diff options
| -rw-r--r-- | src/ChangeLog | 25 | ||||
| -rw-r--r-- | src/algebra/sf.spad.pamphlet | 2 | ||||
| -rw-r--r-- | src/boot/includer.boot | 86 | ||||
| -rw-r--r-- | src/boot/scanner.boot | 5 | ||||
| -rw-r--r-- | src/boot/strap/includer.clisp | 112 | ||||
| -rw-r--r-- | src/boot/strap/scanner.clisp | 11 | ||||
| -rw-r--r-- | src/boot/strap/tokens.clisp | 1 | ||||
| -rw-r--r-- | src/boot/strap/translator.clisp | 88 | ||||
| -rw-r--r-- | src/boot/tokens.boot | 1 | ||||
| -rw-r--r-- | src/boot/translator.boot | 39 | ||||
| -rw-r--r-- | src/interp/scan.boot | 19 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 642 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1349 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9142 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 32174 |
16 files changed, 22506 insertions, 22764 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index da1e4e31..d03372c5 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,28 @@ +2011-03-19 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * boot/translator.boot (FC): Remove. + (FBO): Likewise. + (FEV): Likewise. + (shoeGeneralFC): Likewise. + (shoeFindName): Likewise. + (shoeFindName2): Likewise. + (shoeTransform2): Likewise. + * boot/scanner.boot (shoeLineToks): Don't support `)package' line + anymore. + * boot/includer.boot: Remove support for `)package', `)include', + `)includelisp', `)includelines' lines. + (shorPackageStartsAt): Remove. + (shorFindLines): Likewise. + (shoeFileInput): Likewise. + (shoeLispFileInput): Likewise. + (shoeLineFileInput): Likewise. + (shoeFunctionFileInput): Likewise. + (shoePlainLine?): Reflect removal. + (shoeSimpleLine): Likewise. + * boot/tokens.boot (charByName): New builtin library function. + * algebra/sf.spad.pamphlet (RealNumberSystem): Don't re-export + abs. It is already exported by OrderedRing. + 2011-03-17 Gabriel Dos Reis <gdr@cs.tamu.edu> * utils/storage.H: Rework. diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index 54dc881a..ce5b6032 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -83,8 +83,6 @@ RealNumberSystem(): Category == ++ truncate x returns the integer between x and 0 closest to x. round: % -> % ++ round x computes the integer closest to x. - abs : % -> % - ++ abs x returns the absolute value of x. add characteristic == 0 diff --git a/src/boot/includer.boot b/src/boot/includer.boot index 62cc6456..e74542eb 100644 --- a/src/boot/includer.boot +++ b/src/boot/includer.boot @@ -1,6 +1,6 @@ -- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. -- All rights reserved. --- Copyright (C) 2007-2010, Gabriel Dos Reis. +-- Copyright (C) 2007-2011, Gabriel Dos Reis. -- All rights reserved. -- -- Redistribution and use in source and binary forms, with or without @@ -53,14 +53,7 @@ module includer -- )eval line | evaluates the boot line -- nothing included -- )line line | line is reproduced as is in lisp output --- )lisp line | line is read by lisp READ --- )package line | produces (IN-PACKAGE line) in lisp --- output --- )include filename | includes the file as boot code --- )includelisp filename | includes the file as lisp code --- read by lisp READ --- )includelines filename | includes the file as is --- in lisp output +-- )lisp line line is read by lisp READ -- -- If ::= )if SimpleLine* ElseLines )endif -- @@ -140,38 +133,14 @@ lineString p == lineCharacter p == rest p -shoePackageStartsAt (lines,sz,name,stream)== - bStreamNull stream => [[],['nullstream]] - a := CAAR stream - #a >= 8 and subString(a,0,8)='")package" => - shoePackageStartsAt([CAAR stream,:lines],sz,name,rest stream) - #a < sz => - shoePackageStartsAt(lines, sz,name,rest stream) - subString(a,0,sz)=name and (#a>sz and not shoeIdChar(a.sz)) => - [lines,stream] - shoePackageStartsAt(lines,sz,name,rest stream) - -shoeFindLines(fn,name,a)== - a = nil => - shoeNotFound fn - [] - [lines,b]:=shoePackageStartsAt([],#name,name, shoeInclude - bAddLineNumber(bRgen a,bIgen 0)) - b:=shoeTransform2 b - bStreamNull b => - shoeConsole strconc (name,'" not found in ",fn) - [] - lines = nil => shoeConsole '")package not found" - append(reverse lines,first b) - -- Lazy inclusion support. -$bStreamNil:=["nullstream"] +$bStreamNil == ["nullstream"] -bStreamNull x== +bStreamNull x == x = nil or x is ["nullstream",:.] => true - while x is ["nonnullstream",:.] repeat - st:=apply(second x,CDDR x) + while x is ["nonnullstream",op,:args] repeat + st := apply(op,args) x.first := first st x.rest := rest st x is ["nullstream",:.] @@ -180,20 +149,10 @@ bMap(f,x) == bDelay(function bMap1, [f,x]) bMap1(:z)== - [f,x]:=z - if bStreamNull x - then $bStreamNil - else [FUNCALL(f,first x),:bMap(f,rest x)] - -shoeFileMap(f, fn)== - a:=shoeInputFile fn - a = nil => - shoeConsole strconc(fn,'" NOT FOUND") - $bStreamNil - shoeConsole strconc('"READING ",fn) - shoeInclude bAddLineNumber(bMap(f,bRgen a),bIgen 0) + [f,x] := z + bStreamNull x => $bStreamNil + [apply(f,[first x]),:bMap(f,rest x)] - bDelay(f,x) == ["nonnullstream",:[f,:x]] @@ -239,22 +198,12 @@ bAddLineNumber1(:f)== [[first f1,:first f2],:bAddLineNumber(rest f1,rest f2)] - -shoeFileInput fn == - shoeFileMap(function IDENTITY,fn) - shoePrefixLisp x == strconc('")lisp",x) -shoeLispFileInput fn== - shoeFileMap(function shoePrefixLisp,fn) - shoePrefixLine x== strconc('")line",x) -shoeLineFileInput fn== - shoeFileMap(function shoePrefixLine,fn) - shoePrefix?(prefix,whole) == #prefix > #whole => false good:=true @@ -269,18 +218,13 @@ shoePlainLine?(s) == shoeSay? s == shoePrefix?('")say", s) shoeEval? s == shoePrefix?('")eval", s) -shoeInclude? s == shoePrefix?('")include", s) shoeFin? s == shoePrefix?('")fin", s) shoeIf? s == shoePrefix?('")if", s) shoeEndIf? s == shoePrefix?('")endif", s) shoeElse? s == shoePrefix?('")else", s) shoeElseIf? s == shoePrefix?('")elseif", s) -shoePackage? s == shoePrefix?('")package", s) shoeLisp? s == shoePrefix?('")lisp", s) -shoeIncludeLisp? s == shoePrefix?('")includelisp" ,s) shoeLine? s == shoePrefix?('")line", s) -shoeIncludeLines? s == shoePrefix?('")includelines",s) -shoeIncludeFunction? s == shoePrefix?('")includefunction",s) shoeBiteOff x== n:=STRPOSL('" ",x,0,true) @@ -303,10 +247,6 @@ shoeFnFileName x== c = nil => [first a,'""] [first a, c] -shoeFunctionFileInput [fun,fn]== - shoeOpenInputFile (a,fn, - shoeInclude bAddLineNumber( shoeFindLines(fn,fun,a),bIgen 0)) - shoeInclude s == bDelay(function shoeInclude1,[s]) @@ -322,15 +262,7 @@ shoeSimpleLine(h) == string :=first h shoePlainLine? string=> [h] command:=shoeLisp? string => [h] - command:=shoeIncludeLisp? string => - shoeLispFileInput shoeFileName command - command:=shoeIncludeFunction? string => - shoeFunctionFileInput shoeFnFileName command command:=shoeLine? string => [h] - command:=shoeIncludeLines? string => - shoeLineFileInput shoeFileName command - command:=shoeInclude? string => shoeFileInput shoeFileName command - command:=shoePackage? string => [h] command:=shoeSay? string => shoeConsole command nil diff --git a/src/boot/scanner.boot b/src/boot/scanner.boot index 8066ee94..4522e2b1 100644 --- a/src/boot/scanner.boot +++ b/src/boot/scanner.boot @@ -112,11 +112,6 @@ shoeLineToks(s)== ($ln,$linepos,shoeLeafLine command,0) [[dq],:$r] command:=shoeLisp? $ln=> shoeLispToken($r,command) - command:=shoePackage? $ln=> - a := strconc('"(IN-PACKAGE ",command,'")") - dq:=dqUnit shoeConstructToken - ($ln,$linepos,shoeLeafLisp a,0) - [[dq],:$r] shoeLineToks $r toks:=[] while $n<$sz repeat toks:=dqAppend(toks,shoeToken()) diff --git a/src/boot/strap/includer.clisp b/src/boot/strap/includer.clisp index 323a23a9..7d47a96c 100644 --- a/src/boot/strap/includer.clisp +++ b/src/boot/strap/includer.clisp @@ -82,59 +82,27 @@ (DEFUN |lineCharacter| (|p|) (CDR |p|)) -(DEFUN |shoePackageStartsAt| (|lines| |sz| |name| |stream|) - (PROG (|a|) - (RETURN - (COND - ((|bStreamNull| |stream|) (LIST NIL (LIST '|nullstream|))) - (T (SETQ |a| (CAAR |stream|)) - (COND - ((AND (NOT (< (LENGTH |a|) 8)) - (STRING= (|subString| |a| 0 8) ")package")) - (|shoePackageStartsAt| (CONS (CAAR |stream|) |lines|) - |sz| |name| (CDR |stream|))) - ((< (LENGTH |a|) |sz|) - (|shoePackageStartsAt| |lines| |sz| |name| - (CDR |stream|))) - ((AND (STRING= (|subString| |a| 0 |sz|) |name|) - (< |sz| (LENGTH |a|)) - (NOT (|shoeIdChar| (ELT |a| |sz|)))) - (LIST |lines| |stream|)) - (T (|shoePackageStartsAt| |lines| |sz| |name| - (CDR |stream|))))))))) - -(DEFUN |shoeFindLines| (|fn| |name| |a|) - (PROG (|b| |lines| |LETTMP#1|) - (RETURN - (COND - ((NULL |a|) (|shoeNotFound| |fn|) NIL) - (T (SETQ |LETTMP#1| - (|shoePackageStartsAt| NIL (LENGTH |name|) |name| - (|shoeInclude| - (|bAddLineNumber| (|bRgen| |a|) (|bIgen| 0))))) - (SETQ |lines| (CAR |LETTMP#1|)) (SETQ |b| (CADR |LETTMP#1|)) - (SETQ |b| (|shoeTransform2| |b|)) - (COND - ((|bStreamNull| |b|) - (|shoeConsole| (CONCAT |name| " not found in " |fn|)) - NIL) - ((NULL |lines|) (|shoeConsole| ")package not found")) - (T (APPEND (REVERSE |lines|) (CAR |b|))))))))) - -(DEFPARAMETER |$bStreamNil| (LIST '|nullstream|)) +(DEFCONSTANT |$bStreamNil| (LIST '|nullstream|)) (DEFUN |bStreamNull| (|x|) - (PROG (|st|) + (PROG (|st| |args| |op| |ISTMP#1|) (RETURN (COND ((OR (NULL |x|) (AND (CONSP |x|) (EQ (CAR |x|) '|nullstream|))) T) (T (LOOP (COND - ((NOT (AND (CONSP |x|) (EQ (CAR |x|) '|nonnullstream|))) + ((NOT (AND (CONSP |x|) (EQ (CAR |x|) '|nonnullstream|) + (PROGN + (SETQ |ISTMP#1| (CDR |x|)) + (AND (CONSP |ISTMP#1|) + (PROGN + (SETQ |op| (CAR |ISTMP#1|)) + (SETQ |args| (CDR |ISTMP#1|)) + T))))) (RETURN NIL)) (T (PROGN - (SETQ |st| (APPLY (CADR |x|) (CDDR |x|))) + (SETQ |st| (APPLY |op| |args|)) (RPLACA |x| (CAR |st|)) (RPLACD |x| (CDR |st|)))))) (AND (CONSP |x|) (EQ (CAR |x|) '|nullstream|))))))) @@ -143,28 +111,13 @@ (DEFUN |bMap1| (&REST |z|) (PROG (|x| |f|) - (DECLARE (SPECIAL |$bStreamNil|)) (RETURN (PROGN (SETQ |f| (CAR |z|)) (SETQ |x| (CADR |z|)) (COND ((|bStreamNull| |x|) |$bStreamNil|) - (T (CONS (FUNCALL |f| (CAR |x|)) (|bMap| |f| (CDR |x|))))))))) - -(DEFUN |shoeFileMap| (|f| |fn|) - (PROG (|a|) - (DECLARE (SPECIAL |$bStreamNil|)) - (RETURN - (PROGN - (SETQ |a| (|shoeInputFile| |fn|)) - (COND - ((NULL |a|) (|shoeConsole| (CONCAT |fn| " NOT FOUND")) - |$bStreamNil|) - (T (|shoeConsole| (CONCAT "READING " |fn|)) - (|shoeInclude| - (|bAddLineNumber| (|bMap| |f| (|bRgen| |a|)) - (|bIgen| 0))))))))) + (T (CONS (APPLY |f| (LIST (CAR |x|))) (|bMap| |f| (CDR |x|))))))))) (DEFUN |bDelay| (|f| |x|) (CONS '|nonnullstream| (CONS |f| |x|))) @@ -219,18 +172,10 @@ (T (CONS (CONS (CAR |f1|) (CAR |f2|)) (|bAddLineNumber| (CDR |f1|) (CDR |f2|))))))))) -(DEFUN |shoeFileInput| (|fn|) (|shoeFileMap| #'IDENTITY |fn|)) - (DEFUN |shoePrefixLisp| (|x|) (CONCAT ")lisp" |x|)) -(DEFUN |shoeLispFileInput| (|fn|) - (|shoeFileMap| #'|shoePrefixLisp| |fn|)) - (DEFUN |shoePrefixLine| (|x|) (CONCAT ")line" |x|)) -(DEFUN |shoeLineFileInput| (|fn|) - (|shoeFileMap| #'|shoePrefixLine| |fn|)) - (DEFUN |shoePrefix?| (|prefix| |whole|) (PROG (|good|) (RETURN @@ -259,8 +204,6 @@ (DEFUN |shoeEval?| (|s|) (|shoePrefix?| ")eval" |s|)) -(DEFUN |shoeInclude?| (|s|) (|shoePrefix?| ")include" |s|)) - (DEFUN |shoeFin?| (|s|) (|shoePrefix?| ")fin" |s|)) (DEFUN |shoeIf?| (|s|) (|shoePrefix?| ")if" |s|)) @@ -271,19 +214,10 @@ (DEFUN |shoeElseIf?| (|s|) (|shoePrefix?| ")elseif" |s|)) -(DEFUN |shoePackage?| (|s|) (|shoePrefix?| ")package" |s|)) - (DEFUN |shoeLisp?| (|s|) (|shoePrefix?| ")lisp" |s|)) -(DEFUN |shoeIncludeLisp?| (|s|) (|shoePrefix?| ")includelisp" |s|)) - (DEFUN |shoeLine?| (|s|) (|shoePrefix?| ")line" |s|)) -(DEFUN |shoeIncludeLines?| (|s|) (|shoePrefix?| ")includelines" |s|)) - -(DEFUN |shoeIncludeFunction?| (|s|) - (|shoePrefix?| ")includefunction" |s|)) - (DEFUN |shoeBiteOff| (|x|) (PROG (|n1| |n|) (RETURN @@ -321,22 +255,10 @@ ((NULL |c|) (LIST (CAR |a|) "")) (T (LIST (CAR |a|) |c|))))))))) -(DEFUN |shoeFunctionFileInput| (|bfVar#2|) - (PROG (|fn| |fun|) - (RETURN - (PROGN - (SETQ |fun| (CAR |bfVar#2|)) - (SETQ |fn| (CADR |bfVar#2|)) - (|shoeOpenInputFile| |a| |fn| - (|shoeInclude| - (|bAddLineNumber| (|shoeFindLines| |fn| |fun| |a|) - (|bIgen| 0)))))))) - (DEFUN |shoeInclude| (|s|) (|bDelay| #'|shoeInclude1| (LIST |s|))) (DEFUN |shoeInclude1| (|s|) (PROG (|command| |string| |t| |h|) - (DECLARE (SPECIAL |$bStreamNil|)) (RETURN (COND ((|bStreamNull| |s|) |s|) @@ -356,16 +278,7 @@ (COND ((|shoePlainLine?| |string|) (LIST |h|)) ((SETQ |command| (|shoeLisp?| |string|)) (LIST |h|)) - ((SETQ |command| (|shoeIncludeLisp?| |string|)) - (|shoeLispFileInput| (|shoeFileName| |command|))) - ((SETQ |command| (|shoeIncludeFunction?| |string|)) - (|shoeFunctionFileInput| (|shoeFnFileName| |command|))) ((SETQ |command| (|shoeLine?| |string|)) (LIST |h|)) - ((SETQ |command| (|shoeIncludeLines?| |string|)) - (|shoeLineFileInput| (|shoeFileName| |command|))) - ((SETQ |command| (|shoeInclude?| |string|)) - (|shoeFileInput| (|shoeFileName| |command|))) - ((SETQ |command| (|shoePackage?| |string|)) (LIST |h|)) ((SETQ |command| (|shoeSay?| |string|)) (|shoeConsole| |command|) NIL) ((SETQ |command| (|shoeEval?| |string|)) (STTOMC |command|) @@ -457,7 +370,6 @@ (|shoeConsole| "LINE IGNORED"))) (DEFUN |bPremStreamNil| (|h|) - (DECLARE (SPECIAL |$bStreamNil|)) (PROGN (|shoeConsole| (CONCAT "UNEXPECTED )fin IN LINE " (WRITE-TO-STRING (CDR |h|)))) diff --git a/src/boot/strap/scanner.clisp b/src/boot/strap/scanner.clisp index 2df8e320..36c8ef05 100644 --- a/src/boot/strap/scanner.clisp +++ b/src/boot/strap/scanner.clisp @@ -60,8 +60,8 @@ (T T))))))) (DEFUN |shoeLineToks| (|s|) - (PROG (|$linepos| |$floatok| |$sz| |$n| |$ln| |$r| |$f| |toks| |a| - |dq| |command|) + (PROG (|$linepos| |$floatok| |$sz| |$n| |$ln| |$r| |$f| |toks| |dq| + |command|) (DECLARE (SPECIAL |$floatok| |$f| |$sz| |$linepos| |$ln| |$r| |$n|)) (RETURN (PROGN @@ -85,13 +85,6 @@ (CONS (LIST |dq|) |$r|)) ((SETQ |command| (|shoeLisp?| |$ln|)) (|shoeLispToken| |$r| |command|)) - ((SETQ |command| (|shoePackage?| |$ln|)) - (SETQ |a| (CONCAT "(IN-PACKAGE " |command| ")")) - (SETQ |dq| - (|dqUnit| - (|shoeConstructToken| |$ln| |$linepos| - (|shoeLeafLisp| |a|) 0))) - (CONS (LIST |dq|) |$r|)) (T (|shoeLineToks| |$r|)))) (T (SETQ |toks| NIL) (LOOP diff --git a/src/boot/strap/tokens.clisp b/src/boot/strap/tokens.clisp index b33cbc0b..80875ca7 100644 --- a/src/boot/strap/tokens.clisp +++ b/src/boot/strap/tokens.clisp @@ -203,6 +203,7 @@ (LIST '|apply| 'APPLY) (LIST '|arrayRef| 'AREF) (LIST '|atom| 'ATOM) (LIST '|bitmask| 'SBIT) (LIST '|canonicalFilename| 'PROBE-FILE) + (LIST '|charByName| 'NAME-CHAR) (LIST '|charString| 'STRING) (LIST '|char?| 'CHARACTERP) (LIST '|codePoint| 'CHAR-CODE) (LIST '|cons?| 'CONSP) diff --git a/src/boot/strap/translator.clisp b/src/boot/strap/translator.clisp index 5800bc33..0968b9ea 100644 --- a/src/boot/strap/translator.clisp +++ b/src/boot/strap/translator.clisp @@ -1069,79 +1069,24 @@ |stream| |a|)))) (SETQ |bfVar#23| (CDR |bfVar#23|)))))))) -(DEFUN FBO (|name| |fn|) (|shoeGeneralFC| #'BO |name| |fn|)) - -(DEFUN FEV (|name| |fn|) - (|shoeGeneralFC| #'EVAL-BOOT-FILE |name| |fn|)) - -(DEFUN |shoeGeneralFC| (|f| |name| |fn|) - (PROG (|filename| |a| |infn|) - (DECLARE (SPECIAL |$GenVarCounter| |$bfClamming|)) - (RETURN - (PROGN - (SETQ |$bfClamming| NIL) - (SETQ |$GenVarCounter| 0) - (SETQ |infn| (|shoeAddbootIfNec| |fn|)) - (SETQ |a| - (|shoeOpenInputFile| |a| |infn| - (|shoeFindName2| |fn| |name| |a|))) - (SETQ |filename| - (COND - ((< 8 (LENGTH |name|)) (|subString| |name| 0 8)) - (T |name|))) - (COND (|a| (FUNCALL |f| (CONCAT "/tmp/" |filename|))) (T NIL)))))) - -(DEFUN |shoeFindName2| (|fn| |name| |a|) - (PROG (|filename| |lines|) - (RETURN - (PROGN - (SETQ |lines| (|shoeFindLines| |fn| |name| |a|)) - (COND - (|lines| (SETQ |filename| - (COND - ((< 8 (LENGTH |name|)) - (|subString| |name| 0 8)) - (T |name|))) - (SETQ |filename| - (CONCAT "/tmp/" |filename| ".boot")) - (|shoeOpenOutputFile| |stream| |filename| - (LET ((|bfVar#24| |lines|) (|line| NIL)) - (LOOP - (COND - ((OR (ATOM |bfVar#24|) - (PROGN - (SETQ |line| (CAR |bfVar#24|)) - NIL)) - (RETURN NIL)) - (T (|shoeFileLine| |line| |stream|))) - (SETQ |bfVar#24| (CDR |bfVar#24|))))) - T) - (T NIL)))))) - -(DEFUN |shoeTransform2| (|str|) - (|bNext| #'|shoeItem| - (|streamTake| 1 - (|bNext| #'|shoePileInsert| - (|bNext| #'|shoeLineToks| |str|))))) - (DEFUN |shoeItem| (|str|) (PROG (|dq|) (RETURN (PROGN (SETQ |dq| (CAR |str|)) - (CONS (LIST (LET ((|bfVar#26| NIL) - (|bfVar#25| (|shoeDQlines| |dq|)) + (CONS (LIST (LET ((|bfVar#25| NIL) + (|bfVar#24| (|shoeDQlines| |dq|)) (|line| NIL)) (LOOP (COND - ((OR (ATOM |bfVar#25|) + ((OR (ATOM |bfVar#24|) (PROGN - (SETQ |line| (CAR |bfVar#25|)) + (SETQ |line| (CAR |bfVar#24|)) NIL)) - (RETURN (NREVERSE |bfVar#26|))) - (T (SETQ |bfVar#26| - (CONS (CAR |line|) |bfVar#26|)))) - (SETQ |bfVar#25| (CDR |bfVar#25|))))) + (RETURN (NREVERSE |bfVar#25|))) + (T (SETQ |bfVar#25| + (CONS (CAR |line|) |bfVar#25|)))) + (SETQ |bfVar#24| (CDR |bfVar#24|))))) (CDR |str|)))))) (DEFUN |stripm| (|x| |pk| |bt|) @@ -1177,23 +1122,6 @@ (COMPILE |name| (CONS 'LAMBDA (CONS |bv| |body|)))) (T (EVAL |fn|))))))) -(DEFUN FC (|name| |fn|) - (PROG (|infn|) - (DECLARE (SPECIAL |$GenVarCounter|)) - (RETURN - (PROGN - (SETQ |$GenVarCounter| 0) - (SETQ |infn| (|shoeAddbootIfNec| |fn|)) - (|shoeOpenInputFile| |a| |infn| - (|shoeFindName| |fn| |name| |a|)))))) - -(DEFUN |shoeFindName| (|fn| |name| |a|) - (PROG (|lines|) - (RETURN - (PROGN - (SETQ |lines| (|shoeFindLines| |fn| |name| |a|)) - (|shoePCompileTrees| (|shoeTransformString| |lines|)))))) - (DEFUN |shoePCompileTrees| (|s|) (LOOP (COND diff --git a/src/boot/tokens.boot b/src/boot/tokens.boot index af6f83a8..671439c5 100644 --- a/src/boot/tokens.boot +++ b/src/boot/tokens.boot @@ -249,6 +249,7 @@ for i in [ _ ["atom", "ATOM"] , _ ["bitmask", "SBIT"] , _ ["canonicalFilename", "PROBE-FILE"], _ + ["charByName", "NAME-CHAR"] , _ ["charString", "STRING"] , _ ["char?", "CHARACTERP"] , _ ["codePoint", "CHAR-CODE"], _ diff --git a/src/boot/translator.boot b/src/boot/translator.boot index b071fd0a..4b803b0c 100644 --- a/src/boot/translator.boot +++ b/src/boot/translator.boot @@ -620,36 +620,6 @@ shoeXReport stream== a := strconc(PNAME i,'" is used in ") bootOutLines( SSORT GETHASH(i,$bootUsed),stream,a) -FBO (name,fn)== - shoeGeneralFC(function BO,name,fn) - -FEV(name,fn)== - shoeGeneralFC(function EVAL_-BOOT_-FILE,name,fn) - -shoeGeneralFC(f,name,fn)== - $bfClamming :=false - $GenVarCounter := 0 - infn:=shoeAddbootIfNec fn - a:= shoeOpenInputFile(a,infn,shoeFindName2(fn,name, a)) - filename:= if # name > 8 then subString(name,0,8) else name - a => FUNCALL(f, strconc('"/tmp/",filename)) - nil - -shoeFindName2(fn,name,a)== - lines:=shoeFindLines(fn,name,a) - lines => - filename:= if # name > 8 then subString(name,0,8) else name - filename := strconc('"/tmp/",filename,'".boot") - shoeOpenOutputFile(stream, filename, - for line in lines repeat shoeFileLine (line,stream)) - true - false - -shoeTransform2 str== - bNext(function shoeItem, - streamTake(1, bNext(function shoePileInsert, - bNext(function shoeLineToks, str)))) - shoeItem (str)== dq:=first str [[[first line for line in shoeDQlines dq]],:rest str] @@ -668,15 +638,6 @@ shoePCompile fn== COMPILE (name,['LAMBDA,bv,:body]) EVAL fn -FC(name,fn)== - $GenVarCounter := 0 - infn:=shoeAddbootIfNec fn - shoeOpenInputFile(a,infn,shoeFindName(fn,name, a)) - -shoeFindName(fn,name,a)== - lines:=shoeFindLines(fn,name,a) - shoePCompileTrees shoeTransformString lines - shoePCompileTrees s== while not bStreamNull s repeat REALLYPRETTYPRINT shoePCompile first s diff --git a/src/interp/scan.boot b/src/interp/scan.boot index e3110d2f..a1a25fb1 100644 --- a/src/interp/scan.boot +++ b/src/interp/scan.boot @@ -279,7 +279,7 @@ lineoftoks(s)== [[[b,s]],:$r] while $n<$sz repeat toks := dqAppend(toks,scanToken()) - null toks => [[],:$r] + null toks => [nil,:$r] [[[toks,s]],:$r] @@ -312,7 +312,6 @@ scanToken() == -- to pair badge and badgee --- lfid x== ["id",makeSymbol x] lfid x == ["id",makeSymbol(x, '"BOOT")] @@ -320,12 +319,7 @@ lfkey x == ["key",keyword x] lfinteger x== - ["integer",x] --- if x = '"0" --- then ["id",makeSymbol x] --- else if x = '"1" --- then ["id",makeSymbol x] --- else ["integer",x] + ["integer",x] lfrinteger (r,x)== ["integer",strconc (r,strconc('"r",x))] @@ -352,15 +346,14 @@ lfspaces x == ["spaces",x] constoken(ln,lp,b,n)== --- [b.0,b.1,[lp,:n]] a := [b.0,:b.1] ncPutQ(a,"posn",[lp,:n]) a scanEscape()== $n := $n+1 - a := scanEsc() - if a then scanWord true else nil + scanEsc() => scanWord true + nil scanEsc()== $n >= $sz => @@ -379,7 +372,7 @@ scanEsc()== false $n = n1 => true stringChar($ln,n1) = char "__" => - $n:=n1+1 + $n := n1+1 scanEsc() false $n := n1 @@ -432,7 +425,7 @@ scanKeyTr w== lfkey w scanPossFloat (w)== - $n>=$sz or not digit? $ln.$n => lfkey w + $n >= $sz or not digit? $ln.$n => lfkey w w := spleI(function digit?) scanExponent('"0",w) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 36c0b022..f82c32a5 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294709 . 3508975271) +(2294563 . 3509581009) (-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 @@ -56,7 +56,7 @@ 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 `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1613) +(-32 R -4008) ((|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 -1070) (QUOTE (-560))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -1613 UP UPUP -4440) +(-40 -4008 UP UPUP -2661) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2210 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2210 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -1613) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2263 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2263 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2263 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2263 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2263 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2263 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -4008) ((|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}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'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 (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-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."))) ((-4510 . T) (-4511 . 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-3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|))))))) +((-2263 (-12 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#2|))))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-872))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1613) +(-54 |Base| R -4008) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -171,64 +171,64 @@ NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray's."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -3971) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -3754) ((|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 -(-62 -3971) +(-62 -3754) ((|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 -(-63 -3971) +(-63 -3754) ((|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 -(-64 -3971) +(-64 -3754) ((|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 -(-65 -3971) +(-65 -3754) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3971) +(-66 -3754) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -3971) +(-67 -3754) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -3971) +(-68 -3754) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3971) +(-69 -3754) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -3971) +(-70 -3754) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -3971) +(-71 -3754) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -3971) +(-72 -3754) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -3971) +(-73 -3754) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -3971) +(-74 -3754) ((|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 -(-75 -3971) +(-75 -3754) ((|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 @@ -240,51 +240,51 @@ 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 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 -(-78 -3971) +(-78 -3754) ((|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 -(-79 -3971) +(-79 -3754) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3971) +(-80 -3754) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3971) +(-81 -3754) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -3971) +(-82 -3754) ((|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 -(-83 -3971) +(-83 -3754) ((|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 -(-84 -3971) +(-84 -3754) ((|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 -(-85 -3971) +(-85 -3754) ((|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 -(-86 -3971) +(-86 -3754) ((|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 -(-87 -3971) +(-87 -3754) ((|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 -3971) +(-88 -3754) ((|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 -(-89 -3971) +(-89 -3754) ((|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 @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2210 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2263 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -396,7 +396,7 @@ NIL ((|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 [\\spad{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 NIL -(-117 -1613 UP) +(-117 -4008 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 @@ -407,7 +407,7 @@ NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of 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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-2210 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-940))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1052))) (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872))) (-2263 (|HasCategory| (-118 |#1|) (QUOTE (-844))) (|HasCategory| (-118 |#1|) (QUOTE (-872)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1184))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-940)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 @@ -423,7 +423,7 @@ NIL (-123 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"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -443,11 +443,11 @@ NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL @@ -455,7 +455,7 @@ NIL (-131) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2210 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-2210 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-2263 (-12 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2263 (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-130) (QUOTE (-872))) (-2263 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1133))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -476,11 +476,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4512 "*") . T)) NIL -(-137 |minix| -3048 R) +(-137 |minix| -3496 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -3048 S T$) +(-138 |minix| -3496 S T$) ((|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 @@ -503,7 +503,7 @@ NIL (-143) ((|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}."))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-2210 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2263 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-144 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4507 . T)) NIL -(-150 -1613 UP UPUP) +(-150 -4008 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 @@ -568,7 +568,7 @@ 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 -(-160 R -1613) +(-160 R -4008) ((|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})/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.} 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.} 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.} n!/(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 @@ -602,7 +602,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasAttribute| |#2| (QUOTE -4509)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-168 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4503 -2210 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2958 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4503 -2263 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2827 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-169 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4503 -2210 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940)))) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4509 |has| |#1| (-6 -4509)) (-2958 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . 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T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2263 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-940)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-940))))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-1235))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2263 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4509)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-363))))) (-172 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -1613) +(-191 R -4008) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -1613 UP UPUP R) +(-219 -4008 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 -(-220 -1613 FP) +(-220 -4008 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 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 (-221) ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2210 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2263 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -1613) +(-223 R -4008) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |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}."))) ((-4507 . T)) NIL -(-228 R -1613) +(-228 R -4008) ((|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 (-229) ((|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}."))) -((-2947 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2815 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-230) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -855,7 +855,7 @@ NIL (-231 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}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 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 @@ -904,19 +904,19 @@ NIL ((|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 -(-244 S -3048 R) +(-244 S -3496 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-817))) (|HasCategory| |#3| (QUOTE (-872))) (|HasAttribute| |#3| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasCategory| |#3| (QUOTE (-1133)))) -(-245 -3048 R) +(-245 -3496 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . T)) NIL -(-246 -3048 R) +(-246 -3496 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."))) ((-4504 |has| |#2| (-1081)) (-4505 |has| |#2| (-1081)) (-4507 |has| |#2| (-6 -4507)) (-4510 . 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The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL @@ -939,7 +939,7 @@ NIL (-252 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-253 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -951,7 +951,7 @@ NIL (-255 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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T)) -((|HasCategory| |#2| (QUOTE (-940))) (-2210 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2210 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-2263 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2263 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-256) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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} := 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 @@ -1031,7 +1031,7 @@ NIL (-275 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"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1076,11 +1076,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1'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 -(-287 R -1613) +(-287 R -4008) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -1613) +(-288 R -4008) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1132,7 +1132,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-301 S R |Mod| -3734 -3752 |exactQuo|) +(-301 S R |Mod| -4102 -4285 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4507 -2210 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4504 |has| |#1| (-1081)) (-4505 |has| |#1| (-1081))) -((|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2210 (|HasCategory| |#1| (|%list| 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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1144)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2263 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2263 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-748)))) (-306 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL @@ -1159,7 +1159,7 @@ NIL (-307 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#2|)))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102)))) (-308) ((|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 @@ -1172,11 +1172,11 @@ NIL ((|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -1613 S) +(-311 -4008 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -1613) +(-312 E -4008) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -(-322 -1613) +(-322 -4008) ((|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 @@ -1231,11 +1231,11 @@ NIL (-325 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))}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872))) (-2210 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-844))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-872)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-1184))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-1286 |#1| |#2| |#3| 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(|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-940))) (|HasCategory| $ (QUOTE (-147)))) (-2263 (|HasCategory| (-1286 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 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(|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."))) -((-4507 -2210 (-12 (|has| |#1| (-571)) (-2210 (|has| |#1| (-1081)) (|has| |#1| (-487)))) (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) -((-2210 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE 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(|HasCategory| |#1| (QUOTE (-1081)))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-21)))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144)))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (QUOTE (-25)))) (-2263 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1081)))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1081))) (|HasCategory| $ (|%list| (QUOTE -1070) (QUOTE (-560))))) (-327 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 @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -1613) +(-329 R -4008) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1255,7 +1255,7 @@ NIL (-331 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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3463) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4173) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3490) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2787) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-332 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},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1287,12 +1287,12 @@ NIL (-339 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."))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1613) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -4008) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -1613) +(-341 -4008) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -1613 UP UPUP R) +(-346 -4008 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}'s are integers and the \\spad{P}'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 @@ -1320,11 +1320,11 @@ 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 -(-348 S -1613 UP UPUP R) +(-348 S -4008 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}'s are integers and the \\spad{P}'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 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 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 -(-349 -1613 UP UPUP R) +(-349 -4008 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}'s are integers and the \\spad{P}'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 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 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 @@ -1343,12 +1343,12 @@ NIL (-353 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) -(-354 S -1613 UP UPUP) +((-2263 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +(-354 S -4008 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 \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -1613 UP UPUP) +(-355 -4008 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 \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -1359,15 +1359,15 @@ NIL (-357 |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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-2263 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2263 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2263 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(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 @@ -1384,42 +1384,42 @@ NIL ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-364 R UP -1613) +(-364 R UP -4008) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-365 |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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) +((-2263 (|HasCategory| (-936 |#1|) (QUOTE (-147))) (|HasCategory| (-936 |#1|) (QUOTE (-381)))) (|HasCategory| (-936 |#1|) (QUOTE (-149))) (|HasCategory| (-936 |#1|) (QUOTE (-381))) (|HasCategory| (-936 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2263 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2263 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2263 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(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(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(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(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(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(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 -(-370 -1613 GF) +(-370 -4008 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}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 -(-371 -1613 FP FPP) +(-371 -4008 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2263 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 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{ls}."))) NIL @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4493 . T) (-4501 . T) (-2947 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-4493 . T) (-4501 . T) (-2815 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-392 |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 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}."))) @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-406 -1613 UP UPUP R) +(-406 -4008 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 @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-412 -3971 |returnType| -4143 |symbols|) +(-412 -3754 |returnType| -3498 |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 -(-413 -1613 UP) +(-413 -4008 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4493)) (|HasAttribute| |#1| (QUOTE -4501))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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'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'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\"."))) -((-2947 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2815 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-419 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 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."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1254))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1254)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL @@ -1615,7 +1615,7 @@ NIL (-421 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4497 -12 (|has| |#1| (-6 -4508)) (|has| |#1| (-466)) (|has| |#1| (-6 -4497))) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-872)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1636,7 +1636,7 @@ NIL ((|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't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -1613 UP A) +(-427 R -4008 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)}."))) ((-4507 . T)) NIL @@ -1644,7 +1644,7 @@ 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 -(-429 R -1613 UP A |ibasis|) +(-429 R -4008 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 -1070) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-435 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo'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|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4507 -2210 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) +((-4507 -2263 (|has| |#1| (-1081)) (|has| |#1| (-487))) (-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) ((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-571)) (-4502 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -1613) +(-442 R -4008) ((|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 @@ -1704,19 +1704,19 @@ NIL ((|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"))) ((-4497 -12 (|has| |#1| (-6 -4497)) (|has| |#2| (-6 -4497))) (-4504 . T) (-4505 . T) (-4507 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#2| (QUOTE -4497)))) -(-444 R -1613) +(-444 R -4008) ((|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 -(-445 R -1613) +(-445 R -4008) ((|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 -(-446 R -1613) +(-446 R -4008) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-447 R -1613) +(-447 R -4008) ((|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 @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-449 R -1613 UP) +(-449 R -4008 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 -1070) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein'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'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 -(-457 R UP -1613) +(-457 R UP -4008) ((|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 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'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'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's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri'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 @@ -1803,7 +1803,7 @@ NIL (-468 |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"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-2210 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2210 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-2263 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2263 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 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's conditional."))) NIL @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\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 -(-485 |lv| -1613 R) +(-485 |lv| -4008 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 @@ -1883,11 +1883,11 @@ NIL (-488 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") 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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)}"))) ((-4511 . T) (-4510 . T)) @@ -1903,7 +1903,7 @@ NIL (-493 |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."))) ((-4510 . T) (-4511 . 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Hall as given in Serre's book Lie Groups -- 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{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 @@ -1911,11 +1911,11 @@ NIL (-495 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-2263 (|HasCategory| |#2| (QUOTE (-1081))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1133)))) (|HasAttribute| |#2| (QUOTE -4507)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1081)))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-497) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1923,8 +1923,8 @@ NIL (-498 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -1613 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -4008 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}'s are integers and the \\spad{P}'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 @@ -1935,7 +1935,7 @@ NIL (-501) ((|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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2210 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2263 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -1613 UP |AlExt| |AlPol|) +(-508 -4008 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP'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 @@ -1971,16 +1971,16 @@ NIL (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-511 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'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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 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 -(-513 R UP -1613) +(-513 R UP -4008) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the 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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -1613 |Expon| |VarSet| |DPoly|) +(-518 -4008 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1209))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|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 @@ -2059,15 +2059,15 @@ NIL (-532 |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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((-2210 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-2263 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 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."))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-535 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,{} m*h and 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 @@ -2079,7 +2079,7 @@ NIL (-537 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|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 @@ -2112,7 +2112,7 @@ 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 ((-12 (|HasCategory| (-793) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133))))) -(-546 K -1613 |Par|) +(-546 K -4008 |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 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 @@ -2136,7 +2136,7 @@ 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 -(-552 K -1613 |Par|) +(-552 K -4008 |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 @@ -2191,12 +2191,12 @@ NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102)))) -(-566 R -1613) +((-12 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#2|)))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102)))) +(-566 R -4008) ((|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 -(-567 R0 -1613 UP UPUP R) +(-567 R0 -4008 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 @@ -2206,7 +2206,7 @@ NIL NIL (-569 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{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2947 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2815 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-570 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."))) @@ -2216,7 +2216,7 @@ NIL ((|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."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-572 R -1613) +(-572 R -4008) ((|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},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2228,7 +2228,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-575 R -1613 L) +(-575 R -4008 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-577 -1613 UP UPUP R) +(-577 -4008 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 -(-578 -1613 UP) +(-578 -4008 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 @@ -2248,15 +2248,15 @@ NIL ((|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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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 -(-580 R -1613 L) +(-580 R -4008 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -1613) +(-581 R -4008) ((|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 -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -1613 UP) +(-582 -4008 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2264,27 +2264,27 @@ 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 -(-584 -1613) +(-584 -4008) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-585 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."))) -((-2947 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2815 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-586) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-587 R -1613) +(-587 R -4008) ((|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 -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -1613 UP) +(-588 -4008 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -1613) +(-589 R -4008) ((|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 @@ -2316,15 +2316,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-597 -1613) +(-597 -4008) ((|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 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}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-1209))))) -(-598 E -1613) +(-598 E -4008) ((|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 -(-599 R -1613) +(-599 R -4008) ((|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},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2359,7 +2359,7 @@ NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2210 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2210 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2263 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2263 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2263 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-608 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 @@ -2367,7 +2367,7 @@ NIL (-609 |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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4173) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) (((-4512 "*") |has| |#1| (-571)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -2384,7 +2384,7 @@ 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 -(-614 R -1613 FG) +(-614 R -4008 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2395,7 +2395,7 @@ NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-617 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4507 -2210 (-1384 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-2210 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -2263 (-2445 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-2263 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 |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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-102)))) (-628 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 @@ -2464,7 +2464,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -1613 UP) +(-634 -4008 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2492,7 +2492,7 @@ NIL ((|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."))) ((-4507 . T)) NIL -(-641 R -1613) +(-641 R -4008) ((|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 @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{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{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(lp,{} norm?)} decomposes the variety associated with \\axiom{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{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(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{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(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-648 R -1613) +(-648 R -4008) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2528,18 +2528,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-650 |lv| -1613) +(-650 |lv| -4008) ((|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 (-651) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -2715) (QUOTE (-51))))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -1871) (QUOTE (-51))))))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1191) (QUOTE (-872))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (QUOTE (-1133)))) (-652 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)."))) -((-4507 -2210 (-1384 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) -((-2210 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4507 -2263 (-2445 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4505 . T) (-4504 . T)) +((-2263 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 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{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 @@ -2563,7 +2563,7 @@ NIL (-658 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}'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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1373 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-2433 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) ((-4505 . T) (-4504 . T)) @@ -2583,7 +2583,7 @@ NIL (-663 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-664 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 @@ -2607,7 +2607,7 @@ NIL (-669 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL @@ -2628,11 +2628,11 @@ NIL ((|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}."))) ((-4505 . T) (-4504 . T)) ((|HasCategory| |#1| (QUOTE (-814)))) -(-675 R -1613 L) +(-675 R -4008 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 -(-676 A -3307) +(-676 A -1406) ((|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}}"))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ NIL ((|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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-681 -1613 UP) +(-681 -4008 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)))) @@ -2684,11 +2684,11 @@ NIL ((|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}."))) ((-4511 . T) (-4510 . T)) NIL -(-689 -1613 |Row| |Col| M) +(-689 -4008 |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 -(-690 -1613) +(-690 -4008) ((|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'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 @@ -2699,7 +2699,7 @@ NIL (-692 |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."))) ((-4507 . T) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2210 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2263 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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 -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2775,7 +2775,7 @@ NIL (-711 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."))) ((-4510 . T) (-4511 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4512 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-712 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{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 @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-714 S -1613 FLAF FLAS) +(-714 S -4008 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,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{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}."))) 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T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) +((-2815 . T) (-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-722 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."))) @@ -2840,7 +2840,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) 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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4505 |has| |#1| (-175)) (-4504 |has| |#1| (-175)) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -3734 -3752 |exactQuo|) +(-737 R |Mod| -4102 -4285 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4507 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4505 . T) (-4504 . T)) NIL -(-740 -1613) +(-740 -4008) ((|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]]}."))) ((-4507 . T)) NIL @@ -2924,7 +2924,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-749 -1613 UP) +(-749 -4008 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 @@ -2943,7 +2943,7 @@ NIL (-753 |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."))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (-2210 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2210 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (-2263 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2263 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-889 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 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 @@ -3076,11 +3076,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-787 -1613) +(-787 -4008) ((|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 -(-788 P -1613) +(-788 P -4008) ((|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''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -1613) +(-790 UP -4008) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3104,7 +3104,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4512 "*") . T)) NIL -(-794 R -1613) +(-794 R -4008) ((|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 @@ -3124,7 +3124,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}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},{}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 -(-799 -1613 |ExtF| |SUEx| |ExtP| |n|) +(-799 -4008 |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 @@ -3139,11 +3139,11 @@ NIL (-802 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . 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(|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-804 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3219,8 +3219,8 @@ NIL (-822 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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2210 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-823 -2210 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2263 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2263 (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1028 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-823 -2263 R OS S) ((|constructor| (NIL "\\spad{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 @@ -3228,11 +3228,11 @@ NIL ((|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 -(-825 R -1613 L) +(-825 R -4008 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-826 R -1613) +(-826 R -4008) ((|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 @@ -3240,7 +3240,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE'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 -(-828 R -1613) +(-828 R -4008) ((|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 @@ -3248,11 +3248,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE'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'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'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'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'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'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'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's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-830 -1613 UP UPUP R) +(-830 -4008 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 -(-831 -1613 UP L LQ) +(-831 -4008 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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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 @@ -3260,38 +3260,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|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 -(-833 -1613 UP L LQ) +(-833 -4008 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of 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 {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-834 -1613 UP) +(-834 -4008 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}'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}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-835 -1613 L UP A LO) +(-835 -4008 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 -(-836 -1613 UP) +(-836 -4008 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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-837 -1613 LO) +(-837 -4008 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 -(-838 -1613 LODO) +(-838 -4008 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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(|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) (-840 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"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-842 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-841 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4512 "*") |has| |#2| (-376)) (-4503 |has| |#2| (-376)) (-4508 |has| |#2| (-376)) (-4502 |has| |#2| (-376)) (-4507 . T) (-4505 . T) (-4504 . T)) @@ -3355,7 +3355,7 @@ NIL (-856 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."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2210 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2210 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2263 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2263 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-857 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 @@ -3395,7 +3395,7 @@ NIL (-866 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4507 |has| |#1| (-871))) -((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2210 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2210 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-21))) (-2263 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2263 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-867 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3404,7 +3404,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-869 -3048 S) +(-869 -3496 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 @@ -3444,11 +3444,11 @@ NIL ((|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{\\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{\\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{\\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{\\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 (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-879 R |sigma| -3732) +(-879 R |sigma| -4336) ((|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."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-880 |x| R |sigma| -3732) +(-880 |x| R |sigma| -4336) ((|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}."))) ((-4504 . T) (-4505 . T) (-4507 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3515,15 +3515,15 @@ NIL (-896 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-2210 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) +((|HasCategory| (-894 |#1|) (QUOTE (-940))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-894 |#1|) (QUOTE (-1052))) (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872))) (-2263 (|HasCategory| (-894 |#1|) (QUOTE (-844))) (|HasCategory| (-894 |#1|) (QUOTE (-872)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-1184))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -528) (QUOTE (-1209)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -894) (|devaluate| |#1|)) (|%list| (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-940)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))))) (-897 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of 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)}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-2210 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872))) (-2263 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-872)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-898 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))))) (-899) ((|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'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's lowest value."))) NIL @@ -3583,7 +3583,7 @@ NIL (-913 |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 (-1373 (|HasCategory| |#2| (QUOTE (-1081)))) (-1373 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-1373 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) +((-12 (-2433 (|HasCategory| |#2| (QUOTE (-1081)))) (-2433 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (-12 (|HasCategory| |#2| (QUOTE (-1081))) (-2433 (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-1209))))) (-914 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'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},{}\\spad{e1}),{}...,{}(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 @@ -3596,7 +3596,7 @@ NIL ((|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 pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and 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 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 '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 -(-917 R -4349) +(-917 R -1527) ((|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 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 @@ -3624,7 +3624,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-924 UP -1613) +(-924 UP -4008) ((|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 @@ -3655,11 +3655,11 @@ NIL (-931 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-932 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4507 . T)) -((-2210 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) +((-2263 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-872)))) (-933 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 @@ -3692,7 +3692,7 @@ NIL ((|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| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} 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}."))