))) - T (ELT $ 100)) - ((|initiallyReduced?| ((|Boolean|) |#5| $)) T - (ELT $ 67)) - ((|headReduced?| ((|Boolean|) |#5| $)) T (ELT $ 63)) - ((|stronglyReduced?| ((|Boolean|) |#5| $)) T (ELT $ 60)) - ((|reduced?| - ((|Boolean|) |#5| $ - (|Mapping| (|Boolean|) |#5| |#5|))) - T (ELT $ 31)) - ((|normalized?| ((|Boolean|) $)) T (ELT $ 103)) - ((|normalized?| ((|Boolean|) |#5| $)) T (ELT $ 58)) - ((|quasiComponent| - ((|Record| (|:| |close| (|List| |#5|)) - (|:| |open| (|List| |#5|))) - $)) - T (ELT $ 55)) - ((|degree| ((|NonNegativeInteger|) $)) T (ELT $ 52)) - ((|initials| ((|List| |#5|) $)) T (ELT $ 49)) - ((|basicSet| - ((|Union| (|Record| (|:| |bas| $) - (|:| |top| (|List| |#5|))) - "failed") - (|List| |#5|) (|Mapping| (|Boolean|) |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - T (ELT $ 45)) - ((|basicSet| - ((|Union| (|Record| (|:| |bas| $) - (|:| |top| (|List| |#5|))) - "failed") - (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|))) - T (ELT $ 43)) - ((|infRittWu?| ((|Boolean|) $ $)) T (ELT $ 27)) - ((|collectUpper| ($ $ |#4|)) T (ELT $ 122)) - ((|collectUnder| ($ $ |#4|)) T (ELT $ 121)) - ((|mvar| (|#4| $)) T (ELT $ 108)) - ((|retractIfCan| ((|Union| $ "failed") (|List| |#5|))) T - (ELT $ 126)) - ((|coerce| ((|List| |#5|) $)) T (ELT $ 113)) - ((|construct| ($ (|List| |#5|))) T (ELT $ 124)) - ((|reduce| (|#5| (|Mapping| |#5| |#5| |#5|) $)) T - (ELT $ NIL)) - ((|reduce| (|#5| (|Mapping| |#5| |#5| |#5|) $ |#5|)) T - (ELT $ NIL)) - ((|select| ($ (|Mapping| (|Boolean|) |#5|) $)) T - (ELT $ NIL)) - ((|reduce| - (|#5| (|Mapping| |#5| |#5| |#5|) $ |#5| |#5|)) - T (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) T (ELT $ NIL)) - ((= ((|Boolean|) $ $)) T (ELT $ 19))) - (|addModemap| '|TriangularSetCategory&| - '(|TriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) - '((CATEGORY |domain| - (SIGNATURE |coHeight| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |extend| (|#1| |#1| |#5|)) - (SIGNATURE |select| - ((|Union| |#5| "failed") |#1| |#4|)) - (SIGNATURE |algebraic?| ((|Boolean|) |#4| |#1|)) - (SIGNATURE |algebraicVariables| - ((|List| |#4|) |#1|)) - (SIGNATURE |rest| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |last| - ((|Union| |#5| "failed") |#1|)) - (SIGNATURE |first| - ((|Union| |#5| "failed") |#1|)) - (SIGNATURE |reduceByQuasiMonic| - (|#5| |#5| |#1|)) - (SIGNATURE |collectQuasiMonic| (|#1| |#1|)) - (SIGNATURE |removeZero| (|#5| |#5| |#1|)) - (SIGNATURE |initiallyReduce| (|#5| |#5| |#1|)) - (SIGNATURE |headReduce| (|#5| |#5| |#1|)) - (SIGNATURE |stronglyReduce| (|#5| |#5| |#1|)) - (SIGNATURE |rewriteSetWithReduction| - ((|List| |#5|) (|List| |#5|) |#1| - (|Mapping| |#5| |#5| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |reduce| - (|#5| |#5| |#1| (|Mapping| |#5| |#5| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |initiallyReduced?| - ((|Boolean|) |#1|)) - (SIGNATURE |headReduced?| ((|Boolean|) |#1|)) - (SIGNATURE |stronglyReduced?| - ((|Boolean|) |#1|)) - (SIGNATURE |autoReduced?| - ((|Boolean|) |#1| - (|Mapping| (|Boolean|) |#5| (|List| |#5|)))) - (SIGNATURE |initiallyReduced?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |headReduced?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |stronglyReduced?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |reduced?| - ((|Boolean|) |#5| |#1| - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |normalized?| ((|Boolean|) |#1|)) - (SIGNATURE |normalized?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |quasiComponent| - ((|Record| (|:| |close| (|List| |#5|)) - (|:| |open| (|List| |#5|))) - |#1|)) - (SIGNATURE |degree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |initials| ((|List| |#5|) |#1|)) - (SIGNATURE |basicSet| - ((|Union| (|Record| (|:| |bas| |#1|) - (|:| |top| (|List| |#5|))) - "failed") - (|List| |#5|) (|Mapping| (|Boolean|) |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |basicSet| - ((|Union| (|Record| (|:| |bas| |#1|) - (|:| |top| (|List| |#5|))) - "failed") - (|List| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |infRittWu?| ((|Boolean|) |#1| |#1|)) - (SIGNATURE |collectUpper| (|#1| |#1| |#4|)) - (SIGNATURE |collectUnder| (|#1| |#1| |#4|)) - (SIGNATURE |mvar| (|#4| |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#1| "failed") (|List| |#5|))) - (SIGNATURE |coerce| ((|List| |#5|) |#1|)) - (SIGNATURE |construct| (|#1| (|List| |#5|))) - (SIGNATURE |reduce| - (|#5| (|Mapping| |#5| |#5| |#5|) |#1|)) - (SIGNATURE |reduce| - (|#5| (|Mapping| |#5| |#5| |#5|) |#1| |#5|)) - (SIGNATURE |select| - (|#1| (|Mapping| (|Boolean|) |#5|) |#1|)) - (SIGNATURE |reduce| - (|#5| (|Mapping| |#5| |#5| |#5|) |#1| |#5| - |#5|)) - (SIGNATURE |coerce| ((|OutputForm|) |#1|)) - (SIGNATURE = ((|Boolean|) |#1| |#1|))) - (|TriangularSetCategory| |#2| |#3| |#4| |#5|) - (|IntegralDomain|) (|OrderedAbelianMonoidSup|) - (|OrderedSet|) - (|RecursivePolynomialCategory| |#2| |#3| |#4|)) - T '|TriangularSetCategory&| - (|put| '|TriangularSetCategory&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |coHeight| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |extend| (|#1| |#1| |#5|)) - (SIGNATURE |select| - ((|Union| |#5| "failed") |#1| - |#4|)) - (SIGNATURE |algebraic?| - ((|Boolean|) |#4| |#1|)) - (SIGNATURE |algebraicVariables| - ((|List| |#4|) |#1|)) - (SIGNATURE |rest| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |last| - ((|Union| |#5| "failed") |#1|)) - (SIGNATURE |first| - ((|Union| |#5| "failed") |#1|)) - (SIGNATURE |reduceByQuasiMonic| - (|#5| |#5| |#1|)) - (SIGNATURE |collectQuasiMonic| - (|#1| |#1|)) - (SIGNATURE |removeZero| - (|#5| |#5| |#1|)) - (SIGNATURE |initiallyReduce| - (|#5| |#5| |#1|)) - (SIGNATURE |headReduce| - (|#5| |#5| |#1|)) - (SIGNATURE |stronglyReduce| - (|#5| |#5| |#1|)) - (SIGNATURE |rewriteSetWithReduction| - ((|List| |#5|) (|List| |#5|) |#1| - (|Mapping| |#5| |#5| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |reduce| - (|#5| |#5| |#1| - (|Mapping| |#5| |#5| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |initiallyReduced?| - ((|Boolean|) |#1|)) - (SIGNATURE |headReduced?| - ((|Boolean|) |#1|)) - (SIGNATURE |stronglyReduced?| - ((|Boolean|) |#1|)) - (SIGNATURE |autoReduced?| - ((|Boolean|) |#1| - (|Mapping| (|Boolean|) |#5| - (|List| |#5|)))) - (SIGNATURE |initiallyReduced?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |headReduced?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |stronglyReduced?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |reduced?| - ((|Boolean|) |#5| |#1| - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |normalized?| - ((|Boolean|) |#1|)) - (SIGNATURE |normalized?| - ((|Boolean|) |#5| |#1|)) - (SIGNATURE |quasiComponent| - ((|Record| - (|:| |close| (|List| |#5|)) - (|:| |open| (|List| |#5|))) - |#1|)) - (SIGNATURE |degree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |initials| - ((|List| |#5|) |#1|)) - (SIGNATURE |basicSet| - ((|Union| - (|Record| (|:| |bas| |#1|) - (|:| |top| (|List| |#5|))) - "failed") - (|List| |#5|) - (|Mapping| (|Boolean|) |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |basicSet| - ((|Union| - (|Record| (|:| |bas| |#1|) - (|:| |top| (|List| |#5|))) - "failed") - (|List| |#5|) - (|Mapping| (|Boolean|) |#5| |#5|))) - (SIGNATURE |infRittWu?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |collectUpper| - (|#1| |#1| |#4|)) - (SIGNATURE |collectUnder| - (|#1| |#1| |#4|)) - (SIGNATURE |mvar| (|#4| |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| |#1| "failed") - (|List| |#5|))) - (SIGNATURE |coerce| - ((|List| |#5|) |#1|)) - (SIGNATURE |construct| - (|#1| (|List| |#5|))) - (SIGNATURE |reduce| - (|#5| (|Mapping| |#5| |#5| |#5|) - |#1|)) - (SIGNATURE |reduce| - (|#5| (|Mapping| |#5| |#5| |#5|) - |#1| |#5|)) - (SIGNATURE |select| - (|#1| (|Mapping| (|Boolean|) |#5|) - |#1|)) - (SIGNATURE |reduce| - (|#5| (|Mapping| |#5| |#5| |#5|) - |#1| |#5| |#5|)) - (SIGNATURE |coerce| - ((|OutputForm|) |#1|)) - (SIGNATURE = ((|Boolean|) |#1| |#1|))) - (|TriangularSetCategory| |#2| |#3| |#4| - |#5|) - (|IntegralDomain|) - (|OrderedAbelianMonoidSup|) (|OrderedSet|) - (|RecursivePolynomialCategory| |#2| |#3| - |#4|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/TSETCAT.lsp b/src/algebra/strap/TSETCAT.lsp index 12fb6a33..acfb9eb0 100644 --- a/src/algebra/strap/TSETCAT.lsp +++ b/src/algebra/strap/TSETCAT.lsp @@ -179,10 +179,10 @@ (|List| |t#4|) (|List| $)) NIL)) . #1=(|TriangularSetCategory|))))) . #1#) - (SETELT #0# 0 - (LIST '|TriangularSetCategory| (|devaluate| |t#1|) - (|devaluate| |t#2|) (|devaluate| |t#3|) - (|devaluate| |t#4|))))))) + (|setShellEntry| #0# 0 + (LIST '|TriangularSetCategory| (|devaluate| |t#1|) + (|devaluate| |t#2|) (|devaluate| |t#3|) + (|devaluate| |t#4|))))))) (DEFUN |TriangularSetCategory| (&REST #0=#:G1451 &AUX #1=#:G1449) (DSETQ #1# #0#) @@ -198,12 +198,3 @@ #1#))) |TriangularSetCategory;AL|)) #2#)))) - -(SETQ |$CategoryFrame| - (|put| '|TriangularSetCategory| '|isCategory| T - (|addModemap| '|TriangularSetCategory| - '(|TriangularSetCategory| |#1| |#2| |#3| |#4|) - '((|Category|) (|IntegralDomain|) - (|OrderedAbelianMonoidSup|) (|OrderedSet|) - (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) - T '|TriangularSetCategory| |$CategoryFrame|))) diff --git a/src/algebra/strap/UFD-.lsp b/src/algebra/strap/UFD-.lsp index 1b71367c..9b2273b3 100644 --- a/src/algebra/strap/UFD-.lsp +++ b/src/algebra/strap/UFD-.lsp @@ -87,24 +87,3 @@ 0 0 0 15 0 6 0 16 1 6 7 0 18 1 9 21 0 22 1 0 0 0 17 1 0 23 0 24))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|UniqueFactorizationDomain&| '|isFunctor| - '(((|squareFreePart| ($ $)) T (ELT $ 17)) - ((|prime?| ((|Boolean|) $)) T (ELT $ 24))) - (|addModemap| '|UniqueFactorizationDomain&| - '(|UniqueFactorizationDomain&| |#1|) - '((CATEGORY |domain| - (SIGNATURE |squareFreePart| (|#1| |#1|)) - (SIGNATURE |prime?| ((|Boolean|) |#1|))) - (|UniqueFactorizationDomain|)) - T '|UniqueFactorizationDomain&| - (|put| '|UniqueFactorizationDomain&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |squareFreePart| - (|#1| |#1|)) - (SIGNATURE |prime?| - ((|Boolean|) |#1|))) - (|UniqueFactorizationDomain|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/UFD.lsp b/src/algebra/strap/UFD.lsp index f92b4bf5..1379c56d 100644 --- a/src/algebra/strap/UFD.lsp +++ b/src/algebra/strap/UFD.lsp @@ -15,7 +15,7 @@ ((|factor| ((|Factored| $) $)) T)) NIL '((|Factored| $) (|Boolean|)) NIL)) |UniqueFactorizationDomain|) - (SETELT #0# 0 '(|UniqueFactorizationDomain|)))))) + (|setShellEntry| #0# 0 '(|UniqueFactorizationDomain|)))))) (DEFUN |UniqueFactorizationDomain| () (LET () @@ -24,10 +24,4 @@ (T (SETQ |UniqueFactorizationDomain;AL| (|UniqueFactorizationDomain;|)))))) -(SETQ |$CategoryFrame| - (|put| '|UniqueFactorizationDomain| '|isCategory| T - (|addModemap| '|UniqueFactorizationDomain| - '(|UniqueFactorizationDomain|) '((|Category|)) T - '|UniqueFactorizationDomain| |$CategoryFrame|))) - (MAKEPROP '|UniqueFactorizationDomain| 'NILADIC T) diff --git a/src/algebra/strap/ULSCAT.lsp b/src/algebra/strap/ULSCAT.lsp index e87c6157..c3b72800 100644 --- a/src/algebra/strap/ULSCAT.lsp +++ b/src/algebra/strap/ULSCAT.lsp @@ -93,9 +93,9 @@ (|:| |c| |t#1|)))) NIL)) . #2=(|UnivariateLaurentSeriesCategory|)))))) . #2#) - (SETELT #0# 0 - (LIST '|UnivariateLaurentSeriesCategory| - (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|UnivariateLaurentSeriesCategory| + (|devaluate| |t#1|))))))) (DEFUN |UnivariateLaurentSeriesCategory| (#0=#:G1400) (LET (#1=#:G1401) @@ -111,10 +111,3 @@ #0#))) |UnivariateLaurentSeriesCategory;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|UnivariateLaurentSeriesCategory| '|isCategory| T - (|addModemap| '|UnivariateLaurentSeriesCategory| - '(|UnivariateLaurentSeriesCategory| |#1|) - '((|Category|) (|Ring|)) T - '|UnivariateLaurentSeriesCategory| |$CategoryFrame|))) diff --git a/src/algebra/strap/UPOLYC-.lsp b/src/algebra/strap/UPOLYC-.lsp index ceef39e9..ddb992a4 100644 --- a/src/algebra/strap/UPOLYC-.lsp +++ b/src/algebra/strap/UPOLYC-.lsp @@ -1402,642 +1402,3 @@ 19 0 14 20 2 0 0 0 12 125 2 0 120 0 0 161 2 0 156 143 0 157 1 0 0 12 51))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|UnivariatePolynomialCategory&| '|isFunctor| - '(((|coerce| ($ $)) T (ELT $ NIL)) - ((|gcdPolynomial| - ((|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 182)) - ((|squareFree| ((|Factored| $) $)) T (ELT $ 173)) - ((|squareFreePart| ($ $)) T (ELT $ 175)) - ((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ NIL)) - ((|init| ($)) T (ELT $ 119)) - ((|nextItem| ((|Union| $ "failed") $)) T (ELT $ 123)) - ((|elt| ((|Fraction| $) $ (|Fraction| $))) T - (ELT $ 169)) - ((|euclideanSize| ((|NonNegativeInteger|) $)) T - (ELT $ 188)) - ((|divide| - ((|Record| (|:| |quotient| $) (|:| |remainder| $)) - $ $)) - T (ELT $ 191)) - ((|integrate| ($ $)) T (ELT $ 197)) - ((|elt| (|#2| (|Fraction| $) |#2|)) T (ELT $ 187)) - ((|separate| - ((|Record| (|:| |primePart| $) - (|:| |commonPart| $)) - $ $)) - T (ELT $ 130)) - ((|pseudoDivide| - ((|Record| (|:| |coef| |#2|) (|:| |quotient| $) - (|:| |remainder| $)) - $ $)) - T (ELT $ 153)) - ((|pseudoQuotient| ($ $ $)) T (ELT $ 151)) - ((|composite| - ((|Union| (|Fraction| $) "failed") (|Fraction| $) - $)) - T (ELT $ 157)) - ((|composite| ((|Union| $ "failed") $ $)) T (ELT $ 161)) - ((|order| ((|NonNegativeInteger|) $ $)) T (ELT $ 170)) - ((|elt| ((|Fraction| $) (|Fraction| $) (|Fraction| $))) - T (ELT $ 147)) - ((|differentiate| ($ $ (|Mapping| |#2| |#2|) $)) T - (ELT $ 134)) - ((|shiftLeft| ($ $ (|NonNegativeInteger|))) T - (ELT $ 73)) - ((|shiftRight| ($ $ (|NonNegativeInteger|))) T - (ELT $ 71)) - ((|karatsubaDivide| - ((|Record| (|:| |quotient| $) (|:| |remainder| $)) - $ (|NonNegativeInteger|))) - T (ELT $ 70)) - ((|unmakeSUP| ($ (|SparseUnivariatePolynomial| |#2|))) T - (ELT $ 67)) - ((|makeSUP| ((|SparseUnivariatePolynomial| |#2|) $)) T - (ELT $ 59)) - ((|vectorise| - ((|Vector| |#2|) $ (|NonNegativeInteger|))) - T (ELT $ 114)) - ((|differentiate| ($ $ (|Mapping| |#2| |#2|))) T - (ELT $ 137)) - ((|differentiate| - ($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|))) - T (ELT $ NIL)) - ((|differentiate| - ($ $ (|List| (|Symbol|)) - (|List| (|NonNegativeInteger|)))) - T (ELT $ NIL)) - ((|differentiate| - ($ $ (|Symbol|) (|NonNegativeInteger|))) - T (ELT $ NIL)) - ((|differentiate| ($ $ (|List| (|Symbol|)))) T - (ELT $ NIL)) - ((|differentiate| ($ $ (|Symbol|))) T (ELT $ NIL)) - ((|differentiate| ($ $)) T (ELT $ 138)) - ((|differentiate| ($ $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|elt| ($ $ $)) T (ELT $ NIL)) - ((|elt| (|#2| $ |#2|)) T (ELT $ NIL)) - ((|factor| ((|Factored| $) $)) T (ELT $ 107)) - ((|squareFreePolynomial| - ((|Factored| (|SparseUnivariatePolynomial| $)) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 185)) - ((|factorPolynomial| - ((|Factored| (|SparseUnivariatePolynomial| $)) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 86)) - ((|factorSquareFreePolynomial| - ((|Factored| (|SparseUnivariatePolynomial| $)) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 88)) - ((|solveLinearPolynomialEquation| - ((|Union| (|List| (|SparseUnivariatePolynomial| $)) - "failed") - (|List| (|SparseUnivariatePolynomial| $)) - (|SparseUnivariatePolynomial| $))) - T (ELT $ 82)) - ((|content| ($ $ (|SingletonAsOrderedSet|))) T - (ELT $ 125)) - ((|variables| ((|List| (|SingletonAsOrderedSet|)) $)) T - (ELT $ 15)) - ((|totalDegree| - ((|NonNegativeInteger|) $ - (|List| (|SingletonAsOrderedSet|)))) - T (ELT $ 18)) - ((|totalDegree| ((|NonNegativeInteger|) $)) T - (ELT $ NIL)) - ((|monomial| - ($ $ (|List| (|SingletonAsOrderedSet|)) - (|List| (|NonNegativeInteger|)))) - T (ELT $ NIL)) - ((|monomial| - ($ $ (|SingletonAsOrderedSet|) - (|NonNegativeInteger|))) - T (ELT $ 47)) - 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((|eval| ($ $ $ $)) T (ELT $ NIL)) - ((|eval| ($ $ (|Equation| $))) T (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| $)))) T (ELT $ 39)) - ((|degree| ((|NonNegativeInteger|) $)) T (ELT $ NIL)) - ((|monomial| ($ |#2| (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|retract| ((|Integer|) $)) T (ELT $ NIL)) - ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T - (ELT $ NIL)) - ((|retract| ((|Fraction| (|Integer|)) $)) T (ELT $ NIL)) - ((|retractIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") $)) - T (ELT $ NIL)) - ((|coerce| ($ |#2|)) T (ELT $ NIL)) - ((|retractIfCan| ((|Union| |#2| "failed") $)) T - (ELT $ 117)) - ((|retract| (|#2| $)) T (ELT $ 115)) - ((|minimumDegree| ((|NonNegativeInteger|) $)) T - (ELT $ NIL)) - ((|content| (|#2| $)) T (ELT $ NIL)) - ((|differentiate| - ($ $ (|List| (|SingletonAsOrderedSet|)) - (|List| (|NonNegativeInteger|)))) - T (ELT $ NIL)) - ((|differentiate| - ($ $ (|SingletonAsOrderedSet|) - (|NonNegativeInteger|))) - T (ELT $ NIL)) - ((|differentiate| - 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(SIGNATURE |makeSUP| - ((|SparseUnivariatePolynomial| |#2|) |#1|)) - (SIGNATURE |vectorise| - ((|Vector| |#2|) |#1| - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|))) - (SIGNATURE |differentiate| (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |elt| (|#1| |#1| |#1|)) - (SIGNATURE |elt| (|#2| |#1| |#2|)) - (SIGNATURE |factor| ((|Factored| |#1|) |#1|)) - (SIGNATURE |squareFreePolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| |#1|)) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |factorPolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| |#1|)) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |factorSquareFreePolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| |#1|)) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |solveLinearPolynomialEquation| - ((|Union| (|List| - (|SparseUnivariatePolynomial| - |#1|)) - "failed") - (|List| (|SparseUnivariatePolynomial| |#1|)) - (|SparseUnivariatePolynomial| |#1|))) - (SIGNATURE |content| - (|#1| |#1| (|SingletonAsOrderedSet|))) - (SIGNATURE |variables| - ((|List| (|SingletonAsOrderedSet|)) |#1|)) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1| - (|List| (|SingletonAsOrderedSet|)))) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |monomial| - (|#1| |#1| - (|List| (|SingletonAsOrderedSet|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |monomial| - (|#1| |#1| (|SingletonAsOrderedSet|) - (|NonNegativeInteger|))) - (SIGNATURE |minimumDegree| - ((|List| (|NonNegativeInteger|)) |#1| - (|List| (|SingletonAsOrderedSet|)))) - (SIGNATURE |minimumDegree| - ((|NonNegativeInteger|) |#1| - (|SingletonAsOrderedSet|))) - (SIGNATURE |mainVariable| - ((|Union| (|SingletonAsOrderedSet|) - "failed") - |#1|)) - (SIGNATURE |degree| - ((|List| (|NonNegativeInteger|)) |#1| - (|List| (|SingletonAsOrderedSet|)))) - (SIGNATURE |degree| - ((|NonNegativeInteger|) |#1| - (|SingletonAsOrderedSet|))) - (SIGNATURE |retract| - ((|SingletonAsOrderedSet|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|SingletonAsOrderedSet|) - "failed") - |#1|)) - (SIGNATURE |coerce| - (|#1| (|SingletonAsOrderedSet|))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|SingletonAsOrderedSet|)) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|SingletonAsOrderedSet|) |#1|)) - (SIGNATURE |eval| - (|#1| |#1| - (|List| - (|SingletonAsOrderedSet|)) - (|List| |#2|))) - (SIGNATURE |eval| - (|#1| |#1| (|SingletonAsOrderedSet|) |#2|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#1|) (|List| |#1|))) - (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) - (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| (|List| (|Equation| |#1|)))) - (SIGNATURE |degree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |monomial| - (|#1| |#2| (|NonNegativeInteger|))) - (SIGNATURE |retract| ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") |#1|)) - (SIGNATURE |retract| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Fraction| (|Integer|)) "failed") - |#1|)) - (SIGNATURE |coerce| (|#1| |#2|)) - (SIGNATURE |retractIfCan| - ((|Union| |#2| "failed") |#1|)) - (SIGNATURE |retract| (|#2| |#1|)) - (SIGNATURE |minimumDegree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |content| (|#2| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| - (|List| (|SingletonAsOrderedSet|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|SingletonAsOrderedSet|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| - (|List| (|SingletonAsOrderedSet|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|SingletonAsOrderedSet|))) - (SIGNATURE |coerce| (|#1| (|Integer|))) - (SIGNATURE |coerce| ((|OutputForm|) |#1|))) - (|UnivariatePolynomialCategory| |#2|) (|Ring|)) - T '|UnivariatePolynomialCategory&| - (|put| '|UnivariatePolynomialCategory&| '|mode| - '(|Mapping| - (CATEGORY |domain| - (SIGNATURE |coerce| (|#1| |#1|)) - (SIGNATURE |gcdPolynomial| - ((|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE |squareFree| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |squareFreePart| - (|#1| |#1|)) - (SIGNATURE |coerce| - (|#1| (|Fraction| (|Integer|)))) - (SIGNATURE |init| (|#1|)) - (SIGNATURE |nextItem| - ((|Union| |#1| "failed") |#1|)) - (SIGNATURE |elt| - ((|Fraction| |#1|) |#1| - (|Fraction| |#1|))) - (SIGNATURE |euclideanSize| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |divide| - ((|Record| (|:| |quotient| |#1|) - (|:| |remainder| |#1|)) - |#1| |#1|)) - (SIGNATURE |integrate| (|#1| |#1|)) - (SIGNATURE |elt| - (|#2| (|Fraction| |#1|) |#2|)) - (SIGNATURE |separate| - ((|Record| (|:| |primePart| |#1|) - (|:| |commonPart| |#1|)) - |#1| |#1|)) - (SIGNATURE |pseudoDivide| - ((|Record| (|:| |coef| |#2|) - (|:| |quotient| |#1|) - (|:| |remainder| |#1|)) - |#1| |#1|)) - (SIGNATURE |pseudoQuotient| - (|#1| |#1| |#1|)) - (SIGNATURE |composite| - ((|Union| (|Fraction| |#1|) - "failed") - (|Fraction| |#1|) |#1|)) - (SIGNATURE |composite| - ((|Union| |#1| "failed") |#1| - |#1|)) - (SIGNATURE |order| - ((|NonNegativeInteger|) |#1| |#1|)) - (SIGNATURE |elt| - ((|Fraction| |#1|) - (|Fraction| |#1|) - (|Fraction| |#1|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|) - |#1|)) - (SIGNATURE |shiftLeft| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |shiftRight| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |karatsubaDivide| - ((|Record| (|:| |quotient| |#1|) - (|:| |remainder| |#1|)) - |#1| (|NonNegativeInteger|))) - (SIGNATURE |unmakeSUP| - (|#1| - (|SparseUnivariatePolynomial| - |#2|))) - (SIGNATURE |makeSUP| - ((|SparseUnivariatePolynomial| - |#2|) - |#1|)) - (SIGNATURE |vectorise| - ((|Vector| |#2|) |#1| - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Mapping| |#2| |#2|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| (|List| (|Symbol|)))) - (SIGNATURE |differentiate| - (|#1| |#1| (|Symbol|))) - (SIGNATURE |differentiate| - (|#1| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |elt| (|#1| |#1| |#1|)) - (SIGNATURE |elt| (|#2| |#1| |#2|)) - (SIGNATURE |factor| - ((|Factored| |#1|) |#1|)) - (SIGNATURE |squareFreePolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| - |#1|)) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE |factorPolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| - |#1|)) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE - |factorSquareFreePolynomial| - ((|Factored| - (|SparseUnivariatePolynomial| - |#1|)) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE - |solveLinearPolynomialEquation| - ((|Union| - (|List| - (|SparseUnivariatePolynomial| - |#1|)) - "failed") - (|List| - (|SparseUnivariatePolynomial| - |#1|)) - (|SparseUnivariatePolynomial| - |#1|))) - (SIGNATURE |content| - (|#1| |#1| - (|SingletonAsOrderedSet|))) - (SIGNATURE |variables| - ((|List| - (|SingletonAsOrderedSet|)) - |#1|)) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1| - (|List| - (|SingletonAsOrderedSet|)))) - (SIGNATURE |totalDegree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |monomial| - (|#1| |#1| - (|List| - (|SingletonAsOrderedSet|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |monomial| - (|#1| |#1| - (|SingletonAsOrderedSet|) - (|NonNegativeInteger|))) - (SIGNATURE |minimumDegree| - ((|List| (|NonNegativeInteger|)) - |#1| - (|List| - (|SingletonAsOrderedSet|)))) - (SIGNATURE |minimumDegree| - ((|NonNegativeInteger|) |#1| - (|SingletonAsOrderedSet|))) - (SIGNATURE |mainVariable| - ((|Union| - (|SingletonAsOrderedSet|) - "failed") - |#1|)) - (SIGNATURE |degree| - ((|List| (|NonNegativeInteger|)) - |#1| - (|List| - (|SingletonAsOrderedSet|)))) - (SIGNATURE |degree| - ((|NonNegativeInteger|) |#1| - (|SingletonAsOrderedSet|))) - (SIGNATURE |retract| - ((|SingletonAsOrderedSet|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| - (|SingletonAsOrderedSet|) - "failed") - |#1|)) - (SIGNATURE |coerce| - (|#1| (|SingletonAsOrderedSet|))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| - (|SingletonAsOrderedSet|)) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| - (|SingletonAsOrderedSet|) |#1|)) - (SIGNATURE |eval| - (|#1| |#1| - (|List| - (|SingletonAsOrderedSet|)) - (|List| |#2|))) - (SIGNATURE |eval| - (|#1| |#1| - (|SingletonAsOrderedSet|) |#2|)) - (SIGNATURE |eval| - (|#1| |#1| (|List| |#1|) - (|List| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| |#1| |#1|)) - (SIGNATURE |eval| - (|#1| |#1| (|Equation| |#1|))) - (SIGNATURE |eval| - (|#1| |#1| - (|List| (|Equation| |#1|)))) - (SIGNATURE |degree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |monomial| - (|#1| |#2| (|NonNegativeInteger|))) - (SIGNATURE |retract| - ((|Integer|) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Integer|) "failed") - |#1|)) - (SIGNATURE |retract| - ((|Fraction| (|Integer|)) |#1|)) - (SIGNATURE |retractIfCan| - ((|Union| (|Fraction| (|Integer|)) - "failed") - |#1|)) - (SIGNATURE |coerce| (|#1| |#2|)) - (SIGNATURE |retractIfCan| - ((|Union| |#2| "failed") |#1|)) - (SIGNATURE |retract| (|#2| |#1|)) - (SIGNATURE |minimumDegree| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |content| (|#2| |#1|)) - (SIGNATURE |differentiate| - (|#1| |#1| - (|List| - (|SingletonAsOrderedSet|)) - (|List| (|NonNegativeInteger|)))) - (SIGNATURE |differentiate| - (|#1| |#1| - (|SingletonAsOrderedSet|) - (|NonNegativeInteger|))) - (SIGNATURE |differentiate| - (|#1| |#1| - (|List| - (|SingletonAsOrderedSet|)))) - (SIGNATURE |differentiate| - (|#1| |#1| - (|SingletonAsOrderedSet|))) - (SIGNATURE |coerce| - (|#1| (|Integer|))) - (SIGNATURE |coerce| - ((|OutputForm|) |#1|))) - (|UnivariatePolynomialCategory| |#2|) - (|Ring|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/UPOLYC.lsp b/src/algebra/strap/UPOLYC.lsp index a84a5c3a..1a1726c7 100644 --- a/src/algebra/strap/UPOLYC.lsp +++ b/src/algebra/strap/UPOLYC.lsp @@ -138,9 +138,8 @@ (|Vector| |t#1|)) NIL)) . #3=(|UnivariatePolynomialCategory|)))))) . #3#) - (SETELT #0# 0 - (LIST '|UnivariatePolynomialCategory| - (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|UnivariatePolynomialCategory| (|devaluate| |t#1|))))))) (DEFUN |UnivariatePolynomialCategory| (#0=#:G1436) (LET (#1=#:G1437) @@ -156,10 +155,3 @@ #0#))) |UnivariatePolynomialCategory;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|UnivariatePolynomialCategory| '|isCategory| T - (|addModemap| '|UnivariatePolynomialCategory| - '(|UnivariatePolynomialCategory| |#1|) - '((|Category|) (|Ring|)) T - '|UnivariatePolynomialCategory| |$CategoryFrame|))) diff --git a/src/algebra/strap/URAGG-.lsp b/src/algebra/strap/URAGG-.lsp index 9fb56330..c5870cbe 100644 --- a/src/algebra/strap/URAGG-.lsp +++ b/src/algebra/strap/URAGG-.lsp @@ -770,170 +770,3 @@ 1 0 30 0 41 1 0 0 0 40 2 0 0 0 0 58 1 0 25 0 27 2 0 19 0 0 48 1 0 30 0 35))))) '|lookupComplete|)) - -(SETQ |$CategoryFrame| - (|put| '|UnaryRecursiveAggregate&| '|isFunctor| - '(((|split!| ($ $ (|Integer|))) T (ELT $ 64)) - ((|setelt| (|#2| $ "last" |#2|)) T (ELT $ 54)) - ((|setlast!| (|#2| $ |#2|)) T (ELT $ 59)) - ((|setelt| ($ $ "rest" $)) T (ELT $ 56)) - ((|setelt| (|#2| $ "first" |#2|)) T (ELT $ 52)) - ((|cycleSplit!| ($ $)) T (ELT $ 65)) - ((|cycleTail| ($ $)) T (ELT $ 39)) - ((|cycleLength| ((|NonNegativeInteger|) $)) T - (ELT $ 41)) - ((|cycleEntry| ($ $)) T (ELT $ 40)) - ((|third| (|#2| $)) T (ELT $ 18)) - ((|second| (|#2| $)) T (ELT $ 17)) - ((|tail| ($ $)) T (ELT $ 36)) - ((|last| ($ $ (|NonNegativeInteger|))) T (ELT $ 46)) - ((|elt| (|#2| $ "last")) T (ELT $ 13)) - ((|last| (|#2| $)) T (ELT $ 24)) - ((|rest| ($ $ (|NonNegativeInteger|))) T (ELT $ 42)) - ((|elt| ($ $ "rest")) T (ELT $ 16)) - ((|rest| ($ $)) T (ELT $ NIL)) - ((|elt| (|#2| $ "first")) T (ELT $ 10)) - ((|concat| ($ |#2| $)) T (ELT $ NIL)) - ((|concat| ($ $ $)) T (ELT $ 58)) - ((|setvalue!| (|#2| $ |#2|)) T (ELT $ 61)) - ((|setelt| (|#2| $ "value" |#2|)) T (ELT $ NIL)) - ((|setchildren!| ($ $ (|List| $))) T (ELT $ 60)) - ((|node?| ((|Boolean|) $ $)) T (ELT $ 50)) - ((|cyclic?| ((|Boolean|) $)) T (ELT $ 22)) - ((|elt| (|#2| $ "value")) T (ELT $ NIL)) - ((|value| (|#2| $)) T (ELT $ 29)) - ((|leaf?| ((|Boolean|) $)) T (ELT $ 28)) - ((|nodes| ((|List| $) $)) T (ELT $ 26)) - ((|children| ((|List| $) $)) T (ELT $ 27)) - ((= ((|Boolean|) $ $)) T (ELT $ 48)) - ((|#| ((|NonNegativeInteger|) $)) T (ELT $ 35)) - ((|size?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ 33)) - ((|more?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ 32)) - ((|less?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ 31))) - (|addModemap| '|UnaryRecursiveAggregate&| - '(|UnaryRecursiveAggregate&| |#1| |#2|) - '((CATEGORY |domain| - (SIGNATURE |split!| (|#1| |#1| (|Integer|))) - (SIGNATURE |setelt| (|#2| |#1| "last" |#2|)) - (SIGNATURE |setlast!| (|#2| |#1| |#2|)) - (SIGNATURE |setelt| (|#1| |#1| "rest" |#1|)) - (SIGNATURE |setelt| (|#2| |#1| "first" |#2|)) - (SIGNATURE |cycleSplit!| (|#1| |#1|)) - (SIGNATURE |cycleTail| (|#1| |#1|)) - (SIGNATURE |cycleLength| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |cycleEntry| (|#1| |#1|)) - (SIGNATURE |third| (|#2| |#1|)) - (SIGNATURE |second| (|#2| |#1|)) - (SIGNATURE |tail| (|#1| |#1|)) - (SIGNATURE |last| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |elt| (|#2| |#1| "last")) - (SIGNATURE |last| (|#2| |#1|)) - (SIGNATURE |rest| - (|#1| |#1| (|NonNegativeInteger|))) - (SIGNATURE |elt| (|#1| |#1| "rest")) - (SIGNATURE |rest| (|#1| |#1|)) - (SIGNATURE |elt| (|#2| |#1| "first")) - (SIGNATURE |concat| (|#1| |#2| |#1|)) - (SIGNATURE |concat| (|#1| |#1| |#1|)) - (SIGNATURE |setvalue!| (|#2| |#1| |#2|)) - (SIGNATURE |setelt| (|#2| |#1| "value" |#2|)) - (SIGNATURE |setchildren!| - (|#1| |#1| (|List| |#1|))) - (SIGNATURE |node?| ((|Boolean|) |#1| |#1|)) - (SIGNATURE |cyclic?| ((|Boolean|) |#1|)) - (SIGNATURE |elt| (|#2| |#1| "value")) - (SIGNATURE |value| (|#2| |#1|)) - (SIGNATURE |leaf?| ((|Boolean|) |#1|)) - (SIGNATURE |nodes| ((|List| |#1|) |#1|)) - (SIGNATURE |children| ((|List| |#1|) |#1|)) - (SIGNATURE = ((|Boolean|) |#1| |#1|)) - (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |size?| - ((|Boolean|) |#1| (|NonNegativeInteger|))) - (SIGNATURE |more?| - ((|Boolean|) |#1| (|NonNegativeInteger|))) - (SIGNATURE |less?| - ((|Boolean|) |#1| (|NonNegativeInteger|)))) - (|UnaryRecursiveAggregate| |#2|) (|Type|)) - T '|UnaryRecursiveAggregate&| - (|put| '|UnaryRecursiveAggregate&| '|mode| - '(|Mapping| (CATEGORY |domain| - (SIGNATURE |split!| - (|#1| |#1| (|Integer|))) - (SIGNATURE |setelt| - (|#2| |#1| "last" |#2|)) - (SIGNATURE |setlast!| - (|#2| |#1| |#2|)) - (SIGNATURE |setelt| - (|#1| |#1| "rest" |#1|)) - (SIGNATURE |setelt| - (|#2| |#1| "first" |#2|)) - (SIGNATURE |cycleSplit!| - (|#1| |#1|)) - (SIGNATURE |cycleTail| - (|#1| |#1|)) - (SIGNATURE |cycleLength| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |cycleEntry| - (|#1| |#1|)) - (SIGNATURE |third| (|#2| |#1|)) - (SIGNATURE |second| (|#2| |#1|)) - (SIGNATURE |tail| (|#1| |#1|)) - (SIGNATURE |last| - (|#1| |#1| - (|NonNegativeInteger|))) - (SIGNATURE |elt| - (|#2| |#1| "last")) - (SIGNATURE |last| (|#2| |#1|)) - (SIGNATURE |rest| - (|#1| |#1| - (|NonNegativeInteger|))) - (SIGNATURE |elt| - (|#1| |#1| "rest")) - (SIGNATURE |rest| (|#1| |#1|)) - (SIGNATURE |elt| - (|#2| |#1| "first")) - (SIGNATURE |concat| - (|#1| |#2| |#1|)) - (SIGNATURE |concat| - (|#1| |#1| |#1|)) - (SIGNATURE |setvalue!| - (|#2| |#1| |#2|)) - (SIGNATURE |setelt| - (|#2| |#1| "value" |#2|)) - (SIGNATURE |setchildren!| - (|#1| |#1| (|List| |#1|))) - (SIGNATURE |node?| - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |cyclic?| - ((|Boolean|) |#1|)) - (SIGNATURE |elt| - (|#2| |#1| "value")) - (SIGNATURE |value| (|#2| |#1|)) - (SIGNATURE |leaf?| - ((|Boolean|) |#1|)) - (SIGNATURE |nodes| - ((|List| |#1|) |#1|)) - (SIGNATURE |children| - ((|List| |#1|) |#1|)) - (SIGNATURE = - ((|Boolean|) |#1| |#1|)) - (SIGNATURE |#| - ((|NonNegativeInteger|) |#1|)) - (SIGNATURE |size?| - ((|Boolean|) |#1| - (|NonNegativeInteger|))) - (SIGNATURE |more?| - ((|Boolean|) |#1| - (|NonNegativeInteger|))) - (SIGNATURE |less?| - ((|Boolean|) |#1| - (|NonNegativeInteger|)))) - (|UnaryRecursiveAggregate| |#2|) - (|Type|)) - |$CategoryFrame|)))) diff --git a/src/algebra/strap/URAGG.lsp b/src/algebra/strap/URAGG.lsp index 9cd5bea8..acc123db 100644 --- a/src/algebra/strap/URAGG.lsp +++ b/src/algebra/strap/URAGG.lsp @@ -96,8 +96,8 @@ (|NonNegativeInteger|)) NIL)) . #1=(|UnaryRecursiveAggregate|))))) . #1#) - (SETELT #0# 0 - (LIST '|UnaryRecursiveAggregate| (|devaluate| |t#1|))))))) + (|setShellEntry| #0# 0 + (LIST '|UnaryRecursiveAggregate| (|devaluate| |t#1|))))))) (DEFUN |UnaryRecursiveAggregate| (#0=#:G1426) (LET (#1=#:G1427) @@ -111,10 +111,3 @@ (|UnaryRecursiveAggregate;| #0#))) |UnaryRecursiveAggregate;AL|)) #1#)))) - -(SETQ |$CategoryFrame| - (|put| '|UnaryRecursiveAggregate| '|isCategory| T - (|addModemap| '|UnaryRecursiveAggregate| - '(|UnaryRecursiveAggregate| |#1|) - '((|Category|) (|Type|)) T '|UnaryRecursiveAggregate| - |$CategoryFrame|))) diff --git a/src/algebra/strap/VECTOR.lsp b/src/algebra/strap/VECTOR.lsp index 3fb2fb67..61c9ca51 100644 --- a/src/algebra/strap/VECTOR.lsp +++ b/src/algebra/strap/VECTOR.lsp @@ -137,216 +137,3 @@ 13 0 19 1 0 0 7 9 1 0 7 0 15 1 3 13 0 19 1 0 0 7 8))))) '|lookupIncomplete|)) - -(SETQ |$CategoryFrame| - (|put| '|Vector| '|isFunctor| - '(((~= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((= ((|Boolean|) $ $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|coerce| ((|OutputForm|) $)) - (|has| |#1| (|CoercibleTo| (|OutputForm|))) - (ELT $ NIL)) - ((|hash| ((|SingleInteger|) $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|latex| ((|String|) $)) (|has| |#1| (|SetCategory|)) - (ELT $ NIL)) - ((|vector| ($ (|List| |#1|))) T (ELT $ 9)) - ((|magnitude| (|#1| $)) - (AND (|has| |#1| (|RadicalCategory|)) - (|has| |#1| (|Ring|))) - (ELT $ NIL)) - ((|length| (|#1| $)) - (AND (|has| |#1| (|RadicalCategory|)) - (|has| |#1| (|Ring|))) - (ELT $ NIL)) - ((|cross| ($ $ $)) (|has| |#1| (|Ring|)) (ELT $ NIL)) - ((|outerProduct| ((|Matrix| |#1|) $ $)) - (|has| |#1| (|Ring|)) (ELT $ NIL)) - ((|dot| (|#1| $ $)) (|has| |#1| (|Ring|)) (ELT $ NIL)) - ((* ($ $ |#1|)) (|has| |#1| (|Monoid|)) (ELT $ NIL)) - ((* ($ |#1| $)) (|has| |#1| (|Monoid|)) (ELT $ NIL)) - ((* ($ (|Integer|) $)) (|has| |#1| (|AbelianGroup|)) - (ELT $ NIL)) - ((- ($ $ $)) (|has| |#1| (|AbelianGroup|)) (ELT $ NIL)) - ((- ($ $)) (|has| |#1| (|AbelianGroup|)) (ELT $ NIL)) - ((|zero| ($ (|NonNegativeInteger|))) - (|has| |#1| (|AbelianMonoid|)) (ELT $ NIL)) - ((+ ($ $ $)) (|has| |#1| (|AbelianSemiGroup|)) - (ELT $ NIL)) - ((< ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((> ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((>= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((<= ((|Boolean|) $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|max| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|min| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|sort!| ($ $)) - (AND (|has| $ (ATTRIBUTE |shallowlyMutable|)) - (|has| |#1| (|OrderedSet|))) - (ELT $ NIL)) - ((|sort!| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|reverse!| ($ $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|copyInto!| ($ $ $ (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|sorted?| ((|Boolean|) $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|sort| ($ $)) (|has| |#1| (|OrderedSet|)) (ELT $ NIL)) - ((|merge| ($ $ $)) (|has| |#1| (|OrderedSet|)) - (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $ (|Integer|))) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|position| ((|Integer|) |#1| $)) - (|has| |#1| (|SetCategory|)) (ELT $ NIL)) - ((|position| - ((|Integer|) (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|sorted?| - ((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $)) - T (ELT $ NIL)) - ((|sort| ($ (|Mapping| (|Boolean|) |#1| |#1|) $)) T - (ELT $ NIL)) - ((|reverse| ($ $)) T (ELT $ NIL)) - ((|merge| ($ (|Mapping| (|Boolean|) |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|setelt| - (|#1| $ (|UniversalSegment| (|Integer|)) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|insert| ($ $ $ (|Integer|))) T (ELT $ NIL)) - ((|insert| ($ |#1| $ (|Integer|))) T (ELT $ NIL)) - ((|delete| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|delete| ($ $ (|Integer|))) T (ELT $ NIL)) - ((|elt| ($ $ (|UniversalSegment| (|Integer|)))) T - (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1| |#1|) $ $)) T - (ELT $ NIL)) - ((|concat| ($ (|List| $))) T (ELT $ NIL)) - ((|concat| ($ $ $)) T (ELT $ NIL)) - ((|concat| ($ |#1| $)) T (ELT $ NIL)) - ((|concat| ($ $ |#1|)) T (ELT $ NIL)) - ((|new| ($ (|NonNegativeInteger|) |#1|)) T (ELT $ NIL)) - ((|construct| ($ (|List| |#1|))) T (ELT $ 8)) - ((|find| ((|Union| |#1| "failed") - (|Mapping| (|Boolean|) |#1|) $)) - T (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|remove| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|select| ($ (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|reduce| - (|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|remove| ($ |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|removeDuplicates| ($ $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|convert| ((|InputForm|) $)) - (|has| |#1| (|ConvertibleTo| (|InputForm|))) - (ELT $ 19)) - ((|swap!| ((|Void|) $ (|Integer|) (|Integer|))) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|fill!| ($ $ |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|first| (|#1| $)) (|has| (|Integer|) (|OrderedSet|)) - (ELT $ NIL)) - ((|minIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ NIL)) - ((|maxIndex| ((|Integer|) $)) - (|has| (|Integer|) (|OrderedSet|)) (ELT $ NIL)) - ((|entry?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|indices| ((|List| (|Integer|)) $)) T (ELT $ NIL)) - ((|index?| ((|Boolean|) (|Integer|) $)) T (ELT $ NIL)) - ((|entries| ((|List| |#1|) $)) T (ELT $ NIL)) - ((|elt| (|#1| $ (|Integer|))) T (ELT $ NIL)) - ((|elt| (|#1| $ (|Integer|) |#1|)) T (ELT $ NIL)) - ((|qelt| (|#1| $ (|Integer|))) T (ELT $ NIL)) - ((|setelt| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|qsetelt!| (|#1| $ (|Integer|) |#1|)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|eval| ($ $ (|List| |#1|) (|List| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ |#1| |#1|)) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|Equation| |#1|))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|eval| ($ $ (|List| (|Equation| |#1|)))) - (AND (|has| |#1| (|Evalable| |#1|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|member?| ((|Boolean|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|count| ((|NonNegativeInteger|) |#1| $)) - (AND (|has| $ (ATTRIBUTE |finiteAggregate|)) - (|has| |#1| (|SetCategory|))) - (ELT $ NIL)) - ((|members| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|parts| ((|List| |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ 15)) - ((|count| ((|NonNegativeInteger|) - (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|every?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|any?| ((|Boolean|) (|Mapping| (|Boolean|) |#1|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|map!| ($ (|Mapping| |#1| |#1|) $)) - (|has| $ (ATTRIBUTE |shallowlyMutable|)) (ELT $ NIL)) - ((|map| ($ (|Mapping| |#1| |#1|) $)) T (ELT $ NIL)) - ((|#| ((|NonNegativeInteger|) $)) - (|has| $ (ATTRIBUTE |finiteAggregate|)) (ELT $ NIL)) - ((|sample| ($)) T (CONST $ NIL)) - ((|size?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|more?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|less?| ((|Boolean|) $ (|NonNegativeInteger|))) T - (ELT $ NIL)) - ((|empty?| ((|Boolean|) $)) T (ELT $ NIL)) - ((|empty| ($)) T (ELT $ NIL)) - ((|copy| ($ $)) T (ELT $ NIL)) - ((|eq?| ((|Boolean|) $ $)) T (ELT $ NIL))) - (|addModemap| '|Vector| '(|Vector| |#1|) - '((|Join| (|VectorCategory| |#1|) - (CATEGORY |domain| - (SIGNATURE |vector| ($ (|List| |#1|))))) - (|Type|)) - T '|Vector| - (|put| '|Vector| '|mode| - '(|Mapping| - (|Join| (|VectorCategory| |#1|) - (CATEGORY |domain| - (SIGNATURE |vector| - ($ (|List| |#1|))))) - (|Type|)) - |$CategoryFrame|)))) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 7c898d9e..6f5bdb8e 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2271415 . 3433818805) +(2272406 . 3436147953) (-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."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . 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}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4363 . T) (-4361 . T) (-4360 . T) ((-4368 "*") . T) (-4359 . T) (-4364 . T) (-4358 . T) (-2997 . T)) +((-4365 . T) (-4363 . T) (-4362 . T) ((-4370 "*") . T) (-4361 . T) (-4366 . T) (-4360 . T) (-4283 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,17 +56,17 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1935) +(-32 R -3220) ((|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 -1017) (QUOTE (-552))))) +((|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4366))) +((|HasAttribute| |#1| (QUOTE -4368))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2997 . T)) +((-4283 . T)) NIL (-35) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -82,20 +82,20 @@ NIL NIL (-38 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."))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1935 UP UPUP -3484) +(-40 -3220 UP UPUP -3714) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4359 |has| (-401 |#2|) (-357)) (-4364 |has| (-401 |#2|) (-357)) (-4358 |has| (-401 |#2|) (-357)) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-1559 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-1559 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-1559 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-1559 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) -(-41 R -1935) +((-4361 |has| (-401 |#2|) (-357)) (-4366 |has| (-401 |#2|) (-357)) (-4360 |has| (-401 |#2|) (-357)) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-4029 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-4029 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-4029 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-4029 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) +(-41 R -3220) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -424) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -424) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-301)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4363 |has| |#1| (-544)) (-4361 . T) (-4360 . T)) +((-4365 |has| |#1| (-544)) (-4363 . T) (-4362 . T)) ((|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) -((-4366 . T) (-4367 . T)) -((-1559 (-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-830))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|))))))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-830))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-830))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-4029 (-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-832))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|))))))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-832))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-832))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-357)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| $ (QUOTE (-1028))) (|HasCategory| $ (LIST (QUOTE -1017) (QUOTE (-552))))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| $ (QUOTE (-1030))) (|HasCategory| $ (LIST (QUOTE -1019) (QUOTE (-552))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4363 . T)) +((-4365 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1935) +(-54 |Base| R -3220) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -154,7 +154,7 @@ NIL NIL (-56 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL (-57 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),{}...]}."))) @@ -162,65 +162,65 @@ NIL NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-59 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-60 -3112) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-60 -4290) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-61 -3112) +(-61 -4290) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-62 -3112) +(-62 -4290) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -3112) +(-63 -4290) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-64 -3112) +(-64 -4290) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -3112) +(-65 -4290) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-66 -3112) +(-66 -4290) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -3112) +(-67 -4290) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -3112) +(-68 -4290) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-69 -3112) +(-69 -4290) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-70 -3112) +(-70 -4290) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-71 -3112) +(-71 -4290) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-72 -3112) +(-72 -4290) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-73 -3112) +(-73 -4290) ((|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 @@ -232,55 +232,55 @@ 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 -(-76 -3112) +(-76 -4290) ((|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 -(-77 -3112) +(-77 -4290) ((|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 -(-78 -3112) +(-78 -4290) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -3112) +(-79 -4290) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3112) +(-80 -4290) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3112) +(-81 -4290) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -3112) +(-82 -4290) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3112) +(-83 -4290) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3112) +(-84 -4290) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3112) +(-85 -4290) ((|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 -(-86 -3112) +(-86 -4290) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3112) +(-87 -4290) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -3112) +(-88 -4290) ((|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 @@ -290,14 +290,14 @@ NIL ((|HasCategory| |#1| (QUOTE (-357)))) (-90 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-91 S) -((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) +((|constructor| (NIL "This is the category of Spad abstract syntax trees.")) (|coerce| (($ (|Syntax|)) "\\spad{coerce(s)} parses syntax object \\spad{`s'} as a Spad construct."))) NIL NIL (-92) -((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) +((|constructor| (NIL "This is the category of Spad abstract syntax trees.")) (|coerce| (($ (|Syntax|)) "\\spad{coerce(s)} parses syntax object \\spad{`s'} as a Spad construct."))) NIL NIL (-93 S) @@ -314,15 +314,15 @@ NIL NIL (-96) ((|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\"."))) -((-4366 . T)) +((-4368 . T)) NIL (-97) ((|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."))) -((-4366 . T) ((-4368 "*") . T) (-4367 . T) (-4363 . T) (-4361 . T) (-4360 . T) (-4359 . T) (-4364 . T) (-4358 . T) (-4357 . T) (-4356 . T) (-4355 . T) (-4354 . T) (-4362 . T) (-4365 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4353 . T)) +((-4368 . T) ((-4370 "*") . T) (-4369 . T) (-4365 . T) (-4363 . T) (-4362 . T) (-4361 . T) (-4366 . T) (-4360 . T) (-4359 . T) (-4358 . T) (-4357 . T) (-4356 . T) (-4364 . T) (-4367 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4355 . T)) NIL (-98 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}."))) -((-4363 . T)) +((-4365 . T)) NIL (-99 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}."))) @@ -338,15 +338,15 @@ NIL NIL (-102 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-103 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4368 "*")))) +((|HasAttribute| |#1| (QUOTE (-4370 "*")))) (-104) ((|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"))) -((-4366 . T)) +((-4368 . T)) NIL (-105 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."))) @@ -354,23 +354,23 @@ NIL NIL (-106 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4367 . T) (-2997 . T)) +((-4369 . T) (-4283 . T)) NIL (-107) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-552) (QUOTE (-888))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1001))) (|HasCategory| (-552) (QUOTE (-803))) (-1559 (|HasCategory| (-552) (QUOTE (-803))) (|HasCategory| (-552) (QUOTE (-830)))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1127))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1152)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-552) (LIST (QUOTE -623) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (|HasCategory| (-552) (QUOTE (-142))))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-552) (QUOTE (-890))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1003))) (|HasCategory| (-552) (QUOTE (-805))) (-4029 (|HasCategory| (-552) (QUOTE (-805))) (|HasCategory| (-552) (QUOTE (-832)))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1129))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1154)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-552) (LIST (QUOTE -625) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (|HasCategory| (-552) (QUOTE (-142))))) (-108) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-109) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| (-111) (QUOTE (-1076))) (|HasCategory| (-111) (LIST (QUOTE -303) (QUOTE (-111))))) (|HasCategory| (-111) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-111) (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-111) (QUOTE (-1076))) (|HasCategory| (-111) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| (-111) (QUOTE (-1078))) (|HasCategory| (-111) (LIST (QUOTE -303) (QUOTE (-111))))) (|HasCategory| (-111) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-111) (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-111) (QUOTE (-1078))) (|HasCategory| (-111) (LIST (QUOTE -599) (QUOTE (-844))))) (-110 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}"))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) NIL (-111) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -379,30 +379,30 @@ NIL (-112 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) NIL -((|HasCategory| |#1| (QUOTE (-830)))) +((|HasCategory| |#1| (QUOTE (-832)))) (-113) ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-114 -1935 UP) +(-114 -3220 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 (-115 |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}."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-116 |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}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-115 |#1|) (QUOTE (-888))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-144))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-115 |#1|) (QUOTE (-1001))) (|HasCategory| (-115 |#1|) (QUOTE (-803))) (-1559 (|HasCategory| (-115 |#1|) (QUOTE (-803))) (|HasCategory| (-115 |#1|) (QUOTE (-830)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-115 |#1|) (QUOTE (-1127))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| (-115 |#1|) (QUOTE (-228))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -506) (QUOTE (-1152)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -115) (|devaluate| |#1|)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (QUOTE (-301))) (|HasCategory| (-115 |#1|) (QUOTE (-537))) (|HasCategory| (-115 |#1|) (QUOTE (-830))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-888)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-115 |#1|) (QUOTE (-890))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-144))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-115 |#1|) (QUOTE (-1003))) (|HasCategory| (-115 |#1|) (QUOTE (-805))) (-4029 (|HasCategory| (-115 |#1|) (QUOTE (-805))) (|HasCategory| (-115 |#1|) (QUOTE (-832)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-115 |#1|) (QUOTE (-1129))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| (-115 |#1|) (QUOTE (-228))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -506) (QUOTE (-1154)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -115) (|devaluate| |#1|)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (QUOTE (-301))) (|HasCategory| (-115 |#1|) (QUOTE (-537))) (|HasCategory| (-115 |#1|) (QUOTE (-832))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-890)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))))) (-117 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4367))) +((|HasAttribute| |#1| (QUOTE -4369))) (-118 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-2997 . T)) +((-4283 . T)) NIL (-119 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."))) @@ -410,15 +410,15 @@ NIL NIL (-120 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"))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-121 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-122) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL (-123 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -426,20 +426,20 @@ NIL NIL (-124 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-126 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."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-127) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it has it is not as rigid as PrimitiveArray Byte is. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`c'}. The array can then store up to \\spad{`c'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| (-128) (QUOTE (-830))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1076))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128)))))) (-1559 (-12 (|HasCategory| (-128) (QUOTE (-1076))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-128) (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| (-128) (QUOTE (-830))) (|HasCategory| (-128) (QUOTE (-1076)))) (|HasCategory| (-128) (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-128) (QUOTE (-1076))) (-12 (|HasCategory| (-128) (QUOTE (-1076))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| (-128) (QUOTE (-832))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1078))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128)))))) (-4029 (-12 (|HasCategory| (-128) (QUOTE (-1078))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-128) (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| (-128) (QUOTE (-832))) (|HasCategory| (-128) (QUOTE (-1078)))) (|HasCategory| (-128) (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-128) (QUOTE (-1078))) (-12 (|HasCategory| (-128) (QUOTE (-1078))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -599) (QUOTE (-844))))) (-128) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} views \\spad{`c'} a a byte. In particular \\spad{`c'} is supposed to have a numerical value less than 256.") (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -458,13 +458,13 @@ NIL NIL (-132) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4368 "*") . T)) +(((-4370 "*") . T)) NIL -(-133 |minix| -4030 S T$) +(-133 |minix| -2072 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-134 |minix| -4030 R) +(-134 |minix| -2072 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -482,8 +482,8 @@ NIL NIL (-138) ((|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}."))) -((-4366 . T) (-4356 . T) (-4367 . T)) -((-1559 (-12 (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1076))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (QUOTE (-830))) (|HasCategory| (-141) (QUOTE (-1076))) (-12 (|HasCategory| (-141) (QUOTE (-1076))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4358 . T) (-4369 . T)) +((-4029 (-12 (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1078))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (QUOTE (-832))) (|HasCategory| (-141) (QUOTE (-1078))) (-12 (|HasCategory| (-141) (QUOTE (-1078))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-844))))) (-139 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 @@ -498,7 +498,7 @@ NIL NIL (-142) ((|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."))) -((-4363 . T)) +((-4365 . T)) NIL (-143 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}."))) @@ -506,9 +506,9 @@ NIL NIL (-144) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4363 . T)) +((-4365 . T)) NIL -(-145 -1935 UP UPUP) +(-145 -3220 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 @@ -519,14 +519,14 @@ NIL (-147 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 -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasAttribute| |#1| (QUOTE -4366))) +((|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasAttribute| |#1| (QUOTE -4368))) (-148 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."))) -((-2997 . T)) +((-4283 . T)) NIL (-149 |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."))) -((-4361 . T) (-4360 . T) (-4363 . T)) +((-4363 . T) (-4362 . T) (-4365 . T)) NIL (-150) ((|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."))) @@ -548,7 +548,7 @@ 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 -(-155 R -1935) +(-155 R -3220) ((|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 @@ -579,10 +579,10 @@ NIL (-162 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) NIL -((|HasCategory| |#2| (QUOTE (-888))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-981))) (|HasCategory| |#2| (QUOTE (-1174))) (|HasCategory| |#2| (QUOTE (-1037))) (|HasCategory| |#2| (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-357))) (|HasAttribute| |#2| (QUOTE -4362)) (|HasAttribute| |#2| (QUOTE -4365)) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-830)))) +((|HasCategory| |#2| (QUOTE (-890))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-983))) (|HasCategory| |#2| (QUOTE (-1176))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-357))) (|HasAttribute| |#2| (QUOTE -4364)) (|HasAttribute| |#2| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-832)))) (-163 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) -((-4359 -1559 (|has| |#1| (-544)) (-12 (|has| |#1| (-301)) (|has| |#1| (-888)))) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4362 |has| |#1| (-6 -4362)) (-4365 |has| |#1| (-6 -4365)) (-2997 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 -4029 (|has| |#1| (-544)) (-12 (|has| |#1| (-301)) (|has| |#1| (-890)))) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) (-4364 |has| |#1| (-6 -4364)) (-4367 |has| |#1| (-6 -4367)) (-4283 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-164 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."))) @@ -594,8 +594,8 @@ NIL NIL (-166 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4359 -1559 (|has| |#1| (-544)) (-12 (|has| |#1| (-301)) (|has| |#1| (-888)))) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4362 |has| |#1| (-6 -4362)) (-4365 |has| |#1| (-6 -4365)) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . 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(QUOTE -506) (QUOTE (-1154)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-813))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-1176)))) (|HasCategory| |#1| (QUOTE (-537))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-890))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-357)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-228))) (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasAttribute| |#1| (QUOTE -4364)) (|HasAttribute| |#1| (QUOTE -4367)) (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357)))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154))))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-343))))) (-167 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 @@ -606,7 +606,7 @@ NIL NIL (-169) ((|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."))) -(((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-170) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -614,7 +614,7 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4368 "*") . T) (-4359 . T) (-4364 . T) (-4358 . T) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") . T) (-4361 . T) (-4366 . T) (-4360 . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-172) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -631,7 +631,7 @@ NIL (-175 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| (-931 |#2|) (LIST (QUOTE -865) (|devaluate| |#1|)))) +((|HasCategory| (-933 |#2|) (LIST (QUOTE -867) (|devaluate| |#1|)))) (-176 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 @@ -660,7 +660,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|arity| (((|SingleInteger|) $) "\\spad{arity(ctor)} returns the arity of the constructor `ctor'. \\indented{2}{A negative value means that the \\spad{ctor} takes a variable} \\indented{2}{length argument list,{} \\spadignore{e.g.} Mapping,{} Record,{} etc.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'.")) (|name| (((|Identifier|) $) "\\spad{name(ctor)} returns the name of the constructor `ctor'."))) NIL NIL -(-183 R -1935) +(-183 R -3220) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -768,23 +768,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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 -(-210 -1935 UP UPUP R) +(-210 -3220 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 -(-211 -1935 FP) +(-211 -3220 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 (-212) ((|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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-552) (QUOTE (-888))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1001))) (|HasCategory| (-552) (QUOTE (-803))) (-1559 (|HasCategory| (-552) (QUOTE (-803))) (|HasCategory| (-552) (QUOTE (-830)))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1127))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1152)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-552) (LIST (QUOTE -623) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (|HasCategory| (-552) (QUOTE (-142))))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-552) (QUOTE (-890))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1003))) (|HasCategory| (-552) (QUOTE (-805))) (-4029 (|HasCategory| (-552) (QUOTE (-805))) (|HasCategory| (-552) (QUOTE (-832)))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1129))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1154)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-552) (LIST (QUOTE -625) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (|HasCategory| (-552) (QUOTE (-142))))) (-213) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-214 R -1935) +(-214 R -3220) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -798,19 +798,19 @@ NIL NIL (-217 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-218 |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}."))) -((-4363 . T)) +((-4365 . T)) NIL -(-219 R -1935) +(-219 R -3220) ((|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 (-220) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3030 . T) (-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4311 . T) (-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-221) ((|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)}.}"))) @@ -818,23 +818,23 @@ NIL NIL (-222 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}"))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4368 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4370 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-223 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 (-224 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."))) -((-4367 . T) (-2997 . T)) +((-4369 . T) (-4283 . T)) NIL (-225 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 -879) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-228)))) +((|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-228)))) (-226 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}."))) -((-4363 . T)) +((-4365 . T)) NIL (-227 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -842,36 +842,36 @@ NIL NIL (-228) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4363 . T)) +((-4365 . T)) NIL (-229 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4366))) +((|HasAttribute| |#1| (QUOTE -4368))) (-230 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}."))) -((-4367 . T) (-2997 . T)) +((-4369 . T) (-4283 . T)) NIL (-231) ((|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 -(-232 S -4030 R) +(-232 S -2072 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 (-357))) (|HasCategory| |#3| (QUOTE (-776))) (|HasCategory| |#3| (QUOTE (-828))) (|HasAttribute| |#3| (QUOTE -4363)) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-709))) (|HasCategory| |#3| (QUOTE (-129))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1028))) (|HasCategory| |#3| (QUOTE (-1076)))) -(-233 -4030 R) +((|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (QUOTE (-778))) (|HasCategory| |#3| (QUOTE (-830))) (|HasAttribute| |#3| (QUOTE -4365)) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-711))) (|HasCategory| |#3| (QUOTE (-129))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1030))) (|HasCategory| |#3| (QUOTE (-1078)))) +(-233 -2072 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"))) -((-4360 |has| |#2| (-1028)) (-4361 |has| |#2| (-1028)) (-4363 |has| |#2| (-6 -4363)) ((-4368 "*") |has| |#2| (-169)) (-4366 . T) (-2997 . T)) +((-4362 |has| |#2| (-1030)) (-4363 |has| |#2| (-1030)) (-4365 |has| |#2| (-6 -4365)) ((-4370 "*") |has| |#2| (-169)) (-4368 . T) (-4283 . T)) NIL -(-234 -4030 A B) +(-234 -2072 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 -(-235 -4030 R) +(-235 -2072 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."))) -((-4360 |has| |#2| (-1028)) (-4361 |has| |#2| (-1028)) (-4363 |has| |#2| (-6 -4363)) ((-4368 "*") |has| |#2| (-169)) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-129))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-709))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-776))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-828))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 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(|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."))) -((-2997 . T)) +((-4283 . T)) NIL (-240 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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(QUOTE -881) (QUOTE (-1154)))))) (|HasCategory| |#3| (QUOTE (-129))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -599) (QUOTE (-844))))) (-246 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 (-228)))) (-247 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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) NIL (-248 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}."))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL (-249) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -962,8 +962,8 @@ NIL NIL (-258 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"))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-888))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#3| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#3| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#3| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#3| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4364)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-142))))) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-890))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#3| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#3| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#3| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#3| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) (-259 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 @@ -1008,11 +1008,11 @@ 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 -(-270 R -1935) +(-270 R -3220) ((|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 -(-271 R -1935) +(-271 R -3220) ((|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 @@ -1031,10 +1031,10 @@ NIL (-275 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 (-830))) (|HasCategory| |#2| (QUOTE (-1076)))) +((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-1078)))) (-276 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}."))) -((-4367 . T) (-2997 . T)) +((-4369 . T) (-4283 . T)) NIL (-277 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}."))) @@ -1055,18 +1055,18 @@ NIL (-281 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 -4367))) +((|HasAttribute| |#1| (QUOTE -4369))) (-282 |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 -(-283 S R |Mod| -3226 -3759 |exactQuo|) +(-283 S R |Mod| -3098 -1446 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-284) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4359 . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-285) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1082,21 +1082,21 @@ NIL NIL (-288 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."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) (-290) ((|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 -(-291 -1935 S) +(-291 -3220 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-292 E -1935) +(-292 E -3220) ((|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 @@ -1111,7 +1111,7 @@ NIL (-295 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 -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-1028)))) +((|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-1030)))) (-296) ((|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 @@ -1134,7 +1134,7 @@ NIL NIL (-301) ((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-302 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1144,7 +1144,7 @@ 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 -(-304 -1935) +(-304 -3220) ((|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 @@ -1158,8 +1158,8 @@ NIL NIL (-307 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))}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-888))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-1001))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-803))) (-1559 (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-803))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-830)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-1127))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-228))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -506) (QUOTE (-1152)) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -303) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-301))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-537))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-830))) (-12 (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-888))) (|HasCategory| $ (QUOTE (-142)))) (-1559 (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (-12 (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-888))) (|HasCategory| $ (QUOTE (-142)))))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-890))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-1003))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-805))) (-4029 (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-805))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-832)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-1129))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-228))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -506) (QUOTE (-1154)) (LIST (QUOTE -1223) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -303) (LIST (QUOTE -1223) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1223) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1223) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-301))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-537))) (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (-12 (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-890))) (|HasCategory| $ (QUOTE (-142)))) (-4029 (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (-12 (|HasCategory| (-1223 |#1| |#2| |#3| |#4|) (QUOTE (-890))) (|HasCategory| $ (QUOTE (-142)))))) (-308 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1170,9 +1170,9 @@ NIL NIL (-310 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4363 -1559 (-2520 (|has| |#1| (-1028)) (|has| |#1| (-623 (-552)))) (-12 (|has| |#1| (-544)) (-1559 (-2520 (|has| |#1| (-1028)) (|has| |#1| (-623 (-552)))) (|has| |#1| (-1028)) (|has| |#1| (-466)))) (|has| |#1| (-1028)) (|has| |#1| (-466))) (-4361 |has| |#1| (-169)) (-4360 |has| |#1| (-169)) ((-4368 "*") |has| |#1| (-544)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-544)) (-4358 |has| |#1| (-544))) -((-1559 (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-544))) (-1559 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1028)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (-1559 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1088)))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE 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(|HasCategory| |#1| (QUOTE (-1030)))) (-12 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544)))) (-4029 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-544)))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552))))) (-4029 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1090)))) (-4029 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))))) (-4029 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1090)))) (-4029 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))))) (-4029 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1030)))) (-4029 (-12 (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| $ (QUOTE (-1030))) (|HasCategory| $ (LIST (QUOTE -1019) (QUOTE (-552))))) +(-311 R -3220) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1182,8 +1182,8 @@ NIL NIL (-313 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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-552)) (QUOTE (-1088))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-1559 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -1477) (LIST (|devaluate| |#1|) (QUOTE (-1152)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (-1559 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1152))))) (|HasSignature| |#1| (LIST (QUOTE -1853) (LIST (LIST (QUOTE -627) (QUOTE (-1152))) (|devaluate| |#1|))))))) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-552)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -3213) (LIST (|devaluate| |#1|) (QUOTE (-1154)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (-4029 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-1176))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2889) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1154))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -629) (QUOTE (-1154))) (|devaluate| |#1|))))))) (-314 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 @@ -1194,8 +1194,8 @@ NIL NIL (-316 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."))) -((-4361 . T) (-4360 . T)) -((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-775)))) +((-4363 . T) (-4362 . T)) +((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-777)))) (-317 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1203,26 +1203,26 @@ NIL (-318 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-754) (QUOTE (-775)))) +((|HasCategory| (-756) (QUOTE (-777)))) (-319 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL ((|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169)))) (-320 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-321 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."))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-322 S -1935) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-322 S -3220) ((|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 (-362)))) -(-323 -1935) +(-323 -3220) ((|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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-324) ((|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."))) @@ -1240,54 +1240,54 @@ 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 -(-328 S -1935 UP UPUP R) +(-328 S -3220 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 -(-329 -1935 UP UPUP R) +(-329 -3220 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 -(-330 -1935 UP UPUP R) +(-330 -3220 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-331 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -506) (QUOTE (-1152)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -506) (QUOTE (-1154)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|) (|devaluate| |#2|)))) (-332 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-333 |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.}"))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#3| (LIST (QUOTE -1017) (QUOTE (-373)))) (|HasCategory| $ (QUOTE (-1028))) (|HasCategory| $ (LIST (QUOTE -1017) (QUOTE (-552))))) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#3| (LIST (QUOTE -1019) (QUOTE (-373)))) (|HasCategory| $ (QUOTE (-1030))) (|HasCategory| $ (LIST (QUOTE -1019) (QUOTE (-552))))) (-334 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 -(-335 S -1935 UP UPUP) +(-335 S -3220 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-357)))) -(-336 -1935 UP UPUP) +(-336 -3220 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4359 |has| (-401 |#2|) (-357)) (-4364 |has| (-401 |#2|) (-357)) (-4358 |has| (-401 |#2|) (-357)) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 |has| (-401 |#2|) (-357)) (-4366 |has| (-401 |#2|) (-357)) (-4360 |has| (-401 |#2|) (-357)) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-337 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| (-889 |#1|) (QUOTE (-142))) (|HasCategory| (-889 |#1|) (QUOTE (-362)))) (|HasCategory| (-889 |#1|) (QUOTE (-144))) (|HasCategory| (-889 |#1|) (QUOTE (-362))) (|HasCategory| (-889 |#1|) (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| (-891 |#1|) (QUOTE (-142))) (|HasCategory| (-891 |#1|) (QUOTE (-362)))) (|HasCategory| (-891 |#1|) (QUOTE (-144))) (|HasCategory| (-891 |#1|) (QUOTE (-362))) (|HasCategory| (-891 |#1|) (QUOTE (-142)))) (-338 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-339 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-340 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1302,33 +1302,33 @@ NIL NIL (-343) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-344 R UP -1935) +(-344 R UP -3220) ((|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 (-345 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| (-889 |#1|) (QUOTE (-142))) (|HasCategory| (-889 |#1|) (QUOTE (-362)))) (|HasCategory| (-889 |#1|) (QUOTE (-144))) (|HasCategory| (-889 |#1|) (QUOTE (-362))) (|HasCategory| (-889 |#1|) (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| (-891 |#1|) (QUOTE (-142))) (|HasCategory| (-891 |#1|) (QUOTE (-362)))) (|HasCategory| (-891 |#1|) (QUOTE (-144))) (|HasCategory| (-891 |#1|) (QUOTE (-362))) (|HasCategory| (-891 |#1|) (QUOTE (-142)))) (-346 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-347 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-348 |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}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| (-889 |#1|) (QUOTE (-142))) (|HasCategory| (-889 |#1|) (QUOTE (-362)))) (|HasCategory| (-889 |#1|) (QUOTE (-144))) (|HasCategory| (-889 |#1|) (QUOTE (-362))) (|HasCategory| (-889 |#1|) (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| (-891 |#1|) (QUOTE (-142))) (|HasCategory| (-891 |#1|) (QUOTE (-362)))) (|HasCategory| (-891 |#1|) (QUOTE (-144))) (|HasCategory| (-891 |#1|) (QUOTE (-362))) (|HasCategory| (-891 |#1|) (QUOTE (-142)))) (-349 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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) -(-350 -1935 GF) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +(-350 -3220 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 @@ -1336,21 +1336,21 @@ 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 -(-352 -1935 FP FPP) +(-352 -3220 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 (-353 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}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-354 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 (-355 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4363 . T)) +((-4365 . T)) NIL (-356 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1358,7 +1358,7 @@ NIL NIL (-357) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-358 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1374,7 +1374,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-544)))) (-361 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4363 |has| |#1| (-544)) (-4361 . T) (-4360 . T)) +((-4365 |has| |#1| (-544)) (-4363 . T) (-4362 . T)) NIL (-362) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1386,7 +1386,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-357)))) (-364 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL (-365 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1395,14 +1395,14 @@ NIL (-366 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-1076)))) +((|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-1078)))) (-367 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4366 . T) (-2997 . T)) +((-4368 . T) (-4283 . T)) NIL (-368 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4361 . T) (-4360 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4363 . T) (-4362 . T)) NIL (-369 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."))) @@ -1411,10 +1411,10 @@ NIL (-370 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552))))) +((|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552))))) (-371 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}"))) -((-4363 . T)) +((-4365 . T)) NIL (-372 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1422,7 +1422,7 @@ NIL NIL (-373) ((|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}."))) -((-4349 . T) (-4357 . T) (-3030 . T) (-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4351 . T) (-4359 . T) (-4311 . T) (-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-374 |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}."))) @@ -1430,31 +1430,31 @@ NIL NIL (-375 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) ((|HasCategory| |#1| (QUOTE (-169)))) (-376 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}."))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) NIL (-377) ((|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}."))) -((-2997 . T)) +((-4283 . T)) NIL (-378) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2997 . T)) +((-4283 . T)) NIL (-379 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."))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) ((|HasCategory| |#1| (QUOTE (-169)))) (-380 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL -((|HasCategory| |#1| (QUOTE (-830)))) +((|HasCategory| |#1| (QUOTE (-832)))) (-381) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-382) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1466,13 +1466,13 @@ NIL NIL (-384 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) NIL (-385) ((|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 -(-386 -1935 UP UPUP R) +(-386 -3220 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 @@ -1486,27 +1486,27 @@ NIL NIL (-389) ((|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."))) -((-2997 . T)) +((-4283 . T)) NIL (-390) ((|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.}"))) -((-2997 . T)) +((-4283 . T)) NIL (-391) ((|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 -(-392 -3112 |returnType| -4279 |symbols|) +(-392 -4290 |returnType| -3676 |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 -(-393 -1935 UP) +(-393 -3220 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-394 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2997 . T)) +((-4283 . T)) NIL (-395 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1514,15 +1514,15 @@ NIL NIL (-396) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-397 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4349)) (|HasAttribute| |#1| (QUOTE -4357))) +((|HasAttribute| |#1| (QUOTE -4351)) (|HasAttribute| |#1| (QUOTE -4359))) (-398) ((|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\"."))) -((-3030 . T) (-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4311 . T) (-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-399 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1534,20 +1534,20 @@ NIL NIL (-401 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."))) -((-4353 -12 (|has| |#1| (-6 -4364)) (|has| |#1| (-445)) (|has| |#1| (-6 -4353))) (-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-888))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-811)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (QUOTE (-803))) (-1559 (|HasCategory| |#1| (QUOTE (-803))) (|HasCategory| |#1| (QUOTE (-830)))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-811)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1127))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-811)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-811))))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-811))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1152)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-811)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-537))) (-12 (|HasAttribute| |#1| (QUOTE -4364)) (|HasAttribute| |#1| (QUOTE -4353)) (|HasCategory| |#1| (QUOTE (-445)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-142))))) +((-4355 -12 (|has| |#1| (-6 -4366)) (|has| |#1| (-445)) (|has| |#1| (-6 -4355))) (-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-890))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-813)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-805))) (-4029 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#1| (QUOTE (-832)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-813)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1129))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-813)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-813))))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-813))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1154)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-813)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-537))) (-12 (|HasAttribute| |#1| (QUOTE -4366)) (|HasAttribute| |#1| (QUOTE -4355)) (|HasCategory| |#1| (QUOTE (-445)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) (-402 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-403 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL (-404 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552))))) +((|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552))))) (-405 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL @@ -1556,14 +1556,14 @@ 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 -(-407 R -1935 UP A) +(-407 R -3220 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)}."))) -((-4363 . T)) +((-4365 . T)) NIL -(-408 R -1935 UP A |ibasis|) +(-408 R -3220 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1017) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1019) (|devaluate| |#2|)))) (-409 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1574,12 +1574,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-357)))) (-411 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4363 |has| |#1| (-544)) (-4361 . T) (-4360 . T)) +((-4365 |has| |#1| (-544)) (-4363 . T) (-4362 . T)) NIL (-412 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."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1152)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -303) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-1193))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1152)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-445)))) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1154)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -303) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-1195))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1154)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-445)))) (-413 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 @@ -1603,40 +1603,40 @@ NIL (-418 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL -((|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-362)))) +((|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-362)))) (-419 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4366 . T) (-4356 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4358 . T) (-4369 . T) (-4283 . T)) NIL -(-420 R -1935) +(-420 R -3220) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-421 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4353 -12 (|has| |#1| (-6 -4353)) (|has| |#2| (-6 -4353))) (-4360 . T) (-4361 . T) (-4363 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4353)) (|HasAttribute| |#2| (QUOTE -4353)))) -(-422 R -1935) +((-4355 -12 (|has| |#1| (-6 -4355)) (|has| |#2| (-6 -4355))) (-4362 . T) (-4363 . T) (-4365 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4355)) (|HasAttribute| |#2| (QUOTE -4355)))) +(-422 R -3220) ((|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 (-423 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 -1017) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-1088))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) +((|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) (-424 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}."))) -((-4363 -1559 (|has| |#1| (-1028)) (|has| |#1| (-466))) (-4361 |has| |#1| (-169)) (-4360 |has| |#1| (-169)) ((-4368 "*") |has| |#1| (-544)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-544)) (-4358 |has| |#1| (-544)) (-2997 . T)) +((-4365 -4029 (|has| |#1| (-1030)) (|has| |#1| (-466))) (-4363 |has| |#1| (-169)) (-4362 |has| |#1| (-169)) ((-4370 "*") |has| |#1| (-544)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-544)) (-4360 |has| |#1| (-544)) (-4283 . T)) NIL -(-425 R -1935) +(-425 R -3220) ((|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 -(-426 R -1935) +(-426 R -3220) ((|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)))) -(-427 R -1935) +(-427 R -3220) ((|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 @@ -1644,10 +1644,10 @@ 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 -(-429 R -1935 UP) +(-429 R -3220 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 -1017) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-48))))) (-430) ((|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 @@ -1662,17 +1662,17 @@ NIL NIL (-433) ((|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}."))) -((-2997 . T)) +((-4283 . T)) NIL (-434) ((|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.}"))) -((-2997 . T)) +((-4283 . T)) NIL (-435 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 -(-436 R UP -1935) +(-436 R UP -3220) ((|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 @@ -1710,16 +1710,16 @@ NIL NIL (-445) ((|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}."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-446 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"))) -((-4363 |has| (-401 (-931 |#1|)) (-544)) (-4361 . T) (-4360 . T)) -((|HasCategory| (-401 (-931 |#1|)) (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| (-401 (-931 |#1|)) (QUOTE (-544)))) +((-4365 |has| (-401 (-933 |#1|)) (-544)) (-4363 . T) (-4362 . T)) +((|HasCategory| (-401 (-933 |#1|)) (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| (-401 (-933 |#1|)) (QUOTE (-544)))) (-447 |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"))) -(((-4368 "*") |has| |#2| (-169)) (-4359 |has| |#2| (-544)) (-4364 |has| |#2| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#2| (QUOTE (-888))) (-1559 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-888)))) (-1559 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-888)))) (-1559 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (-1559 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-544)))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357))) (-1559 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#2| (QUOTE -4364)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-142))))) +(((-4370 "*") |has| |#2| (-169)) (-4361 |has| |#2| (-544)) (-4366 |has| |#2| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#2| (QUOTE (-890))) (-4029 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-890)))) (-4029 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-890)))) (-4029 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-890)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (-4029 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-544)))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357))) (-4029 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#2| (QUOTE -4366)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-890)))) (|HasCategory| |#2| (QUOTE (-142))))) (-448 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 @@ -1746,7 +1746,7 @@ NIL NIL (-454 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) NIL (-455 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1754,8 +1754,8 @@ NIL NIL (-456 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-844))))) (-457 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 @@ -1784,7 +1784,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-464 |lv| -1935 R) +(-464 |lv| -3220 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1794,23 +1794,23 @@ NIL NIL (-466) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4363 . T)) +((-4365 . T)) NIL (-467 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.") 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T) (-4363 . T) (-4365 . 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T)) -((-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-830))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-832))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) (-469 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)}"))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-844))))) (-470) ((|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}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-471) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1818,29 +1818,29 @@ NIL NIL (-472 |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."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) (-473) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-474 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4368 "*") |has| |#2| (-169)) (-4359 |has| |#2| (-544)) (-4364 |has| |#2| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . 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T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-478 -1935 UP UPUP R) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-478 -3220 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 @@ -1850,15 +1850,15 @@ NIL NIL (-480) ((|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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-552) (QUOTE (-888))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1001))) (|HasCategory| (-552) (QUOTE (-803))) (-1559 (|HasCategory| (-552) (QUOTE (-803))) (|HasCategory| (-552) (QUOTE (-830)))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1127))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1152)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-552) (LIST (QUOTE -623) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (|HasCategory| (-552) (QUOTE (-142))))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-552) (QUOTE (-890))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1003))) (|HasCategory| (-552) (QUOTE (-805))) (-4029 (|HasCategory| (-552) (QUOTE (-805))) (|HasCategory| (-552) (QUOTE (-832)))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1129))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1154)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-552) (LIST (QUOTE -625) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (|HasCategory| (-552) (QUOTE (-142))))) (-481 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 -4366)) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) +((|HasAttribute| |#1| (QUOTE -4368)) (|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (-482 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2997 . T)) +((-4283 . T)) NIL (-483) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) @@ -1872,34 +1872,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-486 -1935 UP |AlExt| |AlPol|) +(-486 -3220 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-487) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| $ (QUOTE (-1028))) (|HasCategory| $ (LIST (QUOTE -1017) (QUOTE (-552))))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| $ (QUOTE (-1030))) (|HasCategory| $ (LIST (QUOTE -1019) (QUOTE (-552))))) (-488 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-489 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."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-490 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 -(-491 R UP -1935) +(-491 R UP -3220) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-492 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| (-111) (QUOTE (-1076))) (|HasCategory| (-111) (LIST (QUOTE -303) (QUOTE (-111))))) (|HasCategory| (-111) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-111) (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-111) (QUOTE (-1076))) (|HasCategory| (-111) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| (-111) (QUOTE (-1078))) (|HasCategory| (-111) (LIST (QUOTE -303) (QUOTE (-111))))) (|HasCategory| (-111) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-111) (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-111) (QUOTE (-1078))) (|HasCategory| (-111) (LIST (QUOTE -599) (QUOTE (-844))))) (-493 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 @@ -1912,10 +1912,10 @@ 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 -(-496 -1935 |Expon| |VarSet| |DPoly|) +(-496 -3220 |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 -600) (QUOTE (-1152))))) +((|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-1154))))) (-497 |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 @@ -1959,39 +1959,39 @@ NIL (-507 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-775)))) +((|HasCategory| |#2| (QUOTE (-777)))) (-508 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}"))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-509) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-510 |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}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((-1559 (|HasCategory| (-569 |#1|) (QUOTE (-142))) (|HasCategory| (-569 |#1|) (QUOTE (-362)))) (|HasCategory| (-569 |#1|) (QUOTE (-144))) (|HasCategory| (-569 |#1|) (QUOTE (-362))) (|HasCategory| (-569 |#1|) (QUOTE (-142)))) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((-4029 (|HasCategory| (-569 |#1|) (QUOTE (-142))) (|HasCategory| (-569 |#1|) (QUOTE (-362)))) (|HasCategory| (-569 |#1|) (QUOTE (-144))) (|HasCategory| (-569 |#1|) (QUOTE (-362))) (|HasCategory| (-569 |#1|) (QUOTE (-142)))) (-511 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}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-512 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."))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-513 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 -4367))) +((|HasAttribute| |#3| (QUOTE -4369))) (-514 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 -4367))) +((|HasAttribute| |#7| (QUOTE -4369))) (-515 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."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4368 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4370 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-516) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2013,7 +2013,7 @@ NIL NIL NIL (-521) -((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{`f'}.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) +((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{`f'}.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) NIL NIL (-522 R) @@ -2024,7 +2024,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-524 K -1935 |Par|) +(-524 K -3220 |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 @@ -2048,7 +2048,7 @@ 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 -(-530 K -1935 |Par|) +(-530 K -3220 |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 @@ -2078,17 +2078,17 @@ NIL NIL (-537) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4364 . T) (-4365 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4366 . T) (-4367 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-538 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) -(-539 R -1935) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) +(-539 R -3220) ((|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 -(-540 R0 -1935 UP UPUP R) +(-540 R0 -3220 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 @@ -2098,7 +2098,7 @@ NIL NIL (-542 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."))) -((-3030 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4311 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-543 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."))) @@ -2106,9 +2106,9 @@ NIL NIL (-544) ((|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."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-545 R -1935) +(-545 R -3220) ((|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 @@ -2120,39 +2120,39 @@ 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 -(-548 R -1935 L) +(-548 R -3220 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 -638) (|devaluate| |#2|)))) +((|HasCategory| |#3| (LIST (QUOTE -640) (|devaluate| |#2|)))) (-549) ((|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 -(-550 -1935 UP UPUP R) +(-550 -3220 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 -(-551 -1935 UP) +(-551 -3220 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 (-552) ((|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}."))) -((-4348 . T) (-4354 . T) (-4358 . T) (-4353 . T) (-4364 . T) (-4365 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4350 . T) (-4356 . T) (-4360 . T) (-4355 . T) (-4366 . T) (-4367 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-553) ((|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 -(-554 R -1935 L) +(-554 R -3220 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 -638) (|devaluate| |#2|)))) -(-555 R -1935) +((|HasCategory| |#3| (LIST (QUOTE -640) (|devaluate| |#2|)))) +(-555 R -3220) ((|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 -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-613))))) -(-556 -1935 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-615))))) +(-556 -3220 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 @@ -2160,27 +2160,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-558 -1935) +(-558 -3220) ((|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 (-559 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."))) -((-3030 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4311 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-560) ((|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 -(-561 R -1935) +(-561 R -3220) ((|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 -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-613))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-1152))))) (-12 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-278)))) (|HasCategory| |#1| (QUOTE (-544)))) -(-562 -1935 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-615))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-1154))))) (-12 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-278)))) (|HasCategory| |#1| (QUOTE (-544)))) +(-562 -3220 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 -(-563 R -1935) +(-563 R -3220) ((|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 @@ -2202,28 +2202,28 @@ NIL NIL (-568 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL (-569 |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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) ((|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-142))) (|HasCategory| $ (QUOTE (-362)))) (-570) ((|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 -(-571 R -1935) +(-571 R -3220) ((|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 -(-572 E -1935) +(-572 E -3220) ((|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 -(-573 -1935) +(-573 -3220) ((|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}."))) -((-4361 . T) (-4360 . T)) -((|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-1152))))) +((-4363 . T) (-4362 . T)) +((|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-1154))))) (-574 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 @@ -2250,19 +2250,19 @@ NIL NIL (-580 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| (-141) (QUOTE (-830))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1076))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (-1559 (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-842)))) (-12 (|HasCategory| (-141) (QUOTE (-1076))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| (-141) (QUOTE (-830))) (|HasCategory| (-141) (QUOTE (-1076)))) (|HasCategory| (-141) (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-141) (QUOTE (-1076))) (-12 (|HasCategory| (-141) (QUOTE (-1076))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| (-141) (QUOTE (-832))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1078))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (-4029 (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-844)))) (-12 (|HasCategory| (-141) (QUOTE (-1078))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| (-141) (QUOTE (-832))) (|HasCategory| (-141) (QUOTE (-1078)))) (|HasCategory| (-141) (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-141) (QUOTE (-1078))) (-12 (|HasCategory| (-141) (QUOTE (-1078))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-844))))) (-581 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 (-582 |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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-552)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-552)) (|devaluate| |#1|)))) (|HasCategory| (-552) (QUOTE (-1088))) (|HasCategory| |#1| (QUOTE (-357))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -1477) (LIST (|devaluate| |#1|) (QUOTE (-1152)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-552)))))) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-552)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-552)) (|devaluate| |#1|)))) (|HasCategory| (-552) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-357))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -3213) (LIST (|devaluate| |#1|) (QUOTE (-1154)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-552)))))) (-583 |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.}"))) -((-4361 |has| |#1| (-544)) (-4360 |has| |#1| (-544)) ((-4368 "*") |has| |#1| (-544)) (-4359 |has| |#1| (-544)) (-4363 . T)) +((-4363 |has| |#1| (-544)) (-4362 |has| |#1| (-544)) ((-4370 "*") |has| |#1| (-544)) (-4361 |has| |#1| (-544)) (-4365 . T)) ((|HasCategory| |#1| (QUOTE (-544)))) (-584 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),{}..]}."))) @@ -2272,7 +2272,7 @@ 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 -(-586 R -1935 FG) +(-586 R -3220 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 @@ -2282,15 +2282,15 @@ NIL NIL (-588 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-709))) (|HasCategory| |#1| (QUOTE (-1028))) (-12 (|HasCategory| |#1| (QUOTE (-981))) (|HasCategory| |#1| (QUOTE (-1028)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-711))) (|HasCategory| |#1| (QUOTE (-1030))) (-12 (|HasCategory| |#1| (QUOTE (-983))) (|HasCategory| |#1| (QUOTE (-1030)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (-589 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 -4367)) (|HasCategory| |#2| (QUOTE (-830))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#3| (QUOTE (-1076)))) +((|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#2| (QUOTE (-832))) (|HasAttribute| |#1| (QUOTE -4368)) (|HasCategory| |#3| (QUOTE (-1078)))) (-590 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2997 . T)) +((-4283 . T)) NIL (-591) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2302,19 +2302,19 @@ NIL NIL (-593 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)."))) -((-4363 -1559 (-2520 (|has| |#2| (-361 |#1|)) (|has| |#1| (-544))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-544)))) (-4361 . T) (-4360 . T)) -((-1559 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) +((-4365 -4029 (-3792 (|has| |#2| (-361 |#1|)) (|has| |#1| (-544))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-544)))) (-4363 . T) (-4362 . T)) +((-4029 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-594 |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."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (QUOTE (-1134))) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| (-1134) (QUOTE (-830))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -599) (QUOTE (-842))))) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (QUOTE (-1136))) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| (-1136) (QUOTE (-832))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -599) (QUOTE (-844))))) (-595 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 (-596 |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}."))) -((-4367 . T) (-2997 . T)) +((-4369 . T) (-4283 . T)) NIL (-597 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"))) @@ -2323,7 +2323,7 @@ NIL (-598 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 -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) +((|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-599 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 @@ -2332,2657 +2332,2665 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-601 -1935 UP) +(-601 -3220 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -(-602) +(-602 S) +((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B}. In symbols \\indented{3}{A has CoercibleFrom \\spad{B}\\space{3}\\spad{<=>}\\space{2}\\spad{B} has CoercibleTo A}")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms \\spad{`s'} into an element of `\\%'."))) +NIL +NIL +(-603) ((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|true| (($) "the definite truth value")) (|unknown| (($) "the indefinite `unknown'")) (|false| (($) "the definite falsehood value"))) NIL NIL -(-603 S R) +(-604 S) +((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain \\spad{B}. In symbols \\indented{3}{A has ConvertibleFrom \\spad{B}\\space{3}\\spad{<=>}\\space{2}\\spad{B} has ConvertibleTo A}")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) +NIL +NIL +(-605 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-604 R) +(-606 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."))) -((-4363 . T)) +((-4365 . T)) NIL -(-605 A R S) +(-607 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}."))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-828)))) -(-606 R -1935) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-830)))) +(-608 R -3220) ((|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 -(-607 R UP) +(-609 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"))) -((-4361 . T) (-4360 . T) ((-4368 "*") . T) (-4359 . T) (-4363 . T)) -((|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552))))) -(-608 R E V P TS ST) +((-4363 . T) (-4362 . T) ((-4370 "*") . T) (-4361 . T) (-4365 . T)) +((|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) +(-610 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 NIL -(-609 OV E Z P) +(-611 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \\spad{\"F\"}.")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,{}unilist,{}plead,{}vl,{}lvar,{}lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod,{} numFacts,{} evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-610) +(-612) ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) NIL NIL -(-611 |VarSet| R |Order|) +(-613 |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}}."))) -((-4363 . T)) +((-4365 . T)) NIL -(-612 R |ls|) +(-614 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}}."))) NIL NIL -(-613) +(-615) ((|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 -(-614 R -1935) +(-616 R -3220) ((|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 -(-615 |lv| -1935) +(-617 |lv| -3220) ((|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 -(-616) +(-618) ((|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."))) -((-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (QUOTE (-1134))) (LIST (QUOTE |:|) (QUOTE -2162) (QUOTE (-52))))))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-52) (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-52) (QUOTE (-1076))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1076))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-1134) (QUOTE (-830))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-52) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842))))) -(-617 S R) +((-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (QUOTE (-1136))) (LIST (QUOTE |:|) (QUOTE -3360) (QUOTE (-52))))))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-52) (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-52) (QUOTE (-1078))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1078))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-1136) (QUOTE (-832))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-52) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844))))) +(-619 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-357)))) -(-618 R) +(-620 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4361 . T) (-4360 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4363 . T) (-4362 . T)) NIL -(-619 R A) +(-621 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4363 -1559 (-2520 (|has| |#2| (-361 |#1|)) (|has| |#1| (-544))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-544)))) (-4361 . T) (-4360 . T)) -((-1559 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) -(-620 R FE) +((-4365 -4029 (-3792 (|has| |#2| (-361 |#1|)) (|has| |#1| (-544))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-544)))) (-4363 . T) (-4362 . T)) +((-4029 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) +(-622 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 NIL -(-621 R) +(-623 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-622 S R) +(-624 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1681 (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-357)))) -(-623 R) +((-4107 (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-357)))) +(-625 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}."))) -((-4363 . T)) +((-4365 . T)) NIL -(-624 A B) +(-626 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-625 A B) +(-627 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) NIL NIL -(-626 A B C) +(-628 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-627 S) +(-629 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."))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-628 T$) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-813))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-630 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-629 S) +(-631 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-630 R) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-632 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL NIL -(-631 S E |un|) +(-633 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,{}y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x,{} y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s,{} e,{} x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s,{} a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a,{} s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l,{} n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l,{} n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s,{} e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l,{} fop,{} fexp,{} unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a,{} b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a,{} n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) NIL NIL -(-632 A S) +(-634 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 -4367))) -(-633 S) +((|HasAttribute| |#1| (QUOTE -4369))) +(-635 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})}."))) -((-2997 . T)) +((-4283 . T)) NIL -(-634 R -1935 L) +(-636 R -3220 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 -(-635 A) +(-637 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}}"))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) -(-636 A M) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) +(-638 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) -(-637 S A) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) +(-639 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-357)))) -(-638 A) +(-640 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}."))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-639 -1935 UP) +(-641 -3220 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)))) -(-640 A -1528) +(-642 A -2000) ((|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}}"))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) -(-641 A L) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) +(-643 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-642 S) +(-644 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-643) +(-645) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-644 M R S) +(-646 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}."))) -((-4361 . T) (-4360 . T)) -((|HasCategory| |#1| (QUOTE (-774)))) -(-645 R) +((-4363 . T) (-4362 . T)) +((|HasCategory| |#1| (QUOTE (-776)))) +(-647 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-646 |VarSet| R) +(-648 |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) (-4361 . T) (-4360 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4363 . T) (-4362 . T)) ((|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-169)))) -(-647 A S) +(-649 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}."))) NIL NIL -(-648 S) +(-650 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}."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-649 -1935) +(-651 -3220) ((|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 -(-650 -1935 |Row| |Col| M) +(-652 -3220 |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 -(-651 R E OV P) +(-653 R E OV P) ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,{}lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) NIL NIL -(-652 |n| R) +(-654 |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."))) -((-4363 . T) (-4366 . T) (-4360 . T) (-4361 . T)) -((|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4368 "*"))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (-1559 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-544))) (-1559 (|HasAttribute| |#2| (QUOTE (-4368 "*"))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-228)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-169)))) -(-653) +((-4365 . T) (-4368 . T) (-4362 . T) (-4363 . T)) +((|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4370 "*"))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (-4029 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-544))) (-4029 (|HasAttribute| |#2| (QUOTE (-4370 "*"))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-228)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-169)))) +(-655) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL NIL -(-654 |VarSet|) +(-656 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-655 A S) +(-657 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\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|) |#2|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) NIL NIL -(-656 S) +(-658 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-2997 . T)) +((-4283 . T)) NIL -(-657 R) +(-659 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 -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (QUOTE (-1028))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-658) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (QUOTE (-1030))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-660) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL NIL -(-659 |VarSet|) +(-661 |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 NIL -(-660 A) +(-662 A) ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,{}g,{}x)} is \\spad{g(n,{}g(n-1,{}..g(1,{}x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,{}n,{}x)} applies \\spad{f n} times to \\spad{x}."))) NIL NIL -(-661 A C) +(-663 A C) ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,{}c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,{}c)} selects its first argument."))) NIL NIL -(-662 A B C) +(-664 A B C) ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,{}g,{}x)} is \\spad{f(g x)}."))) NIL NIL -(-663) +(-665) ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for \\spad{`s'}.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of \\spad{`s'}.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,{}t)} builds the mapping AST \\spad{s} \\spad{->} \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) NIL NIL -(-664 A) +(-666 A) ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,{}x)= g(n,{}g(n-1,{}..g(1,{}x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,{}n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-665 A C) +(-667 A C) ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,{}a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-666 A B C) +(-668 A B C) ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) NIL NIL -(-667 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-669 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-668 S R |Row| |Col|) +(-670 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 (-4368 "*"))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-544)))) -(-669 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-4370 "*"))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-544)))) +(-671 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"))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL -(-670 R |Row| |Col| M) +(-672 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL ((|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-544)))) -(-671 R) +(-673 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."))) -((-4366 . T) (-4367 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4368 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-672 R) +((-4368 . T) (-4369 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4370 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-674 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 -(-673 T$) +(-675 T$) ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) NIL NIL -(-674 S -1935 FLAF FLAS) +(-676 S -3220 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 -(-675 R Q) +(-677 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL NIL -(-676) +(-678) ((|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"))) -((-4359 . T) (-4364 |has| (-681) (-357)) (-4358 |has| (-681) (-357)) (-4365 |has| (-681) (-6 -4365)) (-4362 |has| (-681) (-6 -4362)) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-681) (QUOTE (-144))) (|HasCategory| (-681) (QUOTE (-142))) (|HasCategory| (-681) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-681) (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| (-681) (QUOTE (-362))) (|HasCategory| (-681) (QUOTE (-357))) (|HasCategory| (-681) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-681) (QUOTE (-228))) (-1559 (|HasCategory| (-681) (QUOTE (-357))) (|HasCategory| (-681) (QUOTE (-343)))) (|HasCategory| (-681) (QUOTE (-343))) (|HasCategory| (-681) (LIST (QUOTE -280) (QUOTE (-681)) (QUOTE (-681)))) (|HasCategory| (-681) (LIST (QUOTE -303) (QUOTE (-681)))) (|HasCategory| (-681) (LIST (QUOTE -506) (QUOTE (-1152)) (QUOTE (-681)))) (|HasCategory| (-681) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-681) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-681) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-681) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (-1559 (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-357))) (|HasCategory| (-681) (QUOTE (-343)))) (|HasCategory| (-681) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-681) (QUOTE (-1001))) (|HasCategory| (-681) (QUOTE (-1174))) (-12 (|HasCategory| (-681) (QUOTE (-981))) (|HasCategory| (-681) (QUOTE (-1174)))) (-1559 (-12 (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888)))) (|HasCategory| (-681) (QUOTE (-357))) (-12 (|HasCategory| (-681) (QUOTE (-343))) (|HasCategory| (-681) (QUOTE (-888))))) (-1559 (-12 (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888)))) (-12 (|HasCategory| (-681) (QUOTE (-357))) (|HasCategory| (-681) (QUOTE (-888)))) (-12 (|HasCategory| (-681) (QUOTE (-343))) (|HasCategory| (-681) (QUOTE (-888))))) (|HasCategory| (-681) (QUOTE (-537))) (-12 (|HasCategory| (-681) (QUOTE (-1037))) (|HasCategory| (-681) (QUOTE (-1174)))) (|HasCategory| (-681) (QUOTE (-1037))) (-1559 (|HasCategory| (-681) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-681) (QUOTE (-357)))) (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888))) (-1559 (-12 (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888)))) (|HasCategory| (-681) (QUOTE (-357)))) (-1559 (-12 (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888)))) (|HasCategory| (-681) (QUOTE (-544)))) (-12 (|HasCategory| (-681) (QUOTE (-228))) (|HasCategory| (-681) (QUOTE (-357)))) (-12 (|HasCategory| (-681) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-681) (QUOTE (-357)))) (|HasCategory| (-681) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-681) (QUOTE (-830))) (|HasCategory| (-681) (QUOTE (-544))) (|HasAttribute| (-681) (QUOTE -4365)) (|HasAttribute| (-681) (QUOTE -4362)) (-12 (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888)))) (|HasCategory| (-681) (QUOTE (-142)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-681) (QUOTE (-301))) (|HasCategory| (-681) (QUOTE (-888)))) (|HasCategory| (-681) (QUOTE (-343))))) -(-677 S) +((-4361 . 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T)) +((|HasCategory| (-683) (QUOTE (-144))) (|HasCategory| (-683) (QUOTE (-142))) (|HasCategory| (-683) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-683) (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| (-683) (QUOTE (-362))) (|HasCategory| (-683) (QUOTE (-357))) (|HasCategory| (-683) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-683) (QUOTE (-228))) (-4029 (|HasCategory| (-683) (QUOTE (-357))) (|HasCategory| (-683) (QUOTE (-343)))) (|HasCategory| (-683) (QUOTE (-343))) (|HasCategory| (-683) (LIST (QUOTE -280) (QUOTE (-683)) (QUOTE (-683)))) (|HasCategory| (-683) (LIST (QUOTE -303) (QUOTE (-683)))) (|HasCategory| (-683) (LIST (QUOTE -506) (QUOTE (-1154)) (QUOTE (-683)))) (|HasCategory| (-683) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-683) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-683) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-683) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (-4029 (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-357))) (|HasCategory| (-683) (QUOTE (-343)))) (|HasCategory| (-683) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-683) (QUOTE (-1003))) (|HasCategory| (-683) (QUOTE (-1176))) (-12 (|HasCategory| (-683) (QUOTE (-983))) (|HasCategory| (-683) (QUOTE (-1176)))) (-4029 (-12 (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890)))) (|HasCategory| (-683) (QUOTE (-357))) (-12 (|HasCategory| (-683) (QUOTE (-343))) (|HasCategory| (-683) (QUOTE (-890))))) (-4029 (-12 (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890)))) (-12 (|HasCategory| (-683) (QUOTE (-357))) (|HasCategory| (-683) (QUOTE (-890)))) (-12 (|HasCategory| (-683) (QUOTE (-343))) (|HasCategory| (-683) (QUOTE (-890))))) (|HasCategory| (-683) (QUOTE (-537))) (-12 (|HasCategory| (-683) (QUOTE (-1039))) (|HasCategory| (-683) (QUOTE (-1176)))) (|HasCategory| (-683) (QUOTE (-1039))) (-4029 (|HasCategory| (-683) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-683) (QUOTE (-357)))) (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890))) (-4029 (-12 (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890)))) (|HasCategory| (-683) (QUOTE (-357)))) (-4029 (-12 (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890)))) (|HasCategory| (-683) (QUOTE (-544)))) (-12 (|HasCategory| (-683) (QUOTE (-228))) (|HasCategory| (-683) (QUOTE (-357)))) (-12 (|HasCategory| (-683) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-683) (QUOTE (-357)))) (|HasCategory| (-683) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-683) (QUOTE (-832))) (|HasCategory| (-683) (QUOTE (-544))) (|HasAttribute| (-683) (QUOTE -4367)) (|HasAttribute| (-683) (QUOTE -4364)) (-12 (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890)))) (|HasCategory| (-683) (QUOTE (-142)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-683) (QUOTE (-301))) (|HasCategory| (-683) (QUOTE (-890)))) (|HasCategory| (-683) (QUOTE (-343))))) +(-679 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}."))) -((-4367 . T) (-2997 . T)) +((-4369 . T) (-4283 . T)) NIL -(-678 U) +(-680 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL -(-679) +(-681) ((|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 -(-680 OV E -1935 PG) +(-682 OV E -3220 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 -(-681) +(-683) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3030 . T) (-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4311 . T) (-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-682 R) +(-684 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."))) NIL NIL -(-683) +(-685) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4365 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4367 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-684 S D1 D2 I) +(-686 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-685 S) +(-687 S) ((|constructor| (NIL "MakeCachableSet(\\spad{S}) returns a cachable set which is equal to \\spad{S} as a set.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s} viewed as an element of \\%."))) NIL NIL -(-686 S) +(-688 S) ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x,{} y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-687 S) +(-689 S) ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e,{} foo,{} [x1,{}...,{}xn])} creates a function \\spad{foo(x1,{}...,{}xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x,{} y)} creates a function \\spad{foo(x,{} y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e,{} foo)} creates a function \\spad{foo() == e}."))) NIL NIL -(-688 S T$) +(-690 S T$) ((|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 -(-689 S -4251 I) +(-691 S -1765 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 -(-690 E OV R P) +(-692 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,{}lv,{}lu,{}lr,{}lp,{}lt,{}ln,{}t,{}r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,{}lv,{}lu,{}lr,{}lp,{}ln,{}r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,{}lv,{}lr,{}ln,{}lu,{}t,{}r)} \\undocumented"))) NIL NIL -(-691 R) +(-693 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)}.}"))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-692 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-694 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 -(-693) +(-695) ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-694 R |Mod| -3226 -3759 |exactQuo|) +(-696 R |Mod| -3098 -1446 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-695 R |Rep|) +(-697 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4362 |has| |#1| (-357)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-888))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1058) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| (-1058) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| (-1058) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| (-1058) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| (-1058) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1127))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-343))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4364)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-142))))) -(-696 IS E |ff|) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-890))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1129))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-343))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) +(-698 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL -(-697 R M) +(-699 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4361 |has| |#1| (-169)) (-4360 |has| |#1| (-169)) (-4363 . T)) +((-4363 |has| |#1| (-169)) (-4362 |has| |#1| (-169)) (-4365 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144)))) -(-698 R |Mod| -3226 -3759 |exactQuo|) +(-700 R |Mod| -3098 -1446 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4363 . T)) +((-4365 . T)) NIL -(-699 S R) +(-701 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-700 R) +(-702 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) NIL -(-701 -1935) +(-703 -3220) ((|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]]}."))) -((-4363 . T)) +((-4365 . T)) NIL -(-702 S) +(-704 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-703) +(-705) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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."))) NIL NIL -(-704 S) +(-706 S) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} 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 such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-705) +(-707) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} 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 such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-706 S R UP) +(-708 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL ((|HasCategory| |#2| (QUOTE (-343))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-362)))) -(-707 R UP) +(-709 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."))) -((-4359 |has| |#1| (-357)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 |has| |#1| (-357)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-708 S) +(-710 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-709) +(-711) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-710 -1935 UP) +(-712 -3220 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 -(-711 |VarSet| E1 E2 R S PR PS) +(-713 |VarSet| E1 E2 R S PR PS) ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (\\spad{PG})")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,{}p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,{}p)} \\undocumented"))) NIL NIL -(-712 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-714 |Vars1| |Vars2| E1 E2 R PR1 PR2) ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-713 E OV R PPR) +(-715 E OV R PPR) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|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 -(-714 |vl| R) +(-716 |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."))) -(((-4368 "*") |has| |#2| (-169)) (-4359 |has| |#2| (-544)) (-4364 |has| |#2| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#2| (QUOTE (-888))) (-1559 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-888)))) (-1559 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-888)))) (-1559 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (-1559 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-544)))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357))) (-1559 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#2| (QUOTE -4364)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-142))))) -(-715 E OV R PRF) +(((-4370 "*") |has| |#2| (-169)) (-4361 |has| |#2| (-544)) (-4366 |has| |#2| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#2| (QUOTE (-890))) (-4029 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-890)))) (-4029 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-890)))) (-4029 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-890)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (-4029 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-544)))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| (-846 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357))) (-4029 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#2| (QUOTE -4366)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-890)))) (|HasCategory| |#2| (QUOTE (-142))))) +(-717 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-716 E OV R P) +(-718 E OV R P) ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-717 R S M) +(-719 R S M) ((|constructor| (NIL "MonoidRingFunctions2 implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,{}u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-718 R M) +(-720 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4361 |has| |#1| (-169)) (-4360 |has| |#1| (-169)) (-4363 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-830)))) -(-719 S) +((-4363 |has| |#1| (-169)) (-4362 |has| |#1| (-169)) (-4365 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-832)))) +(-721 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4356 . T) (-4367 . T) (-2997 . T)) +((-4358 . T) (-4369 . T) (-4283 . T)) NIL -(-720 S) +(-722 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}."))) -((-4366 . T) (-4356 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-721) +((-4368 . T) (-4358 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-723) ((|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 NIL -(-722 S) +(-724 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,{}l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) NIL NIL -(-723 |Coef| |Var|) +(-725 |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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4361 . T) (-4360 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4363 . T) (-4362 . T) (-4365 . T)) NIL -(-724 OV E R P) +(-726 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"))) NIL NIL -(-725 E OV R P) +(-727 E OV R P) ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) NIL NIL -(-726 S R) +(-728 S 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}."))) NIL NIL -(-727 R) +(-729 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}."))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) NIL -(-728) +(-730) ((|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}."))) NIL NIL -(-729) +(-731) ((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.) See \\downlink{Manual Page}{manpageXXc05}.")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,{}ldfjac,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,{}b,{}eps,{}eta,{}ifail,{}f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) NIL NIL -(-730) +(-732) ((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations. See \\downlink{Manual Page}{manpageXXc06}.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,{}n,{}x,{}ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,{}n,{}x,{}ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,{}y,{}ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,{}x,{}ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,{}n,{}init,{}x,{}y,{}trigm,{}trign,{}ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,{}n,{}init,{}x,{}y,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,{}n,{}x,{}y,{}ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,{}x,{}y,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) NIL NIL -(-731) +(-733) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules. See \\downlink{Manual Page}{manpageXXd01}.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,{}a,{}b,{}maxcls,{}eps,{}lenwrk,{}mincls,{}wrkstr,{}ifail,{}functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,{}y,{}n,{}ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,{}a,{}b,{}maxpts,{}eps,{}lenwrk,{}minpts,{}ifail,{}functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,{}b,{}itype,{}n,{}gtype,{}ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,{}omega,{}key,{}epsabs,{}limlst,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,{}b,{}c,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,{}b,{}alfa,{}beta,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,{}b,{}omega,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,{}inf,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,{}b,{}npts,{}points,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) NIL NIL -(-732) +(-734) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems. See \\downlink{Manual Page}{manpageXXd02}.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "\\spad{d02raf(n,{}mnp,{}numbeg,{}nummix,{}tol,{}init,{}iy,{}ijac,{}lwork,{}liwork,{}np,{}x,{}y,{}deleps,{}ifail,{}fcn,{}g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval,{}monit,{}report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains Asp12 and Asp33 are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,{}b,{}n,{}tol,{}mnp,{}lw,{}liw,{}c,{}d,{}gam,{}x,{}np,{}ifail,{}fcnf,{}fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,{}v,{}n,{}a,{}b,{}tol,{}mnp,{}lw,{}liw,{}x,{}np,{}ifail,{}fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,{}m,{}n,{}relabs,{}iw,{}x,{}y,{}tol,{}ifail,{}g,{}fcn,{}pederv,{}output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (\\spad{BDF}),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,{}m,{}n,{}tol,{}relabs,{}x,{}y,{}ifail,{}g,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,{}n,{}irelab,{}hmax,{}x,{}y,{}tol,{}ifail,{}g,{}fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,{}m,{}n,{}irelab,{}x,{}y,{}tol,{}ifail,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) NIL NIL -(-733) +(-735) ((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations. See \\downlink{Manual Page}{manpageXXd03}.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03faf(xs,{}xf,{}l,{}lbdcnd,{}bdxs,{}bdxf,{}ys,{}yf,{}m,{}mbdcnd,{}bdys,{}bdyf,{}zs,{}zf,{}n,{}nbdcnd,{}bdzs,{}bdzf,{}lambda,{}ldimf,{}mdimf,{}lwrk,{}f,{}ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,{}xmax,{}ymin,{}ymax,{}ngx,{}ngy,{}lda,{}scheme,{}ifail,{}pdef,{}bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,{}ngy,{}lda,{}maxit,{}acc,{}iout,{}a,{}rhs,{}ub,{}ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) NIL NIL -(-734) +(-736) ((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them. See \\downlink{Manual Page}{manpageXXe01}.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,{}x,{}y,{}f,{}rnw,{}fnodes,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,{}x,{}y,{}f,{}nw,{}nq,{}rnw,{}rnq,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,{}x,{}y,{}f,{}triang,{}grads,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,{}x,{}y,{}f,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,{}my,{}x,{}y,{}f,{}ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,{}x,{}f,{}d,{}a,{}b,{}ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,{}x,{}f,{}ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,{}x,{}y,{}lck,{}lwrk,{}ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) NIL NIL -(-735) +(-737) ((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined. See \\downlink{Manual Page}{manpageXXe02}.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,{}py,{}lamda,{}mu,{}m,{}x,{}y,{}npoint,{}nadres,{}ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,{}la,{}nplus2,{}toler,{}a,{}b,{}ifail)} calculates an \\spad{l} solution to an over-determined system of \\indented{22}{1} linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,{}my,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}lwrk,{}liwrk,{}ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,{}m,{}x,{}y,{}f,{}w,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,{}mx,{}x,{}my,{}y,{}f,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}iwrk,{}ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,{}px,{}py,{}x,{}y,{}f,{}w,{}mu,{}point,{}npoint,{}nc,{}nws,{}eps,{}lamda,{}ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,{}m,{}x,{}y,{}w,{}s,{}nest,{}lwrk,{}n,{}lamda,{}ifail,{}wrk,{}iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,{}lamda,{}c,{}ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,{}lamda,{}c,{}x,{}left,{}ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,{}lamda,{}c,{}x,{}ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,{}ncap7,{}x,{}y,{}w,{}lamda,{}ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}x,{}ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}qatm1,{}iaint1,{}laint,{}ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}iadif1,{}ladif,{}ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,{}kplus1,{}nrows,{}xmin,{}xmax,{}x,{}y,{}w,{}mf,{}xf,{}yf,{}lyf,{}ip,{}lwrk,{}liwrk,{}ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,{}a,{}xcap,{}ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,{}kplus1,{}nrows,{}x,{}y,{}w,{}ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) NIL NIL -(-736) +(-738) ((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}. See \\downlink{Manual Page}{manpageXXe04}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,{}m,{}n,{}fsumsq,{}s,{}lv,{}v,{}ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04ucf(n,{}nclin,{}ncnln,{}nrowa,{}nrowj,{}nrowr,{}a,{}bl,{}bu,{}liwork,{}lwork,{}sta,{}cra,{}der,{}fea,{}fun,{}hes,{}infb,{}infs,{}linf,{}lint,{}list,{}maji,{}majp,{}mini,{}minp,{}mon,{}nonf,{}opt,{}ste,{}stao,{}stac,{}stoo,{}stoc,{}ve,{}istate,{}cjac,{}clamda,{}r,{}x,{}ifail,{}confun,{}objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "\\spad{e04naf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}nrowh,{}ncolh,{}bigbnd,{}a,{}bl,{}bu,{}cvec,{}featol,{}hess,{}cold,{}lpp,{}orthog,{}liwork,{}lwork,{}x,{}istate,{}ifail,{}qphess)} is a comprehensive programming (\\spad{QP}) or linear programming (\\spad{LP}) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04mbf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}a,{}bl,{}bu,{}cvec,{}linobj,{}liwork,{}lwork,{}x,{}ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,{}ibound,{}liw,{}lw,{}bl,{}bu,{}x,{}ifail,{}funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,{}es,{}fu,{}it,{}lin,{}list,{}ma,{}op,{}pr,{}sta,{}sto,{}ve,{}x,{}ifail,{}objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) NIL NIL -(-737) +(-739) ((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations. See \\downlink{Manual Page}{manpageXXf01}.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,{}m,{}n,{}ncolq,{}lda,{}theta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}theta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,{}m,{}n,{}ncolq,{}lda,{}zeta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}zeta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,{}avals,{}lal,{}nrow,{}ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,{}nz,{}licn,{}lirn,{}abort,{}avals,{}irn,{}icn,{}droptl,{}densw,{}ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01bsf(n,{}nz,{}licn,{}ivect,{}jvect,{}icn,{}ikeep,{}grow,{}eta,{}abort,{}idisp,{}avals,{}ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,{}nz,{}licn,{}lirn,{}pivot,{}lblock,{}grow,{}abort,{}a,{}irn,{}icn,{}ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) NIL NIL -(-738) +(-740) ((|constructor| (NIL "This package uses the NAG Library to compute \\begin{items} \\item eigenvalues and eigenvectors of a matrix \\item eigenvalues and eigenvectors of generalized matrix eigenvalue problems \\item singular values and singular vectors of a matrix. \\end{items} See \\downlink{Manual Page}{manpageXXf02}.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldph,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldpt,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image,{}monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,{}ia,{}ib,{}eps1,{}matv,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)\\spad{Bx} where A and \\spad{B} are real,{} square matrices,{} using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,{}n,{}alb,{}ub,{}m,{}iv,{}a,{}ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,{}iar,{}\\spad{ai},{}iai,{}n,{}ivr,{}ivi,{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,{}iai,{}n,{}ivr,{}ivi,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,{}n,{}ivr,{}ivi,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,{}n,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,{}ib,{}n,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,{}ib,{}n,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,{}ia,{}n,{}iv,{}ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,{}n,{}a,{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) NIL NIL -(-739) +(-741) ((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\axiom{AX=B},{} where \\axiom{\\spad{B}} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained. See \\downlink{Manual Page}{manpageXXf04}.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "\\spad{f04qaf(m,{}n,{}damp,{}atol,{}btol,{}conlim,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}b,{}ifail,{}aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,{}al,{}lal,{}d,{}nrow,{}ir,{}b,{}nrb,{}iselct,{}nrx,{}ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,{}b,{}precon,{}shift,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}rtol,{}ifail,{}aprod,{}msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f04maf(n,{}nz,{}avals,{}licn,{}irn,{}lirn,{}icn,{}wkeep,{}ikeep,{}inform,{}b,{}acc,{}noits,{}ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,{}n,{}nra,{}tol,{}lwork,{}a,{}b,{}ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,{}n,{}d,{}e,{}b,{}ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,{}a,{}licn,{}icn,{}ikeep,{}mtype,{}idisp,{}rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A \\spad{x=b},{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,{}ia,{}b,{}n,{}iaa,{}ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,{}b,{}n,{}a,{}ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,{}b,{}n,{}a,{}ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,{}b,{}ib,{}n,{}m,{}ic,{}a,{}ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) NIL NIL -(-740) +(-742) ((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations. See \\downlink{Manual Page}{manpageXXf07}.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,{}n,{}nrhs,{}a,{}lda,{}ldb,{}b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,{}n,{}lda,{}a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,{}n,{}nrhs,{}a,{}lda,{}ipiv,{}ldb,{}b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A \\spad{X=B},{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,{}n,{}lda,{}a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) NIL NIL -(-741) +(-743) ((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions. See \\downlink{Manual Page}{manpageXXs}.