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-941 R0 -1613 UP UPUP R) +(-941 R0 -4008 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 @@ -3720,7 +3720,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik'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's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik'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's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-948 -1613) +(-948 -4008) ((|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 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 @@ -3736,11 +3736,11 @@ NIL ((|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| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} 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)}"))) ((-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL -(-952 |xx| -1613) +(-952 |xx| -4008) ((|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 -(-953 -1613 P) +(-953 -4008 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3768,7 +3768,7 @@ NIL ((|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 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-960 R -1613) +(-960 R -4008) ((|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 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3776,7 +3776,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-962 S R -1613) +(-962 S R -4008) ((|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 @@ -3796,11 +3796,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -912) (|devaluate| |#1|)))) -(-967 -4349) +(-967 -1527) ((|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 fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-968 R -1613 -4349) +(-968 R -4008 -1527) ((|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 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 @@ -3823,7 +3823,7 @@ NIL (-973 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-974 |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 @@ -3835,7 +3835,7 @@ NIL (-976 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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1209) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-977 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 @@ -3852,7 +3852,7 @@ NIL ((|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 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 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 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 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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) NIL -(-981 E V R P -1613) +(-981 E V R P -4008) ((|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},{}...,{}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 @@ -3860,7 +3860,7 @@ NIL ((|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 -(-983 E V R P -1613) +(-983 E V R P -4008) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3875,7 +3875,7 @@ NIL (-986 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4508))) (-987 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 @@ -3883,7 +3883,7 @@ NIL (-988 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-989 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 @@ -3892,7 +3892,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-991 -1613) +(-991 -4008) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3907,7 +3907,7 @@ NIL (-994 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"))) ((-4507 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-817))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-872))))) (-995) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3996,7 +3996,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1017 K R UP -1613) +(-1017 K R UP -4008) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -4043,7 +4043,7 @@ NIL (-1028 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.}"))) ((-4503 |has| |#1| (-302)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2263 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1209)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-559)))) (-1029 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4059,7 +4059,7 @@ NIL (-1032 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1033 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4068,14 +4068,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1035 -1613 UP UPUP |radicnd| |n|) +(-1035 -4008 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4503 |has| (-421 |#2|) (-376)) (-4508 |has| (-421 |#2|) (-376)) (-4502 |has| (-421 |#2|) (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2210 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2210 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2210 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2263 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2263 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2263 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2263 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2263 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2263 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (-1036 |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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2210 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-940))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1052))) (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872))) (-2263 (|HasCategory| (-560) (QUOTE (-844))) (|HasCategory| (-560) (QUOTE (-872)))) (|HasCategory| (-560) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1184))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1209)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-940)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1037) ((|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 @@ -4108,19 +4108,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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}}"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) NIL -(-1045 R -1613) +(-1045 R -4008) ((|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 -(-1046 R -1613) +(-1046 R -4008) ((|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 -(-1047 -1613 UP) +(-1047 -4008 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 -(-1048 -1613 UP) +(-1048 -4008 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 @@ -4155,8 +4155,8 @@ NIL (-1056 |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"))) ((-4503 . T) (-4508 . T) (-4502 . T) (-4505 . T) (-4504 . T) ((-4512 "*") . T) (-4507 . T)) -((-2210 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) -(-1057 -1613 L) +((-2263 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1070) (QUOTE (-560))))) +(-1057 -4008 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4192,14 +4192,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1066 -1613 |Expon| |VarSet| |FPol| |LFPol|) +(-1066 -4008 |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"))) (((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-1067) ((|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.}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -2715) (QUOTE (-51))))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (QUOTE (-1209))) (|%list| (QUOTE |:|) (QUOTE -1871) (QUOTE (-51))))))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1133))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-1133))) (|HasCategory| (-1209) (QUOTE (-872))) (|HasCategory| (-51) (QUOTE (-1133))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888))))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (QUOTE (-102)))) (-1068) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4256,7 +4256,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4507 . T)) NIL -(-1082 |xx| -1613) +(-1082 |xx| -4008) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4275,7 +4275,7 @@ NIL (-1086 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4510 . T) (-4505 . T) (-4504 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-2210 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) +((|HasCategory| |#3| (QUOTE (-175))) (-2263 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-888))))) (-1087 |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 @@ -4293,11 +4293,11 @@ NIL NIL ((|HasCategory| |#1| (QUOTE (-1133)))) (-1091 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) +((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL (-1092) -((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) +((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL (-1093 |TheField| |ThePolDom|) @@ -4311,7 +4311,7 @@ NIL (-1095) ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4510 . T) (-4511 . 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When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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 @@ -4356,7 +4356,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1107 |Base| R -1613) +(-1107 |Base| R -4008) ((|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},{}...,{}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 @@ -4364,7 +4364,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1109 |Base| R -1613) +(-1109 |Base| R -4008) ((|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 @@ -4375,7 +4375,7 @@ NIL (-1111 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."))) ((-4503 |has| |#1| (-376)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (-1112 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 @@ -4407,7 +4407,7 @@ NIL (-1119 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"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1120 (-1209)) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1120 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 @@ -4447,7 +4447,7 @@ NIL (-1129 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)}}"))) ((-4510 . T) (-4500 . T) (-4511 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1130 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 @@ -4511,7 +4511,7 @@ NIL (-1145 |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 \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1133))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1146 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 @@ -4524,7 +4524,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1149 R -1613) +(-1149 R -4008) ((|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 @@ -4559,16 +4559,16 @@ NIL (-1157 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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-940))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2210 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-940))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1158 |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 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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1159 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}"))) ((-4511 . T) (-4510 . T)) NIL -(-1160 UP -1613) +(-1160 UP -4008) ((|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 @@ -4623,11 +4623,11 @@ NIL (-1173 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in 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},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-2210 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-2210 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))) (-2263 (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133)))) (-2263 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1172) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-1133))))) (|HasCategory| (-1172 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-1172 |#1| |#2|) (QUOTE (-102)))) (-1174 |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}."))) ((-4507 . T) (-4499 |has| |#2| (-6 (-4512 "*"))) (-4510 . T) (-4504 . T) (-4505 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2210 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-2210 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1070) (QUOTE (-560)))) (-2263 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-376))) (-2263 (|HasAttribute| |#2| (QUOTE (-4512 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1175 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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4651,7 +4651,7 @@ NIL (-1180 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1181 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 @@ -4663,7 +4663,7 @@ NIL (-1183 |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."))) ((-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133)))) +((-12 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#2|)))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133)))) (-1184) ((|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}'s are never \\spad{nothing}.}")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4679,7 +4679,7 @@ NIL (-1187 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4511 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1188 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 @@ -4695,11 +4695,11 @@ NIL (-1191) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2210 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2210 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2263 (-12 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2263 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-146) (QUOTE (-872))) (-2263 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1133))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-1192 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#1|)))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (QUOTE (-1191))) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#1|)))))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-1133))) (|HasCategory| (-1191) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2263 (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (QUOTE (-102)))) (-1193 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 should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by 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 b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4730,9 +4730,9 @@ NIL NIL (-1200 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-147))))) +(-1201 R -4008) ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4743,7 +4743,7 @@ NIL (-1203 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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(-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1184))) (|HasCategory| |#1| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-940)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1204 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4755,11 +4755,11 @@ NIL (-1206 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . 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We may integrate a series when we can divide coefficients by integers.")) (|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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3463) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4173) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3490) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2787) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1208) ((|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 @@ -4775,7 +4775,7 @@ NIL (-1211 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-6 -4508)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2210 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2263 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1003) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4508))) (-1212) ((|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 @@ -4815,7 +4815,7 @@ NIL (-1221 |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}"))) ((-4510 . T) (-4511 . T)) -((-12 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3837) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2210 (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -1651) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -1871) (|devaluate| |#2|)))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1133)))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1133))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888))))) (-2263 (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (QUOTE (-102)))) (-1222 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 @@ -4875,7 +4875,7 @@ NIL (-1236 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4511 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1133))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1237 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4884,7 +4884,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1239 R -1613) +(-1239 R -4008) ((|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 @@ -4892,14 +4892,14 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1241 R -1613) +(-1241 R -4008) ((|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 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 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 -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -912) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (|devaluate| |#1|))))) (-1242 |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}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1243 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} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}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|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(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{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(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{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(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{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},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}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{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{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},{}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{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},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}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{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}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{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{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 @@ -4920,7 +4920,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) -(-1248 -1613) +(-1248 -4008) ((|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 @@ -4966,8 +4966,8 @@ NIL NIL (-1259 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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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 @@ -5003,7 +5003,7 @@ NIL (-1268 |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}"))) (((-4512 "*") |has| |#2| (-175)) (-4503 |has| |#2| (-571)) (-4506 |has| |#2| (-376)) (-4508 |has| |#2| (-6 -4508)) (-4505 . T) (-4504 . T) (-4507 . T)) -((|HasCategory| |#2| (QUOTE (-940))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2210 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-391))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -912) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -912) (QUOTE (-560))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -916) (QUOTE (-560)))))) (-12 (|HasCategory| (-1114) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| 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(-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1184))) (|HasCategory| |#2| (|%list| (QUOTE -930) (QUOTE (-1209)))) (|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (-2263 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-940)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1269 |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 @@ -5039,7 +5039,7 @@ NIL (-1277 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{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) +((|HasCategory| |#2| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1144))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4173) (|%list| (|devaluate| |#2|) (QUOTE (-1209)))))) (-1278 |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{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5051,7 +5051,7 @@ NIL (-1280 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3463) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4173) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3490) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2787) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1281 |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 @@ -5071,11 +5071,11 @@ NIL (-1285 |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)}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4508 |has| |#1| (-376)) (-4502 |has| |#1| (-376)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2210 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3463) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1144))) (|HasCategory| |#1| (QUOTE (-376))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2263 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -4173) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3490) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2787) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1286 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))}."))) (((-4512 "*") |has| (-1280 |#2| |#3| |#4|) (-175)) (-4503 |has| (-1280 |#2| |#3| |#4|) (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-2210 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-175))) (-2263 (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1280 |#2| |#3| |#4|) (|%list| (QUOTE -1070) (QUOTE (-560)))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1280 |#2| |#3| |#4|) (QUOTE (-571)))) (-1287 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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5087,7 +5087,7 @@ NIL (-1289 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2210 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2590) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2210 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3463) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2263 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -928) (QUOTE (-1209)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1144))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -4173) (|%list| (|devaluate| |#1|) (QUOTE (-1209)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2263 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-990))) (|HasCategory| |#1| (QUOTE (-1235)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3490) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1209))))) (|HasSignature| |#1| (|%list| (QUOTE -2787) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#1|))))))) (-1290 |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 @@ -5095,7 +5095,7 @@ NIL (-1291 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 (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -3589) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3463) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-990))) (|HasCategory| |#2| (QUOTE (-1235))) (|HasSignature| |#2| (|%list| (QUOTE -2787) (|%list| (|%list| (QUOTE -663) (QUOTE (-1209))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3490) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1209))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1292 |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."))) (((-4512 "*") |has| |#1| (-175)) (-4503 |has| |#1| (-571)) (-4504 . T) (-4505 . T) (-4507 . T)) @@ -5104,7 +5104,7 @@ NIL ((|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 -(-1294 -1613 UP L UTS) +(-1294 -4008 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 (-571)))) @@ -5127,7 +5127,7 @@ NIL (-1299 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."))) ((-4511 . T) (-4510 . T)) -((-2210 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2210 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2210 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2210 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2263 (-12 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2263 (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2263 (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-872))) (-2263 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| (-560) (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-888)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1300 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 @@ -5164,7 +5164,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*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 -(-1309 K R UP -1613) +(-1309 K R UP -4008) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5196,11 +5196,11 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.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 -(-1317 S -1613) +(-1317 S -4008) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1318 -1613) +(-1318 -4008) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4502 . T) (-4508 . T) (-4503 . T) ((-4512 "*") . T) (-4504 . T) (-4505 . T) (-4507 . T)) NIL @@ -5264,4 +5264,4 @@ NIL NIL NIL NIL -((-3 NIL 2294689 2294694 2294699 2294704) (-2 NIL 2294669 2294674 2294679 2294684) (-1 NIL 2294649 2294654 2294659 2294664) (0 NIL 2294629 2294634 2294639 2294644) (-1329 "ZMOD.spad" 2294438 2294451 2294567 2294624) (-1328 "ZLINDEP.spad" 2293536 2293547 2294428 2294433) (-1327 "ZDSOLVE.spad" 2283496 2283518 2293526 2293531) (-1326 "YSTREAM.spad" 2282991 2283002 2283486 2283491) (-1325 "YDIAGRAM.spad" 2282625 2282634 2282981 2282986) (-1324 "XRPOLY.spad" 2281845 2281865 2282481 2282550) (-1323 "XPR.spad" 2279640 2279653 2281563 2281662) (-1322 "XPOLYC.spad" 2278959 2278975 2279566 2279635) (-1321 "XPOLY.spad" 2278514 2278525 2278815 2278884) (-1320 "XPBWPOLY.spad" 2276953 2276973 2278288 2278357) (-1319 "XFALG.spad" 2274001 2274017 2276879 2276948) (-1318 "XF.spad" 2272464 2272479 2273903 2273996) (-1317 "XF.spad" 2270907 2270924 2272348 2272353) (-1316 "XEXPPKG.spad" 2270166 2270192 2270897 2270902) (-1315 "XDPOLY.spad" 2269780 2269796 2270022 2270091) (-1314 "XALG.spad" 2269448 2269459 2269736 2269775) (-1313 "WUTSET.spad" 2265418 2265435 2269049 2269076) (-1312 "WP.spad" 2264625 2264669 2265276 2265343) (-1311 "WHILEAST.spad" 2264423 2264432 2264615 2264620) (-1310 "WHEREAST.spad" 2264094 2264103 2264413 2264418) (-1309 "WFFINTBS.spad" 2261757 2261779 2264084 2264089) (-1308 "WEIER.spad" 2259979 2259990 2261747 2261752) (-1307 "VSPACE.spad" 2259652 2259663 2259947 2259974) (-1306 "VSPACE.spad" 2259345 2259358 2259642 2259647) (-1305 "VOID.spad" 2259022 2259031 2259335 2259340) (-1304 "VIEWDEF.spad" 2254223 2254232 2259012 2259017) (-1303 "VIEW3D.spad" 2238184 2238193 2254213 2254218) (-1302 "VIEW2D.spad" 2226083 2226092 2238174 2238179) (-1301 "VIEW.spad" 2223803 2223812 2226073 2226078) (-1300 "VECTOR2.spad" 2222442 2222455 2223793 2223798) (-1299 "VECTOR.spad" 2220942 2220953 2221193 2221220) (-1298 "VECTCAT.spad" 2218854 2218865 2220910 2220937) (-1297 "VECTCAT.spad" 2216573 2216586 2218631 2218636) (-1296 "VARIABLE.spad" 2216353 2216368 2216563 2216568) (-1295 "UTYPE.spad" 2215997 2216006 2216343 2216348) (-1294 "UTSODETL.spad" 2215292 2215316 2215953 2215958) (-1293 "UTSODE.spad" 2213508 2213528 2215282 2215287) (-1292 "UTSCAT.spad" 2210987 2211003 2213406 2213503) (-1291 "UTSCAT.spad" 2208086 2208104 2210507 2210512) (-1290 "UTS2.spad" 2207681 2207716 2208076 2208081) (-1289 "UTS.spad" 2202559 2202587 2206079 2206176) (-1288 "URAGG.spad" 2197280 2197291 2202549 2202554) (-1287 "URAGG.spad" 2191965 2191978 2197236 2197241) (-1286 "UPXSSING.spad" 2189583 2189609 2191019 2191152) (-1285 "UPXSCONS.spad" 2187261 2187281 2187634 2187783) (-1284 "UPXSCCA.spad" 2185832 2185852 2187107 2187256) (-1283 "UPXSCCA.spad" 2184545 2184567 2185822 2185827) (-1282 "UPXSCAT.spad" 2183134 2183150 2184391 2184540) (-1281 "UPXS2.spad" 2182677 2182730 2183124 2183129) (-1280 "UPXS.spad" 2179892 2179920 2180728 2180877) (-1279 "UPSQFREE.spad" 2178306 2178320 2179882 2179887) (-1278 "UPSCAT.spad" 2176101 2176125 2178204 2178301) (-1277 "UPSCAT.spad" 2173581 2173607 2175686 2175691) (-1276 "UPOLYC2.spad" 2173052 2173071 2173571 2173576) (-1275 "UPOLYC.spad" 2168132 2168143 2172894 2173047) (-1274 "UPOLYC.spad" 2163098 2163111 2167862 2167867) (-1273 "UPMP.spad" 2162030 2162043 2163088 2163093) (-1272 "UPDIVP.spad" 2161595 2161609 2162020 2162025) (-1271 "UPDECOMP.spad" 2159856 2159870 2161585 2161590) (-1270 "UPCDEN.spad" 2159073 2159089 2159846 2159851) (-1269 "UP2.spad" 2158437 2158458 2159063 2159068) (-1268 "UP.spad" 2155465 2155480 2155852 2156005) (-1267 "UNISEG2.spad" 2154962 2154975 2155421 2155426) (-1266 "UNISEG.spad" 2154315 2154326 2154881 2154886) (-1265 "UNIFACT.spad" 2153418 2153430 2154305 2154310) (-1264 "ULSCONS.spad" 2144330 2144350 2144700 2144849) (-1263 "ULSCCAT.spad" 2142067 2142087 2144176 2144325) (-1262 "ULSCCAT.spad" 2139912 2139934 2142023 2142028) (-1261 "ULSCAT.spad" 2138152 2138168 2139758 2139907) (-1260 "ULS2.spad" 2137666 2137719 2138142 2138147) (-1259 "ULS.spad" 2127237 2127265 2128182 2128611) (-1258 "UINT8.spad" 2127114 2127123 2127227 2127232) (-1257 "UINT64.spad" 2126990 2126999 2127104 2127109) (-1256 "UINT32.spad" 2126866 2126875 2126980 2126985) (-1255 "UINT16.spad" 2126742 2126751 2126856 2126861) (-1254 "UFD.spad" 2125807 2125816 2126668 2126737) (-1253 "UFD.spad" 2124934 2124945 2125797 2125802) (-1252 "UDVO.spad" 2123815 2123824 2124924 2124929) (-1251 "UDPO.spad" 2121396 2121407 2123771 2123776) (-1250 "TYPEAST.spad" 2121315 2121324 2121386 2121391) (-1249 "TYPE.spad" 2121247 2121256 2121305 2121310) (-1248 "TWOFACT.spad" 2119899 2119914 2121237 2121242) (-1247 "TUPLE.spad" 2119390 2119401 2119795 2119800) (-1246 "TUBETOOL.spad" 2116257 2116266 2119380 2119385) (-1245 "TUBE.spad" 2114904 2114921 2116247 2116252) (-1244 "TSETCAT.spad" 2102975 2102992 2114872 2114899) (-1243 "TSETCAT.spad" 2091032 2091051 2102931 2102936) (-1242 "TS.spad" 2089625 2089641 2090591 2090688) (-1241 "TRMANIP.spad" 2083989 2084006 2089313 2089318) (-1240 "TRIMAT.spad" 2082952 2082977 2083979 2083984) (-1239 "TRIGMNIP.spad" 2081479 2081496 2082942 2082947) (-1238 "TRIGCAT.spad" 2080991 2081000 2081469 2081474) (-1237 "TRIGCAT.spad" 2080501 2080512 2080981 2080986) (-1236 "TREE.spad" 2078947 2078958 2079979 2080006) (-1235 "TRANFUN.spad" 2078786 2078795 2078937 2078942) (-1234 "TRANFUN.spad" 2078623 2078634 2078776 2078781) (-1233 "TOPSP.spad" 2078297 2078306 2078613 2078618) (-1232 "TOOLSIGN.spad" 2077960 2077971 2078287 2078292) (-1231 "TEXTFILE.spad" 2076521 2076530 2077950 2077955) (-1230 "TEX1.spad" 2076077 2076088 2076511 2076516) (-1229 "TEX.spad" 2073271 2073280 2076067 2076072) (-1228 "TEMUTL.spad" 2072826 2072835 2073261 2073266) (-1227 "TBCMPPK.spad" 2070927 2070950 2072816 2072821) (-1226 "TBAGG.spad" 2069985 2070008 2070907 2070922) (-1225 "TBAGG.spad" 2069051 2069076 2069975 2069980) (-1224 "TANEXP.spad" 2068459 2068470 2069041 2069046) (-1223 "TALGOP.spad" 2068183 2068194 2068449 2068454) (-1222 "TABLEAU.spad" 2067664 2067675 2068173 2068178) (-1221 "TABLE.spad" 2065597 2065620 2065867 2065894) (-1220 "TABLBUMP.spad" 2062376 2062387 2065587 2065592) (-1219 "SYSTEM.spad" 2061604 2061613 2062366 2062371) (-1218 "SYSSOLP.spad" 2059087 2059098 2061594 2061599) (-1217 "SYSPTR.spad" 2058986 2058995 2059077 2059082) (-1216 "SYSNNI.spad" 2058209 2058220 2058976 2058981) (-1215 "SYSINT.spad" 2057613 2057624 2058199 2058204) (-1214 "SYNTAX.spad" 2053947 2053956 2057603 2057608) (-1213 "SYMTAB.spad" 2052015 2052024 2053937 2053942) (-1212 "SYMS.spad" 2048038 2048047 2052005 2052010) (-1211 "SYMPOLY.spad" 2047017 2047028 2047099 2047226) (-1210 "SYMFUNC.spad" 2046518 2046529 2047007 2047012) (-1209 "SYMBOL.spad" 2044013 2044022 2046508 2046513) (-1208 "SWITCH.spad" 2040784 2040793 2044003 2044008) (-1207 "SUTS.spad" 2037763 2037791 2039182 2039279) (-1206 "SUPXS.spad" 2034965 2034993 2035814 2035963) (-1205 "SUPFRACF.spad" 2034070 2034088 2034955 2034960) (-1204 "SUP2.spad" 2033462 2033475 2034060 2034065) (-1203 "SUP.spad" 2030104 2030115 2030877 2031030) (-1202 "SUMRF.spad" 2029078 2029089 2030094 2030099) (-1201 "SUMFS.spad" 2028707 2028724 2029068 2029073) (-1200 "SULS.spad" 2018265 2018293 2019223 2019652) (-1199 "SUCHTAST.spad" 2018034 2018043 2018255 2018260) (-1198 "SUCH.spad" 2017724 2017739 2018024 2018029) (-1197 "SUBSPACE.spad" 2009855 2009870 2017714 2017719) (-1196 "SUBRESP.spad" 2009025 2009039 2009811 2009816) (-1195 "STTFNC.spad" 2005493 2005509 2009015 2009020) (-1194 "STTF.spad" 2001592 2001608 2005483 2005488) (-1193 "STTAYLOR.spad" 1994237 1994248 2001467 2001472) (-1192 "STRTBL.spad" 1992252 1992269 1992401 1992428) (-1191 "STRING.spad" 1991018 1991027 1991239 1991266) (-1190 "STREAM3.spad" 1990591 1990606 1991008 1991013) (-1189 "STREAM2.spad" 1989719 1989732 1990581 1990586) (-1188 "STREAM1.spad" 1989425 1989436 1989709 1989714) (-1187 "STREAM.spad" 1986211 1986222 1988818 1988833) (-1186 "STINPROD.spad" 1985147 1985163 1986201 1986206) (-1185 "STEPAST.spad" 1984381 1984390 1985137 1985142) (-1184 "STEP.spad" 1983590 1983599 1984371 1984376) (-1183 "STBL.spad" 1981638 1981666 1981805 1981820) (-1182 "STAGG.spad" 1980713 1980724 1981628 1981633) (-1181 "STAGG.spad" 1979786 1979799 1980703 1980708) (-1180 "STACK.spad" 1979014 1979025 1979264 1979291) (-1179 "SRING.spad" 1978774 1978783 1979004 1979009) (-1178 "SREGSET.spad" 1976473 1976490 1978375 1978402) (-1177 "SRDCMPK.spad" 1975050 1975070 1976463 1976468) (-1176 "SRAGG.spad" 1970233 1970242 1975018 1975045) (-1175 "SRAGG.spad" 1965436 1965447 1970223 1970228) (-1174 "SQMATRIX.spad" 1962931 1962949 1963847 1963934) (-1173 "SPLTREE.spad" 1957397 1957410 1962193 1962220) (-1172 "SPLNODE.spad" 1954017 1954030 1957387 1957392) (-1171 "SPFCAT.spad" 1952826 1952835 1954007 1954012) (-1170 "SPECOUT.spad" 1951378 1951387 1952816 1952821) (-1169 "SPADXPT.spad" 1943469 1943478 1951368 1951373) (-1168 "spad-parser.spad" 1942934 1942943 1943459 1943464) (-1167 "SPADAST.spad" 1942635 1942644 1942924 1942929) (-1166 "SPACEC.spad" 1926850 1926861 1942625 1942630) (-1165 "SPACE3.spad" 1926626 1926637 1926840 1926845) (-1164 "SORTPAK.spad" 1926175 1926188 1926582 1926587) (-1163 "SOLVETRA.spad" 1923938 1923949 1926165 1926170) (-1162 "SOLVESER.spad" 1922394 1922405 1923928 1923933) (-1161 "SOLVERAD.spad" 1918420 1918431 1922384 1922389) (-1160 "SOLVEFOR.spad" 1916882 1916900 1918410 1918415) (-1159 "SNTSCAT.spad" 1916482 1916499 1916850 1916877) (-1158 "SMTS.spad" 1914764 1914790 1916041 1916138) (-1157 "SMP.spad" 1912167 1912187 1912557 1912684) (-1156 "SMITH.spad" 1911012 1911037 1912157 1912162) (-1155 "SMATCAT.spad" 1909130 1909160 1910956 1911007) (-1154 "SMATCAT.spad" 1907180 1907212 1909008 1909013) (-1153 "SKAGG.spad" 1906149 1906160 1907148 1907175) (-1152 "SINT.spad" 1905089 1905098 1906015 1906144) (-1151 "SIMPAN.spad" 1904817 1904826 1905079 1905084) (-1150 "SIGNRF.spad" 1903935 1903946 1904807 1904812) (-1149 "SIGNEF.spad" 1903214 1903231 1903925 1903930) (-1148 "SIGAST.spad" 1902631 1902640 1903204 1903209) (-1147 "SIG.spad" 1901993 1902002 1902621 1902626) (-1146 "SHP.spad" 1899937 1899952 1901949 1901954) (-1145 "SHDP.spad" 1887292 1887319 1887809 1887908) (-1144 "SGROUP.spad" 1886900 1886909 1887282 1887287) (-1143 "SGROUP.spad" 1886506 1886517 1886890 1886895) (-1142 "SGCF.spad" 1879645 1879654 1886496 1886501) (-1141 "SFRTCAT.spad" 1878591 1878608 1879613 1879640) (-1140 "SFRGCD.spad" 1877654 1877674 1878581 1878586) (-1139 "SFQCMPK.spad" 1872467 1872487 1877644 1877649) (-1138 "SFORT.spad" 1871906 1871920 1872457 1872462) (-1137 "SEXOF.spad" 1871749 1871789 1871896 1871901) (-1136 "SEXCAT.spad" 1869577 1869617 1871739 1871744) (-1135 "SEX.spad" 1869469 1869478 1869567 1869572) (-1134 "SETMN.spad" 1867927 1867944 1869459 1869464) (-1133 "SETCAT.spad" 1867412 1867421 1867917 1867922) (-1132 "SETCAT.spad" 1866895 1866906 1867402 1867407) (-1131 "SETAGG.spad" 1863444 1863455 1866875 1866890) (-1130 "SETAGG.spad" 1860001 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(-195 "D01AGNT.spad" 225389 225397 229312 229317) (-194 "CYCLOTOM.spad" 224895 224903 225379 225384) (-193 "CYCLES.spad" 221687 221695 224885 224890) (-192 "CVMP.spad" 221104 221114 221677 221682) (-191 "CTRIGMNP.spad" 219604 219620 221094 221099) (-190 "CTORKIND.spad" 219207 219215 219594 219599) (-189 "CTORCAT.spad" 218448 218456 219197 219202) (-188 "CTORCAT.spad" 217687 217697 218438 218443) (-187 "CTORCALL.spad" 217276 217286 217677 217682) (-186 "CTOR.spad" 216967 216975 217266 217271) (-185 "CSTTOOLS.spad" 216212 216225 216957 216962) (-184 "CRFP.spad" 209984 209997 216202 216207) (-183 "CRCEAST.spad" 209704 209712 209974 209979) (-182 "CRAPACK.spad" 208771 208781 209694 209699) (-181 "CPMATCH.spad" 208272 208287 208693 208698) (-180 "CPIMA.spad" 207977 207996 208262 208267) (-179 "COORDSYS.spad" 202986 202996 207967 207972) (-178 "CONTOUR.spad" 202413 202421 202976 202981) (-177 "CONTFRAC.spad" 198163 198173 202315 202408) (-176 "CONDUIT.spad" 197921 197929 198153 198158) (-175 "COMRING.spad" 197595 197603 197859 197916) (-174 "COMPPROP.spad" 197113 197121 197585 197590) (-173 "COMPLPAT.spad" 196880 196895 197103 197108) (-172 "COMPLEX2.spad" 196595 196607 196870 196875) (-171 "COMPLEX.spad" 191906 191916 192150 192411) (-170 "COMPILER.spad" 191455 191463 191896 191901) (-169 "COMPFACT.spad" 191057 191071 191445 191450) (-168 "COMPCAT.spad" 189129 189139 190791 191052) (-167 "COMPCAT.spad" 186926 186938 188590 188595) (-166 "COMMUPC.spad" 186674 186692 186916 186921) (-165 "COMMONOP.spad" 186207 186215 186664 186669) (-164 "COMMAAST.spad" 185970 185978 186197 186202) (-163 "COMM.spad" 185781 185789 185960 185965) (-162 "COMBOPC.spad" 184704 184712 185771 185776) (-161 "COMBINAT.spad" 183471 183481 184694 184699) (-160 "COMBF.spad" 180893 180909 183461 183466) (-159 "COLOR.spad" 179730 179738 180883 180888) (-158 "COLONAST.spad" 179396 179404 179720 179725) (-157 "CMPLXRT.spad" 179107 179124 179386 179391) (-156 "CLLCTAST.spad" 178769 178777 179097 179102) (-155 "CLIP.spad" 174877 174885 178759 178764) (-154 "CLIF.spad" 173532 173548 174833 174872) (-153 "CLAGG.spad" 170069 170079 173522 173527) (-152 "CLAGG.spad" 166474 166486 169929 169934) (-151 "CINTSLPE.spad" 165829 165842 166464 166469) (-150 "CHVAR.spad" 163967 163989 165819 165824) (-149 "CHARZ.spad" 163882 163890 163947 163962) (-148 "CHARPOL.spad" 163408 163418 163872 163877) (-147 "CHARNZ.spad" 163170 163178 163388 163403) (-146 "CHAR.spad" 160538 160546 163160 163165) (-145 "CFCAT.spad" 159866 159874 160528 160533) (-144 "CDEN.spad" 159086 159100 159856 159861) (-143 "CCLASS.spad" 157182 157190 158444 158483) (-142 "CATEGORY.spad" 156256 156264 157172 157177) (-141 "CATCTOR.spad" 156147 156155 156246 156251) (-140 "CATAST.spad" 155773 155781 156137 156142) (-139 "CASEAST.spad" 155487 155495 155763 155768) (-138 "CARTEN2.spad" 154877 154904 155477 155482) (-137 "CARTEN.spad" 150244 150268 154867 154872) (-136 "CARD.spad" 147539 147547 150218 150239) (-135 "CAPSLAST.spad" 147321 147329 147529 147534) (-134 "CACHSET.spad" 146945 146953 147311 147316) (-133 "CABMON.spad" 146500 146508 146935 146940) (-132 "BYTEORD.spad" 146175 146183 146490 146495) (-131 "BYTEBUF.spad" 143876 143884 145162 145189) (-130 "BYTE.spad" 143351 143359 143866 143871) (-129 "BTREE.spad" 142295 142305 142829 142856) (-128 "BTOURN.spad" 141171 141181 141773 141800) (-127 "BTCAT.spad" 140563 140573 141139 141166) (-126 "BTCAT.spad" 139975 139987 140553 140558) (-125 "BTAGG.spad" 139441 139449 139943 139970) (-124 "BTAGG.spad" 138927 138937 139431 139436) (-123 "BSTREE.spad" 137539 137549 138405 138432) (-122 "BRILL.spad" 135744 135755 137529 137534) (-121 "BRAGG.spad" 134700 134710 135734 135739) (-120 "BRAGG.spad" 133620 133632 134656 134661) (-119 "BPADICRT.spad" 131445 131457 131692 131785) (-118 "BPADIC.spad" 131117 131129 131371 131440) (-117 "BOUNDZRO.spad" 130773 130790 131107 131112) (-116 "BOP1.spad" 128231 128241 130763 130768) (-115 "BOP.spad" 123365 123373 128221 128226) (-114 "BOOLEAN.spad" 122803 122811 123355 123360) (-113 "BOOLE.spad" 122453 122461 122793 122798) (-112 "BOOLE.spad" 122101 122111 122443 122448) (-111 "BMODULE.spad" 121813 121825 122069 122096) (-110 "BITS.spad" 121187 121195 121402 121429) (-109 "BINDING.spad" 120608 120616 121177 121182) (-108 "BINARY.spad" 118577 118585 118933 119026) (-107 "BGAGG.spad" 117782 117792 118557 118572) (-106 "BGAGG.spad" 116995 117007 117772 117777) (-105 "BFUNCT.spad" 116559 116567 116975 116990) (-104 "BEZOUT.spad" 115699 115726 116509 116514) (-103 "BBTREE.spad" 112447 112457 115177 115204) (-102 "BASTYPE.spad" 111946 111954 112437 112442) (-101 "BASTYPE.spad" 111443 111453 111936 111941) (-100 "BALFACT.spad" 110902 110915 111433 111438) (-99 "AUTOMOR.spad" 110353 110362 110882 110897) (-98 "ATTREG.spad" 107076 107083 110105 110348) (-97 "ATTRBUT.spad" 103099 103106 107056 107071) (-96 "ATTRAST.spad" 102816 102823 103089 103094) (-95 "ATRIG.spad" 102286 102293 102806 102811) (-94 "ATRIG.spad" 101754 101763 102276 102281) (-93 "ASTCAT.spad" 101658 101665 101744 101749) (-92 "ASTCAT.spad" 101560 101569 101648 101653) (-91 "ASTACK.spad" 100770 100779 101038 101065) (-90 "ASSOCEQ.spad" 99604 99615 100726 100731) (-89 "ASP9.spad" 98685 98698 99594 99599) (-88 "ASP80.spad" 98007 98020 98675 98680) (-87 "ASP8.spad" 97050 97063 97997 98002) (-86 "ASP78.spad" 96501 96514 97040 97045) (-85 "ASP77.spad" 95870 95883 96491 96496) (-84 "ASP74.spad" 94962 94975 95860 95865) (-83 "ASP73.spad" 94233 94246 94952 94957) (-82 "ASP7.spad" 93393 93406 94223 94228) (-81 "ASP6.spad" 92260 92273 93383 93388) (-80 "ASP55.spad" 90769 90782 92250 92255) (-79 "ASP50.spad" 88586 88599 90759 90764) (-78 "ASP49.spad" 87585 87598 88576 88581) (-77 "ASP42.spad" 86000 86039 87575 87580) (-76 "ASP41.spad" 84587 84626 85990 85995) (-75 "ASP4.spad" 83882 83895 84577 84582) (-74 "ASP35.spad" 82870 82883 83872 83877) (-73 "ASP34.spad" 82171 82184 82860 82865) (-72 "ASP33.spad" 81731 81744 82161 82166) (-71 "ASP31.spad" 80871 80884 81721 81726) (-70 "ASP30.spad" 79763 79776 80861 80866) (-69 "ASP29.spad" 79229 79242 79753 79758) (-68 "ASP28.spad" 70502 70515 79219 79224) (-67 "ASP27.spad" 69399 69412 70492 70497) (-66 "ASP24.spad" 68486 68499 69389 69394) (-65 "ASP20.spad" 67950 67963 68476 68481) (-64 "ASP19.spad" 62636 62649 67940 67945) (-63 "ASP12.spad" 62050 62063 62626 62631) (-62 "ASP10.spad" 61321 61334 62040 62045) (-61 "ASP1.spad" 60702 60715 61311 61316) (-60 "ARRAY2.spad" 59941 59950 60180 60207) (-59 "ARRAY12.spad" 58654 58665 59931 59936) (-58 "ARRAY1.spad" 57317 57326 57663 57690) (-57 "ARR2CAT.spad" 53099 53120 57285 57312) (-56 "ARR2CAT.spad" 48901 48924 53089 53094) (-55 "ARITY.spad" 48273 48280 48891 48896) (-54 "APPRULE.spad" 47557 47579 48263 48268) (-53 "APPLYORE.spad" 47176 47189 47547 47552) (-52 "ANY1.spad" 46247 46256 47166 47171) (-51 "ANY.spad" 45098 45105 46237 46242) (-50 "ANTISYM.spad" 43543 43559 45078 45093) (-49 "ANON.spad" 43252 43259 43533 43538) (-48 "AN.spad" 41558 41565 43065 43158) (-47 "AMR.spad" 39743 39754 41456 41553) (-46 "AMR.spad" 37759 37772 39474 39479) (-45 "ALIST.spad" 34599 34620 34949 34976) (-44 "ALGSC.spad" 33734 33760 34471 34524) (-43 "ALGPKG.spad" 29517 29528 33690 33695) (-42 "ALGMFACT.spad" 28710 28724 29507 29512) (-41 "ALGMANIP.spad" 26194 26209 28537 28542) (-40 "ALGFF.spad" 23799 23826 24016 24172) (-39 "ALGFACT.spad" 22918 22928 23789 23794) (-38 "ALGEBRA.spad" 22751 22760 22874 22913) (-37 "ALGEBRA.spad" 22616 22627 22741 22746) (-36 "ALAGG.spad" 22128 22149 22584 22611) (-35 "AHYP.spad" 21509 21516 22118 22123) (-34 "AGG.spad" 19842 19849 21499 21504) (-33 "AGG.spad" 18139 18148 19798 19803) (-32 "AF.spad" 16567 16582 18071 18076) (-31 "ADDAST.spad" 16253 16260 16557 16562) (-30 "ACPLOT.spad" 14844 14851 16243 16248) (-29 "ACFS.spad" 12701 12710 14746 14839) (-28 "ACFS.spad" 10644 10655 12691 12696) (-27 "ACF.spad" 7398 7405 10546 10639) (-26 "ACF.spad" 4238 4247 7388 7393) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2294543 2294548 2294553 2294558) (-2 NIL 2294523 2294528 2294533 2294538) (-1 NIL 2294503 2294508 2294513 2294518) (0 NIL 2294483 2294488 2294493 2294498) (-1329 "ZMOD.spad" 2294292 2294305 2294421 2294478) (-1328 "ZLINDEP.spad" 2293390 2293401 2294282 2294287) (-1327 "ZDSOLVE.spad" 2283350 2283372 2293380 2293385) (-1326 "YSTREAM.spad" 2282845 2282856 2283340 2283345) (-1325 "YDIAGRAM.spad" 2282479 2282488 2282835 2282840) (-1324 "XRPOLY.spad" 2281699 2281719 2282335 2282404) (-1323 "XPR.spad" 2279494 2279507 2281417 2281516) (-1322 "XPOLYC.spad" 2278813 2278829 2279420 2279489) (-1321 "XPOLY.spad" 2278368 2278379 2278669 2278738) (-1320 "XPBWPOLY.spad" 2276807 2276827 2278142 2278211) (-1319 "XFALG.spad" 2273855 2273871 2276733 2276802) (-1318 "XF.spad" 2272318 2272333 2273757 2273850) (-1317 "XF.spad" 2270761 2270778 2272202 2272207) (-1316 "XEXPPKG.spad" 2270020 2270046 2270751 2270756) (-1315 "XDPOLY.spad" 2269634 2269650 2269876 2269945) (-1314 "XALG.spad" 2269302 2269313 2269590 2269629) (-1313 "WUTSET.spad" 2265272 2265289 2268903 2268930) (-1312 "WP.spad" 2264479 2264523 2265130 2265197) (-1311 "WHILEAST.spad" 2264277 2264286 2264469 2264474) (-1310 "WHEREAST.spad" 2263948 2263957 2264267 2264272) (-1309 "WFFINTBS.spad" 2261611 2261633 2263938 2263943) (-1308 "WEIER.spad" 2259833 2259844 2261601 2261606) (-1307 "VSPACE.spad" 2259506 2259517 2259801 2259828) (-1306 "VSPACE.spad" 2259199 2259212 2259496 2259501) (-1305 "VOID.spad" 2258876 2258885 2259189 2259194) (-1304 "VIEWDEF.spad" 2254077 2254086 2258866 2258871) (-1303 "VIEW3D.spad" 2238038 2238047 2254067 2254072) (-1302 "VIEW2D.spad" 2225937 2225946 2238028 2238033) (-1301 "VIEW.spad" 2223657 2223666 2225927 2225932) (-1300 "VECTOR2.spad" 2222296 2222309 2223647 2223652) (-1299 "VECTOR.spad" 2220796 2220807 2221047 2221074) (-1298 "VECTCAT.spad" 2218708 2218719 2220764 2220791) (-1297 "VECTCAT.spad" 2216427 2216440 2218485 2218490) (-1296 "VARIABLE.spad" 2216207 2216222 2216417 2216422) (-1295 "UTYPE.spad" 2215851 2215860 2216197 2216202) (-1294 "UTSODETL.spad" 2215146 2215170 2215807 2215812) (-1293 "UTSODE.spad" 2213362 2213382 2215136 2215141) (-1292 "UTSCAT.spad" 2210841 2210857 2213260 2213357) (-1291 "UTSCAT.spad" 2207940 2207958 2210361 2210366) (-1290 "UTS2.spad" 2207535 2207570 2207930 2207935) (-1289 "UTS.spad" 2202413 2202441 2205933 2206030) (-1288 "URAGG.spad" 2197134 2197145 2202403 2202408) (-1287 "URAGG.spad" 2191819 2191832 2197090 2197095) (-1286 "UPXSSING.spad" 2189437 2189463 2190873 2191006) (-1285 "UPXSCONS.spad" 2187115 2187135 2187488 2187637) (-1284 "UPXSCCA.spad" 2185686 2185706 2186961 2187110) (-1283 "UPXSCCA.spad" 2184399 2184421 2185676 2185681) (-1282 "UPXSCAT.spad" 2182988 2183004 2184245 2184394) (-1281 "UPXS2.spad" 2182531 2182584 2182978 2182983) (-1280 "UPXS.spad" 2179746 2179774 2180582 2180731) (-1279 "UPSQFREE.spad" 2178160 2178174 2179736 2179741) (-1278 "UPSCAT.spad" 2175955 2175979 2178058 2178155) (-1277 "UPSCAT.spad" 2173435 2173461 2175540 2175545) (-1276 "UPOLYC2.spad" 2172906 2172925 2173425 2173430) (-1275 "UPOLYC.spad" 2167986 2167997 2172748 2172901) (-1274 "UPOLYC.spad" 2162952 2162965 2167716 2167721) (-1273 "UPMP.spad" 2161884 2161897 2162942 2162947) (-1272 "UPDIVP.spad" 2161449 2161463 2161874 2161879) (-1271 "UPDECOMP.spad" 2159710 2159724 2161439 2161444) (-1270 "UPCDEN.spad" 2158927 2158943 2159700 2159705) (-1269 "UP2.spad" 2158291 2158312 2158917 2158922) (-1268 "UP.spad" 2155319 2155334 2155706 2155859) (-1267 "UNISEG2.spad" 2154816 2154829 2155275 2155280) (-1266 "UNISEG.spad" 2154169 2154180 2154735 2154740) (-1265 "UNIFACT.spad" 2153272 2153284 2154159 2154164) (-1264 "ULSCONS.spad" 2144184 2144204 2144554 2144703) (-1263 "ULSCCAT.spad" 2141921 2141941 2144030 2144179) (-1262 "ULSCCAT.spad" 2139766 2139788 2141877 2141882) (-1261 "ULSCAT.spad" 2138006 2138022 2139612 2139761) (-1260 "ULS2.spad" 2137520 2137573 2137996 2138001) (-1259 "ULS.spad" 2127091 2127119 2128036 2128465) (-1258 "UINT8.spad" 2126968 2126977 2127081 2127086) (-1257 "UINT64.spad" 2126844 2126853 2126958 2126963) (-1256 "UINT32.spad" 2126720 2126729 2126834 2126839) (-1255 "UINT16.spad" 2126596 2126605 2126710 2126715) (-1254 "UFD.spad" 2125661 2125670 2126522 2126591) (-1253 "UFD.spad" 2124788 2124799 2125651 2125656) (-1252 "UDVO.spad" 2123669 2123678 2124778 2124783) (-1251 "UDPO.spad" 2121250 2121261 2123625 2123630) (-1250 "TYPEAST.spad" 2121169 2121178 2121240 2121245) (-1249 "TYPE.spad" 2121101 2121110 2121159 2121164) (-1248 "TWOFACT.spad" 2119753 2119768 2121091 2121096) (-1247 "TUPLE.spad" 2119244 2119255 2119649 2119654) (-1246 "TUBETOOL.spad" 2116111 2116120 2119234 2119239) (-1245 "TUBE.spad" 2114758 2114775 2116101 2116106) (-1244 "TSETCAT.spad" 2102829 2102846 2114726 2114753) (-1243 "TSETCAT.spad" 2090886 2090905 2102785 2102790) (-1242 "TS.spad" 2089479 2089495 2090445 2090542) (-1241 "TRMANIP.spad" 2083843 2083860 2089167 2089172) (-1240 "TRIMAT.spad" 2082806 2082831 2083833 2083838) (-1239 "TRIGMNIP.spad" 2081333 2081350 2082796 2082801) (-1238 "TRIGCAT.spad" 2080845 2080854 2081323 2081328) (-1237 "TRIGCAT.spad" 2080355 2080366 2080835 2080840) (-1236 "TREE.spad" 2078801 2078812 2079833 2079860) (-1235 "TRANFUN.spad" 2078640 2078649 2078791 2078796) (-1234 "TRANFUN.spad" 2078477 2078488 2078630 2078635) (-1233 "TOPSP.spad" 2078151 2078160 2078467 2078472) (-1232 "TOOLSIGN.spad" 2077814 2077825 2078141 2078146) (-1231 "TEXTFILE.spad" 2076375 2076384 2077804 2077809) (-1230 "TEX1.spad" 2075931 2075942 2076365 2076370) (-1229 "TEX.spad" 2073125 2073134 2075921 2075926) (-1228 "TEMUTL.spad" 2072680 2072689 2073115 2073120) (-1227 "TBCMPPK.spad" 2070781 2070804 2072670 2072675) (-1226 "TBAGG.spad" 2069839 2069862 2070761 2070776) (-1225 "TBAGG.spad" 2068905 2068930 2069829 2069834) (-1224 "TANEXP.spad" 2068313 2068324 2068895 2068900) (-1223 "TALGOP.spad" 2068037 2068048 2068303 2068308) (-1222 "TABLEAU.spad" 2067518 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(-1203 "SUP.spad" 2029958 2029969 2030731 2030884) (-1202 "SUMRF.spad" 2028932 2028943 2029948 2029953) (-1201 "SUMFS.spad" 2028561 2028578 2028922 2028927) (-1200 "SULS.spad" 2018119 2018147 2019077 2019506) (-1199 "SUCHTAST.spad" 2017888 2017897 2018109 2018114) (-1198 "SUCH.spad" 2017578 2017593 2017878 2017883) (-1197 "SUBSPACE.spad" 2009709 2009724 2017568 2017573) (-1196 "SUBRESP.spad" 2008879 2008893 2009665 2009670) (-1195 "STTFNC.spad" 2005347 2005363 2008869 2008874) (-1194 "STTF.spad" 2001446 2001462 2005337 2005342) (-1193 "STTAYLOR.spad" 1994091 1994102 2001321 2001326) (-1192 "STRTBL.spad" 1992106 1992123 1992255 1992282) (-1191 "STRING.spad" 1990872 1990881 1991093 1991120) (-1190 "STREAM3.spad" 1990445 1990460 1990862 1990867) (-1189 "STREAM2.spad" 1989573 1989586 1990435 1990440) (-1188 "STREAM1.spad" 1989279 1989290 1989563 1989568) (-1187 "STREAM.spad" 1986065 1986076 1988672 1988687) (-1186 "STINPROD.spad" 1985001 1985017 1986055 1986060) (-1185 "STEPAST.spad" 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1843484 1844079 1844214) (-1110 "RURPK.spad" 1841127 1841143 1843458 1843463) (-1109 "RULESET.spad" 1840580 1840604 1841117 1841122) (-1108 "RULECOLD.spad" 1840432 1840445 1840570 1840575) (-1107 "RULE.spad" 1838680 1838704 1840422 1840427) (-1106 "RTVALUE.spad" 1838415 1838424 1838670 1838675) (-1105 "RSTRCAST.spad" 1838132 1838141 1838405 1838410) (-1104 "RSETGCD.spad" 1834574 1834594 1838122 1838127) (-1103 "RSETCAT.spad" 1824542 1824559 1834542 1834569) (-1102 "RSETCAT.spad" 1814530 1814549 1824532 1824537) (-1101 "RSDCMPK.spad" 1813030 1813050 1814520 1814525) (-1100 "RRCC.spad" 1811414 1811444 1813020 1813025) (-1099 "RRCC.spad" 1809796 1809828 1811404 1811409) (-1098 "RPTAST.spad" 1809498 1809507 1809786 1809791) (-1097 "RPOLCAT.spad" 1789002 1789017 1809366 1809493) (-1096 "RPOLCAT.spad" 1768201 1768218 1788567 1788572) (-1095 "ROUTINE.spad" 1763602 1763611 1766350 1766377) (-1094 "ROMAN.spad" 1762930 1762939 1763468 1763597) (-1093 "ROIRC.spad" 1762010 1762042 1762920 1762925) (-1092 "RNS.spad" 1760986 1760995 1761912 1762005) (-1091 "RNS.spad" 1760048 1760059 1760976 1760981) (-1090 "RNGBIND.spad" 1759208 1759222 1760003 1760008) (-1089 "RNG.spad" 1758943 1758952 1759198 1759203) (-1088 "RMODULE.spad" 1758724 1758735 1758933 1758938) (-1087 "RMCAT2.spad" 1758144 1758201 1758714 1758719) (-1086 "RMATRIX.spad" 1756914 1756933 1757257 1757296) (-1085 "RMATCAT.spad" 1752493 1752524 1756870 1756909) (-1084 "RMATCAT.spad" 1747962 1747995 1752341 1752346) (-1083 "RLINSET.spad" 1747666 1747677 1747952 1747957) (-1082 "RINTERP.spad" 1747554 1747574 1747656 1747661) (-1081 "RING.spad" 1747024 1747033 1747534 1747549) (-1080 "RING.spad" 1746502 1746513 1747014 1747019) (-1079 "RIDIST.spad" 1745894 1745903 1746492 1746497) (-1078 "RGCHAIN.spad" 1744415 1744431 1745309 1745336) (-1077 "RGBCSPC.spad" 1744204 1744216 1744405 1744410) (-1076 "RGBCMDL.spad" 1743766 1743778 1744194 1744199) (-1075 "RFFACTOR.spad" 1743228 1743239 1743756 1743761) (-1074 "RFFACT.spad" 1742963 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(-981 "POLYCATQ.spad" 1583662 1583684 1585526 1585531) (-980 "POLYCAT.spad" 1577164 1577185 1583530 1583657) (-979 "POLYCAT.spad" 1569962 1569985 1576330 1576335) (-978 "POLY2UP.spad" 1569414 1569428 1569952 1569957) (-977 "POLY2.spad" 1569011 1569023 1569404 1569409) (-976 "POLY.spad" 1566274 1566284 1566789 1566916) (-975 "POLUTIL.spad" 1565239 1565268 1566230 1566235) (-974 "POLTOPOL.spad" 1563987 1564002 1565229 1565234) (-973 "POINT.spad" 1562651 1562661 1562738 1562765) (-972 "PNTHEORY.spad" 1559353 1559361 1562641 1562646) (-971 "PMTOOLS.spad" 1558128 1558142 1559343 1559348) (-970 "PMSYM.spad" 1557677 1557687 1558118 1558123) (-969 "PMQFCAT.spad" 1557268 1557282 1557667 1557672) (-968 "PMPREDFS.spad" 1556730 1556752 1557258 1557263) (-967 "PMPRED.spad" 1556217 1556231 1556720 1556725) (-966 "PMPLCAT.spad" 1555294 1555312 1556146 1556151) (-965 "PMLSAGG.spad" 1554879 1554893 1555284 1555289) (-964 "PMKERNEL.spad" 1554458 1554470 1554869 1554874) (-963 "PMINS.spad" 1554038 1554048 1554448 1554453) (-962 "PMFS.spad" 1553615 1553633 1554028 1554033) (-961 "PMDOWN.spad" 1552905 1552919 1553605 1553610) (-960 "PMASSFS.spad" 1551880 1551896 1552895 1552900) (-959 "PMASS.spad" 1550898 1550906 1551870 1551875) (-958 "PLOTTOOL.spad" 1550678 1550686 1550888 1550893) (-957 "PLOT3D.spad" 1547142 1547150 1550668 1550673) (-956 "PLOT1.spad" 1546315 1546325 1547132 1547137) (-955 "PLOT.spad" 1541238 1541246 1546305 1546310) (-954 "PLEQN.spad" 1528640 1528667 1541228 1541233) (-953 "PINTERPA.spad" 1528424 1528440 1528630 1528635) (-952 "PINTERP.spad" 1528046 1528065 1528414 1528419) (-951 "PID.spad" 1527020 1527028 1527972 1528041) (-950 "PICOERCE.spad" 1526677 1526687 1527010 1527015) (-949 "PI.spad" 1526294 1526302 1526651 1526672) (-948 "PGROEB.spad" 1524903 1524917 1526284 1526289) (-947 "PGE.spad" 1516576 1516584 1524893 1524898) (-946 "PGCD.spad" 1515530 1515547 1516566 1516571) (-945 "PFRPAC.spad" 1514679 1514689 1515520 1515525) (-944 "PFR.spad" 1511382 1511392 1514581 1514674) (-943 "PFOTOOLS.spad" 1510640 1510656 1511372 1511377) (-942 "PFOQ.spad" 1510010 1510028 1510630 1510635) (-941 "PFO.spad" 1509429 1509456 1510000 1510005) (-940 "PFECAT.spad" 1507139 1507147 1509355 1509424) (-939 "PFECAT.spad" 1504877 1504887 1507095 1507100) (-938 "PFBRU.spad" 1502765 1502777 1504867 1504872) (-937 "PFBR.spad" 1500325 1500348 1502755 1502760) (-936 "PF.spad" 1499899 1499911 1500130 1500223) (-935 "PERMGRP.spad" 1494669 1494679 1499889 1499894) (-934 "PERMCAT.spad" 1493330 1493340 1494649 1494664) (-933 "PERMAN.spad" 1491886 1491900 1493320 1493325) (-932 "PERM.spad" 1487693 1487703 1491716 1491731) (-931 "PENDTREE.spad" 1486913 1486923 1487193 1487198) (-930 "PDSPC.spad" 1485726 1485736 1486903 1486908) (-929 "PDSPC.spad" 1484537 1484549 1485716 1485721) (-928 "PDRING.spad" 1484379 1484389 1484517 1484532) (-927 "PDMOD.spad" 1484195 1484207 1484347 1484374) (-926 "PDEPROB.spad" 1483210 1483218 1484185 1484190) (-925 "PDEPACK.spad" 1477346 1477354 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index bea6c4c9..6960a465 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205732 . 3508975277) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) #0#) |has| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))))) -((((-560)) . T) (($) -2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +(205732 . 3509581014) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) #0#) |has| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (-321 (-2 (|:| -1651 |#1|) (|:| -1871 |#2|))))) +((((-560)) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-940)) ((((-888)) . T)) ((((-888)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1191)) . T) (((-229)) . T) (((-391)) . T) (((-916 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-888)) . T)) -(-2210 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-2210 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) +(-2263 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2263 (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (-12 (|has| |#1| (-872)) (|has| |#2| (-872)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-2210 (|has| |#1| (-21)) (|has| |#1| (-871))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2210 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . 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T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1214)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -(-2210 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(((|#2| (-496 (-2327 |#1|) (-793))) . T)) -((((-1209)) -2210 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +(-2263 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(((|#2| (-496 (-2140 |#1|) (-793))) . T)) +((((-1209)) -2263 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((|#1| (-545 (-1209))) . T)) ((((-1191)) . T) (((-988 (-130))) . T) (((-888)) . T)) ((((-888)) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((#0=(-894 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -2210 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -4021 |#1|) (|:| -1525 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -2263 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1070 (-421 (-560))))) ((|#2|) . T) (($) -2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((-889 |#1|)) . T)) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -3731 |#1|) (|:| -1952 |#2|))) . T)) ((($) . T)) ((((-888)) |has| |#1| (-632 (-888))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-560)) . T) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T) (($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((-1209)) . T)) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1209)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-888)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2210 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . 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T) (((-560)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2210 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2263 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) ((($ $) . T)) ((($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) @@ -132,30 +132,30 @@ (|has| |#1| (-381)) (((|#1|) . T)) ((((-888)) . T)) -((((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) -(((|#1|) . 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T)) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2210 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-872)) (|has| |#1| (-1133))) (|has| |#1| (-1133)) -(-2210 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-872)) (|has| |#1| (-1133))) (|has| |#1| (-1133)) -(-2210 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-872)) (|has| |#1| (-1133))) (|has| |#1| (-871)) (((|#1| |#1|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -170,12 +170,12 @@ (|has| |#3| (-817)) (|has| |#3| (-817)) (((|#1| |#2|) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1214)) . T)) (((|#1| |#2|) . T)) (((|#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) (((-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|)))) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1| (-1209) (-1120 (-1209)) (-545 (-1120 (-1209)))) . T)) ((((-560) |#1|) . T)) @@ -195,29 +195,29 @@ ((((-1191) |#1|) . T)) ((((-1266 (-560)) $) . T) (((-560) (-130)) . T)) (((|#1|) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#3| (-793)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1266 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -2210 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2263 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (((|#1| |#2|) . T)) ((((-888)) . T)) @@ -241,13 +241,13 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -((($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T) (($) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((($) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(((|#2|) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) (($) |has| |#2| (-1081)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081)))) ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -258,10 +258,10 @@ ((((-171 (-229))) |has| |#1| (-1052)) (((-171 (-391))) |has| |#1| (-1052)) (((-549)) |has| |#1| (-633 (-549))) (((-1203 |#1|)) . T) (((-916 (-560))) |has| |#1| (-633 (-916 (-560)))) (((-916 (-391))) |has| |#1| (-633 (-916 (-391))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1|) . 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T)) -((((-2 (|:| -4021 |#1|) (|:| -1525 |#2|))) . T) (((-888)) . T)) +((((-2 (|:| -3731 |#1|) (|:| -1952 |#2|))) . T) (((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549))) (((-916 (-391))) |has| |#1| (-633 (-916 (-391)))) (((-916 (-560))) |has| |#1| (-633 (-916 (-560))))) -(((|#4|) -2210 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081)))) -(((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081)))) -((((-2 (|:| -4021 |#1|) (|:| -1525 |#2|))) . T)) +(((|#4|) -2263 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081)))) +(((|#3|) -2263 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081)))) +((((-2 (|:| -3731 |#1|) (|:| -1952 |#2|))) . T)) ((((-888)) . T)) ((((-888)) . T)) ((((-549)) . T) (((-560)) . T) (((-916 (-560))) . T) (((-391)) . T) (((-229)) . T)) @@ -326,15 +326,15 @@ (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) ((($) . 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T)) @@ -349,15 +349,15 @@ (|has| |#1| (-1133)) ((((-936 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-888)) . T) (((-1214)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((((-1214)) . 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T)) (((|#1| (-1003)) . T)) ((((-560)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1184)) -((((-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) +((((-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1286 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) -((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-842 (-1209))) . T) (($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . 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T)) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-888)) . T)) ((((-888)) . T)) (|has| (-1280 |#2| |#3| |#4|) (-149)) @@ -415,18 +415,18 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2210 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-2263 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (((|#1|) . T)) ((($) . T)) ((((-560) |#1|) . T)) (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) -(-2210 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-2263 (|has| |#1| (-21)) (|has| |#1| (-871))) ((((-888)) |has| |#1| (-1133))) -((($) -2210 (|has| |#1| (-240)) (|has| |#1| (-239)))) -(-2210 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-363))) +((($) -2263 (|has| |#1| (-240)) (|has| |#1| (-239)))) +(-2263 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-936 |#1|)) . T)) ((((-421 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) @@ -437,7 +437,7 @@ ((((-888)) . T)) ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) (|has| |#1| (-376)) -(-2210 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2263 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-793) |#1|))) @@ -451,23 +451,23 @@ ((((-1266 (-560)) $) . T) (((-560) |#1|) . T)) ((((-888)) . T)) (((|#2|) . T)) -(-2210 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2263 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571)) (((-560)) . T)) (|has| |#2| (-817)) (|has| |#2| (-817)) -((((-1289 |#1| |#2| |#3|)) . 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T) (($) -2263 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T)) (((|#1|) . T)) ((((-1209)) -12 (|has| |#3| (-928 (-1209))) (|has| |#3| (-1081)))) (((|#1|) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-844))) -(-2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-571)))) +(-2263 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($ $) |has| |#1| (-571)) ((|#1| |#1|) . T)) -((($ (-1209)) -2210 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((($ (-1209)) -2263 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((#0=(-721) (-1203 #0#)) . T)) ((((-595 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-421 (-560))) . T) (($) . T)) @@ -475,18 +475,18 @@ ((((-888)) . T) (((-1299 |#3|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2210 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2263 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) . T)) ((((-888)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((($) . T)) -((($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((#1=(-1289 |#1| |#2| |#3|) #1#) |has| |#1| (-376)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . T)) -(((|#1|) . 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T) (($) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) (((|#3|) |has| |#3| (-1081))) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($) -2263 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (|has| (-1121 |#1|) (-1133)) (((|#2| (-843 |#1|)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) @@ -494,20 +494,20 @@ (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . 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T)) -((($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-421 $) (-421 $)) |has| |#1| (-571)) (($ $) . T) ((|#1| |#1|) . T)) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((#0=(-1114) |#2|) . T) ((#0# $) . T) (($ $) . T)) ((((-888)) . T)) ((((-936 |#1|)) . T)) @@ -516,22 +516,22 @@ ((((-246 |#1| |#2|) |#2|) . T)) ((((-888)) . T)) (((|#3|) |has| |#3| (-1133)) (((-560)) -12 (|has| |#3| (-1070 (-560))) (|has| |#3| (-1133))) (((-421 (-560))) -12 (|has| |#3| (-1070 (-421 (-560)))) (|has| |#3| (-1133)))) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#1|) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-549)) |has| |#1| (-633 (-549)))) (((|#1|) |has| |#1| (-175))) -((((-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))) . T)) (|has| |#1| (-376)) ((((-1214)) . T)) (((|#1|) . T)) -(-2210 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-2263 (|has| |#1| (-21)) (|has| |#1| (-871))) ((($) . T)) ((((-1209) |#1|) |has| |#1| (-528 (-1209) |#1|)) ((|#1| |#1|) |has| |#1| (-321 |#1|))) (|has| |#2| (-844)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-871)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| (-545 |#3|)) . T)) ((((-888)) . T)) @@ -540,15 +540,15 @@ (|has| |#1| (-381)) ((((-421 (-560))) . T)) (((|#1|) . T)) -(-2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-421 (-560))) . T)) ((((-1191) |#1|) . T)) (|has| |#1| (-381)) ((((-560)) . T)) ((((-560)) . T)) (((|#1|) . T) (((-560)) . T)) -(-2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(-2210 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#1| (-872)) (|has| |#1| (-1133))) ((((-888)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((((-1209)) -12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209))))) @@ -562,12 +562,12 @@ ((((-560) |#3|) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) (|has| |#2| (-1081)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) -(-2210 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) +(-2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-888)) . T)) ((((-1286 |#1| |#2| |#3| |#4|)) . T)) ((((-421 (-560))) . T) (((-560)) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -576,9 +576,9 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((((-560)) . T)) ((((-560)) . T)) -((($) . T) (((-560)) . T) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +((($) . T) (((-560)) . T) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) -((((-560)) -2210 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) +((((-560)) -2263 (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (|has| |#2| (-1081))) ((|#2|) |has| |#2| (-1133)) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -595,7 +595,7 @@ ((((-888)) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . 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T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) @@ -898,15 +898,15 @@ (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((((-888)) . T)) -((((-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) +((((-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) (|has| |#1| (-38 (-421 (-560)))) -((((-402) (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) +((((-402) (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#2| (-1184)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-888)) . T) (((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) @@ -924,7 +924,7 @@ ((((-402) (-1191)) . T)) (|has| |#1| (-571)) ((((-1266 (-560)) $) . T) (((-560) |#1|) . 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T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1209)) . T)) (|has| |#1| (-571)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2327 |#1|) (-793)) (-889 |#1|)) . T)) +(((|#2| (-246 (-2140 |#1|) (-793)) (-889 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . 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T)) -((((-1209)) -2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((((-1209)) -2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-889 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-845)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1121 |#1|) (-1133)) -(((|#2| |#2|) -2210 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) -(((|#2|) -2210 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2210 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2| |#2|) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2|) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) ((((-560)) . T)) ((((-1214)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1214)) . T)) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -((($) -2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -2210 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2263 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2263 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2263 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1209)) -2210 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -2263 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-888)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1209) $) |has| |#1| (-528 (-1209) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1209) |#1|) |has| |#1| (-528 (-1209) |#1|))) ((((-1209)) |has| |#1| (-928 (-1209)))) -(-2210 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2263 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#2|) . T) (((-888)) . T)) ((((-888)) . T)) (((|#2|) . T)) ((((-936 |#1|)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-894 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -2210 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -2263 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2263 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1070 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-817)) (|has| |#2| (-817)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-817)) (|has| |#2| (-817))) (|has| |#2| (-1081)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1235)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((((-888)) . T)) ((((-936 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) -((($) -2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2263 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2263 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-376)) (((|#1|) . T) (($) . T)) (|has| |#1| (-871)) -((($) . T) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2263 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-1209)) |has| |#1| (-928 (-1209)))) (|has| |#1| (-871)) ((((-520)) . T)) @@ -1443,7 +1443,7 @@ ((((-549)) . T)) ((((-888)) . T)) ((($) . T)) -((((-560) (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T) (((-1266 (-560)) $) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T) (((-1266 (-560)) $) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-175))) @@ -1453,22 +1453,22 @@ (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#3|) . 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T)) -(((#0=(-421 (-560)) #0#) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#1| |#1|) . T)) +(((#0=(-421 (-560)) #0#) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#1| |#1|) . T)) ((((-421 (-560))) |has| |#1| (-1070 (-560))) (((-560)) |has| |#1| (-1070 (-560))) (((-1209)) |has| |#1| (-1070 (-1209))) ((|#1|) . T)) ((($) . T)) ((($) . T)) @@ -1485,7 +1485,7 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) |has| |#1| (-912 (-560))) (((-391)) |has| |#1| (-912 (-391)))) -((((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#1|) . 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T)) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) -(((|#2| |#2|) -2210 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) +(((|#2| |#2|) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) (((|#2|) . T) (((-560)) . T)) ((((-888)) . T)) ((((-888)) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T) ((|#2|) . T)) ((((-888)) . T)) ((((-888)) . T)) ((((-1191) (-1209) (-560) (-229) (-888)) . T)) @@ -1559,9 +1559,9 @@ ((((-421 (-560))) . T) (($) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((($) . T) (((-421 (-560))) . T)) -(((|#2|) -2210 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) +(((|#2|) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1070 (-421 (-560)))) (((-560)) |has| #0# (-1070 (-560))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-1028 |#1|)) . T) ((|#1|) . T)) -((((-1209)) -2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-842 (-1209))) . T)) +((((-1209)) -2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-842 (-1209))) . T)) ((((-888)) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((((-421 (-560))) . T) (((-421 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1203 |#1|)) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1622,8 +1622,8 @@ (((|#1|) . T) (((-560)) . T) (($) . T)) (((|#2|) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) -((((-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#2|) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) @@ -1636,30 +1636,30 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1133)))) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) #0#) |has| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((#0=(-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) #0#) |has| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (-321 (-2 (|:| -1651 |#1|) (|:| -1871 |#2|))))) (((|#2| |#2|) . T)) -(-2210 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239)))) +(-2263 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239)))) (|has| |#2| (-376)) (((|#2|) . T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1|) |has| |#1| (-175))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -((($) -2210 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((($) -2263 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#1| (-1133)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-38 (-421 (-560)))) ((((-1191) (-51)) . T)) (((|#1|) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($ (-1209)) -2210 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209)))) (($ (-1114)) . T)) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940)))) +((($) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($ (-1209)) -2263 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209)))) (($ (-1114)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (((|#2|) |has| |#2| (-175))) (((|#2|) . T)) -((((-560)) -2210 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) ((|#2|) -2210 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1081))) (($) |has| |#2| (-1081))) +((((-560)) -2263 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) ((|#2|) -2263 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1081))) (($) |has| |#2| (-1081))) (((|#1|) . T)) ((((-560) |#3|) . T)) ((((-560) (-146)) . T)) @@ -1675,7 +1675,7 @@ ((((-560)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1|) . T)) -((($ (-1209)) -2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((((-146)) . T)) ((((-888)) . T)) @@ -1686,26 +1686,26 @@ (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#2|) . T)) -(-2210 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2263 (|has| |#2| (-240)) (|has| |#2| (-239))) ((((-560) (-146)) . T) (((-1266 (-560)) $) . T)) -(((#0=(-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) #0#) |has| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) -((($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) #0#) |has| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (-321 (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) +((($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#1| (-872)) (((|#2| (-793) (-1114)) . T)) (((|#1| |#2|) . T)) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209))))) (|has| |#1| (-814)) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-571))) -((((-1209)) -2210 (-12 (|has| (-1289 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-930 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-571))) +((((-1209)) -2263 (-12 (|has| (-1289 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-930 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (((|#1|) |has| |#1| (-175))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2210 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-2263 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-2210 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-2263 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1191) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1719,24 +1719,24 @@ (((|#3|) . T)) ((((-1289 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1207 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) ((((-888)) . T)) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-872)) (|has| |#1| (-1133))) (((|#1|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133))) (((-988 |#1|)) . T)) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133))) (((-988 |#1|)) . T)) (|has| |#1| (-871)) (|has| |#1| (-871)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-988 |#1|)) . T)) -(((|#4|) -2210 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) -(((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) +(((|#4|) -2263 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) +(((|#3|) -2263 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) (|has| |#2| (-376)) (((|#1|) |has| |#1| (-175))) -(((|#4|) -2210 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1081)))) -(((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081)))) +(((|#4|) -2263 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1081)))) +(((|#3|) -2263 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081)))) (((|#2|) |has| |#2| (-1081))) (((|#2|) |has| |#2| (-1081))) ((((-1191) |#1|) . T)) @@ -1748,8 +1748,8 @@ ((((-402) (-1191)) . T)) ((($ (-1209)) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-888)) -2210 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-888))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) (((-1299 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3837 (-1191)) (|:| -2715 #0#))) . T)) +((((-888)) -2263 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-888))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-817)) (|has| |#2| (-872)) (|has| |#2| (-1081)) (|has| |#2| (-1133))) (((-1299 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1651 (-1191)) (|:| -1871 #0#))) . T)) (((|#1|) . T)) ((((-888)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) @@ -1758,7 +1758,7 @@ ((((-560)) . T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-2210 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-2263 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) (|has| |#1| (-376)) ((((-888)) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -1769,8 +1769,8 @@ (|has| |#1| (-871)) ((((-888)) . T)) (((|#2|) . T)) -((((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2210 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2210 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2263 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2263 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T) (((-560)) . T) (((-843 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1779,8 +1779,8 @@ ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(((|#2| (-496 (-2327 |#1|) (-793)) (-889 |#1|)) . T)) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(((|#2| (-496 (-2140 |#1|) (-793)) (-889 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1209)) (-1209)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((((-1209) (-51)) . 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T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) (|has| |#1| (-872)) (|has| |#1| (-872)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-2210 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-940))) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . 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T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1|) . T)) -(-2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-871)) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1860,14 +1860,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((((-1209)) |has| |#1| (-928 (-1209))) (((-1114)) . T)) (((|#1|) . T)) (|has| |#1| (-871)) -(((#0=(-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) #0#) |has| (-2 (|:| -3837 (-1191)) (|:| -2715 (-51))) (-321 (-2 (|:| -3837 (-1191)) (|:| -2715 (-51)))))) +(((#0=(-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) #0#) |has| (-2 (|:| -1651 (-1191)) (|:| -1871 (-51))) (-321 (-2 (|:| -1651 (-1191)) (|:| -1871 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (|has| |#1| (-1133)) ((((-888)) . T) (((-1214)) . T)) @@ -1891,14 +1891,14 @@ (((|#3|) . T)) (((|#1| (-793) (-1114)) . T)) ((((-146)) . T)) -((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -2210 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -2263 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1917,31 +1917,31 @@ ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) (((|#2|) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2210 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2263 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) . T)) ((($) |has| |#1| (-871))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) (|has| |#1| (-940)) ((((-1209)) . T)) ((((-888)) . T)) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1289 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . 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T)) -(-2210 (|has| |#2| (-466)) (|has| |#2| (-940))) -(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((#0=(-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) #0#) |has| (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|)) (-321 (-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))))) -(-2210 (|has| |#1| (-466)) (|has| |#1| (-940))) +(-2263 (|has| |#2| (-466)) (|has| |#2| (-940))) +(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((#0=(-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) #0#) |has| (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|)) (-321 (-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))))) +(-2263 (|has| |#1| (-466)) (|has| |#1| (-940))) (((|#1|) . T)) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) @@ -1950,23 +1950,23 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)))) +(((|#3|) -2263 (|has| |#3| (-175)) (|has| |#3| (-376)))) (|has| |#1| (-872)) (|has| |#1| (-571)) ((((-595 |#1|)) . T)) ((($) . 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T)) +((((-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) ((((-694 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1975,7 +1975,7 @@ ((((-888)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-888)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) ((((-1214)) . T)) ((((-421 (-560))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T) (((-560)) . T)) (((|#3|) . T) (((-560)) . T) (((-630 $)) . T)) @@ -1983,12 +1983,12 @@ ((((-888)) . T)) ((((-888)) . T)) (((|#2|) . T)) -(-2210 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-381)) (|has| |#3| (-748)) (|has| |#3| (-817)) (|has| |#3| (-872)) (|has| |#3| (-1081)) (|has| |#3| (-1133))) +(-2263 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-381)) (|has| |#3| (-748)) (|has| |#3| (-817)) (|has| |#3| (-872)) (|has| |#3| (-1081)) (|has| |#3| (-1133))) (|has| |#2| (-1081)) ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . 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T)) ((($) |has| |#1| (-240))) @@ -2243,12 +2243,12 @@ (|has| |#1| (-147)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) |has| |#1| (-175))) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2263 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-560)) . T) ((|#1|) . T) (($) . T) (((-421 (-560))) . T) (((-1209)) |has| |#1| (-1070 (-1209)))) (((|#1| |#2|) . T)) -((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) -2210 (|has| |#1| (-871)) (|has| |#1| (-1070 (-560)))) ((|#1|) . 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T) (($ (-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (|has| |#1| (-940)) @@ -2273,7 +2273,7 @@ (((|#2|) |has| |#2| (-1081))) (|has| |#1| (-376)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) |has| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) |has| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (-321 (-2 (|:| -1651 |#1|) (|:| -1871 |#2|))))) (((|#1|) |has| |#1| (-175))) ((($ (-889 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2284,7 +2284,7 @@ (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-663 $)) . T) (((-1191)) . T) (((-1209)) . T) (((-560)) . T) (((-229)) . T) (((-888)) . T)) -((((-560)) -2210 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) ((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081))) +((((-560)) -2263 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) ((|#3|) -2263 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081))) ((((-421 (-560))) . T) (((-560)) . T) (((-630 $)) . T)) (((|#1|) . T)) ((((-888)) . T)) @@ -2300,7 +2300,7 @@ (((|#1| (-793) (-1114)) . T)) ((((-888)) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-560)) -2210 (|has| (-421 (-560)) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) . T)) +(((|#1|) . T) (((-560)) -2263 (|has| (-421 (-560)) (-1070 (-560))) (|has| |#1| (-1070 (-560)))) (((-421 (-560))) . T)) (((|#1| (-616 |#1| |#3|) (-616 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) @@ -2320,37 +2320,37 @@ ((((-721)) . T)) ((((-721)) . T)) (((|#2|) |has| |#2| (-175))) -(-2210 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2263 (|has| |#1| (-240)) (|has| |#1| (-239))) ((((-560)) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) -((((-114)) |has| |#1| (-1133)) (((-888)) -2210 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133)))) +((((-114)) |has| |#1| (-1133)) (((-888)) -2263 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) -((((-2 (|:| -3837 (-1191)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -1651 (-1191)) (|:| -1871 (-51)))) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) ((((-888)) . T)) -((((-1209)) -2210 (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))))) +((((-1209)) -2263 (-12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081))) (-12 (|has| |#2| (-930 (-1209))) (|has| |#2| (-1081))))) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) ((((-888)) . T)) ((((-721)) . T) (((-421 (-560))) . T) (((-560)) . T)) (((|#1| |#1|) |has| |#1| (-175))) (((|#2|) . T)) -((($) . T) (((-560)) . T) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-560)) . T) (((-421 (-560))) -2263 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-560) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) |has| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3837 |#1|) (|:| -2715 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) (((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) |has| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (-321 (-2 (|:| -1651 |#1|) (|:| -1871 |#2|))))) ((((-391)) . T)) ((((-721)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1|) |has| |#1| (-175))) ((((-421 (-976 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1081))) @@ -2362,7 +2362,7 @@ ((((-1209)) |has| |#2| (-928 (-1209)))) (|has| |#1| (-872)) ((((-888)) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (|has| |#1| (-814)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) -((($) -2210 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1081)) (|has| |#1| (-1144))) +((($) -2263 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2383,7 +2383,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-888)) . T)) (((|#2|) . T) (((-888)) . T)) -((($ (-1209)) -2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2393,18 +2393,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-872)) -((((-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) +((((-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) |has| (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3837 |#1|) (|:| -2715 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) |has| (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)) (-321 (-2 (|:| -1651 |#1|) (|:| -1871 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-2210 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2263 (-12 (|has| (-1289 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1289 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-872)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T)) @@ -2423,17 +2423,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-888)) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((($ $) . T) (((-630 $) $) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) ((($) . 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T)) -((((-1209)) -2210 (-12 (|has| |#3| (-928 (-1209))) (|has| |#3| (-1081))) (-12 (|has| |#3| (-930 (-1209))) (|has| |#3| (-1081))))) +((((-1209)) -2263 (-12 (|has| |#3| (-928 (-1209))) (|has| |#3| (-1081))) (-12 (|has| |#3| (-930 (-1209))) (|has| |#3| (-1081))))) ((((-663 (-802 |#1| (-889 |#2|)))) . T) (((-888)) . T)) ((((-549)) |has| (-802 |#1| (-889 |#2|)) (-633 (-549)))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -2442,17 +2442,17 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1133)))) (((|#1|) |has| |#1| (-175))) ((((-888)) . T)) -(-2210 (|has| |#2| (-466)) (|has| |#2| (-940))) +(-2263 (|has| |#2| (-466)) (|has| |#2| (-940))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) -2210 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,13 +2460,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1280 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2210 (|has| |#2| (-844)) (|has| |#2| (-872))) +(-2263 (|has| |#2| (-844)) (|has| |#2| (-872))) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1209)) -2210 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -2263 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T)) -(-2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-376)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1280 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560))))) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -(-2210 (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) +(-2263 (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081))) ((((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-888)) . T)) @@ -2832,7 +2832,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . T)) -((($ (-1209)) -2210 (-12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-930 (-1209)))))) +((($ (-1209)) -2263 (-12 (|has| |#1| (-376)) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-930 (-1209)))))) ((((-888)) . T)) (((|#1| (-545 (-1209))) . T)) ((($ $) . T)) @@ -2842,29 +2842,29 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) (((|#2|) . 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T) (((-560)) . T)) -((((-2 (|:| -3837 (-1191)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -1651 (-1191)) (|:| -1871 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((((-888)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-2210 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2263 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-871)) @@ -2880,7 +2880,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-186)) . T) (((-888)) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -2897,8 +2897,8 @@ (|has| |#1| (-872)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) -((($) -2210 (-12 (|has| (-1207 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1207 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) +((((-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) +((($) -2263 (-12 (|has| (-1207 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1207 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) ((((-888)) . T)) (((|#2|) |has| |#2| (-376))) ((((-888)) . T)) @@ -2913,19 +2913,19 @@ (|has| |#3| (-1081)) (|has| |#1| (-1133)) ((((-1209) (-51)) . T)) -(-2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2937,12 +2937,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (|has| |#1| (-844)) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-871)) -((((-1236 |#1|)) . T) (((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-1236 |#1|)) . T) (((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-936 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1081)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1081)))) @@ -2961,36 +2961,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . 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T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-363))) (((#0=(-421 (-560)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-376))) ((((-888)) . T)) (|has| |#1| (-1133)) (((|#1|) . T)) -(((|#1|) -2210 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) -(((|#1|) -2210 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2263 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2263 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) (((|#2|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-593)) . T)) (((|#3| |#3|) . T)) -((($ (-1209)) -2210 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -2263 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (|has| |#1| (-872)) (|has| |#2| (-240)) ((((-889 |#1|)) . T)) @@ -3011,10 +3011,10 @@ (|has| |#1| (-1133)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2210 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2263 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1052)) ((($) . T)) (|has| |#1| (-940)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-936 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . T)) -((($) -2210 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) |has| |#1| (-871)) (((-560)) -2210 (|has| |#1| (-21)) (|has| |#1| (-871)))) +((($) -2263 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) |has| |#1| (-871)) (((-560)) -2263 (|has| |#1| (-21)) (|has| |#1| (-871)))) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) -(-2210 (|has| |#1| (-381)) (|has| |#1| (-872))) +(-2263 (|has| |#1| (-381)) (|has| |#1| (-872))) (((|#1|) . T)) ((((-793)) . T)) ((((-888)) . T)) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-421 |#2|) |#3|) . T)) -(-2210 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) +(-2263 (-12 (|has| |#3| (-240)) (|has| |#3| (-1081))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1081)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-2327 |#1|) (-793))) . T)) +(((|#2| (-246 (-2140 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((((-1191)) . T) (((-888)) . T)) -(((#0=(-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) #0#) |has| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (-321 (-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))))) +(((#0=(-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) #0#) |has| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (-321 (-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))))) ((((-1191)) . T)) (|has| |#1| (-940)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-2210 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2263 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -3109,12 +3109,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2210 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-845))) ((((-888)) . T)) (|has| |#1| (-376)) -((((-1209)) -2210 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) +((((-1209)) -2263 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-928 (-1209)))))) (|has| |#1| (-376)) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-421 (-560))) . T) (($) . T)) @@ -3126,13 +3126,13 @@ ((((-560) |#1|) . T)) ((((-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T)) -(-2210 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2263 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2210 (|has| |#4| (-817)) (|has| |#4| (-872))) -(-2210 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-2263 (|has| |#4| (-817)) (|has| |#4| (-872))) +(-2263 (|has| |#3| (-817)) (|has| |#3| (-872))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3167,7 +3167,7 @@ (|has| |#1| (-872)) ((((-888)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3176,27 +3176,27 @@ (((|#3|) . T)) ((((-1191)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-2210 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2263 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1081)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) -((((-2 (|:| -3837 (-1191)) (|:| -2715 |#1|))) . T)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) +((((-2 (|:| -1651 (-1191)) (|:| -1871 |#1|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3212,7 +3212,7 @@ ((((-421 (-560))) |has| |#2| (-1070 (-560))) (((-560)) |has| |#2| (-1070 (-560))) (((-1209)) |has| |#2| (-1070 (-1209))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2210 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2263 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-888)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-1209)) -2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) +((((-1209)) -2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) (|has| |#1| (-814)) (|has| |#1| (-814)) ((((-888)) . T)) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-888)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-888)) . T)) ((((-888)) . T)) -(-2210 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) +(-2263 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081)))) (((#0=(-936 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-888)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1209)) -2210 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((((-1209)) -2263 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) ((((-888)) . T)) ((((-560)) . T)) -(-2210 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2263 (|has| |#2| (-817)) (|has| |#2| (-872))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-888)) . T)) ((((-888)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-888)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-2210 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-928 (-1209))) (|has| |#1| (-1081)) (|has| |#1| (-1144)) (|has| |#1| (-1133))) (|has| |#1| (-1184)) ((((-936 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-2210 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2263 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-888)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-888)) . T)) -((((-1209)) -2210 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -2263 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1209) |#1|) . T)) -(((|#1|) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1209)) . T)) -(((|#1|) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) +(((|#1|) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1081)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3315,15 +3315,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1133)) ((((-802 |#1| (-889 |#2|))) |has| (-802 |#1| (-889 |#2|)) (-321 (-802 |#1| (-889 |#2|))))) -(-2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3332,17 +3332,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1120 (-1209)))) . 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T) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) +((((-1157 |#1| (-1209))) . T) (((-560)) . T) (((-1120 (-1209))) . T) (($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1070 (-421 (-560))))) (((-1209)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1299 |#1|) (-1299 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3375,7 +3375,7 @@ ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-888)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2210 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2263 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-2210 (|has| |#2| (-817)) (|has| |#2| (-872))) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2263 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1209)) . T) ((|#1|) . T)) @@ -3419,15 +3419,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-2210 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) +(-2263 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1081))) (((|#1|) . T)) (((|#1|) . T)) -(-2210 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2263 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . 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T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) ((((-1114)) . T) ((|#2|) . T) (((-560)) |has| |#2| (-1070 (-560))) (((-421 (-560))) |has| |#2| (-1070 (-421 (-560))))) (((|#1|) . T)) @@ -3477,11 +3477,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-844)) (|has| |#2| (-844)) -((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) ((($ (-1209)) |has| |#1| (-928 (-1209)))) (((|#1|) . T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560))))) -((($) -2210 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) -(((|#1|) . T) (((-421 (-560))) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -2263 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) ((((-560)) |has| |#1| (-912 (-560))) (((-391)) |has| |#1| (-912 (-391)))) (((|#1|) . T)) @@ -3496,7 +3496,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-940))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1133)))) -(((|#2|) -2210 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2263 (|has| |#2| (-6 (-4512 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3510,12 +3510,12 @@ (((|#2| (-793)) . T)) ((((-1209)) . T)) ((((-894 |#1|)) . 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T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-888)) . T)) (|has| |#2| (-940)) -((((-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560))))) ((((-888)) . T)) ((((-888)) . T)) @@ -3553,7 +3553,7 @@ ((((-1203 |#1|)) . T) (((-888)) . T)) ((((-888)) . T)) ((((-421 (-560))) |has| |#2| (-1070 (-421 (-560)))) (((-560)) |has| |#2| (-1070 (-560))) ((|#2|) . T) (((-889 |#1|)) . T)) -((((-1209)) -2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-1114)) . T)) +((((-1209)) -2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209)))) (((-1114)) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-560)) |has| |#1| (-1070 (-560))) ((|#1|) . T) (((-1209)) . T)) ((((-888)) . T)) @@ -3573,10 +3573,10 @@ ((((-663 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((($) . T) (((-560)) . T) (((-1286 |#1| |#2| |#3| |#4|)) . T) (((-421 (-560))) . 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T)) @@ -3591,16 +3591,16 @@ ((((-421 |#2|) |#3|) . T)) (((|#1|) . T)) ((((-888)) . T)) -(-2210 (|has| |#1| (-102)) (|has| |#1| (-1133))) -(((|#2| (-496 (-2327 |#1|) (-793))) . T)) +(-2263 (|has| |#1| (-102)) (|has| |#1| (-1133))) +(((|#2| (-496 (-2140 |#1|) (-793))) . T)) ((((-560) |#1|) . T)) ((((-1191)) . T) (((-888)) . T)) (((|#2| |#2|) . T)) (((|#1| (-545 (-1209))) . T)) -(-2210 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) +(-2263 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-817)) (|has| |#2| (-1081))) ((((-560)) . T)) (((|#2|) . T)) -((($) -2210 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) +((($) -2263 (-12 (|has| |#2| (-240)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))))) (((|#2|) . T)) ((((-1209)) |has| |#1| (-928 (-1209))) (((-1114)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) @@ -3609,9 +3609,9 @@ ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . T)) -(-2210 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-872)) (|has| |#1| (-1133))) (((|#1|) . T)) -((($) -2210 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2263 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-888)) . T)) ((((-146)) . T)) (((|#1|) . T) (((-421 (-560))) . T)) @@ -3620,7 +3620,7 @@ ((((-888)) . T)) (((|#1|) . T)) (|has| |#1| (-1184)) -((($ (-1209)) -2210 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) +((($ (-1209)) -2263 (|has| (-421 |#2|) (-928 (-1209))) (|has| (-421 |#2|) (-930 (-1209))))) (((|#1|) . T)) (((|#1| (-545 (-889 |#2|)) (-889 |#2|) (-802 |#1| (-889 |#2|))) . T)) ((((-421 $) (-421 $)) |has| |#1| (-571)) (($ $) . T) ((|#1| |#1|) . T)) @@ -3645,44 +3645,44 @@ (|has| |#1| (-1133)) (|has| |#1| (-1133)) (|has| |#2| (-376)) -(((|#1|) . T) (($) -2210 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) +(((|#1|) . T) (($) -2263 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) (|has| |#1| (-376)) (|has| |#1| (-376)) -((($) -2210 (|has| |#2| (-240)) (|has| |#2| (-239)))) +((($) -2263 (|has| |#2| (-240)) (|has| |#2| (-239)))) ((((-560)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1133)) -((($ (-1209)) -2210 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((($ (-1209)) -2263 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) ((((-1209)) -12 (|has| |#4| (-928 (-1209))) (|has| |#4| (-1081)))) ((((-1209)) -12 (|has| |#3| (-928 (-1209))) (|has| |#3| (-1081)))) (((|#1|) . T)) (|has| |#1| (-240)) -(((|#2| (-246 (-2327 |#1|) (-793))) . T)) +(((|#2| (-246 (-2140 |#1|) (-793))) . 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T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2263 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((($) -2263 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) @@ -3724,11 +3724,11 @@ (((|#1|) . 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T)) ((((-888)) . T) (((-1214)) . T)) -((((-663 |#1|)) . T) (((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-663 |#1|)) . T) (((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-1214)) . T)) ((((-1214)) . T)) ((((-1214)) . T)) @@ -3752,19 +3752,19 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))) |has| (-2 (|:| -3837 (-1209)) (|:| -2715 (-51))) (-321 (-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))))) -(-2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +((((-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))) |has| (-2 (|:| -1651 (-1209)) (|:| -1871 (-51))) (-321 (-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))))) +(-2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) ((((-560) |#1|) . T)) ((((-560) |#1|) . T)) ((((-560) |#1|) . 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T) (((-560)) |has| |#1| (-1070 (-560))) (((-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) (((-1209)) . T)) ((($) . T)) @@ -3810,12 +3810,12 @@ (((#0=(-1286 |#1| |#2| |#3| |#4|)) |has| #0# (-321 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2| |#2|) |has| |#1| (-376)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -2210 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2210 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) +((($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2| |#2|) |has| |#1| (-376)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . T) (($ $) -2263 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2263 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) (|has| |#2| (-240)) (|has| $ (-149)) ((((-888)) . T)) -((($) . T) (((-421 (-560))) -2210 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) +((($) . T) (((-421 (-560))) -2263 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((((-888)) . T)) (|has| |#1| (-871)) ((((-130)) . T)) @@ -3823,7 +3823,7 @@ ((((-421 (-560))) . T) (((-721)) . T) (($) . T) (((-560)) . T)) (((|#1|) . T)) ((((-130)) . T)) -((($ (-1209)) -2210 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) +((($ (-1209)) -2263 (|has| |#1| (-928 (-1209))) (|has| |#1| (-930 (-1209))))) ((((-888)) . T)) (-12 (|has| |#1| (-319)) (|has| |#1| (-940))) (((|#2| (-694 |#1|)) . T)) @@ -3832,24 +3832,24 @@ ((((-888)) |has| |#1| (-1133))) (((|#4|) . 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T)) (((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-421 (-560))) . T) (($) . T)) @@ -3886,7 +3886,7 @@ ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) -(-2210 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2263 (|has| |#1| (-240)) (|has| |#1| (-239))) (((|#1|) . T) (((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) ((((-888)) . T)) @@ -3895,21 +3895,21 @@ ((((-657 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133)))) (((|#1| (-545 (-889 |#2|)) (-889 |#2|) (-802 |#1| (-889 |#2|))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((($) . 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T)) -((($) -2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#2| (-940)) (((|#1| |#2| (-246 |#1| |#2|) (-246 |#1| |#2|)) . T)) ((((-888)) . T)) @@ -3925,9 +3925,9 @@ (((|#1| |#1|) |has| |#1| (-175))) ((((-721)) . T)) ((((-721)) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-1214)) . T)) -(-2210 (|has| |#2| (-817)) (|has| |#2| (-872))) +(-2263 (|has| |#2| (-817)) (|has| |#2| (-872))) (((|#1|) |has| |#1| (-175))) ((((-1214)) . T)) (((|#1| |#1|) . T)) @@ -3940,19 +3940,19 @@ (((|#1| (-560)) . T)) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . T) (($) . 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T)) ((((-1209)) -12 (|has| |#2| (-928 (-1209))) (|has| |#2| (-1081)))) (|has| |#2| (-1081)) -(-2210 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-2263 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4010,7 +4010,7 @@ (((|#1| |#2|) . T)) ((((-560)) . T) ((|#2|) |has| |#2| (-175))) ((((-115)) . T) ((|#1|) . T) (((-560)) . T)) -(-2210 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2263 (|has| |#1| (-363)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) @@ -4019,11 +4019,11 @@ ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1133)) (((-560)) -12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133))) (((-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133)))) -(-2210 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2263 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-872)) (|has| |#1| (-1133)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-940)) @@ -4035,14 +4035,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1214)) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2210 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2263 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#2|) . T)) -(-2210 (|has| |#1| (-21)) (|has| |#1| (-871))) +(-2263 (|has| |#1| (-21)) (|has| |#1| (-871))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-888)) -2210 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) +((((-888)) -2263 (-12 (|has| |#1| (-632 (-888))) (|has| |#2| (-632 (-888)))) (-12 (|has| |#1| (-1133)) (|has| |#2| (-1133))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4051,7 +4051,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-2210 (|has| |#3| (-817)) (|has| |#3| (-872))) +(-2263 (|has| |#3| (-817)) (|has| |#3| (-872))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4067,7 +4067,7 @@ ((((-1214)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1209)) -2210 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) +((((-1209)) -2263 (-12 (|has| (-1207 |#1| |#2| |#3|) (-928 (-1209))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-928 (-1209)))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-928 (-1209))))) ((((-1209)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-928 (-1209))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1172 |#1| |#2|)) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) -((((-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) +((((-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1052)) -(((|#2|) . T) (((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) ((($) . T)) ((((-888)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-916 (-560))) |has| |#2| (-633 (-916 (-560)))) (((-916 (-391))) |has| |#2| (-633 (-916 (-391)))) (((-391)) . #0=(|has| |#2| (-1052))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1209)) -2210 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) +((((-1209)) -2263 (|has| |#2| (-928 (-1209))) (|has| |#2| (-930 (-1209))))) ((((-888)) . T)) (((|#2|) . T)) ((((-888)) . T)) @@ -4106,15 +4106,15 @@ ((((-1207 |#1| |#2| |#3|)) . T)) ((((-1207 |#1| |#2| |#3|)) . T) (((-1200 |#1| |#2| |#3|)) . T)) ((((-888)) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T)) ((((-1207 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2210 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) -(((|#2|) . T) ((|#3|) -2210 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2263 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1081))) (($) |has| |#4| (-1081)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1081)))) +(((|#2|) . T) ((|#3|) -2263 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1081))) (($) |has| |#3| (-1081)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1081)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4128,7 +4128,7 @@ ((((-186)) . T) (((-888)) . T)) ((((-888)) . T)) (((|#1|) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) ((((-560) |#1|) . T) (((-1266 (-560)) $) . T)) ((((-888)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-2210 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) +(-2263 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-940))) ((($ (-1209)) |has| |#1| (-1081))) -(-2210 (|has| |#1| (-872)) (|has| |#1| (-1133))) +(-2263 (|has| |#1| (-872)) (|has| |#1| (-1133))) ((((-888)) . T)) ((((-888)) . T)) ((((-888)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -3837 (-1209)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -1651 (-1209)) (|:| -1871 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4158,8 +4158,8 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) -(-2210 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) -(-2210 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) +(-2263 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-940))) +(-2263 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-940))) ((($) . T)) (((|#2| (-545 (-889 |#1|))) . T)) ((((-1214)) . T)) @@ -4174,7 +4174,7 @@ ((((-1214)) . T)) ((((-888)) . T) (((-1214)) . T)) ((((-1214)) . T)) -((((-888)) -2210 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) +((((-888)) -2263 (|has| |#1| (-632 (-888))) (|has| |#1| (-1133)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1191) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -3837 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -1651 |#1|) (|:| -1871 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4192,14 +4192,14 @@ ((((-560)) . T) (($) . 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-1249) T) ((-534 . -1249) T) ((-1200 . -351) 199571) ((-1173 . -503) 199542) ((-1200 . -390) 199494) ((-1119 . -1089) T) ((-450 . -102) T) ((-187 . -1133) T) ((-260 . -34) T) ((-259 . -34) T) ((-1191 . -875) T) ((-873 . -635) 199478) ((-803 . -1089) T) ((-802 . -1089) T) ((-753 . -928) 199455) ((-468 . -1089) T) ((-58 . -503) 199439) ((-1066 . -1088) 199413) ((-533 . -503) 199397) ((-530 . -503) 199381) ((-511 . -503) 199365) ((-510 . -503) 199349) ((-252 . -528) 199282) ((-1066 . -111) 199249) ((-1207 . -928) 199162) ((-1206 . -928) 199068) ((-692 . -1144) T) ((-1200 . -928) 198901) ((-667 . -93) T) ((-1158 . -928) 198885) ((-353 . -1184) T) ((-334 . -1088) 198867) ((-31 . -504) 198848) ((-260 . -818) 198827) ((-260 . -817) 198806) ((-259 . -818) 198785) ((-259 . -817) 198764) ((-31 . -632) 198730) ((-50 . -1089) T) ((-260 . -748) 198708) ((-259 . -748) 198686) ((-1242 . -1133) T) ((-692 . -23) T) ((-595 . -1089) T) ((-532 . -1089) T) ((-391 . -1088) 198651) ((-334 . -111) 198626) 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196913) ((-1203 . -670) 196802) ((-1157 . -670) 196691) ((-879 . -670) 196665) ((-740 . -632) 196647) ((-561 . -381) T) ((-1321 . -23) T) ((-716 . -930) NIL) ((-1320 . -23) T) ((-505 . -1133) T) ((-391 . -635) 196597) ((-391 . -637) 196579) ((-1066 . -1081) T) ((-890 . -102) T) ((-1221 . -298) 196558) ((-171 . -381) 196509) ((-1036 . -1249) T) ((-1003 . -1249) T) ((-944 . -1249) T) ((-858 . -635) 196463) ((-852 . -635) 196418) ((-44 . -23) T) ((-1329 . -102) T) ((-493 . -298) 196397) ((-597 . -1133) T) ((-1178 . -1141) 196366) ((-443 . -1249) T) ((-1135 . -1136) 196318) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1144) T) ((-1242 . -739) 196215) ((-1229 . -1133) T) ((-1036 . -910) 196197) ((-1036 . -912) 196179) ((-642 . -234) 196163) ((-642 . -274) 196147) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1036 . -1070) 196107) ((-733 . -739) 196072) ((-246 . -390) 196041) ((-391 . -1081) T) ((-227 . -1089) T) ((-119 . -274) 196018) ((-119 . -234) 195995) ((-58 . -298) 195947) 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T) ((-530 . -19) 194521) ((-510 . -19) 194505) ((-58 . -618) 194482) ((-1035 . -239) 194419) ((-931 . -102) 194369) ((-879 . -748) T) ((-803 . -1133) T) ((-530 . -618) 194346) ((-510 . -618) 194323) ((-802 . -1133) T) ((-802 . -1097) 194290) ((-475 . -1133) T) ((-468 . -1133) T) ((-597 . -739) 194265) ((-671 . -1133) T) ((-1289 . -47) 194242) ((-1286 . -102) T) ((-1280 . -47) 194212) ((-1259 . -47) 194189) ((-1242 . -175) 194140) ((-1206 . -319) 194119) ((-1200 . -319) 194098) ((-1128 . -635) 194079) ((-1123 . -635) 194060) ((-1111 . -571) 194011) ((-1111 . -1254) 193962) ((-1105 . -635) 193943) ((-1036 . -928) NIL) ((-1098 . -635) 193924) ((-692 . -133) T) ((-646 . -1144) T) ((-1068 . -635) 193905) ((-1051 . -635) 193886) ((-736 . -1088) 193856) ((-734 . -922) 193759) ((-721 . -668) 193709) ((-286 . -1133) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1088) 193693) ((-50 . -1133) T) ((-609 . -47) 193670) ((-229 . -670) 193635) ((-595 . -1133) T) ((-532 . -1133) T) 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T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1173 . -632) 190662) ((-1152 . -662) 190649) ((-1152 . -1083) 190636) ((-843 . -748) T) ((-843 . -882) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-936 . -632) 190487) ((-936 . -633) 190469) ((-400 . -748) T) ((-897 . -1088) 190421) ((-897 . -111) 190359) ((-736 . -1081) T) ((-734 . -1275) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -821) T) ((-170 . -1249) T) ((-227 . -1133) T) ((-391 . -816) T) ((-58 . -633) 190236) ((-229 . -818) T) ((-229 . -814) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1111 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1249) T) ((-896 . -940) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1249) T) ((-661 . -1133) T) ((-1259 . -351) 189637) ((-896 . -670) 189582) ((-1259 . -390) 189534) ((-994 . -133) 189389) ((-839 . -133) 189260) ((-45 . -875) NIL) ((-988 . -673) 189244) ((-1258 . -684) T) ((-1119 . -175) 189155) ((-988 . -385) 189139) ((-1094 . -818) T) ((-1094 . -814) T) ((-897 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-840 . -47) 188801) ((-1094 . -748) T) ((-339 . -503) 188785) ((-976 . -748) T) ((-1313 . -321) 188723) ((-1289 . -928) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1285 . -1088) 188334) ((-1280 . -928) 188240) ((-1264 . -1088) 188048) ((-495 . -748) T) ((-1259 . -928) 187881) 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186944) ((-1264 . -111) 186733) ((-252 . -1288) 186717) ((-560 . -871) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1036 . -1052) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1083) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1133) T) ((-678 . -662) 186541) ((-1286 . -38) 186433) ((-1268 . -940) 186412) ((-114 . -1133) T) ((-840 . -1249) T) ((-427 . -1249) T) ((-1067 . -102) T) ((-1268 . -670) 186301) ((-896 . -818) NIL) ((-880 . -670) 186275) ((-896 . -814) NIL) ((-840 . -912) NIL) ((-896 . -748) T) ((-1119 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-840 . -1070) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1285 . -635) 185618) ((-1264 . -635) 185366) ((-60 . -1249) T) ((-638 . -872) 185345) ((-514 . -684) T) ((-1178 . -1008) 185314) ((-1056 . -668) 185251) ((-1035 . -466) T) ((-721 . -871) T) ((-525 . -816) T) 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-1133) T) ((-919 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-880 . -748) T) ((-119 . -871) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1067 . -321) 183173) ((-901 . -504) 183154) ((-901 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1180 . -34) T) ((-973 . -1249) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1209 . -635) 182524) ((-343 . -1249) T) ((-488 . -1081) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1152 . -1184) T) ((-1280 . -319) 182433) ((-734 . -1083) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1259 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1249) T) ((-734 . -662) 181995) ((-1259 . -1052) NIL) ((-1111 . -133) T) ((-897 . -821) 181974) ((-146 . -102) T) ((-40 . -1133) T) ((-897 . -816) 181953) ((-663 . -1042) 181937) ((-594 . -1089) T) ((-560 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1214 . -1133) T) ((-1152 . -38) 181869) ((-1121 . -632) 181836) ((-108 . -133) T) ((-984 . -1133) T) ((-949 . -1133) T) ((-793 . -1133) T) ((-694 . -1133) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1321 . -21) T) ((-1321 . -25) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-686 . -1088) 181820) ((-545 . -872) T) ((-514 . -872) T) ((-377 . -1249) T) ((-368 . -1088) 181772) ((-366 . -1088) 181724) ((-358 . -1088) 181676) ((-260 . -1249) T) ((-259 . -1249) T) ((-275 . -1088) 181519) ((-255 . -1088) 181362) ((-686 . -111) 181341) ((-841 . -1254) 181320) ((-562 . -868) T) ((-326 . -930) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -930) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-932 . -875) 180693) ((-130 . -684) T) ((-839 . -660) 180599) ((-841 . -571) 180578) ((-501 . -875) T) ((-260 . -1070) 180405) ((-259 . -1070) 180232) ((-128 . -121) 180216) ((-221 . -875) T) ((-936 . -1088) 180181) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-936 . -111) 179984) ((-40 . -739) 179929) ((-894 . -1133) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1133) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1249) T) ((-1264 . -816) 179062) ((-1264 . -821) 179015) ((-260 . -390) 178984) ((-259 . -390) 178953) ((-564 . -875) T) ((-678 . -38) 178923) ((-627 . -34) T) ((-496 . -1144) 178901) ((-489 . -34) T) ((-1145 . -133) 178772) ((-994 . -25) 178583) ((-936 . -635) 178533) ((-899 . -632) 178515) ((-218 . -868) T) ((-994 . -21) 178470) ((-839 . -25) 178303) ((-839 . -21) 178214) ((-1256 . -381) T) ((-642 . -1089) T) ((-1211 . -571) 178193) ((-1203 . -47) 178170) ((-368 . -1081) T) ((-366 . -1081) T) ((-496 . -23) 178022) ((-358 . -1081) T) ((-275 . -1081) T) ((-255 . -1081) T) ((-1157 . -47) 177994) ((-119 . -1089) T) ((-1066 . -670) 177968) ((-988 . -34) T) ((-368 . -240) 177947) ((-368 . -250) T) ((-366 . -240) 177926) ((-366 . -250) T) ((-358 . -240) 177905) ((-358 . -250) T) ((-275 . -338) 177877) ((-255 . -338) 177834) ((-275 . -240) 177813) ((-1187 . -153) 177797) ((-260 . -928) 177729) ((-259 . -928) 177661) ((-1174 . -922) 177582) ((-1114 . -872) T) ((-1266 . -1249) 177560) ((-429 . -1144) T) ((-1242 . -1034) 177526) ((-1086 . -23) T) ((-1056 . -871) T) ((-936 . -1081) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1206 . -951) 177432) ((-1200 . -951) 177411) ((-1200 . -844) NIL) ((-1028 . -1083) 177307) ((-997 . -1249) T) ((-936 . -250) T) ((-841 . -376) 177286) ((-218 . -1133) T) ((-394 . -23) T) ((-129 . -1133) 177264) ((-123 . -1133) 177242) ((-936 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1028 . -662) 177155) ((-894 . -739) 177142) ((-1329 . -668) 177114) ((-1078 . -153) 177079) ((-1025 . -1249) T) ((-888 . -1249) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-858 . -670) 177008) ((-852 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1133) T) ((-560 . -1133) T) ((-509 . -1133) T) ((-1203 . -1249) T) ((-252 . -300) 176938) ((-1157 . -1249) T) ((-879 . -1249) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1255 . -875) T) ((-1203 . -912) NIL) ((-55 . -1133) T) ((-1157 . -912) 176719) ((-130 . -872) T) ((-1203 . -1070) 176599) ((-1157 . -1070) 176482) ((-187 . -632) 176464) ((-879 . -1070) 176360) ((-803 . -298) 176287) ((-841 . -1144) T) ((-1066 . -748) T) ((-1078 . -1008) 176216) ((-616 . -673) 176200) ((-1035 . -922) 176107) ((-1028 . -102) T) ((-841 . -23) T) ((-734 . -1184) 176085) ((-716 . -1089) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1302 . -1133) T) ((-256 . -1133) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1133) T) ((-721 . -1133) T) ((-374 . -487) T) ((-1242 . -632) 176051) ((-1203 . -390) 176035) ((-1157 . -390) 176019) ((-1056 . -426) 175981) ((-143 . -233) 175963) ((-391 . -818) T) ((-391 . -814) T) ((-894 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1299 . -1298) 175758) ((-365 . -416) T) ((-1299 . -1133) 175708) ((-1223 . -1133) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1286 . -668) 175537) ((-326 . -649) 175516) ((-858 . -748) T) 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T) ((-901 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1254) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1254) T) ((-421 . -922) 174525) ((-229 . -1070) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1094 . -1249) T) ((-976 . -1249) T) ((-735 . -1249) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1249) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1129 . -107) 173800) ((-1094 . -912) 173782) ((-976 . -912) 173707) ((-677 . -1144) T) ((-642 . -739) 173694) ((-495 . -912) NIL) ((-1178 . -102) T) ((-1121 . -637) 173678) ((-1094 . -1070) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-976 . -1070) 173522) ((-119 . -739) 173467) ((-734 . -930) 173374) ((-677 . -23) T) ((-495 . -1070) 173250) ((-1119 . -633) NIL) ((-1119 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1145 . -660) 172647) ((-822 . -875) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1067 . -233) 172397) ((-897 . -940) 172376) ((-128 . -34) T) ((-841 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1318) 172342) ((-366 . -1318) 172326) ((-358 . -1318) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -816) T) ((-526 . -821) T) ((-525 . -818) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1133) T) ((-897 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-976 . -390) 171946) ((-894 . -302) T) ((-50 . -632) 171928) ((-1152 . -668) 171900) ((-1028 . -38) 171848) ((-626 . -1133) T) ((-621 . -1133) T) ((-595 . -632) 171830) ((-495 . -390) 171814) ((-595 . -633) 171796) ((-532 . -632) 171778) ((-936 . -1318) 171765) ((-896 . -1249) T) ((-723 . -466) T) ((-509 . -528) 171731) ((-1311 . -1249) T) ((-1310 . -1249) T) ((-501 . -376) T) ((-368 . -381) 171710) ((-366 . -381) 171689) ((-358 . -381) 171668) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1323 . -1314) 171652) ((-896 . -910) 171629) ((-896 . -912) NIL) ((-994 . -872) 171528) ((-839 . -872) 171479) ((-1257 . -102) T) ((-678 . -680) 171463) ((-1236 . -34) T) ((-174 . -632) 171445) ((-1145 . -25) 171278) ((-1145 . -21) 171189) ((-896 . -1070) 171166) ((-976 . -928) 171147) ((-1268 . -47) 171124) ((-936 . -381) T) ((-607 . -875) T) ((-58 . -673) 171108) ((-530 . -673) 171092) ((-495 . -928) 171069) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171053) ((-58 . -385) 171037) ((-642 . -175) T) ((-530 . -385) 171021) ((-510 . -385) 171005) ((-561 . -1249) T) 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169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1324 . -1319) 169581) ((-699 . -1070) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1268 . -1249) T) ((-137 . -484) 169520) ((-880 . -1249) T) ((-678 . -668) 169479) ((-48 . -1133) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-896 . -928) NIL) ((-585 . -1249) T) ((-1268 . -912) NIL) ((-914 . -102) T) ((-911 . -102) T) ((-661 . -632) 169429) ((-402 . -1133) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1268 . -1070) 169277) ((-880 . -1070) 169173) ((-1174 . -102) T) ((-1028 . -930) 169096) ((-677 . -133) T) ((-674 . -816) 169075) ((-674 . -821) 169054) ((-119 . -528) 168962) ((-585 . -1070) 168944) ((-305 . -1307) 168914) ((-1200 . -875) NIL) ((-891 . -102) T) ((-986 . -571) 168893) ((-1242 . -1088) 168776) ((-1035 . -1083) 168721) ((-496 . -660) 168627) ((-935 . -1133) T) ((-1056 . -739) 168564) ((-733 . -1088) 168529) ((-1035 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1180 . -1249) T) ((-1242 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -928) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1329 . -1089) T) ((-1268 . -390) 168084) ((-419 . -1254) 168062) ((-1147 . -632) 168044) ((-325 . -871) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1264 . -814) 167997) ((-1264 . -818) 167950) ((-1285 . -748) T) ((-1264 . -748) T) ((-48 . -739) 167915) ((-229 . -1052) T) ((-1286 . -426) 167881) ((-1268 . -928) 167824) ((-365 . -1307) 167801) ((-1242 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -875) 167644) ((-1145 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1323 . -1083) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1323 . -662) 167115) ((-642 . -302) T) ((-597 . -1088) 167090) 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-1249) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1323 . -102) T) ((-1231 . -1249) T) ((-1229 . -635) 166423) ((-1120 . -1249) T) ((-1119 . -1088) 166266) ((-1107 . -1249) T) ((-275 . -940) 166245) ((-255 . -940) 166224) ((-803 . -1088) 166047) ((-802 . -1088) 165890) ((-627 . -1249) T) ((-1197 . -632) 165872) ((-1119 . -111) 165701) ((-1078 . -102) T) ((-489 . -1249) T) ((-475 . -1088) 165672) ((-468 . -1088) 165515) ((-686 . -670) 165499) ((-896 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1191 . -872) T) ((-1120 . -1070) 164755) ((-1107 . -1070) 164732) ((-1036 . -875) T) ((-1032 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1003 . -875) T) ((-996 . -632) 164504) ((-988 . -1249) T) ((-986 . -1144) T) ((-128 . -1042) 164488) ((-873 . -1249) T) ((-896 . -1052) NIL) ((-757 . -1144) T) ((-737 . -1144) T) ((-676 . -635) 164406) ((-1299 . -503) 164390) ((-1217 . -1249) T) ((-1216 . -1249) T) ((-1174 . -38) 164350) ((-986 . -23) T) ((-936 . -670) 164315) ((-890 . -1133) T) ((-866 . -102) T) ((-841 . -21) T) ((-652 . -1083) 164299) ((-620 . -1083) 164283) ((-841 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1088) 164216) ((-532 . -1088) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1215 . -1249) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-891 . -38) 164089) ((-1119 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1144) T) ((-326 . -1089) 163600) ((-325 . -1089) T) ((-132 . -1249) T) ((-131 . -1249) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1081) T) ((-1329 . -1133) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1023) 162778) ((-118 . -895) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) ((-1236 . -1042) 162696) ((-1214 . -632) 162663) ((-1221 . -34) T) ((-984 . -632) 162629) ((-949 . -632) 162611) ((-1145 . -872) 162562) ((-793 . -632) 162544) ((-694 . -632) 162526) ((-531 . -1249) T) ((-1268 . -319) 162505) ((-1187 . -321) 162443) ((-1173 . -34) T) ((-493 . -34) T) ((-1124 . -1249) T) ((-491 . -466) T) ((-1066 . -1249) T) ((-1119 . -1081) T) ((-50 . -635) 162412) ((-803 . -1081) T) ((-802 . -1081) T) ((-669 . -242) 162396) ((-651 . -242) 162342) ((-1211 . -21) T) ((-595 . -635) 162292) ((-532 . -635) 162222) ((-496 . -236) 162113) ((-1211 . -25) T) ((-1119 . -338) 162074) ((-468 . -1081) T) ((-1119 . -240) 162053) ((-803 . -338) 162030) ((-803 . -240) T) ((-802 . -338) 162002) ((-753 . -1254) 161981) ((-533 . -34) T) ((-339 . -673) 161965) ((-530 . -34) T) ((-58 . -34) T) ((-511 . -34) T) ((-510 . -34) T) ((-468 . -338) 161944) ((-339 . -385) 161928) ((-374 . -1249) T) ((-334 . -1249) T) ((-1035 . -1184) NIL) ((-753 . -571) 161859) ((-652 . -102) T) ((-620 . -102) T) 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-1133) T) ((-421 . -321) 161010) ((-1174 . -930) 160933) ((-894 . -632) 160915) ((-858 . -1070) 160884) ((-661 . -1088) 160868) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160850) ((-509 . -1034) T) ((-285 . -863) T) ((-284 . -863) T) ((-283 . -863) T) ((-282 . -863) T) ((-48 . -302) T) ((-281 . -863) T) ((-280 . -863) T) ((-279 . -863) T) ((-196 . -809) T) ((-661 . -111) 160829) ((-630 . -872) T) ((-678 . -426) 160813) ((-692 . -239) 160764) ((-227 . -635) 160726) ((-110 . -872) T) ((-677 . -21) T) ((-677 . -25) T) ((-1323 . -38) 160696) ((-119 . -298) 160647) ((-1299 . -19) 160631) ((-1259 . -875) NIL) ((-1299 . -618) 160608) ((-1313 . -1133) T) ((-365 . -1083) 160553) ((-1109 . -1133) T) ((-1018 . -1133) T) ((-986 . -133) T) ((-841 . -236) 160540) ((-758 . -1133) T) ((-365 . -662) 160485) ((-757 . -133) T) ((-737 . -133) T) ((-526 . 