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,{}y,{}z,{}r,{}ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,{}y,{}ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,{}ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,{}ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,{}ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,{}ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,{}ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,{}fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}\\space{8}(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,{}ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,{}ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,{}ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,{}ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,{}ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,{}ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,{}x,{}tol,{}ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,{}ifail)} returns a value for the log,{} \\spad{ln}(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,{}ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,{}ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,{}ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,{}ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,{}ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}."))) NIL NIL -(-742) +(-744) ((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}"))) NIL NIL -(-743 S) +(-745 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-744) +(-746) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-745 S) +(-747 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-746) +(-748) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-747 |Par|) +(-749 |Par|) ((|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 -(-748 -1935) +(-750 -3220) ((|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 -(-749 P -1935) +(-751 P -3220) ((|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 -(-750 T$) +(-752 T$) NIL NIL NIL -(-751 UP -1935) +(-753 UP -3220) ((|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 -(-752) +(-754) ((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-753 R) +(-755 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-754) +(-756) ((|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."))) -(((-4368 "*") . T)) +(((-4370 "*") . T)) NIL -(-755 R -1935) +(-757 R -3220) ((|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 -(-756 S) +(-758 S) ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-757) +(-759) ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-758 R |PolR| E |PolE|) +(-760 R |PolR| E |PolE|) ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) NIL NIL -(-759 R E V P TS) +(-761 R E V P TS) ((|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 -(-760 -1935 |ExtF| |SUEx| |ExtP| |n|) +(-762 -3220 |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 -(-761 BP E OV R P) +(-763 BP E OV R P) ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) NIL NIL -(-762 |Par|) +(-764 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,{}eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with variable \\spad{x}. Fraction \\spad{P} \\spad{RN}.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable."))) NIL NIL -(-763 R |VarSet|) +(-765 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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . 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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 -(-765 R) +(-767 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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T)) +((|HasCategory| |#1| (QUOTE (-890))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| (-1060) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1129))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) +(-768 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) -(-767 R E V P) +(-769 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.}"))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-768 S) +(-770 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-169)))) -(-769) +((-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-169)))) +(-771) ((|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 NIL -(-770) +(-772) ((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|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.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|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 -(-771) +(-773) ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,{}y,{}x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})\\spad{**}(-1/5)}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try ,{} did ,{} next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is the same as \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation\\spad{'s} right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-772) +(-774) ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-773 |Curve|) +(-775 |Curve|) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,{}r,{}n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) NIL NIL -(-774) +(-776) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) NIL NIL -(-775) +(-777) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-776) +(-778) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,{}y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-777) +(-779) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-778) +(-780) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-779 S R) +(-781 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1037))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-362)))) -(-780 R) +((|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-362)))) +(-782 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-781 -1559 R OS S) +(-783 -4029 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-782 R) +(-784 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1152)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-1559 (|HasCategory| (-978 |#1|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (-1559 (|HasCategory| (-978 |#1|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1037))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| (-978 |#1|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-978 |#1|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552))))) -(-783) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1154)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-4029 (|HasCategory| (-980 |#1|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (-4029 (|HasCategory| (-980 |#1|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| (-980 |#1|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-980 |#1|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) +(-785) ((|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 -(-784 R -1935 L) +(-786 R -3220 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 -(-785 R -1935) +(-787 R -3220) ((|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 -(-786) +(-788) ((|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 -(-787 R -1935) +(-789 R -3220) ((|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 -(-788) +(-790) ((|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 -(-789 -1935 UP UPUP R) +(-791 -3220 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 -(-790 -1935 UP L LQ) +(-792 -3220 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 -(-791) +(-793) ((|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 -(-792 -1935 UP L LQ) +(-794 -3220 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 -(-793 -1935 UP) +(-795 -3220 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 -(-794 -1935 L UP A LO) +(-796 -3220 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 -(-795 -1935 UP) +(-797 -3220 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)))) -(-796 -1935 LO) +(-798 -3220 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 -(-797 -1935 LODO) +(-799 -3220 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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(|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-778))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))))) (|HasCategory| (-552) (QUOTE (-832))) (-12 (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (QUOTE (-1030)))) (-12 (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154))))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552))))) (-4029 (|HasCategory| |#2| (QUOTE (-1030))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-1078)))) (|HasAttribute| |#2| (QUOTE -4365)) (|HasCategory| |#2| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) +(-801 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-888))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-801 (-1152)) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| (-801 (-1152)) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| (-801 (-1152)) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| (-801 (-1152)) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| (-801 (-1152)) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4364)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-142))))) -(-800 |Kernels| R |var|) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-890))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-803 (-1154)) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| (-803 (-1154)) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| (-803 (-1154)) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| (-803 (-1154)) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| (-803 (-1154)) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) +(-802 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) -(((-4368 "*") |has| |#2| (-357)) (-4359 |has| |#2| (-357)) (-4364 |has| |#2| (-357)) (-4358 |has| |#2| (-357)) (-4363 . T) (-4361 . T) (-4360 . T)) +(((-4370 "*") |has| |#2| (-357)) (-4361 |has| |#2| (-357)) (-4366 |has| |#2| (-357)) (-4360 |has| |#2| (-357)) (-4365 . T) (-4363 . T) (-4362 . T)) ((|HasCategory| |#2| (QUOTE (-357)))) -(-801 S) +(-803 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}))."))) NIL NIL -(-802 S) +(-804 S) ((|constructor| (NIL "\\indented{3}{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 non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the \\spad{n-th} monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the \\spad{n-th} monomial of \\spad{x}.")) (|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} and \\spad{y = m * r} hold and such that \\spad{l} and \\spad{r} have no overlap,{} that is \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l,{} r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x,{} s)} returns the exact right quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} that is \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x,{} s)} returns the exact left quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = y * q},{}} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,{}y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL NIL -(-803) +(-805) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-804) +(-806) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) NIL NIL -(-805) +(-807) ((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) NIL NIL -(-806) +(-808) ((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL -(-807) +(-809) ((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) NIL NIL -(-808) +(-810) ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-809 R) +(-811 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-810 P R) +(-812 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) ((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-228)))) -(-811) +(-813) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) NIL NIL -(-812) +(-814) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) NIL NIL -(-813 S) +(-815 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4366 . T) (-4356 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4358 . T) (-4369 . T) (-4283 . T)) NIL -(-814) +(-816) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) NIL NIL -(-815 R S) +(-817 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-816 R) +(-818 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."))) -((-4363 |has| |#1| (-828))) -((|HasCategory| |#1| (QUOTE (-828))) (-1559 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-537))) (-1559 (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-21)))) -(-817 R) +((-4365 |has| |#1| (-830))) +((|HasCategory| |#1| (QUOTE (-830))) (-4029 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-537))) (-4029 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-21)))) +(-819 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4361 |has| |#1| (-169)) (-4360 |has| |#1| (-169)) (-4363 . T)) +((-4363 |has| |#1| (-169)) (-4362 |has| |#1| (-169)) (-4365 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144)))) -(-818) +(-820) ((|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)."))) NIL NIL -(-819) +(-821) ((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization 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.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization 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 -(-820) +(-822) ((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,{}start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,{}start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,{}start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}cons,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,{}routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|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 optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} 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|)))) (|NumericalOptimizationProblem|)) "\\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 optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} 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."))) NIL NIL -(-821) +(-823) ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-822 R S) +(-824 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-823 R) +(-825 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."))) -((-4363 |has| |#1| (-828))) -((|HasCategory| |#1| (QUOTE (-828))) (-1559 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-537))) (-1559 (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-21)))) -(-824) +((-4365 |has| |#1| (-830))) +((|HasCategory| |#1| (QUOTE (-830))) (-4029 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-537))) (-4029 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-21)))) +(-826) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-825 -4030 S) +(-827 -2072 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 -(-826) +(-828) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-827 S) +(-829 S) ((|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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) NIL NIL -(-828) +(-830) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4363 . T)) +((-4365 . T)) NIL -(-829 S) +(-831 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-830) +(-832) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-831 S R) +(-833 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169)))) -(-832 R) +(-834 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-833 R C) +(-835 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 (-357))) (|HasCategory| |#1| (QUOTE (-544)))) -(-834 R |sigma| -3427) +(-836 R |sigma| -2696) ((|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."))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) -(-835 |x| R |sigma| -3427) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) +(-837 |x| R |sigma| -2696) ((|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."))) -((-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-357)))) -(-836 R) +((-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-357)))) +(-838 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) -(-837) +(-839) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-838) +(-840) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-839 S) +(-841 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) NIL NIL -(-840) +(-842) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) NIL NIL -(-841) +(-843) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) NIL NIL -(-842) +(-844) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-843) +(-845) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-844 |VariableList|) +(-846 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-845 R |vl| |wl| |wtlevel|) +(-847 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"))) -((-4361 |has| |#1| (-169)) (-4360 |has| |#1| (-169)) (-4363 . T)) +((-4363 |has| |#1| (-169)) (-4362 |has| |#1| (-169)) (-4365 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357)))) -(-846 R PS UP) +(-848 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)."))) NIL NIL -(-847 R |x| |pt|) +(-849 R |x| |pt|) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}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.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\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)."))) NIL NIL -(-848 |p|) +(-850 |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}."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-849 |p|) +(-851 |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)."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-850 |p|) +(-852 |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)."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-849 |#1|) (QUOTE (-888))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| (-849 |#1|) (QUOTE (-142))) (|HasCategory| (-849 |#1|) (QUOTE (-144))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-849 |#1|) (QUOTE (-1001))) (|HasCategory| (-849 |#1|) (QUOTE (-803))) (-1559 (|HasCategory| (-849 |#1|) (QUOTE (-803))) (|HasCategory| (-849 |#1|) (QUOTE (-830)))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-849 |#1|) (QUOTE (-1127))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| (-849 |#1|) (QUOTE (-228))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -506) (QUOTE (-1152)) (LIST (QUOTE -849) (|devaluate| |#1|)))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -849) (|devaluate| |#1|)))) (|HasCategory| (-849 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -849) (|devaluate| |#1|)) (LIST (QUOTE -849) (|devaluate| |#1|)))) (|HasCategory| (-849 |#1|) (QUOTE (-301))) (|HasCategory| (-849 |#1|) (QUOTE (-537))) (|HasCategory| (-849 |#1|) (QUOTE (-830))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-849 |#1|) (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-849 |#1|) (QUOTE (-888)))) (|HasCategory| (-849 |#1|) (QUOTE (-142))))) -(-851 |p| PADIC) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-851 |#1|) (QUOTE (-890))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| (-851 |#1|) (QUOTE (-142))) (|HasCategory| (-851 |#1|) (QUOTE (-144))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-851 |#1|) (QUOTE (-1003))) (|HasCategory| (-851 |#1|) (QUOTE (-805))) (-4029 (|HasCategory| (-851 |#1|) (QUOTE (-805))) (|HasCategory| (-851 |#1|) (QUOTE (-832)))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-851 |#1|) (QUOTE (-1129))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| (-851 |#1|) (QUOTE (-228))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -506) (QUOTE (-1154)) (LIST (QUOTE -851) (|devaluate| |#1|)))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -851) (|devaluate| |#1|)))) (|HasCategory| (-851 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -851) (|devaluate| |#1|)) (LIST (QUOTE -851) (|devaluate| |#1|)))) (|HasCategory| (-851 |#1|) (QUOTE (-301))) (|HasCategory| (-851 |#1|) (QUOTE (-537))) (|HasCategory| (-851 |#1|) (QUOTE (-832))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-851 |#1|) (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-851 |#1|) (QUOTE (-890)))) (|HasCategory| (-851 |#1|) (QUOTE (-142))))) +(-853 |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)}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#2| (QUOTE (-888))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-803))) (-1559 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (QUOTE (-830)))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1127))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#2| (LIST (QUOTE -506) (QUOTE (-1152)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-830))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-142))))) -(-852 S T$) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#2| (QUOTE (-890))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-805))) (-4029 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1129))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#2| (LIST (QUOTE -506) (QUOTE (-1154)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-832))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-890)))) (|HasCategory| |#2| (QUOTE (-142))))) +(-854 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 (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))))) -(-853) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))))) +(-855) ((|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 -(-854) +(-856) ((|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 -(-855 CF1 CF2) +(-857 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-856 |ComponentFunction|) +(-858 |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 -(-857 CF1 CF2) +(-859 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-858 |ComponentFunction|) +(-860 |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 -(-859) +(-861) ((|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 -(-860 CF1 CF2) +(-862 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-861 |ComponentFunction|) +(-863 |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 -(-862) +(-864) ((|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 -(-863 R) +(-865 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 -(-864 R S L) +(-866 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 -(-865 S) +(-867 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 -(-866 |Base| |Subject| |Pat|) +(-868 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-1681 (|HasCategory| |#2| (QUOTE (-1028)))) (-1681 (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-1152)))))) (-12 (|HasCategory| |#2| (QUOTE (-1028))) (-1681 (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-1152)))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-1152))))) -(-867 R A B) +((-12 (-4107 (|HasCategory| |#2| (QUOTE (-1030)))) (-4107 (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-1154)))))) (-12 (|HasCategory| |#2| (QUOTE (-1030))) (-4107 (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-1154)))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-1154))))) +(-869 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 -(-868 R S) +(-870 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 -(-869 R -4251) +(-871 R -1765) ((|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 -(-870 R S) +(-872 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 -(-871 R) +(-873 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 -(-872 |VarSet|) +(-874 |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 -(-873 UP R) +(-875 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented"))) NIL NIL -(-874) +(-876) ((|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 -(-875 UP -1935) +(-877 UP -3220) ((|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 -(-876) +(-878) ((|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 -(-877) +(-879) ((|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 -(-878 A S) +(-880 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 -(-879 S) +(-881 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}."))) -((-4363 . T)) +((-4365 . T)) NIL -(-880 S) +(-882 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-881 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-883 |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 -(-882 S) +(-884 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."))) -((-4363 . T)) +((-4365 . T)) NIL -(-883 S) +(-885 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-884 S) +(-886 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4363 . T)) -((-1559 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-830)))) -(-885 R E |VarSet| S) +((-4365 . T)) +((-4029 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-832)))) +(-887 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 -(-886 R S) +(-888 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 -(-887 S) +(-889 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 (-142)))) -(-888) +(-890) ((|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}."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-889 |p|) +(-891 |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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) ((|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-142))) (|HasCategory| $ (QUOTE (-362)))) -(-890 R0 -1935 UP UPUP R) +(-892 R0 -3220 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 -(-891 UP UPUP R) +(-893 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 -(-892 UP UPUP) +(-894 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 -(-893 R) +(-895 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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-894 R) +(-896 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 -(-895 E OV R P) +(-897 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 -(-896) +(-898) ((|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 -(-897 -1935) +(-899 -3220) ((|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 -(-898 R) +(-900 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 -(-899) +(-901) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-900) +(-902) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4368 "*") . T)) +(((-4370 "*") . T)) NIL -(-901 -1935 P) +(-903 -3220 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-902 |xx| -1935) +(-904 |xx| -3220) ((|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 -(-903 R |Var| |Expon| GR) +(-905 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 -(-904 S) +(-906 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 -(-905) +(-907) ((|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 -(-906) +(-908) ((|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 -(-907) +(-909) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-908 R -1935) +(-910 R -3220) ((|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 -(-909) +(-911) ((|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 -(-910 S A B) +(-912 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 -(-911 S R -1935) +(-913 S R -3220) ((|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 -(-912 I) +(-914 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 -(-913 S E) +(-915 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 -(-914 S R L) +(-916 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 -(-915 S E V R P) +(-917 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 -865) (|devaluate| |#1|)))) -(-916 R -1935 -4251) +((|HasCategory| |#3| (LIST (QUOTE -867) (|devaluate| |#1|)))) +(-918 R -3220 -1765) ((|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 -(-917 -4251) +(-919 -1765) ((|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 -(-918 S R Q) +(-920 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 -(-919 S) +(-921 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 -(-920 S R P) +(-922 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 -(-921) +(-923) ((|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 -(-922 R) +(-924 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-709))) (|HasCategory| |#1| (QUOTE (-1028))) (-12 (|HasCategory| |#1| (QUOTE (-981))) (|HasCategory| |#1| (QUOTE (-1028)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-923 |lv| R) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-711))) (|HasCategory| |#1| (QUOTE (-1030))) (-12 (|HasCategory| |#1| (QUOTE (-983))) (|HasCategory| |#1| (QUOTE (-1030)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-925 |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 -(-924 |TheField| |ThePols|) +(-926 |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 (-828)))) -(-925 R S) +((|HasCategory| |#1| (QUOTE (-830)))) +(-927 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 -(-926 |x| R) +(-928 |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 -(-927 S R E |VarSet|) +(-929 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 (-888))) (|HasAttribute| |#2| (QUOTE -4364)) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#4| (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#4| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#4| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#4| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-830)))) -(-928 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-890))) (|HasAttribute| |#2| (QUOTE -4366)) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#4| (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#4| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#4| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#4| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-832)))) +(-930 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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) NIL -(-929 E V R P -1935) +(-931 E V R P -3220) ((|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 -(-930 E |Vars| R P S) +(-932 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 -(-931 R) +(-933 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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-888))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1152) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| (-1152) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| (-1152) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| (-1152) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| (-1152) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4364)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-142))))) -(-932 E V R P -1935) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-890))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1154) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| (-1154) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| (-1154) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| (-1154) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| (-1154) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) +(-934 E V R P -3220) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-445)))) -(-933) +(-935) ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) NIL NIL -(-934) +(-936) ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-935 R L) +(-937 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-936 A B) +(-938 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -(-937 S) +(-939 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"))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-938) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-940) ((|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 -(-939 -1935) +(-941 -3220) ((|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 -(-940 I) +(-942 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 -(-941) +(-943) ((|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 -(-942 R E) +(-944 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}"))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-129)))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4364))) -(-943 A B) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-129)))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4366))) +(-945 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"))) -((-4363 -12 (|has| |#2| (-466)) (|has| |#1| (-466)))) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| |#2| (QUOTE (-776)))) (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-830))))) (-12 (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| |#2| (QUOTE (-776)))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| |#2| (QUOTE (-776))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-776))) (|HasCategory| |#2| (QUOTE 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(|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-830))))) -(-944) +((-4365 -12 (|has| |#2| (-466)) (|has| |#1| (-466)))) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-778))) (|HasCategory| |#2| (QUOTE (-778)))) (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-832))))) (-12 (|HasCategory| |#1| (QUOTE (-778))) (|HasCategory| |#2| (QUOTE (-778)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-778))) (|HasCategory| |#2| (QUOTE (-778))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-778))) (|HasCategory| |#2| (QUOTE (-778))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-12 (|HasCategory| |#1| (QUOTE (-711))) (|HasCategory| |#2| (QUOTE (-711))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-362)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-12 (|HasCategory| |#1| (QUOTE (-711))) (|HasCategory| |#2| (QUOTE (-711)))) (-12 (|HasCategory| |#1| (QUOTE (-778))) (|HasCategory| |#2| (QUOTE (-778))))) (-12 (|HasCategory| |#1| (QUOTE (-711))) (|HasCategory| |#2| (QUOTE (-711)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-832))))) +(-946) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-945 T$) +(-947 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the variable name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula"))) NIL NIL -(-946) +(-948) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}."))) NIL NIL -(-947 S) +(-949 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL -(-948 R |polR|) +(-950 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 (-445)))) -(-949) +(-951) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-950) +(-952) ((|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 -(-951 S |Coef| |Expon| |Var|) +(-953 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 -(-952 |Coef| |Expon| |Var|) +(-954 |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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-953) +(-955) ((|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 -(-954 S R E |VarSet| P) +(-956 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 (-544)))) -(-955 R E |VarSet| P) +(-957 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."))) -((-4366 . T) (-2997 . T)) +((-4368 . T) (-4283 . T)) NIL -(-956 R E V P) +(-958 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 (-144))) (|HasCategory| |#1| (QUOTE (-301)))) (|HasCategory| |#1| (QUOTE (-445)))) -(-957 K) +(-959 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 -(-958 |VarSet| E RC P) +(-960 |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 -(-959 R) +(-961 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}."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-960 R1 R2) +(-962 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) NIL NIL -(-961 R) +(-963 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 -(-962 K) +(-964 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 -(-963 R E OV PPR) +(-965 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 -(-964 K R UP -1935) +(-966 K R UP -3220) ((|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 -(-965 |vl| |nv|) +(-967 |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 -(-966 R |Var| |Expon| |Dpoly|) +(-968 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 (-144))) (|HasCategory| |#1| (QUOTE (-301))))) -(-967 R E V P TS) +(-969 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 -(-968) +(-970) ((|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 -(-969 A B R S) +(-971 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 -(-970 A S) +(-972 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 (-888))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1127)))) -(-971 S) +((|HasCategory| |#2| (QUOTE (-890))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1129)))) +(-973 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}."))) -((-2997 . T) (-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4283 . T) (-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-972 |n| K) +(-974 |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 -(-973) +(-975) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-974 S) +(-976 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."))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL -(-975 S R) +(-977 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 (-537))) (|HasCategory| |#2| (QUOTE (-1037))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-284)))) -(-976 R) +((|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-284)))) +(-978 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}."))) -((-4359 |has| |#1| (-284)) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 |has| |#1| (-284)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-977 QR R QS S) +(-979 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 -(-978 R) +(-980 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.}"))) -((-4359 |has| |#1| (-284)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1152)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-1037))) (|HasCategory| |#1| (QUOTE (-537))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357))))) -(-979 S) +((-4361 |has| |#1| (-284)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -506) (QUOTE (-1154)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-537))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357))))) +(-981 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}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-980 S) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-982 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-981) +(-983) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-982 -1935 UP UPUP |radicnd| |n|) +(-984 -3220 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4359 |has| (-401 |#2|) (-357)) (-4364 |has| (-401 |#2|) (-357)) (-4358 |has| (-401 |#2|) (-357)) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-1559 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-1559 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-1559 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-1559 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) -(-983 |bb|) +((-4361 |has| (-401 |#2|) (-357)) (-4366 |has| (-401 |#2|) (-357)) (-4360 |has| (-401 |#2|) (-357)) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-4029 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-4029 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-4029 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-4029 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) +(-985 |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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-552) (QUOTE (-888))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-1152)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1001))) (|HasCategory| (-552) (QUOTE (-803))) (-1559 (|HasCategory| (-552) (QUOTE (-803))) (|HasCategory| (-552) (QUOTE (-830)))) (|HasCategory| (-552) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1127))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1152)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-552) (LIST (QUOTE -623) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-888)))) (|HasCategory| (-552) (QUOTE (-142))))) -(-984) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-552) (QUOTE (-890))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-1154)))) (|HasCategory| (-552) (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-144))) (|HasCategory| (-552) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-1003))) (|HasCategory| (-552) (QUOTE (-805))) (-4029 (|HasCategory| (-552) (QUOTE (-805))) (|HasCategory| (-552) (QUOTE (-832)))) (|HasCategory| (-552) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1129))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| (-552) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-228))) (|HasCategory| (-552) (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| (-552) (LIST (QUOTE -506) (QUOTE (-1154)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -303) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -280) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-301))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-552) (LIST (QUOTE -625) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-552) (QUOTE (-890)))) (|HasCategory| (-552) (QUOTE (-142))))) +(-986) ((|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 -(-985) +(-987) ((|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 -(-986 RP) +(-988 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 -(-987 S) +(-989 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 -(-988 A S) +(-990 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 -4367)) (|HasCategory| |#2| (QUOTE (-1076)))) -(-989 S) +((|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#2| (QUOTE (-1078)))) +(-991 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}."))) -((-2997 . T)) +((-4283 . T)) NIL -(-990 S) +(-992 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-991) +(-993) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4359 . T) (-4364 . T) (-4358 . T) (-4361 . T) (-4360 . T) ((-4368 "*") . T) (-4363 . T)) +((-4361 . T) (-4366 . T) (-4360 . T) (-4363 . T) (-4362 . T) ((-4370 "*") . T) (-4365 . T)) NIL -(-992 R -1935) +(-994 R -3220) ((|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 -(-993 R -1935) +(-995 R -3220) ((|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 -(-994 -1935 UP) +(-996 -3220 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 -(-995 -1935 UP) +(-997 -3220 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 -(-996 S) +(-998 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 -(-997 F1 UP UPUP R F2) +(-999 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 -(-998) +(-1000) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-999 |Pol|) +(-1001 |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 -(-1000 |Pol|) +(-1002 |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 -(-1001) +(-1003) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1002) +(-1004) ((|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 -(-1003 |TheField|) +(-1005 |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"))) -((-4359 . T) (-4364 . T) (-4358 . T) (-4361 . T) (-4360 . T) ((-4368 "*") . T) (-4363 . T)) -((-1559 (|HasCategory| (-401 (-552)) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-401 (-552)) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 (-552)) (LIST (QUOTE -1017) (QUOTE (-552))))) -(-1004 -1935 L) +((-4361 . T) (-4366 . T) (-4360 . T) (-4363 . T) (-4362 . T) ((-4370 "*") . T) (-4365 . T)) +((-4029 (|HasCategory| (-401 (-552)) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-401 (-552)) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-401 (-552)) (LIST (QUOTE -1019) (QUOTE (-552))))) +(-1006 -3220 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 -(-1005 S) +(-1007 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 (-1076)))) -(-1006 R E V P) +((|HasCategory| |#1| (QUOTE (-1078)))) +(-1008 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."))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1007 R) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1009 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 (-4368 "*")))) -(-1008 R) +((|HasAttribute| |#1| (QUOTE (-4370 "*")))) +(-1010 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-301)))) -(-1009 S) +(-1011 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 -(-1010) +(-1012) ((|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 -(-1011 S) +(-1013 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 -(-1012 S) +(-1014 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 -(-1013 -1935 |Expon| |VarSet| |FPol| |LFPol|) +(-1015 -3220 |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"))) -(((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1014) +(-1016) ((|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.}"))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2162) (QUOTE (-52))))))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-52) (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-52) (QUOTE (-1076))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1076))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-1152) (QUOTE (-830))) (|HasCategory| (-52) (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1015) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (QUOTE (-1154))) (LIST (QUOTE |:|) (QUOTE -3360) (QUOTE (-52))))))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-52) (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-52) (QUOTE (-1078))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1078))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-1154) (QUOTE (-832))) (|HasCategory| (-52) (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1017) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1016 A S) +(-1018 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 -(-1017 S) +(-1019 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 -(-1018 Q R) +(-1020 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 -(-1019) +(-1021) ((|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 -(-1020 UP) +(-1022 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 -(-1021 R) +(-1023 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 -(-1022 R) +(-1024 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 -(-1023 T$) +(-1025 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1024 T$) -((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitepoint is the contant indicating the white point of this color space."))) +(-1026 T$) +((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-1025 R |ls|) +(-1027 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}."))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| (-763 |#1| (-844 |#2|)) (QUOTE (-1076))) (|HasCategory| (-763 |#1| (-844 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -763) (|devaluate| |#1|) (LIST (QUOTE -844) (|devaluate| |#2|)))))) (|HasCategory| (-763 |#1| (-844 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-763 |#1| (-844 |#2|)) (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| (-844 |#2|) (QUOTE (-362))) (|HasCategory| (-763 |#1| (-844 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1026) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| (-765 |#1| (-846 |#2|)) (QUOTE (-1078))) (|HasCategory| (-765 |#1| (-846 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -765) (|devaluate| |#1|) (LIST (QUOTE -846) (|devaluate| |#2|)))))) (|HasCategory| (-765 |#1| (-846 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-765 |#1| (-846 |#2|)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| (-846 |#2|) (QUOTE (-362))) (|HasCategory| (-765 |#1| (-846 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1028) ((|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 -(-1027 S) +(-1029 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 -(-1028) +(-1030) ((|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."))) -((-4363 . T)) +((-4365 . T)) NIL -(-1029 |xx| -1935) +(-1031 |xx| -3220) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1030 S |m| |n| R |Row| |Col|) +(-1032 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 (-301))) (|HasCategory| |#4| (QUOTE (-357))) (|HasCategory| |#4| (QUOTE (-544))) (|HasCategory| |#4| (QUOTE (-169)))) -(-1031 |m| |n| R |Row| |Col|) +(-1033 |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"))) -((-4366 . T) (-2997 . T) (-4361 . T) (-4360 . T)) +((-4368 . T) (-4283 . T) (-4363 . T) (-4362 . T)) NIL -(-1032 |m| |n| R) +(-1034 |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}."))) -((-4366 . T) (-4361 . T) (-4360 . T)) -((-1559 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1076))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-357)))) (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (QUOTE (-1076))) (|HasCategory| |#3| (QUOTE (-301))) (|HasCategory| |#3| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -599) (QUOTE (-842)))) (-12 (|HasCategory| |#3| (QUOTE (-1076))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) -(-1033 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4368 . T) (-4363 . T) (-4362 . T)) +((-4029 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-357)))) (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (QUOTE (-301))) (|HasCategory| |#3| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -599) (QUOTE (-844)))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) +(-1035 |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 -(-1034 R) +(-1036 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 -(-1035) +(-1037) ((|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 -(-1036 S) +(-1038 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1037) +(-1039) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1038 |TheField| |ThePolDom|) +(-1040 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1039) +(-1041) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4354 . T) (-4358 . T) (-4353 . T) (-4364 . T) (-4365 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4356 . T) (-4360 . T) (-4355 . T) (-4366 . T) (-4367 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1040) +(-1042) ((|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}"))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2162) (QUOTE (-52))))))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-52) (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-52) (QUOTE (-1076))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1076))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (QUOTE (-1076))) (|HasCategory| (-1152) (QUOTE (-830))) (|HasCategory| (-52) (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 (-1152)) (|:| -2162 (-52))) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1041 S R E V) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (QUOTE (-1154))) (LIST (QUOTE |:|) (QUOTE -3360) (QUOTE (-52))))))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-52) (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-52) (QUOTE (-1078))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1078))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (QUOTE (-1078))) (|HasCategory| (-1154) (QUOTE (-832))) (|HasCategory| (-52) (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-52) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 (-1154)) (|:| -3360 (-52))) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1043 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -971) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-1152))))) -(-1042 R E V) +((|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -973) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-1154))))) +(-1044 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) NIL -(-1043) +(-1045) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-1044 S |TheField| |ThePols|) +(-1046 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 -(-1045 |TheField| |ThePols|) +(-1047 |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 -(-1046 R E V P TS) +(-1048 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 -(-1047 S R E V P) +(-1049 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 -(-1048 R E V P) +(-1050 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}."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-1049 R E V P TS) +(-1051 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 -(-1050) +(-1052) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1051 |f|) +(-1053 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1052 |Base| R -1935) +(-1054 |Base| R -3220) ((|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 -(-1053 |Base| R -1935) +(-1055 |Base| R -3220) ((|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 -(-1054 R |ls|) +(-1056 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 -(-1055 UP SAE UPA) +(-1057 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 -(-1056 R UP M) +(-1058 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."))) -((-4359 |has| |#1| (-357)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-343))) (-1559 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-343)))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152))))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357)))) (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357))))) -(-1057 UP SAE UPA) +((-4361 |has| |#1| (-357)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-343))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-343)))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154))))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357)))) (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357))))) +(-1059 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 -(-1058) +(-1060) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1059) +(-1061) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1060 S) +(-1062 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 -(-1061) +(-1063) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,{}s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(n,{}s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `failed'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1062 R) +(-1064 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 -(-1063 R) +(-1065 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"))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-888))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1064 (-1152)) (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| (-1064 (-1152)) (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| (-1064 (-1152)) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| (-1064 (-1152)) (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| (-1064 (-1152)) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4364)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-142))))) -(-1064 S) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-890))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1066 (-1154)) (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| (-1066 (-1154)) (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| (-1066 (-1154)) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| (-1066 (-1154)) (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| (-1066 (-1154)) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) +(-1066 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 -(-1065 R S) +(-1067 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 (-828)))) -(-1066) +((|HasCategory| |#1| (QUOTE (-830)))) +(-1068) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1067 R S) +(-1069 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 -(-1068 S) +(-1070 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 (-1076)))) -(-1069 S) +((|HasCategory| |#1| (QUOTE (-1078)))) +(-1071 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."))) -((-2997 . T)) +((-4283 . T)) NIL -(-1070 S) +(-1072 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-1076)))) -(-1071 S L) +((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1078)))) +(-1073 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]}."))) -((-2997 . T)) +((-4283 . T)) NIL -(-1072) +(-1074) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1073 A S) +(-1075 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1074 S) +(-1076 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4356 . T) (-2997 . T)) +((-4358 . T) (-4283 . T)) NIL -(-1075 S) +(-1077 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 -(-1076) +(-1078) ((|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 -(-1077 |m| |n|) +(-1079 |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 -(-1078 S) +(-1080 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)}}"))) -((-4366 . T) (-4356 . T) (-4367 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-830))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1079 |Str| |Sym| |Int| |Flt| |Expr|) +((-4368 . T) (-4358 . T) (-4369 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-832))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1081 |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|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1080) +(-1082) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1081 |Str| |Sym| |Int| |Flt| |Expr|) +(-1083 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1082 R FS) +(-1084 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 -(-1083 R E V P TS) +(-1085 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 -(-1084 R E V P TS) +(-1086 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 -(-1085 R E V P) +(-1087 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.}"))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-1086) +(-1088) ((|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 -(-1087 S) +(-1089 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1088) +(-1090) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1089 |dimtot| |dim1| S) +(-1091 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4360 |has| |#3| (-1028)) (-4361 |has| |#3| (-1028)) (-4363 |has| |#3| (-6 -4363)) ((-4368 "*") |has| |#3| (-169)) (-4366 . 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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 (-445)))) -(-1091) +(-1093) ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1092 R -1935) +(-1094 R -3220) ((|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 -(-1093 R) +(-1095 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 -(-1094) +(-1096) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL -(-1095) +(-1097) ((|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 -(-1096) +(-1098) ((|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."))) -((-4354 . T) (-4358 . T) (-4353 . T) (-4364 . T) (-4365 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4356 . T) (-4360 . T) (-4355 . T) (-4366 . T) (-4367 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1097 S) +(-1099 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4366 . T) (-4367 . T) (-2997 . T)) +((-4368 . T) (-4369 . T) (-4283 . T)) NIL -(-1098 S |ndim| R |Row| |Col|) +(-1100 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-357))) (|HasAttribute| |#3| (QUOTE (-4368 "*"))) (|HasCategory| |#3| (QUOTE (-169)))) -(-1099 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-357))) (|HasAttribute| |#3| (QUOTE (-4370 "*"))) (|HasCategory| |#3| (QUOTE (-169)))) +(-1101 |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."))) -((-2997 . T) (-4366 . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4283 . T) (-4368 . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1100 R |Row| |Col| M) +(-1102 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 -(-1101 R |VarSet|) +(-1103 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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-888))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -865) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -865) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4364)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (-1559 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-142))))) -(-1102 |Coef| |Var| SMP) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-890))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -867) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -867) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (-4029 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-890)))) (|HasCategory| |#1| (QUOTE (-142))))) +(-1104 |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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-357)))) -(-1103 R E V P) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-357)))) +(-1105 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}"))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-1104 UP -1935) +(-1106 UP -3220) ((|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 -(-1105 R) +(-1107 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 -(-1106 R) +(-1108 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 -(-1107 R) +(-1109 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 -(-1108 S A) +(-1110 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 (-830)))) -(-1109 R) +((|HasCategory| |#1| (QUOTE (-832)))) +(-1111 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 -(-1110 R) +(-1112 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 -(-1111) +(-1113) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1112) +(-1114) ((|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 -(-1113) +(-1115) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) -((-2997 . T)) +((-4283 . T)) NIL -(-1114) +(-1116) ((|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 -(-1115) +(-1117) ((|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 -(-1116 V C) +(-1118 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 -(-1117 V C) +(-1119 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-1116 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1116) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1116 |#1| |#2|) (QUOTE (-1076)))) (|HasCategory| (-1116 |#1| |#2|) (QUOTE (-1076))) (-1559 (|HasCategory| (-1116 |#1| |#2|) (LIST (QUOTE -599) (QUOTE (-842)))) (-12 (|HasCategory| (-1116 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1116) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1116 |#1| |#2|) (QUOTE (-1076))))) (|HasCategory| (-1116 |#1| |#2|) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1118 |ndim| R) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-1118 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1118) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1118 |#1| |#2|) (QUOTE (-1078)))) (|HasCategory| (-1118 |#1| |#2|) (QUOTE (-1078))) (-4029 (|HasCategory| (-1118 |#1| |#2|) (LIST (QUOTE -599) (QUOTE (-844)))) (-12 (|HasCategory| (-1118 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1118) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1118 |#1| |#2|) (QUOTE (-1078))))) (|HasCategory| (-1118 |#1| |#2|) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1120 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((-4363 . T) (-4355 |has| |#2| (-6 (-4368 "*"))) (-4366 . T) (-4360 . T) (-4361 . T)) -((|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4368 "*"))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-552)))) (-1559 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-357))) (-1559 (|HasAttribute| |#2| (QUOTE (-4368 "*"))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasCategory| |#2| (QUOTE (-228)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-169)))) -(-1119 S) +((-4365 . T) (-4357 |has| |#2| (-6 (-4370 "*"))) (-4368 . T) (-4362 . T) (-4363 . T)) +((|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4370 "*"))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1019) (QUOTE (-552)))) (-4029 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-357))) (-4029 (|HasAttribute| |#2| (QUOTE (-4370 "*"))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasCategory| |#2| (QUOTE (-228)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-169)))) +(-1121 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1120) +(-1122) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-1121 R E V P TS) +(-1123 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 -(-1122 R E V P) +(-1124 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."))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1123 S) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1125 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}."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1124 A S) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1126 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 -(-1125 S) +(-1127 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})}."))) -((-2997 . T)) +((-4283 . T)) NIL -(-1126 |Key| |Ent| |dent|) +(-1128 |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."))) -((-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-830))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1127) +((-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-832))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1129) ((|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 -(-1128 |Coef|) +(-1130 |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 -(-1129 S) +(-1131 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 -(-1130 A B) +(-1132 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 -(-1131 A B C) +(-1133 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 -(-1132 S) +(-1134 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."))) -((-4367 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1133) +((-4369 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1135) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-1134) +(-1136) NIL -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| (-141) (QUOTE (-830))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1076))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-141) (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| (-141) (QUOTE (-1076))) (-12 (|HasCategory| (-141) (QUOTE (-1076))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1135 |Entry|) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| (-141) (QUOTE (-832))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1078))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| (-141) (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| (-141) (QUOTE (-1078))) (-12 (|HasCategory| (-141) (QUOTE (-1078))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1137 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (QUOTE (-1134))) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#1|)))))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (QUOTE (-1076))) (|HasCategory| (-1134) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 (-1134)) (|:| -2162 |#1|)) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1136 A) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (QUOTE (-1136))) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#1|)))))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (QUOTE (-1078))) (|HasCategory| (-1136) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 (-1136)) (|:| -3360 |#1|)) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1138 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 (-357))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) -(-1137 |Coef|) +(-1139 |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 -(-1138 |Coef|) +(-1140 |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 -(-1139 R UP) +(-1141 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 (-301)))) -(-1140 |n| R) +(-1142 |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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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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-754)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-754)) (|devaluate| |#1|)))) (|HasCategory| (-754) (QUOTE (-1088))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-754))))) (|HasSignature| |#1| (LIST (QUOTE -1477) (LIST (|devaluate| |#1|) (QUOTE (-1152)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-754))))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1152))))) (|HasSignature| |#1| (LIST (QUOTE -1853) (LIST (LIST (QUOTE -627) (QUOTE (-1152))) (|devaluate| |#1|))))))) -(-1151) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-756)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-756)) (|devaluate| |#1|)))) (|HasCategory| (-756) (QUOTE (-1090))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-756))))) (|HasSignature| |#1| (LIST (QUOTE -3213) (LIST (|devaluate| |#1|) (QUOTE (-1154)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-756))))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-1176))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2889) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1154))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -629) (QUOTE (-1154))) (|devaluate| |#1|))))))) +(-1153) ((|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 -(-1152) +(-1154) ((|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,{}[],{}[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts the string \\spad{s} to a symbol.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1153 R) +(-1155 R) ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|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 -(-1154 R) +(-1156 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-6 -4364)) (-4360 . T) (-4361 . T) (-4363 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| (-952) (QUOTE (-129))) (|HasCategory| |#1| (QUOTE (-544)))) (-4029 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4366))) +(-1157) ((|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 -(-1156) +(-1158) ((|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 -(-1157) +(-1159) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{symbols,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: Integer,{} DoubleFloat,{} Symbol,{} String,{} SExpression. See Also: SExpression. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} if \\spad{`x'} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is 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 value returned 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'}.") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|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 cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1158 R) +(-1160 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 -(-1159) +(-1161) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1160 S) +(-1162 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 -(-1161 S) +(-1163 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 -(-1162 |Key| |Entry|) +(-1164 |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}"))) -((-4366 . T) (-4367 . T)) -((-12 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3998) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2162) (|devaluate| |#2|)))))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1076)))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-1076))) (-1559 (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-842)))) (|HasCategory| (-2 (|:| -3998 |#1|) (|:| -2162 |#2|)) (LIST (QUOTE -599) (QUOTE (-842))))) -(-1163 R) +((-4368 . T) (-4369 . T)) +((-12 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2670) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3360) (|devaluate| |#2|)))))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1078)))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -600) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-1078))) (-4029 (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#2| (LIST (QUOTE -599) (QUOTE (-844)))) (|HasCategory| (-2 (|:| -2670 |#1|) (|:| -3360 |#2|)) (LIST (QUOTE -599) (QUOTE (-844))))) +(-1165 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 -(-1164 S |Key| |Entry|) +(-1166 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 -(-1165 |Key| |Entry|) +(-1167 |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})}."))) -((-4367 . T) (-2997 . T)) +((-4369 . T) (-4283 . T)) NIL -(-1166 |Key| |Entry|) +(-1168 |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 -(-1167) +(-1169) ((|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 -(-1168 S) +(-1170 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 -(-1169) +(-1171) ((|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 -(-1170) +(-1172) ((|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 -(-1171 R) +(-1173 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 -(-1172) +(-1174) ((|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 -(-1173 S) +(-1175 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1174) +(-1176) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1175 S) +(-1177 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1076))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1176 S) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1078))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1178 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1177) +(-1179) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1178 R -1935) +(-1180 R -3220) ((|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 -(-1179 R |Row| |Col| M) +(-1181 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 -(-1180 R -1935) +(-1182 R -3220) ((|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 -600) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -865) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -865) (|devaluate| |#1|))))) -(-1181 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -600) (LIST (QUOTE -873) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -867) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -600) (LIST (QUOTE -873) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -867) (|devaluate| |#1|))))) +(-1183 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 (-362)))) -(-1182 R E V P) +(-1184 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-1183 |Coef|) +(-1185 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-357)))) -(-1184 |Curve|) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-357)))) +(-1186 |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 -(-1185) +(-1187) ((|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 -(-1186 S) +(-1188 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 (-1076))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1187 -1935) +((|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1189 -3220) ((|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 -(-1188) +(-1190) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1189) +(-1191) ((|constructor| (NIL "The fundamental Type."))) -((-2997 . T)) +((-4283 . T)) NIL -(-1190 S) +(-1192 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 (-830)))) -(-1191) +((|HasCategory| |#1| (QUOTE (-832)))) +(-1193) ((|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 -(-1192 S) +(-1194 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 -(-1193) +(-1195) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1194 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1196 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1195 |Coef|) +(-1197 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1196 S |Coef| UTS) +(-1198 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| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) 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Error: if this is not possible.")) (|coerce| (($ |#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. 