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. -1083) 148993) ((-1200 . -660) 148945) ((-491 . -662) 148910) ((-663 . -875) 148889) ((-499 . -25) T) ((-499 . -21) T) ((-1264 . -1052) 148841) ((-1090 . -1249) T) ((-1 . -1249) T) ((-642 . -1081) T) ((-391 . -418) T) ((-404 . -102) T) ((-1137 . -637) 148756) ((-275 . -928) 148702) ((-255 . -928) 148679) ((-119 . -1081) T) ((-1119 . -748) T) ((-840 . -1144) T) ((-843 . -875) T) ((-642 . -240) 148658) ((-638 . -102) T) ((-526 . -1249) T) ((-521 . -1249) T) ((-803 . -748) T) ((-802 . -748) T) ((-1255 . -872) T) ((-427 . -1144) T) ((-119 . -250) T) ((-40 . -381) NIL) ((-119 . -240) NIL) ((-400 . -875) 148637) ((-468 . -748) T) ((-840 . -23) T) ((-753 . -25) T) ((-753 . -21) T) ((-692 . -922) 148558) ((-1109 . -298) 148537) ((-75 . -411) T) ((-75 . -410) T) ((-547 . -789) 148519) ((-229 . -875) T) ((-716 . -1088) 148469) ((-1325 . -102) T) ((-1289 . -133) T) ((-1280 . -133) T) ((-1259 . -133) T) ((-1207 . -25) T) ((-1174 . -426) 148453) ((-652 . -380) 148385) ((-620 . -380) 148317) 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-1133) 146013) ((-1257 . -868) T) ((-331 . -1005) 145975) ((-105 . -102) T) ((-48 . -1088) 145940) ((-896 . -875) NIL) ((-1324 . -102) T) ((-395 . -102) T) ((-1286 . -632) 145922) ((-1165 . -1166) 145906) ((-1036 . -660) 145888) ((-901 . -1249) T) ((-48 . -111) 145844) ((-703 . -1249) T) ((-698 . -1249) T) ((-674 . -1249) T) ((-839 . -922) 145711) ((-492 . -1249) T) ((-252 . -1249) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1307) 145695) ((-140 . -1249) T) ((-139 . -1249) T) ((-135 . -1249) T) ((-1250 . -102) T) ((-1056 . -635) 145632) ((-841 . -239) T) ((-1203 . -1254) 145611) ((-218 . -381) T) ((-353 . -635) 145541) ((-1157 . -1254) 145520) ((-246 . -25) 145353) ((-246 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1203 . -571) 145127) ((-1157 . -571) 145058) ((-1257 . -1133) T) ((-561 . -875) T) ((-1067 . -298) 145033) ((-1199 . -1115) T) ((-1026 . -1115) T) ((-840 . -133) T) ((-119 . -821) NIL) ((-119 . -816) NIL) ((-368 . -319) T) 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143042) ((-1221 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1226) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1152 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1152 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1259 . -660) 142704) ((-493 . -107) 142654) ((-1025 . -23) T) ((-1324 . -38) 142624) ((-1203 . -1144) T) ((-1157 . -1144) T) ((-1094 . -1254) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-879 . -1144) T) ((-976 . -1254) 142494) ((-495 . -1254) 142473) ((-1094 . -571) T) ((-976 . -571) 142404) ((-1203 . -23) T) ((-1185 . -1115) T) ((-1157 . -23) T) ((-879 . -23) T) ((-495 . -571) 142335) ((-1174 . -739) 142267) ((-692 . -1083) 142251) ((-1178 . -528) 142184) ((-692 . -662) 142168) ((-1067 . -633) NIL) ((-1067 . -632) 142150) ((-96 . -1115) T) ((-1329 . -1088) 142137) ((-891 . -739) 142107) ((-1329 . -111) 142092) ((-1242 . -47) 142061) ((-1200 . -872) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1135 . -1133) T) ((-1035 . -1133) T) ((-63 . -632) 142043) ((-1111 . -922) 141912) ((-1056 . -816) T) ((-1056 . -821) T) ((-1289 . -25) T) ((-1289 . -21) T) ((-1280 . -21) T) ((-1280 . -25) T) ((-894 . -670) 141899) ((-1259 . -21) T) ((-1259 . -25) T) ((-1059 . -153) 141883) ((-1036 . -236) 141870) ((-897 . -844) 141849) ((-897 . -951) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -922) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1249) T) ((-949 . -818) T) ((-949 . -748) T) ((-793 . -817) T) ((-793 . -818) T) ((-520 . -1133) T) ((-516 . -1133) T) ((-793 . -748) T) ((-229 . -376) T) ((-1321 . -1083) 141537) ((-1320 . -1083) 141521) ((-1321 . -662) 141491) ((-1187 . -1133) 141469) ((-896 . -1254) T) ((-1320 . -662) 141439) ((-1120 . -875) T) ((-678 . -632) 141421) ((-896 . -571) T) ((-716 . -381) NIL) ((-44 . -1083) 141405) ((-1329 . -635) 141387) ((-1323 . -1133) T) ((-692 . -102) T) ((-372 . -1307) 141371) ((-367 . -1307) 141355) ((-44 . -662) 141339) ((-359 . -1307) 141323) ((-563 . -102) T) ((-1242 . -1249) T) ((-534 . -872) 141302) ((-733 . -1249) T) ((-988 . -875) 141281) ((-873 . -875) T) ((-501 . -239) T) ((-221 . -239) T) ((-1078 . -1133) T) ((-841 . -466) 141260) ((-154 . -1083) 141244) ((-1078 . -1103) 141173) ((-1059 . -1008) 141142) ((-843 . -1144) T) ((-1035 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1144) T) ((-490 . -1008) 141040) ((-477 . -1008) 141009) ((-1216 . -875) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-919 . -632) 140955) ((-1215 . -875) T) ((-1111 . -746) 140934) ((-1329 . -1081) T) ((-840 . -660) 140882) ((-305 . -1089) 140824) ((-171 . -1254) 140729) ((-229 . -1144) T) ((-336 . -23) T) ((-1200 . -1023) 140681) ((-1286 . -1088) 140586) ((-866 . -1133) T) ((-131 . -875) T) ((-1158 . -762) 140565) ((-1285 . -951) 140544) ((-1264 . -951) 140523) ((-894 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1133) T) ((-270 . -1133) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1264 . -844) 140278) ((-1321 . -102) T) ((-505 . -1249) T) ((-353 . -1318) 140255) ((-1320 . -102) T) ((-1286 . -111) 140147) ((-1145 . -922) 140014) ((-839 . -1083) 139915) ((-839 . -662) 139837) ((-146 . -632) 139819) ((-1025 . -133) T) ((-44 . -102) T) ((-246 . -872) 139770) ((-597 . -1249) T) ((-1268 . -1254) 139749) ((-103 . -503) 139733) ((-1323 . -739) 139703) ((-1119 . -47) 139664) ((-1094 . -1144) T) ((-976 . -1144) T) ((-129 . -34) T) ((-123 . -34) T) ((-1268 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1229 . -1249) T) ((-1203 . -133) T) ((-353 . -381) T) ((-495 . -1144) T) ((-1157 . -133) T) ((-896 . -376) T) ((-468 . -47) 139503) ((-879 . -133) T) ((-334 . -875) 139482) ((-154 . -102) T) ((-1094 . -23) T) ((-976 . -23) T) ((-585 . -571) T) ((-840 . -25) T) ((-840 . -21) T) 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137363) ((-1119 . -1249) T) ((-1067 . -300) 137338) ((-594 . -748) T) ((-560 . -818) T) ((-171 . -376) 137289) ((-560 . -814) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1249) T) ((-802 . -1249) T) ((-1178 . -503) 137273) ((-475 . -1249) T) ((-468 . -1249) T) ((-1321 . -1322) 137249) ((-1119 . -912) NIL) ((-896 . -1144) T) ((-119 . -940) NIL) ((-1320 . -1322) 137228) ((-671 . -1249) T) ((-803 . -912) NIL) ((-802 . -912) 137087) ((-1315 . -25) T) ((-1315 . -21) T) ((-1247 . -102) 137065) ((-1138 . -410) T) ((-642 . -670) 137052) ((-468 . -912) NIL) ((-697 . -102) 137002) ((-1119 . -1070) 136829) ((-896 . -23) T) ((-803 . -1070) 136688) ((-802 . -1070) 136545) ((-119 . -670) 136490) ((-468 . -1070) 136366) ((-286 . -1249) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1249) T) ((-404 . -668) 135782) ((-671 . -1070) 135766) ((-646 . -102) T) ((-595 . -1249) T) ((-532 . -1249) T) ((-226 . -503) 135750) ((-1299 . -34) T) ((-638 . -668) 135709) ((-301 . -1083) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1152 . -1088) 135582) ((-86 . -632) 135564) ((-50 . -1070) 135548) ((-1119 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -818) T) ((-721 . -814) T) ((-60 . -57) 135478) ((-595 . -1070) 135465) ((-532 . -1070) 135442) ((-174 . -1249) T) ((-336 . -133) T) ((-326 . -1081) 135332) ((-325 . -1081) T) ((-171 . -1144) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1036 . -1023) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1133) 134993) ((-229 . -133) T) ((-1152 . -111) 134978) ((-171 . -23) T) ((-822 . -149) 134957) ((-822 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1187 . -528) 134647) ((-491 . -668) 134597) ((-657 . -868) T) ((-496 . -922) 134464) ((-1165 . -1133) T) ((-229 . -1092) T) ((-839 . -321) 134402) ((-1119 . -928) 134337) ((-803 . -928) 134280) ((-802 . -928) 134264) ((-1321 . -38) 134234) ((-1320 . -38) 134204) ((-1268 . -1144) T) ((-880 . -1144) T) ((-468 . -928) 134181) ((-883 . -1133) T) ((-1268 . -23) T) ((-1152 . -635) 134153) ((-1094 . -133) T) ((-880 . -23) T) ((-585 . -1144) T) ((-642 . -748) T) ((-525 . -875) T) ((-368 . -951) T) ((-366 . -951) T) ((-301 . -102) T) ((-358 . -951) T) ((-1002 . -1115) T) ((-976 . -133) T) ((-840 . -236) 134098) ((-119 . -818) NIL) ((-119 . -814) NIL) ((-119 . -748) T) ((-1078 . -528) 133999) ((-716 . -940) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1249) T) ((-657 . -1133) T) ((-652 . -783) T) ((-620 . -783) T) ((-1259 . -872) NIL) ((-1111 . -1083) 133798) ((-1035 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1133) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-936 . -951) T) ((-1111 . -662) 133600) ((-496 . -1307) 133570) ((-1152 . -1081) T) ((-733 . -319) T) ((-723 . -1089) T) ((-372 . -1083) 133522) ((-367 . -1083) 133474) ((-359 . -1083) 133426) ((-372 . -662) 133378) ((-227 . -1070) 133355) ((-367 . -662) 133307) ((-108 . -1083) 133257) ((-359 . -662) 133209) ((-305 . -739) 133151) ((-661 . -1249) T) ((-501 . -466) T) ((-421 . -528) 133063) ((-108 . -662) 133013) ((-221 . -466) T) ((-1152 . -240) T) ((-307 . -153) 132963) ((-1028 . -633) 132924) ((-1028 . -632) 132906) ((-1021 . -632) 132888) ((-118 . -1089) T) ((-678 . -1088) 132872) ((-229 . -507) T) ((-413 . -632) 132854) ((-413 . -633) 132831) ((-1086 . -1307) 132801) ((-678 . -111) 132780) ((-692 . -930) 132703) ((-1174 . -503) 132687) ((-1324 . -668) 132646) ((-395 . -668) 132615) ((-64 . -455) T) ((-64 . -410) T) ((-1192 . -102) T) ((-896 . -133) T) ((-498 . -102) 132565) ((-1147 . -1249) T) ((-1256 . -875) T) ((-1329 . -381) T) ((-1111 . -102) T) ((-1093 . -102) T) ((-365 . -739) 132510) ((-897 . -875) 132461) ((-753 . -149) 132440) ((-753 . -147) 132419) 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131166) ((-1191 . -102) T) ((-1268 . -133) T) ((-1264 . -875) 131065) ((-1203 . -25) T) ((-1203 . -21) T) ((-1192 . -321) 130860) ((-357 . -1249) T) ((-1157 . -25) T) ((-880 . -133) T) ((-407 . -1249) T) ((-1157 . -21) T) ((-879 . -25) T) ((-879 . -21) T) ((-803 . -319) 130839) ((-1187 . -503) 130823) ((-1183 . -153) 130773) ((-1178 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1178 . -633) 130646) ((-585 . -133) T) ((-638 . -871) 130625) ((-1056 . -814) T) ((-1056 . -818) T) ((-1056 . -748) T) ((-839 . -930) 130494) ((-734 . -1088) 130317) ((-616 . -875) 130296) ((-498 . -321) 130234) ((-467 . -432) 130204) ((-365 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1070) 129950) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-734 . -111) 129759) ((-353 . -748) T) ((-692 . -274) 129743) ((-692 . -234) 129727) ((-595 . -319) T) ((-532 . -319) T) ((-305 . -528) 129676) ((-1197 . -1249) T) ((-108 . -321) NIL) ((-72 . -410) T) ((-1145 . -102) 129408) ((-856 . -426) 129392) ((-1152 . -821) T) ((-1152 . -816) T) ((-723 . -1133) T) ((-592 . -632) 129374) ((-391 . -376) T) ((-171 . -507) 129352) ((-226 . -632) 129284) ((-136 . -1133) T) ((-118 . -1133) T) ((-996 . -1249) T) ((-48 . -748) T) ((-1078 . -503) 129249) ((-143 . -440) 129231) ((-143 . -381) T) ((-1059 . -102) T) ((-524 . -523) 129210) ((-734 . -635) 128966) ((-1257 . -632) 128948) ((-1214 . -1249) T) ((-1214 . -1070) 128884) ((-1207 . -239) 128843) ((-490 . -102) T) ((-477 . -102) T) ((-1206 . -239) 128795) ((-1200 . -239) 128618) ((-1066 . -1144) T) ((-331 . -930) 128524) ((-1209 . -875) T) ((-1207 . -35) 128490) ((-1207 . -95) 128456) ((-1207 . -1238) 128422) ((-1207 . -1235) 128388) ((-1206 . -1235) 128354) ((-1206 . -1238) 128320) ((-1206 . -95) 128286) ((-1206 . -35) 128252) ((-1200 . -1235) 128218) ((-1200 . -1238) 128184) ((-1191 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1111 . -1184) 128163) ((-40 . -1249) T) ((-1200 . -95) 128129) ((-1066 . -23) T) ((-1200 . -35) 128095) ((-585 . -507) T) ((-1158 . -35) 128061) ((-1158 . -95) 128027) ((-1158 . -1238) 127993) ((-1158 . -1235) 127959) ((-374 . -1144) T) ((-372 . -1184) 127938) ((-367 . -1184) 127917) ((-359 . -1184) 127896) ((-1135 . -298) 127852) ((-984 . -1249) T) ((-949 . -1249) T) ((-108 . -1184) T) ((-856 . -1089) 127831) ((-793 . -1249) T) ((-669 . -321) 127769) ((-651 . -321) 127620) ((-694 . -1249) T) ((-734 . -1081) T) ((-1094 . -660) 127602) ((-1111 . -38) 127470) ((-976 . -660) 127418) ((-1036 . -149) T) ((-1036 . -147) NIL) ((-391 . -1144) T) ((-336 . -25) T) ((-334 . -23) T) ((-973 . 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. -47) 98886) ((-372 . -175) T) ((-367 . -175) T) ((-533 . -57) 98860) ((-511 . -57) 98810) ((-365 . -1318) 98787) ((-229 . -466) T) ((-331 . -302) 98738) ((-359 . -175) T) ((-177 . -250) T) ((-1264 . -872) 98637) ((-108 . -175) T) ((-897 . -1023) 98621) ((-676 . -1144) T) ((-595 . -376) T) ((-595 . -341) 98608) ((-532 . -341) 98585) ((-532 . -376) T) ((-326 . -319) 98564) ((-325 . -319) T) ((-616 . -872) 98543) ((-1145 . -739) 98485) ((-623 . -1249) T) ((-534 . -294) 98469) ((-676 . -23) T) ((-419 . -234) 98453) ((-419 . -274) 98437) ((-325 . -1052) NIL) ((-346 . -23) T) ((-103 . -1042) 98421) ((-657 . -381) T) ((-45 . -36) 98400) ((-630 . -1133) T) ((-365 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-246 . -321) 98338) ((-1119 . -1144) T) ((-1323 . -670) 98312) ((-803 . -1144) T) ((-802 . -1144) T) ((-1211 . -426) 98296) ((-468 . -1144) T) ((-1094 . -466) T) ((-1185 . -1133) T) ((-976 . -466) 98247) ((-1148 . -1115) T) ((-110 . -1133) T) ((-1119 . -23) T) ((-1192 . -528) 98030) 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. -1089) T) ((-1242 . -149) 63676) ((-334 . -1083) 63658) ((-1242 . -147) 63637) ((-1217 . -102) T) ((-1216 . -102) T) ((-1215 . -102) T) ((-1207 . -175) 63588) ((-334 . -662) 63570) ((-723 . -1249) T) ((-1206 . -175) 63501) ((-1200 . -175) 63432) ((-1185 . -635) 63413) ((-1158 . -175) 63364) ((-610 . -1089) T) ((-609 . -1089) T) ((-1036 . -1133) T) ((-1003 . -1133) T) ((-391 . -1083) 63329) ((-136 . -1249) T) ((-118 . -1249) T) ((-944 . -1133) T) ((-896 . -930) NIL) ((-391 . -662) 63294) ((-146 . -875) T) ((-822 . -820) 63278) ((-721 . -25) T) ((-721 . -21) T) ((-119 . -660) 63255) ((-723 . -912) 63237) ((-443 . -1133) T) ((-326 . -1254) 63216) ((-325 . -1254) T) ((-171 . -414) 63200) ((-858 . -1083) 63170) ((-488 . -1005) 63132) ((-72 . -632) 63114) ((-132 . -102) T) ((-131 . -102) T) ((-852 . -1083) 63098) ((-108 . -821) T) ((-108 . -816) T) ((-723 . -1070) 63080) ((-326 . -571) 63059) ((-325 . -571) T) ((-858 . -662) 63029) ((-852 . -662) 62999) ((-1329 . -23) T) ((-136 . -1070) 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. -922) 60880) ((-988 . -321) 60818) ((-858 . -102) T) ((-443 . -739) 60802) ((-229 . -845) T) ((-852 . -102) T) ((-849 . -102) T) ((-1321 . -670) 60776) ((-1285 . -1284) 60755) ((-493 . -153) 60705) ((-1285 . -1278) 60675) ((-1152 . -1254) T) ((-352 . -1070) 60642) ((-1285 . -1282) 60626) ((-1268 . -930) 60533) ((-1264 . -1263) 60512) ((-80 . -632) 60494) ((-932 . -632) 60476) ((-1264 . -1278) 60453) ((-1152 . -571) T) ((-949 . -872) T) ((-793 . -872) T) ((-694 . -872) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-391 . -296) T) ((-1264 . -1261) 60308) ((-1286 . -1144) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1095 . -618) 60154) ((-842 . -635) 60138) ((-560 . -236) 60125) ((-530 . -153) 60109) ((-58 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1318) 60048) ((-367 . -1318) 60032) ((-359 . -1318) 60016) ((-326 . -376) 59995) ((-325 . -376) T) ((-496 . -1081) 59973) ((-716 . -660) 59955) ((-1320 . -670) 59929) ((-131 . -321) NIL) ((-1286 . -23) T) 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. -872) T) ((-1035 . -951) T) ((-1211 . -635) 56019) ((-154 . -748) T) ((-1145 . -381) 55998) ((-659 . -102) T) ((-1056 . -25) T) ((-1036 . -528) NIL) ((-260 . -426) 55967) ((-259 . -426) 55936) ((-1056 . -21) T) ((-897 . -1083) 55888) ((-610 . -739) 55861) ((-609 . -739) 55758) ((-822 . -298) 55716) ((-128 . -102) 55666) ((-856 . -1070) 55562) ((-171 . -845) 55541) ((-331 . -670) 55438) ((-839 . -34) T) ((-736 . -102) T) ((-1152 . -1144) T) ((-1058 . -1249) T) ((-897 . -662) 55390) ((-391 . -38) 55355) ((-353 . -25) T) ((-353 . -21) T) ((-186 . -102) T) ((-163 . -102) T) ((-257 . -102) T) ((-159 . -102) T) ((-368 . -1307) 55339) ((-366 . -1307) 55323) ((-358 . -1307) 55307) ((-171 . -363) 55286) ((-560 . -872) T) ((-1119 . -239) 55237) ((-1152 . -23) T) ((-88 . -632) 55219) ((-803 . -239) T) ((-723 . -319) T) ((-858 . -38) 55189) ((-852 . -38) 55159) ((-1312 . -635) 55101) ((-1286 . -133) T) ((-1183 . -300) 55080) ((-994 . -748) 54979) ((-994 . -817) 54932) ((-994 . -818) 54885) 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-1133) T) ((-31 . -102) T) ((-1268 . -668) 52265) ((-880 . -668) 52224) ((-840 . -739) 52073) ((-1303 . -1249) T) ((-591 . -886) T) ((-585 . -668) 52045) ((-119 . -872) NIL) ((-1203 . -426) 52029) ((-1157 . -426) 52013) ((-879 . -426) 51997) ((-898 . -102) 51948) ((-1285 . -102) T) ((-1264 . -102) T) ((-1259 . -528) 51717) ((-1236 . -321) 51655) ((-1207 . -298) 51620) ((-1206 . -298) 51578) ((-539 . -93) T) ((-1200 . -298) 51406) ((-323 . -632) 51388) ((-1129 . -1133) T) ((-1111 . -670) 51262) ((-733 . -466) T) ((-711 . -632) 51194) ((-301 . -748) T) ((-108 . -940) NIL) ((-711 . -633) 51155) ((-615 . -632) 51137) ((-591 . -632) 51119) ((-565 . -633) NIL) ((-565 . -632) 51101) ((-543 . -632) 51083) ((-526 . -523) 51062) ((-501 . -1088) 51012) ((-488 . -1083) 50847) ((-521 . -523) 50826) ((-488 . -662) 50667) ((-221 . -1088) 50617) ((-372 . -670) 50569) ((-367 . -670) 50521) ((-229 . -871) T) ((-359 . -670) 50473) ((-616 . -102) 50403) ((-501 . -111) 50337) ((-496 . -381) 50316) ((-108 . -670) 50266) ((-357 . -149) 50248) ((-246 . -503) 50232) ((-357 . -147) T) ((-353 . -236) 50219) ((-171 . -383) 50190) ((-973 . -1298) 50174) ((-105 . -1249) T) ((-221 . -111) 50108) ((-897 . -321) 50073) ((-973 . -1133) 50023) ((-822 . -633) 49984) ((-822 . -632) 49966) ((-740 . -102) T) ((-1324 . -1249) T) ((-395 . -1249) T) ((-343 . -1133) T) ((-217 . -635) 49943) ((-1152 . -133) T) ((-1315 . -739) 49913) ((-736 . -38) 49883) ((-326 . -507) 49862) ((-545 . -1249) T) ((-514 . -1249) T) ((-1285 . -296) 49828) ((-1264 . -296) 49794) ((-339 . -153) 49778) ((-453 . -1133) T) ((-1250 . -1249) T) ((-1095 . -300) 49753) ((-1257 . -875) T) ((-48 . -236) 49740) ((-1192 . -34) T) ((-1324 . -1070) 49717) ((-498 . -34) T) ((-482 . -632) 49699) ((-258 . -298) 49673) ((-395 . -1070) 49657) ((-1203 . -1089) T) ((-1157 . -1089) T) ((-879 . -1089) T) ((-1094 . -871) T) ((-501 . -635) 49607) ((-221 . -635) 49557) ((-840 . -175) 49468) ((-534 . -298) 49420) ((-1289 . -302) 49399) ((-1231 . -378) 49373) 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1744) ((-171 . -111) 1640) ((-856 . -133) 1592) ((-1299 . -321) 1530) ((-758 . -153) 1514) ((-994 . -875) 1413) ((-839 . -875) 1364) ((-501 . -319) T) ((-391 . -632) 1331) ((-534 . -1042) 1315) ((-391 . -633) 1229) ((-221 . -319) T) ((-143 . -153) 1211) ((-736 . -298) 1190) ((-501 . -1052) T) ((-594 . -38) 1177) ((-560 . -38) 1164) ((-509 . -38) 1129) ((-661 . -668) 1098) ((-221 . -1052) T) ((-896 . -1081) T) ((-858 . -632) 1080) ((-852 . -632) 1062) ((-849 . -632) 1044) ((-840 . -940) 1023) ((-1324 . -1144) T) ((-323 . -1249) T) ((-1268 . -1088) 846) ((-880 . -1088) 830) ((-896 . -250) T) ((-896 . -240) NIL) ((-711 . -1249) T) ((-1324 . -23) T) ((-840 . -670) 719) ((-565 . -1249) T) ((-419 . -351) 703) ((-585 . -1088) 690) ((-1268 . -111) 499) ((-723 . -660) 481) ((-880 . -111) 460) ((-395 . -23) T) ((-171 . -635) 238) ((-1221 . -528) 30) ((-901 . -1133) T) ((-703 . -1133) T) ((-698 . -1133) T) ((-674 . -1133) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 6828a93c..49b4ff38 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3508975270) +(30 . 3509581008) (4513 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -489,675 +489,678 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |bubbleSort!| |rightLcm| - |ParCond| |number?| |e02bbf| |s19adf| |tryFunctionalDecomposition| - |f02abf| |e| |numberOfComposites| |factorials| |unit?| |sin?| - |bivariateSLPEBR| |createGenericMatrix| |OMgetVariable| |invmultisect| - |graphCurves| |reify| |irCtor| |getRef| |kernel| |characteristicSet| - |exponential1| |simplify| |d01ajf| |charthRoot| |null| |clikeUniv| - |tubeRadius| |getMultiplicationTable| |permutations| |list| - |absolutelyIrreducible?| |integer?| |viewThetaDefault| - |factorAndSplit| |bumprow| |rightMinimalPolynomial| |not| - |extractBottom!| |draw| |henselFact| |discriminant| |gramschmidt| - |iifact| |repSq| |besselI| |spherical| |bright| |and| |isPower| - |relativeApprox| |doubleFloatFormat| |pquo| |isEquiv| |newLine| - |exptMod| |generalPosition| |csch2sinh| |linearAssociatedExp| |or| - |OMputApp| |schwerpunkt| |lazyPquo| |trueEqual| - |tableForDiscreteLogarithm| |generateIrredPoly| |logical?| |floor| - |genericLeftMinimalPolynomial| |xor| |newSubProgram| |cache| |iitan| - |redmat| |irreducibleRepresentation| |iiacosh| |zCoord| - |resultantReduitEuclidean| |hostPlatform| |children| |case| - |makeObject| |torsionIfCan| |measure| |repeating?| |ratpart| - |intChoose| |pol| |clearTheSymbolTable| |droot| |firstSubsetGray| - |Zero| |factorPolynomial| |infieldint| |OMputVariable| |whitePoint| - |coef| |e02zaf| |sturmSequence| |decimal| |getDatabase| |green| - |pointData| |One| |viewPhiDefault| |fortranLinkerArgs| - |representationType| |lieAlgebra?| |signAround| |bivariate?| - |fprindINFO| |jvmPublic| |c02agf| |topPredicate| |factorGroebnerBasis| - |invertible?| |lfintegrate| |hspace| |thetaCoord| |scalarTypeOf| - |colorFunction| |splitConstant| |algintegrate| |monomials| |pToHdmp| - |digits| |cExp| |goodnessOfFit| |s13adf| |left| |implies| |OMgetApp| - |setAdaptive| |mainDefiningPolynomial| |composites| |increment| - |retractIfCan| |mathieu23| |iiGamma| |denomLODE| |iteratedInitials| - |right| |hex| |size| |basisOfCentroid| |cycleLength| |has?| |closed?| - |listLoops| |realZeros| |generalSqFr| |less?| |mappingAst| |ef2edf| - |complexNumericIfCan| |leftRegularRepresentation| |stFuncN| - |pushdterm| |elt| |indicialEquations| |dictionary| - |createNormalPrimitivePoly| |mainForm| EQ |nthExpon| |s17acf| - |autoReduced?| |abelianGroup| |iterationVar| |saturate| |cSec| - |useSingleFactorBound| |lighting| |eigenvector| |OMgetEndError| - |quote| |rewriteSetByReducingWithParticularGenerators| |backspace| - |setref| |d01fcf| |sinh2csch| |pushup| |lambert| |leadingTerm| - |leftGcd| |setvalue!| |selectSumOfSquaresRoutines| |cAcsc| - |leftDivide| |exponent| |fractRadix| |expandLog| |characteristicSerie| - |possiblyInfinite?| |tanAn| |vectorise| |skewSFunction| |seed| - |split!| |signature| |selectPDERoutines| |printStatement| - |minRowIndex| |rotatex| |identityMatrix| |modifyPoint| |point?| - |lowerCase!| |changeVar| |cyclicParents| |bit?| |chebyshevT| - |genericLeftTraceForm| |multiset| |tan2trig| |wordInGenerators| - |showArrayValues| |zoom| |conditionP| |transform| |OMputBVar| - |predicates| |chvar| |patternMatch| |lifting1| |infiniteProduct| - |lfextlimint| |internalDecompose| |constantOpIfCan| |laguerre| - |binding| |operation| |node| |OMclose| |inverseColeman| |trace2PowMod| - |isAbsolutelyIrreducible?| |stronglyReduced?| |coord| |rightTrace| - |setelt!| |resetVariableOrder| |createNormalPoly| |numberOfComponents| - |forLoop| |cCoth| |cCosh| |ReduceOrder| |OMParseError?| |froot| - |sayLength| |symbol| |decrease| |iflist2Result| |heap| |OMgetEndBVar| - |maxIndex| |inc| SEGMENT |univariatePolynomial| |unitNormal| - |karatsubaDivide| |style| |expression| |airyAi| |setTex!| - |collectUnder| |replaceKthElement| |completeSmith| |oblateSpheroidal| - |mesh?| |highCommonTerms| |unknown| |rootOfIrreduciblePoly| |integer| - |limit| |myDegree| F |rootKerSimp| |red| |testDim| |goodPoint| - |readable?| |subMatrix| |rischDE| |s18acf| |algebraicDecompose| - |iiacsc| |innerEigenvectors| UTS2UP |top!| |precision| |quadraticNorm| - |solveLinearPolynomialEquationByFractions| |showFortranOutputStack| - |ref| |extractClosed| |getlo| |Hausdorff| |size?| - |setAttributeButtonStep| |extractTop!| |elRow2!| |squareFree| - |fortranLiteral| |f07fdf| |outputAsScript| |qfactor| |curryLeft| - |physicalLength!| |moebiusMu| |polyRicDE| |numberOfFractionalTerms| - |minPoints| |derivative| |leadingIndex| |cAsec| |insertBottom!| - |subTriSet?| |c06ebf| |cond| |sylvesterMatrix| |setLabelValue| |call| - |preprocess| |squareMatrix| |musserTrials| |zeroMatrix| |roman| - |ramified?| |nthFractionalTerm| |setIntersection| |rquo| |leastPower| - |OMputEndAttr| |comp| |c06gqf| |createIrreduciblePoly| |palgRDE0| - |symbolTable| |makeUnit| |outputAsTex| |leftFactor| |stopTableInvSet!| - |elColumn2!| |color| |shape| |pointColorPalette| - |tryFunctionalDecomposition?| |insertRoot!| |getSyntaxFormsFromFile| - |fullDisplay| |magnitude| |atanhIfCan| |extractProperty| |makeop| - |pushFortranOutputStack| |lookup| |OMunhandledSymbol| |palgint0| - |halfExtendedSubResultantGcd1| |pack!| |reduceLODE| |f02akf| - |internalZeroSetSplit| |totalGroebner| |popFortranOutputStack| - |equation| |ScanFloatIgnoreSpacesIfCan| |infinite?| |c06frf| - |showClipRegion| |solveLinearlyOverQ| |f02aff| |lazyVariations| - |isNot| |bipolar| |makeGraphImage| |d01gbf| |outputAsFortran| - |unmakeSUP| |categoryFrame| |f01ref| |youngGroup| |ridHack1| |redpps| - |resultantEuclidean| |normDeriv2| |OMgetEndAtp| |divide| |terms| - |useEisensteinCriterion| |evaluateInverse| |OMUnknownSymbol?| - |groebner| |integral?| |outputForm| |f07aef| |lieAdmissible?| - |lowerBound| |hdmpToP| |compound?| |e02ahf| |nil?| |triangularSystems| - |expandPower| |complement| |innerSolve| |shallowExpand| |jvmNative| - |extract!| |getVariableOrder| |OMgetAtp| |bat| |curryRight| |irDef| - |deepestTail| |extractSplittingLeaf| |laguerreL| - |clearFortranOutputStack| |pureLex| |nextLatticePermutation| |graphs| - |readLineIfCan!| |changeName| |any| |curveColorPalette| |minIndex| - |computeBasis| |insert| |mapUnivariate| |coerceL| |d03edf| |birth| - |rightGcd| |s18aff| |leadingBasisTerm| |gbasis| |s21bdf| - |compiledFunction| |unvectorise| |ramifiedAtInfinity?| - |primextintfrac| |f01mcf| |sortConstraints| |e02aef| |radix| - |nextsousResultant2| |dn| |componentUpperBound| |string?| |ran| - |setRow!| |super| |getButtonValue| |assert| |dflist| |integerBound| - |transcendenceDegree| |iiasech| |backOldPos| |mapdiv| |stop| - |upperBound| |ranges| |purelyAlgebraicLeadingMonomial?| - |partialDenominators| |mkIntegral| |localReal?| - |integralLastSubResultant| |bumptab| |f01brf| |s17aef| |iitanh| - |getMultiplicationMatrix| |systemCommand| |nodeOf?| |splitSquarefree| - |integral| |formula| |functionIsOscillatory| |bernoulliB| |intensity| - |mainVariables| |firstNumer| |fillPascalTriangle| |rk4| - |problemPoints| |setAdaptive3D| |setMinPoints3D| |numberOfChildren| - |e01bef| |e02baf| |normal| |colorDef| |OMgetEndBind| |LazardQuotient2| - |leftUnits| |elRow1!| |iicosh| |elaboration| |romberg| - |factorsOfDegree| |any?| |addPoint2| |fi2df| |primintegrate| - |clipBoolean| |cPower| |jvmInterface| |f01bsf| |hermite| |palgRDE| - |overlabel| |lfextendedint| |resultantEuclideannaif| - |removeDuplicates!| |reverseLex| |nrows| |basisOfCenter| |e02daf| - |minus!| |fortran| |iisec| |exactQuotient!| |cosSinInfo| |close| - |jacobian| |e04mbf| |cycles| |semiIndiceSubResultantEuclidean| - |f04arf| |ncols| |generalizedContinuumHypothesisAssumed?| |minset| - |complexIntegrate| |limitPlus| |singRicDE| |rightAlternative?| |exQuo| - |determinant| |matrixDimensions| |hasoln| |eq| |norm| |perfectSqrt| - |f01qdf| |solveLinearPolynomialEquation| |log| |queue| |display| - |subResultantGcdEuclidean| |interpolate| |ip4Address| |polygon| |iter| - |s20adf| |lowerCase| |drawComplex| |yCoord| |iisech| |pop!| |presuper| - |csubst| |OMwrite| |range| |fortranLiteralLine| |tanh2trigh| - |karatsuba| |permutationRepresentation| |readByte!| |mdeg| - |irreducible?| |OMUnknownCD?| |raisePolynomial| |basisOfMiddleNucleus| - |mvar| |integralDerivationMatrix| |latex| |OMgetString| |s17ajf| - |stopTable!| |monicLeftDivide| |resize| |mapExpon| |primitive?| - |generic| |idealiserMatrix| |bivariatePolynomials| |f07fef| - |numFunEvals| |algebraicSort| |nodes| |child| |s15adf| |subspace| - |certainlySubVariety?| |length| |dequeue!| |getZechTable| - |listYoungTableaus| |lhs| |argumentList!| |coordinates| |mpsode| - |nextsubResultant2| |eulerPhi| |chainSubResultants| |sincos| |linear| - |predicate| |scripts| |setCondition!| |output| - |drawComplexVectorField| |semiSubResultantGcdEuclidean1| |rhs| - |viewport3D| |composite| |changeWeightLevel| |bezoutMatrix| - |stiffnessAndStabilityFactor| |test| |complete| |digamma| - |setFormula!| |printTypes| |exp| |medialSet| |point| |readUInt16!| - |true| |supersub| |contours| |iprint| |legendre| |freeOf?| - |primitiveElement| |arg1| |setScreenResolution| |stoseSquareFreePart| - |polynomial| |littleEndian| |mapUnivariateIfCan| |rangePascalTriangle| - |lambda| |currentEnv| |cRationalPower| |laplacian| |width| - |SturmHabichtSequence| |leaves| |scalarMatrix| - |numberOfComputedEntries| |lllp| |arg2| |fixedPoint| |distance| - |clearTheFTable| |makeViewport3D| |cycleSplit!| |map| |denominators| - |semiSubResultantGcdEuclidean2| |localUnquote| |mesh| |symbol?| |unit| - |script| |extendedEuclidean| |physicalLength| |selectsecond| |series| - |unitCanonical| |loadNativeModule| |divideExponents| - |indicialEquation| |poisson| |mkPrim| |li| |conditions| |nlde| |cAcot| - |member?| |fglmIfCan| |message| |conditionsForIdempotents| |e02ajf| - |f02axf| |bumptab1| |mindegTerm| |directSum| |d01apf| |match| - |primlimitedint| |radicalEigenvalues| |An| F2FG |e02bdf| |commutator| - |root| |nextPrime| |eulerE| |setleft!| |jvmStringConstantTag| - |listexp| |readUInt32!| |iisinh| |rightZero| |limitedIntegrate| - |antisymmetric?| |tubeRadiusDefault| |even?| |numerator| - |rationalApproximation| |coth2tanh| |airyBi| |min| |f02agf| - |symmetricGroup| |optional| |variable?| |rowEchelon| |useNagFunctions| - |increase| |debug3D| |parameters| |cotIfCan| |stoseLastSubResultant| - |noValueMode| |initiallyReduce| |trigs2explogs| |coshIfCan| - |antiCommutator| |fortranInteger| |showIntensityFunctions| - |cyclicCopy| |remove| |polygamma| |s17dhf| |purelyTranscendental?| - |nonQsign| |lflimitedint| |rk4f| |setColumn!| |result| |shift| - |swapColumns!| |changeThreshhold| |scale| |makeprod| |bombieriNorm| - |errorKind| |failed?| |isExpt| |iibinom| |matrixGcd| |OMmakeConn| - |calcRanges| |last| |nativeModuleExtension| |ScanFloatIgnoreSpaces| - |mr| |linGenPos| |Gamma| |noLinearFactor?| |s21baf| |leadingExponent| - |totalfract| |binaryFunction| |getOperator| |kmax| - |factorSquareFreePolynomial| |pole?| |routines| |bracket| - |cyclicGroup| |readBytes!| |moebius| |stopMusserTrials| |s17dgf| - |rarrow| |computeCycleEntry| |wordInStrongGenerators| |ignore?| |f2st| - |reduceBasisAtInfinity| BY |selectOrPolynomials| |degree| |iidsum| - |open?| |showScalarValues| |expr| |leftRecip| |positiveSolve| - |PDESolve| |nthRoot| |OMputError| |structuralConstants| |pushucoef| - |toseInvertibleSet| |ellipticCylindrical| |dmp2rfi| |merge!| - |setProperty| |frobenius| |lift| |mainCoefficients| |label| - |setButtonValue| |rotatey| |dec| |cyclicEqual?| |hostByteOrder| - |reorder| |notelem| |deepCopy| |subscript| |prepareSubResAlgo| - |reduce| |condition| |monomialIntPoly| |numeric| |lp| |sncndn| - |disjunction| |OMgetBind| |minimize| |depth| |postfix| - |scanOneDimSubspaces| |rules| |separate| |plenaryPower| |prefix| - |radical| |totalLex| |showTheFTable| |over| |evenlambert| |variable| - |push| |traverse| |computeCycleLength| |acothIfCan| |conjug| |infLex?| - |minPol| |e01daf| |twist| |iterators| |printCode| |frst| - |signatureAst| |trim| |expandTrigProducts| |getProperties| |direction| - GT |internalLastSubResultant| |e02gaf| NOT |sylvesterSequence| - |factors| |nthFactor| |addiag| |laurentIfCan| |identity| |pdf2df| - |inconsistent?| |createMultiplicationMatrix| LE |getCode| OR - |shellSort| |makeSin| |d03faf| |primextendedint| |f04mbf| |iicos| - |printStats!| |ocf2ocdf| LT |nthRootIfCan| |toseLastSubResultant| - |setUnion| AND |overset?| |chineseRemainder| |epilogue| |critMTonD1| - |s18dcf| |atom?| |option| |LyndonCoordinates| |domainTemplate| |sPol| - |internal?| |normalized?| |move| |randomLC| |abs| |alternatingGroup| - |build| |interval| |center| |mathieu11| |fixedPointExquo| - |sizePascalTriangle| |setsubMatrix!| |setErrorBound| |polygon?| - |deleteProperty!| |component| |innerSolve1| |update| |closeComponent| - |removeCoshSq| |imagj| |startTableInvSet!| |normal01| |round| |plot| - |OMputEndAtp| |fortranComplex| |internalInfRittWu?| - |subscriptedVariables| |rem| |jvmVolatile| |headAst| - |internalIntegrate| |inspect| |uniform| |genericLeftDiscriminant| - |leftDiscriminant| |s17aff| |denominator| |external?| |quo| - |dimensionOfIrreducibleRepresentation| - |removeIrreducibleRedundantFactors| |lookupFunction| |coHeight| - |generalizedContinuumHypothesisAssumed| |transcendentalDecompose| - |leftReducedSystem| |OMputFloat| |approximants| |safeCeiling| - |lineColorDefault| |elaborateFile| |outputBinaryFile| |vark| - |patternMatchTimes| |inverseIntegralMatrixAtInfinity| |writeBytes!| - |qqq| |div| |iiexp| |jvmLongConstantTag| |reflect| |ldf2vmf| |byte| - |argument| |virtualDegree| |unitVector| |mantissa| |wronskianMatrix| - |extendedIntegrate| |exquo| |optAttributes| |lepol| |graeffe| |dual| - |oddInfiniteProduct| |augment| |mappingMode| |roughBase?| |lfunc| * ~= - |rationalPoint?| |coerceS| |basisOfRightNucleus| |leftRankPolynomial| - |close!| |cot2tan| |roughBasicSet| |startTable!| |limitedint| |#| - |exists?| |OMgetFloat| |OMencodingUnknown| |clipSurface| |changeBase| - |makeCrit| |s14baf| |viewDeltaYDefault| |ptFunc| ~ |nilFactor| - |FormatRoman| |irreducibleFactor| |stoseInvertible?reg| RF2UTS - |isConnected?| |clearTheIFTable| |largest| |ratPoly| = |divideIfCan!| - |maxint| |OMgetError| |categories| |middle| |bernoulli| |ListOfTerms| - |jordanAlgebra?| |firstUncouplingMatrix| |genericRightTraceForm| - |removeSuperfluousCases| |tex| |elements| |integralBasis| - |OMencodingXML| |exponential| |d01bbf| |elaborate| |function| - |surface| |setEpilogue!| |mathieu22| |oddlambert| |/\\| < |imagi| - |power| |position!| |initiallyReduced?| |Lazard2| |int| |inRadical?| - |cscIfCan| |clipParametric| |sequence| |\\/| > |qPot| |s14abf| - |countable?| |coerceP| |isMult| |setleaves!| |explicitEntries?| - |printInfo!| |splitNodeOf!| <= |printingInfo?| |Frobenius| |divisor| - |primes| |tanhIfCan| |iidprod| |numberOfPrimitivePoly| - |unprotectedRemoveRedundantFactors| |pdf2ef| >= |setClipValue| - |createLowComplexityNormalBasis| |distdfact| |yCoordinates| - |genericRightDiscriminant| |subCase?| |prinb| |anticoord| |lazyPrem| - |OMconnInDevice| |sdf2lst| |rk4a| |horizontalTab| |every?| |wreath| - |f02adf| |reducedDiscriminant| |quasiRegular| |makeTerm| |laurent| - |showRegion| |generalizedEigenvector| |createLowComplexityTable| - |d02bhf| |packageCall| |separant| |voidMode| |lazyPremWithDefault| - |triangSolve| |iiacoth| + |permanent| |puiseux| - |balancedFactorisation| |duplicates| |expextendedint| - |removeSquaresIfCan| |linearMatrix| |extractIfCan| |safeFloor| - - |f02bbf| |midpoints| |simpleBounds?| |defineProperty| |associative?| - |sechIfCan| |exponents| |xn| |cons| / |inv| |OMputEndApp| |readInt32!| - |UpTriBddDenomInv| |region| |returns| |useEisensteinCriterion?| - |sinhIfCan| |declare| |s17agf| |ground?| |algint| - |evenInfiniteProduct| |normalForm| |getOrder| |basisOfLeftNucleus| - |imagK| |curry| |conjugate| |ravel| |imagI| |alphanumeric| |ground| - |flatten| |cSech| |checkRur| |cos2sec| |tableau| |doubleRank| |bits| - |isOr| |lcm| |operators| |Ei| |reshape| |leadingMonomial| |hasHi| - |strongGenerators| |branchPoint?| |OMsupportsSymbol?| |times!| - |vector| |applyRules| |set| |groebner?| |OMputString| - |leadingCoefficient| |createNormalElement| |tanh2coth| |dmpToP| - |rotatez| |gcdprim| |jvmProtected| |differentiate| |append| - |linkToFortran| |source| |chebyshevU| |primitiveMonomials| - |infRittWu?| |cycleElt| |singularitiesOf| |particularSolution| - |lazyPseudoDivide| |leftAlternative?| |rightExtendedGcd| |gcd| - |equality| |rootSplit| |Lazard| |reductum| |write!| |sumSquares| - |jokerMode| |expintegrate| |bothWays| |baseRDE| |false| - |OMputEndObject| |monomRDEsys| |complexNormalize| |cycleEntry| - |makeYoungTableau| |findBinding| |qroot| |subresultantSequence| - |wholeRadix| |target| |element?| |cAsin| |badNum| |quasiComponent| - |indices| |jvmInterfaceMethodConstantTag| |critT| |root?| |cdr| - |members| |tab1| |probablyZeroDim?| |polyRDE| |paren| |getProperty| - |setDifference| |d01amf| |tanIfCan| |createPrimitiveNormalPoly| - |iomode| |verticalTab| |leastMonomial| |cyclePartition| |OMputInteger| - |car| |collectQuasiMonic| |LiePoly| |c02aff| |table| - |fortranCompilerName| |outerProduct| |resultantnaif| |printInfo| - |components| |inputBinaryFile| |OMserve| |deriv| |critB| |setnext!| - |new| |sorted?| |position| |startPolynomial| |connect| |rubiksGroup| - |quasiAlgebraicSet| |coerce| |e01bgf| |euler| |quadraticForm| - |deleteRoutine!| |graphState| |topFortranOutputStack| - |stoseIntegralLastSubResultant| |bezoutResultant| |branchIfCan| - |construct| |sumOfKthPowerDivisors| |showTheIFTable| - |numericalOptimization| |rightExactQuotient| |readIfCan!| |tubePoints| - |returnType!| |algebraicCoefficients?| |solve1| |integerIfCan| - |rowEchLocal| |coleman| |lazyIntegrate| |harmonic| |expintfldpoly| - |octon| |void| |unexpand| |minordet| |stoseInternalLastSubResultant| - |ParCondList| |rationalIfCan| |divideIfCan| |isList| |sample| - |matrixConcat3D| |mainSquareFreePart| |intermediateResultsIF| - |lazyPseudoQuotient| |algDsolve| |invertibleElseSplit?| |var2Steps| - |setPoly| |cAcosh| |lifting| |kovacic| |lllip| |powmod| - |useSingleFactorBound?| |zero?| |endSubProgram| |singleFactorBound| - |zero| |OMencodingSGML| |discriminantEuclidean| |makeSketch| |d01gaf| - |bigEndian| |monomialIntegrate| |basisOfLeftNucloid| |multinomial| - |factor1| |modularFactor| |transpose| |makeVariable| |shade| - |properties| |OMencodingBinary| |maxdeg| |mapCoef| |acschIfCan| - |heapSort| |And| |comment| |continuedFraction| |shuffle| - |combineFeatureCompatibility| |selectODEIVPRoutines| |translate| - |getOperands| |selectMultiDimensionalRoutines| - |createPrimitiveElement| |BumInSepFFE| |nthExponent| |constant?| - |polCase| |Or| |bandedJacobian| |monicDivide| |scaleRoots| - |linearlyDependentOverZ?| |stirling1| |outputArgs| |relerror| |cfirst| - |bytes| |distFact| |failed| |Not| |iiatanh| |acscIfCan| |symmetric?| - |supDimElseRittWu?| |legendreP| |distribute| |maxRowIndex| |copy!| - |linearDependenceOverZ| |elem?| |d01alf| |s14aaf| - |modularGcdPrimitive| |dimensionsOf| |quoted?| |directory| |zerosOf| - |primlimintfrac| |lastSubResultantEuclidean| |toseSquareFreePart| - |alphabetic?| |scopes| |e02adf| |writeLine!| |doubleResultant| |entry| - |updateStatus!| |knownInfBasis| |radicalRoots| |symmetricDifference| - |match?| |weakBiRank| |dark| |stoseInvertibleSetreg| |zeroSetSplit| - |power!| |error| |parametric?| |omError| |byteBuffer| |nextNormalPoly| - 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|remove!| |explicitlyFinite?| |plus!| |factorByRecursion| |tValues| - |univariatePolynomialsGcds| |maxPoints| |degreeSubResultant| - |squareFreePrim| |write| |moreAlgebraic?| |insert!| |typeList| - |mirror| |triangulate| |bipolarCylindrical| |primaryDecomp| - |taylorQuoByVar| |rCoord| |definingEquations| |nthr| ** |save| - |rightFactorIfCan| |screenResolution| |fintegrate| |quadratic| |empty| - |palgLODE0| |prinpolINFO| |solveid| |index| |superHeight| |part?| - |monom| |HenselLift| |asimpson| |zeroDimPrime?| |binaryTree| - |polarCoordinates| |swap| |decompose| |max| |testModulus| - |decomposeFunc| |gderiv| |leftOne| |roughUnitIdeal?| |partialFraction| - |factorial| |makeSUP| |fixedPoints| |primPartElseUnitCanonical| - |genericLeftNorm| |integralAtInfinity?| |pair| |sqfrFactor| - |parseString| |listRepresentation| |setlast!| |triangular?| |assoc| - |normalizeAtInfinity| |s17def| |uncouplingMatrices| |enterPointData| - |f01maf| |show| |common| |perfectSquare?| |s19aaf| |primitivePart!| - |iisqrt3| |status| |lquo| |rangeIsFinite| |cosIfCan| |iicsc| - |leadingSupport| |coth2trigh| FG2F |complexSolve| |normInvertible?| - |satisfy?| |exactQuotient| |toScale| |finiteBasis| |cAcoth| - |leftCharacteristicPolynomial| |groebSolve| |iiacot| |trace| - |factorset| |fortranDouble| |OMputBind| |complex?| |subPolSet?| - |invertibleSet| |singular?| |currentSubProgram| |nextIrreduciblePoly| - |c05pbf| |optpair| |reverse| |lazyResidueClass| |shufflein| |besselY| - |flagFactor| |minPoints3D| |tubePlot| |digit?| |curve| |rootNormalize| - |oddintegers| |powern| |balancedBinaryTree| |karatsubaOnce| |solid?| - |polar| |conical| |say| |indiceSubResultantEuclidean| |iisin| - |RemainderList| |linearPolynomials| |extendIfCan| |validExponential| - |qelt| |setFieldInfo| |critM| |constantCoefficientRicDE| |UnVectorise| - |OMconnectTCP| |overbar| |next| |setImagSteps| - |extendedSubResultantGcd| |doublyTransitive?| |minimumExponent| - |df2st| |qsetelt| |sort!| |regularRepresentation| |squareTop| |front| - |viewWriteDefault| |endOfFile?| |s17dlf| |leftFactorIfCan| - |binomThmExpt| |palgintegrate| |jvmFieldrefConstantTag| |xRange| - |arguments| |monicCompleteDecompose| |perfectNthPower?| |s19acf| - |checkForZero| |leftExtendedGcd| |commutative?| |parabolicCylindrical| - |addMatch| |normalDeriv| |prevPrime| |unaryFunction| |union| |yRange| - |dihedral| |parts| |diagonalMatrix| |subResultantGcd| |addBadValue| - |fractionPart| |eisensteinIrreducible?| |isAtom| |unitsColorDefault| - |ord| |rightTraceMatrix| |hue| |zRange| |slash| |socf2socdf| - |qinterval| |pleskenSplit| |enumerate| |orbit| |parents| |SFunction| - |search| |numberOfVariables| |lexGroebner| |extensionDegree| - |seriesToOutputForm| |initTable!| |map!| |lazyIrreducibleFactors| - |pdct| |pseudoRemainder| |bfEntry| |pair?| |viewZoomDefault| - |dioSolve| |rischDEsys| |drawToScale| |lex| |exprHasAlgebraicWeight| - |double?| |qsetelt!| |zag| |OMsend| |extractIndex| |recolor| - |duplicates?| |besselJ| |singularAtInfinity?| |polyPart| - |selectOptimizationRoutines| |nextColeman| |controlPanel| |equiv| - |rewriteIdealWithHeadRemainder| |localIntegralBasis| |d02raf| - |rectangularMatrix| |entry?| |genericRightTrace| |LyndonWordsList| - |block| |constantIfCan| |zeroDimPrimary?| |adaptive| |lintgcd| - |weights| LODO2FUN |relationsIdeal| |getMatch| |getGoodPrime| - |datalist| |numberOfCycles| |support| |cLog| |c06ekf| |adaptive?| - |SturmHabichtMultiple| |atoms| |primitivePart| |inrootof| - |cyclotomicFactorization| |figureUnits| |intcompBasis| |f04atf| - |e01saf| |secIfCan| |bounds| |redPo| |lowerPolynomial| |youngDiagram| - |partialQuotients| |cSin| |pow| |orthonormalBasis| |usingTable?| - |differentialVariables| |normalElement| |monomial?| |cAsech| - |fortranLogical| |pmintegrate| |createZechTable| |f07adf| - |groebnerIdeal| |summation| |firstDenom| |orbits| |recip| - |infieldIntegrate| |basisOfCommutingElements| |sup| - |subresultantVector| |ddFact| |s15aef| |inverseIntegralMatrix| - |outputFloating| |gcdPrimitive| |doubleComplex?| |drawStyle| |pade| - |setMinPoints| |externalList| |LiePolyIfCan| |psolve| |linear?| - |child?| |powers| |complexForm| |jvmStrict| |f01rdf| |axes| - |modularGcd| |headRemainder| |plusInfinity| |rroot| |corrPoly| - |d02cjf| |substitute| |tablePow| |ode2| |exprToXXP| |OMputEndError| - |iiacsch| |rootsOf| |minusInfinity| |internalSubPolSet?| |powerSum| - |f04adf| |ffactor| |submod| |f01qef| |quotientByP| |cAcos| - |setMaxPoints| |deref| |cyclotomicDecomposition| |clearTable!| - |zeroOf| |rootOf| |associatedEquations| |iicsch| |character?| - |interpretString| |f04jgf| |mathieu24| |characteristic| - |clipWithRanges| |roughEqualIdeals?| |cTanh| |makingStats?| |e02ddf| - |intPatternMatch| |presub| |expint| |explimitedint| |atanIfCan| - |rowEchelonLocal| |select!| |cardinality| |linearForm| |FormatArabic| - |pattern| |vspace| |debug| |gradient| |stopTableGcd!| |e02agf| - |checkPrecision| |writeUInt8!| |completeEchelonBasis| |biRank| - |iFTable| D |transcendent?| |squareFreePolynomial| |randomR| |collect| - |cTan| |type| |unparse| |positiveRemainder| |degreePartition| - |messagePrint| |linearPart| |isAnd| |prepareDecompose| - |linearDependence| |jvmNameAndTypeConstantTag| |mathieu12| |jvmFinal| - |SturmHabicht| |cAsinh| |factorList| |ricDsolve| |flexibleArray| - |choosemon| |monicModulo| |nullary?| |pmComplexintegrate| - |makeViewport2D| |crest| |inputOutputBinaryFile| |concat| |Si| - |changeMeasure| |separateDegrees| |removeRoughlyRedundantFactorsInPol| - |semiResultantEuclidean1| |aQuadratic| |leftNorm| - |coercePreimagesImages| |maxColIndex| |compBound| |mainMonomials| - |symmetricTensors| |push!| |associatedSystem| |linearlyDependent?| - |node?| |chiSquare| |attributeData| |rischNormalize| |ldf2lst| |cCsc| - |lastSubResultantElseSplit| |clearCache| - |rewriteIdealWithQuasiMonicGenerators| |ratDsolve| |constant| - |belong?| |loopPoints| |environment| |fracPart| |rationalPower| - |symbolIfCan| |upperCase| |reciprocalPolynomial| |listOfMonoms| - |padecf| |gcdcofact| |prologue| |simplifyLog| |doubleDisc| - |upDateBranches| |Nul| |maxrank| |setPrologue!| |odd?| |sts2stst| - |print| |sec2cos| |invmod| |getExplanations| |createRandomElement| - |OMlistSymbols| |squareFreePart| |resolve| |resultant| |nonLinearPart| - |overlap| |vedf2vef| |expenseOfEvaluationIF| |whatInfinity| |modulus| - |toseInvertible?| |processTemplate| |cschIfCan| |cAtanh| |numer| - |nsqfree| |selectFiniteRoutines| |empty?| |d01asf| |LazardQuotient| - |cyclic| |subHeight| |denom| |simplifyExp| |numberOfOperations| - |ptree| |extendedint| |perspective| |host| |float?| |generalLambert| - |splitDenominator| |e01sff| |f04faf| |elliptic| |recur| |acoshIfCan| - |showTheRoutinesTable| |writable?| |ksec| |title| |isTimes| |pi| - |product| |coefChoose| |outputList| |aCubic| |real?| |iiasinh| - |e02def| |badValues| |jvmStatic| |lexTriangular| |infinity| - |pseudoDivide| |ipow| |exprToGenUPS| |d02kef| |connectTo| - |OMsupportsCD?| |nil| |infinite| |arbitraryExponent| |approximate| - |complex| |shallowMutable| |canonical| |noetherian| |central| - |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| - |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| - |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| - |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |Enumeration| |Mapping| |Record| |Union| |lists| |epilogue| |torsion?| + |generalTwoFactor| |yCoord| |ode| |members| |factorFraction| + |firstDenom| |decrease| |critMTonD1| |qualifier| |leaves| + |purelyAlgebraic?| |currentCategoryFrame| |zCoord| |iisech| |makeFR| + |multiEuclideanTree| |tab1| |orbits| |iflist2Result| |s18dcf| + |acosIfCan| |alternative?| |dominantTerm| |rightDivide| |pop!| + |moduloP| |probablyZeroDim?| |recip| |heap| |atom?| |rotate| + |anfactor| |HermiteIntegrate| |min| |resultantReduitEuclidean| + |lexico| |presuper| |branchPointAtInfinity?| |polyRDE| + |infieldIntegrate| |ratpart| |OMgetEndBVar| |LyndonCoordinates| |mix| + |OMgetEndObject| |rational| |hostPlatform| + |semiResultantReduitEuclidean| |csubst| |linSolve| |paren| + |basisOfCommutingElements| |mantissa| |next| |domainTemplate| + |maxIndex| |intChoose| |definingPolynomial| |halfExtendedResultant1| + |stoseInvertible?| |children| |OMwrite| |reduced?| |getProperty| + |solveLinearPolynomialEquationByRecursion| |sup| + |generalizedEigenvectors| |sPol| |univariatePolynomial| |diff| |box| + |pol| |just| |range| |variationOfParameters| |setDifference| + |coefficients| |subresultantVector| |flatten| |unitNormal| + |definingInequation| |internal?| |permutation| |setTopPredicate| + |fortranLiteralLine| |complexElementary| |prinshINFO| |d01amf| + |ddFact| |karatsubaDivide| |elseBranch| |normalized?| |gethi| + |minColIndex| |linearAssociatedOrder| |fortranDoubleComplex| + |tanh2trigh| |tanIfCan| |autoReduced?| |s15aef| |style| |f02aef| + |move| |fill!| |algebraic?| |createPrimitiveNormalPoly| |pushdown| + |karatsuba| |totolex| |abelianGroup| |inverseIntegralMatrix| |airyAi| + |alphabetic| |randomLC| |putColorInfo| |subNode?| |iomode| + |horizConcat| |permutationRepresentation| |parametersOf| + |iterationVar| |outputFloating| |setTex!| |charClass| |abs| |nor| + |rationalPoints| |readByte!| |equation| |stosePrepareSubResAlgo| + |verticalTab| |tubePointsDefault| |gcdPrimitive| |collectUnder| + |beauzamyBound| |alternatingGroup| |laplace| |removeRedundantFactors| + |invertible?| |ideal| |mdeg| |e02bef| |leastMonomial| |doubleComplex?| + |constant| |replaceKthElement| |exprHasLogarithmicWeights| |build| + |exteriorDifferential| |c06gsf| |lfintegrate| |irreducible?| |list?| + |cyclePartition| |realSolve| |drawStyle| |completeSmith| |interval| + |startStats!| |f01qcf| |intersect| |hspace| |c06fqf| |OMUnknownCD?| + |OMputInteger| |bsolve| |pade| |oblateSpheroidal| |approxNthRoot| + |mathieu11| |f02wef| |primPartElseUnitCanonical!| EQ |raisePolynomial| + |readUInt8!| |reverse!| |dec| |car| |setMinPoints| |debug| |mesh?| + |palglimint| |fixedPointExquo| |homogeneous?| |permutationGroup| + |basisOfMiddleNucleus| |subResultantsChain| |removeSinhSq| + |collectQuasiMonic| |externalList| D |highCommonTerms| |depth| + |iiatan| |sizePascalTriangle| |iilog| |asinIfCan| |withPredicates| + |mvar| |LiePoly| |meshPar1Var| |LiePolyIfCan| |qelt| + |rootOfIrreduciblePoly| |setsubMatrix!| |errorInfo| |e01baf| + |rational?| |integralDerivationMatrix| |crushedSet| |nary?| |c02aff| + |psolve| |qsetelt| |limit| |setErrorBound| |moduleSum| + |prolateSpheroidal| |phiCoord| |e04gcf| |latex| |pointLists| + |fortranCompilerName| |linear?| |xRange| |myDegree| |polygon?| |slex| + |coerceListOfPairs| |nullSpace| |constantOperator| |OMgetString| + |selectAndPolynomials| |type| |resultantnaif| |child?| |yRange| + |rootKerSimp| |deleteProperty!| |leftPower| |changeNameToObjf| + |quotedOperators| |rootRadius| |s17ajf| |iisqrt2| |components| + |powers| |zRange| |red| |component| |finite?| |unravel| |f02bjf| |Is| + |stopTable!| |inputBinaryFile| |identification| |complexForm| |map!| + |testDim| |innerSolve1| |OMputAttr| |semiResultantEuclideannaif| + |normalise| |monicLeftDivide| |ode1| |e02dff| |OMserve| |jvmStrict| + |qsetelt!| |goodPoint| |contract| |expIfCan| |closeComponent| + |declare| |noKaratsuba| |s17ahf| |resize| |OMgetEndAttr| |deriv| + |f01rdf| |readable?| |s18aef| |removeCoshSq| |setOrder| |more?| + |mapExpon| |delay| |iicot| |critB| |axes| |print| |subMatrix| + |composites| |mapGen| |imagj| |traceMatrix| |hermiteH| |datalist| + |primitive?| |f04axf| |setnext!| |option?| |modularGcd| |resolve| + |increment| |rischDE| |tanQ| |startTableInvSet!| |asinhIfCan| + |truncate| |generic| |apply| |makeResult| |key| |sorted?| |chiSquare1| + |headRemainder| |s18acf| |mathieu23| |isImplies| |normal01| |formfeed| + |cothIfCan| |idealiserMatrix| |superscript| |first| |startPolynomial| + |key?| |rroot| |algebraicDecompose| |normalizedDivide| |round| |clip| + |integralMatrix| |filename| |lfinfieldint| |bivariatePolynomials| + |rest| |currentScope| |connect| |corrPoly| |iiacsc| |plot| |bat1| + |radicalEigenvector| |multisect| |close| |f07fef| |s18adf| |linefeed| + |rubiksGroup| |d02cjf| |innerEigenvectors| |OMputEndAtp| + |diophantineSystem| |minGbasis| |remove!| |numFunEvals| |parse| + |sin2csc| |reducedForm| |quasiAlgebraicSet| |substitute| + |fortranComplex| UTS2UP |log| |KrullNumber| |OMputSymbol| + |explicitlyFinite?| |display| |iipow| |algebraicSort| |modTree| + |e01bgf| |tablePow| |rotate!| |internalInfRittWu?| |plus!| |d02gaf| + |palgextint0| |nodes| |clikeUniv| |euler| |setValue!| |ode2| + |subscriptedVariables| |baseRDEsys| |palgextint| |factorByRecursion| + |tubeRadius| |allRootsOf| |lp| |child| |quadraticForm| + |stoseInvertibleSet| |exprToXXP| |saturate| |jvmVolatile| |findCycle| + |commaSeparate| |tValues| |copies| |getMultiplicationTable| |s15adf| + |rightDiscriminant| |deleteRoutine!| |OMputEndError| |cSec| |rules| + |headAst| |isPlus| |univariatePolynomialsGcds| |dimension| |eof?| + |graphState| |iiacsch| |useSingleFactorBound| |critBonD| + |internalIntegrate| |value| |setRealSteps| |maxPoints| |input| + |f02aaf| |s17aef| |edf2df| |topFortranOutputStack| |rootsOf| + |lighting| |inspect| |reseed| |e01sef| |degreeSubResultant| |library| + |iitanh| |argumentListOf| |janko2| |stoseIntegralLastSubResultant| + |internalSubPolSet?| |eigenvector| |pascalTriangle| |uniform| + |squareFreePrim| |OMgetType| |getMultiplicationMatrix| |setClosed| + |bezoutResultant| |numberOfIrreduciblePoly| |whitePoint| |powerSum| + |OMgetEndError| |OMreadFile| |moreAlgebraic?| + |setLegalFortranSourceExtensions| |e02zaf| |nodeOf?| |bright| |super| + |degreeSubResultantEuclidean| |branchIfCan| |f04adf| |quote| + |nextNormalPrimitivePoly| |structuralConstants| + |semiResultantEuclidean2| |insert!| |diag| |splitSquarefree| + |typeForm| |in?| |sumOfKthPowerDivisors| |sturmSequence| |ffactor| + |rewriteSetByReducingWithParticularGenerators| + |stiffnessAndStabilityOfODEIF| |pushucoef| |dmpToHdmp| |typeList| + |oneDimensionalArray| |integral| |showTheIFTable| |regime| |init| + |submod| |backspace| |nextPrimitiveNormalPoly| |toseInvertibleSet| + |Ci| |mirror| |functionIsOscillatory| |algebraicVariables| |f01qef| + |setref| |ellipticCylindrical| |trapezoidal| |comparison| + |triangulate| |bernoulliB| |meatAxe| |algint| |lyndon| |quotientByP| + |d01fcf| |units| |dmp2rfi| |setScreenResolution3D| + |bipolarCylindrical| |content| |intensity| |outlineRender| + |addMatchRestricted| |evenInfiniteProduct| |cAcos| |sinh2csch| + |merge!| |viewport2D| |primaryDecomp| |deepestInitial| |infix| + |mainVariables| |resetBadValues| |normalForm| |setMaxPoints| |pushup| + |setProperty| |removeDuplicates| |getOrder| |firstNumer| + |mainPrimitivePart| |stFunc1| |vector| |constantToUnaryFunction| + |deref| |entry| |lambert| |thenBranch| |frobenius| |coordinate| + |remove| |basisOfLeftNucleus| |leastAffineMultiple| + |fillPascalTriangle| |c05nbf| |differentiate| + |cyclotomicDecomposition| |leadingTerm| |label| |mainCoefficients| + |symFunc| |simpsono| |sturmVariationsOf| |normalize| |rk4| + |rightFactorCandidate| |imagK| |setButtonValue| |clearTable!| |code| + |leftGcd| |iiasec| |c06gbf| |monomRDE| |last| |expr| |isobaric?| + |problemPoints| |curry| |makeFloatFunction| |assoc| |setvalue!| + |rotatey| |head| |graphImage| |tanNa| |show| |f02ajf| |setAdaptive3D| + |assign| |conjugate| |OMsend| |selectSumOfSquaresRoutines| |iCompose| + |cyclicEqual?| |decreasePrecision| |OMsetEncoding| |btwFact| + |setMinPoints3D| |jvmSynchronized| |imagI| |extractIndex| |cAcsc| + |putProperty| |hostByteOrder| |represents| |showAll?| |trace| + |mapSolve| |numberOfChildren| |alphanumeric| |setrest!| |recolor| + |reorder| |leftDivide| |level| |gcdPolynomial| |hMonic| + |getPickedPoints| |variable| |rootPoly| |e01bef| |cSech| |shiftRight| + |duplicates?| |notelem| |exponent| |logIfCan| |LowTriBddDenomInv| + |positive?| |printInfo| |totalDifferential| |iterators| |e02baf| + |headReduce| |checkRur| |predicate| |besselJ| |option| |fractRadix| + |initializeGroupForWordProblem| |deepCopy| |e01bff| |drawCurves| + |aLinear| |colorDef| |edf2ef| |cos2sec| |singularAtInfinity?| |top| + |expandLog| |pToDmp| |subscript| |associatorDependence| |aQuartic| + |findConstructor| |OMgetEndBind| |numFunEvals3D| |tableau| |polyPart| + |continue| |characteristicSerie| |integralMatrixAtInfinity| + |prepareSubResAlgo| |cartesian| |simpson| |aromberg| |LazardQuotient2| + |doubleRank| |trunc| |selectOptimizationRoutines| |possiblyInfinite?| + |monomialIntPoly| |d02bbf| |rewriteIdealWithRemainder| + |multiplyCoefficients| |leftUnits| |addPointLast| |bits| |mulmod| + |delete| |nextColeman| |tanAn| |brillhartTrials| |sncndn| |e04dgf| + |ScanRoman| |contains?| |elRow1!| |adaptive3D?| |isOr| |controlPanel| + |vectorise| |rightScalarTimes!| |disjunction| |rootPower| + |exprHasWeightCosWXorSinWX| |iicosh| |npcoef| |operators| |fTable| + |rightMinimalPolynomial| |equiv| |skewSFunction| |basisOfNucleus| + |OMgetBind| |readInt8!| |normalDenom| |elaboration| |leadingIdeal| + |Ei| |s17akf| |extractBottom!| |rewriteIdealWithHeadRemainder| |seed| + |bfKeys| |minimize| |removeSinSq| |getCurve| |loadNativeModule| + |romberg| |check| |removeZero| |hasHi| |henselFact| + |localIntegralBasis| |split!| |constantLeft| |postfix| |expPot| + |lazyEvaluate| |systemSizeIF| |comp| |factorsOfDegree| |parameters| + |strongGenerators| |screenResolution3D| |d02raf| |selectPDERoutines| + |isPower| |scanOneDimSubspaces| |shiftLeft| |parent| |tube| |rem| + |any?| |semicolonSeparate| |branchPoint?| |quartic| + |rectangularMatrix| |printStatement| |basis| |relativeApprox| + |separate| |s19abf| |viewDefaults| |quo| |s13aaf| |addPoint2| + |OMsupportsSymbol?| |se2rfi| |entry?| |plenaryPower| |minRowIndex| + |doubleFloatFormat| |zeroSetSplitIntoTriangularSystems| |evaluate| + |factorSFBRlcUnit| |fi2df| |euclideanNormalForm| |Aleph| |times!| + |genericRightTrace| |rotatex| |totalLex| |showTheSymbolTable| + |setprevious!| |quasiRegular?| |div| |primintegrate| |radicalSolve| + |applyRules| |complexZeros| |LyndonWordsList| |identityMatrix| + |pattern| |showTheFTable| |jvmClassConstantTag| |eq?| |pointPlot| + |showSummary| |exquo| |clipBoolean| |df2mf| |groebner?| |d01akf| + |block| |modifyPoint| |over| |setVariableOrder| |log2| |critMonD1| ~= + |antiCommutative?| |cPower| |principal?| |OMputString| |constantIfCan| + |point?| |hexDigit| |evenlambert| |reducedQPowers| |squareFreeFactors| + |showAttributes| |#| |edf2efi| |jvmInterface| |createNormalElement| + |imports| |zeroDimPrimary?| |lowerCase!| |push| |logGamma| |e01sbf| + |newTypeLists| ~ |f01bsf| |typeLists| |vertConcat| |tanh2coth| |log10| + |adaptive| |d02gbf| |changeVar| |s13acf| |traverse| |is?| + |clearTheSymbolTable| |delete!| |GospersMethod| |hermite| |concat| + |lintgcd| |dmpToP| BY |bitand| |droot| |cyclicParents| + |computeCycleLength| |OMputObject| |nullary| |pseudoQuotient| + |palgRDE| |goodnessOfFit| |LagrangeInterpolation| |rotatez| + |mergeDifference| |weights| |bitior| |mapUp!| |bit?| |firstSubsetGray| + |acothIfCan| |f04mcf| |prime?| |/\\| |s13adf| |overlabel| |scan| + |gcdprim| |padicallyExpand| |operation| LODO2FUN |chebyshevT| + |completeHensel| |conjug| |pomopo!| |leftQuotient| |lfextendedint| + |\\/| |categoryMode| |implies| |jvmProtected| |OMlistCDs| + |relationsIdeal| |multiEuclidean| |genericLeftTraceForm| |open| + |infLex?| |mapMatrixIfCan| |selectNonFiniteRoutines| + |leftScalarTimes!| |resultantEuclideannaif| |linkToFortran| |tan2cot| + |getMatch| |minPol| |multiset| |parts| |insertionSort!| |supRittWu?| + |generalInfiniteProduct| |localAbs| |removeDuplicates!| + |leftTraceMatrix| |chebyshevU| |getGoodPrime| |clearCache| |tan2trig| + |e01daf| |rightRemainder| |index?| |SturmHabichtCoefficients| + |reverseLex| |getMeasure| |rightRank| |infRittWu?| |parents| + |numberOfCycles| |wordInGenerators| |nthCoef| |twist| + |LyndonWordsList1| |conjugates| NOT |basisOfCenter| |cycleElt| + |factorSquareFreeByRecursion| |bottom!| |mainForm| |support| + |operations| |showArrayValues| |printCode| |module| |radPoly| + |normFactors| OR |mkcomm| |singularitiesOf| |e02daf| |nthExpon| + |s21bbf| |cLog| |comment| |zoom| |mainKernel| |frst| |realElementary| + |idealSimplify| AND |true| |innerint| |minus!| |refine| + |particularSolution| |c06ekf| |trailingCoefficient| |conditionP| + |exptMod| |signatureAst| |multMonom| |mainVariable| |iisec| + |eyeDistance| |sizeLess?| |lazyPseudoDivide| |adaptive?| |minPoly| + |generalPosition| |transform| |removeRedundantFactorsInPols| |trim| + |title| |numer| |ceiling| |reindex| |exactQuotient!| + |leftAlternative?| |outputFixed| |SturmHabichtMultiple| |convert| + |stirling2| |OMputBVar| |csch2sinh| |hasTopPredicate?| + |expandTrigProducts| |numericIfCan| |denom| |squareFreeLexTriangular| + |cosSinInfo| |prindINFO| |rightExtendedGcd| |atoms| |cup| |predicates| + |getProperties| |bandedHessian| |lcm| |const| |jacobian| + |setchildren!| |equality| |stronglyReduce| |primitivePart| |morphism| + |chvar| |e| |direction| |setfirst!| |pi| |cyclicEntries| |set| + |symmetricProduct| |e04mbf| |rootSplit| |taylorRep| |inrootof| + |mapDown!| |mapExponents| |patternMatch| |nthFlag| + |internalLastSubResultant| |append| |infinity| |aspFilename| |cycles| + |makeCos| |Lazard| |cyclotomicFactorization| |macroExpand| + |jvmUTF8ConstantTag| |lifting1| |e02gaf| |gcd| |setMaxPoints3D| + |totalDegree| |hypergeometric0F1| |semiIndiceSubResultantEuclidean| + |write!| |groebnerFactorize| |figureUnits| |linearAssociatedExp| + |constantRight| |sylvesterSequence| |asechIfCan| |false| |rur| + |f04arf| |arity| |sumSquares| |clipPointsDefault| |intcompBasis| + |parabolic| |factors| |generalizedInverse| |OMputApp| |kernel| + |incrementKthElement| * |generalizedContinuumHypothesisAssumed?| + |fortranReal| |jokerMode| |semiDegreeSubResultantEuclidean| |f04atf| + |schwerpunkt| |nthFactor| |computePowers| |uniform01| |rightPower| + |list| |minset| |prem| |expintegrate| |cyclotomic| |e01saf| |draw| + |tanintegrate| |arg1| |addiag| |realEigenvectors| |extend| |bothWays| + |compose| |currentEnv| |secIfCan| |sort| |arg2| |c06ecf| + |laurentIfCan| |ScanArabic| |removeSuperfluousQuasiComponents| + |getVariableOrder| = |polyred| |baseRDE| |bounds| |null| |fortran| + |identity| |d01anf| |rightRegularRepresentation| |create| |OMgetAtp| + |OMputEndObject| |high| |redPo| |not| |random| |pointColor| |pdf2df| + |conditions| |univariatePolynomials| |besselK| |bat| < |monomRDEsys| + |cycleTail| |lowerPolynomial| |and| |arbitrary| |makeObject| + |property| |curryRight| > |generator| |acotIfCan| |complexNormalize| + |youngDiagram| |or| |cyclicCopy| |trigs| |upperCase?| |zero| + |OMputEndBVar| |coef| |thetaCoord| |irDef| <= |lprop| |cycleEntry| + |partialQuotients| |xor| |negative?| |polygamma| |hdmpToDmp| |expt| + |scalarTypeOf| |deepestTail| >= |retractable?| |makeYoungTableau| + |cSin| |condition| |case| |s17dhf| |dot| |formula| |And| + |mightHaveRoots| |curve?| |colorFunction| |extractSplittingLeaf| |pow| + |Zero| |RittWuCompare| |purelyTranscendental?| |f2df| + |expenseOfEvaluation| |Or| |tower| |laguerreL| |numberOfPrimitivePoly| + |diagonalProduct| |orthonormalBasis| |One| |newline| |nonQsign| + |numberOfDivisors| |Not| |OMgetObject| |clearFortranOutputStack| + |redmat| |match?| + |unprotectedRemoveRedundantFactors| + |multiplyExponents| |usingTable?| |hclf| |lflimitedint| |central?| + |jvmAbstract| |irreducibleRepresentation| |pureLex| - |pdf2ef| + |outputGeneral| |differentialVariables| |rk4f| |setStatus| |nrows| + |iiacosh| |pushdterm| |nextLatticePermutation| |signature| / + |setClipValue| |functionIsFracPolynomial?| |normalElement| + |setColumn!| |quasiMonic?| |setelt| |omError| |radicalSimplify| + |ncols| |has?| |graphs| |createLowComplexityNormalBasis| + |prefixRagits| |monomial?| |euclideanSize| |swapColumns!| |byteBuffer| + |setOfMinN| |readLineIfCan!| |distdfact| |s20acf| |integralRepresents| + |cAsech| |script| |elt| |changeThreshhold| |copy| |nextNormalPoly| + |jvmDoubleConstantTag| |changeName| |yCoordinates| |complexNumeric| + |prefix| |laurentRep| |incr| |minrank| |scale| |neglist| |e04jaf| + |curveColorPalette| |elliptic?| |genericRightDiscriminant| |squareTop| + |hi| |perfectNthRoot| |closed?| |makeprod| |autoCoerce| + |functionIsContinuousAtEndPoints| |mainValue| |kernels| |minIndex| + |subCase?| |sh| |front| |tex| |bombieriNorm| |iExquo| |genus| + |removeZeroes| |capacity| |computeBasis| |prinb| |operator| + |viewWriteDefault| |listLoops| |errorKind| |subset?| |imaginary| + |entries| |mapUnivariate| |anticoord| |pile| |univariate| |endOfFile?| + |integralBasisAtInfinity| |realZeros| |failed?| |mainMonomial| + |f02xef| |lazyPquo| |overlap| |coerceL| |functorData| |lazyPrem| + |s17dlf| |read!| |generalSqFr| |UP2ifCan| |isExpt| |trueEqual| + |e02akf| |vedf2vef| |torsionIfCan| |d03edf| |OMgetApp| |df2fi| + |OMconnInDevice| |leftFactorIfCan| |iibinom| + |tableForDiscreteLogarithm| |jacobi| |zeroDim?| |irreducibleFactors| + |expenseOfEvaluationIF| |measure| |sdf2lst| |setAdaptive| |birth| + |compdegd| |factor| |binomThmExpt| |compile| |matrixGcd| |idealiser| + |dequeue| |removeConstantTerm| |whatInfinity| |repeating?| |rk4a| + |rightGcd| |mainDefiningPolynomial| |randnum| |sqrt| |palgintegrate| + |constDsolve| |OMmakeConn| |addmod| |removeRedundantFactorsInContents| + |modulus| |horizontalTab| |cond| |s18aff| |finiteBound| |real| + |jvmFieldrefConstantTag| GF2FG |calcRanges| |one?| |f02fjf| + |toseInvertible?| |leadingBasisTerm| |every?| |leftRemainder| |imag| + |monicCompleteDecompose| |jvmIntegerConstantTag| + |nativeModuleExtension| |dfRange| |OMopenFile| |processTemplate| + |wreath| |gbasis| |directProduct| |primintfldpoly| |perfectNthPower?| + |ScanFloatIgnoreSpaces| |closedCurve| |complexEigenvalues| + |shallowCopy| |cschIfCan| |s21bdf| |f02adf| |realEigenvalues| |s19acf| + |partialNumerators| |less?| |linGenPos| |tree| |getConstant| + |trapezoidalo| |cAtanh| |genericLeftMinimalPolynomial| + |euclideanGroebner| |compiledFunction| |reducedDiscriminant| |brace| + |checkForZero| |generate| |mappingAst| |OMcloseConn| |Gamma| + |specialTrigs| |noncommutativeJordanAlgebra?| |nsqfree| + |newSubProgram| |readInt16!| |unvectorise| |destruct| |quasiRegular| + |leftExtendedGcd| |ef2edf| |noLinearFactor?| |xCoord| |seriesSolve| + |createPrimitivePoly| |selectFiniteRoutines| |iitan| + |ramifiedAtInfinity?| |iiabs| |makeTerm| |commutative?| |incrementBy| + |escape| |s21baf| |invertIfCan| |patternVariable| |empty?| + |primextintfrac| |shiftRoots| |showRegion| |parabolicCylindrical| + |expand| |leadingExponent| |getStream| |jordanAdmissible?| + |partitions| |d01asf| |f01mcf| |rootProduct| |generalizedEigenvector| + |addMatch| |filterWhile| |exponentialOrder| |totalfract| |df2ef| + |padicFraction| |LazardQuotient| |sortConstraints| + |createLowComplexityTable| |monomial| |rationalFunction| |normalDeriv| + |filterUntil| |computeInt| |binaryFunction| |outputMeasure| + |factorSquareFree| |cyclic| |unary?| |e02aef| |d02bhf| |multivariate| + |prevPrime| |select| |getOperator| |var2StepsDefault| |space| + |measure2Result| |subHeight| |iiperm| |nil| |insert| |radix| + |packageCall| |variables| |unaryFunction| |basisOfRightNucloid| |kmax| + |cCot| |countRealRoots| |simplifyExp| |nextsousResultant2| |separant| + |polynomialZeros| |dihedral| |initial| |bezoutDiscriminant| + |factorSquareFreePolynomial| |carriageReturn| |e02bcf| + |numberOfOperations| |lift| |dn| |complexExpand| |voidMode| + |diagonalMatrix| |primeFactor| |pole?| |associates?| |userOrdered?| + |extendedint| |reduce| |approximate| |componentUpperBound| + |lazyPremWithDefault| |integers| |stack| |subResultantGcd| |stop| + |routines| |llprop| |makeSeries| |OMgetAttr| |perspective| |complex| + |keys| |string?| |schema| |triangSolve| |addBadValue| |bracket| + |putGraph| |associator| |remainder| |host| |iiacoth| |ran| + |trivialIdeal?| |taylor| |fractionPart| |cyclicGroup| |imagJ| |irForm| + |modifyPointData| |float?| |setRow!| |f01rcf| |double| |permanent| + |laurent| |eisensteinIrreducible?| |readBytes!| |palginfieldint| + |jvmFloatConstantTag| |initials| |generalLambert| |getButtonValue| + |balancedFactorisation| |outerProduct| |adjoint| |puiseux| |isAtom| + |moebius| |outputList| |nullity| |sizeMultiplication| |jvmSuper| + |splitDenominator| |dom| |dflist| |cCsch| |duplicates| + |unitsColorDefault| |stopMusserTrials| |univcase| |s17adf| + |OMconnOutDevice| |e01sff| |obj| |integerBound| |expextendedint| |inv| + |hasPredicate?| |ord| |eigenvalues| |c02agf| |repeatUntilLoop| + |s17dgf| |makeRecord| |dimensions| |f04faf| |numberOfHues| + |transcendenceDegree| |ground?| |removeSquaresIfCan| + |rightTraceMatrix| |topPredicate| |consnewpol| |rarrow| |newReduc| + |expressIdealMember| |elliptic| |sumOfSquares| |iiasech| |precision| + |op| |linearMatrix| |ground| |hue| |factorGroebnerBasis| + |computeCycleEntry| |exp1| |zeroVector| |outputSpacing| |recur| + |backOldPos| |inverseLaplace| |leadingMonomial| |extractIfCan| |slash| + |cSinh| |wordInStrongGenerators| |lazyPseudoRemainder| |vconcat| + |acoshIfCan| |alphanumeric?| |splitConstant| |mapdiv| |declare!| + |safeFloor| |leadingCoefficient| |socf2socdf| |ignore?| |f02awf| + |diagonal| |createThreeSpace| |optimize| |showTheRoutinesTable| + |algintegrate| |f02bbf| |primitiveMonomials| |upperBound| + |stripCommentsAndBlanks| |tail| |qinterval| |f2st| |pushuconst| + |nextSubsetGray| |lazy?| |writable?| |monomials| |copyInto!| |ranges| + |midpoints| |reductum| |pleskenSplit| |reduceBasisAtInfinity| + |OMgetSymbol| |subQuasiComponent?| |cyclic?| |byte| |ksec| + |purelyAlgebraicLeadingMonomial?| |simpleBounds?| |normal?| + |enumerate| |identitySquareMatrix| |selectOrPolynomials| + |nonSingularModel| |numberOfNormalPoly| |isTimes| + |partialDenominators| |kind| |cAcsch| |defineProperty| |lhs| |orbit| + |e02dcf| |degree| |solid| |makeEq| |product| |mkIntegral| + |associative?| |pointData| |tensorProduct| |rhs| |SFunction| |iidsum| + |repeating| |radicalOfLeftTraceForm| |exprToUPS| |coefChoose| |eq| + |localReal?| |viewPhiDefault| |f04qaf| |sechIfCan| |numberOfVariables| + |insertMatch| |open?| |atrapezoidal| |mainVariable?| |iter| |aCubic| + |exponents| |fortranLinkerArgs| |integralLastSubResultant| |segment| + |BasicMethod| |width| |lexGroebner| |c06eaf| |showScalarValues| + |fibonacci| |jvmTransient| |real?| |bumptab| |redPol| |xn| + |extensionDegree| |leftRecip| |selectfirst| |hyperelliptic| |e04ycf| + |iiasinh| |f01brf| |OMputEndApp| |fractRagits| |seriesToOutputForm| + |genericRightMinimalPolynomial| |positiveSolve| |interactiveEnv| + |createMultiplicationTable| |e02def| |int| |someBasis| |readInt32!| + |initTable!| |erf| |leftMult| |PDESolve| |infinityNorm| |f04maf| + |badValues| |output| |fullDisplay| |any| |UpTriBddDenomInv| + |var1StepsDefault| |lazyIrreducibleFactors| |void| |s18def| |nthRoot| + |mat| |imagk| |test| |jvmStatic| |magnitude| |OMread| |region| |pdct| + |OMputError| |taylorIfCan| |s21bcf| |monicRightFactorIfCan| + |lexTriangular| |atanhIfCan| |returns| |OMreadStr| |optional| + |pseudoRemainder| |dilog| |linearAssociatedLog| |charpol| + |pseudoDivide| |extractProperty| |hash| |useEisensteinCriterion?| + |cAtan| |bfEntry| |sin| |leftZero| |selectsecond| |swap!| + |fixedDivisor| |ipow| |makeop| |count| |explogs2trigs| |sinhIfCan| + |pair?| |cos| |bitCoef| |unitCanonical| |antiAssociative?| |d02ejf| + |exprToGenUPS| |message| |lookup| |s17agf| |rename!| |viewZoomDefault| + |tan| |separateFactors| |divideExponents| |multiple?| |setEmpty!