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for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1201 R S) +(-1203 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 (-828)))) -(-1202 S) +((|HasCategory| |#1| (QUOTE (-830)))) +(-1204 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 (-828))) (|HasCategory| |#1| (QUOTE (-1076)))) -(-1203 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1078)))) +(-1205 |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 -(-1204 R Q UP) +(-1206 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 -(-1205 R UP) +(-1207 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 -(-1206 R UP) +(-1208 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 -(-1207 R U) +(-1209 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1208 |x| R) +(-1210 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) -(((-4368 "*") |has| |#2| (-169)) (-4359 |has| |#2| (-544)) (-4362 |has| |#2| (-357)) (-4364 |has| |#2| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1210 S R) +(-1212 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-1127)))) -(-1211 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-1129)))) +(-1213 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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4362 |has| |#1| (-357)) (-4364 |has| |#1| (-6 -4364)) (-4361 . T) (-4360 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4366 |has| |#1| (-6 -4366)) (-4363 . T) (-4362 . T) (-4365 . T)) NIL -(-1212 S |Coef| |Expon|) +(-1214 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 -879) (QUOTE (-1152)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1088))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1477) (LIST (|devaluate| |#2|) (QUOTE (-1152)))))) -(-1213 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1090))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3213) (LIST (|devaluate| |#2|) (QUOTE (-1154)))))) +(-1215 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1214 RC P) +(-1216 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1215 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1217 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1216 |Coef|) +(-1218 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1217 S |Coef| ULS) +(-1219 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 -(-1218 |Coef| ULS) +(-1220 |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)}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1219 |Coef| ULS) +(-1221 |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)}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-552)) (QUOTE (-1088))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-1559 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -1477) (LIST (|devaluate| |#1|) (QUOTE (-1152)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (-1559 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1152))))) (|HasSignature| |#1| (LIST (QUOTE -1853) (LIST (LIST (QUOTE -627) (QUOTE (-1152))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) -(-1220 |Coef| |var| |cen|) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-552)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -3213) (LIST (|devaluate| |#1|) (QUOTE (-1154)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (-4029 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-1176))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2889) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1154))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -629) (QUOTE (-1154))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) +(-1222 |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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4364 |has| |#1| (-357)) (-4358 |has| |#1| (-357)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-552)) (QUOTE (-1088))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-1559 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -1477) (LIST (|devaluate| |#1|) (QUOTE (-1152)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (-1559 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1152))))) (|HasSignature| |#1| (LIST (QUOTE -1853) (LIST (LIST (QUOTE -627) (QUOTE (-1152))) (|devaluate| |#1|))))))) -(-1221 R FE |var| |cen|) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4366 |has| |#1| (-357)) (-4360 |has| |#1| (-357)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-169))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-552)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-4029 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -3213) (LIST (|devaluate| |#1|) (QUOTE (-1154)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-552)))))) (-4029 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-1176))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2889) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1154))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -629) (QUOTE (-1154))) (|devaluate| |#1|))))))) +(-1223 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))}."))) -(((-4368 "*") |has| (-1220 |#2| |#3| |#4|) (-169)) (-4359 |has| (-1220 |#2| |#3| |#4|) (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-169))) (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -1017) (QUOTE (-552)))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-357))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-445))) (-1559 (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -1017) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-544)))) -(-1222 A S) +(((-4370 "*") |has| (-1222 |#2| |#3| |#4|) (-169)) (-4361 |has| (-1222 |#2| |#3| |#4|) (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| (-1222 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-1222 |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1222 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1222 |#2| |#3| |#4|) (QUOTE (-169))) (|HasCategory| (-1222 |#2| |#3| |#4|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-1222 |#2| |#3| |#4|) (LIST (QUOTE -1019) (QUOTE (-552)))) (|HasCategory| (-1222 |#2| |#3| |#4|) (QUOTE (-357))) (|HasCategory| (-1222 |#2| |#3| |#4|) (QUOTE (-445))) (-4029 (|HasCategory| (-1222 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| (-1222 |#2| |#3| |#4|) (LIST (QUOTE -1019) (LIST (QUOTE -401) (QUOTE (-552)))))) (|HasCategory| (-1222 |#2| |#3| |#4|) (QUOTE (-544)))) +(-1224 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4367))) -(-1223 S) +((|HasAttribute| |#1| (QUOTE -4369))) +(-1225 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2997 . T)) +((-4283 . T)) NIL -(-1224 |Coef1| |Coef2| UTS1 UTS2) +(-1226 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1225 S |Coef|) +(-1227 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-552)))) (|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-1174))) (|HasSignature| |#2| (LIST (QUOTE -1853) (LIST (LIST (QUOTE -627) (QUOTE (-1152))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2747) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1152))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357)))) -(-1226 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-1176))) (|HasSignature| |#2| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -629) (QUOTE (-1154))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2889) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1154))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-357)))) +(-1228 |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."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1227 |Coef| |var| |cen|) +(-1229 |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}."))) -(((-4368 "*") |has| |#1| (-169)) (-4359 |has| |#1| (-544)) (-4360 . T) (-4361 . T) (-4363 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1559 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-1152)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-754)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-754)) (|devaluate| |#1|)))) (|HasCategory| (-754) (QUOTE (-1088))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-754))))) (|HasSignature| |#1| (LIST (QUOTE -1477) (LIST (|devaluate| |#1|) (QUOTE (-1152)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-754))))) (|HasCategory| |#1| (QUOTE (-357))) (-1559 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-1174))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1152))))) (|HasSignature| |#1| (LIST (QUOTE -1853) (LIST (LIST (QUOTE -627) (QUOTE (-1152))) (|devaluate| |#1|))))))) -(-1228 |Coef| UTS) +(((-4370 "*") |has| |#1| (-169)) (-4361 |has| |#1| (-544)) (-4362 . T) (-4363 . T) (-4365 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-4029 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-1154)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-756)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-756)) (|devaluate| |#1|)))) (|HasCategory| (-756) (QUOTE (-1090))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-756))))) (|HasSignature| |#1| (LIST (QUOTE -3213) (LIST (|devaluate| |#1|) (QUOTE (-1154)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-756))))) (|HasCategory| |#1| (QUOTE (-357))) (-4029 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (QUOTE (-1176))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2889) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1154))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -629) (QUOTE (-1154))) (|devaluate| |#1|))))))) +(-1230 |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 -(-1229 -1935 UP L UTS) +(-1231 -3220 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 (-544)))) -(-1230) +(-1232) ((|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."))) -((-2997 . T)) +((-4283 . T)) NIL -(-1231 |sym|) +(-1233 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1232 S R) +(-1234 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 (-981))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-709))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1233 R) +((|HasCategory| |#2| (QUOTE (-983))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-711))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1235 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4367 . T) (-4366 . T) (-2997 . T)) +((-4369 . T) (-4368 . T) (-4283 . T)) NIL -(-1234 A B) +(-1236 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1235 R) +(-1237 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4367 . T) (-4366 . T)) -((-1559 (-12 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1559 (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-1559 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076)))) (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| (-552) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-709))) (|HasCategory| |#1| (QUOTE (-1028))) (-12 (|HasCategory| |#1| (QUOTE (-981))) (|HasCategory| |#1| (QUOTE (-1028)))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1236) +((-4369 . T) (-4368 . T)) +((-4029 (-12 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4029 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-528)))) (-4029 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| (-552) (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-711))) (|HasCategory| |#1| (QUOTE (-1030))) (-12 (|HasCategory| |#1| (QUOTE (-983))) (|HasCategory| |#1| (QUOTE (-1030)))) (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1238) ((|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 -(-1237) +(-1239) ((|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 -(-1238) +(-1240) ((|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 -(-1239) +(-1241) ((|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 -(-1240) +(-1242) ((|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 -(-1241 A S) +(-1243 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 -(-1242 S) +(-1244 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}."))) -((-4361 . T) (-4360 . T)) +((-4363 . T) (-4362 . T)) NIL -(-1243 R) +(-1245 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 -(-1244 K R UP -1935) +(-1246 K R UP -3220) ((|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 -(-1245) +(-1247) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1246) +(-1248) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1247 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1249 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"))) -((-4361 |has| |#1| (-169)) (-4360 |has| |#1| (-169)) (-4363 . T)) +((-4363 |has| |#1| (-169)) (-4362 |has| |#1| (-169)) (-4365 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357)))) -(-1248 R E V P) +(-1250 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}}."))) -((-4367 . T) (-4366 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-842))))) -(-1249 R) +((-4369 . T) (-4368 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -599) (QUOTE (-844))))) +(-1251 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}."))) -((-4360 . T) (-4361 . T) (-4363 . T)) +((-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1250 |vl| R) +(-1252 |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."))) -((-4363 . T) (-4359 |has| |#2| (-6 -4359)) (-4361 . T) (-4360 . T)) -((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4359))) -(-1251 R |VarSet| XPOLY) +((-4365 . T) (-4361 |has| |#2| (-6 -4361)) (-4363 . T) (-4362 . T)) +((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4361))) +(-1253 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 -(-1252 |vl| R) +(-1254 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4359 |has| |#2| (-6 -4359)) (-4361 . T) (-4360 . T) (-4363 . T)) +((-4361 |has| |#2| (-6 -4361)) (-4363 . T) (-4362 . T) (-4365 . T)) NIL -(-1253 S -1935) +(-1255 S -3220) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144)))) -(-1254 -1935) +(-1256 -3220) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4358 . T) (-4364 . T) (-4359 . T) ((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +((-4360 . T) (-4366 . T) (-4361 . T) ((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL -(-1255 |VarSet| R) +(-1257 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4359 |has| |#2| (-6 -4359)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -700) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasAttribute| |#2| (QUOTE -4359))) -(-1256 |vl| R) +((-4361 |has| |#2| (-6 -4361)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -702) (LIST (QUOTE -401) (QUOTE (-552))))) (|HasAttribute| |#2| (QUOTE -4361))) +(-1258 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4359 |has| |#2| (-6 -4359)) (-4361 . T) (-4360 . T) (-4363 . T)) +((-4361 |has| |#2| (-6 -4361)) (-4363 . T) (-4362 . T) (-4365 . T)) NIL -(-1257 R) +(-1259 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4359 |has| |#1| (-6 -4359)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasAttribute| |#1| (QUOTE -4359))) -(-1258 R E) +((-4361 |has| |#1| (-6 -4361)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasAttribute| |#1| (QUOTE -4361))) +(-1260 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4363 . T) (-4364 |has| |#1| (-6 -4364)) (-4359 |has| |#1| (-6 -4359)) (-4361 . T) (-4360 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4363)) (|HasAttribute| |#1| (QUOTE -4364)) (|HasAttribute| |#1| (QUOTE -4359))) -(-1259 |VarSet| R) +((-4365 . T) (-4366 |has| |#1| (-6 -4366)) (-4361 |has| |#1| (-6 -4361)) (-4363 . T) (-4362 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4365)) (|HasAttribute| |#1| (QUOTE -4366)) (|HasAttribute| |#1| (QUOTE -4361))) +(-1261 |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."))) -((-4359 |has| |#2| (-6 -4359)) (-4361 . T) (-4360 . T) (-4363 . T)) -((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4359))) -(-1260 A) +((-4361 |has| |#2| (-6 -4361)) (-4363 . T) (-4362 . T) (-4365 . T)) +((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4361))) +(-1262 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 -(-1261 R |ls| |ls2|) +(-1263 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 -(-1262 R) +(-1264 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 -(-1263 |p|) +(-1265 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4368 "*") . T) (-4360 . T) (-4361 . T) (-4363 . T)) +(((-4370 "*") . T) (-4362 . T) (-4363 . T) (-4365 . T)) NIL NIL NIL @@ -5000,4 +5008,4 @@ NIL NIL NIL NIL -((-3 NIL 2271395 2271400 2271405 2271410) (-2 NIL 2271375 2271380 2271385 2271390) (-1 NIL 2271355 2271360 2271365 2271370) (0 NIL 2271335 2271340 2271345 2271350) (-1263 "ZMOD.spad" 2271144 2271157 2271273 2271330) (-1262 "ZLINDEP.spad" 2270188 2270199 2271134 2271139) (-1261 "ZDSOLVE.spad" 2260037 2260059 2270178 2270183) (-1260 "YSTREAM.spad" 2259530 2259541 2260027 2260032) (-1259 "XRPOLY.spad" 2258750 2258770 2259386 2259455) (-1258 "XPR.spad" 2256479 2256492 2258468 2258567) (-1257 "XPOLY.spad" 2256034 2256045 2256335 2256404) (-1256 "XPOLYC.spad" 2255351 2255367 2255960 2256029) (-1255 "XPBWPOLY.spad" 2253788 2253808 2255131 2255200) (-1254 "XF.spad" 2252249 2252264 2253690 2253783) (-1253 "XF.spad" 2250690 2250707 2252133 2252138) (-1252 "XFALG.spad" 2247714 2247730 2250616 2250685) (-1251 "XEXPPKG.spad" 2246965 2246991 2247704 2247709) (-1250 "XDPOLY.spad" 2246579 2246595 2246821 2246890) (-1249 "XALG.spad" 2246177 2246188 2246535 2246574) (-1248 "WUTSET.spad" 2242016 2242033 2245823 2245850) (-1247 "WP.spad" 2241030 2241074 2241874 2241941) (-1246 "WHILEAST.spad" 2240828 2240837 2241020 2241025) (-1245 "WHEREAST.spad" 2240499 2240508 2240818 2240823) (-1244 "WFFINTBS.spad" 2238062 2238084 2240489 2240494) (-1243 "WEIER.spad" 2236276 2236287 2238052 2238057) (-1242 "VSPACE.spad" 2235949 2235960 2236244 2236271) (-1241 "VSPACE.spad" 2235642 2235655 2235939 2235944) (-1240 "VOID.spad" 2235232 2235241 2235632 2235637) (-1239 "VIEW.spad" 2232854 2232863 2235222 2235227) (-1238 "VIEWDEF.spad" 2228051 2228060 2232844 2232849) (-1237 "VIEW3D.spad" 2211886 2211895 2228041 2228046) (-1236 "VIEW2D.spad" 2199623 2199632 2211876 2211881) (-1235 "VECTOR.spad" 2198298 2198309 2198549 2198576) (-1234 "VECTOR2.spad" 2196925 2196938 2198288 2198293) (-1233 "VECTCAT.spad" 2194813 2194824 2196881 2196920) (-1232 "VECTCAT.spad" 2192521 2192534 2194591 2194596) (-1231 "VARIABLE.spad" 2192301 2192316 2192511 2192516) (-1230 "UTYPE.spad" 2191935 2191944 2192281 2192296) (-1229 "UTSODETL.spad" 2191228 2191252 2191891 2191896) (-1228 "UTSODE.spad" 2189416 2189436 2191218 2191223) (-1227 "UTS.spad" 2184205 2184233 2187883 2187980) (-1226 "UTSCAT.spad" 2181656 2181672 2184103 2184200) (-1225 "UTSCAT.spad" 2178751 2178769 2181200 2181205) (-1224 "UTS2.spad" 2178344 2178379 2178741 2178746) (-1223 "URAGG.spad" 2172966 2172977 2178324 2178339) (-1222 "URAGG.spad" 2167562 2167575 2172922 2172927) (-1221 "UPXSSING.spad" 2165205 2165231 2166643 2166776) (-1220 "UPXS.spad" 2162232 2162260 2163337 2163486) (-1219 "UPXSCONS.spad" 2159989 2160009 2160364 2160513) (-1218 "UPXSCCA.spad" 2158447 2158467 2159835 2159984) (-1217 "UPXSCCA.spad" 2157047 2157069 2158437 2158442) (-1216 "UPXSCAT.spad" 2155628 2155644 2156893 2157042) (-1215 "UPXS2.spad" 2155169 2155222 2155618 2155623) (-1214 "UPSQFREE.spad" 2153581 2153595 2155159 2155164) (-1213 "UPSCAT.spad" 2151174 2151198 2153479 2153576) (-1212 "UPSCAT.spad" 2148473 2148499 2150780 2150785) (-1211 "UPOLYC.spad" 2143451 2143462 2148315 2148468) (-1210 "UPOLYC.spad" 2138321 2138334 2143187 2143192) (-1209 "UPOLYC2.spad" 2137790 2137809 2138311 2138316) (-1208 "UP.spad" 2134832 2134847 2135340 2135493) (-1207 "UPMP.spad" 2133722 2133735 2134822 2134827) (-1206 "UPDIVP.spad" 2133285 2133299 2133712 2133717) (-1205 "UPDECOMP.spad" 2131522 2131536 2133275 2133280) (-1204 "UPCDEN.spad" 2130729 2130745 2131512 2131517) (-1203 "UP2.spad" 2130091 2130112 2130719 2130724) (-1202 "UNISEG.spad" 2129444 2129455 2130010 2130015) (-1201 "UNISEG2.spad" 2128937 2128950 2129400 2129405) (-1200 "UNIFACT.spad" 2128038 2128050 2128927 2128932) (-1199 "ULS.spad" 2118590 2118618 2119683 2120112) (-1198 "ULSCONS.spad" 2112627 2112647 2112999 2113148) (-1197 "ULSCCAT.spad" 2110224 2110244 2112447 2112622) (-1196 "ULSCCAT.spad" 2107955 2107977 2110180 2110185) (-1195 "ULSCAT.spad" 2106171 2106187 2107801 2107950) (-1194 "ULS2.spad" 2105683 2105736 2106161 2106166) (-1193 "UFD.spad" 2104748 2104757 2105609 2105678) (-1192 "UFD.spad" 2103875 2103886 2104738 2104743) (-1191 "UDVO.spad" 2102722 2102731 2103865 2103870) (-1190 "UDPO.spad" 2100149 2100160 2102678 2102683) (-1189 "TYPE.spad" 2100071 2100080 2100129 2100144) (-1188 "TYPEAST.spad" 2099990 2099999 2100061 2100066) (-1187 "TWOFACT.spad" 2098640 2098655 2099980 2099985) (-1186 "TUPLE.spad" 2098026 2098037 2098539 2098544) (-1185 "TUBETOOL.spad" 2094863 2094872 2098016 2098021) (-1184 "TUBE.spad" 2093504 2093521 2094853 2094858) (-1183 "TS.spad" 2092093 2092109 2093069 2093166) (-1182 "TSETCAT.spad" 2079208 2079225 2092049 2092088) (-1181 "TSETCAT.spad" 2066321 2066340 2079164 2079169) (-1180 "TRMANIP.spad" 2060687 2060704 2066027 2066032) (-1179 "TRIMAT.spad" 2059646 2059671 2060677 2060682) (-1178 "TRIGMNIP.spad" 2058163 2058180 2059636 2059641) (-1177 "TRIGCAT.spad" 2057675 2057684 2058153 2058158) (-1176 "TRIGCAT.spad" 2057185 2057196 2057665 2057670) (-1175 "TREE.spad" 2055756 2055767 2056792 2056819) (-1174 "TRANFUN.spad" 2055587 2055596 2055746 2055751) (-1173 "TRANFUN.spad" 2055416 2055427 2055577 2055582) (-1172 "TOPSP.spad" 2055090 2055099 2055406 2055411) (-1171 "TOOLSIGN.spad" 2054753 2054764 2055080 2055085) (-1170 "TEXTFILE.spad" 2053310 2053319 2054743 2054748) (-1169 "TEX.spad" 2050327 2050336 2053300 2053305) (-1168 "TEX1.spad" 2049883 2049894 2050317 2050322) (-1167 "TEMUTL.spad" 2049438 2049447 2049873 2049878) (-1166 "TBCMPPK.spad" 2047531 2047554 2049428 2049433) (-1165 "TBAGG.spad" 2046555 2046578 2047499 2047526) (-1164 "TBAGG.spad" 2045599 2045624 2046545 2046550) (-1163 "TANEXP.spad" 2044975 2044986 2045589 2045594) (-1162 "TABLE.spad" 2043386 2043409 2043656 2043683) (-1161 "TABLEAU.spad" 2042867 2042878 2043376 2043381) (-1160 "TABLBUMP.spad" 2039650 2039661 2042857 2042862) (-1159 "SYSTEM.spad" 2038924 2038933 2039640 2039645) (-1158 "SYSSOLP.spad" 2036397 2036408 2038914 2038919) (-1157 "SYNTAX.spad" 2032667 2032676 2036387 2036392) (-1156 "SYMTAB.spad" 2030723 2030732 2032657 2032662) (-1155 "SYMS.spad" 2026708 2026717 2030713 2030718) (-1154 "SYMPOLY.spad" 2025715 2025726 2025797 2025924) (-1153 "SYMFUNC.spad" 2025190 2025201 2025705 2025710) (-1152 "SYMBOL.spad" 2022526 2022535 2025180 2025185) (-1151 "SWITCH.spad" 2019283 2019292 2022516 2022521) (-1150 "SUTS.spad" 2016182 2016210 2017750 2017847) (-1149 "SUPXS.spad" 2013196 2013224 2014314 2014463) (-1148 "SUP.spad" 2009965 2009976 2010746 2010899) (-1147 "SUPFRACF.spad" 2009070 2009088 2009955 2009960) (-1146 "SUP2.spad" 2008460 2008473 2009060 2009065) (-1145 "SUMRF.spad" 2007426 2007437 2008450 2008455) (-1144 "SUMFS.spad" 2007059 2007076 2007416 2007421) (-1143 "SULS.spad" 1997598 1997626 1998704 1999133) (-1142 "SUCHTAST.spad" 1997367 1997376 1997588 1997593) (-1141 "SUCH.spad" 1997047 1997062 1997357 1997362) (-1140 "SUBSPACE.spad" 1989054 1989069 1997037 1997042) (-1139 "SUBRESP.spad" 1988214 1988228 1989010 1989015) (-1138 "STTF.spad" 1984313 1984329 1988204 1988209) (-1137 "STTFNC.spad" 1980781 1980797 1984303 1984308) (-1136 "STTAYLOR.spad" 1973179 1973190 1980662 1980667) (-1135 "STRTBL.spad" 1971684 1971701 1971833 1971860) (-1134 "STRING.spad" 1971093 1971102 1971107 1971134) (-1133 "STRICAT.spad" 1970869 1970878 1971049 1971088) (-1132 "STREAM.spad" 1967637 1967648 1970394 1970409) (-1131 "STREAM3.spad" 1967182 1967197 1967627 1967632) (-1130 "STREAM2.spad" 1966250 1966263 1967172 1967177) (-1129 "STREAM1.spad" 1965954 1965965 1966240 1966245) (-1128 "STINPROD.spad" 1964860 1964876 1965944 1965949) (-1127 "STEP.spad" 1964061 1964070 1964850 1964855) (-1126 "STBL.spad" 1962587 1962615 1962754 1962769) (-1125 "STAGG.spad" 1961652 1961663 1962567 1962582) (-1124 "STAGG.spad" 1960725 1960738 1961642 1961647) (-1123 "STACK.spad" 1960076 1960087 1960332 1960359) (-1122 "SREGSET.spad" 1957780 1957797 1959722 1959749) (-1121 "SRDCMPK.spad" 1956325 1956345 1957770 1957775) (-1120 "SRAGG.spad" 1951410 1951419 1956281 1956320) (-1119 "SRAGG.spad" 1946527 1946538 1951400 1951405) (-1118 "SQMATRIX.spad" 1944143 1944161 1945059 1945146) (-1117 "SPLTREE.spad" 1938695 1938708 1943579 1943606) (-1116 "SPLNODE.spad" 1935283 1935296 1938685 1938690) (-1115 "SPFCAT.spad" 1934060 1934069 1935273 1935278) (-1114 "SPECOUT.spad" 1932610 1932619 1934050 1934055) (-1113 "SPADXPT.spad" 1924739 1924748 1932590 1932605) (-1112 "spad-parser.spad" 1924204 1924213 1924729 1924734) (-1111 "SPADAST.spad" 1923905 1923914 1924194 1924199) (-1110 "SPACEC.spad" 1907918 1907929 1923895 1923900) (-1109 "SPACE3.spad" 1907694 1907705 1907908 1907913) (-1108 "SORTPAK.spad" 1907239 1907252 1907650 1907655) (-1107 "SOLVETRA.spad" 1904996 1905007 1907229 1907234) (-1106 "SOLVESER.spad" 1903516 1903527 1904986 1904991) (-1105 "SOLVERAD.spad" 1899526 1899537 1903506 1903511) (-1104 "SOLVEFOR.spad" 1897946 1897964 1899516 1899521) (-1103 "SNTSCAT.spad" 1897534 1897551 1897902 1897941) (-1102 "SMTS.spad" 1895794 1895820 1897099 1897196) (-1101 "SMP.spad" 1893233 1893253 1893623 1893750) (-1100 "SMITH.spad" 1892076 1892101 1893223 1893228) (-1099 "SMATCAT.spad" 1890174 1890204 1892008 1892071) (-1098 "SMATCAT.spad" 1888216 1888248 1890052 1890057) (-1097 "SKAGG.spad" 1887165 1887176 1888172 1888211) (-1096 "SINT.spad" 1885473 1885482 1887031 1887160) (-1095 "SIMPAN.spad" 1885201 1885210 1885463 1885468) (-1094 "SIG.spad" 1884529 1884538 1885191 1885196) (-1093 "SIGNRF.spad" 1883637 1883648 1884519 1884524) (-1092 "SIGNEF.spad" 1882906 1882923 1883627 1883632) (-1091 "SIGAST.spad" 1882287 1882296 1882896 1882901) (-1090 "SHP.spad" 1880205 1880220 1882243 1882248) (-1089 "SHDP.spad" 1871190 1871217 1871699 1871830) (-1088 "SGROUP.spad" 1870798 1870807 1871180 1871185) (-1087 "SGROUP.spad" 1870404 1870415 1870788 1870793) (-1086 "SGCF.spad" 1863285 1863294 1870394 1870399) (-1085 "SFRTCAT.spad" 1862201 1862218 1863241 1863280) (-1084 "SFRGCD.spad" 1861264 1861284 1862191 1862196) (-1083 "SFQCMPK.spad" 1855901 1855921 1861254 1861259) (-1082 "SFORT.spad" 1855336 1855350 1855891 1855896) (-1081 "SEXOF.spad" 1855179 1855219 1855326 1855331) (-1080 "SEX.spad" 1855071 1855080 1855169 1855174) (-1079 "SEXCAT.spad" 1852175 1852215 1855061 1855066) (-1078 "SET.spad" 1850475 1850486 1851596 1851635) (-1077 "SETMN.spad" 1848909 1848926 1850465 1850470) (-1076 "SETCAT.spad" 1848394 1848403 1848899 1848904) (-1075 "SETCAT.spad" 1847877 1847888 1848384 1848389) (-1074 "SETAGG.spad" 1844386 1844397 1847845 1847872) (-1073 "SETAGG.spad" 1840915 1840928 1844376 1844381) (-1072 "SEQAST.spad" 1840618 1840627 1840905 1840910) (-1071 "SEGXCAT.spad" 1839730 1839743 1840598 1840613) (-1070 "SEG.spad" 1839543 1839554 1839649 1839654) (-1069 "SEGCAT.spad" 1838362 1838373 1839523 1839538) (-1068 "SEGBIND.spad" 1837434 1837445 1838317 1838322) (-1067 "SEGBIND2.spad" 1837130 1837143 1837424 1837429) (-1066 "SEGAST.spad" 1836844 1836853 1837120 1837125) (-1065 "SEG2.spad" 1836269 1836282 1836800 1836805) (-1064 "SDVAR.spad" 1835545 1835556 1836259 1836264) (-1063 "SDPOL.spad" 1832935 1832946 1833226 1833353) (-1062 "SCPKG.spad" 1831014 1831025 1832925 1832930) (-1061 "SCOPE.spad" 1830159 1830168 1831004 1831009) (-1060 "SCACHE.spad" 1828841 1828852 1830149 1830154) (-1059 "SASTCAT.spad" 1828750 1828759 1828831 1828836) (-1058 "SAOS.spad" 1828622 1828631 1828740 1828745) (-1057 "SAERFFC.spad" 1828335 1828355 1828612 1828617) (-1056 "SAE.spad" 1826510 1826526 1827121 1827256) (-1055 "SAEFACT.spad" 1826211 1826231 1826500 1826505) (-1054 "RURPK.spad" 1823852 1823868 1826201 1826206) (-1053 "RULESET.spad" 1823293 1823317 1823842 1823847) (-1052 "RULE.spad" 1821497 1821521 1823283 1823288) (-1051 "RULECOLD.spad" 1821349 1821362 1821487 1821492) (-1050 "RSTRCAST.spad" 1821066 1821075 1821339 1821344) (-1049 "RSETGCD.spad" 1817444 1817464 1821056 1821061) (-1048 "RSETCAT.spad" 1807216 1807233 1817400 1817439) (-1047 "RSETCAT.spad" 1797020 1797039 1807206 1807211) (-1046 "RSDCMPK.spad" 1795472 1795492 1797010 1797015) (-1045 "RRCC.spad" 1793856 1793886 1795462 1795467) (-1044 "RRCC.spad" 1792238 1792270 1793846 1793851) (-1043 "RPTAST.spad" 1791940 1791949 1792228 1792233) (-1042 "RPOLCAT.spad" 1771300 1771315 1791808 1791935) (-1041 "RPOLCAT.spad" 1750374 1750391 1770884 1770889) (-1040 "ROUTINE.spad" 1746237 1746246 1749021 1749048) (-1039 "ROMAN.spad" 1745469 1745478 1746103 1746232) (-1038 "ROIRC.spad" 1744549 1744581 1745459 1745464) (-1037 "RNS.spad" 1743452 1743461 1744451 1744544) (-1036 "RNS.spad" 1742441 1742452 1743442 1743447) (-1035 "RNG.spad" 1742176 1742185 1742431 1742436) (-1034 "RMODULE.spad" 1741814 1741825 1742166 1742171) (-1033 "RMCAT2.spad" 1741222 1741279 1741804 1741809) (-1032 "RMATRIX.spad" 1739901 1739920 1740389 1740428) (-1031 "RMATCAT.spad" 1735422 1735453 1739845 1739896) (-1030 "RMATCAT.spad" 1730845 1730878 1735270 1735275) (-1029 "RINTERP.spad" 1730733 1730753 1730835 1730840) (-1028 "RING.spad" 1730090 1730099 1730713 1730728) (-1027 "RING.spad" 1729455 1729466 1730080 1730085) (-1026 "RIDIST.spad" 1728839 1728848 1729445 1729450) (-1025 "RGCHAIN.spad" 1727418 1727434 1728324 1728351) (-1024 "RGBCSPC.spad" 1727199 1727211 1727408 1727413) (-1023 "RGBCMDL.spad" 1726729 1726741 1727189 1727194) (-1022 "RF.spad" 1724343 1724354 1726719 1726724) (-1021 "RFFACTOR.spad" 1723805 1723816 1724333 1724338) (-1020 "RFFACT.spad" 1723540 1723552 1723795 1723800) (-1019 "RFDIST.spad" 1722528 1722537 1723530 1723535) (-1018 "RETSOL.spad" 1721945 1721958 1722518 1722523) (-1017 "RETRACT.spad" 1721294 1721305 1721935 1721940) (-1016 "RETRACT.spad" 1720641 1720654 1721284 1721289) (-1015 "RETAST.spad" 1720453 1720462 1720631 1720636) (-1014 "RESULT.spad" 1718513 1718522 1719100 1719127) (-1013 "RESRING.spad" 1717860 1717907 1718451 1718508) (-1012 "RESLATC.spad" 1717184 1717195 1717850 1717855) (-1011 "REPSQ.spad" 1716913 1716924 1717174 1717179) (-1010 "REP.spad" 1714465 1714474 1716903 1716908) (-1009 "REPDB.spad" 1714170 1714181 1714455 1714460) (-1008 "REP2.spad" 1703742 1703753 1714012 1714017) (-1007 "REP1.spad" 1697732 1697743 1703692 1703697) (-1006 "REGSET.spad" 1695529 1695546 1697378 1697405) (-1005 "REF.spad" 1694858 1694869 1695484 1695489) (-1004 "REDORDER.spad" 1694034 1694051 1694848 1694853) (-1003 "RECLOS.spad" 1692817 1692837 1693521 1693614) (-1002 "REALSOLV.spad" 1691949 1691958 1692807 1692812) (-1001 "REAL.spad" 1691821 1691830 1691939 1691944) (-1000 "REAL0Q.spad" 1689103 1689118 1691811 1691816) (-999 "REAL0.spad" 1685932 1685946 1689093 1689098) (-998 "RDUCEAST.spad" 1685654 1685662 1685922 1685927) (-997 "RDIV.spad" 1685306 1685330 1685644 1685649) (-996 "RDIST.spad" 1684870 1684880 1685296 1685301) (-995 "RDETRS.spad" 1683667 1683684 1684860 1684865) (-994 "RDETR.spad" 1681775 1681792 1683657 1683662) (-993 "RDEEFS.spad" 1680849 1680865 1681765 1681770) (-992 "RDEEF.spad" 1679846 1679862 1680839 1680844) (-991 "RCFIELD.spad" 1677033 1677041 1679748 1679841) (-990 "RCFIELD.spad" 1674306 1674316 1677023 1677028) (-989 "RCAGG.spad" 1672209 1672219 1674286 1674301) (-988 "RCAGG.spad" 1670049 1670061 1672128 1672133) (-987 "RATRET.spad" 1669410 1669420 1670039 1670044) (-986 "RATFACT.spad" 1669103 1669114 1669400 1669405) (-985 "RANDSRC.spad" 1668423 1668431 1669093 1669098) (-984 "RADUTIL.spad" 1668178 1668186 1668413 1668418) (-983 "RADIX.spad" 1664968 1664981 1666645 1666738) (-982 "RADFF.spad" 1663382 1663418 1663500 1663656) (-981 "RADCAT.spad" 1662976 1662984 1663372 1663377) (-980 "RADCAT.spad" 1662568 1662578 1662966 1662971) (-979 "QUEUE.spad" 1661911 1661921 1662175 1662202) (-978 "QUAT.spad" 1660493 1660503 1660835 1660900) (-977 "QUATCT2.spad" 1660112 1660130 1660483 1660488) (-976 "QUATCAT.spad" 1658277 1658287 1660042 1660107) (-975 "QUATCAT.spad" 1656193 1656205 1657960 1657965) (-974 "QUAGG.spad" 1655007 1655017 1656149 1656188) (-973 "QQUTAST.spad" 1654776 1654784 1654997 1655002) (-972 "QFORM.spad" 1654239 1654253 1654766 1654771) (-971 "QFCAT.spad" 1652930 1652940 1654129 1654234) (-970 "QFCAT.spad" 1651224 1651236 1652425 1652430) (-969 "QFCAT2.spad" 1650915 1650931 1651214 1651219) (-968 "QEQUAT.spad" 1650472 1650480 1650905 1650910) (-967 "QCMPACK.spad" 1645219 1645238 1650462 1650467) (-966 "QALGSET.spad" 1641294 1641326 1645133 1645138) (-965 "QALGSET2.spad" 1639290 1639308 1641284 1641289) (-964 "PWFFINTB.spad" 1636600 1636621 1639280 1639285) (-963 "PUSHVAR.spad" 1635929 1635948 1636590 1636595) (-962 "PTRANFN.spad" 1632055 1632065 1635919 1635924) (-961 "PTPACK.spad" 1629143 1629153 1632045 1632050) (-960 "PTFUNC2.spad" 1628964 1628978 1629133 1629138) (-959 "PTCAT.spad" 1628046 1628056 1628920 1628959) (-958 "PSQFR.spad" 1627353 1627377 1628036 1628041) (-957 "PSEUDLIN.spad" 1626211 1626221 1627343 1627348) (-956 "PSETPK.spad" 1611644 1611660 1626089 1626094) (-955 "PSETCAT.spad" 1605552 1605575 1611612 1611639) (-954 "PSETCAT.spad" 1599446 1599471 1605508 1605513) (-953 "PSCURVE.spad" 1598429 1598437 1599436 1599441) (-952 "PSCAT.spad" 1597196 1597225 1598327 1598424) (-951 "PSCAT.spad" 1596053 1596084 1597186 1597191) (-950 "PRTITION.spad" 1594896 1594904 1596043 1596048) (-949 "PRTDAST.spad" 1594615 1594623 1594886 1594891) (-948 "PRS.spad" 1584177 1584194 1594571 1594576) (-947 "PRQAGG.spad" 1583596 1583606 1584133 1584172) (-946 "PROPLOG.spad" 1582999 1583007 1583586 1583591) (-945 "PROPFRML.spad" 1580917 1580928 1582989 1582994) (-944 "PROPERTY.spad" 1580411 1580419 1580907 1580912) (-943 "PRODUCT.spad" 1578091 1578103 1578377 1578432) (-942 "PR.spad" 1576477 1576489 1577182 1577309) (-941 "PRINT.spad" 1576229 1576237 1576467 1576472) (-940 "PRIMES.spad" 1574480 1574490 1576219 1576224) (-939 "PRIMELT.spad" 1572461 1572475 1574470 1574475) (-938 "PRIMCAT.spad" 1572084 1572092 1572451 1572456) (-937 "PRIMARR.spad" 1571089 1571099 1571267 1571294) (-936 "PRIMARR2.spad" 1569812 1569824 1571079 1571084) (-935 "PREASSOC.spad" 1569184 1569196 1569802 1569807) (-934 "PPCURVE.spad" 1568321 1568329 1569174 1569179) (-933 "PORTNUM.spad" 1568096 1568104 1568311 1568316) (-932 "POLYROOT.spad" 1566868 1566890 1568052 1568057) (-931 "POLY.spad" 1564165 1564175 1564682 1564809) (-930 "POLYLIFT.spad" 1563426 1563449 1564155 1564160) (-929 "POLYCATQ.spad" 1561528 1561550 1563416 1563421) (-928 "POLYCAT.spad" 1554934 1554955 1561396 1561523) (-927 "POLYCAT.spad" 1547642 1547665 1554106 1554111) (-926 "POLY2UP.spad" 1547090 1547104 1547632 1547637) (-925 "POLY2.spad" 1546685 1546697 1547080 1547085) (-924 "POLUTIL.spad" 1545626 1545655 1546641 1546646) (-923 "POLTOPOL.spad" 1544374 1544389 1545616 1545621) (-922 "POINT.spad" 1543213 1543223 1543300 1543327) (-921 "PNTHEORY.spad" 1539879 1539887 1543203 1543208) (-920 "PMTOOLS.spad" 1538636 1538650 1539869 1539874) (-919 "PMSYM.spad" 1538181 1538191 1538626 1538631) (-918 "PMQFCAT.spad" 1537768 1537782 1538171 1538176) (-917 "PMPRED.spad" 1537237 1537251 1537758 1537763) (-916 "PMPREDFS.spad" 1536681 1536703 1537227 1537232) (-915 "PMPLCAT.spad" 1535751 1535769 1536613 1536618) (-914 "PMLSAGG.spad" 1535332 1535346 1535741 1535746) (-913 "PMKERNEL.spad" 1534899 1534911 1535322 1535327) (-912 "PMINS.spad" 1534475 1534485 1534889 1534894) (-911 "PMFS.spad" 1534048 1534066 1534465 1534470) (-910 "PMDOWN.spad" 1533334 1533348 1534038 1534043) (-909 "PMASS.spad" 1532346 1532354 1533324 1533329) (-908 "PMASSFS.spad" 1531315 1531331 1532336 1532341) (-907 "PLOTTOOL.spad" 1531095 1531103 1531305 1531310) (-906 "PLOT.spad" 1525926 1525934 1531085 1531090) (-905 "PLOT3D.spad" 1522346 1522354 1525916 1525921) (-904 "PLOT1.spad" 1521487 1521497 1522336 1522341) (-903 "PLEQN.spad" 1508703 1508730 1521477 1521482) (-902 "PINTERP.spad" 1508319 1508338 1508693 1508698) (-901 "PINTERPA.spad" 1508101 1508117 1508309 1508314) (-900 "PI.spad" 1507708 1507716 1508075 1508096) (-899 "PID.spad" 1506664 1506672 1507634 1507703) (-898 "PICOERCE.spad" 1506321 1506331 1506654 1506659) (-897 "PGROEB.spad" 1504918 1504932 1506311 1506316) (-896 "PGE.spad" 1496171 1496179 1504908 1504913) (-895 "PGCD.spad" 1495053 1495070 1496161 1496166) (-894 "PFRPAC.spad" 1494196 1494206 1495043 1495048) (-893 "PFR.spad" 1490853 1490863 1494098 1494191) (-892 "PFOTOOLS.spad" 1490111 1490127 1490843 1490848) (-891 "PFOQ.spad" 1489481 1489499 1490101 1490106) (-890 "PFO.spad" 1488900 1488927 1489471 1489476) (-889 "PF.spad" 1488474 1488486 1488705 1488798) (-888 "PFECAT.spad" 1486140 1486148 1488400 1488469) (-887 "PFECAT.spad" 1483834 1483844 1486096 1486101) (-886 "PFBRU.spad" 1481704 1481716 1483824 1483829) (-885 "PFBR.spad" 1479242 1479265 1481694 1481699) (-884 "PERM.spad" 1474923 1474933 1479072 1479087) (-883 "PERMGRP.spad" 1469659 1469669 1474913 1474918) (-882 "PERMCAT.spad" 1468211 1468221 1469639 1469654) (-881 "PERMAN.spad" 1466743 1466757 1468201 1468206) (-880 "PENDTREE.spad" 1466016 1466026 1466372 1466377) (-879 "PDRING.spad" 1464507 1464517 1465996 1466011) (-878 "PDRING.spad" 1463006 1463018 1464497 1464502) (-877 "PDEPROB.spad" 1461963 1461971 1462996 1463001) (-876 "PDEPACK.spad" 1455965 1455973 1461953 1461958) (-875 "PDECOMP.spad" 1455427 1455444 1455955 1455960) (-874 "PDECAT.spad" 1453781 1453789 1455417 1455422) (-873 "PCOMP.spad" 1453632 1453645 1453771 1453776) (-872 "PBWLB.spad" 1452214 1452231 1453622 1453627) (-871 "PATTERN.spad" 1446645 1446655 1452204 1452209) (-870 "PATTERN2.spad" 1446381 1446393 1446635 1446640) (-869 "PATTERN1.spad" 1444683 1444699 1446371 1446376) (-868 "PATRES.spad" 1442230 1442242 1444673 1444678) (-867 "PATRES2.spad" 1441892 1441906 1442220 1442225) (-866 "PATMATCH.spad" 1440049 1440080 1441600 1441605) (-865 "PATMAB.spad" 1439474 1439484 1440039 1440044) (-864 "PATLRES.spad" 1438558 1438572 1439464 1439469) (-863 "PATAB.spad" 1438322 1438332 1438548 1438553) (-862 "PARTPERM.spad" 1435684 1435692 1438312 1438317) (-861 "PARSURF.spad" 1435112 1435140 1435674 1435679) (-860 "PARSU2.spad" 1434907 1434923 1435102 1435107) (-859 "script-parser.spad" 1434427 1434435 1434897 1434902) (-858 "PARSCURV.spad" 1433855 1433883 1434417 1434422) (-857 "PARSC2.spad" 1433644 1433660 1433845 1433850) (-856 "PARPCURV.spad" 1433102 1433130 1433634 1433639) (-855 "PARPC2.spad" 1432891 1432907 1433092 1433097) (-854 "PAN2EXPR.spad" 1432303 1432311 1432881 1432886) (-853 "PALETTE.spad" 1431273 1431281 1432293 1432298) (-852 "PAIR.spad" 1430256 1430269 1430861 1430866) (-851 "PADICRC.spad" 1427586 1427604 1428761 1428854) (-850 "PADICRAT.spad" 1425601 1425613 1425822 1425915) (-849 "PADIC.spad" 1425296 1425308 1425527 1425596) (-848 "PADICCT.spad" 1423837 1423849 1425222 1425291) (-847 "PADEPAC.spad" 1422516 1422535 1423827 1423832) (-846 "PADE.spad" 1421256 1421272 1422506 1422511) (-845 "OWP.spad" 1420240 1420270 1421114 1421181) (-844 "OVAR.spad" 1420021 1420044 1420230 1420235) (-843 "OUT.spad" 1419105 1419113 1420011 1420016) (-842 "OUTFORM.spad" 1408401 1408409 1419095 1419100) (-841 "OUTBFILE.spad" 1407819 1407827 1408391 1408396) (-840 "OUTBCON.spad" 1407097 1407105 1407809 1407814) (-839 "OUTBCON.spad" 1406373 1406383 1407087 1407092) (-838 "OSI.spad" 1405848 1405856 1406363 1406368) (-837 "OSGROUP.spad" 1405766 1405774 1405838 1405843) (-836 "ORTHPOL.spad" 1404227 1404237 1405683 1405688) (-835 "OREUP.spad" 1403585 1403613 1403907 1403946) (-834 "ORESUP.spad" 1402884 1402908 1403265 1403304) (-833 "OREPCTO.spad" 1400703 1400715 1402804 1402809) (-832 "OREPCAT.spad" 1394760 1394770 1400659 1400698) (-831 "OREPCAT.spad" 1388707 1388719 1394608 1394613) (-830 "ORDSET.spad" 1387873 1387881 1388697 1388702) (-829 "ORDSET.spad" 1387037 1387047 1387863 1387868) (-828 "ORDRING.spad" 1386427 1386435 1387017 1387032) (-827 "ORDRING.spad" 1385825 1385835 1386417 1386422) (-826 "ORDMON.spad" 1385680 1385688 1385815 1385820) (-825 "ORDFUNS.spad" 1384806 1384822 1385670 1385675) (-824 "ORDFIN.spad" 1384740 1384748 1384796 1384801) (-823 "ORDCOMP.spad" 1383205 1383215 1384287 1384316) (-822 "ORDCOMP2.spad" 1382490 1382502 1383195 1383200) (-821 "OPTPROB.spad" 1381070 1381078 1382480 1382485) (-820 "OPTPACK.spad" 1373455 1373463 1381060 1381065) (-819 "OPTCAT.spad" 1371130 1371138 1373445 1373450) (-818 "OPQUERY.spad" 1370679 1370687 1371120 1371125) (-817 "OP.spad" 1370421 1370431 1370501 1370568) (-816 "ONECOMP.spad" 1369166 1369176 1369968 1369997) (-815 "ONECOMP2.spad" 1368584 1368596 1369156 1369161) (-814 "OMSERVER.spad" 1367586 1367594 1368574 1368579) (-813 "OMSAGG.spad" 1367362 1367372 1367530 1367581) (-812 "OMPKG.spad" 1365974 1365982 1367352 1367357) (-811 "OM.spad" 1364939 1364947 1365964 1365969) (-810 "OMLO.spad" 1364364 1364376 1364825 1364864) (-809 "OMEXPR.spad" 1364198 1364208 1364354 1364359) (-808 "OMERR.spad" 1363741 1363749 1364188 1364193) (-807 "OMERRK.spad" 1362775 1362783 1363731 1363736) (-806 "OMENC.spad" 1362119 1362127 1362765 1362770) (-805 "OMDEV.spad" 1356408 1356416 1362109 1362114) (-804 "OMCONN.spad" 1355817 1355825 1356398 1356403) (-803 "OINTDOM.spad" 1355580 1355588 1355743 1355812) (-802 "OFMONOID.spad" 1351767 1351777 1355570 1355575) (-801 "ODVAR.spad" 1351028 1351038 1351757 1351762) (-800 "ODR.spad" 1350476 1350502 1350840 1350989) (-799 "ODPOL.spad" 1347822 1347832 1348162 1348289) (-798 "ODP.spad" 1338943 1338963 1339316 1339447) (-797 "ODETOOLS.spad" 1337526 1337545 1338933 1338938) (-796 "ODESYS.spad" 1335176 1335193 1337516 1337521) (-795 "ODERTRIC.spad" 1331117 1331134 1335133 1335138) (-794 "ODERED.spad" 1330504 1330528 1331107 1331112) (-793 "ODERAT.spad" 1328055 1328072 1330494 1330499) (-792 "ODEPRRIC.spad" 1324946 1324968 1328045 1328050) (-791 "ODEPROB.spad" 1324145 1324153 1324936 1324941) (-790 "ODEPRIM.spad" 1321419 1321441 1324135 1324140) (-789 "ODEPAL.spad" 1320795 1320819 1321409 1321414) (-788 "ODEPACK.spad" 1307397 1307405 1320785 1320790) (-787 "ODEINT.spad" 1306828 1306844 1307387 1307392) (-786 "ODEIFTBL.spad" 1304223 1304231 1306818 1306823) (-785 "ODEEF.spad" 1299590 1299606 1304213 1304218) (-784 "ODECONST.spad" 1299109 1299127 1299580 1299585) (-783 "ODECAT.spad" 1297705 1297713 1299099 1299104) (-782 "OCT.spad" 1295843 1295853 1296559 1296598) (-781 "OCTCT2.spad" 1295487 1295508 1295833 1295838) (-780 "OC.spad" 1293261 1293271 1295443 1295482) (-779 "OC.spad" 1290760 1290772 1292944 1292949) (-778 "OCAMON.spad" 1290608 1290616 1290750 1290755) (-777 "OASGP.spad" 1290423 1290431 1290598 1290603) (-776 "OAMONS.spad" 1289943 1289951 1290413 1290418) (-775 "OAMON.spad" 1289804 1289812 1289933 1289938) (-774 "OAGROUP.spad" 1289666 1289674 1289794 1289799) (-773 "NUMTUBE.spad" 1289253 1289269 1289656 1289661) (-772 "NUMQUAD.spad" 1277115 1277123 1289243 1289248) (-771 "NUMODE.spad" 1268251 1268259 1277105 1277110) (-770 "NUMINT.spad" 1265809 1265817 1268241 1268246) (-769 "NUMFMT.spad" 1264649 1264657 1265799 1265804) (-768 "NUMERIC.spad" 1256721 1256731 1264454 1264459) (-767 "NTSCAT.spad" 1255211 1255227 1256677 1256716) (-766 "NTPOLFN.spad" 1254756 1254766 1255128 1255133) (-765 "NSUP.spad" 1247766 1247776 1252306 1252459) (-764 "NSUP2.spad" 1247158 1247170 1247756 1247761) (-763 "NSMP.spad" 1243353 1243372 1243661 1243788) (-762 "NREP.spad" 1241725 1241739 1243343 1243348) (-761 "NPCOEF.spad" 1240971 1240991 1241715 1241720) (-760 "NORMRETR.spad" 1240569 1240608 1240961 1240966) (-759 "NORMPK.spad" 1238471 1238490 1240559 1240564) (-758 "NORMMA.spad" 1238159 1238185 1238461 1238466) (-757 "NONE.spad" 1237900 1237908 1238149 1238154) (-756 "NONE1.spad" 1237576 1237586 1237890 1237895) (-755 "NODE1.spad" 1237045 1237061 1237566 1237571) (-754 "NNI.spad" 1235932 1235940 1237019 1237040) (-753 "NLINSOL.spad" 1234554 1234564 1235922 1235927) (-752 "NIPROB.spad" 1233037 1233045 1234544 1234549) (-751 "NFINTBAS.spad" 1230497 1230514 1233027 1233032) (-750 "NETCLT.spad" 1230471 1230482 1230487 1230492) (-749 "NCODIV.spad" 1228669 1228685 1230461 1230466) (-748 "NCNTFRAC.spad" 1228311 1228325 1228659 1228664) (-747 "NCEP.spad" 1226471 1226485 1228301 1228306) (-746 "NASRING.spad" 1226067 1226075 1226461 1226466) (-745 "NASRING.spad" 1225661 1225671 1226057 1226062) (-744 "NARNG.spad" 1225005 1225013 1225651 1225656) (-743 "NARNG.spad" 1224347 1224357 1224995 1225000) (-742 "NAGSP.spad" 1223420 1223428 1224337 1224342) (-741 "NAGS.spad" 1212945 1212953 1223410 1223415) (-740 "NAGF07.spad" 1211338 1211346 1212935 1212940) (-739 "NAGF04.spad" 1205570 1205578 1211328 1211333) (-738 "NAGF02.spad" 1199379 1199387 1205560 1205565) (-737 "NAGF01.spad" 1194982 1194990 1199369 1199374) (-736 "NAGE04.spad" 1188442 1188450 1194972 1194977) (-735 "NAGE02.spad" 1178784 1178792 1188432 1188437) (-734 "NAGE01.spad" 1174668 1174676 1178774 1178779) (-733 "NAGD03.spad" 1172588 1172596 1174658 1174663) (-732 "NAGD02.spad" 1165119 1165127 1172578 1172583) (-731 "NAGD01.spad" 1159232 1159240 1165109 1165114) (-730 "NAGC06.spad" 1155019 1155027 1159222 1159227) (-729 "NAGC05.spad" 1153488 1153496 1155009 1155014) (-728 "NAGC02.spad" 1152743 1152751 1153478 1153483) (-727 "NAALG.spad" 1152278 1152288 1152711 1152738) (-726 "NAALG.spad" 1151833 1151845 1152268 1152273) (-725 "MULTSQFR.spad" 1148791 1148808 1151823 1151828) (-724 "MULTFACT.spad" 1148174 1148191 1148781 1148786) (-723 "MTSCAT.spad" 1146208 1146229 1148072 1148169) (-722 "MTHING.spad" 1145865 1145875 1146198 1146203) (-721 "MSYSCMD.spad" 1145299 1145307 1145855 1145860) (-720 "MSET.spad" 1143241 1143251 1145005 1145044) (-719 "MSETAGG.spad" 1143074 1143084 1143197 1143236) (-718 "MRING.spad" 1140045 1140057 1142782 1142849) (-717 "MRF2.spad" 1139613 1139627 1140035 1140040) (-716 "MRATFAC.spad" 1139159 1139176 1139603 1139608) (-715 "MPRFF.spad" 1137189 1137208 1139149 1139154) (-714 "MPOLY.spad" 1134624 1134639 1134983 1135110) (-713 "MPCPF.spad" 1133888 1133907 1134614 1134619) (-712 "MPC3.spad" 1133703 1133743 1133878 1133883) (-711 "MPC2.spad" 1133345 1133378 1133693 1133698) (-710 "MONOTOOL.spad" 1131680 1131697 1133335 1133340) (-709 "MONOID.spad" 1130999 1131007 1131670 1131675) (-708 "MONOID.spad" 1130316 1130326 1130989 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559564 559657) (-347 "FFNBX.spad" 557843 557863 559047 559140) (-346 "FFNBP.spad" 556356 556373 557559 557652) (-345 "FFNB.spad" 554821 554842 556037 556130) (-344 "FFINTBAS.spad" 552235 552254 554811 554816) (-343 "FFIELDC.spad" 549810 549818 552137 552230) (-342 "FFIELDC.spad" 547471 547481 549800 549805) (-341 "FFHOM.spad" 546219 546236 547461 547466) (-340 "FFF.spad" 543654 543665 546209 546214) (-339 "FFCGX.spad" 542501 542521 543370 543463) (-338 "FFCGP.spad" 541390 541410 542217 542310) (-337 "FFCG.spad" 540182 540203 541071 541164) (-336 "FFCAT.spad" 533209 533231 540021 540177) (-335 "FFCAT.spad" 526315 526339 533129 533134) (-334 "FFCAT2.spad" 526060 526100 526305 526310) (-333 "FEXPR.spad" 517769 517815 525816 525855) (-332 "FEVALAB.spad" 517475 517485 517759 517764) (-331 "FEVALAB.spad" 516966 516978 517252 517257) (-330 "FDIV.spad" 516408 516432 516956 516961) (-329 "FDIVCAT.spad" 514450 514474 516398 516403) (-328 "FDIVCAT.spad" 512490 512516 514440 514445) (-327 "FDIV2.spad" 512144 512184 512480 512485) (-326 "FCPAK1.spad" 510697 510705 512134 512139) (-325 "FCOMP.spad" 510076 510086 510687 510692) (-324 "FC.spad" 499901 499909 510066 510071) (-323 "FAXF.spad" 492836 492850 499803 499896) (-322 "FAXF.spad" 485823 485839 492792 492797) (-321 "FARRAY.spad" 483969 483979 485006 485033) (-320 "FAMR.spad" 482089 482101 483867 483964) (-319 "FAMR.spad" 480193 480207 481973 481978) (-318 "FAMONOID.spad" 479843 479853 480147 480152) (-317 "FAMONC.spad" 478065 478077 479833 479838) (-316 "FAGROUP.spad" 477671 477681 477961 477988) (-315 "FACUTIL.spad" 475867 475884 477661 477666) (-314 "FACTFUNC.spad" 475043 475053 475857 475862) (-313 "EXPUPXS.spad" 471876 471899 473175 473324) (-312 "EXPRTUBE.spad" 469104 469112 471866 471871) (-311 "EXPRODE.spad" 465976 465992 469094 469099) (-310 "EXPR.spad" 461251 461261 461965 462372) (-309 "EXPR2UPS.spad" 457343 457356 461241 461246) (-308 "EXPR2.spad" 457046 457058 457333 457338) (-307 "EXPEXPAN.spad" 453984 454009 454618 454711) (-306 "EXIT.spad" 453655 453663 453974 453979) (-305 "EXITAST.spad" 453391 453399 453645 453650) (-304 "EVALCYC.spad" 452849 452863 453381 453386) (-303 "EVALAB.spad" 452413 452423 452839 452844) (-302 "EVALAB.spad" 451975 451987 452403 452408) (-301 "EUCDOM.spad" 449517 449525 451901 451970) (-300 "EUCDOM.spad" 447121 447131 449507 449512) (-299 "ESTOOLS.spad" 438961 438969 447111 447116) (-298 "ESTOOLS2.spad" 438562 438576 438951 438956) (-297 "ESTOOLS1.spad" 438247 438258 438552 438557) (-296 "ES.spad" 430794 430802 438237 438242) (-295 "ES.spad" 423247 423257 430692 430697) (-294 "ESCONT.spad" 420020 420028 423237 423242) (-293 "ESCONT1.spad" 419769 419781 420010 420015) (-292 "ES2.spad" 419264 419280 419759 419764) (-291 "ES1.spad" 418830 418846 419254 419259) (-290 "ERROR.spad" 416151 416159 418820 418825) (-289 "EQTBL.spad" 414623 414645 414832 414859) (-288 "EQ.spad" 409497 409507 412296 412408) (-287 "EQ2.spad" 409213 409225 409487 409492) (-286 "EP.spad" 405527 405537 409203 409208) (-285 "ENV.spad" 404229 404237 405517 405522) (-284 "ENTIRER.spad" 403897 403905 404173 404224) (-283 "EMR.spad" 403098 403139 403823 403892) (-282 "ELTAGG.spad" 401338 401357 403088 403093) (-281 "ELTAGG.spad" 399542 399563 401294 401299) (-280 "ELTAB.spad" 398989 399007 399532 399537) (-279 "ELFUTS.spad" 398368 398387 398979 398984) (-278 "ELEMFUN.spad" 398057 398065 398358 398363) (-277 "ELEMFUN.spad" 397744 397754 398047 398052) (-276 "ELAGG.spad" 395675 395685 397712 397739) (-275 "ELAGG.spad" 393555 393567 395594 395599) (-274 "ELABEXPR.spad" 392486 392494 393545 393550) (-273 "EFUPXS.spad" 389262 389292 392442 392447) (-272 "EFULS.spad" 386098 386121 389218 389223) (-271 "EFSTRUC.spad" 384053 384069 386088 386093) (-270 "EF.spad" 378819 378835 384043 384048) (-269 "EAB.spad" 377095 377103 378809 378814) (-268 "E04UCFA.spad" 376631 376639 377085 377090) (-267 "E04NAFA.spad" 376208 376216 376621 376626) (-266 "E04MBFA.spad" 375788 375796 376198 376203) (-265 "E04JAFA.spad" 375324 375332 375778 375783) (-264 "E04GCFA.spad" 374860 374868 375314 375319) (-263 "E04FDFA.spad" 374396 374404 374850 374855) (-262 "E04DGFA.spad" 373932 373940 374386 374391) (-261 "E04AGNT.spad" 369774 369782 373922 373927) (-260 "DVARCAT.spad" 366459 366469 369764 369769) (-259 "DVARCAT.spad" 363142 363154 366449 366454) (-258 "DSMP.spad" 360573 360587 360878 361005) (-257 "DROPT.spad" 354518 354526 360563 360568) (-256 "DROPT1.spad" 354181 354191 354508 354513) (-255 "DROPT0.spad" 349008 349016 354171 354176) (-254 "DRAWPT.spad" 347163 347171 348998 349003) (-253 "DRAW.spad" 339763 339776 347153 347158) (-252 "DRAWHACK.spad" 339071 339081 339753 339758) (-251 "DRAWCX.spad" 336513 336521 339061 339066) (-250 "DRAWCURV.spad" 336050 336065 336503 336508) (-249 "DRAWCFUN.spad" 325222 325230 336040 336045) (-248 "DQAGG.spad" 323378 323388 325178 325217) (-247 "DPOLCAT.spad" 318719 318735 323246 323373) (-246 "DPOLCAT.spad" 314146 314164 318675 318680) (-245 "DPMO.spad" 307449 307465 307587 307888) (-244 "DPMM.spad" 300765 300783 300890 301191) (-243 "DOMAIN.spad" 300036 300044 300755 300760) (-242 "DMP.spad" 297258 297273 297830 297957) (-241 "DLP.spad" 296606 296616 297248 297253) (-240 "DLIST.spad" 295018 295028 295789 295816) (-239 "DLAGG.spad" 293419 293429 294998 295013) (-238 "DIVRING.spad" 292961 292969 293363 293414) (-237 "DIVRING.spad" 292547 292557 292951 292956) (-236 "DISPLAY.spad" 290727 290735 292537 292542) (-235 "DIRPROD.spad" 281581 281597 282221 282352) (-234 "DIRPROD2.spad" 280389 280407 281571 281576) (-233 "DIRPCAT.spad" 279319 279335 280241 280384) (-232 "DIRPCAT.spad" 277990 278008 278914 278919) (-231 "DIOSP.spad" 276815 276823 277980 277985) (-230 "DIOPS.spad" 275787 275797 276783 276810) (-229 "DIOPS.spad" 274745 274757 275743 275748) (-228 "DIFRING.spad" 274037 274045 274725 274740) (-227 "DIFRING.spad" 273337 273347 274027 274032) (-226 "DIFEXT.spad" 272496 272506 273317 273332) (-225 "DIFEXT.spad" 271572 271584 272395 272400) (-224 "DIAGG.spad" 271190 271200 271540 271567) (-223 "DIAGG.spad" 270828 270840 271180 271185) (-222 "DHMATRIX.spad" 269132 269142 270285 270312) (-221 "DFSFUN.spad" 262540 262548 269122 269127) (-220 "DFLOAT.spad" 259261 259269 262430 262535) (-219 "DFINTTLS.spad" 257470 257486 259251 259256) (-218 "DERHAM.spad" 255380 255412 257450 257465) (-217 "DEQUEUE.spad" 254698 254708 254987 255014) (-216 "DEGRED.spad" 254313 254327 254688 254693) (-215 "DEFINTRF.spad" 251838 251848 254303 254308) (-214 "DEFINTEF.spad" 250334 250350 251828 251833) (-213 "DEFAST.spad" 249702 249710 250324 250329) (-212 "DECIMAL.spad" 247583 247591 248169 248262) (-211 "DDFACT.spad" 245382 245399 247573 247578) (-210 "DBLRESP.spad" 244980 245004 245372 245377) (-209 "DBASE.spad" 243552 243562 244970 244975) (-208 "DATAARY.spad" 243014 243027 243542 243547) (-207 "D03FAFA.spad" 242842 242850 243004 243009) (-206 "D03EEFA.spad" 242662 242670 242832 242837) (-205 "D03AGNT.spad" 241742 241750 242652 242657) (-204 "D02EJFA.spad" 241204 241212 241732 241737) (-203 "D02CJFA.spad" 240682 240690 241194 241199) (-202 "D02BHFA.spad" 240172 240180 240672 240677) (-201 "D02BBFA.spad" 239662 239670 240162 240167) (-200 "D02AGNT.spad" 234466 234474 239652 239657) (-199 "D01WGTS.spad" 232785 232793 234456 234461) (-198 "D01TRNS.spad" 232762 232770 232775 232780) (-197 "D01GBFA.spad" 232284 232292 232752 232757) (-196 "D01FCFA.spad" 231806 231814 232274 232279) (-195 "D01ASFA.spad" 231274 231282 231796 231801) (-194 "D01AQFA.spad" 230720 230728 231264 231269) (-193 "D01APFA.spad" 230144 230152 230710 230715) (-192 "D01ANFA.spad" 229638 229646 230134 230139) (-191 "D01AMFA.spad" 229148 229156 229628 229633) (-190 "D01ALFA.spad" 228688 228696 229138 229143) (-189 "D01AKFA.spad" 228214 228222 228678 228683) (-188 "D01AJFA.spad" 227737 227745 228204 228209) (-187 "D01AGNT.spad" 223796 223804 227727 227732) (-186 "CYCLOTOM.spad" 223302 223310 223786 223791) (-185 "CYCLES.spad" 220134 220142 223292 223297) (-184 "CVMP.spad" 219551 219561 220124 220129) (-183 "CTRIGMNP.spad" 218041 218057 219541 219546) (-182 "CTOR.spad" 217484 217492 218031 218036) (-181 "CTORKIND.spad" 217099 217107 217474 217479) (-180 "CTORCALL.spad" 216687 216695 217089 217094) (-179 "CSTTOOLS.spad" 215930 215943 216677 216682) (-178 "CRFP.spad" 209634 209647 215920 215925) (-177 "CRCEAST.spad" 209354 209362 209624 209629) (-176 "CRAPACK.spad" 208397 208407 209344 209349) (-175 "CPMATCH.spad" 207897 207912 208322 208327) (-174 "CPIMA.spad" 207602 207621 207887 207892) (-173 "COORDSYS.spad" 202495 202505 207592 207597) (-172 "CONTOUR.spad" 201897 201905 202485 202490) (-171 "CONTFRAC.spad" 197509 197519 201799 201892) (-170 "CONDUIT.spad" 197267 197275 197499 197504) (-169 "COMRING.spad" 196941 196949 197205 197262) (-168 "COMPPROP.spad" 196455 196463 196931 196936) (-167 "COMPLPAT.spad" 196222 196237 196445 196450) (-166 "COMPLEX.spad" 190258 190268 190502 190751) (-165 "COMPLEX2.spad" 189971 189983 190248 190253) (-164 "COMPFACT.spad" 189573 189587 189961 189966) (-163 "COMPCAT.spad" 187699 187709 189307 189568) (-162 "COMPCAT.spad" 185518 185530 187128 187133) (-161 "COMMUPC.spad" 185264 185282 185508 185513) (-160 "COMMONOP.spad" 184797 184805 185254 185259) (-159 "COMM.spad" 184606 184614 184787 184792) (-158 "COMMAAST.spad" 184369 184377 184596 184601) (-157 "COMBOPC.spad" 183274 183282 184359 184364) (-156 "COMBINAT.spad" 182019 182029 183264 183269) (-155 "COMBF.spad" 179387 179403 182009 182014) (-154 "COLOR.spad" 178224 178232 179377 179382) (-153 "COLONAST.spad" 177890 177898 178214 178219) (-152 "CMPLXRT.spad" 177599 177616 177880 177885) (-151 "CLLCTAST.spad" 177261 177269 177589 177594) (-150 "CLIP.spad" 173353 173361 177251 177256) (-149 "CLIF.spad" 171992 172008 173309 173348) (-148 "CLAGG.spad" 168467 168477 171972 171987) (-147 "CLAGG.spad" 164823 164835 168330 168335) (-146 "CINTSLPE.spad" 164148 164161 164813 164818) (-145 "CHVAR.spad" 162226 162248 164138 164143) (-144 "CHARZ.spad" 162141 162149 162206 162221) (-143 "CHARPOL.spad" 161649 161659 162131 162136) (-142 "CHARNZ.spad" 161402 161410 161629 161644) (-141 "CHAR.spad" 159270 159278 161392 161397) (-140 "CFCAT.spad" 158586 158594 159260 159265) (-139 "CDEN.spad" 157744 157758 158576 158581) (-138 "CCLASS.spad" 155893 155901 157155 157194) (-137 "CATEGORY.spad" 155672 155680 155883 155888) (-136 "CATAST.spad" 155299 155307 155662 155667) (-135 "CASEAST.spad" 155013 155021 155289 155294) (-134 "CARTEN.spad" 150116 150140 155003 155008) (-133 "CARTEN2.spad" 149502 149529 150106 150111) (-132 "CARD.spad" 146791 146799 149476 149497) (-131 "CAPSLAST.spad" 146565 146573 146781 146786) (-130 "CACHSET.spad" 146187 146195 146555 146560) (-129 "CABMON.spad" 145740 145748 146177 146182) (-128 "BYTE.spad" 144914 144922 145730 145735) (-127 "BYTEBUF.spad" 142736 142744 144083 144110) (-126 "BTREE.spad" 141805 141815 142343 142370) (-125 "BTOURN.spad" 140808 140818 141412 141439) (-124 "BTCAT.spad" 140184 140194 140764 140803) (-123 "BTCAT.spad" 139592 139604 140174 140179) (-122 "BTAGG.spad" 138702 138710 139548 139587) (-121 "BTAGG.spad" 137844 137854 138692 138697) (-120 "BSTREE.spad" 136579 136589 137451 137478) (-119 "BRILL.spad" 134774 134785 136569 136574) (-118 "BRAGG.spad" 133688 133698 134754 134769) (-117 "BRAGG.spad" 132576 132588 133644 133649) (-116 "BPADICRT.spad" 130557 130569 130812 130905) (-115 "BPADIC.spad" 130221 130233 130483 130552) (-114 "BOUNDZRO.spad" 129877 129894 130211 130216) (-113 "BOP.spad" 125341 125349 129867 129872) (-112 "BOP1.spad" 122727 122737 125297 125302) (-111 "BOOLEAN.spad" 122051 122059 122717 122722) (-110 "BMODULE.spad" 121763 121775 122019 122046) (-109 "BITS.spad" 121182 121190 121399 121426) (-108 "BINDING.spad" 120601 120609 121172 121177) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 "BALFACT.spad" 111180 111192 111730 111735) (-98 "AUTOMOR.spad" 110627 110636 111160 111175) (-97 "ATTREG.spad" 107346 107353 110379 110622) (-96 "ATTRBUT.spad" 103369 103376 107326 107341) (-95 "ATTRAST.spad" 103086 103093 103359 103364) (-94 "ATRIG.spad" 102556 102563 103076 103081) (-93 "ATRIG.spad" 102024 102033 102546 102551) (-92 "ASTCAT.spad" 101928 101935 102014 102019) (-91 "ASTCAT.spad" 101830 101839 101918 101923) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP8.spad" 98087 98100 99034 99039) (-86 "ASP80.spad" 97409 97422 98077 98082) (-85 "ASP7.spad" 96569 96582 97399 97404) (-84 "ASP78.spad" 96020 96033 96559 96564) (-83 "ASP77.spad" 95389 95402 96010 96015) (-82 "ASP74.spad" 94481 94494 95379 95384) (-81 "ASP73.spad" 93752 93765 94471 94476) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP4.spad" 88005 88018 88700 88705) (-76 "ASP49.spad" 87004 87017 87995 88000) (-75 "ASP42.spad" 85411 85450 86994 86999) (-74 "ASP41.spad" 83990 84029 85401 85406) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP1.spad" 67191 67204 67800 67805) (-62 "ASP19.spad" 61877 61890 67181 67186) (-61 "ASP12.spad" 61291 61304 61867 61872) (-60 "ASP10.spad" 60562 60575 61281 61286) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY1.spad" 58757 58766 59105 59132) (-57 "ARRAY12.spad" 57426 57437 58747 58752) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY.spad" 45959 45966 47607 47612) (-51 "ANY1.spad" 45030 45039 45949 45954) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2272386 2272391 2272396 2272401) (-2 NIL 2272366 2272371 2272376 2272381) (-1 NIL 2272346 2272351 2272356 2272361) (0 NIL 2272326 2272331 2272336 2272341) (-1265 "ZMOD.spad" 2272135 2272148 2272264 2272321) (-1264 "ZLINDEP.spad" 2271179 2271190 2272125 2272130) (-1263 "ZDSOLVE.spad" 2261028 2261050 2271169 2271174) (-1262 "YSTREAM.spad" 2260521 2260532 2261018 2261023) (-1261 "XRPOLY.spad" 2259741 2259761 2260377 2260446) (-1260 "XPR.spad" 2257470 2257483 2259459 2259558) (-1259 "XPOLY.spad" 2257025 2257036 2257326 2257395) (-1258 "XPOLYC.spad" 2256342 2256358 2256951 2257020) (-1257 "XPBWPOLY.spad" 2254779 2254799 2256122 2256191) (-1256 "XF.spad" 2253240 2253255 2254681 2254774) (-1255 "XF.spad" 2251681 2251698 2253124 2253129) (-1254 "XFALG.spad" 2248705 2248721 2251607 2251676) (-1253 "XEXPPKG.spad" 2247956 2247982 2248695 2248700) (-1252 "XDPOLY.spad" 2247570 2247586 2247812 2247881) (-1251 "XALG.spad" 2247168 2247179 2247526 2247565) (-1250 "WUTSET.spad" 2243007 2243024 2246814 2246841) (-1249 "WP.spad" 2242021 2242065 2242865 2242932) (-1248 "WHILEAST.spad" 2241819 2241828 2242011 2242016) (-1247 "WHEREAST.spad" 2241490 2241499 2241809 2241814) (-1246 "WFFINTBS.spad" 2239053 2239075 2241480 2241485) (-1245 "WEIER.spad" 2237267 2237278 2239043 2239048) (-1244 "VSPACE.spad" 2236940 2236951 2237235 2237262) (-1243 "VSPACE.spad" 2236633 2236646 2236930 2236935) (-1242 "VOID.spad" 2236223 2236232 2236623 2236628) (-1241 "VIEW.spad" 2233845 2233854 2236213 2236218) (-1240 "VIEWDEF.spad" 2229042 2229051 2233835 2233840) (-1239 "VIEW3D.spad" 2212877 2212886 2229032 2229037) (-1238 "VIEW2D.spad" 2200614 2200623 2212867 2212872) (-1237 "VECTOR.spad" 2199289 2199300 2199540 2199567) (-1236 "VECTOR2.spad" 2197916 2197929 2199279 2199284) (-1235 "VECTCAT.spad" 2195804 2195815 2197872 2197911) (-1234 "VECTCAT.spad" 2193512 2193525 2195582 2195587) (-1233 "VARIABLE.spad" 2193292 2193307 2193502 2193507) (-1232 "UTYPE.spad" 2192926 2192935 2193272 2193287) (-1231 "UTSODETL.spad" 2192219 2192243 2192882 2192887) (-1230 "UTSODE.spad" 2190407 2190427 2192209 2192214) (-1229 "UTS.spad" 2185196 2185224 2188874 2188971) (-1228 "UTSCAT.spad" 2182647 2182663 2185094 2185191) (-1227 "UTSCAT.spad" 2179742 2179760 2182191 2182196) (-1226 "UTS2.spad" 2179335 2179370 2179732 2179737) (-1225 "URAGG.spad" 2173957 2173968 2179315 2179330) (-1224 "URAGG.spad" 2168553 2168566 2173913 2173918) (-1223 "UPXSSING.spad" 2166196 2166222 2167634 2167767) (-1222 "UPXS.spad" 2163223 2163251 2164328 2164477) (-1221 "UPXSCONS.spad" 2160980 2161000 2161355 2161504) (-1220 "UPXSCCA.spad" 2159438 2159458 2160826 2160975) (-1219 "UPXSCCA.spad" 2158038 2158060 2159428 2159433) (-1218 "UPXSCAT.spad" 2156619 2156635 2157884 2158033) (-1217 "UPXS2.spad" 2156160 2156213 2156609 2156614) (-1216 "UPSQFREE.spad" 2154572 2154586 2156150 2156155) (-1215 "UPSCAT.spad" 2152165 2152189 2154470 2154567) (-1214 "UPSCAT.spad" 2149464 2149490 2151771 2151776) (-1213 "UPOLYC.spad" 2144442 2144453 2149306 2149459) (-1212 "UPOLYC.spad" 2139312 2139325 2144178 2144183) (-1211 "UPOLYC2.spad" 2138781 2138800 2139302 2139307) (-1210 "UP.spad" 2135823 2135838 2136331 2136484) (-1209 "UPMP.spad" 2134713 2134726 2135813 2135818) (-1208 "UPDIVP.spad" 2134276 2134290 2134703 2134708) (-1207 "UPDECOMP.spad" 2132513 2132527 2134266 2134271) (-1206 "UPCDEN.spad" 2131720 2131736 2132503 2132508) (-1205 "UP2.spad" 2131082 2131103 2131710 2131715) (-1204 "UNISEG.spad" 2130435 2130446 2131001 2131006) (-1203 "UNISEG2.spad" 2129928 2129941 2130391 2130396) (-1202 "UNIFACT.spad" 2129029 2129041 2129918 2129923) (-1201 "ULS.spad" 2119581 2119609 2120674 2121103) (-1200 "ULSCONS.spad" 2113618 2113638 2113990 2114139) (-1199 "ULSCCAT.spad" 2111215 2111235 2113438 2113613) (-1198 "ULSCCAT.spad" 2108946 2108968 2111171 2111176) (-1197 "ULSCAT.spad" 2107162 2107178 2108792 2108941) (-1196 "ULS2.spad" 2106674 2106727 2107152 2107157) (-1195 "UFD.spad" 2105739 2105748 2106600 2106669) (-1194 "UFD.spad" 2104866 2104877 2105729 2105734) (-1193 "UDVO.spad" 2103713 2103722 2104856 2104861) (-1192 "UDPO.spad" 2101140 2101151 2103669 2103674) (-1191 "TYPE.spad" 2101062 2101071 2101120 2101135) (-1190 "TYPEAST.spad" 2100981 2100990 2101052 2101057) (-1189 "TWOFACT.spad" 2099631 2099646 2100971 2100976) (-1188 "TUPLE.spad" 2099017 2099028 2099530 2099535) (-1187 "TUBETOOL.spad" 2095854 2095863 2099007 2099012) (-1186 "TUBE.spad" 2094495 2094512 2095844 2095849) (-1185 "TS.spad" 2093084 2093100 2094060 2094157) (-1184 "TSETCAT.spad" 2080199 2080216 2093040 2093079) (-1183 "TSETCAT.spad" 2067312 2067331 2080155 2080160) (-1182 "TRMANIP.spad" 2061678 2061695 2067018 2067023) (-1181 "TRIMAT.spad" 2060637 2060662 2061668 2061673) (-1180 "TRIGMNIP.spad" 2059154 2059171 2060627 2060632) (-1179 "TRIGCAT.spad" 2058666 2058675 2059144 2059149) (-1178 "TRIGCAT.spad" 2058176 2058187 2058656 2058661) (-1177 "TREE.spad" 2056747 2056758 2057783 2057810) (-1176 "TRANFUN.spad" 2056578 2056587 2056737 2056742) (-1175 "TRANFUN.spad" 2056407 2056418 2056568 2056573) (-1174 "TOPSP.spad" 2056081 2056090 2056397 2056402) (-1173 "TOOLSIGN.spad" 2055744 2055755 2056071 2056076) (-1172 "TEXTFILE.spad" 2054301 2054310 2055734 2055739) (-1171 "TEX.spad" 2051318 2051327 2054291 2054296) (-1170 "TEX1.spad" 2050874 2050885 2051308 2051313) (-1169 "TEMUTL.spad" 2050429 2050438 2050864 2050869) (-1168 "TBCMPPK.spad" 2048522 2048545 2050419 2050424) (-1167 "TBAGG.spad" 2047546 2047569 2048490 2048517) (-1166 "TBAGG.spad" 2046590 2046615 2047536 2047541) (-1165 "TANEXP.spad" 2045966 2045977 2046580 2046585) (-1164 "TABLE.spad" 2044377 2044400 2044647 2044674) (-1163 "TABLEAU.spad" 2043858 2043869 2044367 2044372) (-1162 "TABLBUMP.spad" 2040641 2040652 2043848 2043853) (-1161 "SYSTEM.spad" 2039915 2039924 2040631 2040636) (-1160 "SYSSOLP.spad" 2037388 2037399 2039905 2039910) (-1159 "SYNTAX.spad" 2033658 2033667 2037378 2037383) (-1158 "SYMTAB.spad" 2031714 2031723 2033648 2033653) (-1157 "SYMS.spad" 2027699 2027708 2031704 2031709) (-1156 "SYMPOLY.spad" 2026706 2026717 2026788 2026915) (-1155 "SYMFUNC.spad" 2026181 2026192 2026696 2026701) (-1154 "SYMBOL.spad" 2023517 2023526 2026171 2026176) (-1153 "SWITCH.spad" 2020274 2020283 2023507 2023512) (-1152 "SUTS.spad" 2017173 2017201 2018741 2018838) (-1151 "SUPXS.spad" 2014187 2014215 2015305 2015454) (-1150 "SUP.spad" 2010956 2010967 2011737 2011890) (-1149 "SUPFRACF.spad" 2010061 2010079 2010946 2010951) (-1148 "SUP2.spad" 2009451 2009464 2010051 2010056) (-1147 "SUMRF.spad" 2008417 2008428 2009441 2009446) (-1146 "SUMFS.spad" 2008050 2008067 2008407 2008412) (-1145 "SULS.spad" 1998589 1998617 1999695 2000124) (-1144 "SUCHTAST.spad" 1998358 1998367 1998579 1998584) (-1143 "SUCH.spad" 1998038 1998053 1998348 1998353) (-1142 "SUBSPACE.spad" 1990045 1990060 1998028 1998033) (-1141 "SUBRESP.spad" 1989205 1989219 1990001 1990006) (-1140 "STTF.spad" 1985304 1985320 1989195 1989200) (-1139 "STTFNC.spad" 1981772 1981788 1985294 1985299) (-1138 "STTAYLOR.spad" 1974170 1974181 1981653 1981658) (-1137 "STRTBL.spad" 1972675 1972692 1972824 1972851) (-1136 "STRING.spad" 1972084 1972093 1972098 1972125) (-1135 "STRICAT.spad" 1971860 1971869 1972040 1972079) (-1134 "STREAM.spad" 1968628 1968639 1971385 1971400) (-1133 "STREAM3.spad" 1968173 1968188 1968618 1968623) (-1132 "STREAM2.spad" 1967241 1967254 1968163 1968168) (-1131 "STREAM1.spad" 1966945 1966956 1967231 1967236) (-1130 "STINPROD.spad" 1965851 1965867 1966935 1966940) (-1129 "STEP.spad" 1965052 1965061 1965841 1965846) (-1128 "STBL.spad" 1963578 1963606 1963745 1963760) (-1127 "STAGG.spad" 1962643 1962654 1963558 1963573) (-1126 "STAGG.spad" 1961716 1961729 1962633 1962638) (-1125 "STACK.spad" 1961067 1961078 1961323 1961350) (-1124 "SREGSET.spad" 1958771 1958788 1960713 1960740) (-1123 "SRDCMPK.spad" 1957316 1957336 1958761 1958766) (-1122 "SRAGG.spad" 1952401 1952410 1957272 1957311) (-1121 "SRAGG.spad" 1947518 1947529 1952391 1952396) (-1120 "SQMATRIX.spad" 1945134 1945152 1946050 1946137) (-1119 "SPLTREE.spad" 1939686 1939699 1944570 1944597) (-1118 "SPLNODE.spad" 1936274 1936287 1939676 1939681) (-1117 "SPFCAT.spad" 1935051 1935060 1936264 1936269) (-1116 "SPECOUT.spad" 1933601 1933610 1935041 1935046) (-1115 "SPADXPT.spad" 1925730 1925739 1933581 1933596) (-1114 "spad-parser.spad" 1925195 1925204 1925720 1925725) (-1113 "SPADAST.spad" 1924896 1924905 1925185 1925190) (-1112 "SPACEC.spad" 1908909 1908920 1924886 1924891) (-1111 "SPACE3.spad" 1908685 1908696 1908899 1908904) (-1110 "SORTPAK.spad" 1908230 1908243 1908641 1908646) (-1109 "SOLVETRA.spad" 1905987 1905998 1908220 1908225) (-1108 "SOLVESER.spad" 1904507 1904518 1905977 1905982) (-1107 "SOLVERAD.spad" 1900517 1900528 1904497 1904502) (-1106 "SOLVEFOR.spad" 1898937 1898955 1900507 1900512) (-1105 "SNTSCAT.spad" 1898525 1898542 1898893 1898932) (-1104 "SMTS.spad" 1896785 1896811 1898090 1898187) (-1103 "SMP.spad" 1894224 1894244 1894614 1894741) (-1102 "SMITH.spad" 1893067 1893092 1894214 1894219) (-1101 "SMATCAT.spad" 1891165 1891195 1892999 1893062) (-1100 "SMATCAT.spad" 1889207 1889239 1891043 1891048) (-1099 "SKAGG.spad" 1888156 1888167 1889163 1889202) (-1098 "SINT.spad" 1886464 1886473 1888022 1888151) (-1097 "SIMPAN.spad" 1886192 1886201 1886454 1886459) (-1096 "SIG.spad" 1885520 1885529 1886182 1886187) (-1095 "SIGNRF.spad" 1884628 1884639 1885510 1885515) (-1094 "SIGNEF.spad" 1883897 1883914 1884618 1884623) (-1093 "SIGAST.spad" 1883278 1883287 1883887 1883892) (-1092 "SHP.spad" 1881196 1881211 1883234 1883239) (-1091 "SHDP.spad" 1872181 1872208 1872690 1872821) (-1090 "SGROUP.spad" 1871789 1871798 1872171 1872176) (-1089 "SGROUP.spad" 1871395 1871406 1871779 1871784) (-1088 "SGCF.spad" 1864276 1864285 1871385 1871390) (-1087 "SFRTCAT.spad" 1863192 1863209 1864232 1864271) (-1086 "SFRGCD.spad" 1862255 1862275 1863182 1863187) (-1085 "SFQCMPK.spad" 1856892 1856912 1862245 1862250) (-1084 "SFORT.spad" 1856327 1856341 1856882 1856887) (-1083 "SEXOF.spad" 1856170 1856210 1856317 1856322) (-1082 "SEX.spad" 1856062 1856071 1856160 1856165) (-1081 "SEXCAT.spad" 1853166 1853206 1856052 1856057) (-1080 "SET.spad" 1851466 1851477 1852587 1852626) (-1079 "SETMN.spad" 1849900 1849917 1851456 1851461) (-1078 "SETCAT.spad" 1849385 1849394 1849890 1849895) (-1077 "SETCAT.spad" 1848868 1848879 1849375 1849380) (-1076 "SETAGG.spad" 1845377 1845388 1848836 1848863) (-1075 "SETAGG.spad" 1841906 1841919 1845367 1845372) (-1074 "SEQAST.spad" 1841609 1841618 1841896 1841901) (-1073 "SEGXCAT.spad" 1840721 1840734 1841589 1841604) (-1072 "SEG.spad" 1840534 1840545 1840640 1840645) (-1071 "SEGCAT.spad" 1839353 1839364 1840514 1840529) (-1070 "SEGBIND.spad" 1838425 1838436 1839308 1839313) (-1069 "SEGBIND2.spad" 1838121 1838134 1838415 1838420) (-1068 "SEGAST.spad" 1837835 1837844 1838111 1838116) (-1067 "SEG2.spad" 1837260 1837273 1837791 1837796) (-1066 "SDVAR.spad" 1836536 1836547 1837250 1837255) (-1065 "SDPOL.spad" 1833926 1833937 1834217 1834344) (-1064 "SCPKG.spad" 1832005 1832016 1833916 1833921) (-1063 "SCOPE.spad" 1831150 1831159 1831995 1832000) (-1062 "SCACHE.spad" 1829832 1829843 1831140 1831145) (-1061 "SASTCAT.spad" 1829741 1829750 1829822 1829827) (-1060 "SAOS.spad" 1829613 1829622 1829731 1829736) (-1059 "SAERFFC.spad" 1829326 1829346 1829603 1829608) (-1058 "SAE.spad" 1827501 1827517 1828112 1828247) (-1057 "SAEFACT.spad" 1827202 1827222 1827491 1827496) (-1056 "RURPK.spad" 1824843 1824859 1827192 1827197) (-1055 "RULESET.spad" 1824284 1824308 1824833 1824838) (-1054 "RULE.spad" 1822488 1822512 1824274 1824279) (-1053 "RULECOLD.spad" 1822340 1822353 1822478 1822483) (-1052 "RSTRCAST.spad" 1822057 1822066 1822330 1822335) (-1051 "RSETGCD.spad" 1818435 1818455 1822047 1822052) (-1050 "RSETCAT.spad" 1808207 1808224 1818391 1818430) (-1049 "RSETCAT.spad" 1798011 1798030 1808197 1808202) (-1048 "RSDCMPK.spad" 1796463 1796483 1798001 1798006) (-1047 "RRCC.spad" 1794847 1794877 1796453 1796458) (-1046 "RRCC.spad" 1793229 1793261 1794837 1794842) (-1045 "RPTAST.spad" 1792931 1792940 1793219 1793224) (-1044 "RPOLCAT.spad" 1772291 1772306 1792799 1792926) (-1043 "RPOLCAT.spad" 1751365 1751382 1771875 1771880) (-1042 "ROUTINE.spad" 1747228 1747237 1750012 1750039) (-1041 "ROMAN.spad" 1746460 1746469 1747094 1747223) (-1040 "ROIRC.spad" 1745540 1745572 1746450 1746455) (-1039 "RNS.spad" 1744443 1744452 1745442 1745535) (-1038 "RNS.spad" 1743432 1743443 1744433 1744438) (-1037 "RNG.spad" 1743167 1743176 1743422 1743427) (-1036 "RMODULE.spad" 1742805 1742816 1743157 1743162) (-1035 "RMCAT2.spad" 1742213 1742270 1742795 1742800) (-1034 "RMATRIX.spad" 1740892 1740911 1741380 1741419) (-1033 "RMATCAT.spad" 1736413 1736444 1740836 1740887) (-1032 "RMATCAT.spad" 1731836 1731869 1736261 1736266) (-1031 "RINTERP.spad" 1731724 1731744 1731826 1731831) (-1030 "RING.spad" 1731081 1731090 1731704 1731719) (-1029 "RING.spad" 1730446 1730457 1731071 1731076) (-1028 "RIDIST.spad" 1729830 1729839 1730436 1730441) (-1027 "RGCHAIN.spad" 1728409 1728425 1729315 1729342) (-1026 "RGBCSPC.spad" 1728190 1728202 1728399 1728404) (-1025 "RGBCMDL.spad" 1727720 1727732 1728180 1728185) (-1024 "RF.spad" 1725334 1725345 1727710 1727715) (-1023 "RFFACTOR.spad" 1724796 1724807 1725324 1725329) (-1022 "RFFACT.spad" 1724531 1724543 1724786 1724791) (-1021 "RFDIST.spad" 1723519 1723528 1724521 1724526) (-1020 "RETSOL.spad" 1722936 1722949 1723509 1723514) (-1019 "RETRACT.spad" 1722285 1722296 1722926 1722931) (-1018 "RETRACT.spad" 1721632 1721645 1722275 1722280) (-1017 "RETAST.spad" 1721444 1721453 1721622 1721627) (-1016 "RESULT.spad" 1719504 1719513 1720091 1720118) (-1015 "RESRING.spad" 1718851 1718898 1719442 1719499) (-1014 "RESLATC.spad" 1718175 1718186 1718841 1718846) (-1013 "REPSQ.spad" 1717904 1717915 1718165 1718170) (-1012 "REP.spad" 1715456 1715465 1717894 1717899) (-1011 "REPDB.spad" 1715161 1715172 1715446 1715451) (-1010 "REP2.spad" 1704733 1704744 1715003 1715008) (-1009 "REP1.spad" 1698723 1698734 1704683 1704688) (-1008 "REGSET.spad" 1696520 1696537 1698369 1698396) (-1007 "REF.spad" 1695849 1695860 1696475 1696480) (-1006 "REDORDER.spad" 1695025 1695042 1695839 1695844) (-1005 "RECLOS.spad" 1693808 1693828 1694512 1694605) (-1004 "REALSOLV.spad" 1692940 1692949 1693798 1693803) (-1003 "REAL.spad" 1692812 1692821 1692930 1692935) (-1002 "REAL0Q.spad" 1690094 1690109 1692802 1692807) (-1001 "REAL0.spad" 1686922 1686937 1690084 1690089) (-1000 "RDUCEAST.spad" 1686643 1686652 1686912 1686917) (-999 "RDIV.spad" 1686295 1686319 1686633 1686638) (-998 "RDIST.spad" 1685859 1685869 1686285 1686290) (-997 "RDETRS.spad" 1684656 1684673 1685849 1685854) (-996 "RDETR.spad" 1682764 1682781 1684646 1684651) (-995 "RDEEFS.spad" 1681838 1681854 1682754 1682759) (-994 "RDEEF.spad" 1680835 1680851 1681828 1681833) (-993 "RCFIELD.spad" 1678022 1678030 1680737 1680830) (-992 "RCFIELD.spad" 1675295 1675305 1678012 1678017) (-991 "RCAGG.spad" 1673198 1673208 1675275 1675290) (-990 "RCAGG.spad" 1671038 1671050 1673117 1673122) (-989 "RATRET.spad" 1670399 1670409 1671028 1671033) (-988 "RATFACT.spad" 1670092 1670103 1670389 1670394) (-987 "RANDSRC.spad" 1669412 1669420 1670082 1670087) (-986 "RADUTIL.spad" 1669167 1669175 1669402 1669407) (-985 "RADIX.spad" 1665957 1665970 1667634 1667727) (-984 "RADFF.spad" 1664371 1664407 1664489 1664645) (-983 "RADCAT.spad" 1663965 1663973 1664361 1664366) (-982 "RADCAT.spad" 1663557 1663567 1663955 1663960) (-981 "QUEUE.spad" 1662900 1662910 1663164 1663191) (-980 "QUAT.spad" 1661482 1661492 1661824 1661889) (-979 "QUATCT2.spad" 1661101 1661119 1661472 1661477) (-978 "QUATCAT.spad" 1659266 1659276 1661031 1661096) (-977 "QUATCAT.spad" 1657182 1657194 1658949 1658954) (-976 "QUAGG.spad" 1655996 1656006 1657138 1657177) (-975 "QQUTAST.spad" 1655765 1655773 1655986 1655991) (-974 "QFORM.spad" 1655228 1655242 1655755 1655760) (-973 "QFCAT.spad" 1653919 1653929 1655118 1655223) (-972 "QFCAT.spad" 1652213 1652225 1653414 1653419) (-971 "QFCAT2.spad" 1651904 1651920 1652203 1652208) (-970 "QEQUAT.spad" 1651461 1651469 1651894 1651899) (-969 "QCMPACK.spad" 1646208 1646227 1651451 1651456) (-968 "QALGSET.spad" 1642283 1642315 1646122 1646127) (-967 "QALGSET2.spad" 1640279 1640297 1642273 1642278) (-966 "PWFFINTB.spad" 1637589 1637610 1640269 1640274) (-965 "PUSHVAR.spad" 1636918 1636937 1637579 1637584) (-964 "PTRANFN.spad" 1633044 1633054 1636908 1636913) (-963 "PTPACK.spad" 1630132 1630142 1633034 1633039) (-962 "PTFUNC2.spad" 1629953 1629967 1630122 1630127) (-961 "PTCAT.spad" 1629035 1629045 1629909 1629948) (-960 "PSQFR.spad" 1628342 1628366 1629025 1629030) (-959 "PSEUDLIN.spad" 1627200 1627210 1628332 1628337) (-958 "PSETPK.spad" 1612633 1612649 1627078 1627083) (-957 "PSETCAT.spad" 1606541 1606564 1612601 1612628) (-956 "PSETCAT.spad" 1600435 1600460 1606497 1606502) (-955 "PSCURVE.spad" 1599418 1599426 1600425 1600430) (-954 "PSCAT.spad" 1598185 1598214 1599316 1599413) (-953 "PSCAT.spad" 1597042 1597073 1598175 1598180) (-952 "PRTITION.spad" 1595885 1595893 1597032 1597037) (-951 "PRTDAST.spad" 1595604 1595612 1595875 1595880) (-950 "PRS.spad" 1585166 1585183 1595560 1595565) (-949 "PRQAGG.spad" 1584585 1584595 1585122 1585161) (-948 "PROPLOG.spad" 1583988 1583996 1584575 1584580) (-947 "PROPFRML.spad" 1581906 1581917 1583978 1583983) (-946 "PROPERTY.spad" 1581400 1581408 1581896 1581901) (-945 "PRODUCT.spad" 1579080 1579092 1579366 1579421) (-944 "PR.spad" 1577466 1577478 1578171 1578298) (-943 "PRINT.spad" 1577218 1577226 1577456 1577461) (-942 "PRIMES.spad" 1575469 1575479 1577208 1577213) (-941 "PRIMELT.spad" 1573450 1573464 1575459 1575464) (-940 "PRIMCAT.spad" 1573073 1573081 1573440 1573445) (-939 "PRIMARR.spad" 1572078 1572088 1572256 1572283) (-938 "PRIMARR2.spad" 1570801 1570813 1572068 1572073) (-937 "PREASSOC.spad" 1570173 1570185 1570791 1570796) (-936 "PPCURVE.spad" 1569310 1569318 1570163 1570168) (-935 "PORTNUM.spad" 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(-916 "PMLSAGG.spad" 1536321 1536335 1536730 1536735) (-915 "PMKERNEL.spad" 1535888 1535900 1536311 1536316) (-914 "PMINS.spad" 1535464 1535474 1535878 1535883) (-913 "PMFS.spad" 1535037 1535055 1535454 1535459) (-912 "PMDOWN.spad" 1534323 1534337 1535027 1535032) (-911 "PMASS.spad" 1533335 1533343 1534313 1534318) (-910 "PMASSFS.spad" 1532304 1532320 1533325 1533330) (-909 "PLOTTOOL.spad" 1532084 1532092 1532294 1532299) (-908 "PLOT.spad" 1526915 1526923 1532074 1532079) (-907 "PLOT3D.spad" 1523335 1523343 1526905 1526910) (-906 "PLOT1.spad" 1522476 1522486 1523325 1523330) (-905 "PLEQN.spad" 1509692 1509719 1522466 1522471) (-904 "PINTERP.spad" 1509308 1509327 1509682 1509687) (-903 "PINTERPA.spad" 1509090 1509106 1509298 1509303) (-902 "PI.spad" 1508697 1508705 1509064 1509085) (-901 "PID.spad" 1507653 1507661 1508623 1508692) (-900 "PICOERCE.spad" 1507310 1507320 1507643 1507648) (-899 "PGROEB.spad" 1505907 1505921 1507300 1507305) (-898 "PGE.spad" 1497160 1497168 1505897 1505902) (-897 "PGCD.spad" 1496042 1496059 1497150 1497155) (-896 "PFRPAC.spad" 1495185 1495195 1496032 1496037) (-895 "PFR.spad" 1491842 1491852 1495087 1495180) (-894 "PFOTOOLS.spad" 1491100 1491116 1491832 1491837) (-893 "PFOQ.spad" 1490470 1490488 1491090 1491095) (-892 "PFO.spad" 1489889 1489916 1490460 1490465) (-891 "PF.spad" 1489463 1489475 1489694 1489787) (-890 "PFECAT.spad" 1487129 1487137 1489389 1489458) (-889 "PFECAT.spad" 1484823 1484833 1487085 1487090) (-888 "PFBRU.spad" 1482693 1482705 1484813 1484818) (-887 "PFBR.spad" 1480231 1480254 1482683 1482688) (-886 "PERM.spad" 1475912 1475922 1480061 1480076) (-885 "PERMGRP.spad" 1470648 1470658 1475902 1475907) (-884 "PERMCAT.spad" 1469200 1469210 1470628 1470643) (-883 "PERMAN.spad" 1467732 1467746 1469190 1469195) (-882 "PENDTREE.spad" 1467005 1467015 1467361 1467366) (-881 "PDRING.spad" 1465496 1465506 1466985 1467000) (-880 "PDRING.spad" 1463995 1464007 1465486 1465491) (-879 "PDEPROB.spad" 1462952 1462960 1463985 1463990) (-878 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1434872 1435406 1435411) (-859 "PARSC2.spad" 1434633 1434649 1434834 1434839) (-858 "PARPCURV.spad" 1434091 1434119 1434623 1434628) (-857 "PARPC2.spad" 1433880 1433896 1434081 1434086) (-856 "PAN2EXPR.spad" 1433292 1433300 1433870 1433875) (-855 "PALETTE.spad" 1432262 1432270 1433282 1433287) (-854 "PAIR.spad" 1431245 1431258 1431850 1431855) (-853 "PADICRC.spad" 1428575 1428593 1429750 1429843) (-852 "PADICRAT.spad" 1426590 1426602 1426811 1426904) (-851 "PADIC.spad" 1426285 1426297 1426516 1426585) (-850 "PADICCT.spad" 1424826 1424838 1426211 1426280) (-849 "PADEPAC.spad" 1423505 1423524 1424816 1424821) (-848 "PADE.spad" 1422245 1422261 1423495 1423500) (-847 "OWP.spad" 1421229 1421259 1422103 1422170) (-846 "OVAR.spad" 1421010 1421033 1421219 1421224) (-845 "OUT.spad" 1420094 1420102 1421000 1421005) (-844 "OUTFORM.spad" 1409390 1409398 1420084 1420089) (-843 "OUTBFILE.spad" 1408808 1408816 1409380 1409385) (-842 "OUTBCON.spad" 1408086 1408094 1408798 1408803) (-841 "OUTBCON.spad" 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"OPTPACK.spad" 1374444 1374452 1382049 1382054) (-821 "OPTCAT.spad" 1372119 1372127 1374434 1374439) (-820 "OPQUERY.spad" 1371668 1371676 1372109 1372114) (-819 "OP.spad" 1371410 1371420 1371490 1371557) (-818 "ONECOMP.spad" 1370155 1370165 1370957 1370986) (-817 "ONECOMP2.spad" 1369573 1369585 1370145 1370150) (-816 "OMSERVER.spad" 1368575 1368583 1369563 1369568) (-815 "OMSAGG.spad" 1368351 1368361 1368519 1368570) (-814 "OMPKG.spad" 1366963 1366971 1368341 1368346) (-813 "OM.spad" 1365928 1365936 1366953 1366958) (-812 "OMLO.spad" 1365353 1365365 1365814 1365853) (-811 "OMEXPR.spad" 1365187 1365197 1365343 1365348) (-810 "OMERR.spad" 1364730 1364738 1365177 1365182) (-809 "OMERRK.spad" 1363764 1363772 1364720 1364725) (-808 "OMENC.spad" 1363108 1363116 1363754 1363759) (-807 "OMDEV.spad" 1357397 1357405 1363098 1363103) (-806 "OMCONN.spad" 1356806 1356814 1357387 1357392) (-805 "OINTDOM.spad" 1356569 1356577 1356732 1356801) (-804 "OFMONOID.spad" 1352756 1352766 1356559 1356564) (-803 "ODVAR.spad" 1352017 1352027 1352746 1352751) (-802 "ODR.spad" 1351465 1351491 1351829 1351978) (-801 "ODPOL.spad" 1348811 1348821 1349151 1349278) (-800 "ODP.spad" 1339932 1339952 1340305 1340436) (-799 "ODETOOLS.spad" 1338515 1338534 1339922 1339927) (-798 "ODESYS.spad" 1336165 1336182 1338505 1338510) (-797 "ODERTRIC.spad" 1332106 1332123 1336122 1336127) (-796 "ODERED.spad" 1331493 1331517 1332096 1332101) (-795 "ODERAT.spad" 1329044 1329061 1331483 1331488) (-794 "ODEPRRIC.spad" 1325935 1325957 1329034 1329039) (-793 "ODEPROB.spad" 1325134 1325142 1325925 1325930) (-792 "ODEPRIM.spad" 1322408 1322430 1325124 1325129) (-791 "ODEPAL.spad" 1321784 1321808 1322398 1322403) (-790 "ODEPACK.spad" 1308386 1308394 1321774 1321779) (-789 "ODEINT.spad" 1307817 1307833 1308376 1308381) (-788 "ODEIFTBL.spad" 1305212 1305220 1307807 1307812) (-787 "ODEEF.spad" 1300579 1300595 1305202 1305207) (-786 "ODECONST.spad" 1300098 1300116 1300569 1300574) (-785 "ODECAT.spad" 1298694 1298702 1300088 1300093) (-784 "OCT.spad" 1296832 1296842 1297548 1297587) (-783 "OCTCT2.spad" 1296476 1296497 1296822 1296827) (-782 "OC.spad" 1294250 1294260 1296432 1296471) (-781 "OC.spad" 1291749 1291761 1293933 1293938) (-780 "OCAMON.spad" 1291597 1291605 1291739 1291744) (-779 "OASGP.spad" 1291412 1291420 1291587 1291592) (-778 "OAMONS.spad" 1290932 1290940 1291402 1291407) (-777 "OAMON.spad" 1290793 1290801 1290922 1290927) (-776 "OAGROUP.spad" 1290655 1290663 1290783 1290788) (-775 "NUMTUBE.spad" 1290242 1290258 1290645 1290650) (-774 "NUMQUAD.spad" 1278104 1278112 1290232 1290237) (-773 "NUMODE.spad" 1269240 1269248 1278094 1278099) (-772 "NUMINT.spad" 1266798 1266806 1269230 1269235) (-771 "NUMFMT.spad" 1265638 1265646 1266788 1266793) (-770 "NUMERIC.spad" 1257710 1257720 1265443 1265448) (-769 "NTSCAT.spad" 1256200 1256216 1257666 1257705) (-768 "NTPOLFN.spad" 1255745 1255755 1256117 1256122) (-767 "NSUP.spad" 1248755 1248765 1253295 1253448) (-766 "NSUP2.spad" 1248147 1248159 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1152834 1153257 1153262) (-727 "MULTSQFR.spad" 1149780 1149797 1152812 1152817) (-726 "MULTFACT.spad" 1149163 1149180 1149770 1149775) (-725 "MTSCAT.spad" 1147197 1147218 1149061 1149158) (-724 "MTHING.spad" 1146854 1146864 1147187 1147192) (-723 "MSYSCMD.spad" 1146288 1146296 1146844 1146849) (-722 "MSET.spad" 1144230 1144240 1145994 1146033) (-721 "MSETAGG.spad" 1144063 1144073 1144186 1144225) (-720 "MRING.spad" 1141034 1141046 1143771 1143838) (-719 "MRF2.spad" 1140602 1140616 1141024 1141029) (-718 "MRATFAC.spad" 1140148 1140165 1140592 1140597) (-717 "MPRFF.spad" 1138178 1138197 1140138 1140143) (-716 "MPOLY.spad" 1135613 1135628 1135972 1136099) (-715 "MPCPF.spad" 1134877 1134896 1135603 1135608) (-714 "MPC3.spad" 1134692 1134732 1134867 1134872) (-713 "MPC2.spad" 1134334 1134367 1134682 1134687) (-712 "MONOTOOL.spad" 1132669 1132686 1134324 1134329) (-711 "MONOID.spad" 1131988 1131996 1132659 1132664) (-710 "MONOID.spad" 1131305 1131315 1131978 1131983) (-709 "MONOGEN.spad" 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1085961) (-671 "MATCAT.spad" 1074971 1074993 1083354 1083393) (-670 "MATCAT.spad" 1066428 1066452 1074813 1074818) (-669 "MATCAT2.spad" 1065696 1065744 1066418 1066423) (-668 "MAPPKG3.spad" 1064595 1064609 1065686 1065691) (-667 "MAPPKG2.spad" 1063929 1063941 1064585 1064590) (-666 "MAPPKG1.spad" 1062747 1062757 1063919 1063924) (-665 "MAPPAST.spad" 1062060 1062068 1062737 1062742) (-664 "MAPHACK3.spad" 1061868 1061882 1062050 1062055) (-663 "MAPHACK2.spad" 1061633 1061645 1061858 1061863) (-662 "MAPHACK1.spad" 1061263 1061273 1061623 1061628) (-661 "MAGMA.spad" 1059053 1059070 1061253 1061258) (-660 "MACROAST.spad" 1058632 1058640 1059043 1059048) (-659 "M3D.spad" 1056328 1056338 1058010 1058015) (-658 "LZSTAGG.spad" 1053546 1053556 1056308 1056323) (-657 "LZSTAGG.spad" 1050772 1050784 1053536 1053541) (-656 "LWORD.spad" 1047477 1047494 1050762 1050767) (-655 "LSTAST.spad" 1047261 1047269 1047467 1047472) (-654 "LSQM.spad" 1045487 1045501 1045885 1045936) (-653 "LSPP.spad" 1045020 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1025677 1025682) (-633 "LMOPS.spad" 1018223 1018240 1021477 1021482) (-632 "LMODULE.spad" 1017865 1017875 1018213 1018218) (-631 "LMDICT.spad" 1017148 1017158 1017416 1017443) (-630 "LITERAL.spad" 1017054 1017065 1017138 1017143) (-629 "LIST.spad" 1014772 1014782 1016201 1016228) (-628 "LIST3.spad" 1014063 1014077 1014762 1014767) (-627 "LIST2.spad" 1012703 1012715 1014053 1014058) (-626 "LIST2MAP.spad" 1009580 1009592 1012693 1012698) (-625 "LINEXP.spad" 1009012 1009022 1009560 1009575) (-624 "LINDEP.spad" 1007789 1007801 1008924 1008929) (-623 "LIMITRF.spad" 1005703 1005713 1007779 1007784) (-622 "LIMITPS.spad" 1004586 1004599 1005693 1005698) (-621 "LIE.spad" 1002600 1002612 1003876 1004021) (-620 "LIECAT.spad" 1002076 1002086 1002526 1002595) (-619 "LIECAT.spad" 1001580 1001592 1002032 1002037) (-618 "LIB.spad" 999628 999636 1000239 1000254) (-617 "LGROBP.spad" 996981 997000 999618 999623) (-616 "LF.spad" 995900 995916 996971 996976) (-615 "LFCAT.spad" 994919 994927 995890 995895) (-614 "LEXTRIPK.spad" 990422 990437 994909 994914) (-613 "LEXP.spad" 988425 988452 990402 990417) (-612 "LETAST.spad" 988124 988132 988415 988420) (-611 "LEADCDET.spad" 986508 986525 988114 988119) (-610 "LAZM3PK.spad" 985212 985234 986498 986503) (-609 "LAUPOL.spad" 983901 983914 984805 984874) (-608 "LAPLACE.spad" 983474 983490 983891 983896) (-607 "LA.spad" 982914 982928 983396 983435) (-606 "LALG.spad" 982690 982700 982894 982909) (-605 "LALG.spad" 982474 982486 982680 982685) (-604 "KVTFROM.spad" 982083 982093 982464 982469) (-603 "KTVLOGIC.spad" 981506 981514 982073 982078) (-602 "KRCFROM.spad" 981122 981132 981496 981501) (-601 "KOVACIC.spad" 979835 979852 981112 981117) (-600 "KONVERT.spad" 979557 979567 979825 979830) (-599 "KOERCE.spad" 979294 979304 979547 979552) (-598 "KERNEL.spad" 977829 977839 979078 979083) (-597 "KERNEL2.spad" 977532 977544 977819 977824) (-596 "KDAGG.spad" 976623 976645 977500 977527) (-595 "KDAGG.spad" 975734 975758 976613 976618) (-594 "KAFILE.spad" 974697 974713 974932 974959) (-593 "JORDAN.spad" 972524 972536 973987 974132) (-592 "JOINAST.spad" 972218 972226 972514 972519) (-591 "JAVACODE.spad" 971984 971992 972208 972213) (-590 "IXAGG.spad" 970097 970121 971964 971979) (-589 "IXAGG.spad" 968075 968101 969944 969949) (-588 "IVECTOR.spad" 966846 966861 967001 967028) (-587 "ITUPLE.spad" 965991 966001 966836 966841) (-586 "ITRIGMNP.spad" 964802 964821 965981 965986) (-585 "ITFUN3.spad" 964296 964310 964792 964797) (-584 "ITFUN2.spad" 964026 964038 964286 964291) (-583 "ITAYLOR.spad" 961818 961833 963862 963987) (-582 "ISUPS.spad" 954229 954244 960792 960889) (-581 "ISUMP.spad" 953726 953742 954219 954224) (-580 "ISTRING.spad" 952729 952742 952895 952922) (-579 "ISAST.spad" 952448 952456 952719 952724) (-578 "IRURPK.spad" 951161 951180 952438 952443) (-577 "IRSN.spad" 949121 949129 951151 951156) (-576 "IRRF2F.spad" 947596 947606 949077 949082) (-575 "IRREDFFX.spad" 947197 947208 947586 947591) (-574 "IROOT.spad" 945528 945538 947187 947192) (-573 "IR.spad" 943317 943331 945383 945410) (-572 "IR2.spad" 942337 942353 943307 943312) (-571 "IR2F.spad" 941537 941553 942327 942332) (-570 "IPRNTPK.spad" 941297 941305 941527 941532) (-569 "IPF.spad" 940862 940874 941102 941195) (-568 "IPADIC.spad" 940623 940649 940788 940857) (-567 "IP4ADDR.spad" 940171 940179 940613 940618) (-566 "IOMODE.spad" 939792 939800 940161 940166) (-565 "IOBFILE.spad" 939153 939161 939782 939787) (-564 "IOBCON.spad" 939018 939026 939143 939148) (-563 "INVLAPLA.spad" 938663 938679 939008 939013) (-562 "INTTR.spad" 931909 931926 938653 938658) (-561 "INTTOOLS.spad" 929620 929636 931483 931488) (-560 "INTSLPE.spad" 928926 928934 929610 929615) (-559 "INTRVL.spad" 928492 928502 928840 928921) (-558 "INTRF.spad" 926856 926870 928482 928487) (-557 "INTRET.spad" 926288 926298 926846 926851) (-556 "INTRAT.spad" 924963 924980 926278 926283) (-555 "INTPM.spad" 923326 923342 924606 924611) (-554 "INTPAF.spad" 921094 921112 923258 923263) (-553 "INTPACK.spad" 911404 911412 921084 921089) (-552 "INT.spad" 910765 910773 911258 911399) (-551 "INTHERTR.spad" 910031 910048 910755 910760) (-550 "INTHERAL.spad" 909697 909721 910021 910026) (-549 "INTHEORY.spad" 906110 906118 909687 909692) (-548 "INTG0.spad" 899573 899591 906042 906047) (-547 "INTFTBL.spad" 893602 893610 899563 899568) (-546 "INTFACT.spad" 892661 892671 893592 893597) (-545 "INTEF.spad" 890976 890992 892651 892656) (-544 "INTDOM.spad" 889591 889599 890902 890971) (-543 "INTDOM.spad" 888268 888278 889581 889586) (-542 "INTCAT.spad" 886521 886531 888182 888263) (-541 "INTBIT.spad" 886024 886032 886511 886516) (-540 "INTALG.spad" 885206 885233 886014 886019) (-539 "INTAF.spad" 884698 884714 885196 885201) (-538 "INTABL.spad" 883216 883247 883379 883406) (-537 "INS.spad" 880683 880691 883118 883211) (-536 "INS.spad" 878236 878246 880673 880678) (-535 "INPSIGN.spad" 877670 877683 878226 878231) (-534 "INPRODPF.spad" 876736 876755 877660 877665) (-533 "INPRODFF.spad" 875794 875818 876726 876731) (-532 "INNMFACT.spad" 874765 874782 875784 875789) (-531 "INMODGCD.spad" 874249 874279 874755 874760) (-530 "INFSP.spad" 872534 872556 874239 874244) (-529 "INFPROD0.spad" 871584 871603 872524 872529) (-528 "INFORM.spad" 868745 868753 871574 871579) (-527 "INFORM1.spad" 868370 868380 868735 868740) (-526 "INFINITY.spad" 867922 867930 868360 868365) (-525 "INETCLTS.spad" 867899 867907 867912 867917) (-524 "INEP.spad" 866431 866453 867889 867894) (-523 "INDE.spad" 866160 866177 866421 866426) (-522 "INCRMAPS.spad" 865581 865591 866150 866155) (-521 "INBFILE.spad" 864653 864661 865571 865576) (-520 "INBFF.spad" 860423 860434 864643 864648) (-519 "INBCON.spad" 859722 859730 860413 860418) (-518 "INBCON.spad" 859019 859029 859712 859717) (-517 "INAST.spad" 858684 858692 859009 859014) (-516 "IMPTAST.spad" 858392 858400 858674 858679) (-515 "IMATRIX.spad" 857337 857363 857849 857876) (-514 "IMATQF.spad" 856431 856475 857293 857298) (-513 "IMATLIN.spad" 855036 855060 856387 856392) (-512 "ILIST.spad" 853692 853707 854219 854246) (-511 "IIARRAY2.spad" 853080 853118 853299 853326) (-510 "IFF.spad" 852490 852506 852761 852854) (-509 "IFAST.spad" 852104 852112 852480 852485) (-508 "IFARRAY.spad" 849591 849606 851287 851314) (-507 "IFAMON.spad" 849453 849470 849547 849552) (-506 "IEVALAB.spad" 848842 848854 849443 849448) (-505 "IEVALAB.spad" 848229 848243 848832 848837) (-504 "IDPO.spad" 848027 848039 848219 848224) (-503 "IDPOAMS.spad" 847783 847795 848017 848022) (-502 "IDPOAM.spad" 847503 847515 847773 847778) (-501 "IDPC.spad" 846437 846449 847493 847498) (-500 "IDPAM.spad" 846182 846194 846427 846432) (-499 "IDPAG.spad" 845929 845941 846172 846177) (-498 "IDENT.spad" 845846 845854 845919 845924) (-497 "IDECOMP.spad" 843083 843101 845836 845841) (-496 "IDEAL.spad" 838006 838045 843018 843023) (-495 "ICDEN.spad" 837157 837173 837996 838001) (-494 "ICARD.spad" 836346 836354 837147 837152) (-493 "IBPTOOLS.spad" 834939 834956 836336 836341) (-492 "IBITS.spad" 834138 834151 834575 834602) (-491 "IBATOOL.spad" 831013 831032 834128 834133) (-490 "IBACHIN.spad" 829500 829515 831003 831008) (-489 "IARRAY2.spad" 828488 828514 829107 829134) (-488 "IARRAY1.spad" 827533 827548 827671 827698) (-487 "IAN.spad" 825746 825754 827349 827442) (-486 "IALGFACT.spad" 825347 825380 825736 825741) (-485 "HYPCAT.spad" 824771 824779 825337 825342) (-484 "HYPCAT.spad" 824193 824203 824761 824766) (-483 "HOSTNAME.spad" 824001 824009 824183 824188) (-482 "HOAGG.spad" 821259 821269 823981 823996) (-481 "HOAGG.spad" 818302 818314 821026 821031) (-480 "HEXADEC.spad" 816171 816179 816769 816862) (-479 "HEUGCD.spad" 815186 815197 816161 816166) (-478 "HELLFDIV.spad" 814776 814800 815176 815181) (-477 "HEAP.spad" 814168 814178 814383 814410) (-476 "HEADAST.spad" 813699 813707 814158 814163) (-475 "HDP.spad" 804816 804832 805193 805324) (-474 "HDMP.spad" 801992 802007 802610 802737) (-473 "HB.spad" 800229 800237 801982 801987) (-472 "HASHTBL.spad" 798699 798730 798910 798937) (-471 "HASAST.spad" 798415 798423 798689 798694) (-470 "HACKPI.spad" 797898 797906 798317 798410) (-469 "GTSET.spad" 796837 796853 797544 797571) (-468 "GSTBL.spad" 795356 795391 795530 795545) (-467 "GSERIES.spad" 792523 792550 793488 793637) (-466 "GROUP.spad" 791792 791800 792503 792518) (-465 "GROUP.spad" 791069 791079 791782 791787) (-464 "GROEBSOL.spad" 789557 789578 791059 791064) (-463 "GRMOD.spad" 788128 788140 789547 789552) (-462 "GRMOD.spad" 786697 786711 788118 788123) (-461 "GRIMAGE.spad" 779302 779310 786687 786692) (-460 "GRDEF.spad" 777681 777689 779292 779297) (-459 "GRAY.spad" 776140 776148 777671 777676) (-458 "GRALG.spad" 775187 775199 776130 776135) (-457 "GRALG.spad" 774232 774246 775177 775182) (-456 "GPOLSET.spad" 773686 773709 773914 773941) (-455 "GOSPER.spad" 772951 772969 773676 773681) (-454 "GMODPOL.spad" 772089 772116 772919 772946) (-453 "GHENSEL.spad" 771158 771172 772079 772084) (-452 "GENUPS.spad" 767259 767272 771148 771153) (-451 "GENUFACT.spad" 766836 766846 767249 767254) (-450 "GENPGCD.spad" 766420 766437 766826 766831) (-449 "GENMFACT.spad" 765872 765891 766410 766415) (-448 "GENEEZ.spad" 763811 763824 765862 765867) (-447 "GDMP.spad" 760829 760846 761605 761732) (-446 "GCNAALG.spad" 754724 754751 760623 760690) (-445 "GCDDOM.spad" 753896 753904 754650 754719) (-444 "GCDDOM.spad" 753130 753140 753886 753891) (-443 "GB.spad" 750648 750686 753086 753091) (-442 "GBINTERN.spad" 746668 746706 750638 750643) (-441 "GBF.spad" 742425 742463 746658 746663) (-440 "GBEUCLID.spad" 740299 740337 742415 742420) (-439 "GAUSSFAC.spad" 739596 739604 740289 740294) (-438 "GALUTIL.spad" 737918 737928 739552 739557) (-437 "GALPOLYU.spad" 736364 736377 737908 737913) (-436 "GALFACTU.spad" 734529 734548 736354 736359) (-435 "GALFACT.spad" 724662 724673 734519 734524) (-434 "FVFUN.spad" 721675 721683 724642 724657) (-433 "FVC.spad" 720717 720725 721655 721670) (-432 "FUNCTION.spad" 720566 720578 720707 720712) (-431 "FT.spad" 718778 718786 720556 720561) (-430 "FTEM.spad" 717941 717949 718768 718773) (-429 "FSUPFACT.spad" 716841 716860 717877 717882) (-428 "FST.spad" 714927 714935 716831 716836) (-427 "FSRED.spad" 714405 714421 714917 714922) (-426 "FSPRMELT.spad" 713229 713245 714362 714367) (-425 "FSPECF.spad" 711306 711322 713219 713224) (-424 "FS.spad" 705356 705366 711069 711301) (-423 "FS.spad" 699196 699208 704911 704916) (-422 "FSINT.spad" 698854 698870 699186 699191) (-421 "FSERIES.spad" 698041 698053 698674 698773) (-420 "FSCINT.spad" 697354 697370 698031 698036) (-419 "FSAGG.spad" 696459 696469 697298 697349) (-418 "FSAGG.spad" 695538 695550 696379 696384) (-417 "FSAGG2.spad" 694237 694253 695528 695533) (-416 "FS2UPS.spad" 688626 688660 694227 694232) (-415 "FS2.spad" 688271 688287 688616 688621) (-414 "FS2EXPXP.spad" 687394 687417 688261 688266) (-413 "FRUTIL.spad" 686336 686346 687384 687389) (-412 "FR.spad" 680030 680040 685360 685429) (-411 "FRNAALG.spad" 675117 675127 679972 680025) (-410 "FRNAALG.spad" 670216 670228 675073 675078) (-409 "FRNAAF2.spad" 669670 669688 670206 670211) (-408 "FRMOD.spad" 669064 669094 669601 669606) (-407 "FRIDEAL.spad" 668259 668280 669044 669059) (-406 "FRIDEAL2.spad" 667861 667893 668249 668254) (-405 "FRETRCT.spad" 667372 667382 667851 667856) (-404 "FRETRCT.spad" 666749 666761 667230 667235) (-403 "FRAMALG.spad" 665077 665090 666705 666744) (-402 "FRAMALG.spad" 663437 663452 665067 665072) (-401 "FRAC.spad" 660536 660546 660939 661112) (-400 "FRAC2.spad" 660139 660151 660526 660531) (-399 "FR2.spad" 659473 659485 660129 660134) (-398 "FPS.spad" 656282 656290 659363 659468) (-397 "FPS.spad" 653119 653129 656202 656207) (-396 "FPC.spad" 652161 652169 653021 653114) (-395 "FPC.spad" 651289 651299 652151 652156) (-394 "FPATMAB.spad" 651041 651051 651269 651284) (-393 "FPARFRAC.spad" 649514 649531 651031 651036) (-392 "FORTRAN.spad" 648020 648063 649504 649509) (-391 "FORT.spad" 646949 646957 648010 648015) (-390 "FORTFN.spad" 644109 644117 646929 646944) (-389 "FORTCAT.spad" 643783 643791 644089 644104) (-388 "FORMULA.spad" 641121 641129 643773 643778) (-387 "FORMULA1.spad" 640600 640610 641111 641116) (-386 "FORDER.spad" 640291 640315 640590 640595) (-385 "FOP.spad" 639492 639500 640281 640286) (-384 "FNLA.spad" 638916 638938 639460 639487) (-383 "FNCAT.spad" 637244 637252 638906 638911) (-382 "FNAME.spad" 637136 637144 637234 637239) (-381 "FMTC.spad" 636934 636942 637062 637131) (-380 "FMONOID.spad" 633989 633999 636890 636895) (-379 "FM.spad" 633684 633696 633923 633950) (-378 "FMFUN.spad" 630704 630712 633664 633679) (-377 "FMC.spad" 629746 629754 630684 630699) (-376 "FMCAT.spad" 627400 627418 629714 629741) (-375 "FM1.spad" 626757 626769 627334 627361) (-374 "FLOATRP.spad" 624478 624492 626747 626752) (-373 "FLOAT.spad" 617642 617650 624344 624473) (-372 "FLOATCP.spad" 615059 615073 617632 617637) (-371 "FLINEXP.spad" 614771 614781 615039 615054) (-370 "FLINEXP.spad" 614437 614449 614707 614712) (-369 "FLASORT.spad" 613757 613769 614427 614432) (-368 "FLALG.spad" 611403 611422 613683 613752) (-367 "FLAGG.spad" 608409 608419 611371 611398) (-366 "FLAGG.spad" 605328 605340 608292 608297) (-365 "FLAGG2.spad" 604009 604025 605318 605323) (-364 "FINRALG.spad" 602038 602051 603965 604004) (-363 "FINRALG.spad" 599993 600008 601922 601927) (-362 "FINITE.spad" 599145 599153 599983 599988) (-361 "FINAALG.spad" 588126 588136 599087 599140) (-360 "FINAALG.spad" 577119 577131 588082 588087) (-359 "FILE.spad" 576702 576712 577109 577114) (-358 "FILECAT.spad" 575220 575237 576692 576697) (-357 "FIELD.spad" 574626 574634 575122 575215) (-356 "FIELD.spad" 574118 574128 574616 574621) (-355 "FGROUP.spad" 572727 572737 574098 574113) (-354 "FGLMICPK.spad" 571514 571529 572717 572722) (-353 "FFX.spad" 570889 570904 571230 571323) (-352 "FFSLPE.spad" 570378 570399 570879 570884) (-351 "FFPOLY.spad" 561630 561641 570368 570373) (-350 "FFPOLY2.spad" 560690 560707 561620 561625) (-349 "FFP.spad" 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-1034) 135615) ((-353 . -544) T) ((-347 . -544) T) ((-339 . -544) T) ((-107 . -544) T) ((-640 . -700) 135585) ((-1143 . -1001) NIL) ((-313 . -23) T) ((-66 . -1189) T) ((-979 . -599) 135517) ((-676 . -226) 135499) ((-697 . -110) 135464) ((-627 . -34) T) ((-240 . -482) 135448) ((-1078 . -1074) 135432) ((-168 . -1076) T) ((-931 . -888) 135411) ((-474 . -888) 135390) ((-1263 . -1127) T) ((-1259 . -21) T) ((-1259 . -25) T) ((-1257 . -129) T) ((-1255 . -129) T) ((-1063 . -700) 135239) ((-1039 . -630) 135226) ((-931 . -630) 135151) ((-765 . -700) 134980) ((-528 . -599) 134962) ((-528 . -600) 134943) ((-763 . -700) 134792) ((-1248 . -101) T) ((-1053 . -101) T) ((-375 . -25) T) ((-375 . -21) T) ((-474 . -630) 134717) ((-454 . -700) 134688) ((-447 . -700) 134537) ((-966 . -101) T) ((-1231 . -599) 134503) ((-1220 . -1017) 134438) ((-1199 . -1189) 134417) ((-720 . -101) T) ((-1199 . -865) NIL) ((-1199 . -863) 134369) ((-1162 . -600) NIL) ((-1162 . -599) 134351) ((-523 . -25) T) ((-1118 . -1099) 134296) ((-1025 . -1182) 134225) ((-880 . -303) 134163) ((-337 . -1035) T) ((-138 . -101) T) ((-44 . -129) T) ((-283 . -1088) T) ((-663 . -92) T) ((-658 . -92) T) ((-646 . -599) 134145) ((-628 . -599) 134098) ((-471 . -92) T) ((-349 . -599) 134080) ((-346 . -599) 134062) ((-338 . -599) 134044) ((-258 . -600) 133792) ((-258 . -599) 133774) ((-242 . -599) 133756) ((-242 . -600) 133617) ((-136 . -92) T) ((-135 . -92) T) ((-131 . -92) T) ((-1199 . -1017) 133583) ((-1183 . -506) 133550) ((-1117 . -599) 133532) ((-802 . -837) T) ((-802 . -709) T) ((-588 . -282) 133509) ((-569 . -700) 133474) ((-472 . -600) NIL) ((-472 . -599) 133456) ((-510 . -700) 133401) ((-310 . -101) T) ((-307 . -101) T) ((-283 . -23) T) ((-149 . -129) T) ((-380 . -709) T) ((-851 . -1034) 133353) ((-889 . -599) 133335) ((-889 . -600) 133317) ((-851 . -110) 133255) ((-134 . -101) T) ((-113 . -101) T) ((-695 . -1211) 133239) ((-697 . -1028) T) ((-676 . -343) NIL) ((-511 . -599) 133171) ((-373 . -778) T) ((-218 . -1076) T) 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-700) 123081) ((-1025 . -148) 123046) ((-40 . -169) T) ((-676 . -405) 123028) ((-695 . -303) 123015) ((-817 . -630) 122975) ((-810 . -630) 122949) ((-313 . -25) T) ((-313 . -21) T) ((-640 . -280) 122928) ((-568 . -1076) T) ((-552 . -1076) T) ((-487 . -1076) T) ((-240 . -282) 122905) ((-307 . -226) 122866) ((-1148 . -865) NIL) ((-1101 . -865) 122725) ((-128 . -830) T) ((-1148 . -1017) 122605) ((-1101 . -1017) 122488) ((-180 . -599) 122470) ((-834 . -1017) 122366) ((-765 . -280) 122293) ((-800 . -1088) T) ((-1013 . -709) T) ((-588 . -633) 122277) ((-1025 . -955) 122206) ((-978 . -101) T) ((-800 . -23) T) ((-695 . -1127) 122184) ((-676 . -1035) T) ((-588 . -367) 122168) ((-345 . -445) T) ((-337 . -284) T) ((-1236 . -1076) T) ((-243 . -1076) T) ((-393 . -101) T) ((-283 . -21) T) ((-283 . -25) T) ((-355 . -709) T) ((-693 . -1076) T) ((-681 . -1076) T) ((-355 . -466) T) ((-1183 . -599) 122150) ((-1148 . -371) 122134) ((-1101 . -371) 122118) ((-1003 . -405) 122080) ((-138 . -224) 122062) 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. -144) 90982) ((-373 . -544) T) ((-1149 . -144) 90961) ((-1149 . -142) 90940) ((-1143 . -142) 90847) ((-401 . -284) T) ((-1143 . -144) 90754) ((-1102 . -144) 90733) ((-1102 . -142) 90712) ((-313 . -38) 90553) ((-166 . -129) T) ((-307 . -778) NIL) ((-307 . -775) NIL) ((-636 . -1028) T) ((-48 . -630) 90518) ((-1142 . -101) T) ((-973 . -101) T) ((-972 . -21) T) ((-126 . -989) 90502) ((-120 . -989) 90486) ((-972 . -25) T) ((-880 . -118) 90470) ((-1134 . -101) T) ((-799 . -830) 90449) ((-1208 . -129) T) ((-1148 . -25) T) ((-1148 . -21) T) ((-835 . -129) T) ((-1101 . -25) T) ((-1101 . -21) T) ((-834 . -25) T) ((-834 . -21) T) ((-765 . -301) 90428) ((-629 . -101) 90406) ((-616 . -101) T) ((-1135 . -303) 90201) ((-559 . -129) T) ((-605 . -828) 90180) ((-1132 . -482) 90164) ((-1126 . -148) 90114) ((-1122 . -599) 90076) ((-1122 . -600) 90037) ((-1003 . -774) T) ((-1003 . -777) T) ((-1003 . -709) T) ((-477 . -303) 89975) ((-446 . -411) 89945) ((-345 . -169) T) ((-283 . -38) 89932) ((-268 . -101) 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. -600) 85815) ((-978 . -238) 85794) ((-978 . -228) 85773) ((-1263 . -709) T) ((-1227 . -142) 85752) ((-816 . -1076) T) ((-1227 . -144) 85731) ((-1220 . -144) 85710) ((-1220 . -142) 85689) ((-1219 . -1193) 85668) ((-1199 . -142) 85575) ((-1199 . -144) 85482) ((-1198 . -1193) 85461) ((-373 . -129) T) ((-552 . -865) 85443) ((0 . -1076) T) ((-171 . -169) T) ((-166 . -21) T) ((-166 . -25) T) ((-49 . -1076) T) ((-1221 . -630) 85348) ((-1219 . -544) 85299) ((-697 . -1088) T) ((-1198 . -544) 85250) ((-552 . -1017) 85232) ((-582 . -144) 85211) ((-582 . -142) 85190) ((-487 . -1017) 85133) ((-1111 . -1113) T) ((-86 . -378) T) ((-86 . -389) T) ((-851 . -357) T) ((-817 . -129) T) ((-810 . -129) T) ((-697 . -23) T) ((-498 . -599) 85083) ((-494 . -599) 85065) ((-1259 . -1035) T) ((-373 . -1037) T) ((-1005 . -1076) 85043) ((-880 . -34) T) ((-475 . -303) 84981) ((-579 . -101) T) ((-1132 . -600) 84942) ((-1132 . -599) 84874) ((-1148 . -830) 84853) ((-45 . -101) T) ((-1101 . -830) 84832) ((-800 . -101) 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T) ((-676 . -1189) T) ((-349 . -544) T) ((-346 . -544) T) ((-338 . -544) T) ((-258 . -544) 81849) ((-242 . -544) 81780) ((-517 . -1059) T) ((-1118 . -110) 81759) ((-446 . -727) 81729) ((-845 . -1034) 81699) ((-800 . -38) 81641) ((-676 . -863) 81623) ((-676 . -865) 81605) ((-289 . -303) 81409) ((-889 . -1193) T) ((-652 . -405) 81393) ((-845 . -110) 81358) ((-676 . -1017) 81303) ((-983 . -445) T) ((-889 . -544) T) ((-525 . -599) 81285) ((-569 . -899) T) ((-467 . -1088) T) ((-510 . -899) T) ((-1132 . -282) 81262) ((-893 . -445) T) ((-64 . -599) 81244) ((-616 . -224) 81190) ((-467 . -23) T) ((-1096 . -777) T) ((-851 . -129) T) ((-1096 . -774) T) ((-1250 . -1252) 81169) ((-1096 . -709) T) ((-636 . -630) 81143) ((-288 . -599) 80884) ((-1014 . -34) T) ((-798 . -828) 80863) ((-568 . -301) T) ((-552 . -301) T) ((-487 . -301) T) ((-1259 . -700) 80833) ((-676 . -371) 80815) ((-676 . -332) 80797) ((-470 . -169) T) ((-375 . -700) 80767) ((-850 . -830) NIL) ((-552 . -1001) T) ((-487 . -1001) T) 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. -25) T) ((-499 . -23) T) ((-1143 . -1195) 78357) ((-401 . -1028) T) ((-313 . -1035) T) ((-676 . -301) T) ((-107 . -828) T) ((-401 . -238) T) ((-401 . -228) 78336) ((-695 . -709) T) ((-480 . -38) 78286) ((-212 . -38) 78236) ((-467 . -485) 78202) ((-1134 . -1120) T) ((-1077 . -101) T) ((-683 . -599) 78184) ((-683 . -600) 78099) ((-697 . -21) T) ((-697 . -25) T) ((-1111 . -101) T) ((-132 . -599) 78081) ((-115 . -599) 78063) ((-154 . -25) T) ((-1257 . -1076) T) ((-851 . -623) 78011) ((-1255 . -1076) T) ((-942 . -101) T) ((-718 . -101) T) ((-698 . -101) T) ((-446 . -101) T) ((-799 . -445) 77962) ((-44 . -1076) T) ((-1064 . -830) T) ((-646 . -129) T) ((-1040 . -303) 77813) ((-652 . -700) 77797) ((-283 . -1035) T) ((-349 . -129) T) ((-346 . -129) T) ((-338 . -129) T) ((-258 . -129) T) ((-242 . -129) T) ((-412 . -101) T) ((-149 . -1076) T) ((-45 . -224) 77747) ((-937 . -830) 77726) ((-978 . -630) 77664) ((-235 . -1242) 77634) ((-1003 . -301) T) ((-288 . -1034) 77555) ((-889 . -129) T) ((-40 . -899) T) ((-480 . -394) 77537) ((-348 . -301) T) ((-212 . -394) 77519) ((-1056 . -405) 77503) ((-288 . -110) 77419) ((-851 . -25) T) ((-851 . -21) T) ((-333 . -599) 77401) ((-1221 . -47) 77345) ((-220 . -144) T) ((-171 . -599) 77327) ((-1089 . -828) 77306) ((-757 . -599) 77288) ((-127 . -830) T) ((-594 . -230) 77235) ((-468 . -230) 77185) ((-1257 . -700) 77155) ((-48 . -301) T) ((-1255 . -700) 77125) ((-943 . -1076) T) ((-798 . -1076) 76915) ((-306 . -101) T) ((-880 . -1189) T) ((-48 . -1001) T) ((-1198 . -623) 76823) ((-671 . -101) 76801) ((-44 . -700) 76785) ((-538 . -101) T) ((-66 . -377) T) ((-66 . -389) T) ((-644 . -23) T) ((-652 . -744) T) ((-1186 . -1076) 76763) ((-345 . -1034) 76708) ((-657 . -1076) 76686) ((-1039 . -144) T) ((-931 . -144) 76665) ((-931 . -142) 76644) ((-782 . -101) T) ((-149 . -700) 76628) ((-474 . -144) 76607) ((-474 . -142) 76586) ((-345 . -110) 76515) ((-1056 . -1035) T) ((-316 . -830) 76494) ((-1227 . -952) 76463) ((-611 . -1076) T) ((-1220 . -952) 76425) ((-503 . -129) T) ((-499 . -129) T) ((-289 . -224) 76375) ((-353 . -1035) T) ((-347 . -1035) T) ((-339 . -1035) T) ((-288 . -1028) 76317) ((-1199 . -952) 76286) ((-373 . -830) T) ((-107 . -1035) T) ((-978 . -709) T) ((-849 . -899) T) ((-823 . -778) 76265) ((-823 . -775) 76244) ((-412 . -303) 76183) ((-461 . -101) T) ((-582 . -952) 76152) ((-313 . -1076) T) ((-401 . -778) 76131) ((-401 . -775) 76110) ((-492 . -482) 76092) ((-1221 . -1017) 76058) ((-1219 . -21) T) ((-1219 . -25) T) ((-1198 . -21) T) ((-1198 . -25) T) ((-798 . -700) 76000) ((-681 . -398) T) ((-1248 . -1189) T) ((-592 . -101) T) ((-1089 . -405) 75969) ((-982 . -362) NIL) ((-653 . -101) T) ((-177 . -101) T) ((-158 . -101) T) ((-153 . -101) T) ((-151 . -101) T) ((-102 . -34) T) ((-720 . -1189) T) ((-44 . -744) T) ((-580 . -101) T) ((-76 . -390) T) ((-76 . -389) T) ((-635 . -638) 75953) ((-138 . -1189) T) ((-850 . -144) T) ((-850 . -142) NIL) ((-1188 . -92) T) ((-345 . -1028) T) ((-69 . -377) T) ((-69 . -389) T) 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. -1035) T) ((-480 . -226) 74414) ((-477 . -947) 74398) ((-475 . -828) 74377) ((-212 . -226) 74359) ((-80 . -434) T) ((-80 . -389) T) ((-1122 . -34) T) ((-798 . -169) 74338) ((-714 . -101) T) ((-1005 . -599) 74305) ((-492 . -280) 74280) ((-310 . -371) 74249) ((-307 . -371) 74210) ((-307 . -332) 74171) ((-1061 . -599) 74153) ((-799 . -928) 74100) ((-644 . -129) T) ((-1208 . -142) 74079) ((-1208 . -144) 74058) ((-1150 . -101) T) ((-1149 . -101) T) ((-1143 . -101) T) ((-1135 . -1076) T) ((-1102 . -101) T) ((-217 . -34) T) ((-283 . -700) 74045) ((-1135 . -596) 74021) ((-580 . -303) NIL) ((-477 . -1076) 73999) ((-384 . -599) 73981) ((-502 . -830) T) ((-1126 . -224) 73931) ((-1227 . -1226) 73915) ((-1227 . -1213) 73892) ((-1220 . -1218) 73853) ((-1220 . -1213) 73823) ((-1220 . -1216) 73807) ((-1199 . -1197) 73768) ((-1199 . -1213) 73745) ((-605 . -599) 73727) ((-1199 . -1195) 73711) ((-681 . -899) T) ((-1150 . -278) 73677) ((-1149 . -278) 73643) ((-1143 . -278) 73609) ((-1056 . -1076) T) 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. -1189) T) ((-807 . -599) 21227) ((-1258 . -1088) T) ((-1250 . -599) 21209) ((-1208 . -169) 21100) ((-107 . -371) 21082) ((-107 . -332) 21064) ((-1039 . -284) T) ((-931 . -284) 20995) ((-782 . -362) 20974) ((-629 . -1189) T) ((-616 . -1189) T) ((-474 . -284) 20905) ((-559 . -169) T) ((-321 . -276) 20889) ((-1258 . -23) T) ((-1183 . -101) T) ((-1170 . -1076) T) ((-1064 . -1076) T) ((-1052 . -1076) T) ((-82 . -599) 20871) ((-694 . -101) T) ((-349 . -343) 20850) ((-594 . -1076) T) ((-346 . -343) 20829) ((-338 . -343) 20808) ((-468 . -1076) T) ((-1162 . -224) 20758) ((-258 . -247) 20720) ((-1118 . -129) T) ((-594 . -596) 20696) ((-1056 . -879) 20629) ((-983 . -1028) T) ((-893 . -1028) T) ((-468 . -596) 20608) ((-1143 . -775) NIL) ((-1143 . -778) NIL) ((-1078 . -600) 20569) ((-472 . -224) 20519) ((-1078 . -599) 20501) ((-983 . -238) T) ((-983 . -228) T) ((-421 . -1028) T) ((-937 . -1076) 20451) ((-893 . -238) T) ((-845 . -129) T) ((-681 . -445) T) ((-823 . -1088) 20430) ((-107 . -879) NIL) 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. -599) 126999) ((-135 . -599) 126965) ((-131 . -599) 126931) ((-1125 . -34) T) ((-924 . -1191) T) ((-337 . -702) 126876) ((-654 . -25) T) ((-654 . -21) T) ((-467 . -1030) T) ((-621 . -411) 126841) ((-593 . -411) 126806) ((-1098 . -1129) T) ((-569 . -284) T) ((-510 . -284) T) ((-1222 . -301) 126785) ((-467 . -228) 126737) ((-467 . -238) 126716) ((-1201 . -301) 126695) ((-1201 . -1003) NIL) ((-1058 . -129) T) ((-853 . -780) 126674) ((-141 . -101) T) ((-40 . -1078) T) ((-853 . -777) 126653) ((-629 . -991) 126637) ((-568 . -1037) T) ((-552 . -1037) T) ((-487 . -1037) T) ((-401 . -445) T) ((-353 . -129) T) ((-310 . -394) 126621) ((-307 . -394) 126582) ((-347 . -129) T) ((-339 . -129) T) ((-1159 . -1078) T) ((-1098 . -38) 126569) ((-1072 . -599) 126536) ((-107 . -129) T) ((-935 . -1078) T) ((-902 . -1078) T) ((-756 . -1078) T) ((-656 . -1078) T) ((-498 . -1061) T) ((-685 . -144) T) ((-115 . -144) T) ((-1259 . -21) T) ((-1259 . -25) T) ((-1257 . -21) T) ((-1257 . -25) T) ((-648 . -1036) 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-711) T) ((-115 . -445) T) ((-1260 . -1251) 118988) ((-852 . -865) 118965) ((-852 . -867) NIL) ((-945 . -832) 118864) ((-800 . -832) 118815) ((-638 . -640) 118799) ((-1177 . -34) T) ((-168 . -599) 118781) ((-1091 . -21) 118691) ((-1091 . -25) 118542) ((-852 . -1019) 118519) ((-933 . -881) 118500) ((-1210 . -47) 118477) ((-891 . -362) T) ((-58 . -635) 118461) ((-508 . -635) 118445) ((-474 . -881) 118422) ((-70 . -434) T) ((-70 . -389) T) ((-488 . -635) 118406) ((-58 . -367) 118390) ((-609 . -169) T) ((-508 . -367) 118374) ((-488 . -367) 118358) ((-812 . -693) 118342) ((-1150 . -301) 118321) ((-1156 . -129) T) ((-116 . -169) T) ((-1124 . -303) 118259) ((-166 . -1191) T) ((-621 . -729) 118243) ((-593 . -729) 118227) ((-1249 . -129) T) ((-1222 . -901) 118206) ((-1201 . -901) 118185) ((-1201 . -805) NIL) ((-678 . -702) 118135) ((-1200 . -890) 118088) ((-1005 . -1078) T) ((-852 . -371) 118065) ((-852 . -332) 118042) ((-886 . -1090) T) ((-166 . -865) 118026) ((-166 . -867) 117951) ((-480 . 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. -1078) T) ((-1005 . -702) 116594) ((-696 . -1036) 116559) ((-603 . -101) T) ((-588 . -34) T) ((-1125 . -1191) T) ((-1185 . -110) 116428) ((-467 . -632) 116325) ((-348 . -702) 116270) ((-166 . -881) 116229) ((-683 . -284) T) ((-678 . -169) T) ((-696 . -110) 116185) ((-1265 . -1037) T) ((-1210 . -371) 116169) ((-412 . -1195) 116147) ((-1096 . -599) 116129) ((-307 . -830) NIL) ((-412 . -544) T) ((-220 . -301) T) ((-1200 . -776) 116082) ((-1200 . -779) 116035) ((-1221 . -711) T) ((-1200 . -711) T) ((-48 . -702) 116000) ((-220 . -1003) T) ((-345 . -1244) 115977) ((-1223 . -405) 115943) ((-703 . -711) T) ((-1210 . -881) 115886) ((-111 . -599) 115868) ((-111 . -600) 115850) ((-703 . -466) T) ((-475 . -21) 115760) ((-126 . -482) 115744) ((-120 . -482) 115728) ((-475 . -25) 115579) ((-609 . -284) T) ((-573 . -1036) 115554) ((-431 . -1078) T) ((-1041 . -301) T) ((-116 . -284) T) ((-1082 . -101) T) ((-984 . -101) T) ((-573 . -110) 115522) ((-1120 . -303) 115460) ((-1185 . -1030) T) ((-1041 . 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. -1036) 114292) ((-648 . -632) 114276) ((-852 . -301) T) ((-767 . -110) 114085) ((-765 . -110) 113914) ((-349 . -632) 113866) ((-346 . -632) 113818) ((-338 . -632) 113770) ((-258 . -632) 113695) ((-242 . -632) 113620) ((-1136 . -832) T) ((-1066 . -1019) 113604) ((-454 . -110) 113565) ((-447 . -110) 113394) ((-1054 . -1019) 113371) ((-981 . -34) T) ((-947 . -599) 113353) ((-939 . -1191) T) ((-125 . -991) 113337) ((-944 . -1090) T) ((-852 . -1003) NIL) ((-720 . -1090) T) ((-700 . -1090) T) ((-1237 . -482) 113321) ((-1120 . -38) 113281) ((-944 . -23) T) ((-825 . -101) T) ((-802 . -21) T) ((-802 . -25) T) ((-720 . -23) T) ((-700 . -23) T) ((-109 . -645) T) ((-891 . -632) 113246) ((-569 . -1036) 113211) ((-510 . -1036) 113156) ((-222 . -56) 113114) ((-446 . -23) T) ((-401 . -101) T) ((-257 . -101) T) ((-678 . -284) T) ((-847 . -38) 113084) ((-569 . -110) 113040) ((-510 . -110) 112969) ((-412 . -1090) T) ((-310 . -1037) 112859) ((-307 . -1037) T) ((-127 . -1191) T) ((-642 . -1030) T) 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T) ((-349 . -711) T) ((-346 . -711) T) ((-338 . -711) T) ((-258 . -711) T) ((-242 . -711) T) ((-1027 . -303) 112018) ((-882 . -1078) 111996) ((-50 . -1030) T) ((-1249 . -21) T) ((-1249 . -25) T) ((-1152 . -544) 111975) ((-1151 . -1195) 111954) ((-569 . -1030) T) ((-510 . -1030) T) ((-1145 . -1195) 111933) ((-355 . -1019) 111917) ((-316 . -1019) 111901) ((-1005 . -284) T) ((-373 . -867) 111883) ((-1151 . -544) 111834) ((-1145 . -544) 111785) ((-984 . -38) 111730) ((-784 . -1090) T) ((-891 . -711) T) ((-569 . -238) T) ((-569 . -228) T) ((-510 . -228) T) ((-510 . -238) T) ((-1104 . -544) 111709) ((-348 . -284) T) ((-631 . -679) 111693) ((-373 . -1019) 111653) ((-1098 . -1037) T) ((-102 . -124) 111637) ((-784 . -23) T) ((-1237 . -280) 111614) ((-401 . -303) 111579) ((-1259 . -1254) 111555) ((-1257 . -1254) 111534) ((-1223 . -1078) T) ((-851 . -599) 111516) ((-819 . -1019) 111485) ((-198 . -772) T) ((-197 . -772) T) ((-196 . -772) T) ((-195 . -772) T) ((-194 . -772) T) ((-193 . -772) T) 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104038) ((-472 . -1191) T) ((-337 . -362) T) ((-138 . -482) 104020) ((-765 . -632) 103945) ((-1119 . -1191) T) ((-454 . -632) 103916) ((-258 . -867) 103775) ((-242 . -867) NIL) ((-116 . -1036) 103720) ((-447 . -632) 103645) ((-648 . -1019) 103622) ((-609 . -110) 103607) ((-349 . -1019) 103591) ((-346 . -1019) 103575) ((-338 . -1019) 103559) ((-258 . -1019) 103403) ((-242 . -1019) 103279) ((-116 . -110) 103208) ((-58 . -1191) T) ((-511 . -1191) T) ((-508 . -1191) T) ((-489 . -1191) T) ((-488 . -1191) T) ((-431 . -599) 103190) ((-428 . -599) 103172) ((-3 . -101) T) ((-1008 . -1184) 103141) ((-818 . -101) T) ((-673 . -56) 103099) ((-683 . -1030) T) ((-50 . -632) 103073) ((-283 . -445) T) ((-469 . -1184) 103042) ((0 . -101) T) ((-569 . -632) 103007) ((-510 . -632) 102952) ((-49 . -101) T) ((-891 . -1019) 102939) ((-683 . -238) T) ((-1058 . -403) 102918) ((-716 . -625) 102866) ((-980 . -1078) T) ((-697 . -169) 102757) ((-480 . -973) 102739) ((-258 . -371) 102723) ((-242 . -371) 102707) 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. -599) 98062) ((-212 . -144) T) ((-212 . -142) NIL) ((-1098 . -599) 98044) ((-128 . -101) T) ((-52 . -101) T) ((-1201 . -625) 97996) ((-472 . -106) 97946) ((-974 . -23) T) ((-1261 . -38) 97916) ((-1150 . -1090) T) ((-1103 . -1090) T) ((-1041 . -1195) T) ((-305 . -101) T) ((-836 . -1090) T) ((-933 . -1195) 97895) ((-474 . -1195) 97874) ((-716 . -832) 97853) ((-1041 . -544) T) ((-933 . -544) 97784) ((-1150 . -23) T) ((-1103 . -23) T) ((-836 . -23) T) ((-474 . -544) 97715) ((-1120 . -702) 97647) ((-1124 . -506) 97580) ((-1016 . -600) NIL) ((-1016 . -599) 97562) ((-95 . -1061) T) ((-847 . -702) 97532) ((-1185 . -47) 97501) ((-244 . -129) T) ((-245 . -129) T) ((-1082 . -1078) T) ((-984 . -1078) T) ((-61 . -599) 97483) ((-1145 . -832) NIL) ((-1005 . -777) T) ((-1005 . -780) T) ((-1265 . -1036) 97470) ((-1265 . -110) 97455) ((-851 . -632) 97442) ((-1229 . -25) T) ((-1229 . -21) T) ((-1222 . -21) T) ((-1222 . -25) T) ((-1201 . -21) T) ((-1201 . -25) T) ((-1008 . -148) 97426) ((-853 . -805) 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. -101) T) ((-1103 . -832) 84832) ((-802 . -101) T) ((-1210 . -25) T) ((-1210 . -21) T) ((-837 . -25) T) ((-44 . -361) 84816) ((-837 . -21) T) ((-716 . -445) 84767) ((-1260 . -599) 84749) ((-1034 . -303) 84687) ((-655 . -1061) T) ((-592 . -1061) T) ((-384 . -1078) T) ((-559 . -25) T) ((-559 . -21) T) ((-177 . -1061) T) ((-158 . -1061) T) ((-153 . -1061) T) ((-151 . -1061) T) ((-607 . -1078) T) ((-683 . -867) 84669) ((-1237 . -1191) T) ((-222 . -303) 84607) ((-141 . -362) T) ((-1027 . -600) 84549) ((-1027 . -599) 84492) ((-307 . -890) NIL) ((-683 . -1019) 84437) ((-696 . -901) T) ((-467 . -1195) 84416) ((-1151 . -445) 84395) ((-1145 . -445) 84374) ((-324 . -101) T) ((-853 . -1090) T) ((-310 . -632) 84195) ((-307 . -632) 84124) ((-467 . -544) 84075) ((-333 . -506) 84041) ((-538 . -148) 83991) ((-40 . -301) T) ((-825 . -599) 83973) ((-685 . -284) T) ((-853 . -23) T) ((-373 . -485) T) ((-1058 . -226) 83943) ((-504 . -101) T) ((-401 . -600) 83750) ((-401 . -599) 83732) ((-257 . -599) 83714) 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. -1036) 81918) ((-384 . -746) T) ((-1136 . -813) T) ((-678 . -1191) T) ((-349 . -544) T) ((-346 . -544) T) ((-338 . -544) T) ((-258 . -544) 81849) ((-242 . -544) 81780) ((-517 . -1061) T) ((-1120 . -110) 81759) ((-446 . -729) 81729) ((-847 . -1036) 81699) ((-802 . -38) 81641) ((-678 . -865) 81623) ((-678 . -867) 81605) ((-289 . -303) 81409) ((-891 . -1195) T) ((-654 . -405) 81393) ((-847 . -110) 81358) ((-678 . -1019) 81303) ((-985 . -445) T) ((-891 . -544) T) ((-525 . -599) 81285) ((-569 . -901) T) ((-467 . -1090) T) ((-510 . -901) T) ((-1134 . -282) 81262) ((-895 . -445) T) ((-64 . -599) 81244) ((-618 . -224) 81190) ((-467 . -23) T) ((-1098 . -779) T) ((-853 . -129) T) ((-1098 . -776) T) ((-1252 . -1254) 81169) ((-1098 . -711) T) ((-638 . -632) 81143) ((-288 . -599) 80884) ((-1016 . -34) T) ((-800 . -830) 80863) ((-568 . -301) T) ((-552 . -301) T) ((-487 . -301) T) ((-1261 . -702) 80833) ((-678 . -371) 80815) ((-678 . -332) 80797) ((-470 . -169) T) ((-375 . -702) 80767) ((-852 . 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. -21) T) ((-891 . -323) 79884) ((-85 . -599) 79866) ((-683 . -1003) T) ((-661 . -832) T) ((-1221 . -129) T) ((-1200 . -129) T) ((-882 . -991) 79850) ((-819 . -21) T) ((-48 . -1019) 79793) ((-819 . -25) T) ((-812 . -25) T) ((-812 . -21) T) ((-1259 . -1037) T) ((-1257 . -1037) T) ((-638 . -711) T) ((-1260 . -1036) 79777) ((-1210 . -832) 79756) ((-800 . -405) 79725) ((-102 . -118) 79709) ((-128 . -1078) T) ((-52 . -1078) T) ((-907 . -599) 79691) ((-852 . -973) 79668) ((-808 . -101) T) ((-1260 . -110) 79647) ((-637 . -38) 79617) ((-559 . -832) T) ((-349 . -1090) T) ((-346 . -1090) T) ((-338 . -1090) T) ((-258 . -1090) T) ((-242 . -1090) T) ((-609 . -301) 79596) ((-1128 . -303) 79400) ((-516 . -1061) T) ((-305 . -1078) T) ((-648 . -23) T) ((-475 . -226) 79369) ((-149 . -1037) T) ((-349 . -23) T) ((-346 . -23) T) ((-338 . -23) T) ((-116 . -301) T) ((-258 . -23) T) ((-242 . -23) T) ((-984 . -1030) T) ((-697 . -890) 79348) ((-984 . -228) 79320) ((-984 . -238) T) ((-116 . -1003) NIL) ((-891 . 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76463) ((-613 . -1078) T) ((-1222 . -954) 76425) ((-503 . -129) T) ((-499 . -129) T) ((-289 . -224) 76375) ((-353 . -1037) T) ((-347 . -1037) T) ((-339 . -1037) T) ((-288 . -1030) 76317) ((-1201 . -954) 76286) ((-373 . -832) T) ((-107 . -1037) T) ((-980 . -711) T) ((-851 . -901) T) ((-825 . -780) 76265) ((-825 . -777) 76244) ((-412 . -303) 76183) ((-461 . -101) T) ((-582 . -954) 76152) ((-313 . -1078) T) ((-401 . -780) 76131) ((-401 . -777) 76110) ((-492 . -482) 76092) ((-1223 . -1019) 76058) ((-1221 . -21) T) ((-1221 . -25) T) ((-1200 . -21) T) ((-1200 . -25) T) ((-800 . -702) 76000) ((-683 . -398) T) ((-1250 . -1191) T) ((-592 . -101) T) ((-1091 . -405) 75969) ((-984 . -362) NIL) ((-655 . -101) T) ((-177 . -101) T) ((-158 . -101) T) ((-153 . -101) T) ((-151 . -101) T) ((-102 . -34) T) ((-722 . -1191) T) ((-44 . -746) T) ((-580 . -101) T) ((-76 . -390) T) ((-76 . -389) T) ((-637 . -640) 75953) ((-138 . -1191) T) ((-852 . -144) T) ((-852 . -142) NIL) ((-1190 . -92) T) ((-345 . -1030) T) ((-69 . -377) T) ((-69 . -389) T) ((-1143 . -101) T) ((-654 . -506) 75886) ((-673 . -303) 75824) ((-944 . -38) 75721) ((-720 . -38) 75691) ((-538 . -303) 75495) ((-310 . -1191) T) ((-345 . -228) T) ((-345 . -238) T) ((-307 . -1191) T) ((-283 . -1078) T) ((-1158 . -599) 75477) ((-696 . -1195) T) ((-1134 . -635) 75461) ((-1185 . -544) 75440) ((-696 . -544) T) ((-310 . -865) 75424) ((-310 . -867) 75349) ((-307 . -865) 75310) ((-307 . -867) NIL) ((-784 . -303) 75275) ((-313 . -702) 75116) ((-318 . -317) 75093) ((-478 . -101) T) ((-467 . -25) T) ((-467 . -21) T) ((-412 . -38) 75067) ((-310 . -1019) 74730) ((-220 . -1176) T) ((-220 . -1179) T) ((-3 . -599) 74712) ((-307 . -1019) 74642) ((-2 . -1078) T) ((-2 . |RecordCategory|) T) ((-818 . -599) 74624) ((-1091 . -1037) 74554) ((-568 . -901) T) ((-552 . -805) T) ((-552 . -901) T) ((-487 . -901) T) ((-134 . -1019) 74538) ((-220 . -94) T) ((-74 . -434) T) ((-74 . -389) T) ((0 . -599) 74520) ((-166 . -144) 74499) ((-166 . -142) 74450) ((-220 . 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. -599) 59132) ((-65 . -390) T) ((-65 . -389) T) ((-107 . -600) 59062) ((-107 . -599) 59044) ((-206 . -876) T) ((-939 . -148) 59028) ((-1221 . -94) 58994) ((-756 . -129) T) ((-132 . -711) T) ((-115 . -711) T) ((-1221 . -35) 58960) ((-1034 . -482) 58944) ((-568 . -23) T) ((-552 . -23) T) ((-487 . -23) T) ((-1200 . -94) 58910) ((-1200 . -35) 58876) ((-1150 . -101) T) ((-1103 . -101) T) ((-836 . -101) T) ((-222 . -482) 58860) ((-1259 . -110) 58839) ((-1257 . -110) 58818) ((-44 . -1036) 58802) ((-1210 . -1213) 58786) ((-837 . -834) 58770) ((-1156 . -284) 58749) ((-109 . -280) 58724) ((-127 . -148) 58706) ((-1120 . -881) 58665) ((-44 . -110) 58644) ((-1159 . -1232) T) ((-1144 . -599) 58610) ((-654 . -1030) T) ((-1136 . -600) NIL) ((-1136 . -599) 58592) ((-1042 . -596) 58567) ((-1042 . -1078) T) ((-975 . -599) 58533) ((-73 . -434) T) ((-73 . -389) T) ((-654 . -228) 58512) ((-149 . -1036) 58496) ((-559 . -542) 58480) ((-349 . -144) 58459) ((-349 . -142) 58410) ((-346 . -144) 58389) ((-687 . 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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 0b28009d..ab6f5f67 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3433818803) -(4369 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3436147951) +(4371 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -214,11 +214,11 @@ |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| |JavaBytecode| |JoinAst| |AssociatedJordanAlgebra| |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| - |CoercibleTo| |ConvertibleTo| |Kovacic| |KleeneTrivalentLogic| - |LeftAlgebra&| |LeftAlgebra| |LocalAlgebra| |LaplaceTransform| - |LaurentPolynomial| |LazardSetSolvingPackage| - |LeadingCoefDetermination| |LetAst| |LieExponentials| - |LexTriangularPackage| |LiouvillianFunctionCategory| + |CoercibleTo| |ConvertibleTo| |Kovacic| |CoercibleFrom| + |KleeneTrivalentLogic| |ConvertibleFrom| |LeftAlgebra&| |LeftAlgebra| + |LocalAlgebra| |LaplaceTransform| |LaurentPolynomial| + |LazardSetSolvingPackage| |LeadingCoefDetermination| |LetAst| + |LieExponentials| |LexTriangularPackage| |LiouvillianFunctionCategory| |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearDependence| @@ -471,659 +471,661 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |input| |fortranInteger| |mapDown!| |systemCommand| - |localAbs| |OMputEndAttr| |relerror| |empty?| |lcm| |print| - |iterationVar| |random| |iterators| |rationalFunction| |geometric| - 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|leadingSupport| |setClipValue| |merge!| |sorted?| |mapUnivariate| - |mainValue| |iibinom| |f02wef| |problemPoints| |sin| |palginfieldint| - |dAndcExp| |smith| |cyclicCopy| |inverseLaplace| |prod| |shift| - |idealiser| |rotate| |numberOfVariables| |cos| |expenseOfEvaluation| - |genericLeftTraceForm| |setsubMatrix!| |OMsend| |gbasis| - |removeSuperfluousCases| |parabolicCylindrical| |complexExpand| ~= - |cCsc| |tan| |iitan| |fracPart| |tableau| |iiabs| |rowEchelon| - |critMTonD1| |setrest!| |c06gqf| |viewPosDefault| |coerce| - |deepestTail| |cot| |sinhcosh| |property| |divisorCascade| - |primPartElseUnitCanonical!| |limit| |OMParseError?| - |inverseIntegralMatrixAtInfinity| |createMultiplicationTable| - |nullary| |numericIfCan| |construct| |expressIdealMember| |sec| - |coefficients| |pr2dmp| |hdmpToP| |reopen!| |quotientByP| |hash| - |froot| |powern| |argumentListOf| |csc| |find| |f04faf| |integral?| - |OMputSymbol| |even?| |negative?| |count| |spherical| |cyclic| - |besselI| |asin| |listOfMonoms| |e02ajf| |units| |firstSubsetGray| - F2FG |unparse| |lllp| |brillhartTrials| |monicRightFactorIfCan| - |henselFact| |acos| |writeBytes!| |mdeg| |iiasinh| |diff| - |squareFreePrim| |determinant| |has?| |module| |enterInCache| |atan| - |logical?| |impliesOperands| |stirling1| |ran| |bandedJacobian| |plot| - |outerProduct| |genericRightTrace| |lquo| |colorFunction| NOT - |factorSFBRlcUnit| |acot| |leftRankPolynomial| |enqueue!| |modularGcd| - |lyndon| |color| |stronglyReduce| |binarySearchTree| |declare| - |rowEchLocal| |write| |scalarTypeOf| OR |csubst| |asec| - |semiDiscriminantEuclidean| |numberOfHues| |saturate| - |coercePreimagesImages| |setRow!| |e04gcf| |save| - |createIrreduciblePoly| |branchIfCan| |radicalRoots| |directory| AND - |minPoints3D| |acsc| |cAcsch| |code| |makeSUP| |polynomialZeros| - |c06ecf| |e04fdf| |perfectNthRoot| |denominator| |sinh| |palglimint0| - |e02bbf| |Lazard| |expIfCan| |doubleRank| |pointLists| |previous| - |rightRecip| |cosh2sech| |safeFloor| |latex| |cosh| |bezoutMatrix| - |RittWuCompare| |rootPoly| |OMReadError?| |d01alf| |more?| |ScanRoman| - 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|surface| |newReduc| |mesh?| |sup| |curveColorPalette| - |leftCharacteristicPolynomial| |innerSolve| |bandedHessian| |setlast!| - |outputAsFortran| UP2UTS |besselY| |setOrder| |leftDiscriminant| - |cTan| |stFunc1| |parameters| |f02abf| |aCubic| |leftGcd| |rem| |mix| - |commutativeEquality| |target| |normDeriv2| |asechIfCan| - |genericLeftMinimalPolynomial| |removeDuplicates!| |s21baf| - |getMultiplicationTable| |dimensionOfIrreducibleRepresentation| - |coerceP| |functionIsOscillatory| |s17adf| |c06frf| |f02ajf| - |csch2sinh| |overbar| ~ |axes| |noKaratsuba| |constructorName| - |euclideanGroebner| |null?| |weakBiRank| |cPower| |clipSurface| - |d02gaf| |stosePrepareSubResAlgo| |cSin| |split| |tanNa| |xn| - |quasiRegular?| |infieldint| |functionIsFracPolynomial?| |open| - |OMputEndAtp| |rubiksGroup| |calcRanges| |viewWriteAvailable| - |clearTable!| |computeInt| |rightRankPolynomial| |sin?| - |sturmSequence| |rationalIfCan| |rst| |scripted?| |region| - |nextIrreduciblePoly| |simpsono| |oblateSpheroidal| |matrixDimensions| - 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|algebraicSort| |getMultiplicationMatrix| |iiGamma| |groebgen| - |rootDirectory| |differentiate| |linear?| |setPosition| |normalDeriv| - |someBasis| |thenBranch| |mantissa| |mathieu12| |setelt| |pi| - |inverse| |failed| |over| |modularGcdPrimitive| |invmultisect| |basis| - |restorePrecision| |genericRightTraceForm| |nullSpace| - |lazyPseudoDivide| |infinity| |imagI| |btwFact| |s17dlf| - |complexEigenvalues| |position| |createPrimitiveNormalPoly| - |wordsForStrongGenerators| |reciprocalPolynomial| |iicot| |socf2socdf| - |copy| |basisOfMiddleNucleus| |ptFunc| |OMopenFile| - |getSyntaxFormsFromFile| |cyclic?| |d01amf| |e04jaf| |bezoutResultant| - |weighted| |positive?| |iiperm| |expenseOfEvaluationIF| |morphism| - |mkAnswer| |OMgetString| |bringDown| |f07fdf| |kernel| |atoms| - |localIntegralBasis| |c06gsf| |e01bef| |repSq| |nil| - |linearlyDependent?| |match?| |f04arf| |rur| |init| |OMmakeConn| - |drawComplex| |draw| |prevPrime| |autoCoerce| |leftExtendedGcd| - |principalIdeal| |delete!| |f02agf| |hasoln| |splitNodeOf!| |LiePoly| - |lazyPquo| |padicallyExpand| |univariatePolynomial| |Vectorise| - |returnTypeOf| |iicsc| |topPredicate| |rotate!| |lighting| |zero?| - |bumptab| |iprint| |meatAxe| |dictionary| |rightRegularRepresentation| - |approximate| |rowEch| |rightFactorCandidate| |quasiAlgebraicSet| - |e02def| |selectsecond| |LyndonWordsList1| |c06ebf| |hessian| - |subResultantsChain| |complex| |OMgetEndApp| |stirling2| |polyPart| - |fractRadix| |multiplyCoefficients| |makeObject| |f02xef| - |cyclePartition| |gcdprim| |charthRoot| |listLoops| - |setAttributeButtonStep| |lowerCase!| |goodPoint| |makeFR| |monomials| - |drawStyle| |functionIsContinuousAtEndPoints| |ReduceOrder| |e01bhf| - |rotatey| |printingInfo?| |makeMulti| |trim| |universe| |groebSolve| - |complexIntegrate| |fortranCarriageReturn| |coef| |properties| - |nothing| |interpret| |newTypeLists| |s13adf| |besselJ| - |explicitEntries?| |unrankImproperPartitions1| |lhs| |mapUp!| |digits| - |symmetricGroup| |member?| |shrinkable| |translate| - |createGenericMatrix| |taylorRep| |c06ekf| |replaceKthElement| |rhs| - |iitanh| |viewSizeDefault| |box| |integralRepresents| |exactQuotient!| - |chainSubResultants| |integral| |option?| |chineseRemainder| - |mathieu23| |lllip| |innerSolve1| |simpson| |ideal| |f04mcf| - |sechIfCan| |computeBasis| |monicRightDivide| |characteristicSet| - |endSubProgram| |diagonals| |f02aaf| |name| |rightFactorIfCan| - |members| |removeSuperfluousQuasiComponents| |resultant| |gradient| - |tanIfCan| |rightDiscriminant| |viewWriteDefault| |nthRootIfCan| - |body| |shiftLeft| |selectIntegrationRoutines| |tanh2trigh| |node| - |listOfLists| |gcdPolynomial| |completeSmith| |balancedBinaryTree| - |duplicates| |componentUpperBound| |coordinates| |head| |ode| - |genericRightNorm| |numberOfIrreduciblePoly| |dominantTerm| |rombergo| - |overlabel| |pointColorPalette| |errorKind| |idealiserMatrix| |pol| - |primPartElseUnitCanonical| |linearMatrix| |useSingleFactorBound?| - |fortranCharacter| |makeYoungTableau| |aQuadratic| |concat!| |d01gbf| - |infiniteProduct| |exp| |prepareDecompose| Y |droot| |trace2PowMod| - |basisOfRightNucloid| |predicates| |sqfree| |acscIfCan| |partitions| - |quasiRegular| |elementary| |readBytes!| |closedCurve?| |tubeRadius| - |d02ejf| |nand| |iiexp| |resetVariableOrder| |maxPoints| |center| - |unitNormalize| |e04ucf| |integralAtInfinity?| |axesColorDefault| - |interpolate| |high| |flexibleArray| |sumOfKthPowerDivisors| |c02aff| - |check| |getIdentifier| |bernoulliB| |clipPointsDefault| |roughBase?| - |var1Steps| |maxdeg| |term?| |mapdiv| |updatD| |f02awf| |rootSplit| - |asimpson| |identitySquareMatrix| |numericalIntegration| |aQuartic| - |subresultantVector| |radPoly| |diagonalMatrix| - |purelyTranscendental?| |showRegion| |domainOf| |ref| |clipParametric| - |selectODEIVPRoutines| |iisin| |integralMatrixAtInfinity| |dihedral| - |OMsupportsCD?| |zerosOf| |getGraph| |parts| |internalIntegrate0| - |highCommonTerms| |lyndon?| |critM| |compdegd| |retractable?| |sh| - |tValues| |cyclotomic| |f02bjf| |reduction| |d03edf| |mainContent| - |power| |uncouplingMatrices| |createNormalElement| |paraboloidal| - 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|integralLastSubResultant| |alphanumeric?| |validExponential| - |cyclicEqual?| |fortranLinkerArgs| |particularSolution| |obj| |c05nbf| - |c06gbf| |semiResultantEuclidean1| |prindINFO| |conditionP| - |symbolIfCan| |eval| |multiplyExponents| |intPatternMatch| - |approxNthRoot| |cache| |cyclicGroup| |stiffnessAndStabilityOfODEIF| - |buildSyntax| |abs| |graphState| |elliptic?| - |subResultantGcdEuclidean| |identification| |outputArgs| |say| - |extractBottom!| |approxSqrt| |leftZero| |complexElementary| |first| - |karatsubaDivide| |kind| |rightMinimalPolynomial| |simplifyLog| - |safetyMargin| |mainMonomial| |extendedEuclidean| |rootOf| - |LyndonWordsList| |resultantnaif| |rest| |quadraticForm| |copy!| |op| - |dmp2rfi| |iiacot| |lflimitedint| |pleskenSplit| |comp| |tanQ| - |flexible?| |mainKernel| |noncommutativeJordanAlgebra?| |substitute| - |show| |complexNumericIfCan| |newSubProgram| |innerEigenvectors| - |fixedPoint| |removeDuplicates| |generalInfiniteProduct| |leftFactor| - |dmpToP| |getCode| |elseBranch| |edf2ef| |s17ahf| |f01qdf| |rk4qc| - |s14abf| |parametric?| |semiSubResultantGcdEuclidean1| |intersect| - |cycleSplit!| |trace| |s19acf| |OMputVariable| |upperCase?| - |monomialIntegrate| |unary?| |tensorProduct| |coshIfCan| |baseRDEsys| - |internalIntegrate| GF2FG |besselK| |extractSplittingLeaf| |cAcosh| - |palgRDE| |lexGroebner| |remainder| |integralBasis| |singRicDE| - |modifyPoint| |removeRedundantFactorsInContents| |Frobenius| - |showSummary| |OMbindTCP| |recolor| |randomLC| |indicialEquations| - |minus!| |qelt| |basisOfCentroid| |child?| |union| |binomThmExpt| - |monomRDE| |any| |boundOfCauchy| |qsetelt| |increment| |ScanArabic| - |randnum| |isQuotient| |padicFraction| |delta| |powmod| |reverse| - |makeViewport3D| |showAttributes| |firstUncouplingMatrix| |setright!| - |factorials| |cRationalPower| |bothWays| |xRange| |toScale| - |createPrimitiveElement| |cscIfCan| |powerSum| |cup| |tower| - |groebner?| |inc| |ratpart| |yRange| |factorFraction| - |structuralConstants| |harmonic| |algebraicDecompose| |deref| - |associatedSystem| |vedf2vef| |rationalPower| |laguerreL| |zRange| - |aLinear| |e02dcf| |andOperands| |kroneckerDelta| - |selectSumOfSquaresRoutines| |map!| |limitedIntegrate| |minimumDegree| - |numericalOptimization| |pdct| |push!| |primlimitedint| |f02bbf| - |wholePart| |complexNormalize| |qsetelt!| |graphImage| - |constantKernel| |height| |iisqrt3| |thetaCoord| |maxRowIndex| - |eyeDistance| |f01maf| |s13acf| |ricDsolve| |modulus| - |leftAlternative?| |OMencodingSGML| |gderiv| |constant| |acoshIfCan| - |halfExtendedResultant2| |antisymmetricTensors| |iicosh| |infinite?| - |lambda| |content| |gcdcofactprim| |modularFactor| |readLineIfCan!| - |packageCall| |OMputAttr| |mkIntegral| |f04mbf| |rk4a| |printTypes| - |linearDependence| |bat| |f01ref| |changeThreshhold| |every?| - |insertBottom!| |minColIndex| |datalist| |lazyPseudoRemainder| - |ParCondList| |fractRagits| |map| |badValues| |repeating?| |acsch| - |linearAssociatedExp| |ramified?| |numberOfMonomials| |summation| - |aromberg| |formula| |addPoint2| |label| |algebraic?| |adaptive| - |ode2| |palglimint| |shuffle| |checkPrecision| |green| - |mainPrimitivePart| |bounds| |positiveRemainder| |d01gaf| |Hausdorff| - |clip| |solveRetract| |trigs2explogs| |cycleLength| - |intermediateResultsIF| |completeHensel| |asecIfCan| |nthCoef| - |fortranCompilerName| |setFormula!| |cardinality| |denomLODE| - |univariateSolve| |perfectSqrt| |ParCond| |showTheFTable| |invmod| - |rightDivide| |abelianGroup| |bernoulli| |nrows| |polygon| |convert| - |oneDimensionalArray| |setleaves!| |invertIfCan| |frst| |degree| - |partialNumerators| |roughUnitIdeal?| |jordanAlgebra?| - |rightExtendedGcd| |ncols| |lineColorDefault| |iilog| |elements| - |showAllElements| |coerceL| |secIfCan| |critBonD| |bits| |bytes| - |countRealRootsMultiple| |zeroDimensional?| |lazyGintegrate| |qfactor| - |e02daf| |insertionSort!| |rightScalarTimes!| |makeSketch| - |oddInfiniteProduct| |supersub| |possiblyInfinite?| |length| |pow| - |transpose| |plusInfinity| |debug3D| |sPol| |lfextendedint| |s17def| - |bitLength| |search| |d02raf| |addiag| |s14aaf| |scripts| |direction| - |qqq| |realElementary| |minusInfinity| |cycle| - |algebraicCoefficients?| |optional?| |minPoints| |PDESolve| - |symmetricTensors| |tubePoints| |prinshINFO| |key?| |solve1| |deriv| - |topFortranOutputStack| |commonDenominator| |arrayStack| - |complexEigenvectors| |graphStates| |mirror| |option| |reduceLODE| - |duplicates?| |pair?| |subset?| |submod| |hypergeometric0F1| - |selectPolynomials| |subscriptedVariables| |lexico| |simplifyExp| - |factorset| |updateStatus!| |f04atf| |setErrorBound| |c05adf| - |factorPolynomial| |semiResultantEuclidean2| |wrregime| |mindeg| - |triangular?| |innerint| |iiacoth| |subscript| |scopes| |quadratic| - |divisor| |radix| |associative?| |monomRDEsys| |nary?| - |symmetricSquare| |whileLoop| |minIndex| |pureLex| |hexDigit?| - |isConnected?| |OMputObject| |fTable| |deepestInitial| |comparison| - |type| |ptree| |getExplanations| |extendIfCan| - |indiceSubResultantEuclidean| |leastMonomial| |isobaric?| - |factorSquareFreePolynomial| |exQuo| |simpleBounds?| |outputSpacing| - |integerBound| |FormatArabic| |nor| |s17agf| |opeval| |cfirst| - |nilFactor| |OMputBVar| |nextPrimitiveNormalPoly| |read!| |stack| - |stronglyReduced?| |iidprod| |dequeue| |symmetricDifference| |s19abf| - |getGoodPrime| |binomial| |selectNonFiniteRoutines| |alternative?| - |swapColumns!| |subPolSet?| |rightTrim| |factorsOfCyclicGroupSize| - |polyred| |f04axf| |integerIfCan| |or?| |coleman| |digamma| |s18dcf| - |closedCurve| |leftTrim| |laurentRep| |basisOfLeftNucloid| |cSec| - |semiLastSubResultantEuclidean| |eigenvectors| - |semiResultantEuclideannaif| |divideExponents| |distdfact| - |pushNewContour| |error| |unitsColorDefault| |rootNormalize| - |inputOutputBinaryFile| |node?| |representationType| |lieAdmissible?| - |leftRank| |useSingleFactorBound| |sequence| |assert| - |leadingBasisTerm| |f07aef| |numeric| |convergents| |mkPrim| |revert| - |degreeSubResultantEuclidean| |lfunc| |OMgetAtp| |generalPosition| - |argumentList!| |radical| |iflist2Result| |distFact| |s15adf| - |acosIfCan| |belong?| |presub| |plus!| |moduloP| |OMsetEncoding| - |replace| |monom| |getBadValues| |subspace| |relativeApprox| |merge| - |nil?| |rewriteIdealWithHeadRemainder| |viewDeltaXDefault| |pattern| - |create3Space| |iiatan| |splitConstant| |const| |showTypeInOutput| - |lowerCase| |iisinh| |findCycle| RF2UTS |rules| |f01qcf| |denomRicDE| - |elRow2!| |critpOrder| |associates?| |processTemplate| |binary| - |common| |setEmpty!| |octon| |seed| |appendPoint| |zeroMatrix| - |separateFactors| |linSolve| |f01rdf| |bivariatePolynomials| - |expintfldpoly| |coerceImages| |exprHasWeightCosWXorSinWX| |airyBi| - |operators| |ceiling| |arg1| |numerator| |message| |infix| |directSum| - |real?| |cycleElt| |extensionDegree| |in?| |infieldIntegrate| |arg2| - |hue| |printInfo| |leaf?| |f2st| - |removeRoughlyRedundantFactorsInContents| |mapExponents| - |rationalPoints| |isExpt| |pdf2df| |idealSimplify| |rootBound| - |modTree| |paren| |numberOfPrimitivePoly| |changeVar| |s17dgf| - |OMputAtp| |omError| |conditions| |typeList| |getButtonValue| - |rischDEsys| |conjug| |laguerre| |midpoint| |tab| |changeMeasure| - |match| |generalizedContinuumHypothesisAssumed?| |fibonacci| - |horizConcat| |Nul| |outputFixed| |traceMatrix| |graeffe| |d02cjf| - |curryRight| |completeEchelonBasis| |pop!| |antisymmetric?| |cons| - |sparsityIF| |normalized?| |chiSquare| |setVariableOrder| |sncndn| - |bright| |point?| |extractClosed| |recoverAfterFail| |d03eef| - |firstNumer| |numberOfDivisors| |hermiteH| |rationalPoint?| |po| - |quasiMonicPolynomials| |singularAtInfinity?| |alphanumeric| - |LazardQuotient| |variable?| |removeRoughlyRedundantFactorsInPol| - |e02bdf| |rarrow| |exponential1| |minset| |logpart| - |nextsousResultant2| |hconcat| |diagonalProduct| |OMgetEndBind| - |OMencodingBinary| |numberOfChildren| |specialTrigs| ** |pastel| |row| - |void| |mapUnivariateIfCan| |sample| |leadingTerm| |character?| - |polarCoordinates| |qinterval| |indices| |reorder| |setAdaptive| - |OMlistCDs| |fortranTypeOf| |generic| |setClosed| |padecf| |split!| - |source| |birth| |Si| |pushdterm| |constantRight| |tanh2coth| |delete| - |e01sbf| EQ |cCosh| |collect| |exprToUPS| |LowTriBddDenomInv| - |relationsIdeal| |iter| |npcoef| |cross| |setprevious!| - |fortranLogical| |rootProduct| |initiallyReduce| |lfextlimint| - |virtualDegree| |f02aef| |addBadValue| |setTex!| |sqfrFactor| - |writeByteIfCan!| |simplifyPower| |primaryDecomp| |wordInGenerators| - |meshPar2Var| |colorDef| |multMonom| |stopTable!| |intcompBasis| - |isList| |refine| |numberOfComputedEntries| |sinIfCan| - |makeGraphImage| |expandTrigProducts| |wronskianMatrix| |square?| - |hyperelliptic| |rCoord| |twoFactor| |ksec| |internalInfRittWu?| - |OMgetEndError| |removeSquaresIfCan| |makeUnit| |totalLex| |insert!| - |pseudoQuotient| |csc2sin| |semicolonSeparate| |polygamma| |tubePlot| - |readable?| |stoseInvertibleSet| |OMgetBVar| |divide| - |increasePrecision| |ravel| |permanent| |taylorIfCan| - |clearTheIFTable| |unitVector| |log2| |less?| |powerAssociative?| - |setImagSteps| |reshape| |positiveSolve| |nthFlag| |pointPlot| - |reducedContinuedFraction| |s17aff| |OMputEndBind| |basicSet| |recur| - |setScreenResolution| |invertible?| |reflect| |createThreeSpace| - |hexDigit| |infLex?| |localUnquote| |noLinearFactor?| |xCoord| - |OMreceive| |realZeros| |rightUnit| |characteristic| |weights| - |limitedint| |key| |eisensteinIrreducible?| |iCompose| |subNodeOf?| - |rightZero| |substring?| |decompose| |neglist| - |indicialEquationAtInfinity| |pushup| |writeLine!| |leftQuotient| - |transcendenceDegree| GE |tab1| |rdregime| |squareFreePart| |addMatch| - |filename| |setchildren!| |discreteLog| |truncate| |presuper| - |rightExactQuotient| |hdmpToDmp| GT |critT| |suffix?| |redmat| - |unmakeSUP| |numerators| |not?| |dim| |size?| |sylvesterSequence| - |leader| |leftUnits| |isTimes| |addPoint| LE |ipow| |retractIfCan| - |printInfo!| |e04ycf| |OMclose| |parse| |squareFreeLexTriangular| - |e01sff| |symFunc| |prefix| LT |genericLeftTrace| |prefix?| - |OMputInteger| |mindegTerm| |generalizedContinuumHypothesisAssumed| - |double| |primintfldpoly| |pile| |bindings| |unit?| - |pointColorDefault| |getRef| |binaryFunction| |deepExpand| |test| - |diagonal?| |pToDmp| |normal01| |exponent| |listRepresentation| - |toseInvertibleSet| |derivationCoordinates| |defineProperty| - |contractSolve| |branchPointAtInfinity?| |univariatePolynomialsGcds| - |mightHaveRoots| |elRow1!| |prinb| |realSolve| |degreePartition| - |numberOfComponents| |conical| |computeCycleEntry| |minRowIndex| - |exprToXXP| |LazardQuotient2| |mapExpon| |f07adf| - |regularRepresentation| |bivariate?| |algSplitSimple| |rischDE| - |createLowComplexityTable| |max| |freeOf?| |outputGeneral| |s17acf| - |rewriteIdealWithRemainder| |eof?| |postfix| |OMgetBind| |atanhIfCan| - |failed?| |fullDisplay| |reduced?| |copyInto!| |moebiusMu| |infix?| - |cLog| |root?| |outputMeasure| |exp1| |iiacsch| |realEigenvalues| - |stopTableInvSet!| |createNormalPoly| |headReduce| |mask| - |basisOfLeftAnnihilator| |bombieriNorm| |declare!| |eulerPhi| - |initials| |s20adf| |factorsOfDegree| |OMUnknownSymbol?| |Lazard2| - |d02bhf| |UpTriBddDenomInv| |karatsubaOnce| |externalList| |leftTrace| - |useEisensteinCriterion| |extract!| |movedPoints| |log| - |subtractIfCan| |schwerpunkt| |cAcsc| |satisfy?| |SturmHabicht| - |setnext!| |groebnerIdeal| |second| |signatureAst| |OMgetInteger| - |byteBuffer| |mvar| |operator| |cycleEntry| |d01akf| - |irreducibleFactors| |getConstant| |index| |rank| |third| |orbits| - |OMwrite| |pushdown| |unaryFunction| |radicalSimplify| |inHallBasis?| - |mainExpression| |nextPartition| |internalDecompose| |inspect| |dn| - |removeZero| |extend| |rename| |depth| |rightRank| |roman| |Ci| - |nthFractionalTerm| |cyclicSubmodule| |matrix| |corrPoly| |rightMult| - |extendedResultant| |OMgetType| |scaleRoots| |symmetricProduct| - |coefChoose| |getPickedPoints| |llprop| |composites| |realRoots| - |e02ahf| |pair| |loadNativeModule| |inf| |linearlyDependentOverZ?| - |splitSquarefree| |separate| |makeCrit| |notelem| |OMputApp| - |mainVariables| |signature| |clipWithRanges| |OMgetEndAttr| |segment| - |heap| |messagePrint| |minimalPolynomial| |measure2Result| |exptMod| - |patternMatch| |bezoutDiscriminant| |constantToUnaryFunction| - |totalfract| |open?| |linGenPos| |rightGcd| |twist| |edf2fi| - |pmintegrate| |function| |internalZeroSetSplit| |jacobian| - |notOperand| |changeBase| |equiv?| |sizeLess?| |e01saf| |lists| |slex| - |setScreenResolution3D| |rational?| |setButtonValue| |endOfFile?| - |solid| |startTable!| |dequeue!| |flagFactor| - |genericRightDiscriminant| |collectUpper| - |removeIrreducibleRedundantFactors| |debug| |countable?| |child| - |genericPosition| |brace| |lazy?| |terms| |skewSFunction| |qPot| - |cAtan| |meshPar1Var| |makeVariable| D |e02akf| |rotatez| |light| - |createNormalPrimitivePoly| |setOfMinN| |sortConstraints| |lagrange| - |laplacian| |e01baf| |printStats!| |optAttributes| |setRealSteps| - |adaptive?| |zeroVector| |leftExactQuotient| |close| |block| - |anticoord| |basisOfRightNucleus| |chebyshevU| |vspace| |leftDivide| - |iisech| |midpoints| |computePowers| |OMencodingUnknown| |kmax| - |arguments| |isAbsolutelyIrreducible?| |rightLcm| |zCoord| |comment| - |pquo| |f02adf| |evenlambert| |quotedOperators| |value| |select!| - |parametersOf| |display| |supRittWu?| |tanAn| |primeFrobenius| - |setStatus| |e02aef| |associator| |sort| |mpsode| |firstDenom| |expr| - |lepol| |hasTopPredicate?| |stoseLastSubResultant| - |genericRightMinimalPolynomial| |identity| |extractIfCan| |makeprod| - |yellow| |logIfCan| |subResultantChain| |OMputEndObject| - |mainSquareFreePart| |invertibleSet| |rowEchelonLocal| - |semiResultantReduitEuclidean| |nextItem| |lastSubResultant| - |uniform01| |alphabetic| |irreducibleRepresentation| |basisOfCenter| - |getStream| |imagE| |startTableGcd!| |setMaxPoints| |getOrder| - |fractionPart| |cAcos| |nextNormalPoly| |blankSeparate| - |showTheIFTable| |solveLinearlyOverQ| |cond| - |solveLinearPolynomialEquationByRecursion| |leftRecip| |algebraicOf| - |sec2cos| |addMatchRestricted| |separateDegrees| - |univariatePolynomials| |remove| |numFunEvals| |variable| - |tryFunctionalDecomposition| |LyndonBasis| |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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|d01alf| |ratpart| + |initializeGroupForWordProblem| |listRepresentation| + |localIntegralBasis| |iisqrt2| |getBadValues| |equivOperands| |more?| + |factorFraction| BY |internal?| |c06gsf| |toseInvertibleSet| |iiatanh| + |cExp| |subspace| |kind| |ScanRoman| |nonSingularModel| + |associatorDependence| |makeEq| |structuralConstants| + |derivationCoordinates| |e01bef| |ode1| |f04adf| |relativeApprox| + |atrapezoidal| |set| |cond| |repSq| |cCos| |op| |defineProperty| + |finite?| |merge| |qualifier| |nonLinearPart| |fortranLinkerArgs| + |printInfo| |halfExtendedResultant1| |expr| |linearlyDependent?| + |contractSolve| |mainDefiningPolynomial| |position| |f04qaf| |nil?| + |integralDerivationMatrix| |irreducibleFactor| |particularSolution| + |call| |segment| |branchPointAtInfinity?| |f04arf| |deleteProperty!| + |fixedPoints| |rewriteIdealWithHeadRemainder| + |rightCharacteristicPolynomial| |setelt| |c05nbf| + |squareFreePolynomial| |univariatePolynomialsGcds| |rur| + |numberOfFactors| |decomposeFunc| |map| |c06gbf| + |removeRoughlyRedundantFactorsInPols| |OMmakeConn| |mightHaveRoots| + |parseString| |factorset| |viewThetaDefault| |variable| |nullity| + |copy| |semiResultantEuclidean1| |untab| |drawComplex| |elRow1!| + |s18aff| |integralCoordinates| |updateStatus!| |prindINFO| + |shiftRight| |iterators| |inGroundField?| |prinb| |prevPrime| |union| + |equality| |f04atf| |poisson| |setfirst!| |computeCycleLength| + |conditionP| |match?| |createLowComplexityNormalBasis| |biRank| + |setErrorBound| |autoCoerce| |viewDefaults| |symbolIfCan| |pushucoef| + |twoFactor| |quoByVar| |fill!| |c05adf| |d03faf| |lazyVariations| + |convert| |separant| |multiplyExponents| |ksec| |RemainderList| + |headRemainder| |factorPolynomial| |string?| |fortranComplex| |show| + |intPatternMatch| |e02dff| |hspace| |internalInfRittWu?| |asinhIfCan| + |semiResultantEuclidean2| |startStats!| |inconsistent?| |heapSort| + |approxNthRoot| |groebner| |OMgetEndError| |f01bsf| |wrregime| + |coth2tanh| 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|identification| |lSpaceBasis| |polygamma| + |OMconnectTCP| |divisor| |OMgetSymbol| |midpoints| |setMinPoints3D| + |outputArgs| |remove!| |numberOfOperations| |tubePlot| + |nextNormalPrimitivePoly| |radix| |KrullNumber| |computePowers| < + |extractBottom!| |showScalarValues| |readable?| |cycleRagits| |lookup| + |plusInfinity| |ip4Address| |associative?| |makeFloatFunction| + |OMencodingUnknown| |changeNameToObjf| > |approxSqrt| |systemCommand| + |outputForm| |minusInfinity| |stoseInvertibleSet| |viewPhiDefault| + |rootKerSimp| |OMputFloat| |monomRDEsys| |kmax| <= |setLabelValue| + |stack| |leftZero| |pade| |OMgetBVar| |alternatingGroup| + |squareMatrix| |bag| |nary?| |isAbsolutelyIrreducible?| >= |integers| + |ratDsolve| |complexElementary| |divide| |clikeUniv| |s19aaf| + |symmetricSquare| |generic?| |rightLcm| |increasePrecision| |prime?| + |selectOrPolynomials| |karatsubaDivide| |complete| |normal| |times| + |makeop| |whileLoop| |prinpolINFO| |zCoord| |OMreadStr| + 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|explicitlyEmpty?| |makeSeries| |deepestInitial| |supRittWu?| D + |basisOfRightAnnihilator| |arg2| |adjoint| |resultantnaif| + |setImagSteps| |exactQuotient| |min| |isOpen?| |splitDenominator| + |comparison| |cosSinInfo| |tanAn| |algint| |objectOf| |quadraticForm| + |rewriteIdealWithQuasiMonicGenerators| |positiveSolve| |exprex| + |patternVariable| |tail| |crushedSet| |getExplanations| + |primeFrobenius| |datalist| |HermiteIntegrate| |copy!| |super| + |conditions| |nthFlag| |standardBasisOfCyclicSubmodule| |polar| + |selectOptimizationRoutines| |limitPlus| |outputList| |extendIfCan| + |setStatus| |flatten| |bfEntry| |dmp2rfi| |schema| |match| |pointPlot| + |halfExtendedSubResultantGcd2| |sumOfSquares| + |extendedSubResultantGcd| |rule| |Beta| |indiceSubResultantEuclidean| + |mr| |e02aef| |unrankImproperPartitions0| |iiacot| |linkToFortran| + |reducedContinuedFraction| |univcase| |rootsOf| |maxPoints3D| + |leastMonomial| |viewport2D| |error| |associator| |double?| + |stopMusserTrials| |lflimitedint| |zeroSetSplit| |s17aff| |back| + |mantissa| |setProperties!