| + |d02kef| |OMunhandledSymbol| |dioSolve| |cot| |indicialEquation| + |subSet| |factorOfDegree| |contractSolve| |connectTo| + |indicialEquations| |palgint0| |s14baf| |headReduced?| |rischDEsys| + |sec| |rdregime| |poisson| |char| |goto| |imagE| |dictionary| + |OMsupportsCD?| |halfExtendedSubResultantGcd1| |logpart| + |viewDeltaYDefault| |drawToScale| |csc| |mkPrim| |rombergo| |f04asf| + |listBranches| |pack!| |ptFunc| |generic?| |mr| |lex| |asin| |nlde| + |revert| |reduceLODE| |nilFactor| |mergeFactors| + |exprHasAlgebraicWeight| |acos| |closed| |cAcot| |setright!| + |heapSort| |f02akf| |FormatRoman| |back| |double?| |atan| |member?| + |setStatus!| |continuedFraction| |pointColorDefault| |float| |result| + |internalZeroSetSplit| |eigenvectors| |irreducibleFactor| |zag| + |alternating| |acot| |fglmIfCan| |buildSyntax| |shuffle| |monom| + |totalGroebner| |updatD| |stoseInvertible?reg| |asec| + |conditionsForIdempotents| |fractionFreeGauss!| + |combineFeatureCompatibility| |iicoth| |ScanFloatIgnoreSpacesIfCan| + |LyndonBasis| RF2UTS |complexSolve| |acsc| |options| |e02ajf| + |inverse| |find| |selectODEIVPRoutines| |constructor| |infinite?| + |isConnected?| |halfExtendedSubResultantGcd2| |normInvertible?| + |edf2fi| |sinh| |discreteLog| |f02axf| |common| |getOperands| |c06frf| + |clearTheIFTable| |wrregime| |satisfy?| |inR?| |cosh| |string| + |monic?| |bumptab1| |factorPolynomial| + |selectMultiDimensionalRoutines| |credPol| |showClipRegion| |largest| + |length| |exactQuotient| |createPrimitiveElement| |tanh| |exprex| + |mindegTerm| |infieldint| |optional?| |pmComplexintegrate| |ratPoly| + |solveLinearlyOverQ| |meshPar2Var| |scripts| |toScale| |reverse| + |directSum| |coth| |rowEch| |getGraph| |OMputVariable| |BumInSepFFE| + |makeViewport2D| |f02aff| |divideIfCan!| |extendedResultant| + |finiteBasis| |sech| |d01apf| |restorePrecision| |nthExponent| + |sech2cosh| |crest| GE |lazyVariations| |maxint| |OMgetEndApp| + |lambda| |cAcoth| |csch| |primlimitedint| UP2UTS |column| |constant?| + |inputOutputBinaryFile| GT |isNot| |PollardSmallFactor| |OMgetError| + |leftCharacteristicPolynomial| |asinh| |generators| + |radicalEigenvalues| |polCase| |rewriteSetWithReduction| |Si| LE + |bipolar| |rightMult| |middle| |groebSolve| |acosh| |An| + |closedCurve?| |rst| |bandedJacobian| |changeMeasure| LT + |makeGraphImage| |flexible?| |bernoulli| |iiacot| |atanh| + |appendPoint| F2FG |blue| |monicDivide| |separateDegrees| + |createNormalPrimitivePoly| |d01gbf| |ListOfTerms| |diagonals| + |factorset| |acoth| |e02bdf| |low| |scaleRoots| |constantKernel| + |removeRoughlyRedundantFactorsInPol| |directory| |unmakeSUP| + |jordanAlgebra?| |shrinkable| |fortranDouble| |asech| |commutator| + |unrankImproperPartitions1| |hconcat| |linearlyDependentOverZ?| + |semiResultantEuclidean1| |categoryFrame| |firstUncouplingMatrix| + |readLine!| |OMputBind| |root| |untab| |stirling1| + |removeRoughlyRedundantFactorsInContents| |aQuadratic| |f01ref| + |genericRightTraceForm| |mapmult| |complex?| |multiple| |nextPrime| + |semiLastSubResultantEuclidean| |iiasin| |outputArgs| |leftNorm| + |youngGroup| |removeRoughlyRedundantFactorsInPols| + |removeSuperfluousCases| |subPolSet?| |applyQuote| |eulerE| + |stoseInvertible?sqfreg| |relerror| |po| |coercePreimagesImages| + |ridHack1| |d03eef| |elements| |invertibleSet| |setleft!| + |setPosition| |interReduce| |cfirst| |maxColIndex| + |complexNumericIfCan| |redpps| |brillhartIrreducible?| |integralBasis| + |cn| |singular?| |jvmStringConstantTag| |e04ucf| |bytes| + |selectPolynomials| |compBound| |leftRegularRepresentation| + |resultantEuclidean| |OMencodingXML| |rspace| |currentSubProgram| + |ruleset| |listexp| |recoverAfterFail| |distFact| |cot2trig| + |mainMonomials| |stFuncN| |normDeriv2| |OMbindTCP| |exponential| + |nextIrreduciblePoly| |readUInt32!| |countRealRootsMultiple| + |basisOfRightAnnihilator| |iiatanh| |symmetricTensors| |OMgetEndAtp| + |d01bbf| |principalIdeal| |c05pbf| |plusInfinity| |iisinh| + |inHallBasis?| |commutativeEquality| |acscIfCan| |push!| |divide| + |elaborate| |divisorCascade| |minusInfinity| |optpair| |suchThat| + |rightZero| |solveLinear| |hasSolution?| |symmetric?| + |associatedSystem| |terms| |solveInField| |surface| |lazyResidueClass| + |ratDenom| |limitedIntegrate| |s17acf| |supDimElseRittWu?| + |internalAugment| |linearlyDependent?| |categories| + |useEisensteinCriterion| |id| |fullPartialFraction| |setEpilogue!| + |shufflein| |sinIfCan| |antisymmetric?| |increasePrecision| + |legendreP| |function| |node?| |lo| |evaluateInverse| |coerceImages| + |mathieu22| |besselY| |setProperties| |tubeRadiusDefault| |distribute| + |weighted| |chiSquare| |step| |OMUnknownSymbol?| |prime| |oddlambert| + |flagFactor| |mapBivariate| |even?| |makeMulti| |maxRowIndex| + |attributeData| |groebner| |cons| |d01aqf| |imagi| |minPoints3D| + |substring?| |OMreceive| |numerator| |copy!| |completeHermite| + |rischNormalize| |integral?| |plotPolar| |power| |tubePlot| + |rationalApproximation| |roughSubIdeal?| |e04fdf| + |linearDependenceOverZ| |ldf2lst| |ravel| |outputForm| |position!| + |coefficient| |digit?| |suffix?| |palgLODE| |coth2tanh| |elem?| + |minimumDegree| |cCsc| |ptree| |reshape| |f07aef| |initiallyReduced?| + |integrate| |curve| |paraboloidal| |airyBi| |concat!| |d01alf| |dim| + |lastSubResultantElseSplit| |arguments| |lieAdmissible?| |sparsityIF| + |Lazard2| |rootNormalize| |prefix?| |f02agf| |OMgetInteger| |s14aaf| + |viewPosDefault| |rewriteIdealWithQuasiMonicGenerators| |source| + |lowerBound| |inRadical?| |dAndcExp| |oddintegers| |li| |mkAnswer| + |symmetricGroup| |modularGcdPrimitive| |addPoint| |ratDsolve| + |hdmpToP| |dualSignature| |cscIfCan| |powern| |variable?| |e01bhf| + |zeroDimensional?| |dimensionsOf| |belong?| |compound?| + |clipParametric| |characteristicPolynomial| |balancedBinaryTree| + |meshFun2Var| |rowEchelon| |underscore| |quoted?| |loopPoints| + |e02ahf| |target| |sequence| |linears| |karatsubaOnce| + |useNagFunctions| |retract| |subNodeOf?| |zerosOf| |unitNormalize| + |environment| |nil?| |qPot| |smith| |solid?| |increase| |lowerCase?| + |reducedContinuedFraction| |primlimintfrac| |fracPart| + |triangularSystems| |lyndon?| |s14abf| |polar| |infix?| + |viewThetaDefault| |debug3D| |mainContent| |rk4qc| + |lastSubResultantEuclidean| |rationalPower| |expandPower| |countable?| + |jvmMethodrefConstantTag| |conical| |factorAndSplit| |mask| + |resetAttributeButtons| |cotIfCan| |leftRank| |toseSquareFreePart| + |symbolIfCan| |coerceP| |complement| |Vectorise| |position| + |indiceSubResultantEuclidean| |bumprow| |callForm?| + |stoseLastSubResultant| |alphabetic?| |updatF| |upperCase| + |innerSolve| |isMult| |reducedSystem| |iisin| |noValueMode| + |wholeRagits| |scopes| |cubic| |reciprocalPolynomial| |shallowExpand| + |setleaves!| |symmetricSquare| |RemainderList| |blankSeparate| + |initiallyReduce| |e02adf| |s17dcf| |listOfMonoms| |table| |jvmNative| + |explicitEntries?| |leftExactQuotient| |linearPolynomials| + |discriminant| |completeEval| |trigs2explogs| |maximumExponent| + |writeLine!| |padecf| |new| |extract!| |normalizeIfCan| Y |printInfo!| + |gramschmidt| |extendIfCan| |symmetricPower| |coshIfCan| + |doubleResultant| |c06fpf| |gcdcofact| |splitNodeOf!| |inGroundField?| + |iifact| |validExponential| |antiCommutator| |maxPoints3D| + |eigenMatrix| |updateStatus!| |prologue| |top!| |nextPartition| + |printingInfo?| |setFieldInfo| |knownInfBasis| |fortranInteger| + |cyclicSubmodule| |second| |axesColorDefault| |simplifyLog| + |quadraticNorm| |fmecg| |Frobenius| |critM| |convergents| + |showIntensityFunctions| |denomRicDE| |radicalRoots| |third| + |doubleDisc| |solveLinearPolynomialEquationByFractions| |divisor| + |inc| |replace| |constantCoefficientRicDE| |divisors| + |symmetricDifference| |upDateBranches| |showFortranOutputStack| + |acsch| |primes| |quatern| |UnVectorise| |weight| |subspace| + |weakBiRank| |bitTruth| |Nul| |ref| |B1solve| |tanhIfCan| + |OMconnectTCP| |cCos| |certainlySubVariety?| |dark| |isOp| |maxrank| + |extractClosed| |iidprod| |numberOfImproperPartitions| |properties| + |overbar| |univariate?| |dequeue!| |algebraicOf| + |stoseInvertibleSetreg| |setPrologue!| |getlo| |setImagSteps| + |translate| |getZechTable| |antisymmetricTensors| |tRange| + |zeroSetSplit| |odd?| |Hausdorff| |left| |genericLeftDiscriminant| + |cycle| |extendedSubResultantGcd| |indicialEquationAtInfinity| + |listYoungTableaus| |power!| |commonDenominator| |sts2stst| |size?| + |right| |shanksDiscLogAlgorithm| |leftDiscriminant| |call| + |doublyTransitive?| |radicalEigenvectors| |argumentList!| |insertTop!| + |parametric?| |sec2cos| |setAttributeButtonStep| |complexLimit| + |s17aff| |minimumExponent| |index| |coordinates| |extractPoint| + |invmod| |failed| |extractTop!| |denominator| |tab| |df2st| + |wordsForStrongGenerators| |mpsode| |numericalOptimization| |prod| + |getExplanations| |elRow2!| |external?| |monicDecomposeIfCan| |sort!| + |cap| |pair| |nextsubResultant2| |sumOfDivisors| |rightExactQuotient| + |name| |createRandomElement| |retractIfCan| |squareFree| |lSpaceBasis| + |dimensionOfIrreducibleRepresentation| |regularRepresentation| + |tracePowMod| |iiGamma| |eulerPhi| |numberOfMonomials| |readIfCan!| + |body| |OMlistSymbols| |fortranLiteral| + |removeIrreducibleRedundantFactors| |solve| |error| + |chainSubResultants| |quoByVar| |tubePoints| |fortranCarriageReturn| + |squareFreePart| |f07fdf| |pquo| |lookupFunction| |genericRightNorm| + |interpret| |taylorQuoByVar| |splitLinear| |denomLODE| |sincos| + |pr2dmp| |returnType!| |resultant| |isEquiv| |outputAsScript| + |showAllElements| |coHeight| |rCoord| |setCondition!| |basicSet| + |writeInt8!| |algebraicCoefficients?| |nonLinearPart| |newLine| + |qfactor| |generalizedContinuumHypothesisAssumed| + |leadingCoefficientRicDE| |definingEquations| |exportedOperators| + |drawComplexVectorField| |solve1| |rename| |iteratedInitials| + |curryLeft| |geometric| |transcendentalDecompose| |nthr| |att2Result| + |dihedralGroup| |semiSubResultantGcdEuclidean1| |hex| |integerIfCan| + |zeroOf| |physicalLength!| |linear| |leftReducedSystem| + |derivationCoordinates| |rightFactorIfCan| |twoFactor| |viewport3D| + |rowEchLocal| |stFunc2| |rootOf| |moebiusMu| |symbol| |OMputFloat| + |difference| |screenResolution| |resultantReduit| |composite| + |conjunction| |coleman| |associatedEquations| |polyRicDE| |polynomial| + |expression| |approximants| |genericPosition| |fintegrate| |groebgen| + |changeWeightLevel| |arrayStack| |lazyIntegrate| |iicsch| |port| + |numberOfFractionalTerms| |integer| |safeCeiling| |hitherPlane| + |checkPrecision| |quadratic| |bezoutMatrix| |setPredicates| |eval| + |harmonic| |startTableGcd!| |character?| |search| |minPoints| + |divergence| |lineColorDefault| |empty| |stiffnessAndStabilityFactor| + |enterInCache| |varselect| |expintfldpoly| |interpretString| + |derivative| |elaborateFile| |scripted?| |palgLODE0| |digit| + |complete| |octon| |nextItem| |f04jgf| |t| |leadingIndex| + |linearElement| |outputBinaryFile| |prinpolINFO| |deepExpand| + |pToHdmp| |digamma| |opeval| |unexpand| |mathieu24| |cAsec| |vark| + |leftLcm| |solveid| |unknown| |setFormula!| |digits| |order| + |minordet| |split| |characteristic| |insertBottom!| + |patternMatchTimes| |argscript| |superHeight| |whileLoop| |cExp| + |printTypes| |isQuotient| |boundOfCauchy| + |stoseInternalLastSubResultant| |clipWithRanges| |subTriSet?| + |inverseIntegralMatrixAtInfinity| |maxrow| |part?| |rightNorm| + |medialSet| |binarySearchTree| |ParCondList| |roughEqualIdeals?| + |c06ebf| |extension| |writeBytes!| |HenselLift| |readUInt16!| + |complexEigenvectors| |jacobiIdentity?| |rationalIfCan| |cTanh| + |sylvesterMatrix| |areEquivalent?| |qqq| |asimpson| |kroneckerDelta| + |supersub| |unknownEndian| |divideIfCan| |makingStats?| + |setLabelValue| |bubbleSort!| |iiexp| |nextPrimitivePoly| + |zeroDimPrime?| |rightOne| |contours| |sequences| |isList| |e02ddf| + |systemCommand| |rightLcm| |preprocess| |jvmLongConstantTag| + |numericalIntegration| |binaryTree| |leftTrace| |iprint| |height| + |lazyGintegrate| |sample| |intPatternMatch| |ParCond| |rule| + |squareMatrix| |reflect| |null?| |polarCoordinates| |universe| + |legendre| |matrixConcat3D| |rootDirectory| |presub| |normal| + |number?| |musserTrials| |ldf2vmf| |safetyMargin| |swap| |freeOf?| + |realRoots| |reopen!| |mainSquareFreePart| |expint| |nothing| + |zeroMatrix| |e02bbf| |argument| |mindeg| |decompose| + |numberOfFactors| |primitiveElement| |intermediateResultsIF| + |viewWriteAvailable| |explimitedint| |decimal| |s19adf| |roman| + |virtualDegree| |OMgetBVar| |max| |lazyPseudoQuotient| + |setScreenResolution| |internalSubQuasiComponent?| |atanIfCan| + |selectIntegrationRoutines| F ** |ramified?| + |tryFunctionalDecomposition| |numeric| |getDatabase| |pastel| + |unitVector| |testModulus| |stoseSquareFreePart| |viewSizeDefault| + |principalAncestors| |algDsolve| |rowEchelonLocal| |radical| |f02abf| + |nthFractionalTerm| |wronskianMatrix| |possiblyNewVariety?| |green| + |decomposeFunc| |littleEndian| |c06fuf| |ODESolve| + |invertibleElseSplit?| |select!| |setIntersection| + |numberOfComposites| |extendedIntegrate| |midpoint| |gderiv| + |mapUnivariateIfCan| |companionBlocks| |var2Steps| |encodingDirectory| + |cardinality| |factorials| |rquo| |optAttributes| |weierstrass| + |leftOne| |rangePascalTriangle| |symmetricRemainder| |setPoly| + |unrankImproperPartitions0| |linearForm| |leastPower| |unit?| |nand| + |lepol| |roughUnitIdeal?| |cRationalPower| |asecIfCan| |bag| |cAcosh| + |FormatArabic| |sin?| |OMputEndAttr| |graeffe| |rdHack1| + |partialFraction| |laplacian| |diagonal?| |jvmPrivate| |lifting| + |vspace| |c06gqf| |bivariateSLPEBR| |quotient| |dual| |factorial| + |writeByte!| |SturmHabichtSequence| |quickSort| |kovacic| |gradient| + |leader| |createIrreduciblePoly| |createGenericMatrix| + |rightCharacteristicPolynomial| |oddInfiniteProduct| |makeSUP| + |hessian| |scalarMatrix| |lllip| |pointSizeDefault| |stopTableGcd!| + |palgRDE0| |OMgetVariable| |yellow| |augment| |fixedPoints| + |numberOfComputedEntries| |leaf?| |reduction| |powmod| |e02agf| + |makeUnit| |invmultisect| |mappingMode| |cross| + |primPartElseUnitCanonical| |quadratic?| |lllp| + |useSingleFactorBound?| |compactFraction| |writeUInt8!| |outputAsTex| + |graphCurves| |gensym| |roughBase?| |genericLeftNorm| |assert| + |fixedPoint| |univariateSolve| |zero?| |lastSubResultant| + |completeEchelonBasis| |reify| |leftFactor| |lfunc| |sinhcosh| + |integralAtInfinity?| |listConjugateBases| |distance| |matrix| + |endSubProgram| |clearDenominator| |biRank| |bindings| + |stopTableInvSet!| |basisOfLeftAnnihilator| |rationalPoint?| + |sqfrFactor| |sum| |factorsOfCyclicGroupSize| |clearTheFTable| + |singleFactorBound| |semiDiscriminantEuclidean| |iFTable| |elColumn2!| + |leftUnit| |coerceS| |parseString| |row| |makeViewport3D| + |OMencodingSGML| |points| |transcendent?| |color| + |basisOfRightNucleus| |hexDigit?| |listRepresentation| |cycleSplit!| + |viewDeltaXDefault| |minimalPolynomial| |discriminantEuclidean| + |squareFreePolynomial| |shape| |numerators| |leftRankPolynomial| + |setlast!| |makeSketch| |denominators| |sub| |coerce| + |standardBasisOfCyclicSubmodule| |varList| |randomR| + |pointColorPalette| |close!| |symbolTable| |fortranTypeOf| + |triangular?| |repSq| |semiSubResultantGcdEuclidean2| + |stoseInvertibleSetsqfreg| |construct| |d01gaf| |monicRightDivide| + |collect| |tryFunctionalDecomposition?| |before?| |cot2tan| + |normalizeAtInfinity| |localUnquote| |bigEndian| |putProperties| + |solveRetract| |besselI| |cTan| |insertRoot!| |pushFortranOutputStack| + |OMopenString| |roughBasicSet| |s17def| |spherical| |mesh| |resetNew| + |iiacos| |monomialIntegrate| |unparse| |popFortranOutputStack| + |irCtor| |getSyntaxFormsFromFile| |critpOrder| |startTable!| + |uncouplingMatrices| |rootSimp| |basisOfLeftNucloid| |symbol?| + |simplify| |csc2sin| |positiveRemainder| |reset| |curveColor| + |limitedint| |outputAsFortran| |enterPointData| |iroot| |subst| |unit| + |lyndonIfCan| |multinomial| |d01ajf| |degreePartition| + |infiniteProduct| |exists?| |nextSublist| |f01maf| |basisOfCentroid| + |category| |extendedEuclidean| |permutations| |factor1| |cycleRagits| + |charthRoot| |sign| |write| |messagePrint| |representationType| + |lfextlimint| |binaryTournament| |OMgetFloat| |rightTrim| |say| + |perfectSquare?| |domain| |absolutelyIrreducible?| |bringDown| + |genericLeftTrace| |physicalLength| |modularFactor| |cycleLength| + |linearPart| |save| |lieAlgebra?| |internalDecompose| + |internalIntegrate0| |OMencodingUnknown| |leftTrim| |s19aaf| |exp| + |integer?| |explicitlyEmpty?| |transpose| |package| |isAnd| + |constantOpIfCan| |signAround| |complementaryBasis| |clipSurface| + |primitivePart!| |complexIntegrate| |Beta| |objects| |makeVariable| + |merge| |prepareDecompose| |laguerre| |indiceSubResultant| + |changeBase| |iisqrt3| |normalizedAssociate| |limitPlus| |base| |plus| + |shade| |cosh2sech| |linearDependence| |binding| |makeCrit| + |halfExtendedResultant2| |status| |singRicDE| |collectUpper| |palgint| + |OMencodingBinary| |jvmNameAndTypeConstantTag| |OMclose| |cache| + |lquo| |rightAlternative?| |rightQuotient| |rootBound| |maxdeg| + |mathieu12| |algSplitSimple| |inverseColeman| |inconsistent?| |match| + |rangeIsFinite| |exQuo| |shift| |wholePart| |subtractIfCan| |mapCoef| + |center| |times| |jvmFinal| |trace2PowMod| + |createMultiplicationMatrix| |subResultantChain| |cosIfCan| + |quasiMonicPolynomials| |determinant| |getBadValues| |acschIfCan| + |delta| |SturmHabicht| |isAbsolutelyIrreducible?| |getCode| + |OMReadError?| |iicsc| |cylindrical| |matrixDimensions| |cAsinh| + |stronglyReduced?| |shellSort| |complexRoots| |leadingSupport| + |gcdcofactprim| |hasoln| |union| |toroidal| |findBinding| |factorList| + |coord| |leviCivitaSymbol| |makeSin| |coth2trigh| |norm| |listOfLists| + |sqfree| |qroot| |ricDsolve| |rightTrace| |zeroSquareMatrix| |d03faf| + FG2F |perfectSqrt| |size| |upperCase!| |OMputAtp| + |subresultantSequence| |flexibleArray| |setelt!| |bivariate?| + |primextendedint| |s01eaf| |f01qdf| |returnTypeOf| |enqueue!| + |wholeRadix| |choosemon| |fprindINFO| |resetVariableOrder| + |rightRankPolynomial| |f04mbf| |accuracyIF| |primeFrobenius| + |powerAssociative?| |solveLinearPolynomialEquation| |element?| + |tanSum| |monicModulo| |createNormalPoly| |jvmPublic| |iicos| |irVar| + |c05adf| |mainExpression| |previous| |map| |partition| |queue| |cAsin| + |light| |nullary?| |rightRecip| |numberOfComponents| |rank| + |printStats!| |getIdentifier| |square?| |sn| |integralCoordinates| + |subResultantGcdEuclidean| |badNum| |graphStates| |forLoop| |ocf2ocdf| + |viewpoint| |binary| |inf| |elementary| |interpolate| + |reduceByQuasiMonic| |quasiComponent| |fortranLogical| |getRef| + |cCoth| |rightUnit| |nthRootIfCan| |simplifyPower| |bitLength| + |fortranCharacter| |ip4Address| |indices| |lagrange| |pmintegrate| + |characteristicSet| |cCosh| |c06gcf| |toseLastSubResultant| + |palglimint0| |symbolTableOf| |point| |polygon| |create3Space| |hcrf| + |jvmInterfaceMethodConstantTag| |createZechTable| |exponential1| + |ReduceOrder| |leftMinimalPolynomial| |setUnion| |var1Steps| + |removeCosSq| |generateIrredPoly| |s20adf| |fixPredicate| |setLength!| + |critT| |f07adf| |rightUnits| |OMParseError?| |overset?| SEGMENT + |approxSqrt| |htrigs| |node| |logical?| |binomial| |lowerCase| |root?| + |printHeader| |groebnerIdeal| |froot| |chineseRemainder| |swapRows!| + |e04naf| |pushNewContour| |series| |drawComplex| |floor| + |OMputEndBind| |mainCharacterization| |cdr| |summation| |update| + |sayLength| |isOpen?| |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=(-421 (-560))) -2210 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1235)) ((-95) |has| |#1| (-1235)) ((-102) . T) ((-111 #0# #0#) -2210 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2210 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2210 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-888)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1052)) ((-633 (-171 (-391))) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-633 #1=(-1203 |#1|)) . 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T) ((-922 $ #3=(-1209)) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #3#) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) |has| |#1| (-912 (-391))) ((-912 (-560)) |has| |#1| (-912 (-560))) ((-910 |#1|) . T) ((-940) -12 (|has| |#1| (-319)) (|has| |#1| (-940))) ((-951) -2210 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1034) -12 (|has| |#1| (-1034)) (|has| |#1| (-1235))) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1083 #0#) -2210 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1083 |#1|) . T) ((-1083 $) . T) ((-1088 #0#) -2210 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1088 |#1|) . T) ((-1088 $) . T) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-363)) ((-1235) |has| |#1| (-1235)) ((-1238) |has| |#1| (-1235)) ((-1249) . 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(-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-1557 (((-1191) $) NIL T ELT)) (-3080 (((-1152) $) NIL T ELT)) (-4173 (((-888) $) NIL T ELT)) (-4190 (((-114) $ $) NIL T ELT)) (-2419 (((-114) $ $) NIL T ELT))) (((-198) (-809)) (T -198)) NIL (-809) -((-2317 (((-114) $ $) NIL T ELT)) (-3378 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1901 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 63 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -1901 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-1419 (((-2 (|:| -1419 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1901 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -1419 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1901 (-663 (-1121 (-866 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(-229)))) NIL T ELT)) (-1557 (((-1191) $) NIL T ELT)) (-3080 (((-1152) $) NIL T ELT)) (-4173 (((-888) $) NIL T ELT)) (-4190 (((-114) $ $) NIL T ELT)) (-2419 (((-114) $ $) NIL T ELT))) (((-199) (-809)) (T -199)) NIL (-809) -((-2317 (((-114) $ $) NIL T ELT)) (-3378 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1901 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 76 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -1901 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-1419 (((-2 (|:| -1419 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1901 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -1419 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1901 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-1914 (((-1191) $) NIL T ELT)) (-3177 (((-1152) $) NIL T ELT)) (-2590 (((-888) $) NIL T ELT)) (-3409 (((-114) $ $) NIL T ELT)) (-2347 (((-114) $ $) NIL T ELT))) +((-2128 (((-114) $ $) NIL T ELT)) (-3956 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1410 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 76 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -1410 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-2637 (((-2 (|:| -2637 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1410 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -2637 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1410 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-1557 (((-1191) $) NIL T ELT)) 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(((-1152) $) NIL T ELT)) (-2590 (((-888) $) NIL T ELT)) (-3409 (((-114) $ $) NIL T ELT)) (-2347 (((-114) $ $) NIL T ELT))) +((-2128 (((-114) $ $) NIL T ELT)) (-3956 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1410 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 93 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -1410 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-2637 (((-2 (|:| -2637 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1410 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -2637 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1410 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-1557 (((-1191) $) NIL T ELT)) (-3080 (((-1152) $) NIL T ELT)) (-4173 (((-888) $) NIL T 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$ $) NIL T ELT))) (((-202) (-809)) (T -202)) NIL (-809) -((-2317 (((-114) $ $) NIL T ELT)) (-3378 (((-1067) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1901 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) 78 T ELT) (((-1067) (-2 (|:| |fn| (-326 (-229))) (|:| -1901 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1067)) NIL T ELT)) (-1419 (((-2 (|:| -1419 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1901 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -1419 (-391)) (|:| |explanations| (-1191)) (|:| |extra| (-1067))) (-1095) (-2 (|:| |fn| (-326 (-229))) (|:| -1901 (-663 (-1121 (-866 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-1914 (((-1191) $) NIL T ELT)) (-3177 (((-1152) $) NIL T ELT)) (-2590 (((-888) $) NIL T ELT)) (-3409 (((-114) $ $) NIL T ELT)) (-2347 (((-114) $ $) NIL T 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T) ((-102) -2263 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2263 (|has| |#2| (-1081)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2263 (|has| |#2| (-1081)) (|has| |#2| (-817)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1070 (-421 (-560)))) (|has| |#2| (-1133))) ((-635 (-560)) -2263 (|has| |#2| (-1081)) (-12 (|has| |#2| (-1070 (-560))) (|has| |#2| (-1133)))) ((-635 |#2|) |has| |#2| (-1133)) ((-632 (-888)) -2263 (|has| |#2| (-1133)) (|has| |#2| (-1081)) (|has| |#2| (-872)) (|has| |#2| (-817)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-888))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1299 |#2|)) . T) ((-236 $) -2263 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-234 |#2|) |has| |#2| (-1081)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1081))) ((-239) -2263 (-12 (|has| |#2| (-239)) (|has| |#2| (-1081))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1081)))) ((-274 |#2|) |has| |#2| (-1081)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1133))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1081)) ((-426 |#2|) |has| |#2| (-1133)) ((-503 |#2|) . T) ((-618 #1# |#2|) . 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T) ((-571) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T) ((-1254) |has| |#1| (-940))) -((-2317 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-1626 ((|#1| $) 61 T ELT)) (-2810 ((|#1| $) 51 T ELT)) (-1635 (((-114) $ (-793)) 8 T ELT)) (-2625 (($) 7 T CONST)) (-3341 (($ $) 67 T ELT)) (-3007 (($ $) 55 T ELT)) (-4392 ((|#1| |#1| $) 53 T ELT)) (-1897 ((|#1| $) 52 T ELT)) (-4158 (((-663 |#1|) $) 33 (|has| $ (-6 -4510)) ELT)) (-3983 (((-114) $ (-793)) 9 T ELT)) (-2553 (((-663 |#1|) $) 32 (|has| $ (-6 -4510)) ELT)) (-2019 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-4184 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4511)) ELT)) (-1997 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-1487 (((-114) $ (-793)) 10 T ELT)) (-1933 (((-793) $) 68 T ELT)) (-1914 (((-1191) $) 25 (|has| |#1| (-1133)) ELT)) (-2268 ((|#1| $) 46 T ELT)) (-3823 ((|#1| |#1| $) 59 T ELT)) (-1653 ((|#1| |#1| $) 58 T ELT)) (-4001 (($ |#1| $) 47 T ELT)) (-3579 (((-793) $) 62 T ELT)) (-3177 (((-1152) $) 24 (|has| |#1| (-1133)) ELT)) (-4134 ((|#1| $) 69 T ELT)) (-1637 ((|#1| $) 57 T ELT)) (-1374 ((|#1| $) 56 T ELT)) (-1746 ((|#1| $) 48 T ELT)) (-2418 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4510)) ELT)) (-2811 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT)) (-3908 (((-114) $ $) 14 T ELT)) (-3626 ((|#1| |#1| $) 65 T ELT)) (-4448 (((-114) $) 11 T ELT)) (-4017 (($) 12 T ELT)) (-1934 ((|#1| $) 66 T ELT)) (-3835 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-2165 (((-793) $) 50 T ELT)) (-3192 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4510)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-2770 (($ $) 13 T ELT)) (-2590 (((-888) $) 20 (|has| |#1| (-632 (-888))) ELT)) (-3594 ((|#1| $) 60 T ELT)) (-3409 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-3729 (($ (-663 |#1|)) 49 T ELT)) (-3426 ((|#1| $) 70 T ELT)) (-1839 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4510)) ELT)) (-2347 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2327 (((-793) $) 6 (|has| $ (-6 -4510)) ELT))) +((-4284 (*1 *2 *3) (-12 (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-2523 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 *4)))) (-3900 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-3900 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-2981 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-2183 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-3674 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-793)))) (-2183 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-663 (-793))))) (-3674 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1081)) (-4 *3 (-872)) (-4 *5 (-277 *3)) (-4 *6 (-817)) (-5 *2 (-793)))) (-1902 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-114)))) (-4084 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-817)) (-4 *2 (-277 *4)))) (-2798 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-2795 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1081)) (-4 *3 (-872)) (-4 *4 (-277 *3)) (-4 *5 (-817)))) (-4284 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1081)) (-4 *4 (-872)) (-4 *5 (-277 *4)) (-4 *6 (-817)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-980 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1070 |t#2|) (-10 -8 (-15 -4284 ((-1 $ (-793)) |t#2|)) (-15 -2523 ((-663 |t#2|) $)) (-15 -3900 ((-793) $ |t#2|)) (-15 -3900 ((-793) $)) (-15 -2981 ((-793) $ |t#2|)) (-15 -2183 ((-663 (-793)) $)) (-15 -3674 ((-793) $)) (-15 -2183 ((-663 (-793)) $ |t#2|)) (-15 -3674 ((-793) $ |t#2|)) (-15 -1902 ((-114) $)) (-15 -4084 (|t#3| $)) (-15 -2798 ($ $)) (-15 -2795 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -4284 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2263 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-888)) . T) ((-175) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-633 (-916 (-391)))) (|has| |#3| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-633 (-916 (-560)))) (|has| |#3| (-633 (-916 (-560))))) ((-236 $) -2263 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2263 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2263 (|has| |#1| (-940)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-922 $ #2=(-1209)) -2263 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-922 $ |#3|) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-928 |#3|) . T) ((-930 #2#) -2263 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-930 |#3|) . T) ((-912 (-391)) -12 (|has| |#1| (-912 (-391))) (|has| |#3| (-912 (-391)))) ((-912 (-560)) -12 (|has| |#1| (-912 (-560))) (|has| |#3| (-912 (-560)))) ((-980 |#1| |#4| |#3|) . T) ((-940) |has| |#1| (-940)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 |#1|) . T) ((-1070 |#2|) . T) ((-1070 |#3|) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T) ((-1254) |has| |#1| (-940))) +((-2128 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-3641 ((|#1| $) 61 T ELT)) (-1975 ((|#1| $) 51 T ELT)) (-3716 (((-114) $ (-793)) 8 T ELT)) (-3962 (($) 7 T CONST)) (-1713 (($ $) 67 T ELT)) (-1512 (($ $) 55 T ELT)) (-3401 ((|#1| |#1| $) 53 T ELT)) (-1361 ((|#1| $) 52 T ELT)) (-2224 (((-663 |#1|) $) 33 (|has| $ (-6 -4510)) ELT)) (-1622 (((-114) $ (-793)) 9 T ELT)) (-1340 (((-663 |#1|) $) 32 (|has| $ (-6 -4510)) ELT)) (-3164 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-1595 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4511)) ELT)) (-4401 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-2698 (((-114) $ (-793)) 10 T ELT)) (-3223 (((-793) $) 68 T ELT)) (-1557 (((-1191) $) 25 (|has| |#1| (-1133)) ELT)) (-1767 ((|#1| $) 46 T ELT)) (-3724 ((|#1| |#1| $) 59 T ELT)) (-3904 ((|#1| |#1| $) 58 T ELT)) (-1803 (($ |#1| $) 47 T ELT)) (-3960 (((-793) $) 62 T ELT)) (-3080 (((-1152) $) 24 (|has| |#1| (-1133)) ELT)) (-2586 ((|#1| $) 69 T ELT)) (-3736 ((|#1| $) 57 T ELT)) (-2038 ((|#1| $) 56 T ELT)) (-3621 ((|#1| $) 48 T ELT)) (-2674 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4510)) ELT)) (-3859 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ELT)) (-2114 (((-114) $ $) 14 T ELT)) (-4380 ((|#1| |#1| $) 65 T ELT)) (-2739 (((-114) $) 11 T ELT)) (-3867 (($) 12 T ELT)) (-3694 ((|#1| $) 66 T ELT)) (-2647 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-1529 (((-793) $) 50 T ELT)) (-3091 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4510)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1133)) (|has| $ (-6 -4510))) ELT)) (-2558 (($ $) 13 T ELT)) (-4173 (((-888) $) 20 (|has| |#1| (-632 (-888))) ELT)) (-2254 ((|#1| $) 60 T ELT)) (-4190 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-4061 (($ (-663 |#1|)) 49 T ELT)) (-3161 ((|#1| $) 70 T ELT)) (-2071 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4510)) ELT)) (-2419 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2140 (((-793) $) 6 (|has| $ (-6 -4510)) ELT))) (((-263 |#1|) (-142) (-1249)) (T -263)) -((-3835 (*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-3835 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1249)) (-4 *1 (-263 *3)))) (-3579 (*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1249)) (-5 *2 (-793)))) (-1626 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-3594 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-3823 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-1653 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-1637 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-1374 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249)))) (-3007 (*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1249))))) -(-13 (-1153 |t#1|) (-1027 |t#1|) (-10 -8 (-15 -3835 ($)) (-15 -3835 ($ (-663 |t#1|))) (-15 -3579 ((-793) $)) (-15 -1626 (|t#1| $)) (-15 -3594 (|t#1| $)) (-15 -3823 (|t#1| |t#1| $)) (-15 -1653 (|t#1| |t#1| $)) (-15 -1637 (|t#1| $)) (-15 -1374 (|t#1| $)) (-15 -3007 ($ $)))) -(((-34) . T) ((-107 |#1|) . T) ((-102) -2210 (|has| |#1| (-1133)) (|has| |#1| (-102))) ((-632 (-888)) -2210 (|has| |#1| (-1133)) (|has| |#1| (-632 (-888)))) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-503 |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1133))) ((-1027 |#1|) . T) ((-1133) |has| |#1| (-1133)) ((-1153 |#1|) . T) ((-1249) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1081)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-951) |has| |#1| (-571)) ((-1070 (-421 (-560))) -2210 (|has| |#1| (-1070 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1070 (-560))))) ((-1070 #1#) |has| |#1| (-571)) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 #3#) |has| |#1| (-1081)) ((-1070 #4#) . T) ((-1070 |#1|) . T) ((-1083 #0#) |has| |#1| (-571)) ((-1083 |#1|) |has| |#1| (-175)) ((-1083 $) |has| |#1| (-571)) ((-1088 #0#) |has| |#1| (-571)) ((-1088 |#1|) |has| |#1| (-175)) ((-1088 $) |has| |#1| (-571)) ((-1081) -2210 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -2210 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1144) -2210 (|has| |#1| (-1144)) (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1133) . T) ((-1249) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1081)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-951) |has| |#1| (-571)) ((-1070 (-421 (-560))) -2263 (|has| |#1| (-1070 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1070 (-560))))) ((-1070 #1#) |has| |#1| (-571)) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 #3#) |has| |#1| (-1081)) ((-1070 #4#) . T) ((-1070 |#1|) . T) ((-1083 #0#) |has| |#1| (-571)) ((-1083 |#1|) |has| |#1| (-175)) ((-1083 $) |has| |#1| (-571)) ((-1088 #0#) |has| |#1| (-571)) ((-1088 |#1|) |has| |#1| (-175)) ((-1088 $) |has| |#1| (-571)) ((-1081) -2263 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1089) -2263 (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1144) -2263 (|has| |#1| (-1144)) (|has| |#1| (-1081)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1133) . T) ((-1249) . 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|notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1187 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1410 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) (-5 *1 (-574)))) (-2026 (*1 *1 *2) (-12 (-5 *2 (-663 (-2 (|:| -1651 (-2 (|:| |var| (-1209)) (|:| |fn| (-326 (-229))) (|:| -1410 (-1121 (-866 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -1871 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) . T) ((-635 (-560)) . T) ((-635 #1=(-1209)) |has| |#1| (-1070 (-1209))) ((-635 |#1|) . T) ((-635 $) . T) ((-632 (-888)) . T) ((-175) . T) ((-633 (-229)) |has| |#1| (-1052)) ((-633 (-391)) |has| |#1| (-1052)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-916 (-391))) |has| |#1| (-633 (-916 (-391)))) ((-633 (-916 (-560))) |has| |#1| (-633 (-916 (-560)))) ((-236 $) -2263 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2263 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-250) . T) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-302) . T) ((-319) . T) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-376) . T) ((-351 |#1|) . T) ((-390 |#1|) . T) ((-414 |#1|) . T) ((-466) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . 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T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2210 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2263 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2263 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2263 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2263 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1209)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2263 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2263 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-916 (-560))))) ((-236 $) -2263 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2263 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2263 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1144)) ((-302) -2263 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1209) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1209) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2263 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2263 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2263 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . 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T) ((-951) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1034) |has| |#1| (-38 (-421 (-560)))) ((-1052) -12 (|has| |#1| (-376)) (|has| |#2| (-1052))) ((-1070 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-560)))) ((-1070 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1070 (-1209)))) ((-1070 |#2|) . T) ((-1083 #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1083 |#1|) . T) ((-1083 |#2|) |has| |#1| (-376)) ((-1083 $) -2263 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) -2263 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1088 |#1|) . T) ((-1088 |#2|) |has| |#1| (-376)) ((-1088 $) -2263 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) -12 (|has| |#1| (-376)) (|has| |#2| (-1184))) ((-1235) |has| |#1| (-38 (-421 (-560)))) ((-1238) |has| |#1| (-38 (-421 (-560)))) ((-1249) . T) ((-1254) |has| |#1| (-376)) ((-1261 |#1|) . T) ((-1278 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2210 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2210 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -2210 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2210 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . T) ((-1254) |has| |#1| (-940))) -((-1997 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) -(((-1276 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -1997 (|#4| (-1 |#3| |#1|) |#2|))) (-1081) (-1275 |#1|) (-1081) (-1275 |#3|)) (T -1276)) -((-1997 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1081)) (-4 *6 (-1081)) (-4 *2 (-1275 *6)) (-5 *1 (-1276 *5 *4 *6 *2)) (-4 *4 (-1275 *5))))) -(-10 -7 (-15 -1997 (|#4| (-1 |#3| |#1|) |#2|))) -((-3589 (((-663 (-1114)) $) 34 T ELT)) (-2526 (($ $) 31 T ELT)) (-3559 (($ |#2| |#3|) NIL T ELT) (($ $ (-1114) |#3|) 28 T ELT) (($ $ (-663 (-1114)) (-663 |#3|)) 27 T ELT)) (-2491 (($ $) 14 T ELT)) (-2502 ((|#2| $) 12 T ELT)) (-2125 ((|#3| $) 10 T ELT))) -(((-1277 |#1| |#2| |#3|) (-10 -8 (-15 -3589 ((-663 (-1114)) |#1|)) (-15 -3559 (|#1| |#1| (-663 (-1114)) (-663 |#3|))) (-15 -3559 (|#1| |#1| (-1114) |#3|)) (-15 -2526 (|#1| |#1|)) (-15 -3559 (|#1| |#2| |#3|)) (-15 -2125 (|#3| |#1|)) (-15 -2491 (|#1| |#1|)) (-15 -2502 (|#2| |#1|))) (-1278 |#2| |#3|) (-1081) (-816)) (T -1277)) -NIL -(-10 -8 (-15 -3589 ((-663 (-1114)) |#1|)) (-15 -3559 (|#1| |#1| (-663 (-1114)) (-663 |#3|))) (-15 -3559 (|#1| |#1| (-1114) |#3|)) (-15 -2526 (|#1| |#1|)) (-15 -3559 (|#1| |#2| |#3|)) (-15 -2125 (|#3| |#1|)) (-15 -2491 (|#1| |#1|)) (-15 -2502 (|#2| |#1|))) -((-2317 (((-114) $ $) 7 T ELT)) (-2640 (((-114) $) 21 T ELT)) (-3589 (((-663 (-1114)) $) 92 T ELT)) (-2177 (((-1209) $) 126 T ELT)) (-1596 (((-2 (|:| -2003 $) (|:| -4497 $) (|:| |associate| $)) $) 68 (|has| |#1| (-571)) ELT)) (-2009 (($ $) 69 (|has| |#1| (-571)) ELT)) (-1345 (((-114) $) 71 (|has| |#1| (-571)) ELT)) (-2885 (($ $ |#2|) 121 T ELT) (($ $ |#2| |#2|) 120 T ELT)) (-1726 (((-1187 (-2 (|:| |k| |#2|) (|:| |c| |#1|))) $) 127 T ELT)) (-3757 (((-3 $ "failed") $ $) 25 T ELT)) (-2625 (($) 22 T CONST)) (-2526 (($ $) 77 T ELT)) (-4264 (((-3 $ "failed") $) 42 T ELT)) (-2109 (((-114) $) 91 T ELT)) (-3058 ((|#2| $) 123 T ELT) ((|#2| $ |#2|) 122 T ELT)) (-3838 (((-114) $) 40 T ELT)) (-3490 (($ $ (-949)) 124 T ELT)) (-4254 (((-114) $) 79 T ELT)) (-3559 (($ |#1| |#2|) 78 T ELT) (($ $ (-1114) |#2|) 94 T ELT) (($ $ (-663 (-1114)) (-663 |#2|)) 93 T ELT)) (-1997 (($ (-1 |#1| |#1|) $) 80 T ELT)) (-2491 (($ $) 82 T ELT)) (-2502 ((|#1| $) 83 T ELT)) (-1914 (((-1191) $) 11 T ELT)) (-3177 (((-1152) $) 12 T ELT)) (-3933 (($ $ |#2|) 118 T ELT)) (-2306 (((-3 $ "failed") $ $) 67 (|has| |#1| (-571)) ELT)) (-2811 (((-1187 |#1|) $ |#1|) 117 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) ELT)) (-1494 ((|#1| $ |#2|) 128 T ELT) (($ $ $) 104 (|has| |#2| (-1144)) ELT)) (-2509 (($ $ (-1209)) 116 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209))) 114 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-1209) (-793)) 113 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209)) (-663 (-793))) 112 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 108 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-793)) 106 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-2125 ((|#2| $) 81 T ELT)) (-1959 (($ $) 90 T ELT)) (-2590 (((-888) $) 13 T ELT) (($ (-560)) 38 T ELT) (($ (-421 (-560))) 74 (|has| |#1| (-38 (-421 (-560)))) ELT) (($ $) 66 (|has| |#1| (-571)) ELT) (($ |#1|) 64 (|has| |#1| (-175)) ELT)) (-3462 ((|#1| $ |#2|) 76 T ELT)) (-1360 (((-713 $) $) 65 (|has| |#1| (-147)) ELT)) (-4322 (((-793)) 37 T CONST)) (-2242 ((|#1| $) 125 T ELT)) (-3409 (((-114) $ $) 6 T ELT)) (-2754 (((-114) $ $) 70 (|has| |#1| (-571)) ELT)) (-2947 ((|#1| $ |#2|) 119 (-12 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) (|has| |#1| (-15 -2590 (|#1| (-1209))))) ELT)) (-1427 (($) 23 T CONST)) (-1439 (($) 39 T CONST)) (-4349 (($ $ (-1209)) 115 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209))) 111 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-1209) (-793)) 110 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-663 (-1209)) (-663 (-793))) 109 (-12 (|has| |#1| (-928 (-1209))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 107 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-793)) 105 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-2347 (((-114) $ $) 8 T ELT)) (-2455 (($ $ |#1|) 75 (|has| |#1| (-376)) ELT)) (-2445 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-2435 (($ $ $) 18 T ELT)) (** (($ $ (-949)) 33 T ELT) (($ $ (-793)) 41 T ELT)) (* (($ (-949) $) 17 T ELT) (($ (-793) $) 20 T ELT) (($ (-560) $) 29 T ELT) (($ $ $) 32 T ELT) (($ $ |#1|) 85 T ELT) (($ |#1| $) 84 T ELT) (($ (-421 (-560)) $) 73 (|has| |#1| (-38 (-421 (-560)))) ELT) (($ $ (-421 (-560))) 72 (|has| |#1| (-38 (-421 (-560)))) ELT))) +((-2018 (*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-4 *1 (-1275 *4)) (-4 *4 (-1081)) (-5 *2 (-1299 *4)))) (-4089 (*1 *2 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-5 *2 (-1203 *3)))) (-3312 (*1 *1 *2) (-12 (-5 *2 (-1203 *3)) (-4 *3 (-1081)) (-4 *1 (-1275 *3)))) (-2512 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-3108 (*1 *1 *1 *2) (|partial| -12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-3298 (*1 *2 *1 *1) (-12 (-4 *3 (-1081)) (-5 *2 (-2 (|:| -4076 *1) (|:| -2836 *1))) (-4 *1 (-1275 *3)))) (-1426 (*1 *2 *1 *3) (-12 (-5 *3 (-793)) (-4 *4 (-1081)) (-5 *2 (-2 (|:| -4076 *1) (|:| -2836 *1))) (-4 *1 (-1275 *4)))) (-1949 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-2067 (*1 *1 *1 *2) (-12 (-5 *2 (-793)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-3074 (*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)))) (-1881 (*1 *1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)))) (-3614 (*1 *2 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-175)))) (-3788 (*1 *2 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-175)))) (-2556 (*1 *2 *2 *2) (-12 (-5 *2 (-421 *1)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)))) (-3900 (*1 *2 *1 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)) (-5 *2 (-793)))) (-2820 (*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571)))) (-3835 (*1 *1 *1 *1) (|partial| -12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571)))) (-3835 (*1 *2 *2 *1) (|partial| -12 (-5 *2 (-421 *1)) (-4 *1 (-1275 *3)) (-4 *3 (-1081)) (-4 *3 (-571)))) (-2177 (*1 *1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-571)))) (-3078 (*1 *2 *1 *1) (-12 (-4 *3 (-571)) (-4 *3 (-1081)) (-5 *2 (-2 (|:| -2461 *3) (|:| -4076 *1) (|:| -2836 *1))) (-4 *1 (-1275 *3)))) (-2079 (*1 *2 *1 *1) (-12 (-4 *3 (-466)) (-4 *3 (-1081)) (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) (-4 *1 (-1275 *3)))) (-2556 (*1 *2 *3 *2) (-12 (-5 *3 (-421 *1)) (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-376)))) (-3490 (*1 *1 *1) (-12 (-4 *1 (-1275 *2)) (-4 *2 (-1081)) (-4 *2 (-38 (-421 (-560))))))) +(-13 (-980 |t#1| (-793) (-1114)) (-298 |t#1| |t#1|) (-298 $ $) (-240) (-234 |t#1|) (-10 -8 (-15 -2018 ((-1299 |t#1|) $ (-793))) (-15 -4089 ((-1203 |t#1|) $)) (-15 -3312 ($ (-1203 |t#1|))) (-15 -2512 ($ $ (-793))) (-15 -3108 ((-3 $ "failed") $ (-793))) (-15 -3298 ((-2 (|:| -4076 $) (|:| -2836 $)) $ $)) (-15 -1426 ((-2 (|:| -4076 $) (|:| -2836 $)) $ (-793))) (-15 -1949 ($ $ (-793))) (-15 -2067 ($ $ (-793))) (-15 -3074 ($ $ $)) (-15 -1881 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1184)) (-6 (-1184)) |%noBranch|) (IF (|has| |t#1| (-175)) (PROGN (-15 -3614 (|t#1| $)) (-15 -3788 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-571)) (PROGN (-6 (-298 (-421 $) (-421 $))) (-15 -2556 ((-421 $) (-421 $) (-421 $))) (-15 -3900 ((-793) $ $)) (-15 -2820 ($ $ $)) (-15 -3835 ((-3 $ "failed") $ $)) (-15 -3835 ((-3 (-421 $) "failed") (-421 $) $)) (-15 -2177 ($ $ $)) (-15 -3078 ((-2 (|:| -2461 |t#1|) (|:| -4076 $) (|:| -2836 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-466)) (-15 -2079 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-376)) (PROGN (-6 (-319)) (-6 -4506) (-15 -2556 (|t#1| (-421 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-421 (-560)))) (-15 -3490 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2263 (|has| |#1| (-1070 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1114)) . T) ((-635 |#1|) . T) ((-635 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-888)) . T) ((-175) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1114) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-916 (-391))) -12 (|has| (-1114) (-633 (-916 (-391)))) (|has| |#1| (-633 (-916 (-391))))) ((-633 (-916 (-560))) -12 (|has| (-1114) (-633 (-916 (-560)))) (|has| |#1| (-633 (-916 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2263 (|has| |#1| (-940)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-922 $ #2#) . T) ((-922 $ #4=(-1209)) -2263 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-928 #2#) . T) ((-928 (-1209)) |has| |#1| (-928 (-1209))) ((-930 #2#) . T) ((-930 #4#) -2263 (|has| |#1| (-930 (-1209))) (|has| |#1| (-928 (-1209)))) ((-912 (-391)) -12 (|has| (-1114) (-912 (-391))) (|has| |#1| (-912 (-391)))) ((-912 (-560)) -12 (|has| (-1114) (-912 (-560))) (|has| |#1| (-912 (-560)))) ((-980 |#1| #0# #2#) . T) ((-940) |has| |#1| (-940)) ((-951) |has| |#1| (-376)) ((-1070 (-421 (-560))) |has| |#1| (-1070 (-421 (-560)))) ((-1070 (-560)) |has| |#1| (-1070 (-560))) ((-1070 #2#) . T) ((-1070 |#1|) . T) ((-1083 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1088 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2263 (|has| |#1| (-940)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1184) |has| |#1| (-1184)) ((-1249) . T) ((-1254) |has| |#1| (-940))) +((-4401 ((|#4| (-1 |#3| |#1|) |#2|) 22 T ELT))) +(((-1276 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -4401 (|#4| (-1 |#3| |#1|) |#2|))) (-1081) (-1275 |#1|) (-1081) (-1275 |#3|)) (T -1276)) +((-4401 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1081)) (-4 *6 (-1081)) (-4 *2 (-1275 *6)) (-5 *1 (-1276 *5 *4 *6 *2)) (-4 *4 (-1275 *5))))) +(-10 -7 (-15 -4401 (|#4| (-1 |#3| |#1|) |#2|))) +((-2787 (((-663 (-1114)) $) 34 T ELT)) (-2957 (($ $) 31 T ELT)) (-2762 (($ |#2| |#3|) NIL T ELT) (($ $ (-1114) |#3|) 28 T ELT) (($ $ (-663 (-1114)) (-663 |#3|)) 27 T ELT)) (-2920 (($ $) 14 T ELT)) (-2933 ((|#2| $) 12 T ELT)) (-2981 ((|#3| $) 10 T ELT))) +(((-1277 |#1| |#2| |#3|) (-10 -8 (-15 -2787 ((-663 (-1114)) |#1|)) (-15 -2762 (|#1| |#1| (-663 (-1114)) (-663 |#3|))) (-15 -2762 (|#1| |#1| (-1114) |#3|)) (-15 -2957 (|#1| |#1|)) (-15 -2762 (|#1| |#2| |#3|)) (-15 -2981 (|#3| |#1|)) (-15 -2920 (|#1| |#1|)) (-15 -2933 (|#2| |#1|))) (-1278 |#2| |#3|) (-1081) (-816)) (T -1277)) +NIL 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(-15 -3490 ($ $ (-949))) (-15 -3058 (|t#2| $)) (-15 -3058 (|t#2| $ |t#2|)) (-15 -2885 ($ $ |t#2|)) (-15 -2885 ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (-15 -2590 (|t#1| (-1209)))) (IF (|has| |t#1| (-15 ** (|t#1| |t#1| |t#2|))) (-15 -2947 (|t#1| $ |t#2|)) |%noBranch|) |%noBranch|) (-15 -3933 ($ $ |t#2|)) (IF (|has| |t#2| (-1144)) (-6 (-298 $ $)) |%noBranch|) (IF (|has| |t#1| (-15 * (|t#1| |t#2| |t#1|))) (PROGN (-6 (-240)) (IF (|has| |t#1| (-928 (-1209))) (-6 (-928 (-1209))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (-15 ** (|t#1| |t#1| |t#2|))) (-15 -2811 ((-1187 |t#1|) $ |t#1|)) |%noBranch|))) -(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2210 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-888)) . T) ((-175) -2210 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-240) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-239) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-298 |#2| |#1|) . T) ((-298 $ $) |has| |#2| (-1144)) ((-302) |has| |#1| (-571)) ((-571) |has| |#1| (-571)) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) |has| |#1| (-571)) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) |has| |#1| (-571)) ((-748) . T) ((-922 $ #1=(-1209)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-928 (-1209)))) ((-928 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-928 (-1209)))) ((-930 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-928 (-1209)))) ((-1005 |#1| |#2| (-1114)) . T) ((-1083 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1083 |#1|) . T) ((-1083 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1088 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1088 |#1|) . T) ((-1088 $) -2210 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1081) . T) ((-1089) . T) ((-1144) . T) ((-1133) . T) ((-1249) . T)) -((-4432 ((|#2| |#2|) 12 T ELT)) (-1639 (((-419 |#2|) |#2|) 14 T ELT)) (-2673 (((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-560))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-560)))) 30 T ELT))) -(((-1279 |#1| |#2|) (-10 -7 (-15 -1639 ((-419 |#2|) |#2|)) (-15 -4432 (|#2| |#2|)) (-15 -2673 ((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-560))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-560)))))) (-571) (-13 (-1275 |#1|) (-571) (-10 -8 (-15 -2522 ($ $ $))))) (T -1279)) -((-2673 (*1 *2 *2) (-12 (-5 *2 (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (-560)))) (-4 *4 (-13 (-1275 *3) (-571) (-10 -8 (-15 -2522 ($ $ $))))) (-4 *3 (-571)) (-5 *1 (-1279 *3 *4)))) (-4432 (*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-1279 *3 *2)) (-4 *2 (-13 (-1275 *3) (-571) (-10 -8 (-15 -2522 ($ $ $))))))) (-1639 (*1 *2 *3) (-12 (-4 *4 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(-1320 3443097 3445668 3446056 "XPBWPOLY" 3446809 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3437989 3439568 3439623 "XFALG" 3441795 NIL XFALG (NIL T T) -9 NIL 3442584 NIL) (-1318 3433265 3435965 3436007 "XF" 3436628 NIL XF (NIL T) -9 NIL 3437028 NIL) (-1317 3432862 3432974 3433143 "XF-" 3433148 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3431977 3432099 3432304 "XEXPPKG" 3432754 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3429718 3431827 3431923 "XDPOLY" 3431928 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3428373 3429111 3429154 "XALG" 3429159 NIL XALG (NIL T) -9 NIL 3429270 NIL) (-1313 3421283 3426350 3426844 "WUTSET" 3427965 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3419385 3420335 3420658 "WP" 3421094 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3418933 3419207 3419277 "WHILEAST" 3419337 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3418345 3418650 3418744 "WHEREAST" 3418861 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3417219 3417429 3417724 "WFFINTBS" 3418142 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3415087 3415550 3416012 "WEIER" 3416791 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3414011 3414569 3414611 "VSPACE" 3414747 NIL VSPACE (NIL T) -9 NIL 3414821 NIL) (-1306 3413843 3413876 3413967 "VSPACE-" 3413972 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3413640 3413694 3413762 "VOID" 3413797 T VOID (NIL) -8 NIL NIL NIL) (-1304 3409908 3410703 3411440 "VIEWDEF" 3412925 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3398852 3401456 3403629 "VIEW3D" 3407757 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3390869 3392763 3394342 "VIEW2D" 3397295 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3388969 3389364 3389770 "VIEW" 3390485 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3387522 3387805 3388123 "VECTOR2" 3388699 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3382428 3387292 3387384 "VECTOR" 3387465 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3375373 3380132 3380175 "VECTCAT" 3381170 NIL VECTCAT (NIL T) -9 NIL 3381757 NIL) (-1297 3374315 3374641 3375031 "VECTCAT-" 3375036 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3373721 3373966 3374086 "VARIABLE" 3374230 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3373654 3373659 3373689 "UTYPE" 3373694 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3372462 3372638 3372900 "UTSODETL" 3373480 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3369854 3370362 3370886 "UTSODE" 3372003 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3359864 3365787 3365830 "UTSCAT" 3366942 NIL UTSCAT (NIL T) -9 NIL 3367700 NIL) (-1291 3356990 3357934 3358923 "UTSCAT-" 3358928 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3356611 3356660 3356793 "UTS2" 3356941 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3347928 3354372 3354852 "UTS" 3356189 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3341795 3344738 3344781 "URAGG" 3346851 NIL URAGG (NIL T) -9 NIL 3347574 NIL) (-1287 3338518 3339597 3340720 "URAGG-" 3340725 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3333894 3337153 3337618 "UPXSSING" 3338182 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3326323 3333798 3333870 "UPXSCONS" 3333875 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3315081 3322525 3322587 "UPXSCCA" 3323161 NIL UPXSCCA (NIL T T) -9 NIL 3323394 NIL) (-1283 3314701 3314804 3314978 "UPXSCCA-" 3314983 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3303359 3310528 3310571 "UPXSCAT" 3311219 NIL UPXSCAT (NIL T) -9 NIL 3311828 NIL) (-1281 3302783 3302868 3303047 "UPXS2" 3303274 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3294275 3302165 3302429 "UPXS" 3302577 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3292911 3293182 3293533 "UPSQFREE" 3294018 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3285742 3289177 3289232 "UPSCAT" 3290312 NIL UPSCAT (NIL T T) -9 NIL 3291078 NIL) (-1277 3284898 3285153 3285480 "UPSCAT-" 3285485 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3284519 3284568 3284701 "UPOLYC2" 3284849 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3268667 3277646 3277689 "UPOLYC" 3279790 NIL UPOLYC (NIL T) -9 NIL 3281011 NIL) (-1274 3259536 3262435 3265575 "UPOLYC-" 3265580 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3258857 3258982 3259146 "UPMP" 3259425 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3258404 3258491 3258630 "UPDIVP" 3258770 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3256942 3257221 3257537 "UPDECOMP" 3258153 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3256155 3256285 3256471 "UPCDEN" 3256826 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3255668 3255743 3255892 "UP2" 3256080 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3246264 3255351 3255480 "UP" 3255587 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3245469 3245606 3245811 "UNISEG2" 3246107 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3243822 3244673 3244950 "UNISEG" 3245227 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3242864 3243062 3243288 "UNIFACT" 3243638 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3229595 3242768 3242840 "ULSCONS" 3242845 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3209412 3222675 3222737 "ULSCCAT" 3223375 NIL ULSCCAT (NIL T T) -9 NIL 3223664 NIL) (-1262 3208408 3208707 3209095 "ULSCCAT-" 3209100 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3196863 3203954 3203997 "ULSCAT" 3204860 NIL ULSCAT (NIL T) -9 NIL 3205591 NIL) (-1260 3196287 3196372 3196551 "ULS2" 3196778 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3178118 3195599 3195841 "ULS" 3196103 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3177037 3177737 3177851 "UINT8" 3177962 T UINT8 (NIL) -8 NIL NIL 3178054) (-1257 3175955 3176655 3176769 "UINT64" 3176880 T UINT64 (NIL) -8 NIL NIL 3176972) (-1256 3174873 3175573 3175687 "UINT32" 3175798 T UINT32 (NIL) -8 NIL NIL 3175890) (-1255 3173791 3174491 3174605 "UINT16" 3174716 T UINT16 (NIL) -8 NIL NIL 3174808) (-1254 3171870 3173037 3173067 "UFD" 3173279 T UFD (NIL) -9 NIL 3173393 NIL) (-1253 3171652 3171710 3171805 "UFD-" 3171810 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3170710 3170917 3171133 "UDVO" 3171458 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3168476 3168935 3169406 "UDPO" 3170274 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3168188 3168431 3168462 "TYPEAST" 3168467 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3168121 3168126 3168156 "TYPE" 3168161 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3167074 3167294 3167534 "TWOFACT" 3167915 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3166049 3166483 3166718 "TUPLE" 3166874 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3163686 3164259 3164798 "TUBETOOL" 3165532 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3162492 3162733 3162975 "TUBE" 3163479 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3150627 3155249 3155346 "TSETCAT" 3160615 NIL TSETCAT (NIL T T T T) -9 NIL 3162147 NIL) (-1243 3145095 3146959 3148850 "TSETCAT-" 3148855 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3139281 3144067 3144350 "TS" 3144847 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3133754 3134767 3135696 "TRMANIP" 3138417 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3133183 3133258 3133421 "TRIMAT" 3133686 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3130995 3131286 3131643 "TRIGMNIP" 3132932 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3130479 3130628 3130658 "TRIGCAT" 3130871 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3130124 3130227 3130368 "TRIGCAT-" 3130373 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3126738 3128982 3129263 "TREE" 3129878 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3125844 3126540 3126570 "TRANFUN" 3126605 T TRANFUN (NIL) -9 NIL 3126671 NIL) (-1234 3125063 3125314 3125594 "TRANFUN-" 3125599 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3124861 3124899 3124960 "TOPSP" 3125024 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3124191 3124324 3124478 "TOOLSIGN" 3124742 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3122705 3123368 3123607 "TEXTFILE" 3123974 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3122480 3122517 3122589 "TEX1" 3122668 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3120284 3120933 3121362 "TEX" 3122073 T TEX (NIL) -8 NIL NIL NIL) (-1228 3119920 3119995 3120085 "TEMUTL" 3120216 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3118014 3118354 3118679 "TBCMPPK" 3119643 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3109334 3116100 3116156 "TBAGG" 3116556 NIL TBAGG (NIL T T) -9 NIL 3116767 NIL) (-1225 3104218 3105892 3107646 "TBAGG-" 3107651 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103584 3103709 3103854 "TANEXP" 3104107 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3103035 3103359 3103449 "TALGOP" 3103529 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102429 3102546 3102684 "TABLEAU" 3102932 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095443 3102286 3102379 "TABLE" 3102384 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3089973 3091271 3092519 "TABLBUMP" 3094229 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089183 3089342 3089523 "SYSTEM" 3089814 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085588 3086341 3087124 "SYSSOLP" 3088434 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085350 3085543 3085574 "SYSPTR" 3085579 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084189 3084881 3085007 "SYSNNI" 3085193 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085285) (-1215 3083396 3083951 3084030 "SYSINT" 3084090 NIL SYSINT (NIL NIL) -8 NIL NIL 3084135) (-1214 3079494 3080674 3081384 "SYNTAX" 3082708 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076574 3077254 3077886 "SYMTAB" 3078884 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071673 3072725 3073708 "SYMS" 3075613 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068579 3071124 3071357 "SYMPOLY" 3071475 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3068084 3068171 3068294 "SYMFUNC" 3068491 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063882 3065396 3066209 "SYMBOL" 3067293 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057355 3059110 3060830 "SWITCH" 3062184 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3050116 3056311 3056605 "SUTS" 3057119 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041608 3049498 3049762 "SUPXS" 3049910 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040755 3040894 3041111 "SUPFRACF" 3041476 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040370 3040435 3040548 "SUP2" 3040690 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3030914 3039988 3040114 "SUP" 3040279 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029338 3029636 3029992 "SUMRF" 3030613 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028661 3028739 3028931 "SUMFS" 3029259 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010527 3027973 3028215 "SULS" 3028477 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3010075 3010349 3010419 "SUCHTAST" 3010479 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009316 3009600 3009740 "SUCH" 3009983 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3002955 3004222 3005181 "SUBSPACE" 3008404 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002375 3002475 3002639 "SUBRESP" 3002843 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996386 2997668 2998815 "STTFNC" 3001275 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989580 2991051 2992362 "STTF" 2995122 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980696 2982762 2984556 "STTAYLOR" 2987821 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973450 2980560 2980643 "STRTBL" 2980648 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967847 2973159 2973258 "STRING" 2973373 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967351 2967434 2967578 "STREAM3" 2967764 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966315 2966516 2966751 "STREAM2" 2967164 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2965997 2966055 2966148 "STREAM1" 2966257 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2958111 2963616 2964227 "STREAM" 2965421 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957103 2957308 2957539 "STINPROD" 2957927 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956218 2956592 2956740 "STEPAST" 2956977 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955714 2955959 2955989 "STEP" 2956083 T STEP (NIL) -9 NIL 2956154 NIL) (-1183 2948770 2955613 2955690 "STBL" 2955695 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943320 2947933 2947976 "STAGG" 2948129 NIL STAGG (NIL T) -9 NIL 2948218 NIL) (-1181 2940872 2941624 2942496 "STAGG-" 2942501 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938844 2940642 2940734 "STACK" 2940815 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2938161 2938674 2938704 "SRING" 2938709 T SRING (NIL) -9 NIL 2938729 NIL) (-1178 2930169 2936302 2936758 "SREGSET" 2937791 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922516 2923963 2925476 "SRDCMPK" 2928775 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914816 2919875 2919905 "SRAGG" 2921208 T SRAGG (NIL) -9 NIL 2921816 NIL) (-1175 2913767 2914088 2914467 "SRAGG-" 2914472 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907351 2912714 2913135 "SQMATRIX" 2913393 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900763 2904069 2904796 "SPLTREE" 2906696 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896588 2897419 2898065 "SPLNODE" 2900189 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895563 2895868 2895898 "SPFCAT" 2896342 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894258 2894510 2894774 "SPECOUT" 2895321 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884904 2887222 2887252 "SPADXPT" 2891930 T SPADXPT (NIL) -9 NIL 2894096 NIL) (-1168 2884659 2884705 2884774 "SPADPRSR" 2884857 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882262 2884614 2884645 "SPADAST" 2884650 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873863 2875966 2876009 "SPACEC" 2880382 NIL SPACEC (NIL T) -9 NIL 2882198 NIL) (-1165 2871663 2873795 2873844 "SPACE3" 2873849 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870395 2870586 2870877 "SORTPAK" 2871468 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868457 2868790 2869202 "SOLVETRA" 2870059 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867495 2867729 2867990 "SOLVESER" 2868230 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862727 2863687 2864682 "SOLVERAD" 2866547 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858452 2859151 2859880 "SOLVEFOR" 2862094 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2852056 2857800 2857897 "SNTSCAT" 2857902 NIL SNTSCAT (NIL T T T T) -9 NIL 2857972 NIL) (-1158 2845607 2850379 2850770 "SMTS" 2851746 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839329 2845495 2845572 "SMP" 2845577 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837458 2837789 2838187 "SMITH" 2839026 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2828983 2834037 2834140 "SMATCAT" 2835491 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836041 NIL) (-1154 2825755 2826746 2827924 "SMATCAT-" 2827929 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823224 2824963 2825006 "SKAGG" 2825267 NIL SKAGG (NIL T) -9 NIL 2825402 NIL) (-1152 2818744 2822707 2822884 "SINT" 2823036 T SINT (NIL) -8 NIL NIL 2823191) (-1151 2818510 2818554 2818620 "SIMPAN" 2818700 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817330 2817569 2817844 "SIGNRF" 2818269 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2816145 2816314 2816598 "SIGNEF" 2817159 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815385 2815728 2815852 "SIGAST" 2816043 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814610 2814920 2815060 "SIG" 2815267 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812262 2812754 2813260 "SHP" 2814151 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805586 2812163 2812239 "SHDP" 2812244 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2805097 2805337 2805367 "SGROUP" 2805460 T SGROUP (NIL) -9 NIL 2805522 NIL) (-1143 2804949 2804981 2805054 "SGROUP-" 2805059 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801668 2802438 2803161 "SGCF" 2804248 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795370 2801114 2801211 "SFRTCAT" 2801216 NIL SFRTCAT (NIL T T T T) -9 NIL 2801255 NIL) (-1140 2788689 2789809 2790945 "SFRGCD" 2794353 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781707 2782888 2784074 "SFQCMPK" 2787622 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781309 2781416 2781527 "SFORT" 2781648 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780235 2781149 2781270 "SEXOF" 2781275 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775824 2776731 2776826 "SEXCAT" 2779448 NIL SEXCAT (NIL T T T T T) -9 NIL 2780008 NIL) (-1135 2774739 2775705 2775773 "SEX" 2775778 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772861 2773452 2773757 "SETMN" 2774480 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772391 2772579 2772609 "SETCAT" 2772726 T SETCAT (NIL) -9 NIL 2772811 NIL) (-1132 2772159 2772223 2772322 "SETCAT-" 2772327 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768262 2770620 2770663 "SETAGG" 2771533 NIL SETAGG (NIL T) -9 NIL 2771873 NIL) (-1130 2767684 2767836 2768073 "SETAGG-" 2768078 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764493 2767618 2767666 "SET" 2767671 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763876 2764189 2764290 "SEQAST" 2764414 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2763003 2763369 2763430 "SEGXCAT" 2763716 NIL SEGXCAT (NIL T T) -9 NIL 2763836 NIL) (-1126 2761928 2762196 2762239 "SEGCAT" 2762761 NIL SEGCAT (NIL T) -9 NIL 2762982 NIL) (-1125 2761543 2761608 2761721 "SEGBIND2" 2761863 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760433 2760906 2761114 "SEGBIND" 2761370 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2759952 2760234 2760311 "SEGAST" 2760378 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2759161 2759297 2759501 "SEG2" 2759796 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2758077 2758827 2759009 "SEG" 2759014 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757310 2758012 2758059 "SDVAR" 2758064 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748668 2757080 2757210 "SDPOL" 2757215 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747237 2747527 2747846 "SCPKG" 2748383 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746359 2746573 2746765 "SCOPE" 2747067 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745555 2745713 2745892 "SCACHE" 2746214 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2745139 2745373 2745403 "SASTCAT" 2745408 T SASTCAT (NIL) -9 NIL 2745421 NIL) (-1114 2744542 2744974 2745050 "SAOS" 2745085 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2744101 2744142 2744315 "SAERFFC" 2744501 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743688 2743729 2743888 "SAEFACT" 2744060 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736736 2743585 2743665 "SAE" 2743670 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2735039 2735371 2735772 "RURPK" 2736402 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733616 2733982 2734287 "RULESET" 2734873 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733186 2733410 2733493 "RULECOLD" 2733568 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730301 2730939 2731397 "RULE" 2732867 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730085 2730119 2730190 "RTVALUE" 2730252 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729496 2729802 2729896 "RSTRCAST" 2730013 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724266 2725139 2726059 "RSETGCD" 2728695 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712830 2718574 2718671 "RSETCAT" 2722790 NIL RSETCAT (NIL T T T T) -9 NIL 2723887 NIL) (-1102 2710649 2711296 2712120 "RSETCAT-" 2712125 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2702957 2704411 2705931 "RSDCMPK" 2709248 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700826 2701389 2701463 "RRCC" 2702549 NIL RRCC (NIL T T) -9 NIL 2702893 NIL) (-1099 2700147 2700351 2700630 "RRCC-" 2700635 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699530 2699843 2699944 "RPTAST" 2700068 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2671916 2682642 2682709 "RPOLCAT" 2693375 NIL RPOLCAT (NIL T T T) -9 NIL 2696535 NIL) (-1096 2662886 2665754 2668876 "RPOLCAT-" 2668881 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653339 2661097 2661579 "ROUTINE" 2662426 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649402 2652965 2653105 "ROMAN" 2653221 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647514 2648262 2648522 "ROIRC" 2649207 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643234 2646003 2646033 "RNS" 2646337 T RNS (NIL) -9 NIL 2646611 NIL) (-1091 2641641 2642126 2642660 "RNS-" 2642735 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640602 2641006 2641208 "RNGBIND" 2641492 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639895 2640399 2640429 "RNG" 2640434 T RNG (NIL) -9 NIL 2640455 NIL) (-1088 2639190 2639668 2639711 "RMODULE" 2639716 NIL RMODULE (NIL T) -9 NIL 2639743 NIL) (-1087 2638014 2638120 2638456 "RMCAT2" 2639091 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634516 2637360 2637657 "RMATRIX" 2637776 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2627015 2629603 2629718 "RMATCAT" 2633077 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634059 NIL) (-1084 2626354 2626537 2626844 "RMATCAT-" 2626849 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2625927 2626141 2626184 "RLINSET" 2626246 NIL RLINSET (NIL T) -9 NIL 2626290 NIL) (-1082 2625488 2625569 2625697 "RINTERP" 2625846 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624412 2625086 2625116 "RING" 2625172 T RING (NIL) -9 NIL 2625264 NIL) (-1080 2624192 2624248 2624345 "RING-" 2624350 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2623003 2623270 2623528 "RIDIST" 2623956 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613628 2622471 2622677 "RGCHAIN" 2622851 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612886 2613370 2613411 "RGBCSPC" 2613469 NIL RGBCSPC (NIL T) -9 NIL 2613521 NIL) (-1076 2611952 2612411 2612452 "RGBCMDL" 2612684 NIL RGBCMDL (NIL T) -9 NIL 2612798 NIL) (-1075 2611592 2611661 2611764 "RFFACTOR" 2611883 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611311 2611352 2611449 "RFFACT" 2611551 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609362 2609792 2610174 "RFDIST" 2610951 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606302 2606970 2607640 "RF" 2608726 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605749 2605847 2606010 "RETSOL" 2606204 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605367 2605465 2605508 "RETRACT" 2605641 NIL RETRACT (NIL T) -9 NIL 2605728 NIL) (-1069 2605210 2605241 2605328 "RETRACT-" 2605333 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604758 2605032 2605102 "RETAST" 2605162 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2597108 2604411 2604538 "RESULT" 2604653 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595543 2596377 2596576 "RESRING" 2597011 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595167 2595228 2595326 "RESLATC" 2595480 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594866 2594907 2595014 "REPSQ" 2595126 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594557 2594598 2594709 "REPDB" 2594825 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588389 2589846 2591069 "REP2" 2593369 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584692 2585447 2586255 "REP1" 2587616 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2582072 2582694 2583296 "REP" 2584112 T REP (NIL) -7 NIL NIL NIL) (-1059 2574080 2580213 2580669 "REGSET" 2581702 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572789 2573228 2573478 "REF" 2573865 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572154 2572269 2572436 "REDORDER" 2572673 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567525 2571367 2571594 "RECLOS" 2571982 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566559 2566758 2566973 "REALSOLV" 2567332 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2563006 2563844 2564728 "REAL0Q" 2565724 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558559 2559595 2560656 "REAL0" 2561987 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558393 2558446 2558476 "REAL" 2558481 T REAL (NIL) -9 NIL 2558516 NIL) (-1051 2557804 2558110 2558204 "RDUCEAST" 2558321 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557203 2557281 2557488 "RDIV" 2557726 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556253 2556445 2556658 "RDIST" 2557025 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554838 2555137 2555509 "RDETRS" 2555961 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552632 2553104 2553642 "RDETR" 2554380 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551251 2551535 2551932 "RDEEFS" 2552348 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549754 2550066 2550491 "RDEEF" 2550939 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543233 2546708 2546738 "RCFIELD" 2548033 T RCFIELD (NIL) -9 NIL 2548764 NIL) (-1043 2541189 2541801 2542497 "RCFIELD-" 2542572 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537241 2539262 2539305 "RCAGG" 2540389 NIL RCAGG (NIL T) -9 NIL 2540854 NIL) (-1041 2536851 2536963 2537126 "RCAGG-" 2537131 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536168 2536298 2536463 "RATRET" 2536735 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535709 2535788 2535909 "RATFACT" 2536096 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2534987 2535137 2535289 "RANDSRC" 2535579 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534715 2534765 2534838 "RADUTIL" 2534936 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526860 2533546 2533857 "RADIX" 2534438 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516475 2526702 2526832 "RADFF" 2526837 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2516104 2516197 2516227 "RADCAT" 2516387 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515874 2515934 2516034 "RADCAT-" 2516039 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513785 2515644 2515736 "QUEUE" 2515817 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513410 2513459 2513590 "QUATCT2" 2513736 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505788 2509833 2509875 "QUATCAT" 2510666 NIL QUATCAT (NIL T) -9 NIL 2511432 NIL) (-1029 2501669 2502964 2504354 "QUATCAT-" 2504450 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497515 2501602 2501650 "QUAT" 2501655 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494771 2496563 2496606 "QUAGG" 2496987 NIL QUAGG (NIL T) -9 NIL 2497162 NIL) (-1026 2494319 2494593 2494663 "QQUTAST" 2494723 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493230 2493832 2493997 "QFORM" 2494200 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492855 2492904 2493035 "QFCAT2" 2493181 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482552 2488702 2488744 "QFCAT" 2489412 NIL QFCAT (NIL T) -9 NIL 2490413 NIL) (-1022 2477886 2479334 2480921 "QFCAT-" 2481017 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477317 2477451 2477583 "QEQUAT" 2477776 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470335 2471516 2472702 "QCMPACK" 2476250 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469564 2469746 2469982 "QALGSET2" 2470153 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2467014 2467550 2467980 "QALGSET" 2469219 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465681 2465923 2466242 "PWFFINTB" 2466787 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463826 2464024 2464380 "PUSHVAR" 2465495 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459553 2460769 2460812 "PTRANFN" 2462723 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457890 2458235 2458559 "PTPACK" 2459264 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457513 2457576 2457687 "PTFUNC2" 2457827 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451429 2456302 2456345 "PTCAT" 2456645 NIL PTCAT (NIL T) -9 NIL 2456798 NIL) (-1011 2451078 2451119 2451245 "PSQFR" 2451388 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449650 2449966 2450302 "PSEUDLIN" 2450776 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436170 2438745 2441071 "PSETPK" 2447410 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428878 2431906 2432004 "PSETCAT" 2435045 NIL PSETCAT (NIL T T T T) -9 NIL 2435859 NIL) (-1007 2426603 2427345 2428169 "PSETCAT-" 2428174 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2425916 2426111 2426141 "PSCURVE" 2426413 T PSCURVE (NIL) -9 NIL 2426580 NIL) (-1005 2421639 2423406 2423473 "PSCAT" 2424325 NIL PSCAT (NIL T T T) -9 NIL 2424565 NIL) (-1004 2420633 2420915 2421318 "PSCAT-" 2421323 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418801 2419692 2419957 "PRTITION" 2420390 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418212 2418518 2418612 "PRTDAST" 2418729 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2407056 2409478 2411668 "PRS" 2416074 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404671 2406373 2406415 "PRQAGG" 2406601 NIL PRQAGG (NIL T) -9 NIL 2406703 NIL) (-999 2403850 2404299 2404327 "PROPLOG" 2404466 T PROPLOG (NIL) -9 NIL 2404581 NIL) (-998 2403448 2403511 2403634 "PROPFUN2" 2403773 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402745 2402884 2403056 "PROPFUN1" 2403309 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400726 2401492 2401789 "PROPFRML" 2402481 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400171 2400302 2400430 "PROPERTY" 2400618 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2393984 2398337 2399157 "PRODUCT" 2399397 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393774 2393812 2393871 "PRINT" 2393945 T PRINT (NIL) -7 NIL NIL NIL) (-992 2393090 2393231 2393383 "PRIMES" 2393654 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391137 2391556 2392022 "PRIMELT" 2392669 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390854 2390915 2390943 "PRIMCAT" 2391067 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389843 2390039 2390267 "PRIMARR2" 2390672 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385565 2389781 2389826 "PRIMARR" 2389831 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385202 2385264 2385375 "PREASSOC" 2385503 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382167 2384660 2384894 "PR" 2385013 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381618 2381775 2381803 "PPCURVE" 2382008 T PPCURVE (NIL) -9 NIL 2382144 NIL) (-984 2381165 2381413 2381496 "PORTNUM" 2381555 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378502 2378923 2379515 "POLYROOT" 2380746 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377879 2377943 2378177 "POLYLIFT" 2378438 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2374100 2374603 2375232 "POLYCATQ" 2377424 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359748 2365847 2365912 "POLYCAT" 2369426 NIL POLYCAT (NIL T T T) -9 NIL 2371304 NIL) (-979 2352888 2355073 2357450 "POLYCAT-" 2357455 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352469 2352543 2352663 "POLY2UP" 2352814 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2352095 2352158 2352267 "POLY2" 2352406 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345310 2351699 2351859 "POLY" 2351968 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2343971 2344234 2344510 "POLUTIL" 2345084 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342290 2342603 2342934 "POLTOPOL" 2343693 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337286 2342224 2342271 "POINT" 2342276 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335419 2335830 2336205 "PNTHEORY" 2336931 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333865 2334174 2334573 "PMTOOLS" 2335117 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333452 2333536 2333653 "PMSYM" 2333781 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2332954 2333029 2333204 "PMQFCAT" 2333377 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332335 2332433 2332595 "PMPREDFS" 2332855 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331678 2331800 2331956 "PMPRED" 2332212 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330332 2330550 2330928 "PMPLCAT" 2331440 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329858 2329943 2330095 "PMLSAGG" 2330247 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329325 2329407 2329589 "PMKERNEL" 2329776 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2328936 2329017 2329130 "PMINS" 2329244 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328372 2328447 2328656 "PMFS" 2328861 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327588 2327718 2327923 "PMDOWN" 2328249 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326837 2326971 2327134 "PMASSFS" 2327475 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2325980 2326162 2326343 "PMASS" 2326676 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325629 2325703 2325797 "PLOTTOOL" 2325906 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321281 2322475 2323397 "PLOT3D" 2324727 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320169 2320370 2320605 "PLOT1" 2321085 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314590 2315980 2317128 "PLOT" 2319041 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289765 2294656 2299507 "PLEQN" 2309856 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289452 2289505 2289608 "PINTERPA" 2289712 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288758 2288892 2289072 "PINTERP" 2289317 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286842 2288008 2288036 "PID" 2288233 T PID (NIL) -9 NIL 2288360 NIL) (-950 2286587 2286630 2286705 "PICOERCE" 2286799 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285683 2286351 2286438 "PI" 2286478 T PI (NIL) -8 NIL NIL 2286545) (-948 2284991 2285142 2285318 "PGROEB" 2285539 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280430 2281389 2282295 "PGE" 2284105 T PGE (NIL) -7 NIL NIL NIL) (-946 2278511 2278800 2279166 "PGCD" 2280147 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277837 2277952 2278113 "PFRPAC" 2278395 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2274095 2276385 2276738 "PFR" 2277516 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272448 2272728 2273053 "PFOTOOLS" 2273842 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2270963 2271220 2271571 "PFOQ" 2272205 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269446 2269676 2270032 "PFO" 2270747 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266530 2268036 2268064 "PFECAT" 2268657 T PFECAT (NIL) -9 NIL 2269034 NIL) (-939 2265978 2266143 2266350 "PFECAT-" 2266355 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264551 2264833 2265134 "PFBRU" 2265727 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262380 2262769 2263201 "PFBR" 2264202 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258326 2262269 2262338 "PF" 2262343 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253380 2254533 2255403 "PERMGRP" 2257489 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251292 2252404 2252445 "PERMCAT" 2252845 NIL PERMCAT (NIL T) -9 NIL 2253143 NIL) (-933 2250939 2250986 2251110 "PERMAN" 2251245 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246741 2248448 2249096 "PERM" 2250324 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2243982 2246406 2246528 "PENDTREE" 2246652 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242863 2243126 2243167 "PDSPC" 2243700 NIL PDSPC (NIL T) -9 NIL 2243945 NIL) (-929 2241918 2242184 2242546 "PDSPC-" 2242551 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240632 2241568 2241609 "PDRING" 2241614 NIL PDRING (NIL T) -9 NIL 2241642 NIL) (-927 2239375 2240137 2240191 "PDMOD" 2240196 NIL PDMOD (NIL T T) -9 NIL 2240300 NIL) (-926 2236542 2237368 2238036 "PDEPROB" 2238727 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2234051 2234591 2235146 "PDEPACK" 2236007 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2232939 2233153 2233404 "PDECOMP" 2233850 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230456 2231347 2231375 "PDECAT" 2232162 T PDECAT (NIL) -9 NIL 2232875 NIL) (-922 2230073 2230140 2230194 "PDDOM" 2230359 NIL PDDOM (NIL T T) -9 NIL 2230439 NIL) (-921 2229886 2229922 2230029 "PDDOM-" 2230034 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229631 2229670 2229760 "PCOMP" 2229847 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227671 2228432 2228729 "PBWLB" 2229360 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227297 2227360 2227469 "PATTERN2" 2227608 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2225006 2225442 2225899 "PATTERN1" 2226886 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217185 2219079 2220417 "PATTERN" 2223689 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216743 2216816 2216948 "PATRES2" 2217112 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2214009 2214692 2215173 "PATRES" 2216308 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211862 2212297 2212704 "PATMATCH" 2213676 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211316 2211567 2211608 "PATMAB" 2211715 NIL PATMAB (NIL T) -9 NIL 2211798 NIL) (-911 2209762 2210170 2210428 "PATLRES" 2211121 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209300 2209431 2209472 "PATAB" 2209477 NIL PATAB (NIL T) -9 NIL 2209649 NIL) (-909 2207440 2207877 2208300 "PARTPERM" 2208897 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2207049 2207124 2207226 "PARSURF" 2207371 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206675 2206738 2206847 "PARSU2" 2206986 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206433 2206479 2206546 "PARSER" 2206628 T PARSER (NIL) -7 NIL NIL NIL) (-905 2206042 2206117 2206219 "PARSCURV" 2206364 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205668 2205731 2205840 "PARSC2" 2205979 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205295 2205365 2205462 "PARPCURV" 2205604 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2204921 2204984 2205093 "PARPC2" 2205232 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203910 2204294 2204476 "PARAMAST" 2204759 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203418 2203516 2203635 "PAN2EXPR" 2203811 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2202111 2202539 2202767 "PALETTE" 2203210 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200456 2201116 2201476 "PAIR" 2201797 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193389 2199713 2199908 "PADICRC" 2200310 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185646 2192733 2192918 "PADICRAT" 2193236 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182443 2184306 2184346 "PADICCT" 2184927 NIL PADICCT (NIL NIL) -9 NIL 2185209 NIL) (-894 2180459 2182380 2182425 "PADIC" 2182430 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179404 2179616 2179884 "PADEPAC" 2180246 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178604 2178749 2178955 "PADE" 2179266 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176837 2177812 2178092 "OWP" 2178408 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176282 2176543 2176640 "OVERSET" 2176760 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175202 2175887 2176059 "OVAR" 2176150 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163438 2166311 2168511 "OUTFORM" 2173022 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162720 2163035 2163162 "OUTBFILE" 2163331 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2161997 2162192 2162220 "OUTBCON" 2162538 T OUTBCON (NIL) -9 NIL 2162704 NIL) (-885 2161580 2161710 2161867 "OUTBCON-" 2161872 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160820 2160965 2161126 "OUT" 2161439 T OUT (NIL) -7 NIL NIL NIL) (-883 2160116 2160549 2160638 "OSI" 2160751 T OSI (NIL) -8 NIL NIL NIL) (-882 2159535 2159957 2159985 "OSGROUP" 2159990 T OSGROUP (NIL) -9 NIL 2160012 NIL) (-881 2158246 2158507 2158792 "ORTHPOL" 2159282 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155497 2158081 2158202 "OREUP" 2158207 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152600 2155188 2155315 "ORESUP" 2155439 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2150100 2150628 2151189 "OREPCTO" 2152089 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143478 2145973 2146014 "OREPCAT" 2148362 NIL OREPCAT (NIL T) -9 NIL 2149466 NIL) (-876 2140451 2141407 2142465 "OREPCAT-" 2142470 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139643 2139921 2139949 "ORDTYPE" 2140258 T ORDTYPE (NIL) -9 NIL 2140421 NIL) (-874 2138944 2139160 2139415 "ORDTYPE-" 2139420 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138300 2138683 2138841 "ORDSTRCT" 2138846 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137798 2138168 2138196 "ORDSET" 2138201 T ORDSET (NIL) -9 NIL 2138223 NIL) (-871 2136449 2137420 2137448 "ORDRING" 2137453 T ORDRING (NIL) -9 NIL 2137482 NIL) (-870 2135700 2136265 2136293 "ORDMON" 2136298 T ORDMON (NIL) -9 NIL 2136319 NIL) (-869 2134844 2135009 2135204 "ORDFUNS" 2135549 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2134059 2134574 2134602 "ORDFIN" 2134667 T ORDFIN (NIL) -9 NIL 2134741 NIL) (-867 2133313 2133452 2133638 "ORDCOMP2" 2133919 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129660 2131899 2132308 "ORDCOMP" 2132937 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126181 2127151 2127965 "OPTPROB" 2128866 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2122923 2123622 2124326 "OPTPACK" 2125497 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120536 2121362 2121390 "OPTCAT" 2122209 T OPTCAT (NIL) -9 NIL 2122859 NIL) (-862 2119854 2120213 2120318 "OPSIG" 2120451 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119616 2119661 2119727 "OPQUERY" 2119808 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2118922 2119202 2119243 "OPERCAT" 2119455 NIL OPERCAT (NIL T) -9 NIL 2119552 NIL) (-859 2118665 2118733 2118850 "OPERCAT-" 2118855 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115581 2116976 2117480 "OP" 2118194 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114874 2115001 2115175 "ONECOMP2" 2115453 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111487 2113671 2114040 "ONECOMP" 2114538 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110888 2111012 2111142 "OMSERVER" 2111377 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107400 2110326 2110366 "OMSAGG" 2110427 NIL OMSAGG (NIL T) -9 NIL 2110492 NIL) (-853 2105975 2106286 2106568 "OMPKG" 2107138 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104322 2105524 2105693 "OMLO" 2105856 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103258 2103429 2103649 "OMEXPR" 2104148 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102343 2102679 2102839 "OMERRK" 2103118 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101580 2101889 2102025 "OMERR" 2102227 T OMERR (NIL) -8 NIL NIL NIL) (-848 2100971 2101257 2101365 "OMENC" 2101492 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094608 2096051 2097222 "OMDEV" 2099820 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093641 2093848 2094042 "OMCONN" 2094434 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2093047 2093174 2093202 "OM" 2093501 T OM (NIL) -9 NIL NIL NIL) (-844 2091325 2092517 2092545 "OINTDOM" 2092550 T OINTDOM (NIL) -9 NIL 2092571 NIL) (-843 2088400 2090013 2090350 "OFMONOID" 2091020 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087634 2088337 2088382 "ODVAR" 2088387 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084778 2087379 2087534 "ODR" 2087539 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076190 2084554 2084680 "ODPOL" 2084685 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069484 2076062 2076167 "ODP" 2076172 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068226 2068465 2068740 "ODETOOLS" 2069258 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065169 2065851 2066567 "ODESYS" 2067559 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2059999 2060959 2061984 "ODERTRIC" 2064244 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059419 2059507 2059701 "ODERED" 2059911 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056271 2056855 2057532 "ODERAT" 2058842 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053187 2053695 2054292 "ODEPRRIC" 2055800 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2051082 2051726 2052212 "ODEPROB" 2052721 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047548 2048087 2048734 "ODEPRIM" 2050561 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046791 2046899 2047159 "ODEPAL" 2047440 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042893 2043744 2044608 "ODEPACK" 2045947 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2041936 2042061 2042283 "ODEINT" 2042782 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2036001 2037462 2038909 "ODEIFTBL" 2040509 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031351 2032185 2033137 "ODEEF" 2035160 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030694 2030789 2031012 "ODECONST" 2031256 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028757 2029466 2029494 "ODECAT" 2030099 T ODECAT (NIL) -9 NIL 2030630 NIL) (-823 2028389 2028438 2028565 "OCTCT2" 2028708 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024889 2028094 2028216 "OCT" 2028299 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2024082 2024682 2024710 "OCAMON" 2024715 T OCAMON (NIL) -9 NIL 2024736 NIL) (-820 2018353 2021125 2021165 "OC" 2022262 NIL OC (NIL T) -9 NIL 2023120 NIL) (-819 2015388 2016328 2017318 "OC-" 2017412 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014808 2015233 2015261 "OASGP" 2015266 T OASGP (NIL) -9 NIL 2015286 NIL) (-817 2013904 2014531 2014559 "OAMONS" 2014599 T OAMONS (NIL) -9 NIL 2014642 NIL) (-816 2013080 2013639 2013667 "OAMON" 2013725 T OAMON (NIL) -9 NIL 2013777 NIL) (-815 2012938 2012971 2013039 "OAMON-" 2013044 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011719 2012472 2012500 "OAGROUP" 2012647 T OAGROUP (NIL) -9 NIL 2012740 NIL) (-813 2011422 2011510 2011628 "OAGROUP-" 2011633 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2011104 2011160 2011249 "NUMTUBE" 2011366 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004623 2006195 2007731 "NUMQUAD" 2009588 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000303 2001337 2002372 "NUMODE" 2003608 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997584 1998524 1998552 "NUMINT" 1999475 T NUMINT (NIL) -9 NIL 2000239 NIL) (-808 1996496 1996729 1996947 "NUMFMT" 1997386 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982679 1985800 1988332 "NUMERIC" 1994003 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976383 1982127 1982222 "NTSCAT" 1982227 NIL NTSCAT (NIL T T T T) -9 NIL 1982266 NIL) (-805 1975563 1975742 1975935 "NTPOLFN" 1976222 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975189 1975252 1975361 "NSUP2" 1975500 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961971 1972014 1972826 "NSUP" 1974410 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950814 1961745 1961878 "NSMP" 1961883 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949222 1949547 1949904 "NREP" 1950502 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947801 1948065 1948423 "NPCOEF" 1948965 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946849 1946982 1947198 "NORMRETR" 1947682 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944860 1945180 1945589 "NORMPK" 1946557 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944539 1944573 1944697 "NORMMA" 1944826 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944322 1944357 1944426 "NONE1" 1944503 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944086 1944279 1944308 "NONE" 1944313 T NONE (NIL) -8 NIL NIL NIL) (-794 1943577 1943645 1943824 "NODE1" 1944018 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941638 1942700 1942955 "NNI" 1943302 T NNI (NIL) -8 NIL NIL 1943537) (-792 1940034 1940371 1940735 "NLINSOL" 1941306 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936215 1937270 1938169 "NIPROB" 1939155 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934954 1935206 1935508 "NFINTBAS" 1935977 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934038 1934604 1934645 "NETCLT" 1934817 NIL NETCLT (NIL T) -9 NIL 1934899 NIL) (-788 1932710 1932977 1933258 "NCODIV" 1933806 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932466 1932509 1932584 "NCNTFRAC" 1932667 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930622 1931010 1931430 "NCEP" 1932091 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929285 1930232 1930260 "NASRING" 1930370 T NASRING (NIL) -9 NIL 1930450 NIL) (-784 1929068 1929124 1929218 "NASRING-" 1929223 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928035 1928686 1928714 "NARNG" 1928831 T NARNG (NIL) -9 NIL 1928922 NIL) (-782 1927709 1927794 1927928 "NARNG-" 1927933 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926546 1926795 1927030 "NAGSP" 1927494 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917590 1919502 1921175 "NAGS" 1924893 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916114 1916446 1916777 "NAGF07" 1917279 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910586 1911943 1913250 "NAGF04" 1914827 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903458 1905168 1906801 "NAGF02" 1908973 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898622 1899782 1900899 "NAGF01" 1902361 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892202 1893816 1895401 "NAGE04" 1897057 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883263 1885492 1887622 "NAGE02" 1890092 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879156 1880163 1881127 "NAGE01" 1882319 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876933 1877485 1878043 "NAGD03" 1878618 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868629 1870611 1872565 "NAGD02" 1874999 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862368 1863865 1865305 "NAGD01" 1867209 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858505 1859399 1860236 "NAGC06" 1861551 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856952 1857302 1857658 "NAGC05" 1858169 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856316 1856447 1856591 "NAGC02" 1856828 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855117 1855844 1855884 "NAALG" 1855963 NIL NAALG (NIL T) -9 NIL 1856024 NIL) (-765 1854946 1854981 1855071 "NAALG-" 1855076 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848818 1850004 1851191 "MULTSQFR" 1853842 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848125 1848212 1848396 "MULTFACT" 1848730 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840270 1844708 1844761 "MTSCAT" 1845831 NIL MTSCAT (NIL T T) -9 NIL 1846347 NIL) (-761 1839976 1840036 1840128 "MTHING" 1840210 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839762 1839801 1839861 "MSYSCMD" 1839936 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836507 1839323 1839364 "MSETAGG" 1839369 NIL MSETAGG (NIL T) -9 NIL 1839403 NIL) (-758 1832221 1835262 1835582 "MSET" 1836220 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827823 1829600 1830345 "MRING" 1831521 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827383 1827456 1827587 "MRF2" 1827750 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826995 1827036 1827180 "MRATFAC" 1827342 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824565 1824902 1825333 "MPRFF" 1826700 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817899 1824419 1824516 "MPOLY" 1824521 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817383 1817424 1817632 "MPCPF" 1817858 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816891 1816940 1817124 "MPC3" 1817334 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816074 1816167 1816388 "MPC2" 1816806 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814351 1814712 1815102 "MONOTOOL" 1815734 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813496 1813879 1813907 "MONOID" 1814126 T MONOID (NIL) -9 NIL 1814273 NIL) (-747 1813012 1813161 1813342 "MONOID-" 1813347 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801985 1808832 1808891 "MONOGEN" 1809565 NIL MONOGEN (NIL T T) -9 NIL 1810021 NIL) (-745 1799035 1799938 1800938 "MONOGEN-" 1801057 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797752 1798300 1798328 "MONADWU" 1798720 T MONADWU (NIL) -9 NIL 1798958 NIL) (-743 1797082 1797283 1797531 "MONADWU-" 1797536 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796367 1796671 1796699 "MONAD" 1796906 T MONAD (NIL) -9 NIL 1797018 NIL) (-741 1796034 1796130 1796262 "MONAD-" 1796267 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794173 1794947 1795226 "MOEBIUS" 1795787 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793341 1793841 1793881 "MODULE" 1793886 NIL MODULE (NIL T) -9 NIL 1793925 NIL) (-738 1792879 1793005 1793195 "MODULE-" 1793200 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790409 1791243 1791570 "MODRING" 1792703 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787138 1788514 1789035 "MODOP" 1789938 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785624 1786205 1786482 "MODMONOM" 1787001 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774384 1783915 1784329 "MODMON" 1785261 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771217 1773228 1773504 "MODFIELD" 1774259 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770128 1770498 1770688 "MMLFORM" 1771047 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769648 1769697 1769876 "MMAP" 1770079 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767541 1768480 1768521 "MLO" 1768944 NIL MLO (NIL T) -9 NIL 1769186 NIL) (-729 1764889 1765423 1766025 "MLIFT" 1767022 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764268 1764364 1764518 "MKUCFUNC" 1764800 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763861 1763937 1764060 "MKRECORD" 1764191 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762884 1763070 1763298 "MKFUNC" 1763672 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762260 1762376 1762532 "MKFLCFN" 1762767 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761525 1761639 1761824 "MKBCFUNC" 1762153 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757522 1761079 1761215 "MINT" 1761409 T MINT (NIL) -8 NIL NIL NIL) (-722 1756304 1756577 1756854 "MHROWRED" 1757277 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751055 1754839 1755244 "MFLOAT" 1755919 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750400 1750488 1750659 "MFINFACT" 1750967 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746679 1747563 1748447 "MESH" 1749536 T MESH (NIL) -7 NIL NIL NIL) (-718 1745033 1745381 1745734 "MDDFACT" 1746366 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741569 1744164 1744205 "MDAGG" 1744460 NIL MDAGG (NIL T) -9 NIL 1744603 NIL) (-716 1729292 1740862 1741069 "MCMPLX" 1741382 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728411 1728575 1728776 "MCDEN" 1729141 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726259 1726571 1726951 "MCALCFN" 1728141 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725136 1725424 1725657 "MAYBE" 1726065 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722694 1723271 1723833 "MATSTOR" 1724607 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718116 1722066 1722314 "MATRIX" 1722479 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713816 1714589 1715325 "MATLIN" 1717473 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712392 1712563 1712896 "MATCAT2" 1713651 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701731 1705449 1705526 "MATCAT" 1710558 NIL MATCAT (NIL T T T) -9 NIL 1712030 NIL) (-707 1697684 1698994 1700407 "MATCAT-" 1700412 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695760 1696120 1696504 "MAPPKG3" 1697359 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694717 1694914 1695136 "MAPPKG2" 1695584 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693174 1693500 1693827 "MAPPKG1" 1694423 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692175 1692580 1692757 "MAPPAST" 1693017 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691780 1691844 1691967 "MAPHACK3" 1692111 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691360 1691433 1691547 "MAPHACK2" 1691712 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690786 1690901 1691043 "MAPHACK1" 1691251 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688709 1689486 1689790 "MAGMA" 1690514 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688128 1688433 1688524 "MACROAST" 1688638 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684371 1686367 1686828 "M3D" 1687700 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677843 1682682 1682723 "LZSTAGG" 1683505 NIL LZSTAGG (NIL T) -9 NIL 1683800 NIL) (-695 1673525 1674974 1676431 "LZSTAGG-" 1676436 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670438 1671416 1671903 "LWORD" 1673070 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669960 1670242 1670317 "LSTAST" 1670383 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661888 1669731 1669865 "LSQM" 1669870 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661106 1661251 1661479 "LSPP" 1661743 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657843 1658559 1659289 "LSMP1" 1660408 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655625 1655956 1656412 "LSMP" 1657532 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648753 1654715 1654756 "LSAGG" 1654818 NIL LSAGG (NIL T) -9 NIL 1654896 NIL) (-687 1645262 1646372 1647585 "LSAGG-" 1647590 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642557 1644406 1644655 "LPOLY" 1645057 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642133 1642224 1642347 "LPEFRAC" 1642466 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641816 1641895 1641923 "LOGIC" 1642034 T LOGIC (NIL) -9 NIL 1642116 NIL) (-683 1641672 1641701 1641772 "LOGIC-" 1641777 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640847 1641005 1641198 "LODOOPS" 1641528 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639371 1639620 1639973 "LODOF" 1640594 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635247 1638006 1638047 "LODOCAT" 1638485 NIL LODOCAT (NIL T) -9 NIL 1638696 NIL) (-679 1634962 1635038 1635165 "LODOCAT-" 1635170 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631948 1634803 1634921 "LODO2" 1634926 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629055 1631885 1631930 "LODO1" 1631935 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626150 1628971 1629037 "LODO" 1629042 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625019 1625196 1625501 "LODEEF" 1625973 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623005 1624113 1624366 "LO" 1624851 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617977 1621171 1621212 "LNAGG" 1622074 NIL LNAGG (NIL T) -9 NIL 1622509 NIL) (-672 1617070 1617338 1617680 "LNAGG-" 1617685 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613050 1613995 1614634 "LMOPS" 1616485 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612349 1612827 1612868 "LMODULE" 1612873 NIL LMODULE (NIL T) -9 NIL 1612899 NIL) (-669 1609304 1611994 1612117 "LMDICT" 1612259 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608880 1609094 1609135 "LLINSET" 1609196 NIL LLINSET (NIL T) -9 NIL 1609240 NIL) (-667 1608525 1608788 1608848 "LITERAL" 1608853 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608044 1608124 1608263 "LIST3" 1608445 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606142 1606490 1606889 "LIST2MAP" 1607691 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605131 1605327 1605555 "LIST2" 1605960 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597585 1604065 1604369 "LIST" 1604860 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597168 1597404 1597445 "LINSET" 1597450 NIL LINSET (NIL T) -9 NIL 1597484 NIL) (-661 1595982 1596676 1596843 "LINFORM" 1597053 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594281 1595009 1595050 "LINEXP" 1595540 NIL LINEXP (NIL T) -9 NIL 1595813 NIL) (-659 1592857 1593761 1593942 "LINELT" 1594152 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591414 1591694 1592005 "LINDEP" 1592609 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590550 1591146 1591256 "LINBASIS" 1591344 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587287 1588036 1588813 "LIMITRF" 1589805 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585572 1585886 1586295 "LIMITPS" 1586982 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584400 1584975 1585015 "LIECAT" 1585155 NIL LIECAT (NIL T) -9 NIL 1585306 NIL) (-653 1584235 1584268 1584356 "LIECAT-" 1584361 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578255 1583746 1583974 "LIE" 1584056 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570440 1577795 1577951 "LIB" 1578119 T LIB (NIL) -8 NIL NIL NIL) (-650 1566009 1566958 1567893 "LGROBP" 1569557 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564633 1565541 1565569 "LFCAT" 1565776 T LFCAT (NIL) -9 NIL 1565915 NIL) (-648 1562571 1562905 1563255 "LF" 1564354 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559431 1560103 1560791 "LEXTRIPK" 1561935 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556019 1557001 1557504 "LEXP" 1559011 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555435 1555740 1555832 "LETAST" 1555947 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553821 1554146 1554547 "LEADCDET" 1555117 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552999 1553085 1553314 "LAZM3PK" 1553742 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547524 1551076 1551614 "LAUPOL" 1552511 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547097 1547147 1547308 "LAPLACE" 1547474 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545945 1546661 1546702 "LALG" 1546764 NIL LALG (NIL T) -9 NIL 1546823 NIL) (-639 1545641 1545718 1545854 "LALG-" 1545859 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543378 1544742 1544993 "LA" 1545474 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543207 1543237 1543278 "KVTFROM" 1543340 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541964 1542574 1542759 "KTVLOGIC" 1543042 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541793 1541823 1541864 "KRCFROM" 1541926 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540685 1540884 1541183 "KOVACIC" 1541593 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540514 1540544 1540585 "KONVERT" 1540647 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540343 1540373 1540414 "KOERCE" 1540476 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539827 1539920 1540052 "KERNEL2" 1540257 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537514 1538420 1538797 "KERNEL" 1539483 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530985 1535991 1536045 "KDAGG" 1536422 NIL KDAGG (NIL T T) -9 NIL 1536628 NIL) (-628 1530496 1530638 1530843 "KDAGG-" 1530848 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523196 1530157 1530312 "KAFILE" 1530374 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522800 1523085 1523148 "JVMOP" 1523153 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521536 1522040 1522289 "JVMMDACC" 1522571 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520472 1520926 1521131 "JVMFDACC" 1521351 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519053 1519548 1519848 "JVMCSTTG" 1520192 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518189 1518593 1518754 "JVMCFACC" 1518912 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517867 1518106 1518155 "JVMBCODE" 1518160 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511886 1517378 1517606 "JORDAN" 1517688 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511199 1511535 1511656 "JOINAST" 1511785 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507234 1509376 1509430 "IXAGG" 1510359 NIL IXAGG (NIL T T) -9 NIL 1510818 NIL) (-617 1506087 1506459 1506878 "IXAGG-" 1506883 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501176 1506009 1506068 "IVECTOR" 1506073 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499901 1500179 1500445 "ITUPLE" 1500943 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498373 1498580 1498875 "ITRIGMNP" 1499723 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497100 1497322 1497605 "ITFUN3" 1498149 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496698 1496761 1496884 "ITFUN2" 1497023 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495803 1496178 1496352 "ITFORM" 1496544 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493572 1494823 1495101 "ITAYLOR" 1495558 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481976 1487709 1488872 "ISUPS" 1492442 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481068 1481220 1481456 "ISUMP" 1481823 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475918 1481013 1481054 "ISTRING" 1481059 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475334 1475639 1475731 "ISAST" 1475846 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474532 1474625 1474841 "IRURPK" 1475248 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473444 1473669 1473909 "IRSN" 1474312 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471489 1471870 1472299 "IRRF2F" 1473082 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471230 1471274 1471350 "IRREDFFX" 1471445 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469803 1470104 1470403 "IROOT" 1470963 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468942 1469296 1469447 "IRFORM" 1469672 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468024 1468155 1468369 "IR2F" 1468825 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465613 1466132 1466698 "IR2" 1467502 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462053 1463297 1463989 "IR" 1464953 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461838 1461878 1461938 "IPRNTPK" 1462013 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457812 1461727 1461796 "IPF" 1461801 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455840 1457737 1457794 "IPADIC" 1457799 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455098 1455400 1455530 "IP4ADDR" 1455730 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454436 1454727 1454859 "IOMODE" 1454986 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453407 1454033 1454160 "IOBFILE" 1454329 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452817 1453311 1453339 "IOBCON" 1453344 T IOBCON (NIL) -9 NIL 1453365 NIL) (-589 1452322 1452386 1452569 "INVLAPLA" 1452753 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441892 1444324 1446710 "INTTR" 1449986 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438185 1438969 1439834 "INTTOOLS" 1441077 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437765 1437862 1437979 "INTSLPE" 1438088 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435232 1437688 1437747 "INTRVL" 1437752 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432810 1433346 1433921 "INTRF" 1434717 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432203 1432318 1432460 "INTRET" 1432708 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430176 1430589 1431059 "INTRAT" 1431811 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427421 1428022 1428641 "INTPM" 1429661 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424138 1424765 1425503 "INTPAF" 1426807 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419239 1420279 1421330 "INTPACK" 1423107 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418485 1418643 1418851 "INTHERTR" 1419081 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417918 1418004 1418192 "INTHERAL" 1418399 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415686 1416207 1416664 "INTHEORY" 1417481 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407018 1408713 1410485 "INTG0" 1414038 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387543 1392381 1397191 "INTFTBL" 1402228 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386768 1386930 1387103 "INTFACT" 1387402 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384165 1384641 1385198 "INTEF" 1386322 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382362 1383257 1383285 "INTDOM" 1383586 T INTDOM (NIL) -9 NIL 1383793 NIL) (-570 1381701 1381905 1382147 "INTDOM-" 1382152 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377569 1379990 1380044 "INTCAT" 1380843 NIL INTCAT (NIL T) -9 NIL 1381164 NIL) (-568 1377023 1377144 1377272 "INTBIT" 1377461 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375704 1375876 1376183 "INTALG" 1376868 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375181 1375277 1375434 "INTAF" 1375608 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368148 1374991 1375131 "INTABL" 1375136 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367389 1367951 1368016 "INT8" 1368050 T INT8 (NIL) -8 NIL NIL 1368095) (-563 1366629 1367191 1367256 "INT64" 1367290 T INT64 (NIL) -8 NIL NIL 1367335) (-562 1365869 1366431 1366496 "INT32" 1366530 T INT32 (NIL) -8 NIL NIL 1366575) (-561 1365109 1365671 1365736 "INT16" 1365770 T INT16 (NIL) -8 NIL NIL 1365815) (-560 1361313 1364906 1365015 "INT" 1365020 T INT (NIL) -8 NIL NIL NIL) (-559 1355422 1358861 1358889 "INS" 1359823 T INS (NIL) -9 NIL 1360488 NIL) (-558 1352579 1353499 1354440 "INS-" 1354513 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351336 1351581 1351879 "INPSIGN" 1352332 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350430 1350571 1350768 "INPRODPF" 1351216 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349300 1349441 1349678 "INPRODFF" 1350310 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348288 1348452 1348712 "INNMFACT" 1349136 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347467 1347582 1347770 "INMODGCD" 1348187 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345951 1346220 1346544 "INFSP" 1347212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345111 1345252 1345435 "INFPROD0" 1345831 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344709 1344781 1344879 "INFORM1" 1345046 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341276 1342774 1343289 "INFORM" 1344202 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340781 1340888 1341002 "INFINITY" 1341182 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339855 1340501 1340602 "INETCLTS" 1340700 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338453 1338721 1339042 "INEP" 1339603 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337483 1338350 1338415 "INDE" 1338420 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337035 1337115 1337232 "INCRMAPS" 1337410 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335757 1336304 1336510 "INBFILE" 1336849 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330937 1331993 1332937 "INBFF" 1334845 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329791 1330114 1330142 "INBCON" 1330655 T INBCON (NIL) -9 NIL 1330921 NIL) (-540 1329001 1329266 1329542 "INBCON-" 1329547 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328420 1328725 1328816 "INAST" 1328930 T INAST (NIL) -8 NIL NIL NIL) (-538 1327787 1328099 1328205 "IMPTAST" 1328334 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323708 1327631 1327735 "IMATRIX" 1327740 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322400 1322539 1322855 "IMATQF" 1323564 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320580 1320847 1321184 "IMATLIN" 1322156 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314495 1320504 1320562 "ILIST" 1320567 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312161 1314355 1314468 "IIARRAY2" 1314473 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306982 1312072 1312136 "IFF" 1312141 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306263 1306599 1306715 "IFAST" 1306886 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300775 1305555 1305743 "IFARRAY" 1306120 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299813 1300679 1300752 "IFAMON" 1300757 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299385 1299462 1299516 "IEVALAB" 1299723 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299048 1299128 1299288 "IEVALAB-" 1299293 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298081 1298937 1299012 "IDPOAMS" 1299017 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297183 1297970 1298045 "IDPOAM" 1298050 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296564 1297098 1297160 "IDPO" 1297165 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295044 1295571 1295623 "IDPC" 1296135 NIL IDPC (NIL T T) -9 NIL 1296416 NIL) (-522 1294376 1294936 1295009 "IDPAM" 1295014 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293591 1294268 1294341 "IDPAG" 1294346 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293135 1293397 1293487 "IDENT" 1293521 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289354 1290238 1291133 "IDECOMP" 1292292 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281989 1283277 1284324 "IDEAL" 1288390 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281131 1281261 1281461 "ICDEN" 1281873 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280106 1280611 1280758 "ICARD" 1281004 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278136 1278479 1278884 "IBPTOOLS" 1279783 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273251 1277756 1277869 "IBITS" 1278055 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269926 1270550 1271245 "IBATOOL" 1272668 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267687 1268167 1268700 "IBACHIN" 1269461 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265277 1267533 1267636 "IARRAY2" 1267641 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260990 1265203 1265260 "IARRAY1" 1265265 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254007 1259402 1259883 "IAN" 1260529 T IAN (NIL) -8 NIL NIL NIL) (-508 1253512 1253575 1253748 "IALGFACT" 1253944 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253004 1253153 1253181 "HYPCAT" 1253388 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252506 1252659 1252845 "HYPCAT-" 1252850 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252053 1252301 1252384 "HOSTNAME" 1252443 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251886 1251935 1251976 "HOMOTOP" 1251981 NIL HOMOTOP (NIL T) -9 NIL 1252014 NIL) (-503 1248319 1249818 1249859 "HOAGG" 1250840 NIL HOAGG (NIL T) -9 NIL 1251569 NIL) (-502 1246835 1247312 1247838 "HOAGG-" 1247843 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239892 1246428 1246578 "HEXADEC" 1246705 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238604 1238862 1239125 "HEUGCD" 1239669 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237536 1238441 1238571 "HELLFDIV" 1238576 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235544 1237311 1237400 "HEAP" 1237479 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234741 1235096 1235230 "HEADAST" 1235430 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228079 1234656 1234718 "HDP" 1234723 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221098 1227714 1227866 "HDMP" 1227980 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220404 1220562 1220726 "HB" 1220954 T HB (NIL) -7 NIL NIL NIL) (-493 1213414 1220250 1220354 "HASHTBL" 1220359 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212830 1213135 1213227 "HASAST" 1213342 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210243 1212452 1212634 "HACKPI" 1212668 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205415 1210096 1210209 "GTSET" 1210214 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198454 1205293 1205391 "GSTBL" 1205396 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190217 1197619 1197875 "GSERIES" 1198254 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189248 1189761 1189789 "GROUP" 1189992 T GROUP (NIL) -9 NIL 1190126 NIL) (-486 1188572 1188773 1189024 "GROUP-" 1189029 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186921 1187260 1187647 "GROEBSOL" 1188249 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185749 1186109 1186160 "GRMOD" 1186689 NIL GRMOD (NIL T T) -9 NIL 1186857 NIL) (-483 1185505 1185553 1185681 "GRMOD-" 1185686 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180645 1181859 1182859 "GRIMAGE" 1184525 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179039 1179372 1179696 "GRDEF" 1180341 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178471 1178599 1178740 "GRAY" 1178918 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177548 1178050 1178101 "GRALG" 1178254 NIL GRALG (NIL T T) -9 NIL 1178347 NIL) (-478 1177185 1177282 1177445 "GRALG-" 1177450 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173666 1176768 1176947 "GPOLSET" 1177091 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173014 1173077 1173335 "GOSPER" 1173603 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168584 1169452 1169978 "GMODPOL" 1172713 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167571 1167773 1168011 "GHENSEL" 1168396 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161643 1162570 1163590 "GENUPS" 1166655 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161334 1161391 1161480 "GENUFACT" 1161586 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160734 1160823 1160988 "GENPGCD" 1161252 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160202 1160243 1160456 "GENMFACT" 1160693 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158739 1159025 1159332 "GENEEZ" 1159945 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151917 1158350 1158512 "GDMP" 1158662 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140655 1145688 1146794 "GCNAALG" 1150900 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138782 1139830 1139858 "GCDDOM" 1140113 T GCDDOM (NIL) -9 NIL 1140270 NIL) (-465 1138222 1138379 1138594 "GCDDOM-" 1138599 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126694 1129168 1131560 "GBINTERN" 1135913 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124495 1124823 1125244 "GBF" 1126369 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123252 1123441 1123708 "GBEUCLID" 1124311 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121902 1122109 1122413 "GB" 1123031 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121233 1121376 1121525 "GAUSSFAC" 1121773 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119554 1119902 1120216 "GALUTIL" 1120952 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117814 1118136 1118460 "GALPOLYU" 1119281 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115113 1115469 1115876 "GALFACTU" 1117511 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106727 1108418 1110026 "GALFACT" 1113545 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104013 1104773 1104801 "FVFUN" 1105957 T FVFUN (NIL) -9 NIL 1106677 NIL) (-454 1103243 1103461 1103489 "FVC" 1103780 T FVC (NIL) -9 NIL 1103963 NIL) (-453 1102844 1103068 1103136 "FUNDESC" 1103195 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102417 1102641 1102722 "FUNCTION" 1102796 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101094 1101718 1101921 "FTEM" 1102234 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098724 1099416 1099882 "FT" 1100648 T FT (NIL) -8 NIL NIL NIL) (-449 1096993 1097304 1097701 "FSUPFACT" 1098415 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095312 1095679 1096011 "FST" 1096681 T FST (NIL) -8 NIL NIL NIL) (-447 1094493 1094617 1094805 "FSRED" 1095194 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093182 1093448 1093795 "FSPRMELT" 1094208 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090392 1090926 1091412 "FSPECF" 1092745 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089914 1089974 1090144 "FSINT" 1090333 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088050 1088907 1089210 "FSERIES" 1089693 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087074 1087208 1087432 "FSCINT" 1087930 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086098 1086259 1086486 "FSAGG2" 1086927 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081962 1085042 1085083 "FSAGG" 1085453 NIL FSAGG (NIL T) -9 NIL 1085712 NIL) (-439 1079562 1080325 1081121 "FSAGG-" 1081216 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077222 1077520 1078068 "FS2UPS" 1079280 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076088 1076271 1076573 "FS2EXPXP" 1077047 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075716 1075765 1075894 "FS2" 1076039 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055954 1065490 1065531 "FS" 1069415 NIL FS (NIL T) -9 NIL 1071704 NIL) (-434 1044015 1047590 1051647 "FS-" 1051947 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043429 1043556 1043708 "FRUTIL" 1043895 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037940 1041118 1041158 "FRNAALG" 1042478 NIL FRNAALG (NIL T) -9 NIL 1043076 NIL) (-431 1033421 1034689 1035964 "FRNAALG-" 1036714 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033053 1033102 1033229 "FRNAAF2" 1033372 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031340 1031902 1032198 "FRMOD" 1032865 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030525 1030618 1030909 "FRIDEAL2" 1031247 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028130 1028900 1029218 "FRIDEAL" 1030316 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027221 1027677 1027718 "FRETRCT" 1027723 NIL FRETRCT (NIL T) -9 NIL 1027899 NIL) (-425 1026279 1026564 1026915 "FRETRCT-" 1026920 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023100 1024563 1024622 "FRAMALG" 1025504 NIL FRAMALG (NIL T T) -9 NIL 1025796 NIL) (-423 1021138 1021689 1022319 "FRAMALG-" 1022542 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020768 1020831 1020938 "FRAC2" 1021075 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013761 1020241 1020518 "FRAC" 1020523 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013391 1013454 1013561 "FR2" 1013698 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004308 1008886 1010244 "FR" 1012065 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998227 1001687 1001715 "FPS" 1002834 T FPS (NIL) -9 NIL 1003391 NIL) (-417 997652 997785 997949 "FPS-" 998095 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994618 996609 996637 "FPC" 996862 T FPC (NIL) -9 NIL 997004 NIL) (-415 994399 994451 994548 "FPC-" 994553 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993157 993887 993928 "FPATMAB" 993933 NIL FPATMAB (NIL T) -9 NIL 994085 NIL) (-413 991300 991899 992246 "FPARFRAC" 992873 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986592 987192 987874 "FORTRAN" 990732 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984166 984830 984858 "FORTFN" 985918 T FORTFN (NIL) -9 NIL 986542 NIL) (-410 983918 983980 984008 "FORTCAT" 984067 T FORTCAT (NIL) -9 NIL 984129 NIL) (-409 981604 982134 982673 "FORT" 983399 T FORT (NIL) -7 NIL NIL NIL) (-408 981386 981422 981491 "FORMULA1" 981568 