| |palgint| |isobaric?| + |leftRegularRepresentation| |assert| |mpsode| |pleskenSplit| |cSech| + |maxIndex| |bumprow| |fprindINFO| |OMputEndBind| + |stoseInvertibleSetsqfreg| |laurentIfCan| |factorSquareFreePolynomial| + |middle| |firstDenom| |cycles| |tanQ| |collectUnder| |orbit| + |basicSet| |perfectSquare?| |graphCurves| |beauzamyBound| |exQuo| + |lepol| |c06fqf| |removeSinhSq| |getProperties| |flexible?| |recur| + |oddlambert| |dark| |OMencodingXML| |simpleBounds?| + |fullPartialFraction| |hasTopPredicate?| |print| |tubePointsDefault| + |imagk| |mainKernel| |component| |distribute| |setScreenResolution| + |linearAssociatedOrder| |doubleDisc| |outputSpacing| |mainForm| + |stoseLastSubResultant| |resolve| |monicModulo| |equiv| + |noncommutativeJordanAlgebra?| |cosIfCan| |complementaryBasis| + |invertible?| |setPrologue!| |stoseSquareFreePart| |integerBound| + |infinityNorm| |genericRightMinimalPolynomial| |reducedQPowers| + |replace| |sinhIfCan| |void| |complexNumericIfCan| |deepCopy| + |reflect| |c06fpf| |laplace| |bubbleSort!| |FormatArabic| + |closeComponent| |identity| |makeCos| |physicalLength| |shade| + |newSubProgram| |primitivePart!| |createThreeSpace| + |radicalEigenvector| |monicDivide| |nor| |kovacic| |extractIfCan| + |outerProduct| |compBound| |innerEigenvectors| |s18adf| |generalSqFr| + |hexDigit| |solveid| |rangeIsFinite| |c02agf| + |clearFortranOutputStack| |s17agf| |makeprod| |pdf2ef| |fixedPoint| + |qroot| |nthExpon| |bright| |withPredicates| |infLex?| + |doubleResultant| |normalize| |minPoly| |opeval| |yellow| + |localUnquote| |createZechTable| |solveInField| |dmpToHdmp| + |generalInfiniteProduct| |showSummary| |makeViewport2D| |e02gaf| + |s19adf| |loopPoints| |checkPrecision| |cfirst| |logIfCan| + |factorByRecursion| |solveLinearPolynomialEquationByFractions| + |leftFactor| |noLinearFactor?| |linearDependenceOverZ| + |basisOfCommutingElements| |overset?| |nilFactor| |resetBadValues| + |subResultantChain| |showAttributes| |predicate| |dmpToP| + |semiIndiceSubResultantEuclidean| |xCoord| |components| |increase| + |euler| |OMputBVar| |typeLists| |init| |OMputEndObject| |mdeg| + |getCode| |operation| |BasicMethod| |nextSubsetGray| |OMreceive| + |hermite| |transcendent?| |nextPrimitiveNormalPoly| |credPol| + |mainSquareFreePart| |iiasinh| |irreducible?| |elseBranch| |realZeros| + |whitePoint| |characteristicSerie| |resultantEuclideannaif| |read!| + |definingInequation| |invertibleSet| |diff| |edf2ef| + |useEisensteinCriterion?| |var2Steps| |rightUnit| |minPol| |factorial| + |stronglyReduced?| |rowEchelonLocal| |squareFreePrim| |central?| |max| + |delete| |s17ahf| |characteristic| |autoReduced?| |hasPredicate?| + |graphs| |iidprod| |normalElement| |semiResultantReduitEuclidean| + |determinant| |trueEqual| |f01qdf| |arity| |weights| |/\\| |multiple?| + |rewriteSetByReducingWithParticularGenerators| |dequeue| |prem| + |constructorName| |nextItem| |has?| |rk4qc| |reverseLex| |swap| + |limitedint| |\\/| |redPo| |makeSin| |symmetricDifference| + |difference| |lastSubResultant| |module| |dec| + |eisensteinIrreducible?| |radicalEigenvalues| |permutation| + |subQuasiComponent?| |s19abf| |permutationGroup| |uniform01| |forLoop| + |enterInCache| |parameters| |bracket| |iCompose| |overlap| + |setLegalFortranSourceExtensions| |elt| |readLine!| |getGoodPrime| + |fixPredicate| |alphabetic| |logical?| |property| + |rootOfIrreduciblePoly| |cubic| |complexSolve| |subNodeOf?| + |singularitiesOf| |dim| |controlPanel| |conjugate| |binomial| + |irreducibleRepresentation| |impliesOperands| |mkcomm| |moebius| + |rightZero| |reduceByQuasiMonic| |phiCoord| |getProperty| + |basisOfCenter| |label| |stirling1| |iiacos| |useNagFunctions| + |decompose| |tubeRadiusDefault| |bfKeys| |normal?| |lfintegrate| + |coerceL| |getStream| |ran| |units| |factorList| |zeroDimPrime?| + |neglist| |mathieu24| |f02aff| |sequences| |commutator| |secIfCan| + |imagE| |bandedJacobian| |cCot| |usingTable?| + |indicialEquationAtInfinity| |algebraicSort| |resetAttributeButtons| + |capacity| |critBonD| |OMunhandledSymbol| |startTableGcd!| |plot| + |multinomial| |supDimElseRittWu?| |changeName| |f04maf| |bits| + |createRandomElement| |setMaxPoints| |approximants| + |genericRightTrace| |antiAssociative?| |rank| |f02abf| |sample| + |bytes| |subSet| |OMopenString| |subResultantGcd| |next| |getOrder| + |lquo| |constantCoefficientRicDE| |OMconnInDevice| |leadingTerm| + |aCubic| |iiasin| |lieAlgebra?| |quoted?| |countRealRootsMultiple| + |dimensions| |fractionPart| |colorFunction| |code| |coerceS| + |extractPoint| |character?| |leftGcd| |divideIfCan!| |element?| + |zeroDimensional?| |Ei| |mathieu11| |popFortranOutputStack| + |factorSFBRlcUnit| |nthr| |atanIfCan| |polarCoordinates| |mix| |reify| + |ListOfTerms| |space| |lazyGintegrate| |minimalPolynomial| |head| + |systemSizeIF| |subst| |leftRankPolynomial| |sturmVariationsOf| + |outputAsFortran| |qinterval| |commutativeEquality| |measure2Result| + |qfactor| |precision| |getOperator| |linear| |cyclicParents| + |tan2trig| GE |ode| |enqueue!| |f01mcf| |OMputEndApp| |indices| + |normDeriv2| |cylindrical| |genericRightNorm| |ptree| |e04dgf| + |second| |e02daf| |stoseInternalLastSubResultant| |exptMod| GT + |option| |modularGcd| |rroot| |SturmHabichtSequence| |lists| |reorder| + |asechIfCan| |numberOfIrreduciblePoly| |removeRedundantFactorsInPols| + |third| |polynomial| |insertionSort!| |resetNew| |patternMatch| LE + |lyndon| |ignore?| |superHeight| |genericLeftMinimalPolynomial| + |setAdaptive| |bezoutDiscriminant| |directory| |shallowExpand| + |rightTrim| |rightScalarTimes!| |rectangularMatrix| LT |dominantTerm| + |color| |zeroDim?| |monomial?| |removeDuplicates!| |OMlistCDs| + |contours| |leftTrim| |makeSketch| |moreAlgebraic?| + |constantToUnaryFunction| |rombergo| |stronglyReduce| |clearTheFTable| + |algebraicVariables| |s21baf| |fortranTypeOf| |unitNormal| + |taylorQuoByVar| |oddInfiniteProduct| |totalfract| |overlabel| + |binarySearchTree| |fortranLiteralLine| |stoseInvertible?| + |getMultiplicationTable| |generic| |e02baf| |supersub| |univariate?| + |pointColorPalette| |open?| |erf| |rowEchLocal| |insertTop!| + |evaluate| |dimensionOfIrreducibleRepresentation| |setClosed| + |coefficient| |sayLength| |possiblyInfinite?| |linGenPos| |errorKind| + |scalarTypeOf| |exponents| |s18aef| |coerceP| |padecf| + |associatedEquations| |pow| |screenResolution| |idealiserMatrix| + |rightGcd| |csubst| |cTanh| |lazyIntegrate| |functionIsOscillatory| + |split!| |lp| |newLine| |symbol?| |transpose| |removeSinSq| |pol| + |twist| |dilog| |semiDiscriminantEuclidean| |solveLinear| + |extractProperty| |s17adf| |birth| |leftUnit| |internalAugment| + |debug3D| |upperCase| |edf2fi| |primPartElseUnitCanonical| |sin| + |zero| |numberOfHues| |int| |sech2cosh| |Si| |c06frf| |drawCurves| + |sPol| |constantLeft| |linearMatrix| |pmintegrate| + |normalizeAtInfinity| |cos| |ratDenom| |saturate| |stop| + |roughBasicSet| |pushdterm| |f02ajf| |mat| |ranges| + |useSingleFactorBound?| |lfextendedint| |maximumExponent| + |internalZeroSetSplit| |And| |tan| |coercePreimagesImages| + |numberOfCycles| |cschIfCan| |constantRight| |csch2sinh| |formula| + |any| |mapSolve| |push| |s17def| |fortranCharacter| |jacobian| |Or| + |cot| |setRow!| |d01apf| |totalDegree| |overbar| |tanh2coth| + |checkForZero| |style| |bitLength| |pattern| |notOperand| + |makeYoungTableau| |Not| |sec| |e04gcf| |removeRedundantFactors| + |getMeasure| |e01sbf| |axes| |charpol| |reverse!| |d02raf| + |changeBase| |aQuadratic| |csc| |createIrreduciblePoly| |exponential| + |hasHi| |cCosh| |noKaratsuba| |mapmult| |iipow| |addiag| |equiv?| + |concat!| |euclideanGroebner| |asin| |branchIfCan| |height| + |transcendentalDecompose| |sts2stst| |collect| |loadNativeModule| + |nrows| |rquo| |s14aaf| |assign| |sizeLess?| |d01gbf| |acos| + |radicalRoots| |lintgcd| |curry| |exprToUPS| |null?| |ncols| + |complement| |function| |direction| |lambert| |e01saf| + |infiniteProduct| |message| |atan| |minPoints3D| |extension| + |algintegrate| |weakBiRank| |LowTriBddDenomInv| |setAdaptive3D| + |rightTrace| |qqq| |prepareDecompose| |slex| |acot| |cAcsch| + |eigenvalues| |redpps| |relationsIdeal| |cPower| |droot| + |realElementary| |triangSolve| |lex| |log| |setScreenResolution3D| + |eval| |asec| |makeSUP| |integralMatrix| |connect| |npcoef| + |clipSurface| |leadingIdeal| |s20acf| |cycle| |trace2PowMod| + |rational?| |acsc| |polynomialZeros| |fglmIfCan| |delay| |d02gaf| + |cross| |root| |legendre| |algebraicCoefficients?| + |basisOfRightNucloid| |setButtonValue| |sinh| |c06ecf| |sdf2lst| + |completeEval| |setprevious!| |stosePrepareSubResAlgo| |cons| |cAsec| + |normalDenom| |optional?| |predicates| |endOfFile?| |cosh| |e04fdf| + |close!| |UP2ifCan| |fortranLogical| |cSin| |quartic| + |decreasePrecision| |minPoints| |solid| |sqfree| |tanh| + |perfectNthRoot| |factorAndSplit| |elColumn2!| |rootProduct| |split| + |GospersMethod| |setelt!| |s14baf| |PDESolve| |eigenMatrix| + |acscIfCan| |startTable!| |level| |coth| |denominator| |implies| + |Aleph| |currentCategoryFrame| |tanNa| |initiallyReduce| |OMgetObject| + |traverse| |discriminantEuclidean| |symmetricTensors| |preprocess| + |partitions| |dequeue!| |sech| |leader| |palglimint0| |shufflein| + |LiePolyIfCan| |xn| |lfextlimint| |cCsch| |tubePoints| |isOp| + |flagFactor| |quasiRegular| |csch| |e02bbf| |xor| |iiacosh| + |constantIfCan| |virtualDegree| |quasiRegular?| + |reduceBasisAtInfinity| |prinshINFO| |children| |elementary| + |genericRightDiscriminant| |asinh| |Lazard| |palgLODE0| |red| + |infieldint| |f02aef| |source| |readBytes!| |outputAsTex| |key?| + |leftMult| |li| |collectUpper| |acosh| |ocf2ocdf| |expIfCan| + |palgint0| |s01eaf| |functionIsFracPolynomial?| |addBadValue| + |seriesSolve| |hMonic| |lcm| |solve1| + |removeIrreducibleRedundantFactors| |closedCurve?| |length| + |doubleRank| |tablePow| |numFunEvals3D| |viewZoomDefault| + |OMputEndAtp| |setTex!| |list| |countable?| |sumSquares| + |conditionsForIdempotents| |deriv| |tubeRadius| |scripts| |pointLists| + |close| |constantOperator| |expintegrate| |sqfrFactor| |rubiksGroup| + |car| |topFortranOutputStack| |pushuconst| |append| |bsolve| |d02ejf| + |child| |rightRecip| |any?| |e02zaf| |writeByteIfCan!| |calcRanges| + |cdr| |nand| |getDatabase| |lazyIrreducibleFactors| + |commonDenominator| |genericPosition| |gcd| |display| |cosh2sech| + |escape| |showIntensityFunctions| |simplifyPower| |viewWriteAvailable| + |arrayStack| |ravel| |setDifference| |leaves| |iiexp| + |permutationRepresentation| |position!| |false| |lazy?| |fortran| + |safeFloor| |curveColor| |swapRows!| |primaryDecomp| |clearTable!| + |setIntersection| |reshape| |radicalSolve| |differentialVariables| + |complexEigenvectors| |resetVariableOrder| |terms| |latex| |lifting1| + |badNum| |computeInt| |wordInGenerators| |setUnion| |bitTruth| + |isMult| |graphStates| |skewSFunction| |maxPoints| |bezoutMatrix| + |partialDenominators| |clipBoolean| |rightRankPolynomial| + |meshPar2Var| |apply| |palgextint| |intensity| |lexTriangular| + |mirror| |unitNormalize| |qPot| |antiCommutative?| |power!| |sin?| + |colorDef| |imaginary| |leftOne| |cAtan| |s13aaf| |reduceLODE| + |remove| |e04ucf| |#| |expenseOfEvaluation| |prolateSpheroidal| + |swap!| |multMonom| |sturmSequence| |size| |alphabetic?| |iomode| + |duplicates?| |integralAtInfinity?| |meshPar1Var| + |genericLeftTraceForm| |key| |test| |internalSubPolSet?| + |outputAsScript| |rationalIfCan| |stopTable!| |s17aef| |mainVariable?| + |update| |pair?| |last| |makeVariable| |axesColorDefault| + |setsubMatrix!| |yCoordinates| |integralLastSubResultant| + |intcompBasis| |rst| |assoc| |basisOfLeftNucleus| |e02akf| |subset?| + |geometric| |interpolate| |filename| |OMsend| |delta| |alphanumeric?| + |normFactors| |isList| |scripted?| |zoom| |first| |rotatez| |submod| + |meshFun2Var| |monic?| |high| |gbasis| |not?| |validExponential| + |s18def| |refine| |region| |reducedSystem| |rest| |hypergeometric0F1| + |matrixGcd| |flexibleArray| |subresultantSequence| |prefix| |light| + |removeSuperfluousCases| |parse| |f04jgf| |cyclicEqual?| + |nextIrreduciblePoly| |numberOfComputedEntries| |substitute| |f04asf| + |createNormalPrimitivePoly| |selectPolynomials| |currentSubProgram| + |sumOfKthPowerDivisors| |nextPrime| |parabolicCylindrical| |simpsono| + |sinIfCan| |removeDuplicates| |ldf2vmf| |subscriptedVariables| + |listConjugateBases| |c02aff| |setOfMinN| |complexExpand| + |quadraticNorm| |updatD| |oblateSpheroidal| |makeGraphImage| |s17ajf| + |sortConstraints| |multiEuclidean| |lexico| |check| |script| |cCsc| + |f02awf| |orthonormalBasis| |matrixDimensions| |expandTrigProducts| + |cycleTail| |mathieu22| |simplifyExp| |getIdentifier| |lagrange| + |iitan| |rootSplit| |homogeneous?| |normalizedDivide| + |wronskianMatrix| |complexZeros| |eq| |laplacian| |bernoulliB| + |fracPart| |lambda| |asimpson| |queue| |setref| |square?| |ffactor| + |iter| |rk4f| |choosemon| |lazyPseudoRemainder| |clipPointsDefault| + |e01baf| |tex| |tableau| |identitySquareMatrix| |diag| |hyperelliptic| + |quasiMonic?| |generateIrredPoly| |rules| |eq?| |ParCondList| + |roughBase?| |printStats!| |iiabs| |unknown| |generalizedEigenvectors| + |numericalIntegration| |solid?| |rCoord| |minimize| |fractRagits| + |complexForm| |var1Steps| |optAttributes| |rowEchelon| |vertConcat| + |aQuartic| |medialSet| |varList| |d01bbf| |badValues| |setRealSteps| + |maxdeg| |critMTonD1| |subresultantVector| |superscript| |An| + |omError| |checkRur| |nextSublist| |repeating?| |adaptive?| |term?| + |radPoly| |setrest!| |iisec| |retract| |selectPDERoutines| |typeList| + |bipolarCylindrical| |linearAssociatedExp| |normalizedAssociate| + |zeroVector| |mapdiv| |index| |c06gqf| |combineFeatureCompatibility| + |diagonalMatrix| |getButtonValue| |antiCommutator| |iicsch| + |ramified?| |e04mbf| |viewPosDefault| |splitLinear| + |purelyTranscendental?| |strongGenerators| |rischDEsys| |baseRDE| + |exp| |numberOfMonomials| |OMcloseConn| |complexIntegrate| |satisfy?| + |optimize| |deepestTail| |iidsum| |showRegion| |conjug| |viewpoint| + |se2rfi| |summation| |SturmHabichtCoefficients| + |fortranCarriageReturn| |SturmHabicht| |domainOf| |compile| |pair| + |sinhcosh| |fixedDivisor| |hash| |laguerre| |isPlus| + |evenInfiniteProduct| |aromberg| |scale| |setnext!| |newTypeLists| + |divisorCascade| |count| |ref| LODO2FUN |midpoint| |integrate| + |rightAlternative?| |genericLeftNorm| |qelt| |addPoint2| + |groebnerIdeal| |s13adf| |primPartElseUnitCanonical!| |clipParametric| + |inR?| |enumerate| |tab| |qsetelt| |mapCoef| |gramschmidt| + |algebraic?| |signatureAst| |besselJ| |limit| |selectODEIVPRoutines| + |curve| |changeMeasure| |composite| |ldf2lst| |randomR| |adaptive| + |xRange| |explicitEntries?| |OMgetInteger| |OMParseError?| |iisin| + |cos2sec| |generalizedContinuumHypothesisAssumed?| |sn| |commutative?| + |testModulus| |value| |yRange| |ode2| |byteBuffer| + |unrankImproperPartitions1| |inverseIntegralMatrixAtInfinity| + |integralMatrixAtInfinity| |rightNorm| |leastPower| |fibonacci| + |palglimint| |trailingCoefficient| |extendedint| |zRange| |mapUp!| + |mvar| |createMultiplicationTable| |reindex| |dihedral| |horizConcat| + |leftRemainder| |fillPascalTriangle| |map!| |shuffle| |acschIfCan| + |digits| |operator| |nullary| |nsqfree| |OMsupportsCD?| |Nul| + |selectfirst| |qsetelt!| |plus| |clearTheSymbolTable| |green| + |vectorise| |symmetricGroup| |cycleEntry| |numericIfCan| |zerosOf| + |singular?| |outputFixed| |incrementKthElement| |jacobi| + |OMgetEndObject| |mainPrimitivePart| |d01akf| |member?| + |expressIdealMember| |hasSolution?| |getGraph| |traceMatrix| + |stoseIntegralLastSubResultant| |setMinPoints| + |unprotectedRemoveRedundantFactors| |bounds| |shrinkable| + |irreducibleFactors| |coefficients| |internalIntegrate0| + |removeConstantTerm| |graeffe| |genericLeftDiscriminant| |external?| + |positiveRemainder| |varselect| |getConstant| |createGenericMatrix| + |sum| |pr2dmp| |highCommonTerms| |pseudoDivide| |testDim| |d02cjf| + |factor1| |pointSizeDefault| |d01gaf| |polyRDE| |orbits| |taylorRep| + |hdmpToP| |lyndon?| |compound?| |curryRight| |nextLatticePermutation| + |signAround| |maxint| |acsch| |Hausdorff| |c06ekf| |OMwrite| |initial| + |reopen!| |UnVectorise| |critM| |critMonD1| |frobenius| + |completeEchelonBasis| |palgextint0| |clip| |consnewpol| |pushdown| + |replaceKthElement| |quotientByP| |ddFact| |compdegd| + |setTopPredicate| |pop!| |cAtanh| |squareTop| |solveRetract| |iitanh| + |unaryFunction| |froot| |retractable?| |column| |readByteIfCan!| + |antisymmetric?| |box| |polyRicDE| |trigs2explogs| |printHeader| + |radicalSimplify| |viewSizeDefault| |powern| |binding| |sh| + |sparsityIF| |primlimintfrac| |OMputString| |trapezoidalo| + |semiDegreeSubResultantEuclidean| |cycleLength| |integralRepresents| + |inHallBasis?| |argumentListOf| |minrank| |tValues| |getZechTable| + |normalized?| |byte| |intermediateResultsIF| |fortranReal| + |exactQuotient!| |squareFreeFactors| |mainExpression| ~ |find| + |cyclotomic| |clearDenominator| |chiSquare| |upDateBranches| |search| + |fmecg| |completeHensel| |collectQuasiMonic| |chainSubResultants| + |nextPartition| |vector| |f04faf| |polCase| |f02bjf| |e02bcf| + |setVariableOrder| |exponentialOrder| |redPol| |open| |asecIfCan| + |integral| |internalDecompose| |differentiate| |integral?| |reduction| + |selectAndPolynomials| |sncndn| |minimumExponent| |measure| |nthCoef| + |rspace| |inspect| |option?| |OMputSymbol| |d03edf| |repeating| + |continuedFraction| |point?| |nodeOf?| |printStatement| + |fortranCompilerName| |dn| |chineseRemainder| |even?| |s21bbf| + |mainContent| |extractClosed| |leftFactorIfCan| |critB| |setFormula!| + |generalTwoFactor| |mathieu23| |removeZero| |negative?| |iiacsc| + |power| |recoverAfterFail| |lprop| |powers| |cardinality| + |companionBlocks| |lllip| |extend| |spherical| |parts| + |uncouplingMatrices| |genus| |iroot| |d03eef| FG2F |e01sef| + |denomLODE| |innerSolve1| |rename| |cyclic| |createNormalElement| + |headReduced?| |firstNumer| |tanSum| |distance| |nextsubResultant2| + |univariateSolve| |rightRank| |simpson| |besselI| |paraboloidal| + |psolve| |numberOfDivisors| |maxColIndex| |rootSimp| |bottom!| |ideal| + |perfectSqrt| |or| |roman| |listOfMonoms| |roughEqualIdeals?| |atom?| + |tree| |transform| |hermiteH| |prepareSubResAlgo| |s15aef| |ParCond| + |Ci| |f04mcf| |comp| |e02ajf| |addmod| |perspective| |rationalPoint?| + |monicCompleteDecompose| |cotIfCan| |showTheFTable| |setvalue!| + |nthFractionalTerm| |sechIfCan| |firstSubsetGray| |complex?| |sub| + |iicoth| |po| |showAll?| |toroidal| |invmod| |computeBasis| + |cyclicSubmodule| F2FG ~= |OMserve| |modifyPointData| + |quasiMonicPolynomials| |var2StepsDefault| |part?| + |leastAffineMultiple| |rightDivide| |corrPoly| |monicRightDivide| + |unparse| |coerce| |s17akf| |scan| |singularAtInfinity?| |palgRDE0| + |partialQuotients| |s17dcf| F |abelianGroup| |rightMult| + |characteristicSet| |alphanumeric| |lllp| |construct| |integer?| + |rewriteSetWithReduction| |e01bff| |reset| |leftNorm| |iFTable| + |bernoulli| |extendedResultant| |endSubProgram| |brillhartTrials| + |leadingIndex| |cAsin| |LazardQuotient| |toseSquareFreePart| + |addPointLast| |compiledFunction| |polygon| |OMgetType| |diagonals| + |bit?| |monicRightFactorIfCan| |subTriSet?| |variable?| + |purelyAlgebraic?| |write| |expandPower| |oneDimensionalArray| + |rightUnits| |scaleRoots| |f02aaf| |exteriorDifferential| |henselFact| + |save| |monicDecomposeIfCan| |nthFactor| + |removeRoughlyRedundantFactorsInPol| |pointColor| |setleaves!| + |cAsech| |symmetricProduct| |rightFactorIfCan| |writeBytes!| + |quadratic?| |times!| |e02bdf| |surface| |id| |null| |aspFilename| + |invertIfCan| |countRealRoots| |members| |coefChoose| |f2df| + |returnType!| |newReduc| |rarrow| |hex| |case| |frst| + |initiallyReduced?| |removeSuperfluousQuasiComponents| + |getPickedPoints| |Gamma| |startPolynomial| |findBinding| + |exponential1| |mesh?| |table| |nullary?| |Zero| |hostPlatform| + |degree| |llprop| |resultant| |odd?| |unitCanonical| |cAsinh| |sup| + |minset| |new| |e02bef| |One| |partialNumerators| |generalLambert| + |gradient| |composites| |viewDeltaYDefault| |sizeMultiplication| + |shallowCopy| |curveColorPalette| |logpart| |denominators| + |roughUnitIdeal?| |realRoots| |tanIfCan| |d01aqf| |setProperty!| + |expt| |leftCharacteristicPolynomial| |nextsousResultant2| + |conjugates| |jordanAlgebra?| |normalizeIfCan| ** |rightDiscriminant| + |e02ahf| |romberg| |bitCoef| |goodnessOfFit| |innerSolve| |hconcat| + |s21bdf| |char| |inf| |rightExtendedGcd| |squareFree| |reverse| + |viewWriteDefault| |coordinate| |entry?| |prologue| |bandedHessian| + |diagonalProduct| |removeCoshSq| |exprHasAlgebraicWeight| + |lineColorDefault| |nthRootIfCan| |linearlyDependentOverZ?| |sin2csc| + EQ |OMgetEndBind| |setlast!| |entry| |tower| |uniform| |iilog| + |nthExponent| |splitSquarefree| |shiftLeft| |divideIfCan| + |indicialEquation| |equation| |OMencodingBinary| UP2UTS |sincos| + |shiftRoots| |elements| |selectIntegrationRoutines| |separate| + |getCurve| |stFunc2| |OMputBind| |fortranInteger| |besselY| + |numberOfChildren| |lfinfieldint| |c06fuf| |showAllElements| + |makeCrit| |tanh2trigh| |raisePolynomial| |radicalOfLeftTraceForm| + |mapDown!| |specialTrigs| |setOrder| |mergeDifference| |category| + |notelem| |float| |listOfLists| |removeZeroes| |primextintfrac| + |leftDiscriminant| |localAbs| |pastel| |semiSubResultantGcdEuclidean2| + |harmonic| |vark| |domain| |OMputApp| |gcdPolynomial| |setProperties| + |floor| |cTan| |OMputEndAttr| |row| |complexNumeric| + |certainlySubVariety?| |left| |diagonal| |algebraicDecompose| + |package| |mainVariables| |completeSmith| |rightPower| |pomopo!| + |relerror| |mapUnivariateIfCan| |stFunc1| |minordet| |right| |deref| + |empty| |balancedBinaryTree| |clipWithRanges| |setMaxPoints3D| |cAcot| + |empty?| |comment| |alternating| |kernels| |associatedSystem| + |nextColeman| |duplicates| |OMgetEndAttr| |permutations| |plotPolar| + |OMgetEndAtp| |viewDeltaXDefault| |top| |safeCeiling| |univariate| + |vedf2vef| |singleFactorBound| |heap| |componentUpperBound| + |plenaryPower| |repeatUntilLoop| |partialFraction| |create3Space| + |iterationVar| |c06gcf| |initTable!| |prime| |rationalPower| + |messagePrint| |coordinates| |triangularSystems| |reseed| |iiatan| + |makingStats?| |rationalFunction| |fortranDoubleComplex| + |primitivePart| |OMputEndBVar| |laguerreL| |front| + |selectMultiDimensionalRoutines| |zeroOf| |splitConstant| |pointData| + |factor| |maxrank| |aLinear| |leftExtendedGcd| |realSolve| |dflist| + |d02kef| |factorGroebnerBasis| |const| |lowerPolynomial| |sqrt| + |df2ef| |e02dcf| |degreePartition| |principalIdeal| |knownInfBasis| + |s21bcf| |showTypeInOutput| |insertMatch| |whatInfinity| |real| + |andOperands| |simplify| |delete!| |numberOfComponents| |primitive?| + |degreeSubResultant| |mainVariable| |lowerCase| |f02axf| |imag| + |kroneckerDelta| |goto| |conical| |f02agf| |top!| |is?| |matrix| + |drawComplexVectorField| |iisinh| |directProduct| |putGraph| + |definingPolynomial| |headAst| |selectSumOfSquaresRoutines| + |computeCycleEntry| |hasoln| |ridHack1| |stripCommentsAndBlanks| + |findCycle| |outlineRender| |linearPart| |setFieldInfo| + |limitedIntegrate| |OMlistSymbols| |minRowIndex| |splitNodeOf!| + |bipolar| |rischNormalize| |dioSolve| RF2UTS |radicalEigenvectors| + |brace| |symbol| |lowerCase?| |minimumDegree| |LiePoly| |exprToXXP| + |pseudoRemainder| |applyRules| |multiset| |f01qcf| |elliptic| + |destruct| |expression| |mapBivariate| |numericalOptimization| + |LazardQuotient2| |lazyPquo| |f02akf| |mainCoefficients| |denomRicDE| + |closed?| |showArrayValues| |integer| |f01brf| |pdct| |mapExpon| + |padicallyExpand| |imagJ| |setleft!| |elRow2!| + |halfExtendedSubResultantGcd1| |stFuncN| |number?| |push!| |f07adf| + |univariatePolynomial| |derivative| |currentScope| |critpOrder| + |doubleFloatFormat| |expint| |pmComplexintegrate| |primlimitedint| + |regularRepresentation| |Vectorise| |stiffnessAndStabilityFactor| + |definingEquations| |digit| |associates?| |monomial| + |zeroSetSplitIntoTriangularSystems| |f02bbf| |pole?| |bivariate?| + |returnTypeOf| |partition| |setCondition!| |isQuotient| + |processTemplate| |bumptab1| |monomialIntPoly| |multivariate| + |wholePart| |BumInSepFFE| |iicsc| |algSplitSimple| |leftTraceMatrix| + |HenselLift| |binary| |screenResolution3D| |variables| |hitherPlane| + |OMgetAttr| |complexNormalize| |topPredicate| |rischDE| + |possiblyNewVariety?| |numberOfImproperPartitions| |setEmpty!| + |karatsuba| |rightRemainder| |graphImage| |move| + |createLowComplexityTable| |rotate!| |f01rcf| |entries| |df2fi| + |octon| |rk4| |constantKernel| |dot| |freeOf?| |lighting| + |OMgetVariable| |df2mf| |numberOfFractionalTerms| |seed| + |totalGroebner| |iisqrt3| |doubleComplex?| |outputGeneral| |zero?| + |c06eaf| |trigs| |sort!| |appendPoint| |legendreP| + |shanksDiscLogAlgorithm| |thetaCoord| |s17acf| |bumptab| |points| + |wreath| |zeroMatrix| |reducedDiscriminant| |rootPower| |taylor| + |d02gbf| |maxRowIndex| |iprint| |rewriteIdealWithRemainder| + |showClipRegion| |inRadical?| |numberOfNormalPoly| |separateFactors| + |obj| |digit?| |cyclotomicDecomposition| |laurent| + |leadingCoefficientRicDE| |eyeDistance| |eof?| |meatAxe| |charClass| + |arguments| |acothIfCan| |linSolve| |e01daf| |dictionary| + |realEigenvectors| |puiseux| |f01maf| |extractIndex| |postfix| |cache| + |leadingSupport| |OMgetApp| |f01rdf| |resultantReduitEuclidean| + |nothing| |blue| |outputFloating| |s13acf| + |rightRegularRepresentation| |OMgetBind| |setClipValue| + |normInvertible?| |quickSort| |bivariatePolynomials| |inv| |tRange| + |ricDsolve| |wordInStrongGenerators| |rowEch| |atanhIfCan| |merge!| + |hclf| |expintfldpoly| |lazyPrem| |ground?| |c05pbf| |quotient| + |modulus| |failed?| |rightFactorCandidate| |sorted?| |numeric| + |lastSubResultantEuclidean| |finiteBound| |coerceImages| |ground| + |pascalTriangle| |leftAlternative?| |dimension| |fullDisplay| + |quasiAlgebraicSet| |mapUnivariate| |radical| |df2st| + |exprHasWeightCosWXorSinWX| |rangePascalTriangle| |leadingMonomial| + |multisect| |tanintegrate| |OMencodingSGML| |e02def| |reduced?| + |mainValue| |crest| |interval| |airyBi| |leadingCoefficient| |low| + |variationOfParameters| |gderiv| |copyInto!| |selectsecond| |iibinom| + |e04naf| |operators| |elem?| |d01asf| |primitiveMonomials| |nthRoot| + |curryLeft| |acoshIfCan| |moebiusMu| |LyndonWordsList1| |f02wef| + |imports| |minGbasis| |ceiling| |edf2efi| |readIfCan!| |reductum| + |characteristicPolynomial| |halfExtendedResultant2| |cLog| |c06ebf| + |problemPoints| |factors| |numerator| |cot2tan| |true| |cyclicEntries| + |rational| |antisymmetricTensors| |hessian| |root?| |palginfieldint| + |algDsolve| |output| |unit| |infix| |say| |accuracyIF| |iicosh| + |outputMeasure| |chiSquare1| |subResultantsChain| |and| |dAndcExp| + |asinIfCan| |euclideanSize| |directSum| |groebnerFactorize| + |infinite?| UTS2UP |exp1| |OMgetEndApp| |smith| + |nativeModuleExtension| |internalSubQuasiComponent?| |real?| + |extractTop!| |content| |parent| |stirling2| |iiacsch| |cyclicCopy| + |htrigs| |cycleElt| |e02adf| |f02fjf| |gcdcofactprim| |quasiComponent| + |polyPart| |realEigenvalues| |inverseLaplace| |unravel| |wholeRadix| + |extensionDegree| |currentEnv| |drawToScale| |modularFactor| + |adaptive3D?| |fractRadix| |stopTableInvSet!| |prod| |imagi| |in?| + |OMgetFloat| |palgintegrate| |setEpilogue!| |readLineIfCan!| + |createNormalPoly| |multiplyCoefficients| |idealiser| + |extendedIntegrate| |infieldIntegrate| |lifting| |atanh| + |leviCivitaSymbol| |packageCall| |coth2trigh| |f02xef| |headReduce| + |rotate| |principal?| |setPredicates| |hue| |acoth| + |leftMinimalPolynomial| |absolutelyIrreducible?| |OMputAttr| + |basisOfLeftAnnihilator| |cyclePartition| |numberOfVariables| + |wholeRagits| |upperCase!| |leaf?| |asech| |inc| |host| |mkIntegral| + |unexpand| |bombieriNorm| |gcdprim| |constDsolve| |basisOfNucleus| + |f2st| |ellipticCylindrical| |lift| |lazyEvaluate| |f04mbf| |eulerPhi| + |charthRoot| |listYoungTableaus| |contract| + |removeRoughlyRedundantFactorsInContents| |multiple| |primintegrate| + |reduce| |rk4a| |sign| |initials| |listLoops| |getOperands| + |listBranches| |mapExponents| |physicalLength!| |applyQuote| |getlo| + |branchPoint?| |printTypes| |setAttributeButtonStep| |s20adf| + |primeFactor| |zeroDimPrimary?| |rationalPoints| |trivialIdeal?| + |linearDependence| |connectTo| |factorsOfDegree| |lowerCase!| |depth| + |torsionIfCan| |isExpt| |sinh2csch| |incrementBy| |outputBinaryFile| + |infix?| |bat| |fixedPointExquo| |goodPoint| |OMUnknownSymbol?| + |pdf2df| |printCode| |musserTrials| |condition| |mask| |ruleset| + |scalarMatrix| |expand| |exists?| |f01ref| |makeFR| |Lazard2| + |constant| |cAcoth| |idealSimplify| |augment| |setColumn!| + |filterWhile| |build| |changeThreshhold| |d02bhf| |monomials| + |rootBound| |rename!| |rightOne| |filterUntil| |every?| + |expextendedint| |seriesToOutputForm| |UpTriBddDenomInv| |drawStyle| + |stoseInvertible?reg| |modTree| |product| |suchThat| + |integralBasisAtInfinity| |select| |functionIsContinuousAtEndPoints| + |insertBottom!| |oddintegers| |gcdPrimitive| |karatsubaOnce| |options| + |showFortranOutputStack| |matrixConcat3D| |paren| |symbolTableOf| + |finiteBasis| |minColIndex| |ReduceOrder| |externalList| |exquo| + |subHeight| |numberOfPrimitivePoly| |trapezoidal| |dom| + |dihedralGroup| |leftTrace| |e01bhf| |div| |logGamma| |totolex| + |changeVar| |janko2| |s14abf| |float?| |rotatey| + |useEisensteinCriterion| |string| |quo| |probablyZeroDim?| |d02bbf| + |s17dgf| |s17dhf| |fortranDouble| |parametric?| |magnitude| |extract!| + |printingInfo?| |e02ddf| |OMputAtp| |slash| |primitiveElement| + |moduleSum| |createPrimitivePoly| |semiSubResultantGcdEuclidean1| + |makeMulti| |movedPoints| |rem| |largest| |lyndonIfCan| |makeRecord| + |ODESolve| |intersect| |subtractIfCan| |trim| |tracePowMod| |numer| + |selectNonFiniteRoutines| |enterPointData| NOT |OMUnknownCD?| |title| + |symmetric?| |cycleSplit!| |schwerpunkt| |universe| + |symmetricRemainder| |denom| |balancedFactorisation| |alternative?| OR + |subCase?| |s19acf| |regime| |groebSolve| |cAcsc| + |purelyAlgebraicLeadingMonomial?| |rotatex| |swapColumns!| AND + |cartesian| |OMputVariable| |chebyshevT| |callForm?| |pi| |divisors| + |subPolSet?| |center| |e| |lazyResidueClass| |upperCase?| + |mainMonomials| |getMultiplicationMatrix| |pushup| |infinity| |width| + |resultantReduit| |factorsOfCyclicGroupSize| |mapMatrixIfCan| + |factorSquareFree| |monomialIntegrate| |fintegrate| |iiGamma| + |writeLine!| |status| |explogs2trigs| |one?| |polyred| |unary?| + |cothIfCan| |categoryFrame| |log10| |groebgen| |leftQuotient| + |isPower| |complexLimit| |e02agf| |f04axf| |bitand| |maxrow| + |createMultiplicationMatrix| |tensorProduct| |rootDirectory| + |transcendenceDegree| |backOldPos| |e01bgf| |integerIfCan| |kernel| + |categories| |youngGroup| |cAcos| |bitior| |OMsupportsSymbol?| |pack!| + |coshIfCan| |linear?| |tab1| |draw| |OMputEndError| + |nextPrimitivePoly| |or?| |nextNormalPoly| |continue| |pToHdmp| + |OMread| |baseRDEsys| |setPosition| |rdregime| |not| + |jordanAdmissible?| |primes| |coleman| |blankSeparate| + |totalDifferential| |internalIntegrate| |evaluateInverse| + |normalDeriv| |squareFreePart| |acotIfCan| |fortranLiteral| |digamma| + |showTheIFTable| |tan2cot| |cCoth| GF2FG |someBasis| |addMatch| + |generator| |updatF| |optional| |s18dcf| |OMgetError| * + |solveLinearlyOverQ| |ef2edf| |showTheRoutinesTable| |besselK| + |thenBranch| |setchildren!| |ratPoly| |makeObject| |expPot| + |closedCurve| |solveLinearPolynomialEquationByRecursion| |interpret| + |create| |errorInfo| |extractSplittingLeaf| |discreteLog| |mathieu12| + |leftLcm| |mappingAst| |laurentRep| |leftRecip| |solve| |cAcosh| + |unvectorise| |inverse| |truncate| |coef| |resultantEuclidean| + |basisOfLeftNucloid| |divergence| |algebraicOf| |objects| |cap| + |palgRDE| |interReduce| |presuper| |over| |failed| |polygon?| |cSec| + |d01anf| |sec2cos| |base| |stoseInvertibleSetreg| |lexGroebner| + |roughSubIdeal?| |modularGcdPrimitive| |rightExactQuotient| |iExquo| + |var1StepsDefault| |semiLastSubResultantEuclidean| |round| + |addMatchRestricted| |gcdcofact| |remainder| |mesh| |hdmpToDmp| + |invmultisect| |constant?| |eigenvectors| |sizePascalTriangle| |node| + |separateDegrees| |coerceListOfPairs| |setStatus!| |integralBasis| + |critT| |basis| |PollardSmallFactor| |factorOfDegree| + |semiResultantEuclideannaif| |univariatePolynomials| |removeCosSq| + |singRicDE| |inverseColeman| |restorePrecision| |redmat| |lo| + |optpair| |generalizedInverse| |divideExponents| |numFunEvals| + |eulerE| |modifyPoint| |interpretString| |genericRightTraceForm| + |unmakeSUP| |incr| |orOperands| |distdfact| |makeResult| |cn| + |tryFunctionalDecomposition| |brillhartIrreducible?| + |removeRedundantFactorsInContents| |subNode?| |numerators| |nullSpace| + |hi| |triangulate| |rationalApproximation| |pushNewContour| + |LyndonBasis| |range| |nodes| |Frobenius| |size?| |lazyPseudoDivide| + |reducedForm| |order| |unitsColorDefault| |edf2df| |OMbindTCP| + |commaSeparate| |sylvesterSequence| |imagI| |showTheSymbolTable| + |rootNormalize| |areEquivalent?| |returns| |recolor| + |invertibleElseSplit?| |btwFact| |leftUnits| |mergeFactors| + |inputOutputBinaryFile| |s18acf| |anfactor| |randomLC| + |getVariableOrder| |s17dlf| |isTimes| |putColorInfo| |torsion?| + |node?| |epilogue| SEGMENT |ScanFloatIgnoreSpacesIfCan| + |indicialEquations| |complexEigenvalues| |addPoint| |and?| + |representationType| |listexp| |previous| |LyndonCoordinates| + |represents| |minus!| |ipow| |createPrimitiveNormalPoly| |att2Result| + |nil| |lieAdmissible?| |Is| |basisOfCentroid| |lazyPseudoQuotient| + |wordsForStrongGenerators| |OMgetEndBVar| |name| |printInfo!| + |symmetricPower| |leftRank| |bivariateSLPEBR| |reciprocalPolynomial| + |allRootsOf| |jacobiIdentity?| |child?| |e04ycf| |body| |B1solve| + |useSingleFactorBound| |setPoly| |declare| |imagK| |binomThmExpt| + |hcrf| |iicot| |OMclose| |tanhIfCan| |approximate| |rootRadius| + |sequence| |diophantineSystem| |localReal?| |monomRDE| |socf2socdf| + |squareFreeLexTriangular| |concat| |complex| |write!| + |leadingBasisTerm| |scanOneDimSubspaces| |basisOfMiddleNucleus| + |iicos| |sumOfDivisors| |boundOfCauchy| |e01sff| |t| |substring?| + |shellSort| |d01ajf| |f07aef| Y |resize| |increment| |imagj| |ptFunc| + |symFunc| |generate| |SturmHabichtMultiple| |convergents| |infRittWu?| + |doublyTransitive?| |ScanArabic| |norm| |genericLeftTrace| + |OMopenFile| |nil| |infinite| |arbitraryExponent| |approximate| + |complex| |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-401 (-552))) -1559 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-38 |#1|) . T) ((-38 $) -1559 (|has| |#1| (-544)) (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-35) |has| |#1| (-1174)) ((-94) |has| |#1| (-1174)) ((-101) . T) ((-110 #0# #0#) -1559 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-110 |#1| |#1|) . T) ((-110 $ $) . T) ((-129) . T) ((-142) -1559 (|has| |#1| (-343)) (|has| |#1| (-142))) ((-144) |has| |#1| (-144)) ((-599 (-842)) . T) ((-169) . T) ((-600 (-166 (-220))) |has| |#1| (-1001)) ((-600 (-166 (-373))) |has| |#1| (-1001)) ((-600 (-528)) |has| |#1| (-600 (-528))) ((-600 (-871 (-373))) |has| |#1| (-600 (-871 (-373)))) ((-600 (-871 (-552))) |has| |#1| (-600 (-871 (-552)))) ((-600 #1=(-1148 |#1|)) . T) ((-226 |#1|) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-401 (-552))) -4029 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-38 |#1|) . T) ((-38 $) -4029 (|has| |#1| (-544)) (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-35) |has| |#1| (-1176)) ((-94) |has| |#1| (-1176)) ((-101) . T) ((-110 #0# #0#) -4029 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-110 |#1| |#1|) . T) ((-110 $ $) . T) ((-129) . T) ((-142) -4029 (|has| |#1| (-343)) (|has| |#1| (-142))) ((-144) |has| |#1| (-144)) ((-599 (-844)) . T) ((-169) . T) ((-600 (-166 (-220))) |has| |#1| (-1003)) ((-600 (-166 (-373))) |has| |#1| (-1003)) ((-600 (-528)) |has| |#1| (-600 (-528))) ((-600 (-873 (-373))) |has| |#1| (-600 (-873 (-373)))) ((-600 (-873 (-552))) |has| |#1| (-600 (-873 (-552)))) ((-600 #1=(-1150 |#1|)) . T) ((-226 |#1|) . 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T) ((-506 |#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1078))) ((-632 |#2|) -4029 (|has| |#2| (-1030)) (|has| |#2| (-357)) (|has| |#2| (-169))) ((-632 $) -4029 (|has| |#2| (-1030)) (|has| |#2| (-830)) (|has| |#2| (-169))) ((-625 (-552)) -12 (|has| |#2| (-625 (-552))) (|has| |#2| (-1030))) ((-625 |#2|) |has| |#2| (-1030)) ((-702 |#2|) -4029 (|has| |#2| (-357)) (|has| |#2| (-169))) ((-711) -4029 (|has| |#2| (-1030)) (|has| |#2| (-830)) (|has| |#2| (-711)) (|has| |#2| (-169))) ((-776) |has| |#2| (-830)) ((-777) -4029 (|has| |#2| (-830)) (|has| |#2| (-778))) ((-778) |has| |#2| (-778)) ((-779) -4029 (|has| |#2| (-830)) (|has| |#2| (-778))) ((-780) -4029 (|has| |#2| (-830)) (|has| |#2| (-778))) ((-830) |has| |#2| (-830)) ((-832) -4029 (|has| |#2| (-830)) (|has| |#2| (-778))) ((-881 (-1154)) -12 (|has| |#2| (-881 (-1154))) (|has| |#2| (-1030))) ((-1019 (-401 (-552))) -12 (|has| |#2| (-1019 (-401 (-552)))) (|has| |#2| (-1078))) ((-1019 (-552)) -12 (|has| |#2| (-1019 (-552))) (|has| |#2| (-1078))) ((-1019 |#2|) |has| |#2| (-1078)) ((-1036 |#2|) -4029 (|has| |#2| (-1030)) (|has| |#2| (-357)) (|has| |#2| (-169))) ((-1036 $) |has| |#2| (-169)) ((-1030) -4029 (|has| |#2| (-1030)) (|has| |#2| (-830)) (|has| |#2| (-169))) ((-1037) -4029 (|has| |#2| (-1030)) (|has| |#2| (-830)) (|has| |#2| (-169))) ((-1090) -4029 (|has| |#2| (-1030)) (|has| |#2| (-830)) (|has| |#2| (-711)) (|has| |#2| (-169))) ((-1078) -4029 (|has| |#2| (-1078)) (|has| |#2| (-1030)) (|has| |#2| (-830)) (|has| |#2| (-778)) (|has| |#2| (-711)) (|has| |#2| (-362)) (|has| |#2| (-357)) (|has| |#2| (-169)) (|has| |#2| (-129)) (|has| |#2| (-25))) ((-1191) . T) ((-1244 |#2|) |has| |#2| (-357))) +((-3215 (((-235 |#1| |#3|) (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|) 21)) (-3884 ((|#3| (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|) 23)) (-1477 (((-235 |#1| |#3|) (-1 |#3| |#2|) (-235 |#1| |#2|)) 18))) +(((-234 |#1| |#2| |#3|) (-10 -7 (-15 -3215 ((-235 |#1| |#3|) (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|)) (-15 -3884 (|#3| (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|)) (-15 -1477 ((-235 |#1| |#3|) (-1 |#3| |#2|) (-235 |#1| |#2|)))) (-756) (-1191) (-1191)) (T -234)) +((-1477 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-235 *5 *6)) (-14 *5 (-756)) (-4 *6 (-1191)) (-4 *7 (-1191)) (-5 *2 (-235 *5 *7)) (-5 *1 (-234 *5 *6 *7)))) (-3884 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-235 *5 *6)) (-14 *5 (-756)) (-4 *6 (-1191)) (-4 *2 (-1191)) (-5 *1 (-234 *5 *6 *2)))) (-3215 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-235 *6 *7)) (-14 *6 (-756)) (-4 *7 (-1191)) (-4 *5 (-1191)) (-5 *2 (-235 *6 *5)) (-5 *1 (-234 *6 *7 *5))))) +(-10 -7 (-15 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NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1231 3089349 3089519 3089639 "VARIABLE" 3089783 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1230 3089282 3089287 3089317 "UTYPE" 3089322 T UTYPE (NIL) -9 NIL NIL) (-1229 3088112 3088266 3088528 "UTSODETL" 3089108 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1228 3085552 3086012 3086536 "UTSODE" 3087653 NIL UTSODE (NIL T T) -7 NIL NIL) (-1227 3077428 3083178 3083667 "UTS" 3085121 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1226 3068801 3074120 3074163 "UTSCAT" 3075275 NIL UTSCAT (NIL T) -9 NIL 3076032) (-1225 3066155 3066871 3067860 "UTSCAT-" 3067865 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1224 3065782 3065825 3065958 "UTS2" 3066106 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1223 3060057 3062622 3062665 "URAGG" 3064735 NIL URAGG (NIL T) -9 NIL 3065457) (-1222 3056996 3057859 3058982 "URAGG-" 3058987 NIL URAGG- (NIL T T) -8 NIL NIL) (-1221 3052720 3055610 3056082 "UPXSSING" 3056660 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1220 3044690 3051835 3052117 "UPXS" 3052496 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1219 3037803 3044594 3044666 "UPXSCONS" 3044671 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1218 3028161 3034906 3034968 "UPXSCCA" 3035624 NIL UPXSCCA (NIL T T) -9 NIL 3035866) (-1217 3027799 3027884 3028058 "UPXSCCA-" 3028063 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1216 3018083 3024601 3024644 "UPXSCAT" 3025292 NIL UPXSCAT (NIL T) -9 NIL 3025900) (-1215 3017513 3017592 3017771 "UPXS2" 3017998 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1214 3016167 3016420 3016771 "UPSQFREE" 3017256 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1213 3010085 3013094 3013149 "UPSCAT" 3014310 NIL UPSCAT (NIL T T) -9 NIL 3015084) (-1212 3009289 3009496 3009823 "UPSCAT-" 3009828 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1211 2995380 3003376 3003419 "UPOLYC" 3005520 NIL UPOLYC (NIL T) -9 NIL 3006741) (-1210 2986709 2989134 2992281 "UPOLYC-" 2992286 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1209 2986336 2986379 2986512 "UPOLYC2" 2986660 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1208 2977793 2985902 2986040 "UP" 2986246 NIL UP (NIL NIL T) -8 NIL NIL) (-1207 2977132 2977239 2977403 "UPMP" 2977682 NIL UPMP (NIL T T) -7 NIL NIL) (-1206 2976685 2976766 2976905 "UPDIVP" 2977045 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1205 2975253 2975502 2975818 "UPDECOMP" 2976434 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1204 2974488 2974600 2974785 "UPCDEN" 2975137 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1203 2974007 2974076 2974225 "UP2" 2974413 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1202 2972524 2973211 2973488 "UNISEG" 2973765 NIL UNISEG (NIL T) -8 NIL NIL) (-1201 2971739 2971866 2972071 "UNISEG2" 2972367 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1200 2970799 2970979 2971205 "UNIFACT" 2971555 NIL UNIFACT (NIL T) -7 NIL NIL) (-1199 2954766 2969976 2970227 "ULS" 2970606 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1198 2942806 2954670 2954742 "ULSCONS" 2954747 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1197 2925604 2937541 2937603 "ULSCCAT" 2938323 NIL ULSCCAT (NIL T T) -9 NIL 2938620) (-1196 2924654 2924899 2925287 "ULSCCAT-" 2925292 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1195 2914715 2921147 2921190 "ULSCAT" 2922053 NIL ULSCAT (NIL T) -9 NIL 2922783) (-1194 2914145 2914224 2914403 "ULS2" 2914630 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1193 2912583 2913506 2913536 "UFD" 2913748 T UFD (NIL) -9 NIL 2913862) (-1192 2912377 2912423 2912518 "UFD-" 2912523 NIL UFD- (NIL T) -8 NIL NIL) (-1191 2911459 2911642 2911858 "UDVO" 2912183 T UDVO (NIL) -7 NIL NIL) (-1190 2909275 2909684 2910155 "UDPO" 2911023 NIL UDPO (NIL T) -7 NIL NIL) (-1189 2909208 2909213 2909243 "TYPE" 2909248 T TYPE (NIL) -9 NIL NIL) (-1188 2908995 2909163 2909194 "TYPEAST" 2909199 T TYPEAST (NIL) -8 NIL NIL) (-1187 2907966 2908168 2908408 "TWOFACT" 2908789 NIL TWOFACT (NIL T) -7 NIL NIL) (-1186 2906904 2907241 2907504 "TUPLE" 2907738 NIL TUPLE (NIL T) -8 NIL NIL) (-1185 2904595 2905114 2905653 "TUBETOOL" 2906387 T TUBETOOL (NIL) -7 NIL NIL) (-1184 2903444 2903649 2903890 "TUBE" 2904388 NIL TUBE (NIL T) -8 NIL NIL) (-1183 2898208 2902416 2902699 "TS" 2903196 NIL TS (NIL T) -8 NIL NIL) (-1182 2886875 2890967 2891064 "TSETCAT" 2896333 NIL TSETCAT (NIL T T T T) -9 NIL 2897864) (-1181 2881609 2883207 2885098 "TSETCAT-" 2885103 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1180 2875872 2876718 2877660 "TRMANIP" 2880745 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1179 2875313 2875376 2875539 "TRIMAT" 2875804 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1178 2873109 2873346 2873710 "TRIGMNIP" 2875062 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1177 2872629 2872742 2872772 "TRIGCAT" 2872985 T TRIGCAT (NIL) -9 NIL NIL) (-1176 2872298 2872377 2872518 "TRIGCAT-" 2872523 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1175 2869197 2871158 2871438 "TREE" 2872053 NIL TREE (NIL T) -8 NIL NIL) (-1174 2868471 2868999 2869029 "TRANFUN" 2869064 T TRANFUN (NIL) -9 NIL 2869130) (-1173 2867750 2867941 2868221 "TRANFUN-" 2868226 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1172 2867554 2867586 2867647 "TOPSP" 2867711 T TOPSP (NIL) -7 NIL NIL) (-1171 2866902 2867017 2867171 "TOOLSIGN" 2867435 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1170 2865563 2866079 2866318 "TEXTFILE" 2866685 T TEXTFILE (NIL) -8 NIL NIL) (-1169 2863428 2863942 2864380 "TEX" 2865147 T TEX (NIL) -8 NIL NIL) (-1168 2863209 2863240 2863312 "TEX1" 2863391 NIL TEX1 (NIL T) -7 NIL NIL) (-1167 2862857 2862920 2863010 "TEMUTL" 2863141 T TEMUTL (NIL) -7 NIL NIL) (-1166 2861011 2861291 2861616 "TBCMPPK" 2862580 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1165 2852899 2859171 2859227 "TBAGG" 2859627 NIL TBAGG (NIL T T) -9 NIL 2859838) (-1164 2847969 2849457 2851211 "TBAGG-" 2851216 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1163 2847353 2847460 2847605 "TANEXP" 2847858 NIL TANEXP (NIL T) -7 NIL NIL) (-1162 2840854 2847210 2847303 "TABLE" 2847308 NIL TABLE (NIL T T) -8 NIL NIL) (-1161 2840266 2840365 2840503 "TABLEAU" 2840751 NIL TABLEAU (NIL T) -8 NIL NIL) (-1160 2834874 2836094 2837342 "TABLBUMP" 2839052 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1159 2834302 2834402 2834530 "SYSTEM" 2834768 T SYSTEM (NIL) -7 NIL NIL) (-1158 2830765 2831460 2832243 "SYSSOLP" 2833553 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1157 2827143 2828054 2828756 "SYNTAX" 2830085 T SYNTAX (NIL) -8 NIL NIL) (-1156 2824301 2824903 2825535 "SYMTAB" 2826533 T SYMTAB (NIL) -8 NIL NIL) (-1155 2819550 2820452 2821435 "SYMS" 2823340 T SYMS (NIL) -8 NIL NIL) (-1154 2816822 2819008 2819238 "SYMPOLY" 2819355 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1153 2816339 2816414 2816537 "SYMFUNC" 2816734 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1152 2812316 2813576 2814398 "SYMBOL" 2815539 T SYMBOL (NIL) -8 NIL NIL) (-1151 2805855 2807544 2809264 "SWITCH" 2810618 T SWITCH (NIL) -8 NIL NIL) (-1150 2799125 2804676 2804979 "SUTS" 2805610 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1149 2791094 2798240 2798522 "SUPXS" 2798901 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1148 2782623 2790712 2790838 "SUP" 2791003 NIL SUP (NIL T) -8 NIL NIL) (-1147 2781782 2781909 2782126 "SUPFRACF" 2782491 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1146 2781403 2781462 2781575 "SUP2" 2781717 NIL SUP2 (NIL T T) -7 NIL NIL) (-1145 2779816 2780090 2780453 "SUMRF" 2781102 NIL SUMRF (NIL T) -7 NIL NIL) (-1144 2779130 2779196 2779395 "SUMFS" 2779737 NIL SUMFS (NIL T T) -7 NIL NIL) (-1143 2763137 2778307 2778558 "SULS" 2778937 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1142 2762766 2762959 2763029 "SUCHTAST" 2763089 T SUCHTAST (NIL) -8 NIL NIL) (-1141 2762088 2762291 2762431 "SUCH" 2762674 NIL SUCH (NIL T T) -8 NIL NIL) (-1140 2755982 2756994 2757953 "SUBSPACE" 2761176 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1139 2755412 2755502 2755666 "SUBRESP" 2755870 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1138 2748781 2750077 2751388 "STTF" 2754148 NIL STTF (NIL T) -7 NIL NIL) (-1137 2742954 2744074 2745221 "STTFNC" 2747681 NIL STTFNC (NIL T) -7 NIL NIL) (-1136 2734269 2736136 2737930 "STTAYLOR" 2741195 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1135 2727513 2734133 2734216 "STRTBL" 2734221 NIL STRTBL (NIL T) -8 NIL NIL) (-1134 2722904 2727468 2727499 "STRING" 2727504 T STRING (NIL) -8 NIL NIL) (-1133 2717792 2722277 2722307 "STRICAT" 2722366 T STRICAT (NIL) -9 NIL 2722428) (-1132 2710505 2715315 2715935 "STREAM" 2717207 NIL STREAM (NIL T) -8 NIL NIL) (-1131 2710015 2710092 2710236 "STREAM3" 2710422 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1130 2708997 2709180 2709415 "STREAM2" 2709828 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1129 2708685 2708737 2708830 "STREAM1" 2708939 NIL STREAM1 (NIL T) -7 NIL NIL) (-1128 2707701 2707882 2708113 "STINPROD" 2708501 NIL STINPROD (NIL T) -7 NIL NIL) (-1127 2707279 2707463 2707493 "STEP" 2707573 T STEP (NIL) -9 NIL 2707651) (-1126 2700822 2707178 2707255 "STBL" 2707260 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1125 2695997 2700044 2700087 "STAGG" 2700240 NIL STAGG (NIL T) -9 NIL 2700329) (-1124 2693699 2694301 2695173 "STAGG-" 2695178 NIL STAGG- (NIL T T) -8 NIL NIL) (-1123 2691894 2693469 2693561 "STACK" 2693642 NIL STACK (NIL T) -8 NIL NIL) (-1122 2684619 2690035 2690491 "SREGSET" 2691524 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1121 2677045 2678413 2679926 "SRDCMPK" 2683225 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1120 2670012 2674485 2674515 "SRAGG" 2675818 T SRAGG (NIL) -9 NIL 2676426) (-1119 2669029 2669284 2669663 "SRAGG-" 2669668 NIL SRAGG- (NIL T) -8 NIL NIL) (-1118 2663524 2667976 2668397 "SQMATRIX" 2668655 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1117 2657276 2660244 2660970 "SPLTREE" 2662870 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1116 2653266 2653932 2654578 "SPLNODE" 2656702 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1115 2652313 2652546 2652576 "SPFCAT" 2653020 T SPFCAT (NIL) -9 NIL NIL) (-1114 2651050 2651260 2651524 "SPECOUT" 2652071 T SPECOUT (NIL) -7 NIL NIL) (-1113 2642739 2644483 2644513 "SPADXPT" 2648905 T SPADXPT (NIL) -9 NIL 2650939) (-1112 2642500 2642540 2642609 "SPADPRSR" 2642692 T SPADPRSR (NIL) -7 NIL NIL) (-1111 2640683 2642455 2642486 "SPADAST" 2642491 T SPADAST (NIL) -8 NIL NIL) (-1110 2632654 2634401 2634444 "SPACEC" 2638817 NIL SPACEC (NIL T) -9 NIL 2640633) (-1109 2630825 2632586 2632635 "SPACE3" 2632640 NIL SPACE3 (NIL T) -8 NIL NIL) (-1108 2629577 2629748 2630039 "SORTPAK" 2630630 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1107 2627627 2627930 2628349 "SOLVETRA" 2629241 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1106 2626638 2626860 2627134 "SOLVESER" 2627400 NIL SOLVESER (NIL T) -7 NIL NIL) (-1105 2621858 2622739 2623741 "SOLVERAD" 2625690 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1104 2617673 2618282 2619011 "SOLVEFOR" 2621225 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1103 2611970 2617022 2617119 "SNTSCAT" 2617124 NIL SNTSCAT (NIL T T T T) -9 NIL 2617194) (-1102 2606113 2610293 2610684 "SMTS" 2611660 NIL SMTS (NIL T T T) -8 NIL NIL) (-1101 2600563 2606001 2606078 "SMP" 2606083 NIL SMP (NIL T T) -8 NIL NIL) (-1100 2598722 2599023 2599421 "SMITH" 2600260 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1099 2591705 2595860 2595963 "SMATCAT" 2597314 NIL SMATCAT (NIL NIL T T T) -9 NIL 2597864) (-1098 2588645 2589468 2590646 "SMATCAT-" 2590651 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1097 2586358 2587881 2587924 "SKAGG" 2588185 NIL SKAGG (NIL T) -9 NIL 2588320) (-1096 2582474 2585462 2585740 "SINT" 2586102 T SINT (NIL) -8 NIL NIL) (-1095 2582246 2582284 2582350 "SIMPAN" 2582430 T SIMPAN (NIL) -7 NIL NIL) (-1094 2581553 2581781 2581921 "SIG" 2582128 T SIG (NIL) -8 NIL NIL) (-1093 2580391 2580612 2580887 "SIGNRF" 2581312 NIL SIGNRF (NIL T) -7 NIL NIL) (-1092 2579196 2579347 2579638 "SIGNEF" 2580220 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1091 2578529 2578779 2578903 "SIGAST" 2579094 T SIGAST (NIL) -8 NIL NIL) (-1090 2576219 2576673 2577179 "SHP" 2578070 NIL SHP (NIL T NIL) -7 NIL NIL) (-1089 2570125 2576120 2576196 "SHDP" 2576201 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1088 2569724 2569890 2569920 "SGROUP" 2570013 T SGROUP (NIL) -9 NIL 2570075) (-1087 2569582 2569608 2569681 "SGROUP-" 2569686 NIL SGROUP- (NIL T) -8 NIL NIL) (-1086 2566418 2567115 2567838 "SGCF" 2568881 T SGCF (NIL) -7 NIL NIL) (-1085 2560813 2565865 2565962 "SFRTCAT" 2565967 NIL SFRTCAT (NIL T T T T) -9 NIL 2566006) (-1084 2554237 2555252 2556388 "SFRGCD" 2559796 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1083 2547365 2548436 2549622 "SFQCMPK" 2553170 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1082 2546987 2547076 2547186 "SFORT" 2547306 NIL SFORT (NIL T T) -8 NIL NIL) (-1081 2546132 2546827 2546948 "SEXOF" 2546953 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1080 2545266 2546013 2546081 "SEX" 2546086 T SEX (NIL) -8 NIL NIL) (-1079 2540042 2540731 2540826 "SEXCAT" 2544597 NIL SEXCAT (NIL T T T T T) -9 NIL 2545216) (-1078 2537222 2539976 2540024 "SET" 2540029 NIL SET (NIL T) -8 NIL NIL) (-1077 2535473 2535935 2536240 "SETMN" 2536963 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1076 2535079 2535205 2535235 "SETCAT" 2535352 T SETCAT (NIL) -9 NIL 2535437) (-1075 2534859 2534911 2535010 "SETCAT-" 2535015 NIL SETCAT- (NIL T) -8 NIL NIL) (-1074 2531246 2533320 2533363 "SETAGG" 2534233 NIL SETAGG (NIL T) -9 NIL 2534573) (-1073 2530704 2530820 2531057 "SETAGG-" 2531062 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1072 2530174 2530400 2530501 "SEQAST" 2530625 T SEQAST (NIL) -8 NIL NIL) (-1071 2529378 2529671 2529732 "SEGXCAT" 2530018 NIL SEGXCAT (NIL T T) -9 NIL 2530138) (-1070 2528434 2529044 2529226 "SEG" 2529231 NIL SEG (NIL T) -8 NIL NIL) (-1069 2527341 2527554 2527597 "SEGCAT" 2528179 NIL SEGCAT (NIL T) -9 NIL 2528417) (-1068 2526390 2526720 2526920 "SEGBIND" 2527176 NIL SEGBIND (NIL T) -8 NIL NIL) (-1067 2526011 2526070 2526183 "SEGBIND2" 2526325 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1066 2525612 2525812 2525889 "SEGAST" 2525956 T SEGAST (NIL) -8 NIL NIL) (-1065 2524831 2524957 2525161 "SEG2" 2525456 NIL SEG2 (NIL T T) -7 NIL NIL) (-1064 2524268 2524766 2524813 "SDVAR" 2524818 NIL SDVAR (NIL T) -8 NIL NIL) (-1063 2516558 2524038 2524168 "SDPOL" 2524173 NIL SDPOL (NIL T) -8 NIL NIL) (-1062 2515151 2515417 2515736 "SCPKG" 2516273 NIL SCPKG (NIL T) -7 NIL NIL) (-1061 2514287 2514467 2514667 "SCOPE" 2514973 T SCOPE (NIL) -8 NIL NIL) (-1060 2513508 2513641 2513820 "SCACHE" 2514142 NIL SCACHE (NIL T) -7 NIL NIL) (-1059 2513217 2513377 2513407 "SASTCAT" 2513412 T SASTCAT (NIL) -9 NIL 2513425) (-1058 2512656 2512977 2513062 "SAOS" 2513154 T SAOS (NIL) -8 NIL NIL) (-1057 2512221 2512256 2512429 "SAERFFC" 2512615 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1056 2506195 2512118 2512198 "SAE" 2512203 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1055 2505788 2505823 2505982 "SAEFACT" 2506154 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1054 2504109 2504423 2504824 "RURPK" 2505454 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1053 2502745 2503024 2503336 "RULESET" 2503943 NIL RULESET (NIL T T T) -8 NIL NIL) (-1052 2499932 2500435 2500900 "RULE" 2502426 NIL RULE (NIL T T T) -8 NIL NIL) (-1051 2499571 2499726 2499809 "RULECOLD" 2499884 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1050 2499069 2499288 2499382 "RSTRCAST" 2499499 T RSTRCAST (NIL) -8 NIL NIL) (-1049 2493918 2494712 2495632 "RSETGCD" 2498268 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1048 2483175 2488227 2488324 "RSETCAT" 2492443 NIL RSETCAT (NIL T T T T) -9 NIL 2493540) (-1047 2481102 2481641 2482465 "RSETCAT-" 2482470 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1046 2473489 2474864 2476384 "RSDCMPK" 2479701 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1045 2471494 2471935 2472009 "RRCC" 2473095 NIL RRCC (NIL T T) -9 NIL 2473439) (-1044 2470845 2471019 2471298 "RRCC-" 2471303 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1043 2470315 2470541 2470642 "RPTAST" 2470766 T RPTAST (NIL) -8 NIL NIL) (-1042 2444543 2454128 2454195 "RPOLCAT" 2464859 NIL RPOLCAT (NIL T T T) -9 NIL 2468018) (-1041 2436043 2438381 2441503 "RPOLCAT-" 2441508 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1040 2427090 2434254 2434736 "ROUTINE" 2435583 T ROUTINE (NIL) -8 NIL NIL) (-1039 2423848 2426641 2426790 "ROMAN" 2426963 T ROMAN (NIL) -8 NIL NIL) (-1038 2422123 2422708 2422968 "ROIRC" 2423653 NIL ROIRC (NIL T T) -8 NIL NIL) (-1037 2418572 2420811 2420841 "RNS" 2421145 T RNS (NIL) -9 NIL 2421418) (-1036 2417081 2417464 2417998 "RNS-" 2418073 NIL RNS- (NIL T) -8 NIL NIL) (-1035 2416530 2416912 2416942 "RNG" 2416947 T RNG (NIL) -9 NIL 2416968) (-1034 2415922 2416284 2416327 "RMODULE" 2416389 NIL RMODULE (NIL T) -9 NIL 2416431) (-1033 2414758 2414852 2415188 "RMCAT2" 2415823 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1032 2411463 2413932 2414257 "RMATRIX" 2414492 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1031 2404405 2406639 2406754 "RMATCAT" 2410113 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2411095) (-1030 2403780 2403927 2404234 "RMATCAT-" 2404239 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1029 2403347 2403422 2403550 "RINTERP" 2403699 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1028 2402435 2402955 2402985 "RING" 2403097 T RING (NIL) -9 NIL 2403192) (-1027 2402227 2402271 2402368 "RING-" 2402373 NIL RING- (NIL T) -8 NIL NIL) (-1026 2401068 2401305 2401563 "RIDIST" 2401991 T RIDIST (NIL) -7 NIL NIL) (-1025 2392384 2400536 2400742 "RGCHAIN" 2400916 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1024 2391760 2392140 2392181 "RGBCSPC" 2392239 NIL RGBCSPC (NIL T) -9 NIL 2392291) (-1023 2390944 2391299 2391340 "RGBCMDL" 2391572 NIL RGBCMDL (NIL T) -9 NIL 2391686) (-1022 2387938 2388552 2389222 "RF" 2390308 NIL RF (NIL T) -7 NIL NIL) (-1021 2387584 2387647 2387750 "RFFACTOR" 2387869 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1020 2387309 2387344 2387441 "RFFACT" 2387543 NIL RFFACT (NIL T) -7 NIL NIL) (-1019 2385426 2385790 2386172 "RFDIST" 2386949 T RFDIST (NIL) -7 NIL NIL) (-1018 2384879 2384971 2385134 "RETSOL" 2385328 NIL RETSOL (NIL T T) -7 NIL NIL) (-1017 2384467 2384547 2384590 "RETRACT" 2384783 NIL RETRACT (NIL T) -9 NIL NIL) (-1016 2384316 2384341 2384428 "RETRACT-" 2384433 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1015 2383945 2384138 2384208 "RETAST" 2384268 T RETAST (NIL) -8 NIL NIL) (-1014 2376799 2383598 2383725 "RESULT" 2383840 T RESULT (NIL) -8 NIL NIL) (-1013 2375425 2376068 2376267 "RESRING" 2376702 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1012 2375061 2375110 2375208 "RESLATC" 2375362 NIL RESLATC (NIL T) -7 NIL NIL) (-1011 2374767 2374801 2374908 "REPSQ" 2375020 NIL REPSQ (NIL T) -7 NIL NIL) (-1010 2372189 2372769 2373371 "REP" 2374187 T REP (NIL) -7 NIL NIL) (-1009 2371887 2371921 2372032 "REPDB" 2372148 NIL REPDB (NIL T) -7 NIL NIL) (-1008 2365797 2367176 2368399 "REP2" 2370699 NIL REP2 (NIL T) -7 NIL NIL) (-1007 2362174 2362855 2363663 "REP1" 2365024 NIL REP1 (NIL T) -7 NIL NIL) (-1006 2354900 2360315 2360771 "REGSET" 2361804 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1005 2353713 2354048 2354298 "REF" 2354685 NIL REF (NIL T) -8 NIL NIL) (-1004 2353090 2353193 2353360 "REDORDER" 2353597 NIL REDORDER (NIL T T) -7 NIL NIL) (-1003 2349097 2352305 2352531 "RECLOS" 2352919 NIL RECLOS (NIL T) -8 NIL NIL) (-1002 2348149 2348330 2348545 "REALSOLV" 2348904 T REALSOLV (NIL) -7 NIL NIL) (-1001 2347995 2348036 2348066 "REAL" 2348071 T REAL (NIL) -9 NIL 2348106) (-1000 2344478 2345280 2346164 "REAL0Q" 2347160 NIL REAL0Q (NIL T) -7 NIL NIL) (-999 2340089 2341077 2342136 "REAL0" 2343459 NIL REAL0 (NIL T) -7 NIL NIL) (-998 2339591 2339810 2339902 "RDUCEAST" 2340017 T RDUCEAST (NIL) -8 NIL NIL) (-997 2338999 2339071 2339276 "RDIV" 2339513 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-996 2338072 2338246 2338457 "RDIST" 2338821 NIL RDIST (NIL T) -7 NIL NIL) (-995 2336673 2336960 2337330 "RDETRS" 2337780 NIL RDETRS (NIL T T) -7 NIL NIL) (-994 2334490 2334944 2335480 "RDETR" 2336215 NIL RDETR (NIL T T) -7 NIL NIL) (-993 2333104 2333382 2333784 "RDEEFS" 2334206 NIL RDEEFS (NIL T T) -7 NIL NIL) (-992 2331602 2331908 2332338 "RDEEF" 2332792 NIL RDEEF (NIL T T) -7 NIL NIL) (-991 2325939 2328810 2328838 "RCFIELD" 2330115 T RCFIELD (NIL) -9 NIL 2330845) (-990 2324008 2324512 2325205 "RCFIELD-" 2325278 NIL RCFIELD- (NIL T) -8 NIL NIL) (-989 2320339 2322124 2322165 "RCAGG" 2323236 NIL RCAGG (NIL T) -9 NIL 2323701) (-988 2319970 2320064 2320224 "RCAGG-" 2320229 NIL RCAGG- (NIL T T) -8 NIL NIL) (-987 2319310 2319422 2319585 "RATRET" 2319854 NIL RATRET (NIL T) -7 NIL NIL) (-986 2318867 2318934 2319053 "RATFACT" 2319238 NIL RATFACT (NIL T) -7 NIL NIL) (-985 2318182 2318302 2318452 "RANDSRC" 2318737 T RANDSRC (NIL) -7 NIL NIL) (-984 2317919 2317963 2318034 "RADUTIL" 2318131 T RADUTIL (NIL) -7 NIL NIL) (-983 2310982 2316662 2316979 "RADIX" 2317634 NIL RADIX (NIL NIL) -8 NIL NIL) (-982 2302638 2310826 2310954 "RADFF" 2310959 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-981 2302290 2302365 2302393 "RADCAT" 2302550 T RADCAT (NIL) -9 NIL NIL) (-980 2302075 2302123 2302220 "RADCAT-" 2302225 NIL RADCAT- (NIL T) -8 NIL NIL) (-979 2300226 2301850 2301939 "QUEUE" 2302019 NIL QUEUE (NIL T) -8 NIL NIL) (-978 2296802 2300163 2300208 "QUAT" 2300213 NIL QUAT (NIL T) -8 NIL NIL) (-977 2296440 2296483 2296610 "QUATCT2" 2296753 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-976 2290300 2293601 2293641 "QUATCAT" 2294421 NIL QUATCAT (NIL T) -9 NIL 2295187) (-975 2286444 2287481 2288868 "QUATCAT-" 2288962 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-974 2283964 2285528 2285569 "QUAGG" 2285944 NIL QUAGG (NIL T) -9 NIL 2286119) (-973 2283596 2283789 2283857 "QQUTAST" 2283916 T QQUTAST (NIL) -8 NIL NIL) (-972 2282521 2282994 2283166 "QFORM" 2283468 NIL QFORM (NIL NIL T) -8 NIL NIL) (-971 2273846 2279051 2279091 "QFCAT" 2279749 NIL QFCAT (NIL T) -9 NIL 2280750) (-970 2269418 2270619 2272210 "QFCAT-" 2272304 NIL QFCAT- (NIL T T) -8 NIL NIL) (-969 2269056 2269099 2269226 "QFCAT2" 2269369 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-968 2268516 2268626 2268756 "QEQUAT" 2268946 T QEQUAT (NIL) -8 NIL NIL) (-967 2261664 2262735 2263919 "QCMPACK" 2267449 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-966 2259240 2259661 2260089 "QALGSET" 2261319 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-965 2258485 2258659 2258891 "QALGSET2" 2259060 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-964 2257176 2257399 2257716 "PWFFINTB" 2258258 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-963 2255358 2255526 2255880 "PUSHVAR" 2256990 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-962 2251276 2252330 2252371 "PTRANFN" 2254255 NIL PTRANFN (NIL T) -9 NIL NIL) (-961 2249678 2249969 2250291 "PTPACK" 2250987 NIL PTPACK (NIL T) -7 NIL NIL) (-960 2249310 2249367 2249476 "PTFUNC2" 2249615 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-959 2243776 2248121 2248162 "PTCAT" 2248535 NIL PTCAT (NIL T) -9 NIL 2248697) (-958 2243434 2243469 2243593 "PSQFR" 2243735 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-957 2242029 2242327 2242661 "PSEUDLIN" 2243132 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-956 2228798 2231163 2233487 "PSETPK" 2239789 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-955 2221842 2224556 2224652 "PSETCAT" 2227673 NIL PSETCAT (NIL T T T T) -9 NIL 2228487) (-954 2219678 2220312 2221133 "PSETCAT-" 2221138 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-953 2219027 2219192 2219220 "PSCURVE" 2219488 T PSCURVE (NIL) -9 NIL 2219655) (-952 2215508 2216990 2217055 "PSCAT" 2217899 NIL PSCAT (NIL T T T) -9 NIL 2218139) (-951 2214571 2214787 2215187 "PSCAT-" 2215192 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-950 2213223 2213856 2214070 "PRTITION" 2214377 T PRTITION (NIL) -8 NIL NIL) (-949 2212725 2212944 2213036 "PRTDAST" 2213151 T PRTDAST (NIL) -8 NIL NIL) (-948 2201823 2204029 2206217 "PRS" 2210587 NIL PRS (NIL T T) -7 NIL NIL) (-947 2199681 2201173 2201213 "PRQAGG" 2201396 NIL PRQAGG (NIL T) -9 NIL 2201498) (-946 2199067 2199296 2199324 "PROPLOG" 2199509 T PROPLOG (NIL) -9 NIL 2199631) (-945 2196237 2196881 2197345 "PROPFRML" 2198635 NIL PROPFRML (NIL T) -8 NIL NIL) (-944 2195697 2195807 2195937 "PROPERTY" 2196127 T PROPERTY (NIL) -8 NIL NIL) (-943 2189782 2193863 2194683 "PRODUCT" 2194923 NIL PRODUCT (NIL T T) -8 NIL NIL) (-942 2187095 2189240 2189474 "PR" 2189593 NIL PR (NIL T T) -8 NIL NIL) (-941 2186891 2186923 2186982 "PRINT" 2187056 T PRINT (NIL) -7 NIL NIL) (-940 2186231 2186348 2186500 "PRIMES" 2186771 NIL PRIMES (NIL T) -7 NIL NIL) (-939 2184296 2184697 2185163 "PRIMELT" 2185810 NIL PRIMELT (NIL T) -7 NIL NIL) (-938 2184025 2184074 2184102 "PRIMCAT" 2184226 T PRIMCAT (NIL) -9 NIL NIL) (-937 2180186 2183963 2184008 "PRIMARR" 2184013 NIL PRIMARR (NIL T) -8 NIL NIL) (-936 2179193 2179371 2179599 "PRIMARR2" 2180004 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-935 2178836 2178892 2179003 "PREASSOC" 2179131 NIL PREASSOC (NIL T T) -7 NIL NIL) (-934 2178311 2178444 2178472 "PPCURVE" 2178677 T PPCURVE (NIL) -9 NIL 2178813) (-933 2177933 2178106 2178189 "PORTNUM" 2178248 T PORTNUM (NIL) -8 NIL NIL) (-932 2175292 2175691 2176283 "POLYROOT" 2177514 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-931 2169237 2174896 2175056 "POLY" 2175165 NIL POLY (NIL T) -8 NIL NIL) (-930 2168620 2168678 2168912 "POLYLIFT" 2169173 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-929 2164895 2165344 2165973 "POLYCATQ" 2168165 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-928 2151934 2157290 2157355 "POLYCAT" 2160869 NIL POLYCAT (NIL T T T) -9 NIL 2162797) (-927 2145384 2147245 2149629 "POLYCAT-" 2149634 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-926 2144971 2145039 2145159 "POLY2UP" 2145310 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-925 2144603 2144660 2144769 "POLY2" 2144908 NIL POLY2 (NIL T T) -7 NIL NIL) (-924 2143288 2143527 2143803 "POLUTIL" 2144377 NIL POLUTIL (NIL T T) -7 NIL NIL) (-923 2141643 2141920 2142251 "POLTOPOL" 2143010 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-922 2137161 2141579 2141625 "POINT" 2141630 NIL POINT (NIL T) -8 NIL NIL) (-921 2135348 2135705 2136080 "PNTHEORY" 2136806 T PNTHEORY (NIL) -7 NIL NIL) (-920 2133767 2134064 2134476 "PMTOOLS" 2135046 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-919 2133360 2133438 2133555 "PMSYM" 2133683 NIL PMSYM (NIL T) -7 NIL NIL) (-918 2132870 2132939 2133113 "PMQFCAT" 2133285 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-917 2132225 2132335 2132491 "PMPRED" 2132747 NIL PMPRED (NIL T) -7 NIL NIL) (-916 2131621 2131707 2131868 "PMPREDFS" 2132126 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-915 2130264 2130472 2130857 "PMPLCAT" 2131383 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-914 2129796 2129875 2130027 "PMLSAGG" 2130179 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-913 2129271 2129347 2129528 "PMKERNEL" 2129714 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-912 2128888 2128963 2129076 "PMINS" 2129190 NIL PMINS (NIL T) -7 NIL NIL) (-911 2128316 2128385 2128601 "PMFS" 2128813 NIL PMFS (NIL T T T) -7 NIL NIL) (-910 2127544 2127662 2127867 "PMDOWN" 2128193 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-909 2126707 2126866 2127048 "PMASS" 2127382 T PMASS (NIL) -7 NIL NIL) (-908 2125981 2126092 2126255 "PMASSFS" 2126593 NIL PMASSFS (NIL T T) -7 NIL NIL) (-907 2125636 2125704 2125798 "PLOTTOOL" 2125907 T PLOTTOOL (NIL) -7 NIL NIL) (-906 2120258 2121447 2122595 "PLOT" 2124508 T PLOT (NIL) -8 NIL NIL) (-905 2116072 2117106 2118027 "PLOT3D" 2119357 T PLOT3D (NIL) -8 NIL NIL) (-904 2114984 2115161 2115396 "PLOT1" 2115876 NIL PLOT1 (NIL T) -7 NIL NIL) (-903 2090378 2095050 2099901 "PLEQN" 2110250 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-902 2089696 2089818 2089998 "PINTERP" 2090243 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-901 2089389 2089436 2089539 "PINTERPA" 2089643 NIL PINTERPA (NIL T T) -7 NIL NIL) (-900 2088674 2089195 2089282 "PI" 2089322 T PI (NIL) -8 NIL NIL) (-899 2087106 2088047 2088075 "PID" 2088257 T PID (NIL) -9 NIL 2088391) (-898 2086831 2086868 2086956 "PICOERCE" 2087063 NIL PICOERCE (NIL T) -7 NIL NIL) (-897 2086151 2086290 2086466 "PGROEB" 2086687 NIL PGROEB (NIL T) -7 NIL NIL) (-896 2081738 2082552 2083457 "PGE" 2085266 T PGE (NIL) -7 NIL NIL) (-895 2079862 2080108 2080474 "PGCD" 2081455 NIL PGCD (NIL T T T T) -7 NIL NIL) (-894 2079200 2079303 2079464 "PFRPAC" 2079746 NIL PFRPAC (NIL T) -7 NIL NIL) (-893 2075880 2077748 2078101 "PFR" 2078879 NIL PFR (NIL T) -8 NIL NIL) (-892 2074269 2074513 2074838 "PFOTOOLS" 2075627 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-891 2072802 2073041 2073392 "PFOQ" 2074026 NIL PFOQ (NIL T T T) -7 NIL NIL) (-890 2071275 2071487 2071850 "PFO" 2072586 NIL PFO (NIL T T T T T) -7 NIL NIL) (-889 2067863 2071164 2071233 "PF" 2071238 NIL PF (NIL NIL) -8 NIL NIL) (-888 2065332 2066569 2066597 "PFECAT" 2067182 T PFECAT (NIL) -9 NIL 2067566) (-887 2064777 2064931 2065145 "PFECAT-" 2065150 NIL PFECAT- (NIL T) -8 NIL NIL) (-886 2063381 2063632 2063933 "PFBRU" 2064526 NIL PFBRU (NIL T T) -7 NIL NIL) (-885 2061248 2061599 2062031 "PFBR" 2063032 NIL PFBR (NIL T T T T) -7 NIL NIL) (-884 2057164 2058624 2059300 "PERM" 2060605 NIL PERM (NIL T) -8 NIL NIL) (-883 2052430 2053371 2054241 "PERMGRP" 2056327 NIL PERMGRP (NIL T) -8 NIL NIL) (-882 2050562 2051493 2051534 "PERMCAT" 2051980 NIL PERMCAT (NIL T) -9 NIL 2052285) (-881 2050215 2050256 2050380 "PERMAN" 2050515 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-880 2047655 2049784 2049915 "PENDTREE" 2050117 NIL PENDTREE (NIL T) -8 NIL NIL) (-879 2045768 2046502 2046543 "PDRING" 2047200 NIL PDRING (NIL T) -9 NIL 2047486) (-878 2044871 2045089 2045451 "PDRING-" 2045456 NIL PDRING- (NIL T T) -8 NIL NIL) (-877 2042012 2042763 2043454 "PDEPROB" 2044200 T PDEPROB (NIL) -8 NIL NIL) (-876 2039559 2040061 2040616 "PDEPACK" 2041477 T PDEPACK (NIL) -7 NIL NIL) (-875 2038471 2038661 2038912 "PDECOMP" 2039358 NIL PDECOMP (NIL T T) -7 NIL NIL) (-874 2036076 2036893 2036921 "PDECAT" 2037708 T PDECAT (NIL) -9 NIL 2038421) (-873 2035827 2035860 2035950 "PCOMP" 2036037 NIL PCOMP (NIL T T) -7 NIL NIL) (-872 2034032 2034628 2034925 "PBWLB" 2035556 NIL PBWLB (NIL T) -8 NIL NIL) (-871 2026536 2028105 2029443 "PATTERN" 2032715 NIL PATTERN (NIL T) -8 NIL NIL) (-870 2026168 2026225 2026334 "PATTERN2" 2026473 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-869 2023925 2024313 2024770 "PATTERN1" 2025757 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-868 2021320 2021874 2022355 "PATRES" 2023490 NIL PATRES (NIL T T) -8 NIL NIL) (-867 2020884 2020951 2021083 "PATRES2" 2021247 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-866 2018767 2019172 2019579 "PATMATCH" 2020551 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-865 2018303 2018486 2018527 "PATMAB" 2018634 NIL PATMAB (NIL T) -9 NIL 2018717) (-864 2016848 2017157 2017415 "PATLRES" 2018108 NIL PATLRES (NIL T T T) -8 NIL NIL) (-863 2016394 2016517 2016558 "PATAB" 2016563 NIL PATAB (NIL T) -9 NIL 2016735) (-862 2013875 2014407 2014980 "PARTPERM" 2015841 T PARTPERM (NIL) -7 NIL NIL) (-861 2013496 2013559 2013661 "PARSURF" 2013806 NIL PARSURF (NIL T) -8 NIL NIL) (-860 2013128 2013185 2013294 "PARSU2" 2013433 NIL PARSU2 (NIL T T) -7 NIL NIL) (-859 2012892 2012932 2012999 "PARSER" 2013081 T PARSER (NIL) -7 NIL NIL) (-858 2012513 2012576 2012678 "PARSCURV" 2012823 NIL PARSCURV (NIL T) -8 NIL NIL) (-857 2012145 2012202 2012311 "PARSC2" 2012450 NIL PARSC2 (NIL T T) -7 NIL NIL) (-856 2011784 2011842 2011939 "PARPCURV" 2012081 NIL PARPCURV (NIL T) -8 NIL NIL) (-855 2011416 2011473 2011582 "PARPC2" 2011721 NIL PARPC2 (NIL T T) -7 NIL NIL) (-854 2010936 2011022 2011141 "PAN2EXPR" 2011317 T PAN2EXPR (NIL) -7 NIL NIL) (-853 2009742 2010057 2010285 "PALETTE" 2010728 T PALETTE (NIL) -8 NIL NIL) (-852 2008210 2008747 2009107 "PAIR" 2009428 NIL PAIR (NIL T T) -8 NIL NIL) (-851 2002116 2007469 2007663 "PADICRC" 2008065 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-850 1995380 2001462 2001646 "PADICRAT" 2001964 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-849 1993730 1995317 1995362 "PADIC" 1995367 NIL PADIC (NIL NIL) -8 NIL NIL) (-848 1990975 1992505 1992545 "PADICCT" 1993126 NIL PADICCT (NIL NIL) -9 NIL 1993408) (-847 1989932 1990132 1990400 "PADEPAC" 1990762 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-846 1989144 1989277 1989483 "PADE" 1989794 NIL PADE (NIL T T T) -7 NIL NIL) (-845 1987194 1987980 1988297 "OWP" 1988911 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-844 1986303 1986799 1986971 "OVAR" 1987062 NIL OVAR (NIL NIL) -8 NIL NIL) (-843 1985567 1985688 1985849 "OUT" 1986162 T OUT (NIL) -7 NIL NIL) (-842 1974474 1976676 1978876 "OUTFORM" 1983387 T OUTFORM (NIL) -8 NIL NIL) (-841 1973895 1974071 1974198 "OUTBFILE" 1974367 T OUTBFILE (NIL) -8 NIL NIL) (-840 1973532 1973615 1973643 "OUTBCON" 1973794 T OUTBCON (NIL) -9 NIL 1973879) (-839 1973372 1973407 1973483 "OUTBCON-" 1973488 NIL OUTBCON- (NIL T) -8 NIL NIL) (-838 1972780 1973101 1973190 "OSI" 1973303 T OSI (NIL) -8 NIL NIL) (-837 1972336 1972648 1972676 "OSGROUP" 1972681 T OSGROUP (NIL) -9 NIL 1972703) (-836 1971081 1971308 1971593 "ORTHPOL" 1972083 NIL ORTHPOL (NIL T) -7 NIL NIL) (-835 1968491 1970740 1970879 "OREUP" 1971024 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-834 1965929 1968182 1968309 "ORESUP" 1968433 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-833 1963457 1963957 1964518 "OREPCTO" 1965418 NIL OREPCTO (NIL T T) -7 NIL NIL) (-832 1957368 1959535 1959576 "OREPCAT" 1961924 NIL OREPCAT (NIL T) -9 NIL 1963028) (-831 1954515 1955297 1956355 "OREPCAT-" 1956360 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-830 1953692 1953964 1953992 "ORDSET" 1954301 T ORDSET (NIL) -9 NIL 1954465) (-829 1953211 1953333 1953526 "ORDSET-" 1953531 NIL ORDSET- (NIL T) -8 NIL NIL) (-828 1951865 1952622 1952650 "ORDRING" 1952852 T ORDRING (NIL) -9 NIL 1952977) (-827 1951510 1951604 1951748 "ORDRING-" 1951753 NIL ORDRING- (NIL T) -8 NIL NIL) (-826 1950916 1951353 1951381 "ORDMON" 1951386 T ORDMON (NIL) -9 NIL 1951407) (-825 1950078 1950225 1950420 "ORDFUNS" 1950765 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-824 1949589 1949948 1949976 "ORDFIN" 1949981 T ORDFIN (NIL) -9 NIL 1950002) (-823 1946181 1948175 1948584 "ORDCOMP" 1949213 NIL ORDCOMP (NIL T) -8 NIL NIL) (-822 1945447 1945574 1945760 "ORDCOMP2" 1946041 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-821 1941954 1942837 1943674 "OPTPROB" 1944630 T OPTPROB (NIL) -8 NIL NIL) (-820 1938756 1939395 1940099 "OPTPACK" 1941270 T OPTPACK (NIL) -7 NIL NIL) (-819 1936469 1937209 1937237 "OPTCAT" 1938056 T OPTCAT (NIL) -9 NIL 1938706) (-818 1936237 1936276 1936342 "OPQUERY" 1936423 T OPQUERY (NIL) -7 NIL NIL) (-817 1933403 1934548 1935052 "OP" 1935766 NIL OP (NIL T) -8 NIL NIL) (-816 1930248 1932200 1932569 "ONECOMP" 1933067 NIL ONECOMP (NIL T) -8 NIL NIL) (-815 1929553 1929668 1929842 "ONECOMP2" 1930120 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-814 1928972 1929078 1929208 "OMSERVER" 1929443 T OMSERVER (NIL) -7 NIL NIL) (-813 1925860 1928412 1928452 "OMSAGG" 1928513 NIL OMSAGG (NIL T) -9 NIL 1928577) (-812 1924483 1924746 1925028 "OMPKG" 1925598 T OMPKG (NIL) -7 NIL NIL) (-811 1923913 1924016 1924044 "OM" 1924343 T OM (NIL) -9 NIL NIL) (-810 1922495 1923462 1923631 "OMLO" 1923794 NIL OMLO (NIL T T) -8 NIL NIL) (-809 1921420 1921567 1921794 "OMEXPR" 1922321 NIL OMEXPR (NIL T) -7 NIL NIL) (-808 1920738 1920966 1921102 "OMERR" 1921304 T OMERR (NIL) -8 NIL NIL) (-807 1919916 1920159 1920319 "OMERRK" 1920598 T OMERRK (NIL) -8 NIL NIL) (-806 1919394 1919593 1919701 "OMENC" 1919828 T OMENC (NIL) -8 NIL NIL) (-805 1913289 1914474 1915645 "OMDEV" 1918243 T OMDEV (NIL) -8 NIL NIL) (-804 1912358 1912529 1912723 "OMCONN" 1913115 T OMCONN (NIL) -8 NIL NIL) (-803 1911014 1911956 1911984 "OINTDOM" 1911989 T OINTDOM (NIL) -9 NIL 1912010) (-802 1906820 1908004 1908720 "OFMONOID" 1910330 NIL OFMONOID (NIL T) -8 NIL NIL) (-801 1906258 1906757 1906802 "ODVAR" 1906807 NIL ODVAR (NIL T) -8 NIL NIL) (-800 1903468 1905755 1905940 "ODR" 1906133 NIL ODR (NIL T T NIL) -8 NIL NIL) (-799 1895812 1903244 1903370 "ODPOL" 1903375 NIL ODPOL (NIL T) -8 NIL NIL) (-798 1889688 1895684 1895789 "ODP" 1895794 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-797 1888454 1888669 1888944 "ODETOOLS" 1889462 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-796 1885423 1886079 1886795 "ODESYS" 1887787 NIL ODESYS (NIL T T) -7 NIL NIL) (-795 1880305 1881213 1882238 "ODERTRIC" 1884498 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-794 1879731 1879813 1880007 "ODERED" 1880217 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-793 1876619 1877167 1877844 "ODERAT" 1879154 NIL ODERAT (NIL T T) -7 NIL NIL) (-792 1873579 1874043 1874640 "ODEPRRIC" 1876148 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-791 1871448 1872017 1872526 "ODEPROB" 1873090 T ODEPROB (NIL) -8 NIL NIL) (-790 1867970 1868453 1869100 "ODEPRIM" 1870927 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-789 1867219 1867321 1867581 "ODEPAL" 1867862 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-788 1863381 1864172 1865036 "ODEPACK" 1866375 T ODEPACK (NIL) -7 NIL NIL) (-787 1862414 1862521 1862750 "ODEINT" 1863270 NIL ODEINT (NIL T T) -7 NIL NIL) (-786 1856515 1857940 1859387 "ODEIFTBL" 1860987 T ODEIFTBL (NIL) -8 NIL NIL) (-785 1851850 1852636 1853595 "ODEEF" 1855674 NIL ODEEF (NIL T T) -7 NIL NIL) (-784 1851185 1851274 1851504 "ODECONST" 1851755 NIL ODECONST (NIL T T T) -7 NIL NIL) (-783 1849336 1849971 1849999 "ODECAT" 1850604 T ODECAT (NIL) -9 NIL 1851135) (-782 1846243 1849048 1849167 "OCT" 1849249 NIL OCT (NIL T) -8 NIL NIL) (-781 1845881 1845924 1846051 "OCTCT2" 1846194 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-780 1840742 1843142 1843182 "OC" 1844279 NIL OC (NIL T) -9 NIL 1845137) (-779 1837969 1838717 1839707 "OC-" 1839801 NIL OC- (NIL T T) -8 NIL NIL) (-778 1837347 1837789 1837817 "OCAMON" 1837822 T OCAMON (NIL) -9 NIL 1837843) (-777 1836904 1837219 1837247 "OASGP" 1837252 T OASGP (NIL) -9 NIL 1837272) (-776 1836191 1836654 1836682 "OAMONS" 1836722 T OAMONS (NIL) -9 NIL 1836765) (-775 1835631 1836038 1836066 "OAMON" 1836071 T OAMON (NIL) -9 NIL 1836091) (-774 1834935 1835427 1835455 "OAGROUP" 1835460 T OAGROUP (NIL) -9 NIL 1835480) (-773 1834625 1834675 1834763 "NUMTUBE" 1834879 NIL NUMTUBE (NIL T) -7 NIL NIL) (-772 1828198 1829716 1831252 "NUMQUAD" 1833109 T NUMQUAD (NIL) -7 NIL NIL) (-771 1823954 1824942 1825967 "NUMODE" 1827193 T NUMODE (NIL) -7 NIL NIL) (-770 1821335 1822189 1822217 "NUMINT" 1823140 T NUMINT (NIL) -9 NIL 1823904) (-769 1820283 1820480 1820698 "NUMFMT" 1821137 T NUMFMT (NIL) -7 NIL NIL) (-768 1806642 1809587 1812119 "NUMERIC" 1817790 NIL NUMERIC (NIL T) -7 NIL NIL) (-767 1801039 1806091 1806186 "NTSCAT" 1806191 NIL NTSCAT (NIL T T T T) -9 NIL 1806230) (-766 1800233 1800398 1800591 "NTPOLFN" 1800878 NIL NTPOLFN (NIL T) -7 NIL NIL) (-765 1788073 1797058 1797870 "NSUP" 1799454 NIL NSUP (NIL T) -8 NIL NIL) (-764 1787705 1787762 1787871 "NSUP2" 1788010 NIL NSUP2 (NIL T T) -7 NIL NIL) (-763 1777702 1787479 1787612 "NSMP" 1787617 NIL NSMP (NIL T T) -8 NIL NIL) (-762 1776134 1776435 1776792 "NREP" 1777390 NIL NREP (NIL T) -7 NIL NIL) (-761 1774725 1774977 1775335 "NPCOEF" 1775877 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-760 1773791 1773906 1774122 "NORMRETR" 1774606 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-759 1771832 1772122 1772531 "NORMPK" 1773499 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-758 1771517 1771545 1771669 "NORMMA" 1771798 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-757 1771344 1771474 1771503 "NONE" 1771508 T NONE (NIL) -8 NIL NIL) (-756 1771133 1771162 1771231 "NONE1" 1771308 NIL NONE1 (NIL T) -7 NIL NIL) (-755 1770616 1770678 1770864 "NODE1" 1771065 NIL NODE1 (NIL T T) -7 NIL NIL) (-754 1768956 1769779 1770034 "NNI" 1770381 T NNI (NIL) -8 NIL NIL) (-753 1767376 1767689 1768053 "NLINSOL" 1768624 NIL NLINSOL (NIL T) -7 NIL NIL) (-752 1763543 1764511 1765433 "NIPROB" 1766474 T NIPROB (NIL) -8 NIL NIL) (-751 1762300 1762534 1762836 "NFINTBAS" 1763305 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-750 1761744 1761951 1761992 "NETCLT" 1762156 NIL NETCLT (NIL T) -9 NIL 1762245) (-749 1760452 1760683 1760964 "NCODIV" 1761512 NIL NCODIV (NIL T T) -7 NIL NIL) (-748 1760214 1760251 1760326 "NCNTFRAC" 1760409 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-747 1758394 1758758 1759178 "NCEP" 1759839 NIL NCEP (NIL T) -7 NIL NIL) (-746 1757305 1758044 1758072 "NASRING" 1758182 T NASRING (NIL) -9 NIL 1758256) (-745 1757100 1757144 1757238 "NASRING-" 1757243 NIL NASRING- (NIL T) -8 NIL NIL) (-744 1756253 1756752 1756780 "NARNG" 1756897 T NARNG (NIL) -9 NIL 1756988) (-743 1755945 1756012 1756146 "NARNG-" 1756151 NIL NARNG- (NIL T) -8 NIL NIL) (-742 1754824 1755031 1755266 "NAGSP" 1755730 T NAGSP (NIL) -7 NIL NIL) (-741 1746096 1747780 1749453 "NAGS" 1753171 T NAGS (NIL) -7 NIL NIL) (-740 1744644 1744952 1745283 "NAGF07" 1745785 T NAGF07 (NIL) -7 NIL NIL) (-739 1739182 1740473 1741780 "NAGF04" 1743357 T NAGF04 (NIL) -7 NIL NIL) (-738 1732150 1733764 1735397 "NAGF02" 1737569 T NAGF02 (NIL) -7 NIL NIL) (-737 1727374 1728474 1729591 "NAGF01" 1731053 T NAGF01 (NIL) -7 NIL NIL) (-736 1721002 1722568 1724153 "NAGE04" 1725809 T NAGE04 (NIL) -7 NIL NIL) (-735 1712171 1714292 1716422 "NAGE02" 1718892 T NAGE02 (NIL) -7 NIL NIL) (-734 1708124 1709071 1710035 "NAGE01" 1711227 T NAGE01 (NIL) -7 NIL NIL) (-733 1705919 1706453 1707011 "NAGD03" 1707586 T NAGD03 (NIL) -7 NIL NIL) (-732 1697669 1699597 1701551 "NAGD02" 1703985 T NAGD02 (NIL) -7 NIL NIL) (-731 1691480 1692905 1694345 "NAGD01" 1696249 T NAGD01 (NIL) -7 NIL NIL) (-730 1687689 1688511 1689348 "NAGC06" 1690663 T NAGC06 (NIL) -7 NIL NIL) (-729 1686154 1686486 1686842 "NAGC05" 1687353 T NAGC05 (NIL) -7 NIL NIL) (-728 1685530 1685649 1685793 "NAGC02" 1686030 T NAGC02 (NIL) -7 NIL NIL) (-727 1684590 1685147 1685187 "NAALG" 1685266 NIL NAALG (NIL T) -9 NIL 1685327) (-726 1684425 1684454 1684544 "NAALG-" 1684549 NIL NAALG- (NIL T T) -8 NIL NIL) (-725 1678375 1679483 1680670 "MULTSQFR" 1683321 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-724 1677694 1677769 1677953 "MULTFACT" 1678287 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-723 1670917 1674782 1674835 "MTSCAT" 1675905 NIL MTSCAT (NIL T T) -9 NIL 1676419) (-722 1670629 1670683 1670775 "MTHING" 1670857 NIL MTHING (NIL T) -7 NIL NIL) (-721 1670421 1670454 1670514 "MSYSCMD" 1670589 T MSYSCMD (NIL) -7 NIL NIL) (-720 1666533 1669176 1669496 "MSET" 1670134 NIL MSET (NIL T) -8 NIL NIL) (-719 1663628 1666094 1666135 "MSETAGG" 1666140 NIL MSETAGG (NIL T) -9 NIL 1666174) (-718 1659511 1661007 1661752 "MRING" 1662928 NIL MRING (NIL T T) -8 NIL NIL) (-717 1659077 1659144 1659275 "MRF2" 1659438 NIL MRF2 (NIL T T T) -7 NIL NIL) (-716 1658695 1658730 1658874 "MRATFAC" 1659036 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-715 1656307 1656602 1657033 "MPRFF" 1658400 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-714 1650367 1656161 1656258 "MPOLY" 1656263 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-713 1649857 1649892 1650100 "MPCPF" 1650326 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-712 1649371 1649414 1649598 "MPC3" 1649808 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-711 1648566 1648647 1648868 "MPC2" 1649286 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-710 1646867 1647204 1647594 "MONOTOOL" 1648226 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-709 1646118 1646409 1646437 "MONOID" 1646656 T MONOID (NIL) -9 NIL 1646803) (-708 1645664 1645783 1645964 "MONOID-" 1645969 NIL MONOID- (NIL T) -8 NIL NIL) (-707 1636714 1642620 1642679 "MONOGEN" 1643353 NIL MONOGEN (NIL T T) -9 NIL 1643809) (-706 1633932 1634667 1635667 "MONOGEN-" 1635786 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-705 1632791 1633211 1633239 "MONADWU" 1633631 T MONADWU (NIL) -9 NIL 1633869) (-704 1632163 1632322 1632570 "MONADWU-" 1632575 NIL MONADWU- (NIL T) -8 NIL NIL) (-703 1631548 1631766 1631794 "MONAD" 1632001 T MONAD (NIL) -9 NIL 1632113) (-702 1631233 1631311 1631443 "MONAD-" 1631448 NIL MONAD- (NIL T) -8 NIL NIL) (-701 1629549 1630146 1630425 "MOEBIUS" 1630986 NIL MOEBIUS (NIL T) -8 NIL NIL) (-700 1628941 1629319 1629359 "MODULE" 1629364 NIL MODULE (NIL T) -9 NIL 1629390) (-699 1628509 1628605 1628795 "MODULE-" 1628800 NIL MODULE- (NIL T T) -8 NIL NIL) (-698 1626224 1626873 1627200 "MODRING" 1628333 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-697 1623210 1624329 1624850 "MODOP" 1625753 NIL MODOP (NIL T T) -8 NIL NIL) (-696 1621397 1621849 1622190 "MODMONOM" 1623009 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-695 1611105 1619589 1620012 "MODMON" 1621025 NIL MODMON (NIL T T) -8 NIL NIL) (-694 1608296 1609949 1610225 "MODFIELD" 1610980 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-693 1607300 1607577 1607767 "MMLFORM" 1608126 T MMLFORM (NIL) -8 NIL NIL) (-692 1606826 1606869 1607048 "MMAP" 1607251 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-691 1605095 1605828 1605869 "MLO" 1606292 NIL MLO (NIL T) -9 NIL 1606534) (-690 1602462 1602977 1603579 "MLIFT" 1604576 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-689 1601853 1601937 1602091 "MKUCFUNC" 1602373 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-688 1601452 1601522 1601645 "MKRECORD" 1601776 NIL MKRECORD (NIL T T) -7 NIL NIL) (-687 1600500 1600661 1600889 "MKFUNC" 1601263 NIL MKFUNC (NIL T) -7 NIL NIL) (-686 1599888 1599992 1600148 "MKFLCFN" 1600383 NIL MKFLCFN (NIL T) -7 NIL NIL) (-685 1599314 1599681 1599770 "MKCHSET" 1599832 NIL MKCHSET (NIL T) -8 NIL NIL) (-684 1598591 1598693 1598878 "MKBCFUNC" 1599207 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-683 1595333 1598145 1598281 "MINT" 1598475 T MINT (NIL) -8 NIL NIL) (-682 1594145 1594388 1594665 "MHROWRED" 1595088 NIL MHROWRED (NIL T) -7 NIL NIL) (-681 1589571 1592680 1593085 "MFLOAT" 1593760 T MFLOAT (NIL) -8 NIL NIL) (-680 1588928 1589004 1589175 "MFINFACT" 1589483 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-679 1585243 1586091 1586975 "MESH" 1588064 T MESH (NIL) -7 NIL NIL) (-678 1583633 1583945 1584298 "MDDFACT" 1584930 NIL MDDFACT (NIL T) -7 NIL NIL) (-677 1580475 1582792 1582833 "MDAGG" 1583088 NIL MDAGG (NIL T) -9 NIL 1583231) (-676 1570253 1579768 1579975 "MCMPLX" 1580288 T MCMPLX (NIL) -8 NIL NIL) (-675 1569394 1569540 1569740 "MCDEN" 1570102 NIL MCDEN (NIL T T) -7 NIL NIL) (-674 1567284 1567554 1567934 "MCALCFN" 1569124 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-673 1566195 1566368 1566609 "MAYBE" 1567082 NIL MAYBE (NIL T) -8 NIL NIL) (-672 1563807 1564330 1564892 "MATSTOR" 1565666 NIL MATSTOR (NIL T) -7 NIL NIL) (-671 1559813 1563179 1563427 "MATRIX" 1563592 NIL MATRIX (NIL T) -8 NIL NIL) (-670 1555582 1556286 1557022 "MATLIN" 1559170 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-669 1545736 1548874 1548951 "MATCAT" 1553831 NIL MATCAT (NIL T T T) -9 NIL 1555248) (-668 1542100 1543113 1544469 "MATCAT-" 1544474 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-667 1540694 1540847 1541180 "MATCAT2" 1541935 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-666 1538806 1539130 1539514 "MAPPKG3" 1540369 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-665 1537787 1537960 1538182 "MAPPKG2" 1538630 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-664 1536286 1536570 1536897 "MAPPKG1" 1537493 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-663 1535392 1535692 1535869 "MAPPAST" 1536129 T MAPPAST (NIL) -8 NIL NIL) (-662 1535003 1535061 1535184 "MAPHACK3" 1535328 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-661 1534595 1534656 1534770 "MAPHACK2" 1534935 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-660 1534033 1534136 1534278 "MAPHACK1" 1534486 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-659 1532139 1532733 1533037 "MAGMA" 1533761 NIL MAGMA (NIL T) -8 NIL NIL) (-658 1531645 1531863 1531954 "MACROAST" 1532068 T MACROAST (NIL) -8 NIL NIL) (-657 1528112 1529884 1530345 "M3D" 1531217 NIL M3D (NIL T) -8 NIL NIL) (-656 1522267 1526482 1526523 "LZSTAGG" 1527305 NIL LZSTAGG (NIL T) -9 NIL 1527600) (-655 1518240 1519398 1520855 "LZSTAGG-" 1520860 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-654 1515354 1516131 1516618 "LWORD" 1517785 NIL LWORD (NIL T) -8 NIL NIL) (-653 1514957 1515158 1515233 "LSTAST" 1515299 T LSTAST (NIL) -8 NIL NIL) (-652 1508158 1514728 1514862 "LSQM" 1514867 NIL LSQM (NIL NIL T) -8 NIL NIL) (-651 1507382 1507521 1507749 "LSPP" 1508013 NIL LSPP (NIL T T T T) -7 NIL NIL) (-650 1505194 1505495 1505951 "LSMP" 1507071 NIL LSMP (NIL T T T T) -7 NIL NIL) (-649 1501973 1502647 1503377 "LSMP1" 1504496 NIL LSMP1 (NIL T) -7 NIL NIL) (-648 1495899 1501141 1501182 "LSAGG" 1501244 NIL LSAGG (NIL T) -9 NIL 1501322) (-647 1492594 1493518 1494731 "LSAGG-" 1494736 NIL LSAGG- (NIL T T) -8 NIL NIL) (-646 1490220 1491738 1491987 "LPOLY" 1492389 NIL LPOLY (NIL T T) -8 NIL NIL) (-645 1489802 1489887 1490010 "LPEFRAC" 1490129 NIL LPEFRAC (NIL T) -7 NIL NIL) (-644 1488149 1488896 1489149 "LO" 1489634 NIL LO (NIL T T T) -8 NIL NIL) (-643 1487801 1487913 1487941 "LOGIC" 1488052 T LOGIC (NIL) -9 NIL 1488133) (-642 1487663 1487686 1487757 "LOGIC-" 1487762 NIL LOGIC- (NIL T) -8 NIL NIL) (-641 1486856 1486996 1487189 "LODOOPS" 1487519 NIL LODOOPS (NIL T T) -7 NIL NIL) (-640 1484314 1486772 1486838 "LODO" 1486843 NIL LODO (NIL T NIL) -8 NIL NIL) (-639 1482852 1483087 1483440 "LODOF" 1484061 NIL LODOF (NIL T T) -7 NIL NIL) (-638 1479295 1481692 1481733 "LODOCAT" 1482171 NIL LODOCAT (NIL T) -9 NIL 1482382) (-637 1479028 1479086 1479213 "LODOCAT-" 1479218 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-636 1476383 1478869 1478987 "LODO2" 1478992 NIL LODO2 (NIL T T) -8 NIL NIL) (-635 1473853 1476320 1476365 "LODO1" 1476370 NIL LODO1 (NIL T) -8 NIL NIL) (-634 1472713 1472878 1473190 "LODEEF" 1473676 NIL LODEEF (NIL T T T) -7 NIL NIL) (-633 1467999 1470843 1470884 "LNAGG" 1471831 NIL LNAGG (NIL T) -9 NIL 1472275) (-632 1467146 1467360 1467702 "LNAGG-" 1467707 NIL LNAGG- (NIL T T) -8 NIL NIL) (-631 1463309 1464071 1464710 "LMOPS" 1466561 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-630 1462704 1463066 1463107 "LMODULE" 1463168 NIL LMODULE (NIL T) -9 NIL 1463210) (-629 1459950 1462349 1462472 "LMDICT" 1462614 NIL LMDICT (NIL T) -8 NIL NIL) (-628 1459676 1459858 1459918 "LITERAL" 1459923 NIL LITERAL (NIL T) -8 NIL NIL) (-627 1452903 1458622 1458920 "LIST" 1459411 NIL LIST (NIL T) -8 NIL NIL) (-626 1452428 1452502 1452641 "LIST3" 1452823 NIL LIST3 (NIL T T T) -7 NIL NIL) (-625 1451435 1451613 1451841 "LIST2" 1452246 NIL LIST2 (NIL T T) -7 NIL NIL) (-624 1449569 1449881 1450280 "LIST2MAP" 1451082 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-623 1448319 1448955 1448996 "LINEXP" 1449251 NIL LINEXP (NIL T) -9 NIL 1449400) (-622 1446966 1447226 1447523 "LINDEP" 1448071 NIL LINDEP (NIL T T) -7 NIL NIL) (-621 1443733 1444452 1445229 "LIMITRF" 1446221 NIL LIMITRF (NIL T) -7 NIL NIL) (-620 1442009 1442304 1442720 "LIMITPS" 1443428 NIL LIMITPS (NIL T T) -7 NIL NIL) (-619 1436464 1441520 1441748 "LIE" 1441830 NIL LIE (NIL T T) -8 NIL NIL) (-618 1435513 1435956 1435996 "LIECAT" 1436136 NIL LIECAT (NIL T) -9 NIL 1436287) (-617 1435354 1435381 1435469 "LIECAT-" 1435474 NIL LIECAT- (NIL T T) -8 NIL NIL) (-616 1427966 1434803 1434968 "LIB" 1435209 T LIB (NIL) -8 NIL NIL) (-615 1423603 1424484 1425419 "LGROBP" 1427083 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-614 1421469 1421743 1422105 "LF" 1423324 NIL LF (NIL T T) -7 NIL NIL) (-613 1420309 1421001 1421029 "LFCAT" 1421236 T LFCAT (NIL) -9 NIL 1421375) (-612 1417213 1417841 1418529 "LEXTRIPK" 1419673 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-611 1413984 1414783 1415286 "LEXP" 1416793 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-610 1413487 1413705 1413797 "LETAST" 1413912 T LETAST (NIL) -8 NIL NIL) (-609 1411885 1412198 1412599 "LEADCDET" 1413169 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-608 1411075 1411149 1411378 "LAZM3PK" 1411806 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-607 1406031 1409152 1409690 "LAUPOL" 1410587 NIL LAUPOL (NIL T T) -8 NIL NIL) (-606 1405596 1405640 1405808 "LAPLACE" 1405981 NIL LAPLACE (NIL T T) -7 NIL NIL) (-605 1403570 1404697 1404948 "LA" 1405429 NIL LA (NIL T T T) -8 NIL NIL) (-604 1402671 1403221 1403262 "LALG" 1403324 NIL LALG (NIL T) -9 NIL 1403383) (-603 1402385 1402444 1402580 "LALG-" 1402585 NIL LALG- (NIL T T) -8 NIL NIL) (-602 1401185 1401602 1401831 "KTVLOGIC" 1402176 T KTVLOGIC (NIL) -8 NIL NIL) (-601 1400089 1400276 1400575 "KOVACIC" 1400985 NIL KOVACIC (NIL T T) -7 NIL NIL) (-600 1399924 1399948 1399989 "KONVERT" 1400051 NIL KONVERT (NIL T) -9 NIL NIL) (-599 1399759 1399783 1399824 "KOERCE" 1399886 NIL KOERCE (NIL T) -9 NIL NIL) (-598 1397493 1398253 1398646 "KERNEL" 1399398 NIL KERNEL (NIL T) -8 NIL NIL) (-597 1396995 1397076 1397206 "KERNEL2" 1397407 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-596 1390846 1395534 1395588 "KDAGG" 1395965 NIL KDAGG (NIL T T) -9 NIL 1396171) (-595 1390375 1390499 1390704 "KDAGG-" 1390709 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-594 1383550 1390036 1390191 "KAFILE" 1390253 NIL KAFILE (NIL T) -8 NIL NIL) (-593 1378005 1383061 1383289 "JORDAN" 1383371 NIL JORDAN (NIL T T) -8 NIL NIL) (-592 1377411 1377654 1377775 "JOINAST" 1377904 T JOINAST (NIL) -8 NIL NIL) (-591 1377140 1377199 1377286 "JAVACODE" 1377344 T JAVACODE (NIL) -8 NIL NIL) (-590 1373439 1375345 1375399 "IXAGG" 1376328 NIL IXAGG (NIL T T) -9 NIL 1376787) (-589 1372358 1372664 1373083 "IXAGG-" 1373088 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-588 1367938 1372280 1372339 "IVECTOR" 1372344 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-587 1366704 1366941 1367207 "ITUPLE" 1367705 NIL ITUPLE (NIL T) -8 NIL NIL) (-586 1365140 1365317 1365623 "ITRIGMNP" 1366526 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-585 1363885 1364089 1364372 "ITFUN3" 1364916 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-584 1363517 1363574 1363683 "ITFUN2" 1363822 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-583 1361354 1362379 1362678 "ITAYLOR" 1363251 NIL ITAYLOR (NIL T) -8 NIL NIL) (-582 1350336 1355491 1356654 "ISUPS" 1360224 NIL ISUPS (NIL T) -8 NIL NIL) (-581 1349440 1349580 1349816 "ISUMP" 1350183 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-580 1344704 1349241 1349320 "ISTRING" 1349393 NIL ISTRING (NIL NIL) -8 NIL NIL) (-579 1344207 1344425 1344517 "ISAST" 1344632 T ISAST (NIL) -8 NIL NIL) (-578 1343417 1343498 1343714 "IRURPK" 1344121 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-577 1342353 1342554 1342794 "IRSN" 1343197 T IRSN (NIL) -7 NIL NIL) (-576 1340382 1340737 1341173 "IRRF2F" 1341991 NIL IRRF2F (NIL T) -7 NIL NIL) (-575 1340129 1340167 1340243 "IRREDFFX" 1340338 NIL IRREDFFX (NIL T) -7 NIL NIL) (-574 1338744 1339003 1339302 "IROOT" 1339862 NIL IROOT (NIL T) -7 NIL NIL) (-573 1335376 1336428 1337120 "IR" 1338084 NIL IR (NIL T) -8 NIL NIL) (-572 1332989 1333484 1334050 "IR2" 1334854 NIL IR2 (NIL T T) -7 NIL NIL) (-571 1332061 1332174 1332395 "IR2F" 1332872 NIL IR2F (NIL T T) -7 NIL NIL) (-570 1331852 1331886 1331946 "IPRNTPK" 1332021 T IPRNTPK (NIL) -7 NIL NIL) (-569 1328471 1331741 1331810 "IPF" 1331815 NIL IPF (NIL NIL) -8 NIL NIL) (-568 1326834 1328396 1328453 "IPADIC" 1328458 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-567 1326165 1326392 1326529 "IP4ADDR" 1326717 T IP4ADDR (NIL) -8 NIL NIL) (-566 1325665 1325869 1325979 "IOMODE" 1326075 T IOMODE (NIL) -8 NIL NIL) (-565 1325023 1325262 1325389 "IOBFILE" 1325558 T IOBFILE (NIL) -8 NIL NIL) (-564 1324787 1324927 1324955 "IOBCON" 1324960 T IOBCON (NIL) -9 NIL 1324981) (-563 1324284 1324342 1324532 "INVLAPLA" 1324723 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-562 1313933 1316286 1318672 "INTTR" 1321948 NIL INTTR (NIL T T) -7 NIL NIL) (-561 1310277 1311019 1311883 "INTTOOLS" 1313118 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-560 1309863 1309954 1310071 "INTSLPE" 1310180 T INTSLPE (NIL) -7 NIL NIL) (-559 1307858 1309786 1309845 "INTRVL" 1309850 NIL INTRVL (NIL T) -8 NIL NIL) (-558 1305460 1305972 1306547 "INTRF" 1307343 NIL INTRF (NIL T) -7 NIL NIL) (-557 1304871 1304968 1305110 "INTRET" 1305358 NIL INTRET (NIL T) -7 NIL NIL) (-556 1302868 1303257 1303727 "INTRAT" 1304479 NIL INTRAT (NIL T T) -7 NIL NIL) (-555 1300096 1300679 1301305 "INTPM" 1302353 NIL INTPM (NIL T T) -7 NIL NIL) (-554 1296799 1297398 1298143 "INTPAF" 1299482 NIL INTPAF (NIL T T T) -7 NIL NIL) (-553 1291978 1292940 1293991 "INTPACK" 1295768 T INTPACK (NIL) -7 NIL NIL) (-552 1288890 1291707 1291834 "INT" 1291871 T INT (NIL) -8 NIL NIL) (-551 1288142 1288294 1288502 "INTHERTR" 1288732 NIL INTHERTR (NIL T T) -7 NIL NIL) (-550 1287581 1287661 1287849 "INTHERAL" 1288056 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-549 1285427 1285870 1286327 "INTHEORY" 1287144 T INTHEORY (NIL) -7 NIL NIL) (-548 1276735 1278356 1280135 "INTG0" 1283779 NIL INTG0 (NIL T T T) -7 NIL NIL) (-547 1257308 1262098 1266908 "INTFTBL" 1271945 T INTFTBL (NIL) -8 NIL NIL) (-546 1256557 1256695 1256868 "INTFACT" 1257167 NIL INTFACT (NIL T) -7 NIL NIL) (-545 1253942 1254388 1254952 "INTEF" 1256111 NIL INTEF (NIL T T) -7 NIL NIL) (-544 1252444 1253149 1253177 "INTDOM" 1253478 T INTDOM (NIL) -9 NIL 1253685) (-543 1251813 1251987 1252229 "INTDOM-" 1252234 NIL INTDOM- (NIL T) -8 NIL NIL) (-542 1248346 1250232 1250286 "INTCAT" 1251085 NIL INTCAT (NIL T) -9 NIL 1251405) (-541 1247819 1247921 1248049 "INTBIT" 1248238 T INTBIT (NIL) -7 NIL NIL) (-540 1246490 1246644 1246958 "INTALG" 1247664 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-539 1245947 1246037 1246207 "INTAF" 1246394 NIL INTAF (NIL T T) -7 NIL NIL) (-538 1239401 1245757 1245897 "INTABL" 1245902 NIL INTABL (NIL T T T) -8 NIL NIL) (-537 1234454 1237125 1237153 "INS" 1238087 T INS (NIL) -9 NIL 1238752) (-536 1231694 1232465 1233439 "INS-" 1233512 NIL INS- (NIL T) -8 NIL NIL) (-535 1230469 1230696 1230994 "INPSIGN" 1231447 NIL INPSIGN (NIL T T) -7 NIL NIL) (-534 1229587 1229704 1229901 "INPRODPF" 1230349 NIL INPRODPF (NIL T T) -7 NIL NIL) (-533 1228481 1228598 1228835 "INPRODFF" 1229467 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-532 1227481 1227633 1227893 "INNMFACT" 1228317 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-531 1226678 1226775 1226963 "INMODGCD" 1227380 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-530 1225187 1225431 1225755 "INFSP" 1226423 NIL INFSP (NIL T T T) -7 NIL NIL) (-529 1224371 1224488 1224671 "INFPROD0" 1225067 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-528 1221253 1222436 1222951 "INFORM" 1223864 T INFORM (NIL) -8 NIL NIL) (-527 1220863 1220923 1221021 "INFORM1" 1221188 NIL INFORM1 (NIL T) -7 NIL NIL) (-526 1220386 1220475 1220589 "INFINITY" 1220769 T INFINITY (NIL) -7 NIL NIL) (-525 1219829 1220104 1220212 "INETCLTS" 1220298 T INETCLTS (NIL) -8 NIL NIL) (-524 1218446 1218695 1219016 "INEP" 1219577 NIL INEP (NIL T T T) -7 NIL NIL) (-523 1217722 1218343 1218408 "INDE" 1218413 NIL INDE (NIL T) -8 NIL NIL) (-522 1217286 1217354 1217471 "INCRMAPS" 1217649 NIL INCRMAPS (NIL T) -7 NIL NIL) (-521 1216304 1216555 1216761 "INBFILE" 1217100 T INBFILE (NIL) -8 NIL NIL) (-520 1211615 1212540 1213484 "INBFF" 1215392 NIL INBFF (NIL T) -7 NIL NIL) (-519 1211284 1211360 1211388 "INBCON" 1211521 T INBCON (NIL) -9 NIL 1211599) (-518 1211124 1211159 1211235 "INBCON-" 1211240 NIL INBCON- (NIL T) -8 NIL NIL) (-517 1210626 1210845 1210937 "INAST" 1211052 T INAST (NIL) -8 NIL NIL) (-516 1210080 1210305 1210411 "IMPTAST" 1210540 T IMPTAST (NIL) -8 NIL NIL) (-515 1206574 1209924 1210028 "IMATRIX" 1210033 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-514 1205286 1205409 1205724 "IMATQF" 1206430 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-513 1203506 1203733 1204070 "IMATLIN" 1205042 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-512 1198132 1203430 1203488 "ILIST" 1203493 NIL ILIST (NIL T NIL) -8 NIL NIL) (-511 1196085 1197992 1198105 "IIARRAY2" 1198110 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-510 1191518 1195996 1196060 "IFF" 1196065 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-509 1190892 1191135 1191251 "IFAST" 1191422 T IFAST (NIL) -8 NIL NIL) (-508 1185935 1190184 1190372 "IFARRAY" 1190749 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-507 1185142 1185839 1185912 "IFAMON" 1185917 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-506 1184726 1184791 1184845 "IEVALAB" 1185052 NIL IEVALAB (NIL T T) -9 NIL NIL) (-505 1184401 1184469 1184629 "IEVALAB-" 1184634 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-504 1184059 1184315 1184378 "IDPO" 1184383 NIL IDPO (NIL T T) -8 NIL NIL) (-503 1183336 1183948 1184023 "IDPOAMS" 1184028 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-502 1182670 1183225 1183300 "IDPOAM" 1183305 NIL IDPOAM (NIL T T) -8 NIL NIL) (-501 1181755 1182005 1182058 "IDPC" 1182471 NIL IDPC (NIL T T) -9 NIL 1182620) (-500 1181251 1181647 1181720 "IDPAM" 1181725 NIL IDPAM (NIL T T) -8 NIL NIL) (-499 1180654 1181143 1181216 "IDPAG" 1181221 NIL IDPAG (NIL T T) -8 NIL NIL) (-498 1180384 1180569 1180619 "IDENT" 1180624 T IDENT (NIL) -8 NIL NIL) (-497 1176639 1177487 1178382 "IDECOMP" 1179541 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-496 1169512 1170562 1171609 "IDEAL" 1175675 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-495 1168676 1168788 1168987 "ICDEN" 1169396 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-494 1167775 1168156 1168303 "ICARD" 1168549 T ICARD (NIL) -8 NIL NIL) (-493 1165835 1166148 1166553 "IBPTOOLS" 1167452 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-492 1161469 1165455 1165568 "IBITS" 1165754 NIL IBITS (NIL NIL) -8 NIL NIL) (-491 1158192 1158768 1159463 "IBATOOL" 1160886 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-490 1155972 1156433 1156966 "IBACHIN" 1157727 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-489 1153849 1155818 1155921 "IARRAY2" 1155926 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-488 1150002 1153775 1153832 "IARRAY1" 1153837 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-487 1143995 1148414 1148895 "IAN" 1149541 T IAN (NIL) -8 NIL NIL) (-486 1143506 1143563 1143736 "IALGFACT" 1143932 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-485 1143034 1143147 1143175 "HYPCAT" 1143382 T HYPCAT (NIL) -9 NIL NIL) (-484 1142572 1142689 1142875 "HYPCAT-" 1142880 NIL HYPCAT- (NIL T) -8 NIL NIL) (-483 1142194 1142367 1142450 "HOSTNAME" 1142509 T HOSTNAME (NIL) -8 NIL NIL) (-482 1138873 1140204 1140245 "HOAGG" 1141226 NIL HOAGG (NIL T) -9 NIL 1141905) (-481 1137467 1137866 1138392 "HOAGG-" 1138397 NIL HOAGG- (NIL T T) -8 NIL NIL) (-480 1131353 1136908 1137074 "HEXADEC" 1137321 T HEXADEC (NIL) -8 NIL NIL) (-479 1130101 1130323 1130586 "HEUGCD" 1131130 NIL HEUGCD (NIL T) -7 NIL NIL) (-478 1129204 1129938 1130068 "HELLFDIV" 1130073 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-477 1127432 1128981 1129069 "HEAP" 1129148 NIL HEAP (NIL T) -8 NIL NIL) (-476 1126723 1126984 1127118 "HEADAST" 1127318 T HEADAST (NIL) -8 NIL NIL) (-475 1120643 1126638 1126700 "HDP" 1126705 NIL HDP (NIL NIL T) -8 NIL NIL) (-474 1114394 1120278 1120430 "HDMP" 1120544 NIL HDMP (NIL NIL T) -8 NIL NIL) (-473 1113719 1113858 1114022 "HB" 1114250 T HB (NIL) -7 NIL NIL) (-472 1107216 1113565 1113669 "HASHTBL" 1113674 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-471 1106719 1106937 1107029 "HASAST" 1107144 T HASAST (NIL) -8 NIL NIL) (-470 1104531 1106341 1106523 "HACKPI" 1106557 T HACKPI (NIL) -8 NIL NIL) (-469 1100226 1104384 1104497 "GTSET" 1104502 NIL GTSET (NIL T T T T) -8 NIL NIL) (-468 1093752 1100104 1100202 "GSTBL" 1100207 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-467 1086065 1092783 1093048 "GSERIES" 1093543 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-466 1085232 1085623 1085651 "GROUP" 1085854 T GROUP (NIL) -9 NIL 1085988) (-465 1084598 1084757 1085008 "GROUP-" 1085013 NIL GROUP- (NIL T) -8 NIL NIL) (-464 1082967 1083286 1083673 "GROEBSOL" 1084275 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-463 1081907 1082169 1082220 "GRMOD" 1082749 NIL GRMOD (NIL T T) -9 NIL 1082917) (-462 1081675 1081711 1081839 "GRMOD-" 1081844 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-461 1077000 1078029 1079029 "GRIMAGE" 1080695 T GRIMAGE (NIL) -8 NIL NIL) (-460 1075467 1075727 1076051 "GRDEF" 1076696 T GRDEF (NIL) -7 NIL NIL) (-459 1074911 1075027 1075168 "GRAY" 1075346 T GRAY (NIL) -7 NIL NIL) (-458 1074142 1074522 1074573 "GRALG" 1074726 NIL GRALG (NIL T T) -9 NIL 1074819) (-457 1073803 1073876 1074039 "GRALG-" 1074044 NIL GRALG- (NIL T T T) -8 NIL NIL) (-456 1070607 1073388 1073566 "GPOLSET" 1073710 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-455 1069961 1070018 1070276 "GOSPER" 1070544 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-454 1065720 1066399 1066925 "GMODPOL" 1069660 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-453 1064725 1064909 1065147 "GHENSEL" 1065532 NIL GHENSEL (NIL T T) -7 NIL NIL) (-452 1058776 1059619 1060646 "GENUPS" 1063809 NIL GENUPS (NIL T T) -7 NIL NIL) (-451 1058473 1058524 1058613 "GENUFACT" 1058719 NIL GENUFACT (NIL T) -7 NIL NIL) (-450 1057885 1057962 1058127 "GENPGCD" 1058391 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-449 1057359 1057394 1057607 "GENMFACT" 1057844 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-448 1055927 1056182 1056489 "GENEEZ" 1057102 NIL GENEEZ (NIL T T) -7 NIL NIL) (-447 1049840 1055538 1055700 "GDMP" 1055850 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-446 1039217 1043611 1044717 "GCNAALG" 1048823 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-445 1037679 1038507 1038535 "GCDDOM" 1038790 T GCDDOM (NIL) -9 NIL 1038947) (-444 1037149 1037276 1037491 "GCDDOM-" 1037496 NIL GCDDOM- (NIL T) -8 NIL NIL) (-443 1035821 1036006 1036310 "GB" 1036928 NIL GB (NIL T T T T) -7 NIL NIL) (-442 1024441 1026767 1029159 "GBINTERN" 1033512 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-441 1022278 1022570 1022991 "GBF" 1024116 NIL GBF (NIL T T T T) -7 NIL NIL) (-440 1021059 1021224 1021491 "GBEUCLID" 1022094 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-439 1020408 1020533 1020682 "GAUSSFAC" 1020930 T GAUSSFAC (NIL) -7 NIL NIL) (-438 1018775 1019077 1019391 "GALUTIL" 1020127 NIL GALUTIL (NIL T) -7 NIL NIL) (-437 1017083 1017357 1017681 "GALPOLYU" 1018502 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-436 1014448 1014738 1015145 "GALFACTU" 1016780 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-435 1006254 1007753 1009361 "GALFACT" 1012880 NIL GALFACT (NIL T) -7 NIL NIL) (-434 1003642 1004300 1004328 "FVFUN" 1005484 T FVFUN (NIL) -9 NIL 1006204) (-433 1002908 1003090 1003118 "FVC" 1003409 T FVC (NIL) -9 NIL 1003592) (-432 1002550 1002705 1002786 "FUNCTION" 1002860 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-431 1000220 1000771 1001260 "FT" 1002081 T FT (NIL) -8 NIL NIL) (-430 999038 999521 999724 "FTEM" 1000037 T FTEM (NIL) -8 NIL NIL) (-429 997294 997583 997987 "FSUPFACT" 998729 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-428 995691 995980 996312 "FST" 996982 T FST (NIL) -8 NIL NIL) (-427 994862 994968 995163 "FSRED" 995573 NIL FSRED (NIL T T) -7 NIL NIL) (-426 993541 993796 994150 "FSPRMELT" 994577 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-425 990626 991064 991563 "FSPECF" 993104 NIL FSPECF (NIL T T) -7 NIL NIL) (-424 973068 981510 981550 "FS" 985398 NIL FS (NIL T) -9 NIL 987687) (-423 961718 964708 968764 "FS-" 969061 NIL FS- (NIL T T) -8 NIL NIL) (-422 961232 961286 961463 "FSINT" 961659 NIL FSINT (NIL T T) -7 NIL NIL) (-421 959559 960225 960528 "FSERIES" 961011 NIL FSERIES (NIL T T) -8 NIL NIL) (-420 958573 958689 958920 "FSCINT" 959439 NIL FSCINT (NIL T T) -7 NIL NIL) (-419 954807 957517 957558 "FSAGG" 957928 NIL FSAGG (NIL T) -9 NIL 958187) (-418 952569 953170 953966 "FSAGG-" 954061 NIL FSAGG- (NIL T T) -8 NIL NIL) (-417 951611 951754 951981 "FSAGG2" 952422 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-416 949266 949545 950099 "FS2UPS" 951329 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-415 948848 948891 949046 "FS2" 949217 NIL FS2 (NIL T T T T) -7 NIL NIL) (-414 947705 947876 948185 "FS2EXPXP" 948673 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-413 947131 947246 947398 "FRUTIL" 947585 NIL FRUTIL (NIL T) -7 NIL NIL) (-412 938586 942626 943984 "FR" 945805 NIL FR (NIL T) -8 NIL NIL) (-411 933661 936304 936344 "FRNAALG" 937740 NIL FRNAALG (NIL T) -9 NIL 938347) (-410 929339 930410 931685 "FRNAALG-" 932435 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-409 928977 929020 929147 "FRNAAF2" 929290 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-408 927384 927831 928126 "FRMOD" 928789 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-407 925163 925767 926084 "FRIDEAL" 927175 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-406 924358 924445 924734 "FRIDEAL2" 925070 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-405 923600 924014 924055 "FRETRCT" 924060 NIL FRETRCT (NIL T) -9 NIL 924236) (-404 922712 922943 923294 "FRETRCT-" 923299 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-403 919962 921138 921197 "FRAMALG" 922079 NIL FRAMALG (NIL T T) -9 NIL 922371) (-402 918096 918551 919181 "FRAMALG-" 919404 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-401 912054 917571 917847 "FRAC" 917852 NIL FRAC (NIL T) -8 NIL NIL) (-400 911690 911747 911854 "FRAC2" 911991 NIL FRAC2 (NIL T T) -7 NIL NIL) (-399 911326 911383 911490 "FR2" 911627 NIL FR2 (NIL T T) -7 NIL NIL) (-398 906055 908903 908931 "FPS" 910050 T FPS (NIL) -9 NIL 910607) (-397 905504 905613 905777 "FPS-" 905923 NIL FPS- (NIL T) -8 NIL NIL) (-396 903010 904645 904673 "FPC" 904898 T FPC (NIL) -9 NIL 905040) (-395 902803 902843 902940 "FPC-" 902945 NIL FPC- (NIL T) -8 NIL NIL) (-394 901681 902291 902332 "FPATMAB" 902337 NIL FPATMAB (NIL T) -9 NIL 902489) (-393 899381 899857 900283 "FPARFRAC" 901318 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-392 894774 895273 895955 "FORTRAN" 898813 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-391 892490 892990 893529 "FORT" 894255 T FORT (NIL) -7 NIL NIL) (-390 890166 890728 890756 "FORTFN" 891816 T FORTFN (NIL) -9 NIL 892440) (-389 889930 889980 890008 "FORTCAT" 890067 T FORTCAT (NIL) -9 NIL 890129) (-388 887990 888473 888872 "FORMULA" 889551 T FORMULA (NIL) -8 NIL NIL) (-387 887778 887808 887877 "FORMULA1" 887954 NIL FORMULA1 (NIL T) -7 NIL NIL) (-386 887301 887353 887526 "FORDER" 887720 NIL FORDER (NIL T T T T) -7 NIL NIL) (-385 886397 886561 886754 "FOP" 887128 T FOP (NIL) -7 NIL NIL) (-384 885005 885677 885851 "FNLA" 886279 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-383 883673 884062 884090 "FNCAT" 884662 T FNCAT (NIL) -9 NIL 884955) (-382 883239 883632 883660 "FNAME" 883665 T FNAME (NIL) -8 NIL NIL) (-381 881937 882866 882894 "FMTC" 882899 T FMTC (NIL) -9 NIL 882935) (-380 878299 879460 880089 "FMONOID" 881341 NIL FMONOID (NIL T) -8 NIL NIL) (-379 877518 878041 878190 "FM" 878195 NIL FM (NIL T T) -8 NIL NIL) (-378 874942 875588 875616 "FMFUN" 876760 T FMFUN (NIL) -9 NIL 877468) (-377 874211 874392 874420 "FMC" 874710 T FMC (NIL) -9 NIL 874892) (-376 871423 872257 872311 "FMCAT" 873506 NIL FMCAT (NIL T T) -9 NIL 874001) (-375 870316 871189 871289 "FM1" 871368 NIL FM1 (NIL T T) -8 NIL NIL) (-374 868090 868506 869000 "FLOATRP" 869867 NIL FLOATRP (NIL T) -7 NIL NIL) (-373 861641 865746 866376 "FLOAT" 867480 T FLOAT (NIL) -8 NIL NIL) (-372 859079 859579 860157 "FLOATCP" 861108 NIL FLOATCP (NIL T) -7 NIL NIL) (-371 857908 858712 858753 "FLINEXP" 858758 NIL FLINEXP (NIL T) -9 NIL 858851) (-370 857062 857297 857625 "FLINEXP-" 857630 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-369 856138 856282 856506 "FLASORT" 856914 NIL FLASORT (NIL T T) -7 NIL NIL) (-368 853355 854197 854249 "FLALG" 855476 NIL FLALG (NIL T T) -9 NIL 855943) (-367 847139 850841 850882 "FLAGG" 852144 NIL FLAGG (NIL T) -9 NIL 852796) (-366 845865 846204 846694 "FLAGG-" 846699 NIL FLAGG- (NIL T T) -8 NIL NIL) (-365 844907 845050 845277 "FLAGG2" 845718 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-364 841920 842894 842953 "FINRALG" 844081 NIL FINRALG (NIL T T) -9 NIL 844589) (-363 841080 841309 841648 "FINRALG-" 841653 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-362 840486 840699 840727 "FINITE" 840923 T FINITE (NIL) -9 NIL 841030) (-361 832944 835105 835145 "FINAALG" 838812 NIL FINAALG (NIL T) -9 NIL 840265) (-360 828285 829326 830470 "FINAALG-" 831849 NIL FINAALG- (NIL T T) -8 NIL NIL) (-359 827680 828040 828143 "FILE" 828215 NIL FILE (NIL T) -8 NIL NIL) (-358 826364 826676 826730 "FILECAT" 827414 NIL FILECAT (NIL T T) -9 NIL 827630) (-357 824284 825778 825806 "FIELD" 825846 T FIELD (NIL) -9 NIL 825926) (-356 822904 823289 823800 "FIELD-" 823805 NIL FIELD- (NIL T) -8 NIL NIL) (-355 820782 821539 821886 "FGROUP" 822590 NIL FGROUP (NIL T) -8 NIL NIL) (-354 819872 820036 820256 "FGLMICPK" 820614 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-353 815739 819797 819854 "FFX" 819859 NIL FFX (NIL T NIL) -8 NIL NIL) (-352 815340 815401 815536 "FFSLPE" 815672 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-351 811333 812112 812908 "FFPOLY" 814576 NIL FFPOLY (NIL T) -7 NIL NIL) (-350 810837 810873 811082 "FFPOLY2" 811291 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-349 806723 810756 810819 "FFP" 810824 NIL FFP (NIL T NIL) -8 NIL NIL) (-348 802156 806634 806698 "FF" 806703 NIL FF (NIL NIL NIL) -8 NIL NIL) (-347 797317 801499 801689 "FFNBX" 802010 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-346 792291 796452 796710 "FFNBP" 797171 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-345 786959 791575 791786 "FFNB" 792124 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-344 785791 785989 786304 "FFINTBAS" 786756 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-343 782075 784250 784278 "FFIELDC" 784898 T FFIELDC (NIL) -9 NIL 785274) (-342 780738 781108 781605 "FFIELDC-" 781610 NIL FFIELDC- (NIL T) -8 NIL NIL) (-341 780308 780353 780477 "FFHOM" 780680 NIL FFHOM (NIL T T T) -7 NIL NIL) (-340 778006 778490 779007 "FFF" 779823 NIL FFF (NIL T) -7 NIL NIL) (-339 773659 777748 777849 "FFCGX" 777949 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-338 769326 773391 773498 "FFCGP" 773602 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-337 764544 769053 769161 "FFCG" 769262 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-336 746602 755638 755724 "FFCAT" 760889 NIL FFCAT (NIL T T T) -9 NIL 762340) (-335 741800 742847 744161 "FFCAT-" 745391 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-334 741211 741254 741489 "FFCAT2" 741751 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-333 730423 734183 735403 "FEXPR" 740063 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-332 729423 729858 729899 "FEVALAB" 729983 NIL FEVALAB (NIL T) -9 NIL 730244) (-331 728582 728792 729130 "FEVALAB-" 729135 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-330 727175 727965 728168 "FDIV" 728481 NIL FDIV (NIL T T T T) -8 NIL NIL) (-329 724241 724956 725071 "FDIVCAT" 726639 NIL FDIVCAT (NIL T T T T) -9 NIL 727076) (-328 724003 724030 724200 "FDIVCAT-" 724205 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-327 723223 723310 723587 "FDIV2" 723910 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-326 721909 722168 722457 "FCPAK1" 722954 T FCPAK1 (NIL) -7 NIL NIL) (-325 721037 721409 721550 "FCOMP" 721800 NIL FCOMP (NIL T) -8 NIL NIL) (-324 704672 708086 711647 "FC" 717496 T FC (NIL) -8 NIL NIL) (-323 697325 701306 701346 "FAXF" 703148 NIL FAXF (NIL T) -9 NIL 703840) (-322 694604 695259 696084 "FAXF-" 696549 NIL FAXF- (NIL T T) -8 NIL NIL) (-321 689704 693980 694156 "FARRAY" 694461 NIL FARRAY (NIL T) -8 NIL NIL) (-320 685111 687143 687196 "FAMR" 688219 NIL FAMR (NIL T T) -9 NIL 688679) (-319 684001 684303 684738 "FAMR-" 684743 NIL FAMR- (NIL T T T) -8 NIL NIL) (-318 683197 683923 683976 "FAMONOID" 683981 NIL FAMONOID (NIL T) -8 NIL NIL) (-317 681027 681711 681764 "FAMONC" 682705 NIL FAMONC (NIL T T) -9 NIL 683091) (-316 679719 680781 680918 "FAGROUP" 680923 NIL FAGROUP (NIL T) -8 NIL NIL) (-315 677514 677833 678236 "FACUTIL" 679400 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-314 676613 676798 677020 "FACTFUNC" 677324 NIL FACTFUNC (NIL T) -7 NIL NIL) (-313 669018 675864 676076 "EXPUPXS" 676469 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-312 666501 667041 667627 "EXPRTUBE" 668452 T EXPRTUBE (NIL) -7 NIL NIL) (-311 662695 663287 664024 "EXPRODE" 665840 NIL EXPRODE (NIL T T) -7 NIL NIL) (-310 648069 661350 661778 "EXPR" 662299 NIL EXPR (NIL T) -8 NIL NIL) (-309 642476 643063 643876 "EXPR2UPS" 647367 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 642112 642169 642276 "EXPR2" 642413 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 633517 641244 641541 "EXPEXPAN" 641949 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-306 633344 633474 633503 "EXIT" 633508 T EXIT (NIL) -8 NIL NIL) (-305 632851 633068 633159 "EXITAST" 633273 T EXITAST (NIL) -8 NIL NIL) (-304 632478 632540 632653 "EVALCYC" 632783 NIL EVALCYC (NIL T) -7 NIL NIL) (-303 632019 632137 632178 "EVALAB" 632348 NIL EVALAB (NIL T) -9 NIL 632452) (-302 631500 631622 631843 "EVALAB-" 631848 NIL EVALAB- (NIL T T) -8 NIL NIL) (-301 629003 630271 630299 "EUCDOM" 630854 T EUCDOM (NIL) -9 NIL 631204) (-300 627408 627850 628440 "EUCDOM-" 628445 NIL EUCDOM- (NIL T) -8 NIL NIL) (-299 614948 617706 620456 "ESTOOLS" 624678 T ESTOOLS (NIL) -7 NIL NIL) (-298 614580 614637 614746 "ESTOOLS2" 614885 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 614331 614373 614453 "ESTOOLS1" 614532 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 608256 609984 610012 "ES" 612780 T ES (NIL) -9 NIL 614189) (-295 603203 604490 606307 "ES-" 606471 NIL ES- (NIL T) -8 NIL NIL) (-294 599578 600338 601118 "ESCONT" 602443 T ESCONT (NIL) -7 NIL NIL) (-293 599323 599355 599437 "ESCONT1" 599540 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-292 598998 599048 599148 "ES2" 599267 NIL ES2 (NIL T T) -7 NIL NIL) (-291 598628 598686 598795 "ES1" 598934 NIL ES1 (NIL T T) -7 NIL NIL) (-290 597844 597973 598149 "ERROR" 598472 T ERROR (NIL) -7 NIL NIL) (-289 591347 597703 597794 "EQTBL" 597799 NIL EQTBL (NIL T T) -8 NIL NIL) (-288 583904 586661 588110 "EQ" 589931 NIL -3909 (NIL T) -8 NIL NIL) (-287 583536 583593 583702 "EQ2" 583841 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 578828 579874 580967 "EP" 582475 NIL EP (NIL T) -7 NIL NIL) (-285 577410 577711 578028 "ENV" 578531 T ENV (NIL) -8 NIL NIL) (-284 576609 577129 577157 "ENTIRER" 577162 T ENTIRER (NIL) -9 NIL 577208) (-283 573111 574564 574934 "EMR" 576408 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-282 572255 572440 572494 "ELTAGG" 572874 NIL ELTAGG (NIL T T) -9 NIL 573085) (-281 571974 572036 572177 "ELTAGG-" 572182 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-280 571763 571792 571846 "ELTAB" 571930 NIL ELTAB (NIL T T) -9 NIL NIL) (-279 570889 571035 571234 "ELFUTS" 571614 NIL ELFUTS (NIL T T) -7 NIL NIL) (-278 570631 570687 570715 "ELEMFUN" 570820 T ELEMFUN (NIL) -9 NIL NIL) (-277 570501 570522 570590 "ELEMFUN-" 570595 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-276 565392 568601 568642 "ELAGG" 569582 NIL ELAGG (NIL T) -9 NIL 570045) (-275 563677 564111 564774 "ELAGG-" 564779 NIL ELAGG- (NIL T T) -8 NIL NIL) (-274 562334 562614 562909 "ELABEXPR" 563402 T ELABEXPR (NIL) -8 NIL NIL) (-273 555200 557001 557828 "EFUPXS" 561610 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-272 548650 550451 551261 "EFULS" 554476 NIL EFULS (NIL T T T) -8 NIL NIL) (-271 546072 546430 546909 "EFSTRUC" 548282 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-270 535144 536709 538269 "EF" 544587 NIL EF (NIL T T) -7 NIL NIL) (-269 534245 534629 534778 "EAB" 535015 T EAB (NIL) -8 NIL NIL) (-268 533454 534204 534232 "E04UCFA" 534237 T E04UCFA (NIL) -8 NIL NIL) (-267 532663 533413 533441 "E04NAFA" 533446 T E04NAFA (NIL) -8 NIL NIL) (-266 531872 532622 532650 "E04MBFA" 532655 T E04MBFA (NIL) -8 NIL NIL) (-265 531081 531831 531859 "E04JAFA" 531864 T E04JAFA (NIL) -8 NIL NIL) (-264 530292 531040 531068 "E04GCFA" 531073 T E04GCFA (NIL) -8 NIL NIL) (-263 529503 530251 530279 "E04FDFA" 530284 T E04FDFA (NIL) -8 NIL NIL) (-262 528712 529462 529490 "E04DGFA" 529495 T E04DGFA (NIL) -8 NIL NIL) (-261 522890 524237 525601 "E04AGNT" 527368 T E04AGNT (NIL) -7 NIL NIL) (-260 521614 522094 522134 "DVARCAT" 522609 NIL DVARCAT (NIL T) -9 NIL 522808) (-259 520818 521030 521344 "DVARCAT-" 521349 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-258 513718 520617 520746 "DSMP" 520751 NIL DSMP (NIL T T T) -8 NIL NIL) (-257 508528 509663 510731 "DROPT" 512670 T DROPT (NIL) -8 NIL NIL) (-256 508193 508252 508350 "DROPT1" 508463 NIL DROPT1 (NIL T) -7 NIL NIL) (-255 503308 504434 505571 "DROPT0" 507076 T DROPT0 (NIL) -7 NIL NIL) (-254 501653 501978 502364 "DRAWPT" 502942 T DRAWPT (NIL) -7 NIL NIL) (-253 496240 497163 498242 "DRAW" 500627 NIL DRAW (NIL T) -7 NIL NIL) (-252 495873 495926 496044 "DRAWHACK" 496181 NIL DRAWHACK (NIL T) -7 NIL NIL) (-251 494604 494873 495164 "DRAWCX" 495602 T DRAWCX (NIL) -7 NIL NIL) (-250 494120 494188 494339 "DRAWCURV" 494530 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-249 484591 486550 488665 "DRAWCFUN" 492025 T DRAWCFUN (NIL) -7 NIL NIL) (-248 481404 483286 483327 "DQAGG" 483956 NIL DQAGG (NIL T) -9 NIL 484229) (-247 469923 476620 476703 "DPOLCAT" 478555 NIL DPOLCAT (NIL T T T T) -9 NIL 479100) (-246 464762 466108 468066 "DPOLCAT-" 468071 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-245 457917 464623 464721 "DPMO" 464726 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-244 450975 457697 457864 "DPMM" 457869 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-243 450395 450598 450712 "DOMAIN" 450881 T DOMAIN (NIL) -8 NIL NIL) (-242 444146 450030 450182 "DMP" 450296 NIL DMP (NIL NIL T) -8 NIL NIL) (-241 443746 443802 443946 "DLP" 444084 NIL DLP (NIL T) -7 NIL NIL) (-240 437390 442847 443074 "DLIST" 443551 NIL DLIST (NIL T) -8 NIL NIL) (-239 434236 436245 436286 "DLAGG" 436836 NIL DLAGG (NIL T) -9 NIL 437065) (-238 433086 433716 433744 "DIVRING" 433836 T DIVRING (NIL) -9 NIL 433919) (-237 432323 432513 432813 "DIVRING-" 432818 NIL DIVRING- (NIL T) -8 NIL NIL) (-236 430425 430782 431188 "DISPLAY" 431937 T DISPLAY (NIL) -7 NIL NIL) (-235 424367 430339 430402 "DIRPROD" 430407 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-234 423215 423418 423683 "DIRPROD2" 424160 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-233 412753 418705 418758 "DIRPCAT" 419168 NIL DIRPCAT (NIL NIL T) -9 NIL 420008) (-232 410079 410721 411602 "DIRPCAT-" 411939 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-231 409366 409526 409712 "DIOSP" 409913 T DIOSP (NIL) -7 NIL NIL) (-230 406068 408278 408319 "DIOPS" 408753 NIL DIOPS (NIL T) -9 NIL 408982) (-229 405617 405731 405922 "DIOPS-" 405927 NIL DIOPS- (NIL T T) -8 NIL NIL) (-228 404529 405123 405151 "DIFRING" 405338 T DIFRING (NIL) -9 NIL 405448) (-227 404175 404252 404404 "DIFRING-" 404409 NIL DIFRING- (NIL T) -8 NIL NIL) (-226 402000 403238 403279 "DIFEXT" 403642 NIL DIFEXT (NIL T) -9 NIL 403936) (-225 400285 400713 401379 "DIFEXT-" 401384 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-224 397607 399817 399858 "DIAGG" 399863 NIL DIAGG (NIL T) -9 NIL 399883) (-223 396991 397148 397400 "DIAGG-" 397405 NIL DIAGG- (NIL T T) -8 NIL NIL) (-222 392456 395950 396227 "DHMATRIX" 396760 NIL DHMATRIX (NIL T) -8 NIL NIL) (-221 388068 388977 389987 "DFSFUN" 391466 T DFSFUN (NIL) -7 NIL NIL) (-220 383184 386999 387311 "DFLOAT" 387776 T DFLOAT (NIL) -8 NIL NIL) (-219 381412 381693 382089 "DFINTTLS" 382892 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-218 378477 379433 379833 "DERHAM" 381078 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-217 376326 378252 378341 "DEQUEUE" 378421 NIL DEQUEUE (NIL T) -8 NIL NIL) (-216 375541 375674 375870 "DEGRED" 376188 NIL DEGRED (NIL T T) -7 NIL NIL) (-215 371936 372681 373534 "DEFINTRF" 374769 NIL DEFINTRF (NIL T) -7 NIL NIL) (-214 369463 369932 370531 "DEFINTEF" 371455 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-213 368840 369083 369198 "DEFAST" 369368 T DEFAST (NIL) -8 NIL NIL) (-212 362726 368281 368447 "DECIMAL" 368694 T DECIMAL (NIL) -8 NIL NIL) (-211 360238 360696 361202 "DDFACT" 362270 NIL DDFACT (NIL T T) -7 NIL NIL) (-210 359834 359877 360028 "DBLRESP" 360189 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-209 357544 357878 358247 "DBASE" 359592 NIL DBASE (NIL T) -8 NIL NIL) (-208 356813 357024 357170 "DATAARY" 357443 NIL DATAARY (NIL NIL T) -8 NIL NIL) (-207 355946 356772 356800 "D03FAFA" 356805 T D03FAFA (NIL) -8 NIL NIL) (-206 355080 355905 355933 "D03EEFA" 355938 T D03EEFA (NIL) -8 NIL NIL) (-205 353030 353496 353985 "D03AGNT" 354611 T D03AGNT (NIL) -7 NIL NIL) (-204 352346 352989 353017 "D02EJFA" 353022 T D02EJFA (NIL) -8 NIL NIL) (-203 351662 352305 352333 "D02CJFA" 352338 T D02CJFA (NIL) -8 NIL NIL) (-202 350978 351621 351649 "D02BHFA" 351654 T D02BHFA (NIL) -8 NIL NIL) (-201 350294 350937 350965 "D02BBFA" 350970 T D02BBFA (NIL) -8 NIL NIL) (-200 343492 345080 346686 "D02AGNT" 348708 T D02AGNT (NIL) -7 NIL NIL) (-199 341261 341783 342329 "D01WGTS" 342966 T D01WGTS (NIL) -7 NIL NIL) (-198 340356 341220 341248 "D01TRNS" 341253 T D01TRNS (NIL) -8 NIL NIL) (-197 339451 340315 340343 "D01GBFA" 340348 T D01GBFA (NIL) -8 NIL NIL) (-196 338546 339410 339438 "D01FCFA" 339443 T D01FCFA (NIL) -8 NIL NIL) (-195 337641 338505 338533 "D01ASFA" 338538 T D01ASFA (NIL) -8 NIL NIL) (-194 336736 337600 337628 "D01AQFA" 337633 T D01AQFA (NIL) -8 NIL NIL) (-193 335831 336695 336723 "D01APFA" 336728 T D01APFA (NIL) -8 NIL NIL) (-192 334926 335790 335818 "D01ANFA" 335823 T D01ANFA (NIL) -8 NIL NIL) (-191 334021 334885 334913 "D01AMFA" 334918 T D01AMFA (NIL) -8 NIL NIL) (-190 333116 333980 334008 "D01ALFA" 334013 T D01ALFA (NIL) -8 NIL NIL) (-189 332211 333075 333103 "D01AKFA" 333108 T D01AKFA (NIL) -8 NIL NIL) (-188 331306 332170 332198 "D01AJFA" 332203 T D01AJFA (NIL) -8 NIL NIL) (-187 324603 326154 327715 "D01AGNT" 329765 T D01AGNT (NIL) -7 NIL NIL) (-186 323940 324068 324220 "CYCLOTOM" 324471 T CYCLOTOM (NIL) -7 NIL NIL) (-185 320675 321388 322115 "CYCLES" 323233 T CYCLES (NIL) -7 NIL NIL) (-184 319987 320121 320292 "CVMP" 320536 NIL CVMP (NIL T) -7 NIL NIL) (-183 317758 318016 318392 "CTRIGMNP" 319715 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-182 317175 317381 317495 "CTOR" 317664 T CTOR (NIL) -8 NIL NIL) (-181 316711 316906 317007 "CTORKIND" 317094 T CTORKIND (NIL) -8 NIL NIL) (-180 316222 316411 316510 "CTORCALL" 316632 T CTORCALL (NIL) -8 NIL NIL) (-179 315596 315695 315848 "CSTTOOLS" 316119 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-178 311395 312052 312810 "CRFP" 314908 NIL CRFP (NIL T T) -7 NIL NIL) (-177 310897 311116 311208 "CRCEAST" 311323 T CRCEAST (NIL) -8 NIL NIL) (-176 309944 310129 310357 "CRAPACK" 310701 NIL CRAPACK (NIL T) -7 NIL NIL) (-175 309328 309429 309633 "CPMATCH" 309820 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-174 309053 309081 309187 "CPIMA" 309294 NIL CPIMA (NIL T T T) -7 NIL NIL) (-173 305417 306089 306807 "COORDSYS" 308388 NIL COORDSYS (NIL T) -7 NIL NIL) (-172 304801 304930 305080 "CONTOUR" 305287 T CONTOUR (NIL) -8 NIL NIL) (-171 300727 302804 303296 "CONTFRAC" 304341 NIL CONTFRAC (NIL T) -8 NIL NIL) (-170 300607 300628 300656 "CONDUIT" 300693 T CONDUIT (NIL) -9 NIL NIL) (-169 299800 300320 300348 "COMRING" 300353 T COMRING (NIL) -9 NIL 300405) (-168 298881 299158 299342 "COMPPROP" 299636 T COMPPROP (NIL) -8 NIL NIL) (-167 298542 298577 298705 "COMPLPAT" 298840 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-166 288599 298351 298460 "COMPLEX" 298465 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 288235 288292 288399 "COMPLEX2" 288536 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-164 287953 287988 288086 "COMPFACT" 288194 NIL COMPFACT (NIL T T) -7 NIL NIL) (-163 272357 282575 282615 "COMPCAT" 283619 NIL COMPCAT (NIL T) -9 NIL 285004) (-162 261872 264796 268423 "COMPCAT-" 268779 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-161 261601 261629 261732 "COMMUPC" 261838 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-160 261396 261429 261488 "COMMONOP" 261562 T COMMONOP (NIL) -7 NIL NIL) (-159 260979 261147 261234 "COMM" 261329 T COMM (NIL) -8 NIL NIL) (-158 260583 260783 260858 "COMMAAST" 260924 T COMMAAST (NIL) -8 NIL NIL) (-157 259832 260026 260054 "COMBOPC" 260392 T COMBOPC (NIL) -9 NIL 260567) (-156 258728 258938 259180 "COMBINAT" 259622 NIL COMBINAT (NIL T) -7 NIL NIL) (-155 254926 255499 256139 "COMBF" 258150 NIL COMBF (NIL T T) -7 NIL NIL) (-154 253712 254042 254277 "COLOR" 254711 T COLOR (NIL) -8 NIL NIL) (-153 253215 253433 253525 "COLONAST" 253640 T COLONAST (NIL) -8 NIL NIL) (-152 252855 252902 253027 "CMPLXRT" 253162 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-151 252330 252555 252654 "CLLCTAST" 252776 T CLLCTAST (NIL) -8 NIL NIL) (-150 247832 248860 249940 "CLIP" 251270 T CLIP (NIL) -7 NIL NIL) (-149 246214 246938 247177 "CLIF" 247659 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-148 242436 244360 244401 "CLAGG" 245330 NIL CLAGG (NIL T) -9 NIL 245866) (-147 240858 241315 241898 "CLAGG-" 241903 NIL CLAGG- (NIL T T) -8 NIL NIL) (-146 240402 240487 240627 "CINTSLPE" 240767 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-145 237903 238374 238922 "CHVAR" 239930 NIL CHVAR (NIL T T T) -7 NIL NIL) (-144 237166 237686 237714 "CHARZ" 237719 T CHARZ (NIL) -9 NIL 237734) (-143 236920 236960 237038 "CHARPOL" 237120 NIL CHARPOL (NIL T) -7 NIL NIL) (-142 236067 236620 236648 "CHARNZ" 236695 T CHARNZ (NIL) -9 NIL 236751) (-141 234092 234757 235092 "CHAR" 235752 T CHAR (NIL) -8 NIL NIL) (-140 233818 233879 233907 "CFCAT" 234018 T CFCAT (NIL) -9 NIL NIL) (-139 233063 233174 233356 "CDEN" 233702 NIL CDEN (NIL T T T) -7 NIL NIL) (-138 229055 232216 232496 "CCLASS" 232803 T CCLASS (NIL) -8 NIL NIL) (-137 228974 229000 229035 "CATEGORY" 229040 T -10 (NIL) -8 NIL NIL) (-136 228448 228674 228773 "CATAST" 228895 T CATAST (NIL) -8 NIL NIL) (-135 227951 228169 228261 "CASEAST" 228376 T CASEAST (NIL) -8 NIL NIL) (-134 223003 223980 224733 "CARTEN" 227254 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-133 222111 222259 222480 "CARTEN2" 222850 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-132 220453 221261 221518 "CARD" 221874 T CARD (NIL) -8 NIL NIL) (-131 220056 220257 220332 "CAPSLAST" 220398 T CAPSLAST (NIL) -8 NIL NIL) (-130 219428 219756 219784 "CACHSET" 219916 T CACHSET (NIL) -9 NIL 219993) (-129 218924 219220 219248 "CABMON" 219298 T CABMON (NIL) -9 NIL 219354) (-128 217851 218279 218475 "BYTE" 218748 T BYTE (NIL) -8 NIL NIL) (-127 213260 217319 217482 "BYTEBUF" 217708 T BYTEBUF (NIL) -8 NIL NIL) (-126 210817 212952 213059 "BTREE" 213186 NIL BTREE (NIL T) -8 NIL NIL) (-125 208315 210465 210587 "BTOURN" 210727 NIL BTOURN (NIL T) -8 NIL NIL) (-124 205733 207786 207827 "BTCAT" 207895 NIL BTCAT (NIL T) -9 NIL 207972) (-123 205400 205480 205629 "BTCAT-" 205634 NIL BTCAT- (NIL T T) -8 NIL NIL) (-122 200692 204543 204571 "BTAGG" 204793 T BTAGG (NIL) -9 NIL 204954) (-121 200182 200307 200513 "BTAGG-" 200518 NIL BTAGG- (NIL T) -8 NIL NIL) (-120 197226 199460 199675 "BSTREE" 199999 NIL BSTREE (NIL T) -8 NIL NIL) (-119 196364 196490 196674 "BRILL" 197082 NIL BRILL (NIL T) -7 NIL NIL) (-118 193065 195092 195133 "BRAGG" 195782 NIL BRAGG (NIL T) -9 NIL 196039) (-117 191594 192000 192555 "BRAGG-" 192560 NIL BRAGG- (NIL T T) -8 NIL NIL) (-116 184858 190940 191124 "BPADICRT" 191442 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-115 183208 184795 184840 "BPADIC" 184845 NIL BPADIC (NIL NIL) -8 NIL NIL) (-114 182906 182936 183050 "BOUNDZRO" 183172 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-113 178421 179512 180379 "BOP" 182059 T BOP (NIL) -8 NIL NIL) (-112 176042 176486 177006 "BOP1" 177934 NIL BOP1 (NIL T) -7 NIL NIL) (-111 174780 175466 175659 "BOOLEAN" 175869 T BOOLEAN (NIL) -8 NIL NIL) (-110 174142 174520 174574 "BMODULE" 174579 NIL BMODULE (NIL T T) -9 NIL 174644) (-109 169972 173940 174013 "BITS" 174089 T BITS (NIL) -8 NIL NIL) (-108 169384 169506 169648 "BINDING" 169850 T BINDING (NIL) -8 NIL NIL) (-107 163274 168828 168993 "BINARY" 169239 T BINARY (NIL) -8 NIL NIL) (-106 161101 162529 162570 "BGAGG" 162830 NIL BGAGG (NIL T) -9 NIL 162967) (-105 160932 160964 161055 "BGAGG-" 161060 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 160030 160316 160521 "BFUNCT" 160747 T BFUNCT (NIL) -8 NIL NIL) (-103 158720 158898 159186 "BEZOUT" 159854 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 155237 157572 157902 "BBTREE" 158423 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154971 155024 155052 "BASTYPE" 155171 T BASTYPE (NIL) -9 NIL NIL) (-100 154823 154852 154925 "BASTYPE-" 154930 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 154261 154337 154487 "BALFACT" 154734 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 153144 153676 153862 "AUTOMOR" 154106 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152870 152875 152901 "ATTREG" 152906 T ATTREG (NIL) -9 NIL NIL) (-96 151149 151567 151919 "ATTRBUT" 152536 T ATTRBUT (NIL) -8 NIL NIL) (-95 150784 150977 151043 "ATTRAST" 151101 T ATTRAST (NIL) -8 NIL NIL) (-94 150320 150433 150459 "ATRIG" 150660 T ATRIG (NIL) -9 NIL NIL) (-93 150129 150170 150257 "ATRIG-" 150262 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149751 149911 149937 "ASTCAT" 149995 T ASTCAT (NIL) -9 NIL 150058) (-91 149478 149537 149656 "ASTCAT-" 149661 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147675 149254 149342 "ASTACK" 149421 NIL ASTACK (NIL T) -8 NIL NIL) (-89 146180 146477 146842 "ASSOCEQ" 147357 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 145212 145839 145963 "ASP9" 146087 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 144976 145160 145199 "ASP8" 145204 NIL ASP8 (NIL NIL) -8 NIL NIL) (-86 143845 144581 144723 "ASP80" 144865 NIL ASP80 (NIL NIL) -8 NIL NIL) (-85 142744 143480 143612 "ASP7" 143744 NIL ASP7 (NIL NIL) -8 NIL NIL) (-84 141698 142421 142539 "ASP78" 142657 NIL ASP78 (NIL NIL) -8 NIL NIL) (-83 140667 141378 141495 "ASP77" 141612 NIL ASP77 (NIL NIL) -8 NIL NIL) (-82 139579 140305 140436 "ASP74" 140567 NIL ASP74 (NIL NIL) -8 NIL NIL) (-81 138479 139214 139346 "ASP73" 139478 NIL ASP73 (NIL NIL) -8 NIL NIL) (-80 137434 138156 138274 "ASP6" 138392 NIL ASP6 (NIL NIL) -8 NIL NIL) (-79 136382 137111 137229 "ASP55" 137347 NIL ASP55 (NIL NIL) -8 NIL NIL) (-78 135332 136056 136175 "ASP50" 136294 NIL ASP50 (NIL NIL) -8 NIL NIL) (-77 134420 135033 135143 "ASP4" 135253 NIL ASP4 (NIL NIL) -8 NIL NIL) (-76 133508 134121 134231 "ASP49" 134341 NIL ASP49 (NIL NIL) -8 NIL NIL) (-75 132293 133047 133215 "ASP42" 133397 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-74 131070 131826 131996 "ASP41" 132180 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130020 130747 130865 "ASP35" 130983 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129785 129968 130007 "ASP34" 130012 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129522 129589 129665 "ASP33" 129740 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128417 129157 129289 "ASP31" 129421 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 128182 128365 128404 "ASP30" 128409 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 127917 127986 128062 "ASP29" 128137 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127682 127865 127904 "ASP28" 127909 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127447 127630 127669 "ASP27" 127674 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126531 127145 127256 "ASP24" 127367 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125447 126172 126302 "ASP20" 126432 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124535 125148 125258 "ASP1" 125368 NIL ASP1 (NIL NIL) -8 NIL NIL) (-62 123479 124209 124328 "ASP19" 124447 NIL ASP19 (NIL NIL) -8 NIL NIL) (-61 123216 123283 123359 "ASP12" 123434 NIL ASP12 (NIL NIL) -8 NIL NIL) (-60 122068 122815 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+(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-552)) . T) ((-25) . T) ((-38 #1=(-401 (-552))) -4029 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-552))))) ((-38 |#1|) |has| |#1| (-169)) ((-38 |#2|) |has| |#1| (-357)) ((-38 $) -4029 (|has| |#1| (-544)) (|has| |#1| (-357))) ((-35) |has| |#1| (-38 (-401 (-552)))) ((-94) |has| |#1| (-38 (-401 (-552)))) ((-101) . T) ((-110 #1# #1#) -4029 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-552))))) ((-110 |#1| |#1|) . T) ((-110 |#2| |#2|) |has| |#1| (-357)) ((-110 $ $) -4029 (|has| |#1| (-544)) (|has| |#1| (-357)) (|has| |#1| (-169))) ((-129) . T) ((-142) -4029 (-12 (|has| |#1| (-357)) (|has| |#2| (-142))) (|has| |#1| (-142))) ((-144) -4029 (-12 (|has| |#1| (-357)) (|has| |#2| (-144))) (|has| |#1| (-144))) ((-599 (-844)) . T) ((-169) -4029 (|has| |#1| (-544)) (|has| |#1| (-357)) (|has| |#1| (-169))) ((-600 (-220)) -12 (|has| |#1| (-357)) (|has| |#2| (-1003))) ((-600 (-373)) -12 (|has| |#1| (-357)) (|has| |#2| (-1003))) ((-600 (-528)) -12 (|has| |#1| (-357)) (|has| |#2| (-600 (-528)))) ((-600 (-873 (-373))) -12 (|has| |#1| (-357)) (|has| |#2| (-600 (-873 (-373))))) ((-600 (-873 (-552))) -12 (|has| |#1| (-357)) (|has| |#2| (-600 (-873 (-552))))) ((-226 |#2|) |has| |#1| (-357)) ((-228) -4029 (-12 (|has| |#1| (-357)) (|has| |#2| (-228))) (|has| |#1| (-15 * (|#1| (-552) |#1|)))) ((-238) |has| |#1| (-357)) ((-278) |has| |#1| (-38 (-401 (-552)))) ((-280 |#2| $) -12 (|has| |#1| (-357)) (|has| |#2| (-280 |#2| |#2|))) ((-280 $ $) |has| (-552) (-1090)) ((-284) -4029 (|has| |#1| (-544)) (|has| |#1| (-357))) ((-301) |has| |#1| (-357)) ((-303 |#2|) -12 (|has| |#1| (-357)) (|has| |#2| (-303 |#2|))) ((-357) |has| |#1| (-357)) ((-332 |#2|) |has| |#1| (-357)) ((-371 |#2|) |has| |#1| (-357)) ((-394 |#2|) |has| |#1| (-357)) ((-445) |has| |#1| (-357)) ((-485) |has| |#1| (-38 (-401 (-552)))) ((-506 (-1154) |#2|) -12 (|has| |#1| (-357)) (|has| |#2| (-506 (-1154) |#2|))) ((-506 |#2| |#2|) -12 (|has| |#1| (-357)) (|has| |#2| (-303 |#2|))) ((-544) -4029 (|has| |#1| (-544)) (|has| |#1| (-357))) ((-632 #1#) -4029 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-552))))) ((-632 |#1|) . T) ((-632 |#2|) |has| |#1| (-357)) ((-632 $) . T) ((-625 (-552)) -12 (|has| |#1| (-357)) (|has| |#2| (-625 (-552)))) ((-625 |#2|) |has| |#1| (-357)) ((-702 #1#) -4029 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-552))))) ((-702 |#1|) |has| |#1| (-169)) ((-702 |#2|) |has| |#1| (-357)) ((-702 $) -4029 (|has| |#1| (-544)) (|has| |#1| (-357))) ((-711) . 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"STRICAT" 2722708 T STRICAT (NIL) -9 NIL 2722770) (-1134 2710847 2715657 2716277 "STREAM" 2717549 NIL STREAM (NIL T) -8 NIL NIL) (-1133 2710357 2710434 2710578 "STREAM3" 2710764 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1132 2709339 2709522 2709757 "STREAM2" 2710170 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1131 2709027 2709079 2709172 "STREAM1" 2709281 NIL STREAM1 (NIL T) -7 NIL NIL) (-1130 2708043 2708224 2708455 "STINPROD" 2708843 NIL STINPROD (NIL T) -7 NIL NIL) (-1129 2707621 2707805 2707835 "STEP" 2707915 T STEP (NIL) -9 NIL 2707993) (-1128 2701164 2707520 2707597 "STBL" 2707602 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1127 2696339 2700386 2700429 "STAGG" 2700582 NIL STAGG (NIL T) -9 NIL 2700671) (-1126 2694041 2694643 2695515 "STAGG-" 2695520 NIL STAGG- (NIL T T) -8 NIL NIL) (-1125 2692236 2693811 2693903 "STACK" 2693984 NIL STACK (NIL T) -8 NIL NIL) (-1124 2684961 2690377 2690833 "SREGSET" 2691866 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1123 2677387 2678755 2680268 "SRDCMPK" 2683567 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1122 2670354 2674827 2674857 "SRAGG" 2676160 T SRAGG (NIL) -9 NIL 2676768) (-1121 2669371 2669626 2670005 "SRAGG-" 2670010 NIL SRAGG- (NIL T) -8 NIL NIL) (-1120 2663866 2668318 2668739 "SQMATRIX" 2668997 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1119 2657618 2660586 2661312 "SPLTREE" 2663212 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1118 2653608 2654274 2654920 "SPLNODE" 2657044 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1117 2652655 2652888 2652918 "SPFCAT" 2653362 T SPFCAT (NIL) -9 NIL NIL) (-1116 2651392 2651602 2651866 "SPECOUT" 2652413 T SPECOUT (NIL) -7 NIL NIL) (-1115 2643081 2644825 2644855 "SPADXPT" 2649247 T SPADXPT (NIL) -9 NIL 2651281) (-1114 2642842 2642882 2642951 "SPADPRSR" 2643034 T SPADPRSR (NIL) -7 NIL NIL) (-1113 2641025 2642797 2642828 "SPADAST" 2642833 T SPADAST (NIL) -8 NIL NIL) (-1112 2632996 2634743 2634786 "SPACEC" 2639159 NIL SPACEC (NIL T) -9 NIL 2640975) (-1111 2631167 2632928 2632977 "SPACE3" 2632982 NIL SPACE3 (NIL T) -8 NIL NIL) (-1110 2629919 2630090 2630381 "SORTPAK" 2630972 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1109 2627969 2628272 2628691 "SOLVETRA" 2629583 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1108 2626980 2627202 2627476 "SOLVESER" 2627742 NIL SOLVESER (NIL T) -7 NIL NIL) (-1107 2622200 2623081 2624083 "SOLVERAD" 2626032 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1106 2618015 2618624 2619353 "SOLVEFOR" 2621567 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1105 2612312 2617364 2617461 "SNTSCAT" 2617466 NIL SNTSCAT (NIL T T T T) -9 NIL 2617536) (-1104 2606455 2610635 2611026 "SMTS" 2612002 NIL SMTS (NIL T T T) -8 NIL NIL) (-1103 2600905 2606343 2606420 "SMP" 2606425 NIL SMP (NIL T T) -8 NIL NIL) (-1102 2599064 2599365 2599763 "SMITH" 2600602 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1101 2592047 2596202 2596305 "SMATCAT" 2597656 NIL SMATCAT (NIL NIL T T T) -9 NIL 2598206) (-1100 2588987 2589810 2590988 "SMATCAT-" 2590993 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1099 2586700 2588223 2588266 "SKAGG" 2588527 NIL SKAGG (NIL T) -9 NIL 2588662) (-1098 2582816 2585804 2586082 "SINT" 2586444 T SINT (NIL) -8 NIL NIL) (-1097 2582588 2582626 2582692 "SIMPAN" 2582772 T SIMPAN (NIL) -7 NIL NIL) (-1096 2581895 2582123 2582263 "SIG" 2582470 T SIG (NIL) -8 NIL NIL) (-1095 2580733 2580954 2581229 "SIGNRF" 2581654 NIL SIGNRF (NIL T) -7 NIL NIL) (-1094 2579538 2579689 2579980 "SIGNEF" 2580562 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1093 2578871 2579121 2579245 "SIGAST" 2579436 T SIGAST (NIL) -8 NIL NIL) (-1092 2576561 2577015 2577521 "SHP" 2578412 NIL SHP (NIL T NIL) -7 NIL NIL) (-1091 2570467 2576462 2576538 "SHDP" 2576543 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1090 2570066 2570232 2570262 "SGROUP" 2570355 T SGROUP (NIL) -9 NIL 2570417) (-1089 2569924 2569950 2570023 "SGROUP-" 2570028 NIL SGROUP- (NIL T) -8 NIL NIL) (-1088 2566760 2567457 2568180 "SGCF" 2569223 T SGCF (NIL) -7 NIL NIL) (-1087 2561155 2566207 2566304 "SFRTCAT" 2566309 NIL SFRTCAT (NIL T T T T) -9 NIL 2566348) (-1086 2554579 2555594 2556730 "SFRGCD" 2560138 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1085 2547707 2548778 2549964 "SFQCMPK" 2553512 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1084 2547329 2547418 2547528 "SFORT" 2547648 NIL SFORT (NIL T T) -8 NIL NIL) (-1083 2546474 2547169 2547290 "SEXOF" 2547295 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1082 2545608 2546355 2546423 "SEX" 2546428 T SEX (NIL) -8 NIL NIL) (-1081 2540384 2541073 2541168 "SEXCAT" 2544939 NIL SEXCAT (NIL T T T T T) -9 NIL 2545558) (-1080 2537564 2540318 2540366 "SET" 2540371 NIL SET (NIL T) -8 NIL NIL) (-1079 2535815 2536277 2536582 "SETMN" 2537305 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1078 2535421 2535547 2535577 "SETCAT" 2535694 T SETCAT (NIL) -9 NIL 2535779) (-1077 2535201 2535253 2535352 "SETCAT-" 2535357 NIL SETCAT- (NIL T) -8 NIL NIL) (-1076 2531588 2533662 2533705 "SETAGG" 2534575 NIL SETAGG (NIL T) -9 NIL 2534915) (-1075 2531046 2531162 2531399 "SETAGG-" 2531404 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1074 2530516 2530742 2530843 "SEQAST" 2530967 T SEQAST (NIL) -8 NIL NIL) (-1073 2529720 2530013 2530074 "SEGXCAT" 2530360 NIL SEGXCAT (NIL T T) -9 NIL 2530480) (-1072 2528776 2529386 2529568 "SEG" 2529573 NIL SEG (NIL T) -8 NIL NIL) (-1071 2527683 2527896 2527939 "SEGCAT" 2528521 NIL SEGCAT (NIL T) -9 NIL 2528759) (-1070 2526732 2527062 2527262 "SEGBIND" 2527518 NIL SEGBIND (NIL T) -8 NIL NIL) (-1069 2526353 2526412 2526525 "SEGBIND2" 2526667 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1068 2525954 2526154 2526231 "SEGAST" 2526298 T SEGAST (NIL) -8 NIL NIL) (-1067 2525173 2525299 2525503 "SEG2" 2525798 NIL SEG2 (NIL T T) -7 NIL NIL) (-1066 2524610 2525108 2525155 "SDVAR" 2525160 NIL SDVAR (NIL T) -8 NIL NIL) (-1065 2516900 2524380 2524510 "SDPOL" 2524515 NIL SDPOL (NIL T) -8 NIL NIL) (-1064 2515493 2515759 2516078 "SCPKG" 2516615 NIL SCPKG (NIL T) -7 NIL NIL) (-1063 2514629 2514809 2515009 "SCOPE" 2515315 T SCOPE (NIL) -8 NIL NIL) (-1062 2513850 2513983 2514162 "SCACHE" 2514484 NIL SCACHE (NIL T) -7 NIL NIL) (-1061 2513559 2513719 2513749 "SASTCAT" 2513754 T SASTCAT (NIL) -9 NIL 2513767) (-1060 2512998 2513319 2513404 "SAOS" 2513496 T SAOS (NIL) -8 NIL NIL) (-1059 2512563 2512598 2512771 "SAERFFC" 2512957 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1058 2506537 2512460 2512540 "SAE" 2512545 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1057 2506130 2506165 2506324 "SAEFACT" 2506496 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1056 2504451 2504765 2505166 "RURPK" 2505796 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1055 2503087 2503366 2503678 "RULESET" 2504285 NIL RULESET (NIL T T T) -8 NIL NIL) (-1054 2500274 2500777 2501242 "RULE" 2502768 NIL RULE (NIL T T T) -8 NIL NIL) (-1053 2499913 2500068 2500151 "RULECOLD" 2500226 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1052 2499411 2499630 2499724 "RSTRCAST" 2499841 T RSTRCAST (NIL) -8 NIL NIL) (-1051 2494260 2495054 2495974 "RSETGCD" 2498610 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1050 2483517 2488569 2488666 "RSETCAT" 2492785 NIL RSETCAT (NIL T T T T) -9 NIL 2493882) (-1049 2481444 2481983 2482807 "RSETCAT-" 2482812 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1048 2473831 2475206 2476726 "RSDCMPK" 2480043 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1047 2471836 2472277 2472351 "RRCC" 2473437 NIL RRCC (NIL T T) -9 NIL 2473781) (-1046 2471187 2471361 2471640 "RRCC-" 2471645 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1045 2470657 2470883 2470984 "RPTAST" 2471108 T RPTAST (NIL) -8 NIL NIL) (-1044 2444885 2454470 2454537 "RPOLCAT" 2465201 NIL RPOLCAT (NIL T T T) -9 NIL 2468360) (-1043 2436385 2438723 2441845 "RPOLCAT-" 2441850 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1042 2427432 2434596 2435078 "ROUTINE" 2435925 T ROUTINE (NIL) -8 NIL NIL) (-1041 2424190 2426983 2427132 "ROMAN" 2427305 T ROMAN (NIL) -8 NIL NIL) (-1040 2422465 2423050 2423310 "ROIRC" 2423995 NIL ROIRC (NIL T T) -8 NIL NIL) (-1039 2418914 2421153 2421183 "RNS" 2421487 T RNS (NIL) -9 NIL 2421760) (-1038 2417423 2417806 2418340 "RNS-" 2418415 NIL RNS- (NIL T) -8 NIL NIL) (-1037 2416872 2417254 2417284 "RNG" 2417289 T RNG (NIL) -9 NIL 2417310) (-1036 2416264 2416626 2416669 "RMODULE" 2416731 NIL RMODULE (NIL T) -9 NIL 2416773) (-1035 2415100 2415194 2415530 "RMCAT2" 2416165 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1034 2411805 2414274 2414599 "RMATRIX" 2414834 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1033 2404747 2406981 2407096 "RMATCAT" 2410455 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2411437) (-1032 2404122 2404269 2404576 "RMATCAT-" 2404581 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1031 2403689 2403764 2403892 "RINTERP" 2404041 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1030 2402777 2403297 2403327 "RING" 2403439 T RING (NIL) -9 NIL 2403534) (-1029 2402569 2402613 2402710 "RING-" 2402715 NIL RING- (NIL T) -8 NIL NIL) (-1028 2401410 2401647 2401905 "RIDIST" 2402333 T RIDIST (NIL) -7 NIL NIL) (-1027 2392726 2400878 2401084 "RGCHAIN" 2401258 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1026 2392102 2392482 2392523 "RGBCSPC" 2392581 NIL RGBCSPC (NIL T) -9 NIL 2392633) (-1025 2391286 2391641 2391682 "RGBCMDL" 2391914 NIL RGBCMDL (NIL T) -9 NIL 2392028) (-1024 2388280 2388894 2389564 "RF" 2390650 NIL RF (NIL T) -7 NIL NIL) (-1023 2387926 2387989 2388092 "RFFACTOR" 2388211 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1022 2387651 2387686 2387783 "RFFACT" 2387885 NIL RFFACT (NIL T) -7 NIL NIL) (-1021 2385768 2386132 2386514 "RFDIST" 2387291 T RFDIST (NIL) -7 NIL NIL) (-1020 2385221 2385313 2385476 "RETSOL" 2385670 NIL RETSOL (NIL T T) -7 NIL NIL) (-1019 2384809 2384889 2384932 "RETRACT" 2385125 NIL RETRACT (NIL T) -9 NIL NIL) (-1018 2384658 2384683 2384770 "RETRACT-" 2384775 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1017 2384287 2384480 2384550 "RETAST" 2384610 T RETAST (NIL) -8 NIL NIL) (-1016 2377141 2383940 2384067 "RESULT" 2384182 T RESULT (NIL) -8 NIL NIL) (-1015 2375767 2376410 2376609 "RESRING" 2377044 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1014 2375403 2375452 2375550 "RESLATC" 2375704 NIL RESLATC (NIL T) -7 NIL NIL) (-1013 2375109 2375143 2375250 "REPSQ" 2375362 NIL REPSQ (NIL T) -7 NIL NIL) (-1012 2372531 2373111 2373713 "REP" 2374529 T REP (NIL) -7 NIL NIL) (-1011 2372229 2372263 2372374 "REPDB" 2372490 NIL REPDB (NIL T) -7 NIL NIL) (-1010 2366139 2367518 2368741 "REP2" 2371041 NIL REP2 (NIL T) -7 NIL NIL) (-1009 2362516 2363197 2364005 "REP1" 2365366 NIL REP1 (NIL T) -7 NIL NIL) (-1008 2355242 2360657 2361113 "REGSET" 2362146 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1007 2354055 2354390 2354640 "REF" 2355027 NIL REF (NIL T) -8 NIL NIL) (-1006 2353432 2353535 2353702 "REDORDER" 2353939 NIL REDORDER (NIL T T) -7 NIL NIL) (-1005 2349439 2352647 2352873 "RECLOS" 2353261 NIL RECLOS (NIL T) -8 NIL NIL) (-1004 2348491 2348672 2348887 "REALSOLV" 2349246 T REALSOLV (NIL) -7 NIL NIL) (-1003 2348337 2348378 2348408 "REAL" 2348413 T REAL (NIL) -9 NIL 2348448) (-1002 2344820 2345622 2346506 "REAL0Q" 2347502 NIL REAL0Q (NIL T) -7 NIL NIL) (-1001 2340421 2341409 2342470 "REAL0" 2343801 NIL REAL0 (NIL T) -7 NIL NIL) (-1000 2339919 2340138 2340232 "RDUCEAST" 2340349 T RDUCEAST (NIL) -8 NIL NIL) (-999 2339327 2339399 2339604 "RDIV" 2339841 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-998 2338400 2338574 2338785 "RDIST" 2339149 NIL RDIST (NIL T) -7 NIL NIL) (-997 2337001 2337288 2337658 "RDETRS" 2338108 NIL RDETRS (NIL T T) -7 NIL NIL) (-996 2334818 2335272 2335808 "RDETR" 2336543 NIL RDETR (NIL T T) -7 NIL NIL) (-995 2333432 2333710 2334112 "RDEEFS" 2334534 NIL RDEEFS (NIL T T) -7 NIL NIL) (-994 2331930 2332236 2332666 "RDEEF" 2333120 NIL RDEEF (NIL T T) -7 NIL NIL) (-993 2326267 2329138 2329166 "RCFIELD" 2330443 T RCFIELD (NIL) -9 NIL 2331173) (-992 2324336 2324840 2325533 "RCFIELD-" 2325606 NIL RCFIELD- (NIL T) -8 NIL NIL) (-991 2320667 2322452 2322493 "RCAGG" 2323564 NIL RCAGG (NIL T) -9 NIL 2324029) (-990 2320298 2320392 2320552 "RCAGG-" 2320557 NIL RCAGG- (NIL T T) -8 NIL NIL) (-989 2319638 2319750 2319913 "RATRET" 2320182 NIL RATRET (NIL T) -7 NIL NIL) (-988 2319195 2319262 2319381 "RATFACT" 2319566 NIL RATFACT (NIL T) -7 NIL NIL) (-987 2318510 2318630 2318780 "RANDSRC" 2319065 T RANDSRC (NIL) -7 NIL NIL) (-986 2318247 2318291 2318362 "RADUTIL" 2318459 T RADUTIL (NIL) -7 NIL NIL) (-985 2311310 2316990 2317307 "RADIX" 2317962 NIL RADIX (NIL NIL) -8 NIL NIL) (-984 2302966 2311154 2311282 "RADFF" 2311287 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-983 2302618 2302693 2302721 "RADCAT" 2302878 T RADCAT (NIL) -9 NIL NIL) (-982 2302403 2302451 2302548 "RADCAT-" 2302553 NIL RADCAT- (NIL T) -8 NIL NIL) (-981 2300554 2302178 2302267 "QUEUE" 2302347 NIL QUEUE (NIL T) -8 NIL NIL) (-980 2297130 2300491 2300536 "QUAT" 2300541 NIL QUAT (NIL T) -8 NIL NIL) (-979 2296768 2296811 2296938 "QUATCT2" 2297081 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-978 2290628 2293929 2293969 "QUATCAT" 2294749 NIL QUATCAT (NIL T) -9 NIL 2295515) (-977 2286772 2287809 2289196 "QUATCAT-" 2289290 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-976 2284292 2285856 2285897 "QUAGG" 2286272 NIL QUAGG (NIL T) -9 NIL 2286447) (-975 2283924 2284117 2284185 "QQUTAST" 2284244 T QQUTAST (NIL) -8 NIL NIL) (-974 2282849 2283322 2283494 "QFORM" 2283796 NIL QFORM (NIL NIL T) -8 NIL NIL) (-973 2274174 2279379 2279419 "QFCAT" 2280077 NIL QFCAT (NIL T) -9 NIL 2281078) (-972 2269746 2270947 2272538 "QFCAT-" 2272632 NIL QFCAT- (NIL T T) -8 NIL NIL) (-971 2269384 2269427 2269554 "QFCAT2" 2269697 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-970 2268844 2268954 2269084 "QEQUAT" 2269274 T QEQUAT (NIL) -8 NIL NIL) (-969 2261992 2263063 2264247 "QCMPACK" 2267777 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-968 2259568 2259989 2260417 "QALGSET" 2261647 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-967 2258813 2258987 2259219 "QALGSET2" 2259388 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-966 2257504 2257727 2258044 "PWFFINTB" 2258586 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-965 2255686 2255854 2256208 "PUSHVAR" 2257318 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-964 2251604 2252658 2252699 "PTRANFN" 2254583 NIL PTRANFN (NIL T) -9 NIL NIL) (-963 2250006 2250297 2250619 "PTPACK" 2251315 NIL PTPACK (NIL T) -7 NIL NIL) (-962 2249638 2249695 2249804 "PTFUNC2" 2249943 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-961 2244104 2248449 2248490 "PTCAT" 2248863 NIL PTCAT (NIL T) -9 NIL 2249025) (-960 2243762 2243797 2243921 "PSQFR" 2244063 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-959 2242357 2242655 2242989 "PSEUDLIN" 2243460 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-958 2229126 2231491 2233815 "PSETPK" 2240117 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-957 2222170 2224884 2224980 "PSETCAT" 2228001 NIL PSETCAT (NIL T T T T) -9 NIL 2228815) (-956 2220006 2220640 2221461 "PSETCAT-" 2221466 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-955 2219355 2219520 2219548 "PSCURVE" 2219816 T PSCURVE (NIL) -9 NIL 2219983) (-954 2215836 2217318 2217383 "PSCAT" 2218227 NIL PSCAT (NIL T T T) -9 NIL 2218467) (-953 2214899 2215115 2215515 "PSCAT-" 2215520 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-952 2213551 2214184 2214398 "PRTITION" 2214705 T PRTITION (NIL) -8 NIL NIL) (-951 2213053 2213272 2213364 "PRTDAST" 2213479 T PRTDAST (NIL) -8 NIL NIL) (-950 2202151 2204357 2206545 "PRS" 2210915 NIL PRS (NIL T T) -7 NIL NIL) (-949 2200009 2201501 2201541 "PRQAGG" 2201724 NIL PRQAGG (NIL T) -9 NIL 2201826) (-948 2199395 2199624 2199652 "PROPLOG" 2199837 T PROPLOG (NIL) -9 NIL 2199959) (-947 2196565 2197209 2197673 "PROPFRML" 2198963 NIL PROPFRML (NIL T) -8 NIL NIL) (-946 2196025 2196135 2196265 "PROPERTY" 2196455 T PROPERTY (NIL) -8 NIL NIL) (-945 2190110 2194191 2195011 "PRODUCT" 2195251 NIL PRODUCT (NIL T T) -8 NIL NIL) (-944 2187423 2189568 2189802 "PR" 2189921 NIL PR (NIL T T) -8 NIL NIL) (-943 2187219 2187251 2187310 "PRINT" 2187384 T PRINT (NIL) -7 NIL NIL) (-942 2186559 2186676 2186828 "PRIMES" 2187099 NIL PRIMES (NIL T) -7 NIL NIL) (-941 2184624 2185025 2185491 "PRIMELT" 2186138 NIL PRIMELT (NIL T) -7 NIL NIL) (-940 2184353 2184402 2184430 "PRIMCAT" 2184554 T PRIMCAT (NIL) -9 NIL NIL) (-939 2180514 2184291 2184336 "PRIMARR" 2184341 NIL PRIMARR (NIL T) -8 NIL NIL) (-938 2179521 2179699 2179927 "PRIMARR2" 2180332 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-937 2179164 2179220 2179331 "PREASSOC" 2179459 NIL PREASSOC (NIL T T) -7 NIL NIL) (-936 2178639 2178772 2178800 "PPCURVE" 2179005 T PPCURVE (NIL) -9 NIL 2179141) (-935 2178261 2178434 2178517 "PORTNUM" 2178576 T PORTNUM (NIL) -8 NIL NIL) (-934 2175620 2176019 2176611 "POLYROOT" 2177842 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-933 2169565 2175224 2175384 "POLY" 2175493 NIL POLY (NIL T) -8 NIL NIL) (-932 2168948 2169006 2169240 "POLYLIFT" 2169501 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-931 2165223 2165672 2166301 "POLYCATQ" 2168493 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-930 2152262 2157618 2157683 "POLYCAT" 2161197 NIL POLYCAT (NIL T T T) -9 NIL 2163125) (-929 2145712 2147573 2149957 "POLYCAT-" 2149962 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-928 2145299 2145367 2145487 "POLY2UP" 2145638 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-927 2144931 2144988 2145097 "POLY2" 2145236 NIL POLY2 (NIL T T) -7 NIL NIL) (-926 2143616 2143855 2144131 "POLUTIL" 2144705 NIL POLUTIL (NIL T T) -7 NIL NIL) (-925 2141971 2142248 2142579 "POLTOPOL" 2143338 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-924 2137489 2141907 2141953 "POINT" 2141958 NIL POINT (NIL T) -8 NIL NIL) (-923 2135676 2136033 2136408 "PNTHEORY" 2137134 T PNTHEORY (NIL) -7 NIL NIL) (-922 2134095 2134392 2134804 "PMTOOLS" 2135374 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-921 2133688 2133766 2133883 "PMSYM" 2134011 NIL PMSYM (NIL T) -7 NIL NIL) (-920 2133198 2133267 2133441 "PMQFCAT" 2133613 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-919 2132553 2132663 2132819 "PMPRED" 2133075 NIL PMPRED (NIL T) -7 NIL NIL) (-918 2131949 2132035 2132196 "PMPREDFS" 2132454 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-917 2130592 2130800 2131185 "PMPLCAT" 2131711 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-916 2130124 2130203 2130355 "PMLSAGG" 2130507 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-915 2129599 2129675 2129856 "PMKERNEL" 2130042 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-914 2129216 2129291 2129404 "PMINS" 2129518 NIL PMINS (NIL T) -7 NIL NIL) (-913 2128644 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2087196 2087284 "PICOERCE" 2087391 NIL PICOERCE (NIL T) -7 NIL NIL) (-899 2086479 2086618 2086794 "PGROEB" 2087015 NIL PGROEB (NIL T) -7 NIL NIL) (-898 2082066 2082880 2083785 "PGE" 2085594 T PGE (NIL) -7 NIL NIL) (-897 2080190 2080436 2080802 "PGCD" 2081783 NIL PGCD (NIL T T T T) -7 NIL NIL) (-896 2079528 2079631 2079792 "PFRPAC" 2080074 NIL PFRPAC (NIL T) -7 NIL NIL) (-895 2076208 2078076 2078429 "PFR" 2079207 NIL PFR (NIL T) -8 NIL NIL) (-894 2074597 2074841 2075166 "PFOTOOLS" 2075955 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-893 2073130 2073369 2073720 "PFOQ" 2074354 NIL PFOQ (NIL T T T) -7 NIL NIL) (-892 2071603 2071815 2072178 "PFO" 2072914 NIL PFO (NIL T T T T T) -7 NIL NIL) (-891 2068191 2071492 2071561 "PF" 2071566 NIL PF (NIL NIL) -8 NIL NIL) (-890 2065660 2066897 2066925 "PFECAT" 2067510 T PFECAT (NIL) -9 NIL 2067894) (-889 2065105 2065259 2065473 "PFECAT-" 2065478 NIL PFECAT- (NIL T) -8 NIL NIL) (-888 2063709 2063960 2064261 "PFBRU" 2064854 NIL PFBRU (NIL T T) -7 NIL NIL) (-887 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NIL PCOMP (NIL T T) -7 NIL NIL) (-874 2034360 2034956 2035253 "PBWLB" 2035884 NIL PBWLB (NIL T) -8 NIL NIL) (-873 2026864 2028433 2029771 "PATTERN" 2033043 NIL PATTERN (NIL T) -8 NIL NIL) (-872 2026496 2026553 2026662 "PATTERN2" 2026801 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-871 2024253 2024641 2025098 "PATTERN1" 2026085 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-870 2021648 2022202 2022683 "PATRES" 2023818 NIL PATRES (NIL T T) -8 NIL NIL) (-869 2021212 2021279 2021411 "PATRES2" 2021575 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-868 2019095 2019500 2019907 "PATMATCH" 2020879 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-867 2018631 2018814 2018855 "PATMAB" 2018962 NIL PATMAB (NIL T) -9 NIL 2019045) (-866 2017176 2017485 2017743 "PATLRES" 2018436 NIL PATLRES (NIL T T T) -8 NIL NIL) (-865 2016722 2016845 2016886 "PATAB" 2016891 NIL PATAB (NIL T) -9 NIL 2017063) (-864 2014203 2014735 2015308 "PARTPERM" 2016169 T PARTPERM (NIL) -7 NIL NIL) (-863 2013824 2013887 2013989 "PARSURF" 2014134 NIL PARSURF (NIL T) -8 NIL NIL) (-862 2013456 2013513 2013622 "PARSU2" 2013761 NIL PARSU2 (NIL T T) -7 NIL NIL) (-861 2013220 2013260 2013327 "PARSER" 2013409 T PARSER (NIL) -7 NIL NIL) (-860 2012841 2012904 2013006 "PARSCURV" 2013151 NIL PARSCURV (NIL T) -8 NIL NIL) (-859 2012473 2012530 2012639 "PARSC2" 2012778 NIL PARSC2 (NIL T T) -7 NIL NIL) (-858 2012112 2012170 2012267 "PARPCURV" 2012409 NIL PARPCURV (NIL T) -8 NIL NIL) (-857 2011744 2011801 2011910 "PARPC2" 2012049 NIL PARPC2 (NIL T T) -7 NIL NIL) (-856 2011264 2011350 2011469 "PAN2EXPR" 2011645 T PAN2EXPR (NIL) -7 NIL NIL) (-855 2010070 2010385 2010613 "PALETTE" 2011056 T PALETTE (NIL) -8 NIL NIL) (-854 2008538 2009075 2009435 "PAIR" 2009756 NIL PAIR (NIL T T) -8 NIL NIL) (-853 2002444 2007797 2007991 "PADICRC" 2008393 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-852 1995708 2001790 2001974 "PADICRAT" 2002292 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-851 1994058 1995645 1995690 "PADIC" 1995695 NIL PADIC (NIL NIL) -8 NIL NIL) (-850 1991303 1992833 1992873 "PADICCT" 1993454 NIL PADICCT (NIL NIL) -9 NIL 1993736) (-849 1990260 1990460 1990728 "PADEPAC" 1991090 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-848 1989472 1989605 1989811 "PADE" 1990122 NIL PADE (NIL T T T) -7 NIL NIL) (-847 1987522 1988308 1988625 "OWP" 1989239 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-846 1986631 1987127 1987299 "OVAR" 1987390 NIL OVAR (NIL NIL) -8 NIL NIL) (-845 1985895 1986016 1986177 "OUT" 1986490 T OUT (NIL) -7 NIL NIL) (-844 1974802 1977004 1979204 "OUTFORM" 1983715 T OUTFORM (NIL) -8 NIL NIL) (-843 1974223 1974399 1974526 "OUTBFILE" 1974695 T OUTBFILE (NIL) -8 NIL NIL) (-842 1973860 1973943 1973971 "OUTBCON" 1974122 T OUTBCON (NIL) -9 NIL 1974207) (-841 1973700 1973735 1973811 "OUTBCON-" 1973816 NIL OUTBCON- (NIL T) -8 NIL NIL) (-840 1973108 1973429 1973518 "OSI" 1973631 T OSI (NIL) -8 NIL NIL) (-839 1972664 1972976 1973004 "OSGROUP" 1973009 T OSGROUP (NIL) -9 NIL 1973031) (-838 1971409 1971636 1971921 "ORTHPOL" 1972411 NIL ORTHPOL (NIL T) -7 NIL NIL) (-837 1968819 1971068 1971207 "OREUP" 1971352 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-836 1966257 1968510 1968637 "ORESUP" 1968761 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-835 1963785 1964285 1964846 "OREPCTO" 1965746 NIL OREPCTO (NIL T T) -7 NIL NIL) (-834 1957696 1959863 1959904 "OREPCAT" 1962252 NIL OREPCAT (NIL T) -9 NIL 1963356) (-833 1954843 1955625 1956683 "OREPCAT-" 1956688 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-832 1954020 1954292 1954320 "ORDSET" 1954629 T ORDSET (NIL) -9 NIL 1954793) (-831 1953539 1953661 1953854 "ORDSET-" 1953859 NIL ORDSET- (NIL T) -8 NIL NIL) (-830 1952193 1952950 1952978 "ORDRING" 1953180 T ORDRING (NIL) -9 NIL 1953305) (-829 1951838 1951932 1952076 "ORDRING-" 1952081 NIL ORDRING- (NIL T) -8 NIL NIL) (-828 1951244 1951681 1951709 "ORDMON" 1951714 T ORDMON (NIL) -9 NIL 1951735) (-827 1950406 1950553 1950748 "ORDFUNS" 1951093 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-826 1949917 1950276 1950304 "ORDFIN" 1950309 T ORDFIN (NIL) -9 NIL 1950330) (-825 1946509 1948503 1948912 "ORDCOMP" 1949541 NIL ORDCOMP (NIL T) -8 NIL NIL) (-824 1945775 1945902 1946088 "ORDCOMP2" 1946369 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-823 1942282 1943165 1944002 "OPTPROB" 1944958 T OPTPROB (NIL) -8 NIL NIL) (-822 1939084 1939723 1940427 "OPTPACK" 1941598 T OPTPACK (NIL) -7 NIL NIL) (-821 1936797 1937537 1937565 "OPTCAT" 1938384 T OPTCAT (NIL) -9 NIL 1939034) (-820 1936565 1936604 1936670 "OPQUERY" 1936751 T OPQUERY (NIL) -7 NIL NIL) (-819 1933731 1934876 1935380 "OP" 1936094 NIL OP (NIL T) -8 NIL NIL) (-818 1930576 1932528 1932897 "ONECOMP" 1933395 NIL ONECOMP (NIL T) -8 NIL NIL) (-817 1929881 1929996 1930170 "ONECOMP2" 1930448 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-816 1929300 1929406 1929536 "OMSERVER" 1929771 T OMSERVER (NIL) -7 NIL NIL) (-815 1926188 1928740 1928780 "OMSAGG" 1928841 NIL OMSAGG (NIL T) -9 NIL 1928905) (-814 1924811 1925074 1925356 "OMPKG" 1925926 T OMPKG (NIL) -7 NIL NIL) (-813 1924241 1924344 1924372 "OM" 1924671 T OM (NIL) -9 NIL NIL) (-812 1922823 1923790 1923959 "OMLO" 1924122 NIL OMLO (NIL T T) -8 NIL NIL) (-811 1921748 1921895 1922122 "OMEXPR" 1922649 NIL OMEXPR (NIL T) -7 NIL NIL) (-810 1921066 1921294 1921430 "OMERR" 1921632 T OMERR (NIL) -8 NIL NIL) (-809 1920244 1920487 1920647 "OMERRK" 1920926 T OMERRK (NIL) -8 NIL NIL) (-808 1919722 1919921 1920029 "OMENC" 1920156 T OMENC (NIL) -8 NIL NIL) (-807 1913617 1914802 1915973 "OMDEV" 1918571 T OMDEV (NIL) -8 NIL NIL) (-806 1912686 1912857 1913051 "OMCONN" 1913443 T OMCONN (NIL) -8 NIL NIL) (-805 1911342 1912284 1912312 "OINTDOM" 1912317 T OINTDOM (NIL) -9 NIL 1912338) (-804 1907148 1908332 1909048 "OFMONOID" 1910658 NIL OFMONOID (NIL T) -8 NIL NIL) (-803 1906586 1907085 1907130 "ODVAR" 1907135 NIL ODVAR (NIL T) -8 NIL NIL) (-802 1903796 1906083 1906268 "ODR" 1906461 NIL ODR (NIL T T NIL) -8 NIL NIL) (-801 1896140 1903572 1903698 "ODPOL" 1903703 NIL ODPOL (NIL T) -8 NIL NIL) (-800 1890016 1896012 1896117 "ODP" 1896122 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-799 1888782 1888997 1889272 "ODETOOLS" 1889790 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-798 1885751 1886407 1887123 "ODESYS" 1888115 NIL ODESYS (NIL T T) -7 NIL NIL) (-797 1880633 1881541 1882566 "ODERTRIC" 1884826 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-796 1880059 1880141 1880335 "ODERED" 1880545 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-795 1876947 1877495 1878172 "ODERAT" 1879482 NIL ODERAT (NIL T T) -7 NIL NIL) (-794 1873907 1874371 1874968 "ODEPRRIC" 1876476 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-793 1871776 1872345 1872854 "ODEPROB" 1873418 T ODEPROB (NIL) -8 NIL NIL) (-792 1868298 1868781 1869428 "ODEPRIM" 1871255 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-791 1867547 1867649 1867909 "ODEPAL" 1868190 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-790 1863709 1864500 1865364 "ODEPACK" 1866703 T ODEPACK (NIL) -7 NIL NIL) (-789 1862742 1862849 1863078 "ODEINT" 1863598 NIL ODEINT (NIL T T) -7 NIL NIL) (-788 1856843 1858268 1859715 "ODEIFTBL" 1861315 T ODEIFTBL (NIL) -8 NIL NIL) (-787 1852178 1852964 1853923 "ODEEF" 1856002 NIL ODEEF (NIL T T) -7 NIL NIL) (-786 1851513 1851602 1851832 "ODECONST" 1852083 NIL ODECONST (NIL T T T) -7 NIL NIL) (-785 1849664 1850299 1850327 "ODECAT" 1850932 T ODECAT (NIL) -9 NIL 1851463) (-784 1846571 1849376 1849495 "OCT" 1849577 NIL OCT (NIL T) -8 NIL NIL) (-783 1846209 1846252 1846379 "OCTCT2" 1846522 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-782 1841070 1843470 1843510 "OC" 1844607 NIL OC (NIL T) -9 NIL 1845465) (-781 1838297 1839045 1840035 "OC-" 1840129 NIL OC- (NIL T T) -8 NIL NIL) (-780 1837675 1838117 1838145 "OCAMON" 1838150 T OCAMON (NIL) -9 NIL 1838171) (-779 1837232 1837547 1837575 "OASGP" 1837580 T OASGP (NIL) -9 NIL 1837600) (-778 1836519 1836982 1837010 "OAMONS" 1837050 T OAMONS (NIL) -9 NIL 1837093) (-777 1835959 1836366 1836394 "OAMON" 1836399 T OAMON (NIL) -9 NIL 1836419) (-776 1835263 1835755 1835783 "OAGROUP" 1835788 T OAGROUP (NIL) -9 NIL 1835808) (-775 1834953 1835003 1835091 "NUMTUBE" 1835207 NIL NUMTUBE (NIL T) -7 NIL NIL) (-774 1828526 1830044 1831580 "NUMQUAD" 1833437 T NUMQUAD (NIL) -7 NIL NIL) (-773 1824282 1825270 1826295 "NUMODE" 1827521 T NUMODE (NIL) -7 NIL NIL) (-772 1821663 1822517 1822545 "NUMINT" 1823468 T NUMINT (NIL) -9 NIL 1824232) (-771 1820611 1820808 1821026 "NUMFMT" 1821465 T NUMFMT (NIL) -7 NIL NIL) (-770 1806970 1809915 1812447 "NUMERIC" 1818118 NIL NUMERIC (NIL T) -7 NIL NIL) (-769 1801367 1806419 1806514 "NTSCAT" 1806519 NIL NTSCAT (NIL T T T T) -9 NIL 1806558) (-768 1800561 1800726 1800919 "NTPOLFN" 1801206 NIL NTPOLFN (NIL T) -7 NIL NIL) (-767 1788401 1797386 1798198 "NSUP" 1799782 NIL NSUP (NIL T) -8 NIL NIL) (-766 1788033 1788090 1788199 "NSUP2" 1788338 NIL NSUP2 (NIL T T) -7 NIL NIL) (-765 1778030 1787807 1787940 "NSMP" 1787945 NIL NSMP (NIL T T) -8 NIL NIL) (-764 1776462 1776763 1777120 "NREP" 1777718 NIL NREP (NIL T) -7 NIL NIL) (-763 1775053 1775305 1775663 "NPCOEF" 1776205 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-762 1774119 1774234 1774450 "NORMRETR" 1774934 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-761 1772160 1772450 1772859 "NORMPK" 1773827 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-760 1771845 1771873 1771997 "NORMMA" 1772126 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-759 1771672 1771802 1771831 "NONE" 1771836 T NONE (NIL) -8 NIL NIL) (-758 1771461 1771490 1771559 "NONE1" 1771636 NIL NONE1 (NIL T) -7 NIL NIL) (-757 1770944 1771006 1771192 "NODE1" 1771393 NIL NODE1 (NIL T T) -7 NIL NIL) (-756 1769284 1770107 1770362 "NNI" 1770709 T NNI (NIL) -8 NIL NIL) (-755 1767704 1768017 1768381 "NLINSOL" 1768952 NIL NLINSOL (NIL T) -7 NIL NIL) (-754 1763871 1764839 1765761 "NIPROB" 1766802 T NIPROB (NIL) -8 NIL NIL) (-753 1762628 1762862 1763164 "NFINTBAS" 1763633 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-752 1762072 1762279 1762320 "NETCLT" 1762484 NIL NETCLT (NIL T) -9 NIL 1762573) (-751 1760780 1761011 1761292 "NCODIV" 1761840 NIL NCODIV (NIL T T) -7 NIL NIL) (-750 1760542 1760579 1760654 "NCNTFRAC" 1760737 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-749 1758722 1759086 1759506 "NCEP" 1760167 NIL NCEP (NIL T) -7 NIL NIL) (-748 1757633 1758372 1758400 "NASRING" 1758510 T NASRING (NIL) -9 NIL 1758584) (-747 1757428 1757472 1757566 "NASRING-" 1757571 NIL NASRING- (NIL T) -8 NIL NIL) (-746 1756581 1757080 1757108 "NARNG" 1757225 T NARNG (NIL) -9 NIL 1757316) (-745 1756273 1756340 1756474 "NARNG-" 1756479 NIL NARNG- (NIL T) -8 NIL NIL) (-744 1755152 1755359 1755594 "NAGSP" 1756058 T NAGSP (NIL) -7 NIL NIL) (-743 1746424 1748108 1749781 "NAGS" 1753499 T NAGS (NIL) -7 NIL NIL) (-742 1744972 1745280 1745611 "NAGF07" 1746113 T NAGF07 (NIL) -7 NIL NIL) (-741 1739510 1740801 1742108 "NAGF04" 1743685 T NAGF04 (NIL) -7 NIL NIL) (-740 1732478 1734092 1735725 "NAGF02" 1737897 T NAGF02 (NIL) -7 NIL NIL) (-739 1727702 1728802 1729919 "NAGF01" 1731381 T NAGF01 (NIL) -7 NIL NIL) (-738 1721330 1722896 1724481 "NAGE04" 1726137 T NAGE04 (NIL) -7 NIL NIL) (-737 1712499 1714620 1716750 "NAGE02" 1719220 T NAGE02 (NIL) -7 NIL NIL) (-736 1708452 1709399 1710363 "NAGE01" 1711555 T NAGE01 (NIL) -7 NIL NIL) (-735 1706247 1706781 1707339 "NAGD03" 1707914 T NAGD03 (NIL) -7 NIL NIL) (-734 1697997 1699925 1701879 "NAGD02" 1704313 T NAGD02 (NIL) -7 NIL NIL) (-733 1691808 1693233 1694673 "NAGD01" 1696577 T NAGD01 (NIL) -7 NIL NIL) (-732 1688017 1688839 1689676 "NAGC06" 1690991 T NAGC06 (NIL) -7 NIL NIL) (-731 1686482 1686814 1687170 "NAGC05" 1687681 T NAGC05 (NIL) -7 NIL NIL) (-730 1685858 1685977 1686121 "NAGC02" 1686358 T NAGC02 (NIL) -7 NIL NIL) (-729 1684918 1685475 1685515 "NAALG" 1685594 NIL NAALG (NIL T) -9 NIL 1685655) (-728 1684753 1684782 1684872 "NAALG-" 1684877 NIL NAALG- (NIL T T) -8 NIL NIL) (-727 1678703 1679811 1680998 "MULTSQFR" 1683649 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-726 1678022 1678097 1678281 "MULTFACT" 1678615 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-725 1671245 1675110 1675163 "MTSCAT" 1676233 NIL MTSCAT (NIL T T) -9 NIL 1676747) (-724 1670957 1671011 1671103 "MTHING" 1671185 NIL MTHING (NIL T) -7 NIL NIL) (-723 1670749 1670782 1670842 "MSYSCMD" 1670917 T MSYSCMD (NIL) -7 NIL NIL) (-722 1666861 1669504 1669824 "MSET" 1670462 NIL MSET (NIL T) -8 NIL NIL) (-721 1663956 1666422 1666463 "MSETAGG" 1666468 NIL MSETAGG (NIL T) -9 NIL 1666502) (-720 1659839 1661335 1662080 "MRING" 1663256 NIL MRING (NIL T T) -8 NIL NIL) (-719 1659405 1659472 1659603 "MRF2" 1659766 NIL MRF2 (NIL T T T) -7 NIL NIL) (-718 1659023 1659058 1659202 "MRATFAC" 1659364 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-717 1656635 1656930 1657361 "MPRFF" 1658728 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-716 1650695 1656489 1656586 "MPOLY" 1656591 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-715 1650185 1650220 1650428 "MPCPF" 1650654 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-714 1649699 1649742 1649926 "MPC3" 1650136 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-713 1648894 1648975 1649196 "MPC2" 1649614 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-712 1647195 1647532 1647922 "MONOTOOL" 1648554 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-711 1646446 1646737 1646765 "MONOID" 1646984 T MONOID (NIL) -9 NIL 1647131) (-710 1645992 1646111 1646292 "MONOID-" 1646297 NIL MONOID- (NIL T) -8 NIL NIL) (-709 1637042 1642948 1643007 "MONOGEN" 1643681 NIL MONOGEN (NIL T T) -9 NIL 1644137) (-708 1634260 1634995 1635995 "MONOGEN-" 1636114 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-707 1633119 1633539 1633567 "MONADWU" 1633959 T MONADWU (NIL) -9 NIL 1634197) (-706 1632491 1632650 1632898 "MONADWU-" 1632903 NIL MONADWU- (NIL T) -8 NIL NIL) (-705 1631876 1632094 1632122 "MONAD" 1632329 T MONAD (NIL) -9 NIL 1632441) (-704 1631561 1631639 1631771 "MONAD-" 1631776 NIL MONAD- (NIL T) -8 NIL NIL) (-703 1629877 1630474 1630753 "MOEBIUS" 1631314 NIL MOEBIUS (NIL T) -8 NIL NIL) (-702 1629269 1629647 1629687 "MODULE" 1629692 NIL MODULE (NIL T) -9 NIL 1629718) (-701 1628837 1628933 1629123 "MODULE-" 1629128 NIL MODULE- (NIL T T) -8 NIL NIL) (-700 1626552 1627201 1627528 "MODRING" 1628661 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-699 1623538 1624657 1625178 "MODOP" 1626081 NIL MODOP (NIL T T) -8 NIL NIL) (-698 1621725 1622177 1622518 "MODMONOM" 1623337 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-697 1611433 1619917 1620340 "MODMON" 1621353 NIL MODMON (NIL T T) -8 NIL NIL) (-696 1608624 1610277 1610553 "MODFIELD" 1611308 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-695 1607628 1607905 1608095 "MMLFORM" 1608454 T MMLFORM (NIL) -8 NIL NIL) (-694 1607154 1607197 1607376 "MMAP" 1607579 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-693 1605423 1606156 1606197 "MLO" 1606620 NIL MLO (NIL T) -9 NIL 1606862) (-692 1602790 1603305 1603907 "MLIFT" 1604904 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-691 1602181 1602265 1602419 "MKUCFUNC" 1602701 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-690 1601780 1601850 1601973 "MKRECORD" 1602104 NIL MKRECORD (NIL T T) -7 NIL NIL) (-689 1600828 1600989 1601217 "MKFUNC" 1601591 NIL MKFUNC (NIL T) -7 NIL NIL) (-688 1600216 1600320 1600476 "MKFLCFN" 1600711 NIL MKFLCFN (NIL T) -7 NIL NIL) (-687 1599642 1600009 1600098 "MKCHSET" 1600160 NIL MKCHSET (NIL T) -8 NIL NIL) (-686 1598919 1599021 1599206 "MKBCFUNC" 1599535 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-685 1595661 1598473 1598609 "MINT" 1598803 T MINT (NIL) -8 NIL NIL) (-684 1594473 1594716 1594993 "MHROWRED" 1595416 NIL MHROWRED (NIL T) -7 NIL NIL) (-683 1589899 1593008 1593413 "MFLOAT" 1594088 T MFLOAT (NIL) -8 NIL NIL) (-682 1589256 1589332 1589503 "MFINFACT" 1589811 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-681 1585571 1586419 1587303 "MESH" 1588392 T MESH (NIL) -7 NIL NIL) (-680 1583961 1584273 1584626 "MDDFACT" 1585258 NIL MDDFACT (NIL T) -7 NIL NIL) (-679 1580803 1583120 1583161 "MDAGG" 1583416 NIL MDAGG (NIL T) -9 NIL 1583559) (-678 1570581 1580096 1580303 "MCMPLX" 1580616 T MCMPLX (NIL) -8 NIL NIL) (-677 1569722 1569868 1570068 "MCDEN" 1570430 NIL MCDEN (NIL T T) -7 NIL NIL) (-676 1567612 1567882 1568262 "MCALCFN" 1569452 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-675 1566523 1566696 1566937 "MAYBE" 1567410 NIL MAYBE (NIL T) -8 NIL NIL) (-674 1564135 1564658 1565220 "MATSTOR" 1565994 NIL MATSTOR (NIL T) -7 NIL NIL) (-673 1560141 1563507 1563755 "MATRIX" 1563920 NIL MATRIX (NIL T) -8 NIL NIL) (-672 1555910 1556614 1557350 "MATLIN" 1559498 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-671 1546064 1549202 1549279 "MATCAT" 1554159 NIL MATCAT (NIL T T T) -9 NIL 1555576) (-670 1542428 1543441 1544797 "MATCAT-" 1544802 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-669 1541022 1541175 1541508 "MATCAT2" 1542263 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-668 1539134 1539458 1539842 "MAPPKG3" 1540697 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-667 1538115 1538288 1538510 "MAPPKG2" 1538958 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-666 1536614 1536898 1537225 "MAPPKG1" 1537821 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-665 1535720 1536020 1536197 "MAPPAST" 1536457 T MAPPAST (NIL) -8 NIL NIL) (-664 1535331 1535389 1535512 "MAPHACK3" 1535656 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-663 1534923 1534984 1535098 "MAPHACK2" 1535263 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-662 1534361 1534464 1534606 "MAPHACK1" 1534814 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-661 1532467 1533061 1533365 "MAGMA" 1534089 NIL MAGMA (NIL T) -8 NIL NIL) (-660 1531973 1532191 1532282 "MACROAST" 1532396 T MACROAST (NIL) -8 NIL NIL) (-659 1528440 1530212 1530673 "M3D" 1531545 NIL M3D (NIL T) -8 NIL NIL) (-658 1522595 1526810 1526851 "LZSTAGG" 1527633 NIL LZSTAGG (NIL T) -9 NIL 1527928) (-657 1518568 1519726 1521183 "LZSTAGG-" 1521188 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-656 1515682 1516459 1516946 "LWORD" 1518113 NIL LWORD (NIL T) -8 NIL NIL) (-655 1515285 1515486 1515561 "LSTAST" 1515627 T LSTAST (NIL) -8 NIL NIL) (-654 1508486 1515056 1515190 "LSQM" 1515195 NIL LSQM (NIL NIL T) -8 NIL NIL) (-653 1507710 1507849 1508077 "LSPP" 1508341 NIL LSPP (NIL T T T T) -7 NIL NIL) (-652 1505522 1505823 1506279 "LSMP" 1507399 NIL LSMP (NIL T T T T) -7 NIL NIL) (-651 1502301 1502975 1503705 "LSMP1" 1504824 NIL LSMP1 (NIL T) -7 NIL NIL) (-650 1496227 1501469 1501510 "LSAGG" 1501572 NIL LSAGG (NIL T) -9 NIL 1501650) (-649 1492922 1493846 1495059 "LSAGG-" 1495064 NIL LSAGG- (NIL T T) -8 NIL NIL) (-648 1490548 1492066 1492315 "LPOLY" 1492717 NIL LPOLY (NIL T T) -8 NIL NIL) (-647 1490130 1490215 1490338 "LPEFRAC" 1490457 NIL LPEFRAC (NIL T) -7 NIL NIL) (-646 1488477 1489224 1489477 "LO" 1489962 NIL LO (NIL T T T) -8 NIL NIL) (-645 1488129 1488241 1488269 "LOGIC" 1488380 T LOGIC (NIL) -9 NIL 1488461) (-644 1487991 1488014 1488085 "LOGIC-" 1488090 NIL LOGIC- (NIL T) -8 NIL NIL) (-643 1487184 1487324 1487517 "LODOOPS" 1487847 NIL LODOOPS (NIL T T) -7 NIL NIL) (-642 1484642 1487100 1487166 "LODO" 1487171 NIL LODO (NIL T NIL) -8 NIL NIL) (-641 1483180 1483415 1483768 "LODOF" 1484389 NIL LODOF (NIL T T) -7 NIL NIL) (-640 1479623 1482020 1482061 "LODOCAT" 1482499 NIL LODOCAT (NIL T) -9 NIL 1482710) (-639 1479356 1479414 1479541 "LODOCAT-" 1479546 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-638 1476711 1479197 1479315 "LODO2" 1479320 NIL LODO2 (NIL T T) -8 NIL NIL) (-637 1474181 1476648 1476693 "LODO1" 1476698 NIL LODO1 (NIL T) -8 NIL NIL) (-636 1473041 1473206 1473518 "LODEEF" 1474004 NIL LODEEF (NIL T T T) -7 NIL NIL) (-635 1468327 1471171 1471212 "LNAGG" 1472159 NIL LNAGG (NIL T) -9 NIL 1472603) (-634 1467474 1467688 1468030 "LNAGG-" 1468035 NIL LNAGG- (NIL T T) -8 NIL NIL) (-633 1463637 1464399 1465038 "LMOPS" 1466889 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-632 1463032 1463394 1463435 "LMODULE" 1463496 NIL LMODULE (NIL T) -9 NIL 1463538) (-631 1460278 1462677 1462800 "LMDICT" 1462942 NIL LMDICT (NIL T) -8 NIL NIL) (-630 1460004 1460186 1460246 "LITERAL" 1460251 NIL LITERAL (NIL T) -8 NIL NIL) (-629 1453231 1458950 1459248 "LIST" 1459739 NIL LIST (NIL T) -8 NIL NIL) (-628 1452756 1452830 1452969 "LIST3" 1453151 NIL LIST3 (NIL T T T) -7 NIL NIL) (-627 1451763 1451941 1452169 "LIST2" 1452574 NIL LIST2 (NIL T T) -7 NIL NIL) (-626 1449897 1450209 1450608 "LIST2MAP" 1451410 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-625 1448647 1449283 1449324 "LINEXP" 1449579 NIL LINEXP (NIL T) -9 NIL 1449728) (-624 1447294 1447554 1447851 "LINDEP" 1448399 NIL LINDEP (NIL T T) -7 NIL NIL) (-623 1444061 1444780 1445557 "LIMITRF" 1446549 NIL LIMITRF (NIL T) -7 NIL NIL) (-622 1442337 1442632 1443048 "LIMITPS" 1443756 NIL LIMITPS (NIL T T) -7 NIL NIL) (-621 1436792 1441848 1442076 "LIE" 1442158 NIL LIE (NIL T T) -8 NIL NIL) (-620 1435841 1436284 1436324 "LIECAT" 1436464 NIL LIECAT (NIL T) -9 NIL 1436615) (-619 1435682 1435709 1435797 "LIECAT-" 1435802 NIL LIECAT- (NIL T T) -8 NIL NIL) (-618 1428294 1435131 1435296 "LIB" 1435537 T LIB (NIL) -8 NIL NIL) (-617 1423931 1424812 1425747 "LGROBP" 1427411 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-616 1421797 1422071 1422433 "LF" 1423652 NIL LF (NIL T T) -7 NIL NIL) (-615 1420637 1421329 1421357 "LFCAT" 1421564 T LFCAT (NIL) -9 NIL 1421703) (-614 1417541 1418169 1418857 "LEXTRIPK" 1420001 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-613 1414312 1415111 1415614 "LEXP" 1417121 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-612 1413815 1414033 1414125 "LETAST" 1414240 T LETAST (NIL) -8 NIL NIL) (-611 1412213 1412526 1412927 "LEADCDET" 1413497 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-610 1411403 1411477 1411706 "LAZM3PK" 1412134 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-609 1406359 1409480 1410018 "LAUPOL" 1410915 NIL LAUPOL (NIL T T) -8 NIL NIL) (-608 1405924 1405968 1406136 "LAPLACE" 1406309 NIL LAPLACE (NIL T T) -7 NIL NIL) (-607 1403898 1405025 1405276 "LA" 1405757 NIL LA (NIL T T T) -8 NIL NIL) (-606 1402999 1403549 1403590 "LALG" 1403652 NIL LALG (NIL T) -9 NIL 1403711) (-605 1402713 1402772 1402908 "LALG-" 1402913 NIL LALG- (NIL T T) -8 NIL NIL) (-604 1402548 1402572 1402613 "KVTFROM" 1402675 NIL KVTFROM (NIL T) -9 NIL NIL) (-603 1401348 1401765 1401994 "KTVLOGIC" 1402339 T KTVLOGIC (NIL) -8 NIL NIL) (-602 1401183 1401207 1401248 "KRCFROM" 1401310 NIL KRCFROM (NIL T) -9 NIL NIL) (-601 1400087 1400274 1400573 "KOVACIC" 1400983 NIL KOVACIC (NIL T T) -7 NIL NIL) (-600 1399922 1399946 1399987 "KONVERT" 1400049 NIL KONVERT (NIL T) -9 NIL NIL) (-599 1399757 1399781 1399822 "KOERCE" 1399884 NIL KOERCE (NIL T) -9 NIL NIL) (-598 1397491 1398251 1398644 "KERNEL" 1399396 NIL KERNEL (NIL T) -8 NIL NIL) (-597 1396993 1397074 1397204 "KERNEL2" 1397405 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-596 1390844 1395532 1395586 "KDAGG" 1395963 NIL KDAGG (NIL T T) -9 NIL 1396169) (-595 1390373 1390497 1390702 "KDAGG-" 1390707 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-594 1383548 1390034 1390189 "KAFILE" 1390251 NIL KAFILE (NIL T) -8 NIL NIL) (-593 1378003 1383059 1383287 "JORDAN" 1383369 NIL JORDAN (NIL T T) -8 NIL NIL) (-592 1377409 1377652 1377773 "JOINAST" 1377902 T JOINAST (NIL) -8 NIL NIL) (-591 1377138 1377197 1377284 "JAVACODE" 1377342 T JAVACODE (NIL) -8 NIL NIL) (-590 1373437 1375343 1375397 "IXAGG" 1376326 NIL IXAGG (NIL T T) -9 NIL 1376785) (-589 1372356 1372662 1373081 "IXAGG-" 1373086 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-588 1367936 1372278 1372337 "IVECTOR" 1372342 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-587 1366702 1366939 1367205 "ITUPLE" 1367703 NIL ITUPLE (NIL T) -8 NIL NIL) (-586 1365138 1365315 1365621 "ITRIGMNP" 1366524 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-585 1363883 1364087 1364370 "ITFUN3" 1364914 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-584 1363515 1363572 1363681 "ITFUN2" 1363820 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-583 1361352 1362377 1362676 "ITAYLOR" 1363249 NIL ITAYLOR (NIL T) -8 NIL NIL) (-582 1350334 1355489 1356652 "ISUPS" 1360222 NIL ISUPS (NIL T) -8 NIL NIL) (-581 1349438 1349578 1349814 "ISUMP" 1350181 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-580 1344702 1349239 1349318 "ISTRING" 1349391 NIL ISTRING (NIL NIL) -8 NIL NIL) (-579 1344205 1344423 1344515 "ISAST" 1344630 T ISAST (NIL) -8 NIL NIL) (-578 1343415 1343496 1343712 "IRURPK" 1344119 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-577 1342351 1342552 1342792 "IRSN" 1343195 T IRSN (NIL) -7 NIL NIL) (-576 1340380 1340735 1341171 "IRRF2F" 1341989 NIL IRRF2F (NIL T) -7 NIL NIL) (-575 1340127 1340165 1340241 "IRREDFFX" 1340336 NIL IRREDFFX (NIL T) -7 NIL NIL) (-574 1338742 1339001 1339300 "IROOT" 1339860 NIL IROOT (NIL T) -7 NIL NIL) (-573 1335374 1336426 1337118 "IR" 1338082 NIL IR (NIL T) -8 NIL NIL) (-572 1332987 1333482 1334048 "IR2" 1334852 NIL IR2 (NIL T T) -7 NIL NIL) (-571 1332059 1332172 1332393 "IR2F" 1332870 NIL IR2F (NIL T T) -7 NIL NIL) (-570 1331850 1331884 1331944 "IPRNTPK" 1332019 T IPRNTPK (NIL) -7 NIL NIL) (-569 1328469 1331739 1331808 "IPF" 1331813 NIL IPF (NIL NIL) -8 NIL NIL) (-568 1326832 1328394 1328451 "IPADIC" 1328456 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-567 1326163 1326390 1326527 "IP4ADDR" 1326715 T IP4ADDR (NIL) -8 NIL NIL) (-566 1325663 1325867 1325977 "IOMODE" 1326073 T IOMODE (NIL) -8 NIL NIL) (-565 1325021 1325260 1325387 "IOBFILE" 1325556 T IOBFILE (NIL) -8 NIL NIL) (-564 1324785 1324925 1324953 "IOBCON" 1324958 T IOBCON (NIL) -9 NIL 1324979) (-563 1324282 1324340 1324530 "INVLAPLA" 1324721 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-562 1313931 1316284 1318670 "INTTR" 1321946 NIL INTTR (NIL T T) -7 NIL NIL) (-561 1310275 1311017 1311881 "INTTOOLS" 1313116 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-560 1309861 1309952 1310069 "INTSLPE" 1310178 T INTSLPE (NIL) -7 NIL NIL) (-559 1307856 1309784 1309843 "INTRVL" 1309848 NIL INTRVL (NIL T) -8 NIL NIL) (-558 1305458 1305970 1306545 "INTRF" 1307341 NIL INTRF (NIL T) -7 NIL NIL) (-557 1304869 1304966 1305108 "INTRET" 1305356 NIL INTRET (NIL T) -7 NIL NIL) (-556 1302866 1303255 1303725 "INTRAT" 1304477 NIL INTRAT (NIL T T) -7 NIL NIL) (-555 1300094 1300677 1301303 "INTPM" 1302351 NIL INTPM (NIL T T) -7 NIL NIL) (-554 1296797 1297396 1298141 "INTPAF" 1299480 NIL INTPAF (NIL T T T) -7 NIL NIL) (-553 1291976 1292938 1293989 "INTPACK" 1295766 T INTPACK (NIL) -7 NIL NIL) (-552 1288888 1291705 1291832 "INT" 1291869 T INT (NIL) -8 NIL NIL) (-551 1288140 1288292 1288500 "INTHERTR" 1288730 NIL INTHERTR (NIL T T) -7 NIL NIL) (-550 1287579 1287659 1287847 "INTHERAL" 1288054 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-549 1285425 1285868 1286325 "INTHEORY" 1287142 T INTHEORY (NIL) -7 NIL NIL) (-548 1276733 1278354 1280133 "INTG0" 1283777 NIL INTG0 (NIL T T T) -7 NIL NIL) (-547 1257306 1262096 1266906 "INTFTBL" 1271943 T INTFTBL (NIL) -8 NIL NIL) (-546 1256555 1256693 1256866 "INTFACT" 1257165 NIL INTFACT (NIL T) -7 NIL NIL) (-545 1253940 1254386 1254950 "INTEF" 1256109 NIL INTEF (NIL T T) -7 NIL NIL) (-544 1252442 1253147 1253175 "INTDOM" 1253476 T INTDOM (NIL) -9 NIL 1253683) (-543 1251811 1251985 1252227 "INTDOM-" 1252232 NIL INTDOM- (NIL T) -8 NIL NIL) (-542 1248344 1250230 1250284 "INTCAT" 1251083 NIL INTCAT (NIL T) -9 NIL 1251403) (-541 1247817 1247919 1248047 "INTBIT" 1248236 T INTBIT (NIL) -7 NIL NIL) (-540 1246488 1246642 1246956 "INTALG" 1247662 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-539 1245945 1246035 1246205 "INTAF" 1246392 NIL INTAF (NIL T T) -7 NIL NIL) (-538 1239399 1245755 1245895 "INTABL" 1245900 NIL INTABL (NIL T T T) -8 NIL NIL) (-537 1234452 1237123 1237151 "INS" 1238085 T INS (NIL) -9 NIL 1238750) (-536 1231692 1232463 1233437 "INS-" 1233510 NIL INS- (NIL T) -8 NIL NIL) (-535 1230467 1230694 1230992 "INPSIGN" 1231445 NIL INPSIGN (NIL T T) -7 NIL NIL) (-534 1229585 1229702 1229899 "INPRODPF" 1230347 NIL INPRODPF (NIL T T) -7 NIL NIL) (-533 1228479 1228596 1228833 "INPRODFF" 1229465 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-532 1227479 1227631 1227891 "INNMFACT" 1228315 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-531 1226676 1226773 1226961 "INMODGCD" 1227378 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-530 1225185 1225429 1225753 "INFSP" 1226421 NIL INFSP (NIL T T T) -7 NIL NIL) (-529 1224369 1224486 1224669 "INFPROD0" 1225065 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-528 1221251 1222434 1222949 "INFORM" 1223862 T INFORM (NIL) -8 NIL NIL) (-527 1220861 1220921 1221019 "INFORM1" 1221186 NIL INFORM1 (NIL T) -7 NIL NIL) (-526 1220384 1220473 1220587 "INFINITY" 1220767 T INFINITY (NIL) -7 NIL NIL) (-525 1219829 1220102 1220210 "INETCLTS" 1220296 T INETCLTS (NIL) -8 NIL NIL) (-524 1218446 1218695 1219016 "INEP" 1219577 NIL INEP (NIL T T T) -7 NIL NIL) (-523 1217722 1218343 1218408 "INDE" 1218413 NIL INDE (NIL T) -8 NIL NIL) (-522 1217286 1217354 1217471 "INCRMAPS" 1217649 NIL INCRMAPS (NIL T) -7 NIL NIL) (-521 1216304 1216555 1216761 "INBFILE" 1217100 T INBFILE (NIL) -8 NIL NIL) (-520 1211615 1212540 1213484 "INBFF" 1215392 NIL INBFF (NIL T) -7 NIL NIL) (-519 1211284 1211360 1211388 "INBCON" 1211521 T INBCON (NIL) -9 NIL 1211599) (-518 1211124 1211159 1211235 "INBCON-" 1211240 NIL INBCON- (NIL T) -8 NIL NIL) (-517 1210626 1210845 1210937 "INAST" 1211052 T INAST (NIL) -8 NIL NIL) (-516 1210080 1210305 1210411 "IMPTAST" 1210540 T IMPTAST (NIL) -8 NIL NIL) (-515 1206574 1209924 1210028 "IMATRIX" 1210033 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-514 1205286 1205409 1205724 "IMATQF" 1206430 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-513 1203506 1203733 1204070 "IMATLIN" 1205042 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-512 1198132 1203430 1203488 "ILIST" 1203493 NIL ILIST (NIL T NIL) -8 NIL NIL) (-511 1196085 1197992 1198105 "IIARRAY2" 1198110 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-510 1191518 1195996 1196060 "IFF" 1196065 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-509 1190892 1191135 1191251 "IFAST" 1191422 T IFAST (NIL) -8 NIL NIL) (-508 1185935 1190184 1190372 "IFARRAY" 1190749 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-507 1185142 1185839 1185912 "IFAMON" 1185917 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-506 1184726 1184791 1184845 "IEVALAB" 1185052 NIL IEVALAB (NIL T T) -9 NIL NIL) (-505 1184401 1184469 1184629 "IEVALAB-" 1184634 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-504 1184059 1184315 1184378 "IDPO" 1184383 NIL IDPO (NIL T T) -8 NIL NIL) (-503 1183336 1183948 1184023 "IDPOAMS" 1184028 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-502 1182670 1183225 1183300 "IDPOAM" 1183305 NIL IDPOAM (NIL T T) -8 NIL NIL) (-501 1181755 1182005 1182058 "IDPC" 1182471 NIL IDPC (NIL T T) -9 NIL 1182620) (-500 1181251 1181647 1181720 "IDPAM" 1181725 NIL IDPAM (NIL T T) -8 NIL NIL) (-499 1180654 1181143 1181216 "IDPAG" 1181221 NIL IDPAG (NIL T T) -8 NIL NIL) (-498 1180384 1180569 1180619 "IDENT" 1180624 T IDENT (NIL) -8 NIL NIL) (-497 1176639 1177487 1178382 "IDECOMP" 1179541 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-496 1169512 1170562 1171609 "IDEAL" 1175675 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-495 1168676 1168788 1168987 "ICDEN" 1169396 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-494 1167775 1168156 1168303 "ICARD" 1168549 T ICARD (NIL) -8 NIL NIL) (-493 1165835 1166148 1166553 "IBPTOOLS" 1167452 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-492 1161469 1165455 1165568 "IBITS" 1165754 NIL IBITS (NIL NIL) -8 NIL NIL) (-491 1158192 1158768 1159463 "IBATOOL" 1160886 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-490 1155972 1156433 1156966 "IBACHIN" 1157727 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-489 1153849 1155818 1155921 "IARRAY2" 1155926 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-488 1150002 1153775 1153832 "IARRAY1" 1153837 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-487 1143995 1148414 1148895 "IAN" 1149541 T IAN (NIL) -8 NIL NIL) (-486 1143506 1143563 1143736 "IALGFACT" 1143932 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-485 1143034 1143147 1143175 "HYPCAT" 1143382 T HYPCAT (NIL) -9 NIL NIL) (-484 1142572 1142689 1142875 "HYPCAT-" 1142880 NIL HYPCAT- (NIL T) -8 NIL NIL) (-483 1142194 1142367 1142450 "HOSTNAME" 1142509 T HOSTNAME (NIL) -8 NIL NIL) (-482 1138873 1140204 1140245 "HOAGG" 1141226 NIL HOAGG (NIL T) -9 NIL 1141905) (-481 1137467 1137866 1138392 "HOAGG-" 1138397 NIL HOAGG- (NIL T T) -8 NIL NIL) (-480 1131353 1136908 1137074 "HEXADEC" 1137321 T HEXADEC (NIL) -8 NIL NIL) (-479 1130101 1130323 1130586 "HEUGCD" 1131130 NIL HEUGCD (NIL T) -7 NIL NIL) (-478 1129204 1129938 1130068 "HELLFDIV" 1130073 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-477 1127432 1128981 1129069 "HEAP" 1129148 NIL HEAP (NIL T) -8 NIL NIL) (-476 1126723 1126984 1127118 "HEADAST" 1127318 T HEADAST (NIL) -8 NIL NIL) (-475 1120643 1126638 1126700 "HDP" 1126705 NIL HDP (NIL NIL T) -8 NIL NIL) (-474 1114394 1120278 1120430 "HDMP" 1120544 NIL HDMP (NIL NIL T) -8 NIL NIL) (-473 1113719 1113858 1114022 "HB" 1114250 T HB (NIL) -7 NIL NIL) (-472 1107216 1113565 1113669 "HASHTBL" 1113674 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-471 1106719 1106937 1107029 "HASAST" 1107144 T HASAST (NIL) -8 NIL NIL) (-470 1104531 1106341 1106523 "HACKPI" 1106557 T HACKPI (NIL) -8 NIL NIL) (-469 1100226 1104384 1104497 "GTSET" 1104502 NIL GTSET (NIL T T T T) -8 NIL NIL) (-468 1093752 1100104 1100202 "GSTBL" 1100207 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-467 1086065 1092783 1093048 "GSERIES" 1093543 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-466 1085232 1085623 1085651 "GROUP" 1085854 T GROUP (NIL) -9 NIL 1085988) (-465 1084598 1084757 1085008 "GROUP-" 1085013 NIL GROUP- (NIL T) -8 NIL NIL) (-464 1082967 1083286 1083673 "GROEBSOL" 1084275 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-463 1081907 1082169 1082220 "GRMOD" 1082749 NIL GRMOD (NIL T T) -9 NIL 1082917) (-462 1081675 1081711 1081839 "GRMOD-" 1081844 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-461 1077000 1078029 1079029 "GRIMAGE" 1080695 T GRIMAGE (NIL) -8 NIL NIL) (-460 1075467 1075727 1076051 "GRDEF" 1076696 T GRDEF (NIL) -7 NIL NIL) (-459 1074911 1075027 1075168 "GRAY" 1075346 T GRAY (NIL) -7 NIL NIL) (-458 1074142 1074522 1074573 "GRALG" 1074726 NIL GRALG (NIL T T) -9 NIL 1074819) (-457 1073803 1073876 1074039 "GRALG-" 1074044 NIL GRALG- (NIL T T T) -8 NIL NIL) (-456 1070607 1073388 1073566 "GPOLSET" 1073710 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-455 1069961 1070018 1070276 "GOSPER" 1070544 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-454 1065720 1066399 1066925 "GMODPOL" 1069660 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-453 1064725 1064909 1065147 "GHENSEL" 1065532 NIL GHENSEL (NIL T T) -7 NIL NIL) (-452 1058776 1059619 1060646 "GENUPS" 1063809 NIL GENUPS (NIL T T) -7 NIL NIL) (-451 1058473 1058524 1058613 "GENUFACT" 1058719 NIL GENUFACT (NIL T) -7 NIL NIL) (-450 1057885 1057962 1058127 "GENPGCD" 1058391 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-449 1057359 1057394 1057607 "GENMFACT" 1057844 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-448 1055927 1056182 1056489 "GENEEZ" 1057102 NIL GENEEZ (NIL T T) -7 NIL NIL) (-447 1049840 1055538 1055700 "GDMP" 1055850 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-446 1039217 1043611 1044717 "GCNAALG" 1048823 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-445 1037679 1038507 1038535 "GCDDOM" 1038790 T GCDDOM (NIL) -9 NIL 1038947) (-444 1037149 1037276 1037491 "GCDDOM-" 1037496 NIL GCDDOM- (NIL T) -8 NIL NIL) (-443 1035821 1036006 1036310 "GB" 1036928 NIL GB (NIL T T T T) -7 NIL NIL) (-442 1024441 1026767 1029159 "GBINTERN" 1033512 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-441 1022278 1022570 1022991 "GBF" 1024116 NIL GBF (NIL T T T T) -7 NIL NIL) (-440 1021059 1021224 1021491 "GBEUCLID" 1022094 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-439 1020408 1020533 1020682 "GAUSSFAC" 1020930 T GAUSSFAC (NIL) -7 NIL NIL) (-438 1018775 1019077 1019391 "GALUTIL" 1020127 NIL GALUTIL (NIL T) -7 NIL NIL) (-437 1017083 1017357 1017681 "GALPOLYU" 1018502 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-436 1014448 1014738 1015145 "GALFACTU" 1016780 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-435 1006254 1007753 1009361 "GALFACT" 1012880 NIL GALFACT (NIL T) -7 NIL NIL) (-434 1003642 1004300 1004328 "FVFUN" 1005484 T FVFUN (NIL) -9 NIL 1006204) (-433 1002908 1003090 1003118 "FVC" 1003409 T FVC (NIL) -9 NIL 1003592) (-432 1002550 1002705 1002786 "FUNCTION" 1002860 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-431 1000220 1000771 1001260 "FT" 1002081 T FT (NIL) -8 NIL NIL) (-430 999038 999521 999724 "FTEM" 1000037 T FTEM (NIL) -8 NIL NIL) (-429 997294 997583 997987 "FSUPFACT" 998729 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-428 995691 995980 996312 "FST" 996982 T FST (NIL) -8 NIL NIL) (-427 994862 994968 995163 "FSRED" 995573 NIL FSRED (NIL T T) -7 NIL NIL) (-426 993541 993796 994150 "FSPRMELT" 994577 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-425 990626 991064 991563 "FSPECF" 993104 NIL FSPECF (NIL T T) -7 NIL NIL) (-424 973068 981510 981550 "FS" 985398 NIL FS (NIL T) -9 NIL 987687) (-423 961718 964708 968764 "FS-" 969061 NIL FS- (NIL T T) -8 NIL NIL) (-422 961232 961286 961463 "FSINT" 961659 NIL FSINT (NIL T T) -7 NIL NIL) (-421 959559 960225 960528 "FSERIES" 961011 NIL FSERIES (NIL T T) -8 NIL NIL) (-420 958573 958689 958920 "FSCINT" 959439 NIL FSCINT (NIL T T) -7 NIL NIL) (-419 954807 957517 957558 "FSAGG" 957928 NIL FSAGG (NIL T) -9 NIL 958187) (-418 952569 953170 953966 "FSAGG-" 954061 NIL FSAGG- (NIL T T) -8 NIL NIL) (-417 951611 951754 951981 "FSAGG2" 952422 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-416 949266 949545 950099 "FS2UPS" 951329 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-415 948848 948891 949046 "FS2" 949217 NIL FS2 (NIL T T T T) -7 NIL NIL) (-414 947705 947876 948185 "FS2EXPXP" 948673 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-413 947131 947246 947398 "FRUTIL" 947585 NIL FRUTIL (NIL T) -7 NIL NIL) (-412 938586 942626 943984 "FR" 945805 NIL FR (NIL T) -8 NIL NIL) (-411 933661 936304 936344 "FRNAALG" 937740 NIL FRNAALG (NIL T) -9 NIL 938347) (-410 929339 930410 931685 "FRNAALG-" 932435 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-409 928977 929020 929147 "FRNAAF2" 929290 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-408 927384 927831 928126 "FRMOD" 928789 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-407 925163 925767 926084 "FRIDEAL" 927175 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-406 924358 924445 924734 "FRIDEAL2" 925070 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-405 923600 924014 924055 "FRETRCT" 924060 NIL FRETRCT (NIL T) -9 NIL 924236) (-404 922712 922943 923294 "FRETRCT-" 923299 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-403 919962 921138 921197 "FRAMALG" 922079 NIL FRAMALG (NIL T T) -9 NIL 922371) (-402 918096 918551 919181 "FRAMALG-" 919404 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-401 912054 917571 917847 "FRAC" 917852 NIL FRAC (NIL T) -8 NIL NIL) (-400 911690 911747 911854 "FRAC2" 911991 NIL FRAC2 (NIL T T) -7 NIL NIL) (-399 911326 911383 911490 "FR2" 911627 NIL FR2 (NIL T T) -7 NIL NIL) (-398 906055 908903 908931 "FPS" 910050 T FPS (NIL) -9 NIL 910607) (-397 905504 905613 905777 "FPS-" 905923 NIL FPS- (NIL T) -8 NIL NIL) (-396 903010 904645 904673 "FPC" 904898 T FPC (NIL) -9 NIL 905040) (-395 902803 902843 902940 "FPC-" 902945 NIL FPC- (NIL T) -8 NIL NIL) (-394 901681 902291 902332 "FPATMAB" 902337 NIL FPATMAB (NIL T) -9 NIL 902489) (-393 899381 899857 900283 "FPARFRAC" 901318 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-392 894774 895273 895955 "FORTRAN" 898813 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-391 892490 892990 893529 "FORT" 894255 T FORT (NIL) -7 NIL NIL) (-390 890166 890728 890756 "FORTFN" 891816 T FORTFN (NIL) -9 NIL 892440) (-389 889930 889980 890008 "FORTCAT" 890067 T FORTCAT (NIL) -9 NIL 890129) (-388 887990 888473 888872 "FORMULA" 889551 T FORMULA (NIL) -8 NIL NIL) (-387 887778 887808 887877 "FORMULA1" 887954 NIL FORMULA1 (NIL T) -7 NIL NIL) (-386 887301 887353 887526 "FORDER" 887720 NIL FORDER (NIL T T T T) -7 NIL NIL) (-385 886397 886561 886754 "FOP" 887128 T FOP (NIL) -7 NIL NIL) (-384 885005 885677 885851 "FNLA" 886279 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-383 883673 884062 884090 "FNCAT" 884662 T FNCAT (NIL) -9 NIL 884955) (-382 883239 883632 883660 "FNAME" 883665 T FNAME (NIL) -8 NIL NIL) (-381 881937 882866 882894 "FMTC" 882899 T FMTC (NIL) -9 NIL 882935) (-380 878299 879460 880089 "FMONOID" 881341 NIL FMONOID (NIL T) -8 NIL NIL) (-379 877518 878041 878190 "FM" 878195 NIL FM (NIL T T) -8 NIL NIL) (-378 874942 875588 875616 "FMFUN" 876760 T FMFUN (NIL) -9 NIL 877468) (-377 874211 874392 874420 "FMC" 874710 T FMC (NIL) -9 NIL 874892) (-376 871423 872257 872311 "FMCAT" 873506 NIL FMCAT (NIL T T) -9 NIL 874001) (-375 870316 871189 871289 "FM1" 871368 NIL FM1 (NIL T T) -8 NIL NIL) (-374 868090 868506 869000 "FLOATRP" 869867 NIL FLOATRP (NIL T) -7 NIL NIL) (-373 861641 865746 866376 "FLOAT" 867480 T FLOAT (NIL) -8 NIL NIL) (-372 859079 859579 860157 "FLOATCP" 861108 NIL FLOATCP (NIL T) -7 NIL NIL) (-371 857908 858712 858753 "FLINEXP" 858758 NIL FLINEXP (NIL T) -9 NIL 858851) (-370 857062 857297 857625 "FLINEXP-" 857630 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-369 856138 856282 856506 "FLASORT" 856914 NIL FLASORT (NIL T T) -7 NIL NIL) (-368 853355 854197 854249 "FLALG" 855476 NIL FLALG (NIL T T) -9 NIL 855943) (-367 847139 850841 850882 "FLAGG" 852144 NIL FLAGG (NIL T) -9 NIL 852796) (-366 845865 846204 846694 "FLAGG-" 846699 NIL FLAGG- (NIL T T) -8 NIL NIL) (-365 844907 845050 845277 "FLAGG2" 845718 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-364 841920 842894 842953 "FINRALG" 844081 NIL FINRALG (NIL T T) -9 NIL 844589) (-363 841080 841309 841648 "FINRALG-" 841653 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-362 840486 840699 840727 "FINITE" 840923 T FINITE (NIL) -9 NIL 841030) (-361 832944 835105 835145 "FINAALG" 838812 NIL FINAALG (NIL T) -9 NIL 840265) (-360 828285 829326 830470 "FINAALG-" 831849 NIL FINAALG- (NIL T T) -8 NIL NIL) (-359 827680 828040 828143 "FILE" 828215 NIL FILE (NIL T) -8 NIL NIL) (-358 826364 826676 826730 "FILECAT" 827414 NIL FILECAT (NIL T T) -9 NIL 827630) (-357 824284 825778 825806 "FIELD" 825846 T FIELD (NIL) -9 NIL 825926) (-356 822904 823289 823800 "FIELD-" 823805 NIL FIELD- (NIL T) -8 NIL NIL) (-355 820782 821539 821886 "FGROUP" 822590 NIL FGROUP (NIL T) -8 NIL NIL) (-354 819872 820036 820256 "FGLMICPK" 820614 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-353 815739 819797 819854 "FFX" 819859 NIL FFX (NIL T NIL) -8 NIL NIL) (-352 815340 815401 815536 "FFSLPE" 815672 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-351 811333 812112 812908 "FFPOLY" 814576 NIL FFPOLY (NIL T) -7 NIL NIL) (-350 810837 810873 811082 "FFPOLY2" 811291 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-349 806723 810756 810819 "FFP" 810824 NIL FFP (NIL T NIL) -8 NIL NIL) (-348 802156 806634 806698 "FF" 806703 NIL FF (NIL NIL NIL) -8 NIL NIL) (-347 797317 801499 801689 "FFNBX" 802010 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-346 792291 796452 796710 "FFNBP" 797171 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-345 786959 791575 791786 "FFNB" 792124 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-344 785791 785989 786304 "FFINTBAS" 786756 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-343 782075 784250 784278 "FFIELDC" 784898 T FFIELDC (NIL) -9 NIL 785274) (-342 780738 781108 781605 "FFIELDC-" 781610 NIL FFIELDC- (NIL T) -8 NIL NIL) (-341 780308 780353 780477 "FFHOM" 780680 NIL FFHOM (NIL T T T) -7 NIL NIL) (-340 778006 778490 779007 "FFF" 779823 NIL FFF (NIL T) -7 NIL NIL) (-339 773659 777748 777849 "FFCGX" 777949 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-338 769326 773391 773498 "FFCGP" 773602 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-337 764544 769053 769161 "FFCG" 769262 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-336 746602 755638 755724 "FFCAT" 760889 NIL FFCAT (NIL T T T) -9 NIL 762340) (-335 741800 742847 744161 "FFCAT-" 745391 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-334 741211 741254 741489 "FFCAT2" 741751 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-333 730423 734183 735403 "FEXPR" 740063 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-332 729423 729858 729899 "FEVALAB" 729983 NIL FEVALAB (NIL T) -9 NIL 730244) (-331 728582 728792 729130 "FEVALAB-" 729135 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-330 727175 727965 728168 "FDIV" 728481 NIL FDIV (NIL T T T T) -8 NIL NIL) (-329 724241 724956 725071 "FDIVCAT" 726639 NIL FDIVCAT (NIL T T T T) -9 NIL 727076) (-328 724003 724030 724200 "FDIVCAT-" 724205 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-327 723223 723310 723587 "FDIV2" 723910 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-326 721909 722168 722457 "FCPAK1" 722954 T FCPAK1 (NIL) -7 NIL NIL) (-325 721037 721409 721550 "FCOMP" 721800 NIL FCOMP (NIL T) -8 NIL NIL) (-324 704672 708086 711647 "FC" 717496 T FC (NIL) -8 NIL NIL) (-323 697325 701306 701346 "FAXF" 703148 NIL FAXF (NIL T) -9 NIL 703840) (-322 694604 695259 696084 "FAXF-" 696549 NIL FAXF- (NIL T T) -8 NIL NIL) (-321 689704 693980 694156 "FARRAY" 694461 NIL FARRAY (NIL T) -8 NIL NIL) (-320 685111 687143 687196 "FAMR" 688219 NIL FAMR (NIL T T) -9 NIL 688679) (-319 684001 684303 684738 "FAMR-" 684743 NIL FAMR- (NIL T T T) -8 NIL NIL) (-318 683197 683923 683976 "FAMONOID" 683981 NIL FAMONOID (NIL T) -8 NIL NIL) (-317 681027 681711 681764 "FAMONC" 682705 NIL FAMONC (NIL T T) -9 NIL 683091) (-316 679719 680781 680918 "FAGROUP" 680923 NIL FAGROUP (NIL T) -8 NIL NIL) (-315 677514 677833 678236 "FACUTIL" 679400 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-314 676613 676798 677020 "FACTFUNC" 677324 NIL FACTFUNC (NIL T) -7 NIL NIL) (-313 669018 675864 676076 "EXPUPXS" 676469 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-312 666501 667041 667627 "EXPRTUBE" 668452 T EXPRTUBE (NIL) -7 NIL NIL) (-311 662695 663287 664024 "EXPRODE" 665840 NIL EXPRODE (NIL T T) -7 NIL NIL) (-310 648069 661350 661778 "EXPR" 662299 NIL EXPR (NIL T) -8 NIL NIL) (-309 642476 643063 643876 "EXPR2UPS" 647367 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 642112 642169 642276 "EXPR2" 642413 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 633517 641244 641541 "EXPEXPAN" 641949 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-306 633344 633474 633503 "EXIT" 633508 T EXIT (NIL) -8 NIL NIL) (-305 632851 633068 633159 "EXITAST" 633273 T EXITAST (NIL) -8 NIL NIL) (-304 632478 632540 632653 "EVALCYC" 632783 NIL EVALCYC (NIL T) -7 NIL NIL) (-303 632019 632137 632178 "EVALAB" 632348 NIL EVALAB (NIL T) -9 NIL 632452) (-302 631500 631622 631843 "EVALAB-" 631848 NIL EVALAB- (NIL T T) -8 NIL NIL) (-301 629003 630271 630299 "EUCDOM" 630854 T EUCDOM (NIL) -9 NIL 631204) (-300 627408 627850 628440 "EUCDOM-" 628445 NIL EUCDOM- (NIL T) -8 NIL NIL) (-299 614948 617706 620456 "ESTOOLS" 624678 T ESTOOLS (NIL) -7 NIL NIL) (-298 614580 614637 614746 "ESTOOLS2" 614885 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 614331 614373 614453 "ESTOOLS1" 614532 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 608256 609984 610012 "ES" 612780 T ES (NIL) -9 NIL 614189) (-295 603203 604490 606307 "ES-" 606471 NIL ES- (NIL T) -8 NIL NIL) (-294 599578 600338 601118 "ESCONT" 602443 T ESCONT (NIL) -7 NIL NIL) (-293 599323 599355 599437 "ESCONT1" 599540 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-292 598998 599048 599148 "ES2" 599267 NIL ES2 (NIL T T) -7 NIL NIL) (-291 598628 598686 598795 "ES1" 598934 NIL ES1 (NIL T T) -7 NIL NIL) (-290 597844 597973 598149 "ERROR" 598472 T ERROR (NIL) -7 NIL NIL) (-289 591347 597703 597794 "EQTBL" 597799 NIL EQTBL (NIL T T) -8 NIL NIL) (-288 583904 586661 588110 "EQ" 589931 NIL -3357 (NIL T) -8 NIL NIL) (-287 583536 583593 583702 "EQ2" 583841 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 578828 579874 580967 "EP" 582475 NIL EP (NIL T) -7 NIL NIL) (-285 577410 577711 578028 "ENV" 578531 T ENV (NIL) -8 NIL NIL) (-284 576609 577129 577157 "ENTIRER" 577162 T ENTIRER (NIL) -9 NIL 577208) (-283 573111 574564 574934 "EMR" 576408 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-282 572255 572440 572494 "ELTAGG" 572874 NIL ELTAGG (NIL T T) -9 NIL 573085) (-281 571974 572036 572177 "ELTAGG-" 572182 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-280 571763 571792 571846 "ELTAB" 571930 NIL ELTAB (NIL T T) -9 NIL NIL) (-279 570889 571035 571234 "ELFUTS" 571614 NIL ELFUTS (NIL T T) -7 NIL NIL) (-278 570631 570687 570715 "ELEMFUN" 570820 T ELEMFUN (NIL) -9 NIL NIL) (-277 570501 570522 570590 "ELEMFUN-" 570595 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-276 565392 568601 568642 "ELAGG" 569582 NIL ELAGG (NIL T) -9 NIL 570045) (-275 563677 564111 564774 "ELAGG-" 564779 NIL ELAGG- (NIL T T) -8 NIL NIL) (-274 562334 562614 562909 "ELABEXPR" 563402 T ELABEXPR (NIL) -8 NIL NIL) (-273 555200 557001 557828 "EFUPXS" 561610 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-272 548650 550451 551261 "EFULS" 554476 NIL EFULS (NIL T T T) -8 NIL NIL) (-271 546072 546430 546909 "EFSTRUC" 548282 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-270 535144 536709 538269 "EF" 544587 NIL EF (NIL T T) -7 NIL NIL) (-269 534245 534629 534778 "EAB" 535015 T EAB (NIL) -8 NIL NIL) (-268 533454 534204 534232 "E04UCFA" 534237 T E04UCFA (NIL) -8 NIL NIL) (-267 532663 533413 533441 "E04NAFA" 533446 T E04NAFA (NIL) -8 NIL NIL) (-266 531872 532622 532650 "E04MBFA" 532655 T E04MBFA (NIL) -8 NIL NIL) (-265 531081 531831 531859 "E04JAFA" 531864 T E04JAFA (NIL) -8 NIL NIL) (-264 530292 531040 531068 "E04GCFA" 531073 T E04GCFA (NIL) -8 NIL NIL) (-263 529503 530251 530279 "E04FDFA" 530284 T E04FDFA (NIL) -8 NIL NIL) (-262 528712 529462 529490 "E04DGFA" 529495 T E04DGFA (NIL) -8 NIL NIL) (-261 522890 524237 525601 "E04AGNT" 527368 T E04AGNT (NIL) -7 NIL NIL) (-260 521614 522094 522134 "DVARCAT" 522609 NIL DVARCAT (NIL T) -9 NIL 522808) (-259 520818 521030 521344 "DVARCAT-" 521349 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-258 513718 520617 520746 "DSMP" 520751 NIL DSMP (NIL T T T) -8 NIL NIL) (-257 508528 509663 510731 "DROPT" 512670 T DROPT (NIL) -8 NIL NIL) (-256 508193 508252 508350 "DROPT1" 508463 NIL DROPT1 (NIL T) -7 NIL NIL) (-255 503308 504434 505571 "DROPT0" 507076 T DROPT0 (NIL) -7 NIL NIL) (-254 501653 501978 502364 "DRAWPT" 502942 T DRAWPT (NIL) -7 NIL NIL) (-253 496240 497163 498242 "DRAW" 500627 NIL DRAW (NIL T) -7 NIL NIL) (-252 495873 495926 496044 "DRAWHACK" 496181 NIL DRAWHACK (NIL T) -7 NIL NIL) (-251 494604 494873 495164 "DRAWCX" 495602 T DRAWCX (NIL) -7 NIL NIL) (-250 494120 494188 494339 "DRAWCURV" 494530 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-249 484591 486550 488665 "DRAWCFUN" 492025 T DRAWCFUN (NIL) -7 NIL NIL) (-248 481404 483286 483327 "DQAGG" 483956 NIL DQAGG (NIL T) -9 NIL 484229) (-247 469923 476620 476703 "DPOLCAT" 478555 NIL DPOLCAT (NIL T T T T) -9 NIL 479100) (-246 464762 466108 468066 "DPOLCAT-" 468071 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-245 457917 464623 464721 "DPMO" 464726 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-244 450975 457697 457864 "DPMM" 457869 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-243 450395 450598 450712 "DOMAIN" 450881 T DOMAIN (NIL) -8 NIL NIL) (-242 444146 450030 450182 "DMP" 450296 NIL DMP (NIL NIL T) -8 NIL NIL) (-241 443746 443802 443946 "DLP" 444084 NIL DLP (NIL T) -7 NIL NIL) (-240 437390 442847 443074 "DLIST" 443551 NIL DLIST (NIL T) -8 NIL NIL) (-239 434236 436245 436286 "DLAGG" 436836 NIL DLAGG (NIL T) -9 NIL 437065) (-238 433086 433716 433744 "DIVRING" 433836 T DIVRING (NIL) -9 NIL 433919) (-237 432323 432513 432813 "DIVRING-" 432818 NIL DIVRING- (NIL T) -8 NIL NIL) (-236 430425 430782 431188 "DISPLAY" 431937 T DISPLAY (NIL) -7 NIL NIL) (-235 424367 430339 430402 "DIRPROD" 430407 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-234 423215 423418 423683 "DIRPROD2" 424160 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-233 412753 418705 418758 "DIRPCAT" 419168 NIL DIRPCAT (NIL NIL T) -9 NIL 420008) (-232 410079 410721 411602 "DIRPCAT-" 411939 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-231 409366 409526 409712 "DIOSP" 409913 T DIOSP (NIL) -7 NIL NIL) (-230 406068 408278 408319 "DIOPS" 408753 NIL DIOPS (NIL T) -9 NIL 408982) (-229 405617 405731 405922 "DIOPS-" 405927 NIL DIOPS- (NIL T T) -8 NIL NIL) (-228 404529 405123 405151 "DIFRING" 405338 T DIFRING (NIL) -9 NIL 405448) (-227 404175 404252 404404 "DIFRING-" 404409 NIL DIFRING- (NIL T) -8 NIL NIL) (-226 402000 403238 403279 "DIFEXT" 403642 NIL DIFEXT (NIL T) -9 NIL 403936) (-225 400285 400713 401379 "DIFEXT-" 401384 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-224 397607 399817 399858 "DIAGG" 399863 NIL DIAGG (NIL T) -9 NIL 399883) (-223 396991 397148 397400 "DIAGG-" 397405 NIL DIAGG- (NIL T T) -8 NIL NIL) (-222 392456 395950 396227 "DHMATRIX" 396760 NIL DHMATRIX (NIL T) -8 NIL NIL) (-221 388068 388977 389987 "DFSFUN" 391466 T DFSFUN (NIL) -7 NIL NIL) (-220 383184 386999 387311 "DFLOAT" 387776 T DFLOAT (NIL) -8 NIL NIL) (-219 381412 381693 382089 "DFINTTLS" 382892 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-218 378477 379433 379833 "DERHAM" 381078 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-217 376326 378252 378341 "DEQUEUE" 378421 NIL DEQUEUE (NIL T) -8 NIL NIL) (-216 375541 375674 375870 "DEGRED" 376188 NIL DEGRED (NIL T T) -7 NIL NIL) (-215 371936 372681 373534 "DEFINTRF" 374769 NIL DEFINTRF (NIL T) -7 NIL NIL) (-214 369463 369932 370531 "DEFINTEF" 371455 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-213 368840 369083 369198 "DEFAST" 369368 T DEFAST (NIL) -8 NIL NIL) (-212 362726 368281 368447 "DECIMAL" 368694 T DECIMAL (NIL) -8 NIL NIL) (-211 360238 360696 361202 "DDFACT" 362270 NIL DDFACT (NIL T T) -7 NIL NIL) (-210 359834 359877 360028 "DBLRESP" 360189 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-209 357544 357878 358247 "DBASE" 359592 NIL DBASE (NIL T) -8 NIL NIL) (-208 356813 357024 357170 "DATAARY" 357443 NIL DATAARY (NIL NIL T) -8 NIL NIL) (-207 355946 356772 356800 "D03FAFA" 356805 T D03FAFA (NIL) -8 NIL NIL) (-206 355080 355905 355933 "D03EEFA" 355938 T D03EEFA (NIL) -8 NIL NIL) (-205 353030 353496 353985 "D03AGNT" 354611 T D03AGNT (NIL) -7 NIL NIL) (-204 352346 352989 353017 "D02EJFA" 353022 T D02EJFA (NIL) -8 NIL NIL) (-203 351662 352305 352333 "D02CJFA" 352338 T D02CJFA (NIL) -8 NIL NIL) (-202 350978 351621 351649 "D02BHFA" 351654 T D02BHFA (NIL) -8 NIL NIL) (-201 350294 350937 350965 "D02BBFA" 350970 T D02BBFA (NIL) -8 NIL NIL) (-200 343492 345080 346686 "D02AGNT" 348708 T D02AGNT (NIL) -7 NIL NIL) (-199 341261 341783 342329 "D01WGTS" 342966 T D01WGTS (NIL) -7 NIL NIL) (-198 340356 341220 341248 "D01TRNS" 341253 T D01TRNS (NIL) -8 NIL NIL) (-197 339451 340315 340343 "D01GBFA" 340348 T D01GBFA (NIL) -8 NIL NIL) (-196 338546 339410 339438 "D01FCFA" 339443 T D01FCFA (NIL) -8 NIL NIL) (-195 337641 338505 338533 "D01ASFA" 338538 T D01ASFA (NIL) -8 NIL NIL) (-194 336736 337600 337628 "D01AQFA" 337633 T D01AQFA (NIL) -8 NIL NIL) (-193 335831 336695 336723 "D01APFA" 336728 T D01APFA (NIL) -8 NIL NIL) (-192 334926 335790 335818 "D01ANFA" 335823 T D01ANFA (NIL) -8 NIL NIL) (-191 334021 334885 334913 "D01AMFA" 334918 T D01AMFA (NIL) -8 NIL NIL) (-190 333116 333980 334008 "D01ALFA" 334013 T D01ALFA (NIL) -8 NIL NIL) (-189 332211 333075 333103 "D01AKFA" 333108 T D01AKFA (NIL) -8 NIL NIL) (-188 331306 332170 332198 "D01AJFA" 332203 T D01AJFA (NIL) -8 NIL NIL) (-187 324603 326154 327715 "D01AGNT" 329765 T D01AGNT (NIL) -7 NIL NIL) (-186 323940 324068 324220 "CYCLOTOM" 324471 T CYCLOTOM (NIL) -7 NIL NIL) (-185 320675 321388 322115 "CYCLES" 323233 T CYCLES (NIL) -7 NIL NIL) (-184 319987 320121 320292 "CVMP" 320536 NIL CVMP (NIL T) -7 NIL NIL) (-183 317758 318016 318392 "CTRIGMNP" 319715 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-182 317175 317381 317495 "CTOR" 317664 T CTOR (NIL) -8 NIL NIL) (-181 316711 316906 317007 "CTORKIND" 317094 T CTORKIND (NIL) -8 NIL NIL) (-180 316222 316411 316510 "CTORCALL" 316632 T CTORCALL (NIL) -8 NIL NIL) (-179 315596 315695 315848 "CSTTOOLS" 316119 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-178 311395 312052 312810 "CRFP" 314908 NIL CRFP (NIL T T) -7 NIL NIL) (-177 310897 311116 311208 "CRCEAST" 311323 T CRCEAST (NIL) -8 NIL NIL) (-176 309944 310129 310357 "CRAPACK" 310701 NIL CRAPACK (NIL T) -7 NIL NIL) (-175 309328 309429 309633 "CPMATCH" 309820 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-174 309053 309081 309187 "CPIMA" 309294 NIL CPIMA (NIL T T T) -7 NIL NIL) (-173 305417 306089 306807 "COORDSYS" 308388 NIL COORDSYS (NIL T) -7 NIL NIL) (-172 304801 304930 305080 "CONTOUR" 305287 T CONTOUR (NIL) -8 NIL NIL) (-171 300727 302804 303296 "CONTFRAC" 304341 NIL CONTFRAC (NIL T) -8 NIL NIL) (-170 300607 300628 300656 "CONDUIT" 300693 T CONDUIT (NIL) -9 NIL NIL) (-169 299800 300320 300348 "COMRING" 300353 T COMRING (NIL) -9 NIL 300405) (-168 298881 299158 299342 "COMPPROP" 299636 T COMPPROP (NIL) -8 NIL NIL) (-167 298542 298577 298705 "COMPLPAT" 298840 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-166 288599 298351 298460 "COMPLEX" 298465 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 288235 288292 288399 "COMPLEX2" 288536 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-164 287953 287988 288086 "COMPFACT" 288194 NIL COMPFACT (NIL T T) -7 NIL NIL) (-163 272357 282575 282615 "COMPCAT" 283619 NIL COMPCAT (NIL T) -9 NIL 285004) (-162 261872 264796 268423 "COMPCAT-" 268779 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-161 261601 261629 261732 "COMMUPC" 261838 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-160 261396 261429 261488 "COMMONOP" 261562 T COMMONOP (NIL) -7 NIL NIL) (-159 260979 261147 261234 "COMM" 261329 T COMM (NIL) -8 NIL NIL) (-158 260583 260783 260858 "COMMAAST" 260924 T COMMAAST (NIL) -8 NIL NIL) (-157 259832 260026 260054 "COMBOPC" 260392 T COMBOPC (NIL) -9 NIL 260567) (-156 258728 258938 259180 "COMBINAT" 259622 NIL COMBINAT (NIL T) -7 NIL NIL) (-155 254926 255499 256139 "COMBF" 258150 NIL COMBF (NIL T T) -7 NIL NIL) (-154 253712 254042 254277 "COLOR" 254711 T COLOR (NIL) -8 NIL NIL) (-153 253215 253433 253525 "COLONAST" 253640 T COLONAST (NIL) -8 NIL NIL) (-152 252855 252902 253027 "CMPLXRT" 253162 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-151 252330 252555 252654 "CLLCTAST" 252776 T CLLCTAST (NIL) -8 NIL NIL) (-150 247832 248860 249940 "CLIP" 251270 T CLIP (NIL) -7 NIL NIL) (-149 246214 246938 247177 "CLIF" 247659 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-148 242436 244360 244401 "CLAGG" 245330 NIL CLAGG (NIL T) -9 NIL 245866) (-147 240858 241315 241898 "CLAGG-" 241903 NIL CLAGG- (NIL T T) -8 NIL NIL) (-146 240402 240487 240627 "CINTSLPE" 240767 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-145 237903 238374 238922 "CHVAR" 239930 NIL CHVAR (NIL T T T) -7 NIL NIL) (-144 237166 237686 237714 "CHARZ" 237719 T CHARZ (NIL) -9 NIL 237734) (-143 236920 236960 237038 "CHARPOL" 237120 NIL CHARPOL (NIL T) -7 NIL NIL) (-142 236067 236620 236648 "CHARNZ" 236695 T CHARNZ (NIL) -9 NIL 236751) (-141 234092 234757 235092 "CHAR" 235752 T CHAR (NIL) -8 NIL NIL) (-140 233818 233879 233907 "CFCAT" 234018 T CFCAT (NIL) -9 NIL NIL) (-139 233063 233174 233356 "CDEN" 233702 NIL CDEN (NIL T T T) -7 NIL NIL) (-138 229055 232216 232496 "CCLASS" 232803 T CCLASS (NIL) -8 NIL NIL) (-137 228974 229000 229035 "CATEGORY" 229040 T -10 (NIL) -8 NIL NIL) (-136 228448 228674 228773 "CATAST" 228895 T CATAST (NIL) -8 NIL NIL) (-135 227951 228169 228261 "CASEAST" 228376 T CASEAST (NIL) -8 NIL NIL) (-134 223003 223980 224733 "CARTEN" 227254 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-133 222111 222259 222480 "CARTEN2" 222850 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-132 220453 221261 221518 "CARD" 221874 T CARD (NIL) -8 NIL NIL) (-131 220056 220257 220332 "CAPSLAST" 220398 T CAPSLAST (NIL) -8 NIL NIL) (-130 219428 219756 219784 "CACHSET" 219916 T CACHSET (NIL) -9 NIL 219993) (-129 218924 219220 219248 "CABMON" 219298 T CABMON (NIL) -9 NIL 219354) (-128 217851 218279 218475 "BYTE" 218748 T BYTE (NIL) -8 NIL NIL) (-127 213260 217319 217482 "BYTEBUF" 217708 T BYTEBUF (NIL) -8 NIL NIL) (-126 210817 212952 213059 "BTREE" 213186 NIL BTREE (NIL T) -8 NIL NIL) (-125 208315 210465 210587 "BTOURN" 210727 NIL BTOURN (NIL T) -8 NIL NIL) (-124 205733 207786 207827 "BTCAT" 207895 NIL BTCAT (NIL T) -9 NIL 207972) (-123 205400 205480 205629 "BTCAT-" 205634 NIL BTCAT- (NIL T T) -8 NIL NIL) (-122 200692 204543 204571 "BTAGG" 204793 T BTAGG (NIL) -9 NIL 204954) (-121 200182 200307 200513 "BTAGG-" 200518 NIL BTAGG- (NIL T) -8 NIL NIL) (-120 197226 199460 199675 "BSTREE" 199999 NIL BSTREE (NIL T) -8 NIL NIL) (-119 196364 196490 196674 "BRILL" 197082 NIL BRILL (NIL T) -7 NIL NIL) (-118 193065 195092 195133 "BRAGG" 195782 NIL BRAGG (NIL T) -9 NIL 196039) (-117 191594 192000 192555 "BRAGG-" 192560 NIL BRAGG- (NIL T T) -8 NIL NIL) (-116 184858 190940 191124 "BPADICRT" 191442 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-115 183208 184795 184840 "BPADIC" 184845 NIL BPADIC (NIL NIL) -8 NIL NIL) (-114 182906 182936 183050 "BOUNDZRO" 183172 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-113 178421 179512 180379 "BOP" 182059 T BOP (NIL) -8 NIL NIL) (-112 176042 176486 177006 "BOP1" 177934 NIL BOP1 (NIL T) -7 NIL NIL) (-111 174780 175466 175659 "BOOLEAN" 175869 T BOOLEAN (NIL) -8 NIL NIL) (-110 174142 174520 174574 "BMODULE" 174579 NIL BMODULE (NIL T T) -9 NIL 174644) (-109 169972 173940 174013 "BITS" 174089 T BITS (NIL) -8 NIL NIL) (-108 169384 169506 169648 "BINDING" 169850 T BINDING (NIL) -8 NIL NIL) (-107 163274 168828 168993 "BINARY" 169239 T BINARY (NIL) -8 NIL NIL) (-106 161101 162529 162570 "BGAGG" 162830 NIL BGAGG (NIL T) -9 NIL 162967) (-105 160932 160964 161055 "BGAGG-" 161060 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 160030 160316 160521 "BFUNCT" 160747 T BFUNCT (NIL) -8 NIL NIL) (-103 158720 158898 159186 "BEZOUT" 159854 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 155237 157572 157902 "BBTREE" 158423 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154971 155024 155052 "BASTYPE" 155171 T BASTYPE (NIL) -9 NIL NIL) (-100 154823 154852 154925 "BASTYPE-" 154930 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 154261 154337 154487 "BALFACT" 154734 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 153144 153676 153862 "AUTOMOR" 154106 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152870 152875 152901 "ATTREG" 152906 T ATTREG (NIL) -9 NIL NIL) (-96 151149 151567 151919 "ATTRBUT" 152536 T ATTRBUT (NIL) -8 NIL NIL) (-95 150784 150977 151043 "ATTRAST" 151101 T ATTRAST (NIL) -8 NIL NIL) (-94 150320 150433 150459 "ATRIG" 150660 T ATRIG (NIL) -9 NIL NIL) (-93 150129 150170 150257 "ATRIG-" 150262 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149751 149911 149937 "ASTCAT" 149995 T ASTCAT (NIL) -9 NIL 150058) (-91 149478 149537 149656 "ASTCAT-" 149661 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147675 149254 149342 "ASTACK" 149421 NIL ASTACK (NIL T) -8 NIL 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(NIL NIL) -8 NIL NIL) (-75 132293 133047 133215 "ASP42" 133397 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-74 131070 131826 131996 "ASP41" 132180 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130020 130747 130865 "ASP35" 130983 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129785 129968 130007 "ASP34" 130012 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129522 129589 129665 "ASP33" 129740 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128417 129157 129289 "ASP31" 129421 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 128182 128365 128404 "ASP30" 128409 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 127917 127986 128062 "ASP29" 128137 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127682 127865 127904 "ASP28" 127909 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127447 127630 127669 "ASP27" 127674 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126531 127145 127256 "ASP24" 127367 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125447 126172 126302 "ASP20" 126432 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124535 125148 125258 "ASP1" 125368 NIL ASP1 (NIL NIL) -8 NIL NIL) (-62 123479 124209 124328 "ASP19" 124447 NIL ASP19 (NIL NIL) -8 NIL NIL) (-61 123216 123283 123359 "ASP12" 123434 NIL ASP12 (NIL NIL) -8 NIL NIL) (-60 122068 122815 122959 "ASP10" 123103 NIL ASP10 (NIL NIL) -8 NIL NIL) (-59 119967 121912 122003 "ARRAY2" 122008 NIL ARRAY2 (NIL T) -8 NIL NIL) (-58 115783 119615 119729 "ARRAY1" 119884 NIL ARRAY1 (NIL T) -8 NIL NIL) (-57 114815 114988 115209 "ARRAY12" 115606 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-56 109174 111045 111120 "ARR2CAT" 113750 NIL ARR2CAT (NIL T T T) -9 NIL 114508) (-55 106608 107352 108306 "ARR2CAT-" 108311 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-54 105356 105508 105814 "APPRULE" 106444 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 105007 105055 105174 "APPLYORE" 105302 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 103981 104272 104467 "ANY" 104830 T ANY (NIL) -8 NIL NIL) (-51 103259 103382 103539 "ANY1" 103855 NIL ANY1 (NIL T) -7 NIL NIL) (-50 100824 101696 102023 "ANTISYM" 102983 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100339 100528 100625 "ANON" 100745 T ANON (NIL) -8 NIL NIL) (-48 94471 98878 99332 "AN" 99903 T AN (NIL) -8 NIL NIL) (-47 90852 92206 92257 "AMR" 93005 NIL AMR (NIL T T) -9 NIL 93605) (-46 89964 90185 90548 "AMR-" 90553 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74514 89881 89942 "ALIST" 89947 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71351 74108 74277 "ALGSC" 74432 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 67907 68461 69068 "ALGPKG" 70791 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67184 67285 67469 "ALGMFACT" 67793 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 62923 63608 64263 "ALGMANIP" 66707 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54329 62549 62699 "ALGFF" 62856 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53525 53656 53835 "ALGFACT" 54187 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52555 53121 53159 "ALGEBRA" 53219 NIL ALGEBRA (NIL T) -9 NIL 53278) (-37 52273 52332 52464 "ALGEBRA-" 52469 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34533 50276 50328 "ALAGG" 50464 NIL ALAGG (NIL T T) -9 NIL 50625) (-35 34069 34182 34208 "AHYP" 34409 T AHYP (NIL) -9 NIL NIL) (-34 33000 33248 33274 "AGG" 33773 T AGG (NIL) -9 NIL 34052) (-33 32434 32596 32810 "AGG-" 32815 NIL AGG- (NIL T) -8 NIL NIL) (-32 30111 30533 30951 "AF" 32076 NIL AF (NIL T T) -7 NIL NIL) (-31 29618 29836 29926 "ADDAST" 30039 T ADDAST (NIL) -8 NIL NIL) (-30 28887 29145 29301 "ACPLOT" 29480 T ACPLOT (NIL) -8 NIL NIL) (-29 18358 26279 26330 "ACFS" 27041 NIL ACFS (NIL T) -9 NIL 27280) (-28 16372 16862 17637 "ACFS-" 17642 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 36cc0e44..fc2b6c4f 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,3245 +1,4097 @@ -(739292 . 3433818807) -(((*1 *2 *3) - (-12 (-5 *3 (-627 *4)) (-4 *4 (-830)) (-5 *2 (-627 (-646 *4 *5))) - (-5 *1 (-611 *4 *5 *6)) (-4 *5 (-13 (-169) (-700 (-401 (-552))))) - (-14 *6 (-900))))) -(((*1 *2 *2) - (-12 (-5 *2 (-111)) (-5 *1 (-435 *3)) (-4 *3 (-1211 (-552)))))) -(((*1 *2 *1) (-12 (-4 *1 (-260 *2)) (-4 *2 (-830)))) - ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1152)) (-5 *1 (-844 *3)) (-14 *3 (-627 *2)))) - ((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-945 *3)) (-4 *3 (-946)))) - ((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-968)))) - ((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-1068 *3)) (-4 *3 (-1189)))) +(739410 . 3436147955) +(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-1136)) (-5 *3 (-808)) (-5 *1 (-807))))) +(((*1 *2 *1) + (-12 (-5 *2 (-401 (-933 *3))) (-5 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(-4318 . 6510) (-4319 . 5880) (-4320 . 5822) (-4321 . 5742) + (-4322 . 5559) (-4323 . 5404) (-4324 . 5309) (-4325 . 5202) + (-4326 . 5150) (-4327 . 5053) (-4328 . 4919) (-4329 . 4846) + (-4330 . 4772) (-4331 . 4635) (-4332 . 4469) (-4333 . 4315) + (-4334 . 4046) (-4335 . 3894) (-4336 . 3809) (-4337 . 3754) + (-4338 . 3584) (-4339 . 3388) (-4340 . 3073) (-4341 . 2937) + (-4342 . 2854) (-4343 . 2212) (-4344 . 2134) (-4345 . 2066) + (-4346 . 283) (-4347 . 104) (-4348 . 30))
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