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979390 980002 980392 "FORMULA" 981016 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978907 978965 979138 "FORDER" 979332 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977967 978167 978360 "FOP" 978734 T FOP (NIL) -7 NIL NIL NIL) (-404 976380 977247 977421 "FNLA" 977849 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974999 975510 975538 "FNCAT" 975998 T FNCAT (NIL) -9 NIL 976258 NIL) (-402 974442 974958 974986 "FNAME" 974991 T FNAME (NIL) -8 NIL NIL NIL) (-401 972768 973941 973969 "FMTC" 973974 T FMTC (NIL) -9 NIL 974010 NIL) (-400 971317 972704 972750 "FMONOID" 972755 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967906 969272 969313 "FMONCAT" 970530 NIL FMONCAT (NIL T) -9 NIL 971135 NIL) (-398 965228 965976 966004 "FMFUN" 967148 T FMFUN (NIL) -9 NIL 967856 NIL) (-397 962101 963153 963207 "FMCAT" 964402 NIL FMCAT (NIL T T) -9 NIL 964897 NIL) (-396 961334 961551 961579 "FMC" 961869 T FMC (NIL) -9 NIL 962051 NIL) (-395 960002 961100 961200 "FM1" 961279 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959020 959744 959893 "FM" 959898 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956758 957210 957704 "FLOATRP" 958571 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954160 954696 955274 "FLOATCP" 956225 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946823 951889 952510 "FLOAT" 953559 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945341 946415 946456 "FLINEXP" 946461 NIL FLINEXP (NIL T) -9 NIL 946554 NIL) (-389 944471 944730 945058 "FLINEXP-" 945063 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943529 943691 943915 "FLASORT" 944323 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940447 941499 941551 "FLALG" 942778 NIL FLALG (NIL T T) -9 NIL 943245 NIL) (-386 939471 939632 939859 "FLAGG2" 940300 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932726 936880 936921 "FLAGG" 938183 NIL FLAGG (NIL T) -9 NIL 938835 NIL) (-384 931380 931791 932281 "FLAGG-" 932286 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928018 929225 929284 "FINRALG" 930412 NIL FINRALG (NIL T T) -9 NIL 930920 NIL) (-382 927142 927407 927746 "FINRALG-" 927751 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926448 926747 926775 "FINITE" 926971 T FINITE (NIL) -9 NIL 927078 NIL) (-380 918399 920978 921018 "FINAALG" 924685 NIL FINAALG (NIL T) -9 NIL 926138 NIL) (-379 913515 914781 915925 "FINAALG-" 917304 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912075 912497 912551 "FILECAT" 913235 NIL FILECAT (NIL T T) -9 NIL 913451 NIL) (-377 911353 911830 911933 "FILE" 912005 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908756 910583 910611 "FIELD" 910651 T FIELD (NIL) -9 NIL 910731 NIL) (-375 907298 907761 908272 "FIELD-" 908277 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904981 905933 906280 "FGROUP" 906984 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904053 904235 904455 "FGLMICPK" 904813 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899308 903978 904035 "FFX" 904040 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898903 898970 899105 "FFSLPE" 899241 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898401 898443 898652 "FFPOLY2" 898861 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894277 895173 895969 "FFPOLY" 897637 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889546 894196 894259 "FFP" 894264 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884077 888889 889079 "FFNBX" 889400 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878410 883212 883470 "FFNBP" 883931 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872448 877694 877905 "FFNB" 878243 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871268 871478 871793 "FFINTBAS" 872245 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866861 869515 869543 "FFIELDC" 870163 T FFIELDC (NIL) -9 NIL 870539 NIL) (-362 865481 865922 866405 "FFIELDC-" 866410 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865038 865096 865220 "FFHOM" 865423 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862697 863220 863737 "FFF" 864553 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857732 862439 862540 "FFCGX" 862640 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852771 857464 857571 "FFCGP" 857675 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847371 852498 852606 "FFCG" 852707 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846776 846825 847060 "FFCAT2" 847322 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825458 836508 836594 "FFCAT" 841759 NIL FFCAT (NIL T T T) -9 NIL 843210 NIL) (-354 820469 821703 823017 "FFCAT-" 824247 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815290 820380 820444 "FF" 820449 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803943 808262 809482 "FEXPR" 814142 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802871 803340 803381 "FEVALAB" 803465 NIL FEVALAB (NIL T) -9 NIL 803726 NIL) (-350 801988 802240 802578 "FEVALAB-" 802583 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798850 799735 799850 "FDIVCAT" 801418 NIL FDIVCAT (NIL T T T T) -9 NIL 801855 NIL) (-348 798606 798639 798809 "FDIVCAT-" 798814 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797820 797913 798190 "FDIV2" 798513 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796230 797203 797406 "FDIV" 797719 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795138 795525 795727 "FCTRDATA" 796048 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793794 794083 794372 "FCPAK1" 794869 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792797 793294 793435 "FCOMP" 793685 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776111 779947 783485 "FC" 789279 T FC (NIL) -8 NIL NIL NIL) (-341 767820 772432 772472 "FAXF" 774274 NIL FAXF (NIL T) -9 NIL 774966 NIL) (-340 764961 765768 766586 "FAXF-" 767051 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759530 764337 764513 "FARRAY" 764818 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754095 756477 756530 "FAMR" 757553 NIL FAMR (NIL T T) -9 NIL 758013 NIL) (-337 752919 753287 753722 "FAMR-" 753727 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751946 752841 752894 "FAMONOID" 752899 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749576 750428 750481 "FAMONC" 751422 NIL FAMONC (NIL T T) -9 NIL 751808 NIL) (-334 748050 749330 749467 "FAGROUP" 749472 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745803 746164 746567 "FACUTIL" 747731 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744890 745087 745309 "FACTFUNC" 745613 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736631 744193 744392 "EXPUPXS" 744746 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734084 734654 735240 "EXPRTUBE" 736065 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730295 730947 731677 "EXPRODE" 733423 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724729 725436 726242 "EXPR2UPS" 729593 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724355 724418 724527 "EXPR2" 724666 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708663 723004 723433 "EXPR" 723959 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699001 707814 708105 "EXPEXPAN" 708499 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698421 698725 698816 "EXITAST" 698930 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698185 698378 698407 "EXIT" 698412 T EXIT (NIL) -8 NIL NIL NIL) (-322 697806 697874 697987 "EVALCYC" 698117 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697323 697465 697506 "EVALAB" 697676 NIL EVALAB (NIL T) -9 NIL 697780 NIL) (-320 696780 696926 697147 "EVALAB-" 697152 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693895 695436 695464 "EUCDOM" 696019 T EUCDOM (NIL) -9 NIL 696369 NIL) (-318 692255 692756 693339 "EUCDOM-" 693344 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691881 691944 692053 "ESTOOLS2" 692192 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691626 691674 691754 "ESTOOLS1" 691833 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678943 681924 684674 "ESTOOLS" 688896 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678682 678720 678802 "ESCONT1" 678905 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674990 675817 676597 "ESCONT" 677922 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674659 674715 674815 "ES2" 674934 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674283 674347 674456 "ES1" 674595 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667984 669914 669942 "ES" 672710 T ES (NIL) -9 NIL 674120 NIL) (-309 662661 664218 666035 "ES-" 666199 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661853 662006 662182 "ERROR" 662505 T ERROR (NIL) -7 NIL NIL NIL) (-307 654869 661712 661803 "EQTBL" 661808 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654495 654558 654667 "EQ2" 654806 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646754 649809 651258 "EQ" 653079 NIL -1499 (NIL T) -8 NIL NIL NIL) (-304 641996 643092 644185 "EP" 645693 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640536 640887 641193 "ENV" 641710 T ENV (NIL) -8 NIL NIL NIL) (-302 639496 640170 640198 "ENTIRER" 640203 T ENTIRER (NIL) -9 NIL 640249 NIL) (-301 635915 637678 638039 "EMR" 639304 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635019 635230 635284 "ELTAGG" 635664 NIL ELTAGG (NIL T T) -9 NIL 635875 NIL) (-299 634726 634800 634941 "ELTAGG-" 634946 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634484 634519 634573 "ELTAB" 634657 NIL ELTAB (NIL T T) -9 NIL 634709 NIL) (-297 633586 633756 633955 "ELFUTS" 634335 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633310 633384 633412 "ELEMFUN" 633517 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633174 633201 633269 "ELEMFUN-" 633274 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627585 631216 631257 "ELAGG" 632197 NIL ELAGG (NIL T) -9 NIL 632660 NIL) (-293 625762 626304 626967 "ELAGG-" 626972 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625044 625211 625367 "ELABOR" 625626 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623650 623984 624278 "ELABEXPR" 624770 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616162 618287 619116 "EFUPXS" 622925 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609288 611411 612222 "EFULS" 615437 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606725 607131 607603 "EFSTRUC" 608920 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596163 598082 599630 "EF" 605240 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595141 595648 595797 "EAB" 596034 T EAB (NIL) -8 NIL NIL NIL) (-285 594263 595100 595128 "E04UCFA" 595133 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593385 594222 594250 "E04NAFA" 594255 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592507 593344 593372 "E04MBFA" 593377 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591629 592466 592494 "E04JAFA" 592499 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590753 591588 591616 "E04GCFA" 591621 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589877 590712 590740 "E04FDFA" 590745 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588999 589836 589864 "E04DGFA" 589869 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583076 584524 585888 "E04AGNT" 587655 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581696 582377 582417 "DVARCAT" 582758 NIL DVARCAT (NIL T) -9 NIL 582921 NIL) (-276 580846 581112 581426 "DVARCAT-" 581431 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572814 580645 580774 "DSMP" 580779 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571165 571956 571997 "DSEXT" 572360 NIL DSEXT (NIL T) -9 NIL 572654 NIL) (-273 569354 569878 570544 "DSEXT-" 570549 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569013 569078 569176 "DROPT1" 569289 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564032 565254 566391 "DROPT0" 567896 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558615 559977 561045 "DROPT" 562984 T DROPT (NIL) -8 NIL NIL NIL) (-269 556924 557285 557671 "DRAWPT" 558249 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556551 556610 556728 "DRAWHACK" 556865 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555252 555551 555842 "DRAWCX" 556280 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554761 554836 554987 "DRAWCURV" 555178 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545079 547191 549306 "DRAWCFUN" 552666 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539570 540589 541668 "DRAW" 544053 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536041 538235 538276 "DQAGG" 538905 NIL DQAGG (NIL T) -9 NIL 539179 NIL) (-262 522624 530252 530335 "DPOLCAT" 532187 NIL DPOLCAT (NIL T T T T) -9 NIL 532732 NIL) (-261 517143 518809 520767 "DPOLCAT-" 520772 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509951 517004 517102 "DPMO" 517107 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502656 509731 509898 "DPMM" 509903 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502178 502440 502529 "DOMTMPLT" 502587 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501527 501980 502060 "DOMCTOR" 502118 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500679 501007 501158 "DOMAIN" 501396 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493698 500314 500466 "DMP" 500580 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491475 492765 492806 "DMEXT" 492811 NIL DMEXT (NIL T) -9 NIL 492987 NIL) (-253 491069 491131 491275 "DLP" 491413 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484192 490396 490586 "DLIST" 490911 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480730 483017 483058 "DLAGG" 483608 NIL DLAGG (NIL T) -9 NIL 483838 NIL) (-250 479242 480056 480084 "DIVRING" 480176 T DIVRING (NIL) -9 NIL 480259 NIL) (-249 478425 478669 478969 "DIVRING-" 478974 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476467 476884 477290 "DISPLAY" 478039 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475297 475518 475783 "DIRPROD2" 476260 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468655 475211 475274 "DIRPROD" 475279 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456818 463366 463419 "DIRPCAT" 463677 NIL DIRPCAT (NIL NIL T) -9 NIL 464552 NIL) (-244 454018 454786 455667 "DIRPCAT-" 456004 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453299 453465 453651 "DIOSP" 453852 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449713 452183 452224 "DIOPS" 452658 NIL DIOPS (NIL T) -9 NIL 452887 NIL) (-241 449232 449376 449567 "DIOPS-" 449572 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448139 448911 448939 "DIFRING" 448944 T DIFRING (NIL) -9 NIL 448966 NIL) (-239 447787 447885 447913 "DIFFSPC" 448032 T DIFFSPC (NIL) -9 NIL 448107 NIL) (-238 447408 447510 447662 "DIFFSPC-" 447667 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446344 446942 446983 "DIFFMOD" 446988 NIL DIFFMOD (NIL T) -9 NIL 447086 NIL) (-236 446040 446097 446138 "DIFFDOM" 446259 NIL DIFFDOM (NIL T) -9 NIL 446327 NIL) (-235 445887 445917 446001 "DIFFDOM-" 446006 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443627 445091 445132 "DIFEXT" 445137 NIL DIFEXT (NIL T) -9 NIL 445290 NIL) (-233 440661 443131 443172 "DIAGG" 443177 NIL DIAGG (NIL T) -9 NIL 443197 NIL) (-232 440009 440202 440454 "DIAGG-" 440459 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434859 438968 439245 "DHMATRIX" 439778 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430327 431380 432390 "DFSFUN" 433869 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424568 429258 429570 "DFLOAT" 430035 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422807 423112 423501 "DFINTTLS" 424276 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419626 420828 421228 "DERHAM" 422473 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417162 419401 419490 "DEQUEUE" 419570 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416404 416549 416732 "DEGRED" 417024 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412810 413579 414425 "DEFINTRF" 415632 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410347 410834 411426 "DEFINTEF" 412329 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409631 409967 410082 "DEFAST" 410252 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402688 409224 409374 "DECIMAL" 409501 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400146 400658 401164 "DDFACT" 402232 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399736 399785 399936 "DBLRESP" 400097 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398937 399506 399597 "DBASIS" 399685 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396721 397167 397528 "DBASE" 398703 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395909 396201 396347 "DATAARY" 396620 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394967 395868 395896 "D03FAFA" 395901 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394026 394926 394954 "D03EEFA" 394959 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391952 392442 392931 "D03AGNT" 393557 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391193 391911 391939 "D02EJFA" 391944 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390434 391152 391180 "D02CJFA" 391185 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389675 390393 390421 "D02BHFA" 390426 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388916 389634 389662 "D02BBFA" 389667 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382047 383702 385308 "D02AGNT" 387330 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379797 380338 380884 "D01WGTS" 381521 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378804 379756 379784 "D01TRNS" 379789 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377812 378763 378791 "D01GBFA" 378796 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376820 377771 377799 "D01FCFA" 377804 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375828 376779 376807 "D01ASFA" 376812 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374836 375787 375815 "D01AQFA" 375820 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373844 374795 374823 "D01APFA" 374828 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372852 373803 373831 "D01ANFA" 373836 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371860 372811 372839 "D01AMFA" 372844 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370868 371819 371847 "D01ALFA" 371852 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369876 370827 370855 "D01AKFA" 370860 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368884 369835 369863 "D01AJFA" 369868 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362107 363732 365293 "D01AGNT" 367343 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361426 361572 361724 "CYCLOTOM" 361975 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358081 358874 359601 "CYCLES" 360719 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357381 357527 357698 "CVMP" 357942 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355168 355480 355849 "CTRIGMNP" 357109 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354641 354899 355000 "CTORKIND" 355087 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353846 354234 354262 "CTORCAT" 354444 T CTORCAT (NIL) -9 NIL 354557 NIL) (-188 353420 353555 353714 "CTORCAT-" 353719 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352834 353094 353202 "CTORCALL" 353344 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352192 352628 352701 "CTOR" 352781 T CTOR (NIL) -8 NIL NIL NIL) (-185 351548 351665 351818 "CSTTOOLS" 352089 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347245 348004 348762 "CRFP" 350860 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346660 346966 347058 "CRCEAST" 347173 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345683 345892 346120 "CRAPACK" 346464 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345063 345168 345372 "CPMATCH" 345559 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344782 344816 344922 "CPIMA" 345029 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341040 341802 342521 "COORDSYS" 344117 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340428 340573 340715 "CONTOUR" 340918 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335899 338431 338923 "CONTFRAC" 339968 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335773 335800 335828 "CONDUIT" 335865 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334727 335401 335429 "COMRING" 335434 T COMRING (NIL) -9 NIL 335486 NIL) (-174 333709 334085 334269 "COMPPROP" 334563 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333364 333405 333533 "COMPLPAT" 333668 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332994 333057 333164 "COMPLEX2" 333301 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321398 332803 332912 "COMPLEX" 332917 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320719 320858 321018 "COMPILER" 321258 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320431 320472 320570 "COMPFACT" 320678 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301825 314135 314175 "COMPCAT" 315179 NIL COMPCAT (NIL T) -9 NIL 316527 NIL) (-167 290713 294264 297891 "COMPCAT-" 298247 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290436 290470 290573 "COMMUPC" 290679 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290224 290264 290323 "COMMONOP" 290397 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289746 290028 290103 "COMMAAST" 290169 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289253 289497 289584 "COMM" 289679 T COMM (NIL) -8 NIL NIL NIL) (-162 288448 288696 288724 "COMBOPC" 289062 T COMBOPC (NIL) -9 NIL 289237 NIL) (-161 287302 287554 287796 "COMBINAT" 288238 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283645 284333 284960 "COMBF" 286724 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282307 282761 282996 "COLOR" 283430 T COLOR (NIL) -8 NIL NIL NIL) (-158 281723 282028 282120 "COLONAST" 282235 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281357 281410 281535 "CMPLXRT" 281670 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280745 281057 281156 "CLLCTAST" 281278 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276204 277275 278355 "CLIP" 279685 T CLIP (NIL) -7 NIL NIL NIL) (-154 274377 275305 275545 "CLIF" 276031 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270359 272495 272536 "CLAGG" 273465 NIL CLAGG (NIL T) -9 NIL 274001 NIL) (-152 268703 269238 269821 "CLAGG-" 269826 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268241 268332 268472 "CINTSLPE" 268612 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265706 266213 266761 "CHVAR" 267769 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264746 265420 265448 "CHARZ" 265453 T CHARZ (NIL) -9 NIL 265468 NIL) (-148 264494 264540 264618 "CHARPOL" 264700 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263412 264118 264146 "CHARNZ" 264207 T CHARNZ (NIL) -9 NIL 264256 NIL) (-146 260356 261466 261995 "CHAR" 262903 T CHAR (NIL) -8 NIL NIL NIL) (-145 260064 260143 260171 "CFCAT" 260282 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259287 259416 259599 "CDEN" 259948 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254884 258440 258720 "CCLASS" 259027 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254105 254292 254469 "CATEGORY" 254727 T -10 (NIL) -8 NIL NIL NIL) (-141 253600 254024 254072 "CATCTOR" 254077 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252991 253303 253401 "CATAST" 253522 T CATAST (NIL) -8 NIL NIL NIL) (-139 252407 252712 252804 "CASEAST" 252919 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251503 251663 251884 "CARTEN2" 252254 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247660 248404 "CARTEN" 250815 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3472917 3472922 3472927 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472902 3472907 3472912 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472887 3472892 3472897 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472872 3472877 3472882 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1329 3471865 3472747 3472824 "ZMOD" 3472829 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1328 3470901 3471083 3471306 "ZLINDEP" 3471697 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1327 3460063 3461969 3463941 "ZDSOLVE" 3469031 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1326 3459297 3459450 3459639 "YSTREAM" 3459909 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1325 3458657 3458966 3459081 "YDIAGRAM" 3459204 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1324 3456105 3457958 3458162 "XRPOLY" 3458500 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1323 3452372 3453976 3454551 "XPR" 3455577 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1322 3449703 3451379 3451434 "XPOLYC" 3451722 NIL XPOLYC (NIL T T) -9 NIL 3451835 NIL) (-1321 3447098 3449034 3449238 "XPOLY" 3449534 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1320 3443044 3445615 3446003 "XPBWPOLY" 3446756 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1319 3437936 3439515 3439570 "XFALG" 3441742 NIL XFALG (NIL T T) -9 NIL 3442531 NIL) (-1318 3433212 3435912 3435954 "XF" 3436575 NIL XF (NIL T) -9 NIL 3436975 NIL) (-1317 3432809 3432921 3433090 "XF-" 3433095 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1316 3431924 3432046 3432251 "XEXPPKG" 3432701 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1315 3429665 3431774 3431870 "XDPOLY" 3431875 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1314 3428320 3429058 3429101 "XALG" 3429106 NIL XALG (NIL T) -9 NIL 3429217 NIL) (-1313 3421230 3426297 3426791 "WUTSET" 3427912 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1312 3419332 3420282 3420605 "WP" 3421041 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1311 3418880 3419154 3419224 "WHILEAST" 3419284 T WHILEAST (NIL) -8 NIL NIL NIL) (-1310 3418292 3418597 3418691 "WHEREAST" 3418808 T WHEREAST (NIL) -8 NIL NIL NIL) (-1309 3417166 3417376 3417671 "WFFINTBS" 3418089 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1308 3415034 3415497 3415959 "WEIER" 3416738 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1307 3413958 3414516 3414558 "VSPACE" 3414694 NIL VSPACE (NIL T) -9 NIL 3414768 NIL) (-1306 3413790 3413823 3413914 "VSPACE-" 3413919 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1305 3413587 3413641 3413709 "VOID" 3413744 T VOID (NIL) -8 NIL NIL NIL) (-1304 3409855 3410650 3411387 "VIEWDEF" 3412872 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1303 3398799 3401403 3403576 "VIEW3D" 3407704 T VIEW3D (NIL) -8 NIL NIL NIL) (-1302 3390816 3392710 3394289 "VIEW2D" 3397242 T VIEW2D (NIL) -8 NIL NIL NIL) (-1301 3388916 3389311 3389717 "VIEW" 3390432 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3387469 3387752 3388070 "VECTOR2" 3388646 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1299 3382375 3387239 3387331 "VECTOR" 3387412 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1298 3375320 3380079 3380122 "VECTCAT" 3381117 NIL VECTCAT (NIL T) -9 NIL 3381704 NIL) (-1297 3374262 3374588 3374978 "VECTCAT-" 3374983 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1296 3373668 3373913 3374033 "VARIABLE" 3374177 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1295 3373601 3373606 3373636 "UTYPE" 3373641 T UTYPE (NIL) -9 NIL NIL NIL) (-1294 3372409 3372585 3372847 "UTSODETL" 3373427 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1293 3369801 3370309 3370833 "UTSODE" 3371950 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1292 3359811 3365734 3365777 "UTSCAT" 3366889 NIL UTSCAT (NIL T) -9 NIL 3367647 NIL) (-1291 3356937 3357881 3358870 "UTSCAT-" 3358875 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1290 3356558 3356607 3356740 "UTS2" 3356888 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1289 3347875 3354319 3354799 "UTS" 3356136 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3341742 3344685 3344728 "URAGG" 3346798 NIL URAGG (NIL T) -9 NIL 3347521 NIL) (-1287 3338465 3339544 3340667 "URAGG-" 3340672 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1286 3333841 3337100 3337565 "UPXSSING" 3338129 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1285 3326270 3333745 3333817 "UPXSCONS" 3333822 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1284 3315028 3322472 3322534 "UPXSCCA" 3323108 NIL UPXSCCA (NIL T T) -9 NIL 3323341 NIL) (-1283 3314648 3314751 3314925 "UPXSCCA-" 3314930 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1282 3303306 3310475 3310518 "UPXSCAT" 3311166 NIL UPXSCAT (NIL T) -9 NIL 3311775 NIL) (-1281 3302730 3302815 3302994 "UPXS2" 3303221 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1280 3294222 3302112 3302376 "UPXS" 3302524 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1279 3292858 3293129 3293480 "UPSQFREE" 3293965 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1278 3285689 3289124 3289179 "UPSCAT" 3290259 NIL UPSCAT (NIL T T) -9 NIL 3291025 NIL) (-1277 3284845 3285100 3285427 "UPSCAT-" 3285432 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1276 3284466 3284515 3284648 "UPOLYC2" 3284796 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1275 3268614 3277593 3277636 "UPOLYC" 3279737 NIL UPOLYC (NIL T) -9 NIL 3280958 NIL) (-1274 3259483 3262382 3265522 "UPOLYC-" 3265527 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1273 3258804 3258929 3259093 "UPMP" 3259372 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1272 3258351 3258438 3258577 "UPDIVP" 3258717 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1271 3256889 3257168 3257484 "UPDECOMP" 3258100 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1270 3256102 3256232 3256418 "UPCDEN" 3256773 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1269 3255615 3255690 3255839 "UP2" 3256027 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1268 3246211 3255298 3255427 "UP" 3255534 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1267 3245416 3245553 3245758 "UNISEG2" 3246054 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1266 3243769 3244620 3244897 "UNISEG" 3245174 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1265 3242811 3243009 3243235 "UNIFACT" 3243585 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1264 3229542 3242715 3242787 "ULSCONS" 3242792 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1263 3209359 3222622 3222684 "ULSCCAT" 3223322 NIL ULSCCAT (NIL T T) -9 NIL 3223611 NIL) (-1262 3208355 3208654 3209042 "ULSCCAT-" 3209047 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3196810 3203901 3203944 "ULSCAT" 3204807 NIL ULSCAT (NIL T) -9 NIL 3205538 NIL) (-1260 3196234 3196319 3196498 "ULS2" 3196725 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1259 3178065 3195546 3195788 "ULS" 3196050 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1258 3176984 3177684 3177798 "UINT8" 3177909 T UINT8 (NIL) -8 NIL NIL 3178001) (-1257 3175902 3176602 3176716 "UINT64" 3176827 T UINT64 (NIL) -8 NIL NIL 3176919) (-1256 3174820 3175520 3175634 "UINT32" 3175745 T UINT32 (NIL) -8 NIL NIL 3175837) (-1255 3173738 3174438 3174552 "UINT16" 3174663 T UINT16 (NIL) -8 NIL NIL 3174755) (-1254 3171817 3172984 3173014 "UFD" 3173226 T UFD (NIL) -9 NIL 3173340 NIL) (-1253 3171599 3171657 3171752 "UFD-" 3171757 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1252 3170657 3170864 3171080 "UDVO" 3171405 T UDVO (NIL) -7 NIL NIL NIL) (-1251 3168423 3168882 3169353 "UDPO" 3170221 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1250 3168135 3168378 3168409 "TYPEAST" 3168414 T TYPEAST (NIL) -8 NIL NIL NIL) (-1249 3168068 3168073 3168103 "TYPE" 3168108 T TYPE (NIL) -9 NIL NIL NIL) (-1248 3167021 3167241 3167481 "TWOFACT" 3167862 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1247 3165996 3166430 3166665 "TUPLE" 3166821 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1246 3163633 3164206 3164745 "TUBETOOL" 3165479 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1245 3162439 3162680 3162922 "TUBE" 3163426 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1244 3150574 3155196 3155293 "TSETCAT" 3160562 NIL TSETCAT (NIL T T T T) -9 NIL 3162094 NIL) (-1243 3145042 3146906 3148797 "TSETCAT-" 3148802 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1242 3139228 3144014 3144297 "TS" 3144794 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3133701 3134714 3135643 "TRMANIP" 3138364 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1240 3133130 3133205 3133368 "TRIMAT" 3133633 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1239 3130942 3131233 3131590 "TRIGMNIP" 3132879 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1238 3130426 3130575 3130605 "TRIGCAT" 3130818 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1237 3130071 3130174 3130315 "TRIGCAT-" 3130320 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1236 3126685 3128929 3129210 "TREE" 3129825 NIL TREE (NIL T) -8 NIL NIL NIL) (-1235 3125791 3126487 3126517 "TRANFUN" 3126552 T TRANFUN (NIL) -9 NIL 3126618 NIL) (-1234 3125010 3125261 3125541 "TRANFUN-" 3125546 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1233 3124808 3124846 3124907 "TOPSP" 3124971 T TOPSP (NIL) -7 NIL NIL NIL) (-1232 3124138 3124271 3124425 "TOOLSIGN" 3124689 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1231 3122652 3123315 3123554 "TEXTFILE" 3123921 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1230 3122427 3122464 3122536 "TEX1" 3122615 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1229 3120231 3120880 3121309 "TEX" 3122020 T TEX (NIL) -8 NIL NIL NIL) (-1228 3119867 3119942 3120032 "TEMUTL" 3120163 T TEMUTL (NIL) -7 NIL NIL NIL) (-1227 3117961 3118301 3118626 "TBCMPPK" 3119590 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1226 3109281 3116047 3116103 "TBAGG" 3116503 NIL TBAGG (NIL T T) -9 NIL 3116714 NIL) (-1225 3104165 3105839 3107593 "TBAGG-" 3107598 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1224 3103531 3103656 3103801 "TANEXP" 3104054 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1223 3102982 3103306 3103396 "TALGOP" 3103476 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1222 3102376 3102493 3102631 "TABLEAU" 3102879 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1221 3095390 3102233 3102326 "TABLE" 3102331 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1220 3089920 3091218 3092466 "TABLBUMP" 3094176 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1219 3089130 3089289 3089470 "SYSTEM" 3089761 T SYSTEM (NIL) -8 NIL NIL NIL) (-1218 3085535 3086288 3087071 "SYSSOLP" 3088381 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1217 3085297 3085490 3085521 "SYSPTR" 3085526 T SYSPTR (NIL) -8 NIL NIL NIL) (-1216 3084136 3084828 3084954 "SYSNNI" 3085140 NIL SYSNNI (NIL NIL) -8 NIL NIL 3085232) (-1215 3083343 3083898 3083977 "SYSINT" 3084037 NIL SYSINT (NIL NIL) -8 NIL NIL 3084082) (-1214 3079441 3080621 3081331 "SYNTAX" 3082655 T SYNTAX (NIL) -8 NIL NIL NIL) (-1213 3076521 3077201 3077833 "SYMTAB" 3078831 T SYMTAB (NIL) -8 NIL NIL NIL) (-1212 3071620 3072672 3073655 "SYMS" 3075560 T SYMS (NIL) -8 NIL NIL NIL) (-1211 3068526 3071071 3071304 "SYMPOLY" 3071422 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1210 3068031 3068118 3068241 "SYMFUNC" 3068438 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1209 3063829 3065343 3066156 "SYMBOL" 3067240 T SYMBOL (NIL) -8 NIL NIL NIL) (-1208 3057302 3059057 3060777 "SWITCH" 3062131 T SWITCH (NIL) -8 NIL NIL NIL) (-1207 3050063 3056258 3056552 "SUTS" 3057066 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1206 3041555 3049445 3049709 "SUPXS" 3049857 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040702 3040841 3041058 "SUPFRACF" 3041423 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1204 3040317 3040382 3040495 "SUP2" 3040637 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1203 3030861 3039935 3040061 "SUP" 3040226 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029285 3029583 3029939 "SUMRF" 3030560 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1201 3028608 3028686 3028878 "SUMFS" 3029206 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1200 3010474 3027920 3028162 "SULS" 3028424 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1199 3010022 3010296 3010366 "SUCHTAST" 3010426 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1198 3009263 3009547 3009687 "SUCH" 3009930 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1197 3002902 3004169 3005128 "SUBSPACE" 3008351 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1196 3002322 3002422 3002586 "SUBRESP" 3002790 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1195 2996333 2997615 2998762 "STTFNC" 3001222 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1194 2989527 2990998 2992309 "STTF" 2995069 NIL STTF (NIL T) -7 NIL NIL NIL) (-1193 2980643 2982709 2984503 "STTAYLOR" 2987768 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1192 2973397 2980507 2980590 "STRTBL" 2980595 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1191 2967794 2973106 2973205 "STRING" 2973320 T STRING (NIL) -8 NIL NIL NIL) (-1190 2967298 2967381 2967525 "STREAM3" 2967711 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1189 2966262 2966463 2966698 "STREAM2" 2967111 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1188 2965944 2966002 2966095 "STREAM1" 2966204 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1187 2958058 2963563 2964174 "STREAM" 2965368 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957050 2957255 2957486 "STINPROD" 2957874 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1185 2956165 2956539 2956687 "STEPAST" 2956924 T STEPAST (NIL) -8 NIL NIL NIL) (-1184 2955661 2955906 2955936 "STEP" 2956030 T STEP (NIL) -9 NIL 2956101 NIL) (-1183 2948717 2955560 2955637 "STBL" 2955642 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1182 2943267 2947880 2947923 "STAGG" 2948076 NIL STAGG (NIL T) -9 NIL 2948165 NIL) (-1181 2940819 2941571 2942443 "STAGG-" 2942448 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1180 2938791 2940589 2940681 "STACK" 2940762 NIL STACK (NIL T) -8 NIL NIL NIL) (-1179 2938108 2938621 2938651 "SRING" 2938656 T SRING (NIL) -9 NIL 2938676 NIL) (-1178 2930116 2936249 2936705 "SREGSET" 2937738 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1177 2922463 2923910 2925423 "SRDCMPK" 2928722 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1176 2914763 2919822 2919852 "SRAGG" 2921155 T SRAGG (NIL) -9 NIL 2921763 NIL) (-1175 2913714 2914035 2914414 "SRAGG-" 2914419 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1174 2907298 2912661 2913082 "SQMATRIX" 2913340 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1173 2900710 2904016 2904743 "SPLTREE" 2906643 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1172 2896535 2897366 2898012 "SPLNODE" 2900136 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1171 2895510 2895815 2895845 "SPFCAT" 2896289 T SPFCAT (NIL) -9 NIL NIL NIL) (-1170 2894205 2894457 2894721 "SPECOUT" 2895268 T SPECOUT (NIL) -7 NIL NIL NIL) (-1169 2884851 2887169 2887199 "SPADXPT" 2891877 T SPADXPT (NIL) -9 NIL 2894043 NIL) (-1168 2884606 2884652 2884721 "SPADPRSR" 2884804 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1167 2882209 2884561 2884592 "SPADAST" 2884597 T SPADAST (NIL) -8 NIL NIL NIL) (-1166 2873810 2875913 2875956 "SPACEC" 2880329 NIL SPACEC (NIL T) -9 NIL 2882145 NIL) (-1165 2871610 2873742 2873791 "SPACE3" 2873796 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1164 2870342 2870533 2870824 "SORTPAK" 2871415 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1163 2868404 2868737 2869149 "SOLVETRA" 2870006 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1162 2867442 2867676 2867937 "SOLVESER" 2868177 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1161 2862674 2863634 2864629 "SOLVERAD" 2866494 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1160 2858399 2859098 2859827 "SOLVEFOR" 2862041 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1159 2852003 2857747 2857844 "SNTSCAT" 2857849 NIL SNTSCAT (NIL T T T T) -9 NIL 2857919 NIL) (-1158 2845554 2850326 2850717 "SMTS" 2851693 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1157 2839276 2845442 2845519 "SMP" 2845524 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1156 2837405 2837736 2838134 "SMITH" 2838973 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1155 2828930 2833984 2834087 "SMATCAT" 2835438 NIL SMATCAT (NIL NIL T T T) -9 NIL 2835988 NIL) (-1154 2825702 2826693 2827871 "SMATCAT-" 2827876 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1153 2823171 2824910 2824953 "SKAGG" 2825214 NIL SKAGG (NIL T) -9 NIL 2825349 NIL) (-1152 2818691 2822654 2822831 "SINT" 2822983 T SINT (NIL) -8 NIL NIL 2823138) (-1151 2818457 2818501 2818567 "SIMPAN" 2818647 T SIMPAN (NIL) -7 NIL NIL NIL) (-1150 2817277 2817516 2817791 "SIGNRF" 2818216 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1149 2816092 2816261 2816545 "SIGNEF" 2817106 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1148 2815332 2815675 2815799 "SIGAST" 2815990 T SIGAST (NIL) -8 NIL NIL NIL) (-1147 2814557 2814867 2815007 "SIG" 2815214 T SIG (NIL) -8 NIL NIL NIL) (-1146 2812209 2812701 2813207 "SHP" 2814098 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1145 2805533 2812110 2812186 "SHDP" 2812191 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1144 2805044 2805284 2805314 "SGROUP" 2805407 T SGROUP (NIL) -9 NIL 2805469 NIL) (-1143 2804896 2804928 2805001 "SGROUP-" 2805006 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1142 2801615 2802385 2803108 "SGCF" 2804195 T SGCF (NIL) -7 NIL NIL NIL) (-1141 2795317 2801061 2801158 "SFRTCAT" 2801163 NIL SFRTCAT (NIL T T T T) -9 NIL 2801202 NIL) (-1140 2788636 2789756 2790892 "SFRGCD" 2794300 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1139 2781654 2782835 2784021 "SFQCMPK" 2787569 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781256 2781363 2781474 "SFORT" 2781595 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1137 2780182 2781096 2781217 "SEXOF" 2781222 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1136 2775771 2776678 2776773 "SEXCAT" 2779395 NIL SEXCAT (NIL T T T T T) -9 NIL 2779955 NIL) (-1135 2774686 2775652 2775720 "SEX" 2775725 T SEX (NIL) -8 NIL NIL NIL) (-1134 2772808 2773399 2773704 "SETMN" 2774427 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1133 2772338 2772526 2772556 "SETCAT" 2772673 T SETCAT (NIL) -9 NIL 2772758 NIL) (-1132 2772106 2772170 2772269 "SETCAT-" 2772274 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1131 2768209 2770567 2770610 "SETAGG" 2771480 NIL SETAGG (NIL T) -9 NIL 2771820 NIL) (-1130 2767631 2767783 2768020 "SETAGG-" 2768025 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1129 2764440 2767565 2767613 "SET" 2767618 NIL SET (NIL T) -8 NIL NIL NIL) (-1128 2763823 2764136 2764237 "SEQAST" 2764361 T SEQAST (NIL) -8 NIL NIL NIL) (-1127 2762950 2763316 2763377 "SEGXCAT" 2763663 NIL SEGXCAT (NIL T T) -9 NIL 2763783 NIL) (-1126 2761875 2762143 2762186 "SEGCAT" 2762708 NIL SEGCAT (NIL T) -9 NIL 2762929 NIL) (-1125 2761490 2761555 2761668 "SEGBIND2" 2761810 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1124 2760380 2760853 2761061 "SEGBIND" 2761317 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1123 2759899 2760181 2760258 "SEGAST" 2760325 T SEGAST (NIL) -8 NIL NIL NIL) (-1122 2759108 2759244 2759448 "SEG2" 2759743 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1121 2758024 2758774 2758956 "SEG" 2758961 NIL SEG (NIL T) -8 NIL NIL NIL) (-1120 2757257 2757959 2758006 "SDVAR" 2758011 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1119 2748615 2757027 2757157 "SDPOL" 2757162 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1118 2747184 2747474 2747793 "SCPKG" 2748330 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1117 2746306 2746520 2746712 "SCOPE" 2747014 T SCOPE (NIL) -8 NIL NIL NIL) (-1116 2745502 2745660 2745839 "SCACHE" 2746161 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1115 2745086 2745320 2745350 "SASTCAT" 2745355 T SASTCAT (NIL) -9 NIL 2745368 NIL) (-1114 2744489 2744921 2744997 "SAOS" 2745032 T SAOS (NIL) -8 NIL NIL NIL) (-1113 2744048 2744089 2744262 "SAERFFC" 2744448 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1112 2743635 2743676 2743835 "SAEFACT" 2744007 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1111 2736683 2743532 2743612 "SAE" 2743617 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2734986 2735318 2735719 "RURPK" 2736349 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1109 2733563 2733929 2734234 "RULESET" 2734820 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1108 2733133 2733357 2733440 "RULECOLD" 2733515 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1107 2730248 2730886 2731344 "RULE" 2732814 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730032 2730066 2730137 "RTVALUE" 2730199 T RTVALUE (NIL) -8 NIL NIL NIL) (-1105 2729443 2729749 2729843 "RSTRCAST" 2729960 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1104 2724213 2725086 2726006 "RSETGCD" 2728642 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1103 2712777 2718521 2718618 "RSETCAT" 2722737 NIL RSETCAT (NIL T T T T) -9 NIL 2723834 NIL) (-1102 2710596 2711243 2712067 "RSETCAT-" 2712072 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1101 2702904 2704358 2705878 "RSDCMPK" 2709195 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2700773 2701336 2701410 "RRCC" 2702496 NIL RRCC (NIL T T) -9 NIL 2702840 NIL) (-1099 2700094 2700298 2700577 "RRCC-" 2700582 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1098 2699477 2699790 2699891 "RPTAST" 2700015 T RPTAST (NIL) -8 NIL NIL NIL) (-1097 2671863 2682589 2682656 "RPOLCAT" 2693322 NIL RPOLCAT (NIL T T T) -9 NIL 2696482 NIL) (-1096 2662833 2665701 2668823 "RPOLCAT-" 2668828 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1095 2653286 2661044 2661526 "ROUTINE" 2662373 T ROUTINE (NIL) -8 NIL NIL NIL) (-1094 2649349 2652912 2653052 "ROMAN" 2653168 T ROMAN (NIL) -8 NIL NIL NIL) (-1093 2647461 2648209 2648469 "ROIRC" 2649154 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1092 2643234 2646003 2646033 "RNS" 2646302 T RNS (NIL) -9 NIL 2646558 NIL) (-1091 2641641 2642126 2642660 "RNS-" 2642735 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1090 2640602 2641006 2641208 "RNGBIND" 2641492 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1089 2639895 2640399 2640429 "RNG" 2640434 T RNG (NIL) -9 NIL 2640455 NIL) (-1088 2639190 2639668 2639711 "RMODULE" 2639716 NIL RMODULE (NIL T) -9 NIL 2639743 NIL) (-1087 2638014 2638120 2638456 "RMCAT2" 2639091 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1086 2634516 2637360 2637657 "RMATRIX" 2637776 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1085 2627015 2629603 2629718 "RMATCAT" 2633077 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634059 NIL) (-1084 2626354 2626537 2626844 "RMATCAT-" 2626849 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1083 2625927 2626141 2626184 "RLINSET" 2626246 NIL RLINSET (NIL T) -9 NIL 2626290 NIL) (-1082 2625488 2625569 2625697 "RINTERP" 2625846 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1081 2624412 2625086 2625116 "RING" 2625172 T RING (NIL) -9 NIL 2625264 NIL) (-1080 2624192 2624248 2624345 "RING-" 2624350 NIL RING- (NIL T) -8 NIL NIL NIL) (-1079 2623003 2623270 2623528 "RIDIST" 2623956 T RIDIST (NIL) -7 NIL NIL NIL) (-1078 2613628 2622471 2622677 "RGCHAIN" 2622851 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1077 2612886 2613370 2613411 "RGBCSPC" 2613469 NIL RGBCSPC (NIL T) -9 NIL 2613521 NIL) (-1076 2611952 2612411 2612452 "RGBCMDL" 2612684 NIL RGBCMDL (NIL T) -9 NIL 2612798 NIL) (-1075 2611592 2611661 2611764 "RFFACTOR" 2611883 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1074 2611311 2611352 2611449 "RFFACT" 2611551 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1073 2609362 2609792 2610174 "RFDIST" 2610951 T RFDIST (NIL) -7 NIL NIL NIL) (-1072 2606302 2606970 2607640 "RF" 2608726 NIL RF (NIL T) -7 NIL NIL NIL) (-1071 2605749 2605847 2606010 "RETSOL" 2606204 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1070 2605367 2605465 2605508 "RETRACT" 2605641 NIL RETRACT (NIL T) -9 NIL 2605728 NIL) (-1069 2605210 2605241 2605328 "RETRACT-" 2605333 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1068 2604758 2605032 2605102 "RETAST" 2605162 T RETAST (NIL) -8 NIL NIL NIL) (-1067 2597108 2604411 2604538 "RESULT" 2604653 T RESULT (NIL) -8 NIL NIL NIL) (-1066 2595543 2596377 2596576 "RESRING" 2597011 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1065 2595167 2595228 2595326 "RESLATC" 2595480 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1064 2594866 2594907 2595014 "REPSQ" 2595126 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1063 2594557 2594598 2594709 "REPDB" 2594825 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1062 2588389 2589846 2591069 "REP2" 2593369 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1061 2584692 2585447 2586255 "REP1" 2587616 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1060 2582072 2582694 2583296 "REP" 2584112 T REP (NIL) -7 NIL NIL NIL) (-1059 2574080 2580213 2580669 "REGSET" 2581702 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2572789 2573228 2573478 "REF" 2573865 NIL REF (NIL T) -8 NIL NIL NIL) (-1057 2572154 2572269 2572436 "REDORDER" 2572673 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1056 2567525 2571367 2571594 "RECLOS" 2571982 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1055 2566559 2566758 2566973 "REALSOLV" 2567332 T REALSOLV (NIL) -7 NIL NIL NIL) (-1054 2563006 2563844 2564728 "REAL0Q" 2565724 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1053 2558559 2559595 2560656 "REAL0" 2561987 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1052 2558393 2558446 2558476 "REAL" 2558481 T REAL (NIL) -9 NIL 2558516 NIL) (-1051 2557804 2558110 2558204 "RDUCEAST" 2558321 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1050 2557203 2557281 2557488 "RDIV" 2557726 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1049 2556253 2556445 2556658 "RDIST" 2557025 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1048 2554838 2555137 2555509 "RDETRS" 2555961 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1047 2552632 2553104 2553642 "RDETR" 2554380 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1046 2551251 2551535 2551932 "RDEEFS" 2552348 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1045 2549754 2550066 2550491 "RDEEF" 2550939 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1044 2543233 2546708 2546738 "RCFIELD" 2548033 T RCFIELD (NIL) -9 NIL 2548764 NIL) (-1043 2541189 2541801 2542497 "RCFIELD-" 2542572 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1042 2537241 2539262 2539305 "RCAGG" 2540389 NIL RCAGG (NIL T) -9 NIL 2540854 NIL) (-1041 2536851 2536963 2537126 "RCAGG-" 2537131 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1040 2536168 2536298 2536463 "RATRET" 2536735 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1039 2535709 2535788 2535909 "RATFACT" 2536096 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1038 2534987 2535137 2535289 "RANDSRC" 2535579 T RANDSRC (NIL) -7 NIL NIL NIL) (-1037 2534715 2534765 2534838 "RADUTIL" 2534936 T RADUTIL (NIL) -7 NIL NIL NIL) (-1036 2526860 2533546 2533857 "RADIX" 2534438 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1035 2516475 2526702 2526832 "RADFF" 2526837 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1034 2516104 2516197 2516227 "RADCAT" 2516387 T RADCAT (NIL) -9 NIL NIL NIL) (-1033 2515874 2515934 2516034 "RADCAT-" 2516039 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1032 2513785 2515644 2515736 "QUEUE" 2515817 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1031 2513410 2513459 2513590 "QUATCT2" 2513736 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1030 2505788 2509833 2509875 "QUATCAT" 2510666 NIL QUATCAT (NIL T) -9 NIL 2511432 NIL) (-1029 2501669 2502964 2504354 "QUATCAT-" 2504450 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1028 2497515 2501602 2501650 "QUAT" 2501655 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1027 2494771 2496563 2496606 "QUAGG" 2496987 NIL QUAGG (NIL T) -9 NIL 2497162 NIL) (-1026 2494319 2494593 2494663 "QQUTAST" 2494723 T QQUTAST (NIL) -8 NIL NIL NIL) (-1025 2493230 2493832 2493997 "QFORM" 2494200 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1024 2492855 2492904 2493035 "QFCAT2" 2493181 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1023 2482552 2488702 2488744 "QFCAT" 2489412 NIL QFCAT (NIL T) -9 NIL 2490413 NIL) (-1022 2477886 2479334 2480921 "QFCAT-" 2481017 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477317 2477451 2477583 "QEQUAT" 2477776 T QEQUAT (NIL) -8 NIL NIL NIL) (-1020 2470335 2471516 2472702 "QCMPACK" 2476250 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2469564 2469746 2469982 "QALGSET2" 2470153 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1018 2467014 2467550 2467980 "QALGSET" 2469219 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2465681 2465923 2466242 "PWFFINTB" 2466787 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1016 2463826 2464024 2464380 "PUSHVAR" 2465495 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1015 2459553 2460769 2460812 "PTRANFN" 2462723 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1014 2457890 2458235 2458559 "PTPACK" 2459264 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1013 2457513 2457576 2457687 "PTFUNC2" 2457827 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1012 2451429 2456302 2456345 "PTCAT" 2456645 NIL PTCAT (NIL T) -9 NIL 2456798 NIL) (-1011 2451078 2451119 2451245 "PSQFR" 2451388 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1010 2449650 2449966 2450302 "PSEUDLIN" 2450776 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1009 2436170 2438745 2441071 "PSETPK" 2447410 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1008 2428878 2431906 2432004 "PSETCAT" 2435045 NIL PSETCAT (NIL T T T T) -9 NIL 2435859 NIL) (-1007 2426603 2427345 2428169 "PSETCAT-" 2428174 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1006 2425916 2426111 2426141 "PSCURVE" 2426413 T PSCURVE (NIL) -9 NIL 2426580 NIL) (-1005 2421639 2423406 2423473 "PSCAT" 2424325 NIL PSCAT (NIL T T T) -9 NIL 2424565 NIL) (-1004 2420633 2420915 2421318 "PSCAT-" 2421323 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1003 2418801 2419692 2419957 "PRTITION" 2420390 T PRTITION (NIL) -8 NIL NIL NIL) (-1002 2418212 2418518 2418612 "PRTDAST" 2418729 T PRTDAST (NIL) -8 NIL NIL NIL) (-1001 2407056 2409478 2411668 "PRS" 2416074 NIL PRS (NIL T T) -7 NIL NIL NIL) (-1000 2404671 2406373 2406415 "PRQAGG" 2406601 NIL PRQAGG (NIL T) -9 NIL 2406703 NIL) (-999 2403850 2404299 2404327 "PROPLOG" 2404466 T PROPLOG (NIL) -9 NIL 2404581 NIL) (-998 2403448 2403511 2403634 "PROPFUN2" 2403773 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-997 2402745 2402884 2403056 "PROPFUN1" 2403309 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-996 2400726 2401492 2401789 "PROPFRML" 2402481 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-995 2400171 2400302 2400430 "PROPERTY" 2400618 T PROPERTY (NIL) -8 NIL NIL NIL) (-994 2393984 2398337 2399157 "PRODUCT" 2399397 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-993 2393774 2393812 2393871 "PRINT" 2393945 T PRINT (NIL) -7 NIL NIL NIL) (-992 2393090 2393231 2393383 "PRIMES" 2393654 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-991 2391137 2391556 2392022 "PRIMELT" 2392669 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-990 2390854 2390915 2390943 "PRIMCAT" 2391067 T PRIMCAT (NIL) -9 NIL NIL NIL) (-989 2389843 2390039 2390267 "PRIMARR2" 2390672 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-988 2385565 2389781 2389826 "PRIMARR" 2389831 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-987 2385202 2385264 2385375 "PREASSOC" 2385503 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-986 2382167 2384660 2384894 "PR" 2385013 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2381618 2381775 2381803 "PPCURVE" 2382008 T PPCURVE (NIL) -9 NIL 2382144 NIL) (-984 2381165 2381413 2381496 "PORTNUM" 2381555 T PORTNUM (NIL) -8 NIL NIL NIL) (-983 2378502 2378923 2379515 "POLYROOT" 2380746 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-982 2377879 2377943 2378177 "POLYLIFT" 2378438 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-981 2374100 2374603 2375232 "POLYCATQ" 2377424 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-980 2359748 2365847 2365912 "POLYCAT" 2369426 NIL POLYCAT (NIL T T T) -9 NIL 2371304 NIL) (-979 2352888 2355073 2357450 "POLYCAT-" 2357455 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-978 2352469 2352543 2352663 "POLY2UP" 2352814 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-977 2352095 2352158 2352267 "POLY2" 2352406 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-976 2345310 2351699 2351859 "POLY" 2351968 NIL POLY (NIL T) -8 NIL NIL NIL) (-975 2343971 2344234 2344510 "POLUTIL" 2345084 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-974 2342290 2342603 2342934 "POLTOPOL" 2343693 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-973 2337286 2342224 2342271 "POINT" 2342276 NIL POINT (NIL T) -8 NIL NIL NIL) (-972 2335419 2335830 2336205 "PNTHEORY" 2336931 T PNTHEORY (NIL) -7 NIL NIL NIL) (-971 2333865 2334174 2334573 "PMTOOLS" 2335117 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-970 2333452 2333536 2333653 "PMSYM" 2333781 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-969 2332954 2333029 2333204 "PMQFCAT" 2333377 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-968 2332335 2332433 2332595 "PMPREDFS" 2332855 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-967 2331678 2331800 2331956 "PMPRED" 2332212 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2330332 2330550 2330928 "PMPLCAT" 2331440 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-965 2329858 2329943 2330095 "PMLSAGG" 2330247 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-964 2329325 2329407 2329589 "PMKERNEL" 2329776 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-963 2328936 2329017 2329130 "PMINS" 2329244 NIL PMINS (NIL T) -7 NIL NIL NIL) (-962 2328372 2328447 2328656 "PMFS" 2328861 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-961 2327588 2327718 2327923 "PMDOWN" 2328249 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-960 2326837 2326971 2327134 "PMASSFS" 2327475 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-959 2325980 2326162 2326343 "PMASS" 2326676 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325629 2325703 2325797 "PLOTTOOL" 2325906 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-957 2321281 2322475 2323397 "PLOT3D" 2324727 T PLOT3D (NIL) -8 NIL NIL NIL) (-956 2320169 2320370 2320605 "PLOT1" 2321085 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-955 2314590 2315980 2317128 "PLOT" 2319041 T PLOT (NIL) -8 NIL NIL NIL) (-954 2289765 2294656 2299507 "PLEQN" 2309856 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-953 2289452 2289505 2289608 "PINTERPA" 2289712 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-952 2288758 2288892 2289072 "PINTERP" 2289317 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2286842 2288008 2288036 "PID" 2288233 T PID (NIL) -9 NIL 2288360 NIL) (-950 2286587 2286630 2286705 "PICOERCE" 2286799 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-949 2285683 2286351 2286438 "PI" 2286478 T PI (NIL) -8 NIL NIL 2286545) (-948 2284991 2285142 2285318 "PGROEB" 2285539 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-947 2280430 2281389 2282295 "PGE" 2284105 T PGE (NIL) -7 NIL NIL NIL) (-946 2278511 2278800 2279166 "PGCD" 2280147 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-945 2277837 2277952 2278113 "PFRPAC" 2278395 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-944 2274095 2276385 2276738 "PFR" 2277516 NIL PFR (NIL T) -8 NIL NIL NIL) (-943 2272448 2272728 2273053 "PFOTOOLS" 2273842 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-942 2270963 2271220 2271571 "PFOQ" 2272205 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-941 2269446 2269676 2270032 "PFO" 2270747 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-940 2266530 2268036 2268064 "PFECAT" 2268657 T PFECAT (NIL) -9 NIL 2269034 NIL) (-939 2265978 2266143 2266350 "PFECAT-" 2266355 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-938 2264551 2264833 2265134 "PFBRU" 2265727 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-937 2262380 2262769 2263201 "PFBR" 2264202 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-936 2258326 2262269 2262338 "PF" 2262343 NIL PF (NIL NIL) -8 NIL NIL NIL) (-935 2253380 2254533 2255403 "PERMGRP" 2257489 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-934 2251292 2252404 2252445 "PERMCAT" 2252845 NIL PERMCAT (NIL T) -9 NIL 2253143 NIL) (-933 2250939 2250986 2251110 "PERMAN" 2251245 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-932 2246741 2248448 2249096 "PERM" 2250324 NIL PERM (NIL T) -8 NIL NIL NIL) (-931 2243982 2246406 2246528 "PENDTREE" 2246652 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-930 2242863 2243126 2243167 "PDSPC" 2243700 NIL PDSPC (NIL T) -9 NIL 2243945 NIL) (-929 2241918 2242184 2242546 "PDSPC-" 2242551 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-928 2240632 2241568 2241609 "PDRING" 2241614 NIL PDRING (NIL T) -9 NIL 2241642 NIL) (-927 2239375 2240137 2240191 "PDMOD" 2240196 NIL PDMOD (NIL T T) -9 NIL 2240300 NIL) (-926 2236542 2237368 2238036 "PDEPROB" 2238727 T PDEPROB (NIL) -8 NIL NIL NIL) (-925 2234051 2234591 2235146 "PDEPACK" 2236007 T PDEPACK (NIL) -7 NIL NIL NIL) (-924 2232939 2233153 2233404 "PDECOMP" 2233850 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-923 2230456 2231347 2231375 "PDECAT" 2232162 T PDECAT (NIL) -9 NIL 2232875 NIL) (-922 2230073 2230140 2230194 "PDDOM" 2230359 NIL PDDOM (NIL T T) -9 NIL 2230439 NIL) (-921 2229886 2229922 2230029 "PDDOM-" 2230034 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-920 2229631 2229670 2229760 "PCOMP" 2229847 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-919 2227671 2228432 2228729 "PBWLB" 2229360 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-918 2227297 2227360 2227469 "PATTERN2" 2227608 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-917 2225006 2225442 2225899 "PATTERN1" 2226886 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-916 2217185 2219079 2220417 "PATTERN" 2223689 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2216743 2216816 2216948 "PATRES2" 2217112 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-914 2214009 2214692 2215173 "PATRES" 2216308 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2211862 2212297 2212704 "PATMATCH" 2213676 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-912 2211316 2211567 2211608 "PATMAB" 2211715 NIL PATMAB (NIL T) -9 NIL 2211798 NIL) (-911 2209762 2210170 2210428 "PATLRES" 2211121 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-910 2209300 2209431 2209472 "PATAB" 2209477 NIL PATAB (NIL T) -9 NIL 2209649 NIL) (-909 2207440 2207877 2208300 "PARTPERM" 2208897 T PARTPERM (NIL) -7 NIL NIL NIL) (-908 2207049 2207124 2207226 "PARSURF" 2207371 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-907 2206675 2206738 2206847 "PARSU2" 2206986 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-906 2206433 2206479 2206546 "PARSER" 2206628 T PARSER (NIL) -7 NIL NIL NIL) (-905 2206042 2206117 2206219 "PARSCURV" 2206364 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-904 2205668 2205731 2205840 "PARSC2" 2205979 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-903 2205295 2205365 2205462 "PARPCURV" 2205604 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-902 2204921 2204984 2205093 "PARPC2" 2205232 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-901 2203910 2204294 2204476 "PARAMAST" 2204759 T PARAMAST (NIL) -8 NIL NIL NIL) (-900 2203418 2203516 2203635 "PAN2EXPR" 2203811 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-899 2202111 2202539 2202767 "PALETTE" 2203210 T PALETTE (NIL) -8 NIL NIL NIL) (-898 2200456 2201116 2201476 "PAIR" 2201797 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-897 2193389 2199713 2199908 "PADICRC" 2200310 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-896 2185646 2192733 2192918 "PADICRAT" 2193236 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-895 2182443 2184306 2184346 "PADICCT" 2184927 NIL PADICCT (NIL NIL) -9 NIL 2185209 NIL) (-894 2180459 2182380 2182425 "PADIC" 2182430 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179404 2179616 2179884 "PADEPAC" 2180246 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-892 2178604 2178749 2178955 "PADE" 2179266 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-891 2176837 2177812 2178092 "OWP" 2178408 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-890 2176282 2176543 2176640 "OVERSET" 2176760 T OVERSET (NIL) -8 NIL NIL NIL) (-889 2175202 2175887 2176059 "OVAR" 2176150 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-888 2163438 2166311 2168511 "OUTFORM" 2173022 T OUTFORM (NIL) -8 NIL NIL NIL) (-887 2162720 2163035 2163162 "OUTBFILE" 2163331 T OUTBFILE (NIL) -8 NIL NIL NIL) (-886 2161997 2162192 2162220 "OUTBCON" 2162538 T OUTBCON (NIL) -9 NIL 2162704 NIL) (-885 2161580 2161710 2161867 "OUTBCON-" 2161872 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-884 2160820 2160965 2161126 "OUT" 2161439 T OUT (NIL) -7 NIL NIL NIL) (-883 2160116 2160549 2160638 "OSI" 2160751 T OSI (NIL) -8 NIL NIL NIL) (-882 2159535 2159957 2159985 "OSGROUP" 2159990 T OSGROUP (NIL) -9 NIL 2160012 NIL) (-881 2158246 2158507 2158792 "ORTHPOL" 2159282 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-880 2155497 2158081 2158202 "OREUP" 2158207 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-879 2152600 2155188 2155315 "ORESUP" 2155439 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-878 2150100 2150628 2151189 "OREPCTO" 2152089 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-877 2143478 2145973 2146014 "OREPCAT" 2148362 NIL OREPCAT (NIL T) -9 NIL 2149466 NIL) (-876 2140451 2141407 2142465 "OREPCAT-" 2142470 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-875 2139643 2139921 2139949 "ORDTYPE" 2140258 T ORDTYPE (NIL) -9 NIL 2140421 NIL) (-874 2138944 2139160 2139415 "ORDTYPE-" 2139420 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-873 2138300 2138683 2138841 "ORDSTRCT" 2138846 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-872 2137798 2138168 2138196 "ORDSET" 2138201 T ORDSET (NIL) -9 NIL 2138223 NIL) (-871 2136449 2137420 2137448 "ORDRING" 2137453 T ORDRING (NIL) -9 NIL 2137482 NIL) (-870 2135700 2136265 2136293 "ORDMON" 2136298 T ORDMON (NIL) -9 NIL 2136319 NIL) (-869 2134844 2135009 2135204 "ORDFUNS" 2135549 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-868 2134059 2134574 2134602 "ORDFIN" 2134667 T ORDFIN (NIL) -9 NIL 2134741 NIL) (-867 2133313 2133452 2133638 "ORDCOMP2" 2133919 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-866 2129660 2131899 2132308 "ORDCOMP" 2132937 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-865 2126181 2127151 2127965 "OPTPROB" 2128866 T OPTPROB (NIL) -8 NIL NIL NIL) (-864 2122923 2123622 2124326 "OPTPACK" 2125497 T OPTPACK (NIL) -7 NIL NIL NIL) (-863 2120536 2121362 2121390 "OPTCAT" 2122209 T OPTCAT (NIL) -9 NIL 2122859 NIL) (-862 2119854 2120213 2120318 "OPSIG" 2120451 T OPSIG (NIL) -8 NIL NIL NIL) (-861 2119616 2119661 2119727 "OPQUERY" 2119808 T OPQUERY (NIL) -7 NIL NIL NIL) (-860 2118922 2119202 2119243 "OPERCAT" 2119455 NIL OPERCAT (NIL T) -9 NIL 2119552 NIL) (-859 2118665 2118733 2118850 "OPERCAT-" 2118855 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-858 2115581 2116976 2117480 "OP" 2118194 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114874 2115001 2115175 "ONECOMP2" 2115453 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-856 2111487 2113671 2114040 "ONECOMP" 2114538 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-855 2110888 2111012 2111142 "OMSERVER" 2111377 T OMSERVER (NIL) -7 NIL NIL NIL) (-854 2107400 2110326 2110366 "OMSAGG" 2110427 NIL OMSAGG (NIL T) -9 NIL 2110492 NIL) (-853 2105975 2106286 2106568 "OMPKG" 2107138 T OMPKG (NIL) -7 NIL NIL NIL) (-852 2104322 2105524 2105693 "OMLO" 2105856 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-851 2103258 2103429 2103649 "OMEXPR" 2104148 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-850 2102343 2102679 2102839 "OMERRK" 2103118 T OMERRK (NIL) -8 NIL NIL NIL) (-849 2101580 2101889 2102025 "OMERR" 2102227 T OMERR (NIL) -8 NIL NIL NIL) (-848 2100971 2101257 2101365 "OMENC" 2101492 T OMENC (NIL) -8 NIL NIL NIL) (-847 2094608 2096051 2097222 "OMDEV" 2099820 T OMDEV (NIL) -8 NIL NIL NIL) (-846 2093641 2093848 2094042 "OMCONN" 2094434 T OMCONN (NIL) -8 NIL NIL NIL) (-845 2093047 2093174 2093202 "OM" 2093501 T OM (NIL) -9 NIL NIL NIL) (-844 2091325 2092517 2092545 "OINTDOM" 2092550 T OINTDOM (NIL) -9 NIL 2092571 NIL) (-843 2088400 2090013 2090350 "OFMONOID" 2091020 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-842 2087634 2088337 2088382 "ODVAR" 2088387 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-841 2084778 2087379 2087534 "ODR" 2087539 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-840 2076190 2084554 2084680 "ODPOL" 2084685 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-839 2069484 2076062 2076167 "ODP" 2076172 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-838 2068226 2068465 2068740 "ODETOOLS" 2069258 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-837 2065169 2065851 2066567 "ODESYS" 2067559 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-836 2059999 2060959 2061984 "ODERTRIC" 2064244 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-835 2059419 2059507 2059701 "ODERED" 2059911 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-834 2056271 2056855 2057532 "ODERAT" 2058842 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-833 2053187 2053695 2054292 "ODEPRRIC" 2055800 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-832 2051082 2051726 2052212 "ODEPROB" 2052721 T ODEPROB (NIL) -8 NIL NIL NIL) (-831 2047548 2048087 2048734 "ODEPRIM" 2050561 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-830 2046791 2046899 2047159 "ODEPAL" 2047440 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-829 2042893 2043744 2044608 "ODEPACK" 2045947 T ODEPACK (NIL) -7 NIL NIL NIL) (-828 2041936 2042061 2042283 "ODEINT" 2042782 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-827 2036001 2037462 2038909 "ODEIFTBL" 2040509 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-826 2031351 2032185 2033137 "ODEEF" 2035160 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-825 2030694 2030789 2031012 "ODECONST" 2031256 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-824 2028757 2029466 2029494 "ODECAT" 2030099 T ODECAT (NIL) -9 NIL 2030630 NIL) (-823 2028389 2028438 2028565 "OCTCT2" 2028708 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-822 2024889 2028094 2028216 "OCT" 2028299 NIL OCT (NIL T) -8 NIL NIL NIL) (-821 2024082 2024682 2024710 "OCAMON" 2024715 T OCAMON (NIL) -9 NIL 2024736 NIL) (-820 2018353 2021125 2021165 "OC" 2022262 NIL OC (NIL T) -9 NIL 2023120 NIL) (-819 2015388 2016328 2017318 "OC-" 2017412 NIL OC- (NIL T T) -8 NIL NIL NIL) (-818 2014808 2015233 2015261 "OASGP" 2015266 T OASGP (NIL) -9 NIL 2015286 NIL) (-817 2013904 2014531 2014559 "OAMONS" 2014599 T OAMONS (NIL) -9 NIL 2014642 NIL) (-816 2013080 2013639 2013667 "OAMON" 2013725 T OAMON (NIL) -9 NIL 2013777 NIL) (-815 2012938 2012971 2013039 "OAMON-" 2013044 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-814 2011719 2012472 2012500 "OAGROUP" 2012647 T OAGROUP (NIL) -9 NIL 2012740 NIL) (-813 2011422 2011510 2011628 "OAGROUP-" 2011633 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-812 2011104 2011160 2011249 "NUMTUBE" 2011366 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004623 2006195 2007731 "NUMQUAD" 2009588 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000303 2001337 2002372 "NUMODE" 2003608 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997584 1998524 1998552 "NUMINT" 1999475 T NUMINT (NIL) -9 NIL 2000239 NIL) (-808 1996496 1996729 1996947 "NUMFMT" 1997386 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982679 1985800 1988332 "NUMERIC" 1994003 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976383 1982127 1982222 "NTSCAT" 1982227 NIL NTSCAT (NIL T T T T) -9 NIL 1982266 NIL) (-805 1975563 1975742 1975935 "NTPOLFN" 1976222 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975189 1975252 1975361 "NSUP2" 1975500 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961971 1972014 1972826 "NSUP" 1974410 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950814 1961745 1961878 "NSMP" 1961883 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949222 1949547 1949904 "NREP" 1950502 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947801 1948065 1948423 "NPCOEF" 1948965 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946849 1946982 1947198 "NORMRETR" 1947682 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944860 1945180 1945589 "NORMPK" 1946557 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944539 1944573 1944697 "NORMMA" 1944826 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944322 1944357 1944426 "NONE1" 1944503 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944086 1944279 1944308 "NONE" 1944313 T NONE (NIL) -8 NIL NIL NIL) (-794 1943577 1943645 1943824 "NODE1" 1944018 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941638 1942700 1942955 "NNI" 1943302 T NNI (NIL) -8 NIL NIL 1943537) (-792 1940034 1940371 1940735 "NLINSOL" 1941306 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936215 1937270 1938169 "NIPROB" 1939155 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934954 1935206 1935508 "NFINTBAS" 1935977 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934038 1934604 1934645 "NETCLT" 1934817 NIL NETCLT (NIL T) -9 NIL 1934899 NIL) (-788 1932710 1932977 1933258 "NCODIV" 1933806 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932466 1932509 1932584 "NCNTFRAC" 1932667 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930622 1931010 1931430 "NCEP" 1932091 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929285 1930232 1930260 "NASRING" 1930370 T NASRING (NIL) -9 NIL 1930450 NIL) (-784 1929068 1929124 1929218 "NASRING-" 1929223 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928035 1928686 1928714 "NARNG" 1928831 T NARNG (NIL) -9 NIL 1928922 NIL) (-782 1927709 1927794 1927928 "NARNG-" 1927933 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926546 1926795 1927030 "NAGSP" 1927494 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917590 1919502 1921175 "NAGS" 1924893 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916114 1916446 1916777 "NAGF07" 1917279 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910586 1911943 1913250 "NAGF04" 1914827 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903458 1905168 1906801 "NAGF02" 1908973 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898622 1899782 1900899 "NAGF01" 1902361 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892202 1893816 1895401 "NAGE04" 1897057 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883263 1885492 1887622 "NAGE02" 1890092 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879156 1880163 1881127 "NAGE01" 1882319 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876933 1877485 1878043 "NAGD03" 1878618 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868629 1870611 1872565 "NAGD02" 1874999 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862368 1863865 1865305 "NAGD01" 1867209 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858505 1859399 1860236 "NAGC06" 1861551 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856952 1857302 1857658 "NAGC05" 1858169 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856316 1856447 1856591 "NAGC02" 1856828 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855117 1855844 1855884 "NAALG" 1855963 NIL NAALG (NIL T) -9 NIL 1856024 NIL) (-765 1854946 1854981 1855071 "NAALG-" 1855076 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848818 1850004 1851191 "MULTSQFR" 1853842 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848125 1848212 1848396 "MULTFACT" 1848730 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840270 1844708 1844761 "MTSCAT" 1845831 NIL MTSCAT (NIL T T) -9 NIL 1846347 NIL) (-761 1839976 1840036 1840128 "MTHING" 1840210 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839762 1839801 1839861 "MSYSCMD" 1839936 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836507 1839323 1839364 "MSETAGG" 1839369 NIL MSETAGG (NIL T) -9 NIL 1839403 NIL) (-758 1832221 1835262 1835582 "MSET" 1836220 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827823 1829600 1830345 "MRING" 1831521 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827383 1827456 1827587 "MRF2" 1827750 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826995 1827036 1827180 "MRATFAC" 1827342 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824565 1824902 1825333 "MPRFF" 1826700 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817899 1824419 1824516 "MPOLY" 1824521 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817383 1817424 1817632 "MPCPF" 1817858 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816891 1816940 1817124 "MPC3" 1817334 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816074 1816167 1816388 "MPC2" 1816806 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814351 1814712 1815102 "MONOTOOL" 1815734 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813496 1813879 1813907 "MONOID" 1814126 T MONOID (NIL) -9 NIL 1814273 NIL) (-747 1813012 1813161 1813342 "MONOID-" 1813347 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801985 1808832 1808891 "MONOGEN" 1809565 NIL MONOGEN (NIL T T) -9 NIL 1810021 NIL) (-745 1799035 1799938 1800938 "MONOGEN-" 1801057 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797752 1798300 1798328 "MONADWU" 1798720 T MONADWU (NIL) -9 NIL 1798958 NIL) (-743 1797082 1797283 1797531 "MONADWU-" 1797536 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796367 1796671 1796699 "MONAD" 1796906 T MONAD (NIL) -9 NIL 1797018 NIL) (-741 1796034 1796130 1796262 "MONAD-" 1796267 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794173 1794947 1795226 "MOEBIUS" 1795787 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793341 1793841 1793881 "MODULE" 1793886 NIL MODULE (NIL T) -9 NIL 1793925 NIL) (-738 1792879 1793005 1793195 "MODULE-" 1793200 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790409 1791243 1791570 "MODRING" 1792703 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787138 1788514 1789035 "MODOP" 1789938 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785624 1786205 1786482 "MODMONOM" 1787001 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774384 1783915 1784329 "MODMON" 1785261 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771217 1773228 1773504 "MODFIELD" 1774259 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770128 1770498 1770688 "MMLFORM" 1771047 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769648 1769697 1769876 "MMAP" 1770079 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767541 1768480 1768521 "MLO" 1768944 NIL MLO (NIL T) -9 NIL 1769186 NIL) (-729 1764889 1765423 1766025 "MLIFT" 1767022 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764268 1764364 1764518 "MKUCFUNC" 1764800 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763861 1763937 1764060 "MKRECORD" 1764191 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762884 1763070 1763298 "MKFUNC" 1763672 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762260 1762376 1762532 "MKFLCFN" 1762767 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761525 1761639 1761824 "MKBCFUNC" 1762153 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757522 1761079 1761215 "MINT" 1761409 T MINT (NIL) -8 NIL NIL NIL) (-722 1756304 1756577 1756854 "MHROWRED" 1757277 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751055 1754839 1755244 "MFLOAT" 1755919 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750400 1750488 1750659 "MFINFACT" 1750967 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746679 1747563 1748447 "MESH" 1749536 T MESH (NIL) -7 NIL NIL NIL) (-718 1745033 1745381 1745734 "MDDFACT" 1746366 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741569 1744164 1744205 "MDAGG" 1744460 NIL MDAGG (NIL T) -9 NIL 1744603 NIL) (-716 1729292 1740862 1741069 "MCMPLX" 1741382 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728411 1728575 1728776 "MCDEN" 1729141 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726259 1726571 1726951 "MCALCFN" 1728141 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725136 1725424 1725657 "MAYBE" 1726065 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722694 1723271 1723833 "MATSTOR" 1724607 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718116 1722066 1722314 "MATRIX" 1722479 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713816 1714589 1715325 "MATLIN" 1717473 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712392 1712563 1712896 "MATCAT2" 1713651 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701731 1705449 1705526 "MATCAT" 1710558 NIL MATCAT (NIL T T T) -9 NIL 1712030 NIL) (-707 1697684 1698994 1700407 "MATCAT-" 1700412 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695760 1696120 1696504 "MAPPKG3" 1697359 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694717 1694914 1695136 "MAPPKG2" 1695584 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693174 1693500 1693827 "MAPPKG1" 1694423 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692175 1692580 1692757 "MAPPAST" 1693017 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691780 1691844 1691967 "MAPHACK3" 1692111 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691360 1691433 1691547 "MAPHACK2" 1691712 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690786 1690901 1691043 "MAPHACK1" 1691251 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688709 1689486 1689790 "MAGMA" 1690514 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688128 1688433 1688524 "MACROAST" 1688638 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684371 1686367 1686828 "M3D" 1687700 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677843 1682682 1682723 "LZSTAGG" 1683505 NIL LZSTAGG (NIL T) -9 NIL 1683800 NIL) (-695 1673525 1674974 1676431 "LZSTAGG-" 1676436 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670438 1671416 1671903 "LWORD" 1673070 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669960 1670242 1670317 "LSTAST" 1670383 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661888 1669731 1669865 "LSQM" 1669870 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661106 1661251 1661479 "LSPP" 1661743 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657843 1658559 1659289 "LSMP1" 1660408 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655625 1655956 1656412 "LSMP" 1657532 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648753 1654715 1654756 "LSAGG" 1654818 NIL LSAGG (NIL T) -9 NIL 1654896 NIL) (-687 1645262 1646372 1647585 "LSAGG-" 1647590 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642557 1644406 1644655 "LPOLY" 1645057 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642133 1642224 1642347 "LPEFRAC" 1642466 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641816 1641895 1641923 "LOGIC" 1642034 T LOGIC (NIL) -9 NIL 1642116 NIL) (-683 1641672 1641701 1641772 "LOGIC-" 1641777 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640847 1641005 1641198 "LODOOPS" 1641528 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639371 1639620 1639973 "LODOF" 1640594 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635247 1638006 1638047 "LODOCAT" 1638485 NIL LODOCAT (NIL T) -9 NIL 1638696 NIL) (-679 1634962 1635038 1635165 "LODOCAT-" 1635170 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631948 1634803 1634921 "LODO2" 1634926 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629055 1631885 1631930 "LODO1" 1631935 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626150 1628971 1629037 "LODO" 1629042 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625019 1625196 1625501 "LODEEF" 1625973 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623005 1624113 1624366 "LO" 1624851 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617977 1621171 1621212 "LNAGG" 1622074 NIL LNAGG (NIL T) -9 NIL 1622509 NIL) (-672 1617070 1617338 1617680 "LNAGG-" 1617685 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613050 1613995 1614634 "LMOPS" 1616485 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612349 1612827 1612868 "LMODULE" 1612873 NIL LMODULE (NIL T) -9 NIL 1612899 NIL) (-669 1609304 1611994 1612117 "LMDICT" 1612259 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608880 1609094 1609135 "LLINSET" 1609196 NIL LLINSET (NIL T) -9 NIL 1609240 NIL) (-667 1608525 1608788 1608848 "LITERAL" 1608853 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608044 1608124 1608263 "LIST3" 1608445 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606142 1606490 1606889 "LIST2MAP" 1607691 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605131 1605327 1605555 "LIST2" 1605960 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597585 1604065 1604369 "LIST" 1604860 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597168 1597404 1597445 "LINSET" 1597450 NIL LINSET (NIL T) -9 NIL 1597484 NIL) (-661 1595982 1596676 1596843 "LINFORM" 1597053 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594281 1595009 1595050 "LINEXP" 1595540 NIL LINEXP (NIL T) -9 NIL 1595813 NIL) (-659 1592857 1593761 1593942 "LINELT" 1594152 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591414 1591694 1592005 "LINDEP" 1592609 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590550 1591146 1591256 "LINBASIS" 1591344 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587287 1588036 1588813 "LIMITRF" 1589805 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585572 1585886 1586295 "LIMITPS" 1586982 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584400 1584975 1585015 "LIECAT" 1585155 NIL LIECAT (NIL T) -9 NIL 1585306 NIL) (-653 1584235 1584268 1584356 "LIECAT-" 1584361 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578255 1583746 1583974 "LIE" 1584056 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570440 1577795 1577951 "LIB" 1578119 T LIB (NIL) -8 NIL NIL NIL) (-650 1566009 1566958 1567893 "LGROBP" 1569557 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564633 1565541 1565569 "LFCAT" 1565776 T LFCAT (NIL) -9 NIL 1565915 NIL) (-648 1562571 1562905 1563255 "LF" 1564354 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559431 1560103 1560791 "LEXTRIPK" 1561935 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556019 1557001 1557504 "LEXP" 1559011 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555435 1555740 1555832 "LETAST" 1555947 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553821 1554146 1554547 "LEADCDET" 1555117 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552999 1553085 1553314 "LAZM3PK" 1553742 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547524 1551076 1551614 "LAUPOL" 1552511 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547097 1547147 1547308 "LAPLACE" 1547474 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545945 1546661 1546702 "LALG" 1546764 NIL LALG (NIL T) -9 NIL 1546823 NIL) (-639 1545641 1545718 1545854 "LALG-" 1545859 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543378 1544742 1544993 "LA" 1545474 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543207 1543237 1543278 "KVTFROM" 1543340 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541964 1542574 1542759 "KTVLOGIC" 1543042 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541793 1541823 1541864 "KRCFROM" 1541926 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540685 1540884 1541183 "KOVACIC" 1541593 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540514 1540544 1540585 "KONVERT" 1540647 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540343 1540373 1540414 "KOERCE" 1540476 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539827 1539920 1540052 "KERNEL2" 1540257 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537514 1538420 1538797 "KERNEL" 1539483 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530985 1535991 1536045 "KDAGG" 1536422 NIL KDAGG (NIL T T) -9 NIL 1536628 NIL) (-628 1530496 1530638 1530843 "KDAGG-" 1530848 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523196 1530157 1530312 "KAFILE" 1530374 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522800 1523085 1523148 "JVMOP" 1523153 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521536 1522040 1522289 "JVMMDACC" 1522571 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520472 1520926 1521131 "JVMFDACC" 1521351 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519053 1519548 1519848 "JVMCSTTG" 1520192 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518189 1518593 1518754 "JVMCFACC" 1518912 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517867 1518106 1518155 "JVMBCODE" 1518160 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511886 1517378 1517606 "JORDAN" 1517688 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511199 1511535 1511656 "JOINAST" 1511785 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507234 1509376 1509430 "IXAGG" 1510359 NIL IXAGG (NIL T T) -9 NIL 1510818 NIL) (-617 1506087 1506459 1506878 "IXAGG-" 1506883 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501176 1506009 1506068 "IVECTOR" 1506073 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499901 1500179 1500445 "ITUPLE" 1500943 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498373 1498580 1498875 "ITRIGMNP" 1499723 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497100 1497322 1497605 "ITFUN3" 1498149 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496698 1496761 1496884 "ITFUN2" 1497023 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495803 1496178 1496352 "ITFORM" 1496544 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493572 1494823 1495101 "ITAYLOR" 1495558 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481976 1487709 1488872 "ISUPS" 1492442 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481068 1481220 1481456 "ISUMP" 1481823 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475918 1481013 1481054 "ISTRING" 1481059 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475334 1475639 1475731 "ISAST" 1475846 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474532 1474625 1474841 "IRURPK" 1475248 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473444 1473669 1473909 "IRSN" 1474312 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471489 1471870 1472299 "IRRF2F" 1473082 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471230 1471274 1471350 "IRREDFFX" 1471445 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469803 1470104 1470403 "IROOT" 1470963 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468942 1469296 1469447 "IRFORM" 1469672 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468024 1468155 1468369 "IR2F" 1468825 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465613 1466132 1466698 "IR2" 1467502 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462053 1463297 1463989 "IR" 1464953 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461838 1461878 1461938 "IPRNTPK" 1462013 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457812 1461727 1461796 "IPF" 1461801 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455840 1457737 1457794 "IPADIC" 1457799 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455098 1455400 1455530 "IP4ADDR" 1455730 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454436 1454727 1454859 "IOMODE" 1454986 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453407 1454033 1454160 "IOBFILE" 1454329 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452817 1453311 1453339 "IOBCON" 1453344 T IOBCON (NIL) -9 NIL 1453365 NIL) (-589 1452322 1452386 1452569 "INVLAPLA" 1452753 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441892 1444324 1446710 "INTTR" 1449986 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438185 1438969 1439834 "INTTOOLS" 1441077 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437765 1437862 1437979 "INTSLPE" 1438088 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435232 1437688 1437747 "INTRVL" 1437752 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432810 1433346 1433921 "INTRF" 1434717 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432203 1432318 1432460 "INTRET" 1432708 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430176 1430589 1431059 "INTRAT" 1431811 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427421 1428022 1428641 "INTPM" 1429661 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424138 1424765 1425503 "INTPAF" 1426807 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419239 1420279 1421330 "INTPACK" 1423107 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418485 1418643 1418851 "INTHERTR" 1419081 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417918 1418004 1418192 "INTHERAL" 1418399 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415686 1416207 1416664 "INTHEORY" 1417481 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407018 1408713 1410485 "INTG0" 1414038 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387543 1392381 1397191 "INTFTBL" 1402228 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386768 1386930 1387103 "INTFACT" 1387402 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384165 1384641 1385198 "INTEF" 1386322 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382362 1383257 1383285 "INTDOM" 1383586 T INTDOM (NIL) -9 NIL 1383793 NIL) (-570 1381701 1381905 1382147 "INTDOM-" 1382152 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377569 1379990 1380044 "INTCAT" 1380843 NIL INTCAT (NIL T) -9 NIL 1381164 NIL) (-568 1377023 1377144 1377272 "INTBIT" 1377461 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375704 1375876 1376183 "INTALG" 1376868 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375181 1375277 1375434 "INTAF" 1375608 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368148 1374991 1375131 "INTABL" 1375136 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367389 1367951 1368016 "INT8" 1368050 T INT8 (NIL) -8 NIL NIL 1368095) (-563 1366629 1367191 1367256 "INT64" 1367290 T INT64 (NIL) -8 NIL NIL 1367335) (-562 1365869 1366431 1366496 "INT32" 1366530 T INT32 (NIL) -8 NIL NIL 1366575) (-561 1365109 1365671 1365736 "INT16" 1365770 T INT16 (NIL) -8 NIL NIL 1365815) (-560 1361313 1364906 1365015 "INT" 1365020 T INT (NIL) -8 NIL NIL NIL) (-559 1355422 1358861 1358889 "INS" 1359823 T INS (NIL) -9 NIL 1360488 NIL) (-558 1352579 1353499 1354440 "INS-" 1354513 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351336 1351581 1351879 "INPSIGN" 1352332 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350430 1350571 1350768 "INPRODPF" 1351216 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349300 1349441 1349678 "INPRODFF" 1350310 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348288 1348452 1348712 "INNMFACT" 1349136 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347467 1347582 1347770 "INMODGCD" 1348187 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345951 1346220 1346544 "INFSP" 1347212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345111 1345252 1345435 "INFPROD0" 1345831 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344709 1344781 1344879 "INFORM1" 1345046 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341276 1342774 1343289 "INFORM" 1344202 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340781 1340888 1341002 "INFINITY" 1341182 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339855 1340501 1340602 "INETCLTS" 1340700 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338453 1338721 1339042 "INEP" 1339603 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337483 1338350 1338415 "INDE" 1338420 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337035 1337115 1337232 "INCRMAPS" 1337410 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335757 1336304 1336510 "INBFILE" 1336849 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330937 1331993 1332937 "INBFF" 1334845 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329791 1330114 1330142 "INBCON" 1330655 T INBCON (NIL) -9 NIL 1330921 NIL) (-540 1329001 1329266 1329542 "INBCON-" 1329547 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328420 1328725 1328816 "INAST" 1328930 T INAST (NIL) -8 NIL NIL NIL) (-538 1327787 1328099 1328205 "IMPTAST" 1328334 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323708 1327631 1327735 "IMATRIX" 1327740 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322400 1322539 1322855 "IMATQF" 1323564 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320580 1320847 1321184 "IMATLIN" 1322156 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314495 1320504 1320562 "ILIST" 1320567 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312161 1314355 1314468 "IIARRAY2" 1314473 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306982 1312072 1312136 "IFF" 1312141 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306263 1306599 1306715 "IFAST" 1306886 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300775 1305555 1305743 "IFARRAY" 1306120 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299813 1300679 1300752 "IFAMON" 1300757 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299385 1299462 1299516 "IEVALAB" 1299723 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299048 1299128 1299288 "IEVALAB-" 1299293 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298081 1298937 1299012 "IDPOAMS" 1299017 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297183 1297970 1298045 "IDPOAM" 1298050 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296564 1297098 1297160 "IDPO" 1297165 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295044 1295571 1295623 "IDPC" 1296135 NIL IDPC (NIL T T) -9 NIL 1296416 NIL) (-522 1294376 1294936 1295009 "IDPAM" 1295014 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293591 1294268 1294341 "IDPAG" 1294346 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293135 1293397 1293487 "IDENT" 1293521 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289354 1290238 1291133 "IDECOMP" 1292292 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281989 1283277 1284324 "IDEAL" 1288390 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281131 1281261 1281461 "ICDEN" 1281873 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280106 1280611 1280758 "ICARD" 1281004 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278136 1278479 1278884 "IBPTOOLS" 1279783 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273251 1277756 1277869 "IBITS" 1278055 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269926 1270550 1271245 "IBATOOL" 1272668 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267687 1268167 1268700 "IBACHIN" 1269461 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265277 1267533 1267636 "IARRAY2" 1267641 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260990 1265203 1265260 "IARRAY1" 1265265 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254007 1259402 1259883 "IAN" 1260529 T IAN (NIL) -8 NIL NIL NIL) (-508 1253512 1253575 1253748 "IALGFACT" 1253944 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253004 1253153 1253181 "HYPCAT" 1253388 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252506 1252659 1252845 "HYPCAT-" 1252850 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252053 1252301 1252384 "HOSTNAME" 1252443 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251886 1251935 1251976 "HOMOTOP" 1251981 NIL HOMOTOP (NIL T) -9 NIL 1252014 NIL) (-503 1248319 1249818 1249859 "HOAGG" 1250840 NIL HOAGG (NIL T) -9 NIL 1251569 NIL) (-502 1246835 1247312 1247838 "HOAGG-" 1247843 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239892 1246428 1246578 "HEXADEC" 1246705 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238604 1238862 1239125 "HEUGCD" 1239669 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237536 1238441 1238571 "HELLFDIV" 1238576 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235544 1237311 1237400 "HEAP" 1237479 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234741 1235096 1235230 "HEADAST" 1235430 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228079 1234656 1234718 "HDP" 1234723 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221098 1227714 1227866 "HDMP" 1227980 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220404 1220562 1220726 "HB" 1220954 T HB (NIL) -7 NIL NIL NIL) (-493 1213414 1220250 1220354 "HASHTBL" 1220359 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212830 1213135 1213227 "HASAST" 1213342 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210243 1212452 1212634 "HACKPI" 1212668 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205415 1210096 1210209 "GTSET" 1210214 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198454 1205293 1205391 "GSTBL" 1205396 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190217 1197619 1197875 "GSERIES" 1198254 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189248 1189761 1189789 "GROUP" 1189992 T GROUP (NIL) -9 NIL 1190126 NIL) (-486 1188572 1188773 1189024 "GROUP-" 1189029 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186921 1187260 1187647 "GROEBSOL" 1188249 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185749 1186109 1186160 "GRMOD" 1186689 NIL GRMOD (NIL T T) -9 NIL 1186857 NIL) (-483 1185505 1185553 1185681 "GRMOD-" 1185686 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180645 1181859 1182859 "GRIMAGE" 1184525 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179039 1179372 1179696 "GRDEF" 1180341 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178471 1178599 1178740 "GRAY" 1178918 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177548 1178050 1178101 "GRALG" 1178254 NIL GRALG (NIL T T) -9 NIL 1178347 NIL) (-478 1177185 1177282 1177445 "GRALG-" 1177450 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173666 1176768 1176947 "GPOLSET" 1177091 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173014 1173077 1173335 "GOSPER" 1173603 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168584 1169452 1169978 "GMODPOL" 1172713 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167571 1167773 1168011 "GHENSEL" 1168396 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161643 1162570 1163590 "GENUPS" 1166655 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161334 1161391 1161480 "GENUFACT" 1161586 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160734 1160823 1160988 "GENPGCD" 1161252 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160202 1160243 1160456 "GENMFACT" 1160693 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158739 1159025 1159332 "GENEEZ" 1159945 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151917 1158350 1158512 "GDMP" 1158662 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140655 1145688 1146794 "GCNAALG" 1150900 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138782 1139830 1139858 "GCDDOM" 1140113 T GCDDOM (NIL) -9 NIL 1140270 NIL) (-465 1138222 1138379 1138594 "GCDDOM-" 1138599 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126694 1129168 1131560 "GBINTERN" 1135913 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124495 1124823 1125244 "GBF" 1126369 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123252 1123441 1123708 "GBEUCLID" 1124311 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121902 1122109 1122413 "GB" 1123031 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121233 1121376 1121525 "GAUSSFAC" 1121773 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119554 1119902 1120216 "GALUTIL" 1120952 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117814 1118136 1118460 "GALPOLYU" 1119281 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115113 1115469 1115876 "GALFACTU" 1117511 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106727 1108418 1110026 "GALFACT" 1113545 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104013 1104773 1104801 "FVFUN" 1105957 T FVFUN (NIL) -9 NIL 1106677 NIL) (-454 1103243 1103461 1103489 "FVC" 1103780 T FVC (NIL) -9 NIL 1103963 NIL) (-453 1102844 1103068 1103136 "FUNDESC" 1103195 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102417 1102641 1102722 "FUNCTION" 1102796 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101094 1101718 1101921 "FTEM" 1102234 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098724 1099416 1099882 "FT" 1100648 T FT (NIL) -8 NIL NIL NIL) (-449 1096993 1097304 1097701 "FSUPFACT" 1098415 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095312 1095679 1096011 "FST" 1096681 T FST (NIL) -8 NIL NIL NIL) (-447 1094493 1094617 1094805 "FSRED" 1095194 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093182 1093448 1093795 "FSPRMELT" 1094208 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090392 1090926 1091412 "FSPECF" 1092745 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089914 1089974 1090144 "FSINT" 1090333 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088050 1088907 1089210 "FSERIES" 1089693 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087074 1087208 1087432 "FSCINT" 1087930 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086098 1086259 1086486 "FSAGG2" 1086927 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081962 1085042 1085083 "FSAGG" 1085453 NIL FSAGG (NIL T) -9 NIL 1085712 NIL) (-439 1079562 1080325 1081121 "FSAGG-" 1081216 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077222 1077520 1078068 "FS2UPS" 1079280 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076088 1076271 1076573 "FS2EXPXP" 1077047 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075716 1075765 1075894 "FS2" 1076039 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055954 1065490 1065531 "FS" 1069415 NIL FS (NIL T) -9 NIL 1071704 NIL) (-434 1044015 1047590 1051647 "FS-" 1051947 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043429 1043556 1043708 "FRUTIL" 1043895 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037940 1041118 1041158 "FRNAALG" 1042478 NIL FRNAALG (NIL T) -9 NIL 1043076 NIL) (-431 1033421 1034689 1035964 "FRNAALG-" 1036714 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033053 1033102 1033229 "FRNAAF2" 1033372 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031340 1031902 1032198 "FRMOD" 1032865 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030525 1030618 1030909 "FRIDEAL2" 1031247 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028130 1028900 1029218 "FRIDEAL" 1030316 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027221 1027677 1027718 "FRETRCT" 1027723 NIL FRETRCT (NIL T) -9 NIL 1027899 NIL) (-425 1026279 1026564 1026915 "FRETRCT-" 1026920 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023100 1024563 1024622 "FRAMALG" 1025504 NIL FRAMALG (NIL T T) -9 NIL 1025796 NIL) (-423 1021138 1021689 1022319 "FRAMALG-" 1022542 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020768 1020831 1020938 "FRAC2" 1021075 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013761 1020241 1020518 "FRAC" 1020523 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013391 1013454 1013561 "FR2" 1013698 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004308 1008886 1010244 "FR" 1012065 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998227 1001687 1001715 "FPS" 1002834 T FPS (NIL) -9 NIL 1003391 NIL) (-417 997652 997785 997949 "FPS-" 998095 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994618 996609 996637 "FPC" 996862 T FPC (NIL) -9 NIL 997004 NIL) (-415 994399 994451 994548 "FPC-" 994553 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993157 993887 993928 "FPATMAB" 993933 NIL FPATMAB (NIL T) -9 NIL 994085 NIL) (-413 991300 991899 992246 "FPARFRAC" 992873 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986592 987192 987874 "FORTRAN" 990732 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984166 984830 984858 "FORTFN" 985918 T FORTFN (NIL) -9 NIL 986542 NIL) (-410 983918 983980 984008 "FORTCAT" 984067 T FORTCAT (NIL) -9 NIL 984129 NIL) (-409 981604 982134 982673 "FORT" 983399 T FORT (NIL) -7 NIL NIL NIL) (-408 981386 981422 981491 "FORMULA1" 981568 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979390 980002 980392 "FORMULA" 981016 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978907 978965 979138 "FORDER" 979332 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977967 978167 978360 "FOP" 978734 T FOP (NIL) -7 NIL NIL NIL) (-404 976380 977247 977421 "FNLA" 977849 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974999 975510 975538 "FNCAT" 975998 T FNCAT (NIL) -9 NIL 976258 NIL) (-402 974442 974958 974986 "FNAME" 974991 T FNAME (NIL) -8 NIL NIL NIL) (-401 972768 973941 973969 "FMTC" 973974 T FMTC (NIL) -9 NIL 974010 NIL) (-400 971317 972704 972750 "FMONOID" 972755 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967906 969272 969313 "FMONCAT" 970530 NIL FMONCAT (NIL T) -9 NIL 971135 NIL) (-398 965228 965976 966004 "FMFUN" 967148 T FMFUN (NIL) -9 NIL 967856 NIL) (-397 962101 963153 963207 "FMCAT" 964402 NIL FMCAT (NIL T T) -9 NIL 964897 NIL) (-396 961334 961551 961579 "FMC" 961869 T FMC (NIL) -9 NIL 962051 NIL) (-395 960002 961100 961200 "FM1" 961279 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959020 959744 959893 "FM" 959898 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956758 957210 957704 "FLOATRP" 958571 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954160 954696 955274 "FLOATCP" 956225 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946823 951889 952510 "FLOAT" 953559 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945341 946415 946456 "FLINEXP" 946461 NIL FLINEXP (NIL T) -9 NIL 946554 NIL) (-389 944471 944730 945058 "FLINEXP-" 945063 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943529 943691 943915 "FLASORT" 944323 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940447 941499 941551 "FLALG" 942778 NIL FLALG (NIL T T) -9 NIL 943245 NIL) (-386 939471 939632 939859 "FLAGG2" 940300 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932726 936880 936921 "FLAGG" 938183 NIL FLAGG (NIL T) -9 NIL 938835 NIL) (-384 931380 931791 932281 "FLAGG-" 932286 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928018 929225 929284 "FINRALG" 930412 NIL FINRALG (NIL T T) -9 NIL 930920 NIL) (-382 927142 927407 927746 "FINRALG-" 927751 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926448 926747 926775 "FINITE" 926971 T FINITE (NIL) -9 NIL 927078 NIL) (-380 918399 920978 921018 "FINAALG" 924685 NIL FINAALG (NIL T) -9 NIL 926138 NIL) (-379 913515 914781 915925 "FINAALG-" 917304 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912075 912497 912551 "FILECAT" 913235 NIL FILECAT (NIL T T) -9 NIL 913451 NIL) (-377 911353 911830 911933 "FILE" 912005 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908756 910583 910611 "FIELD" 910651 T FIELD (NIL) -9 NIL 910731 NIL) (-375 907298 907761 908272 "FIELD-" 908277 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904981 905933 906280 "FGROUP" 906984 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904053 904235 904455 "FGLMICPK" 904813 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899308 903978 904035 "FFX" 904040 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898903 898970 899105 "FFSLPE" 899241 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898401 898443 898652 "FFPOLY2" 898861 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894277 895173 895969 "FFPOLY" 897637 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889546 894196 894259 "FFP" 894264 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884077 888889 889079 "FFNBX" 889400 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878410 883212 883470 "FFNBP" 883931 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872448 877694 877905 "FFNB" 878243 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871268 871478 871793 "FFINTBAS" 872245 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866861 869515 869543 "FFIELDC" 870163 T FFIELDC (NIL) -9 NIL 870539 NIL) (-362 865481 865922 866405 "FFIELDC-" 866410 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865038 865096 865220 "FFHOM" 865423 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862697 863220 863737 "FFF" 864553 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857732 862439 862540 "FFCGX" 862640 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852771 857464 857571 "FFCGP" 857675 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847371 852498 852606 "FFCG" 852707 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846776 846825 847060 "FFCAT2" 847322 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825458 836508 836594 "FFCAT" 841759 NIL FFCAT (NIL T T T) -9 NIL 843210 NIL) (-354 820469 821703 823017 "FFCAT-" 824247 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815290 820380 820444 "FF" 820449 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803943 808262 809482 "FEXPR" 814142 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802871 803340 803381 "FEVALAB" 803465 NIL FEVALAB (NIL T) -9 NIL 803726 NIL) (-350 801988 802240 802578 "FEVALAB-" 802583 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798850 799735 799850 "FDIVCAT" 801418 NIL FDIVCAT (NIL T T T T) -9 NIL 801855 NIL) (-348 798606 798639 798809 "FDIVCAT-" 798814 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797820 797913 798190 "FDIV2" 798513 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796230 797203 797406 "FDIV" 797719 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795138 795525 795727 "FCTRDATA" 796048 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793794 794083 794372 "FCPAK1" 794869 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792797 793294 793435 "FCOMP" 793685 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776111 779947 783485 "FC" 789279 T FC (NIL) -8 NIL NIL NIL) (-341 767820 772432 772472 "FAXF" 774274 NIL FAXF (NIL T) -9 NIL 774966 NIL) (-340 764961 765768 766586 "FAXF-" 767051 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759530 764337 764513 "FARRAY" 764818 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754095 756477 756530 "FAMR" 757553 NIL FAMR (NIL T T) -9 NIL 758013 NIL) (-337 752919 753287 753722 "FAMR-" 753727 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751946 752841 752894 "FAMONOID" 752899 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749576 750428 750481 "FAMONC" 751422 NIL FAMONC (NIL T T) -9 NIL 751808 NIL) (-334 748050 749330 749467 "FAGROUP" 749472 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745803 746164 746567 "FACUTIL" 747731 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744890 745087 745309 "FACTFUNC" 745613 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736631 744193 744392 "EXPUPXS" 744746 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734084 734654 735240 "EXPRTUBE" 736065 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730295 730947 731677 "EXPRODE" 733423 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724729 725436 726242 "EXPR2UPS" 729593 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724355 724418 724527 "EXPR2" 724666 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708663 723004 723433 "EXPR" 723959 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 699001 707814 708105 "EXPEXPAN" 708499 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698421 698725 698816 "EXITAST" 698930 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698185 698378 698407 "EXIT" 698412 T EXIT (NIL) -8 NIL NIL NIL) (-322 697806 697874 697987 "EVALCYC" 698117 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697323 697465 697506 "EVALAB" 697676 NIL EVALAB (NIL T) -9 NIL 697780 NIL) (-320 696780 696926 697147 "EVALAB-" 697152 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693895 695436 695464 "EUCDOM" 696019 T EUCDOM (NIL) -9 NIL 696369 NIL) (-318 692255 692756 693339 "EUCDOM-" 693344 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691881 691944 692053 "ESTOOLS2" 692192 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691626 691674 691754 "ESTOOLS1" 691833 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678943 681924 684674 "ESTOOLS" 688896 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678682 678720 678802 "ESCONT1" 678905 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674990 675817 676597 "ESCONT" 677922 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674659 674715 674815 "ES2" 674934 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674283 674347 674456 "ES1" 674595 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667984 669914 669942 "ES" 672710 T ES (NIL) -9 NIL 674120 NIL) (-309 662661 664218 666035 "ES-" 666199 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661853 662006 662182 "ERROR" 662505 T ERROR (NIL) -7 NIL NIL NIL) (-307 654869 661712 661803 "EQTBL" 661808 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654495 654558 654667 "EQ2" 654806 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646754 649809 651258 "EQ" 653079 NIL -1509 (NIL T) -8 NIL NIL NIL) (-304 641996 643092 644185 "EP" 645693 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640536 640887 641193 "ENV" 641710 T ENV (NIL) -8 NIL NIL NIL) (-302 639496 640170 640198 "ENTIRER" 640203 T ENTIRER (NIL) -9 NIL 640249 NIL) (-301 635915 637678 638039 "EMR" 639304 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 635019 635230 635284 "ELTAGG" 635664 NIL ELTAGG (NIL T T) -9 NIL 635875 NIL) (-299 634726 634800 634941 "ELTAGG-" 634946 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634484 634519 634573 "ELTAB" 634657 NIL ELTAB (NIL T T) -9 NIL 634709 NIL) (-297 633586 633756 633955 "ELFUTS" 634335 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633310 633384 633412 "ELEMFUN" 633517 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633174 633201 633269 "ELEMFUN-" 633274 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627585 631216 631257 "ELAGG" 632197 NIL ELAGG (NIL T) -9 NIL 632660 NIL) (-293 625762 626304 626967 "ELAGG-" 626972 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 625044 625211 625367 "ELABOR" 625626 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623650 623984 624278 "ELABEXPR" 624770 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616162 618287 619116 "EFUPXS" 622925 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609288 611411 612222 "EFULS" 615437 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606725 607131 607603 "EFSTRUC" 608920 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596163 598082 599630 "EF" 605240 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595141 595648 595797 "EAB" 596034 T EAB (NIL) -8 NIL NIL NIL) (-285 594263 595100 595128 "E04UCFA" 595133 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593385 594222 594250 "E04NAFA" 594255 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592507 593344 593372 "E04MBFA" 593377 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591629 592466 592494 "E04JAFA" 592499 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590753 591588 591616 "E04GCFA" 591621 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589877 590712 590740 "E04FDFA" 590745 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588999 589836 589864 "E04DGFA" 589869 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583076 584524 585888 "E04AGNT" 587655 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581696 582377 582417 "DVARCAT" 582758 NIL DVARCAT (NIL T) -9 NIL 582921 NIL) (-276 580846 581112 581426 "DVARCAT-" 581431 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572814 580645 580774 "DSMP" 580779 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571165 571956 571997 "DSEXT" 572360 NIL DSEXT (NIL T) -9 NIL 572654 NIL) (-273 569354 569878 570544 "DSEXT-" 570549 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 569013 569078 569176 "DROPT1" 569289 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 564032 565254 566391 "DROPT0" 567896 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558615 559977 561045 "DROPT" 562984 T DROPT (NIL) -8 NIL NIL NIL) (-269 556924 557285 557671 "DRAWPT" 558249 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556551 556610 556728 "DRAWHACK" 556865 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555252 555551 555842 "DRAWCX" 556280 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554761 554836 554987 "DRAWCURV" 555178 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545079 547191 549306 "DRAWCFUN" 552666 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539570 540589 541668 "DRAW" 544053 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 536041 538235 538276 "DQAGG" 538905 NIL DQAGG (NIL T) -9 NIL 539179 NIL) (-262 522624 530252 530335 "DPOLCAT" 532187 NIL DPOLCAT (NIL T T T T) -9 NIL 532732 NIL) (-261 517143 518809 520767 "DPOLCAT-" 520772 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509951 517004 517102 "DPMO" 517107 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502656 509731 509898 "DPMM" 509903 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502178 502440 502529 "DOMTMPLT" 502587 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501527 501980 502060 "DOMCTOR" 502118 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500679 501007 501158 "DOMAIN" 501396 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493698 500314 500466 "DMP" 500580 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491475 492765 492806 "DMEXT" 492811 NIL DMEXT (NIL T) -9 NIL 492987 NIL) (-253 491069 491131 491275 "DLP" 491413 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484192 490396 490586 "DLIST" 490911 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480730 483017 483058 "DLAGG" 483608 NIL DLAGG (NIL T) -9 NIL 483838 NIL) (-250 479242 480056 480084 "DIVRING" 480176 T DIVRING (NIL) -9 NIL 480259 NIL) (-249 478425 478669 478969 "DIVRING-" 478974 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476467 476884 477290 "DISPLAY" 478039 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475297 475518 475783 "DIRPROD2" 476260 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468655 475211 475274 "DIRPROD" 475279 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456818 463366 463419 "DIRPCAT" 463677 NIL DIRPCAT (NIL NIL T) -9 NIL 464552 NIL) (-244 454018 454786 455667 "DIRPCAT-" 456004 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453299 453465 453651 "DIOSP" 453852 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449713 452183 452224 "DIOPS" 452658 NIL DIOPS (NIL T) -9 NIL 452887 NIL) (-241 449232 449376 449567 "DIOPS-" 449572 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448139 448911 448939 "DIFRING" 448944 T DIFRING (NIL) -9 NIL 448966 NIL) (-239 447787 447885 447913 "DIFFSPC" 448032 T DIFFSPC (NIL) -9 NIL 448107 NIL) (-238 447408 447510 447662 "DIFFSPC-" 447667 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446344 446942 446983 "DIFFMOD" 446988 NIL DIFFMOD (NIL T) -9 NIL 447086 NIL) (-236 446040 446097 446138 "DIFFDOM" 446259 NIL DIFFDOM (NIL T) -9 NIL 446327 NIL) (-235 445887 445917 446001 "DIFFDOM-" 446006 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443627 445091 445132 "DIFEXT" 445137 NIL DIFEXT (NIL T) -9 NIL 445290 NIL) (-233 440661 443131 443172 "DIAGG" 443177 NIL DIAGG (NIL T) -9 NIL 443197 NIL) (-232 440009 440202 440454 "DIAGG-" 440459 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434859 438968 439245 "DHMATRIX" 439778 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430327 431380 432390 "DFSFUN" 433869 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424568 429258 429570 "DFLOAT" 430035 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422807 423112 423501 "DFINTTLS" 424276 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419626 420828 421228 "DERHAM" 422473 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417162 419401 419490 "DEQUEUE" 419570 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416404 416549 416732 "DEGRED" 417024 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412810 413579 414425 "DEFINTRF" 415632 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410347 410834 411426 "DEFINTEF" 412329 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409631 409967 410082 "DEFAST" 410252 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402688 409224 409374 "DECIMAL" 409501 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400146 400658 401164 "DDFACT" 402232 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399736 399785 399936 "DBLRESP" 400097 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398937 399506 399597 "DBASIS" 399685 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396721 397167 397528 "DBASE" 398703 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395909 396201 396347 "DATAARY" 396620 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394967 395868 395896 "D03FAFA" 395901 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394026 394926 394954 "D03EEFA" 394959 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391952 392442 392931 "D03AGNT" 393557 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391193 391911 391939 "D02EJFA" 391944 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390434 391152 391180 "D02CJFA" 391185 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389675 390393 390421 "D02BHFA" 390426 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388916 389634 389662 "D02BBFA" 389667 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382047 383702 385308 "D02AGNT" 387330 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379797 380338 380884 "D01WGTS" 381521 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378804 379756 379784 "D01TRNS" 379789 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377812 378763 378791 "D01GBFA" 378796 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376820 377771 377799 "D01FCFA" 377804 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375828 376779 376807 "D01ASFA" 376812 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374836 375787 375815 "D01AQFA" 375820 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373844 374795 374823 "D01APFA" 374828 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372852 373803 373831 "D01ANFA" 373836 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371860 372811 372839 "D01AMFA" 372844 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370868 371819 371847 "D01ALFA" 371852 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369876 370827 370855 "D01AKFA" 370860 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368884 369835 369863 "D01AJFA" 369868 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362107 363732 365293 "D01AGNT" 367343 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361426 361572 361724 "CYCLOTOM" 361975 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358081 358874 359601 "CYCLES" 360719 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357381 357527 357698 "CVMP" 357942 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355168 355480 355849 "CTRIGMNP" 357109 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354641 354899 355000 "CTORKIND" 355087 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353846 354234 354262 "CTORCAT" 354444 T CTORCAT (NIL) -9 NIL 354557 NIL) (-188 353420 353555 353714 "CTORCAT-" 353719 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352834 353094 353202 "CTORCALL" 353344 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352192 352628 352701 "CTOR" 352781 T CTOR (NIL) -8 NIL NIL NIL) (-185 351548 351665 351818 "CSTTOOLS" 352089 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347245 348004 348762 "CRFP" 350860 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346660 346966 347058 "CRCEAST" 347173 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345683 345892 346120 "CRAPACK" 346464 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345063 345168 345372 "CPMATCH" 345559 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344782 344816 344922 "CPIMA" 345029 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341040 341802 342521 "COORDSYS" 344117 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340428 340573 340715 "CONTOUR" 340918 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335899 338431 338923 "CONTFRAC" 339968 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335773 335800 335828 "CONDUIT" 335865 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334727 335401 335429 "COMRING" 335434 T COMRING (NIL) -9 NIL 335486 NIL) (-174 333709 334085 334269 "COMPPROP" 334563 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333364 333405 333533 "COMPLPAT" 333668 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332994 333057 333164 "COMPLEX2" 333301 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321398 332803 332912 "COMPLEX" 332917 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320719 320858 321018 "COMPILER" 321258 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320431 320472 320570 "COMPFACT" 320678 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301825 314135 314175 "COMPCAT" 315179 NIL COMPCAT (NIL T) -9 NIL 316527 NIL) (-167 290713 294264 297891 "COMPCAT-" 298247 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290436 290470 290573 "COMMUPC" 290679 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290224 290264 290323 "COMMONOP" 290397 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289746 290028 290103 "COMMAAST" 290169 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289253 289497 289584 "COMM" 289679 T COMM (NIL) -8 NIL NIL NIL) (-162 288448 288696 288724 "COMBOPC" 289062 T COMBOPC (NIL) -9 NIL 289237 NIL) (-161 287302 287554 287796 "COMBINAT" 288238 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283645 284333 284960 "COMBF" 286724 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282307 282761 282996 "COLOR" 283430 T COLOR (NIL) -8 NIL NIL NIL) (-158 281723 282028 282120 "COLONAST" 282235 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281357 281410 281535 "CMPLXRT" 281670 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280745 281057 281156 "CLLCTAST" 281278 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276204 277275 278355 "CLIP" 279685 T CLIP (NIL) -7 NIL NIL NIL) (-154 274377 275305 275545 "CLIF" 276031 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270359 272495 272536 "CLAGG" 273465 NIL CLAGG (NIL T) -9 NIL 274001 NIL) (-152 268703 269238 269821 "CLAGG-" 269826 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268241 268332 268472 "CINTSLPE" 268612 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265706 266213 266761 "CHVAR" 267769 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264746 265420 265448 "CHARZ" 265453 T CHARZ (NIL) -9 NIL 265468 NIL) (-148 264494 264540 264618 "CHARPOL" 264700 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263412 264118 264146 "CHARNZ" 264207 T CHARNZ (NIL) -9 NIL 264256 NIL) (-146 260356 261466 261995 "CHAR" 262903 T CHAR (NIL) -8 NIL NIL NIL) (-145 260064 260143 260171 "CFCAT" 260282 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259287 259416 259599 "CDEN" 259948 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254884 258440 258720 "CCLASS" 259027 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254105 254292 254469 "CATEGORY" 254727 T -10 (NIL) -8 NIL NIL NIL) (-141 253600 254024 254072 "CATCTOR" 254077 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252991 253303 253401 "CATAST" 253522 T CATAST (NIL) -8 NIL NIL NIL) (-139 252407 252712 252804 "CASEAST" 252919 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251503 251663 251884 "CARTEN2" 252254 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247660 248404 "CARTEN" 250815 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 4e0cf62e..0a1d44a3 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,588 +1,946 @@ -(733417 . 3508975273) -(((*1 *2 *3) (-12 (-5 *3 (-1191)) (-5 *2 (-114)) (-5 *1 (-853))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-505)) (-5 *4 (-984)) (-5 *2 (-713 (-547))) - (-5 *1 (-547)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-984)) (-4 *3 (-1133)) (-5 *2 (-713 *1)) - (-4 *1 (-789 *3))))) -(((*1 *2 *3 *4 *4 *5 *4 *4 *5 *5 *3 *4 *4 *6 *7) - (-12 (-5 *3 (-711 (-229))) (-5 *4 (-560)) (-5 *5 (-229)) - (-5 *6 (-3 (|:| |fn| (-402)) (|:| |fp| (-62 COEFFN)))) - (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-88 BDYVAL)))) - (-5 *2 (-1067)) (-5 *1 (-771)))) - ((*1 *2 *3 *4 *4 *5 *4 *4 *5 *5 *3 *4 *4 *6 *7 *8 *8) - (-12 (-5 *3 (-711 (-229))) (-5 *4 (-560)) (-5 *5 (-229)) - (-5 *6 (-3 (|:| |fn| (-402)) (|:| |fp| (-62 COEFFN)))) - (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-88 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*5 (-1191)) (-4 *9 (-1015 *8)) + (-14 *10 (-1209))))) +(((*1 *2 *3 *4 *4 *5 *4 *3 *6 *3 *4 *7 *8 *9 *10) + (-12 (-5 *4 (-560)) (-5 *5 (-1191)) (-5 *6 (-711 (-229))) + (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-89 G)))) + (-5 *8 (-3 (|:| |fn| (-402)) (|:| |fp| (-82 FCN)))) + (-5 *9 (-3 (|:| |fn| (-402)) (|:| |fp| (-71 PEDERV)))) + (-5 *10 (-3 (|:| |fn| (-402)) (|:| |fp| (-87 OUTPUT)))) + (-5 *3 (-229)) (-5 *2 (-1067)) (-5 *1 (-771))))) +(((*1 *2) + (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) + (-4 *3 (-380 *4)))) + ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) +(((*1 *1 *1) (-4 *1 (-571)))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-568))))) (((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1034))))) @@ -6129,273 +8337,36 @@ (-12 (-5 *2 (-1187 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1195 *3)))) ((*1 *1 *1) (-4 *1 (-1238)))) -(((*1 *2 *3) - (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-560))) (-5 *1 (-1079))))) -(((*1 *2 *3) - 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. 50201) (-4321 . 49952) + (-4322 . 49724) (-4323 . 49680) (-4324 . 49579) (-4325 . 49248) + (-4326 . 49121) (-4327 . 49042) (-4328 . 48939) (-4329 . 48798) + (-4330 . 48664) (-4331 . 48597) (-4332 . 48382) (-4333 . 47858) + (-4334 . 47779) (-4335 . 47712) (-4336 . 47603) (-4337 . 47482) + (-4338 . 47232) (-4339 . 47179) (-4340 . 47127) (-4341 . 47032) + (-4342 . 46932) (-4343 . 46851) (-4344 . 46765) (-4345 . 46484) + (-4346 . 46347) (-4347 . 46032) (-4348 . 45959) (-4349 . 45876) + (-4350 . 45612) (-4351 . 45250) (-4352 . 45135) (-4353 . 44978) + (-4354 . 44643) (-4355 . 44298) (-4356 . 44203) (-4357 . 44084) + (-4358 . 43988) (-4359 . 42202) (-4360 . 41853) (-4361 . 41696) + (-4362 . 41358) (-4363 . 39580) (-4364 . 39525) (-4365 . 39427) + (-4366 . 39220) (-4367 . 39064) (-4368 . 38999) (-4369 . 38063) + (-4370 . 38031) (-4371 . 37978) (-4372 . 37843) (-4373 . 37673) + (-4374 . 37588) (-4375 . 37448) (-4376 . 37118) (-4377 . 37020) + (-4378 . 36879) (-4379 . 36766) (-4380 . 36706) 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11272) + (-4442 . 11054) (-4443 . 10264) (-4444 . 10191) (-4445 . 9550) + (-4446 . 9214) (-4447 . 9082) (-4448 . 9023) (-4449 . 8995) + (-4450 . 8893) (-4451 . 8843) (-4452 . 8610) (-4453 . 8516) + (-4454 . 8439) (-4455 . 8310) (-4456 . 8214) (-4457 . 8120) + (-4458 . 8032) (-4459 . 7865) (-4460 . 7810) (-4461 . 7572) + (-4462 . 7468) (-4463 . 7060) (-4464 . 7008) (-4465 . 6784) + (-4466 . 6609) (-4467 . 6554) (-4468 . 6458) (-4469 . 6396) + (-4470 . 6344) (-4471 . 6039) (-4472 . 5953) (-4473 . 5857) + (-4474 . 5667) (-4475 . 5526) (-4476 . 5195) (-4477 . 4609) + (-4478 . 4485) (-4479 . 4205) (-4480 . 4149) (-4481 . 1308) + (-4482 . 1162) (-4483 . 1061) (-4484 . 1008) (-4485 . 867) + (-4486 . 729) (-4487 . 417) (-4488 . 325) (-4489 . 182) (-4490 . 30))
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