diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 11 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 55 | ||||
| -rw-r--r-- | src/algebra/annacat.spad.pamphlet | 496 | ||||
| -rw-r--r-- | src/algebra/asp.spad.pamphlet | 4282 | ||||
| -rw-r--r-- | src/algebra/cont.spad.pamphlet | 354 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 45 | ||||
| -rw-r--r-- | src/algebra/fortcat.spad.pamphlet | 345 | ||||
| -rw-r--r-- | src/algebra/fortmac.spad.pamphlet | 458 | ||||
| -rw-r--r-- | src/algebra/fortpak.spad.pamphlet | 641 | ||||
| -rw-r--r-- | src/algebra/fortran.spad.pamphlet | 1784 | ||||
| -rw-r--r-- | src/algebra/functions.spad.pamphlet | 120 | ||||
| -rw-r--r-- | src/algebra/routines.spad.pamphlet | 647 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 3582 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 7057 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 609 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8133 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 22491 |
17 files changed, 20291 insertions, 30819 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index ed3f4b88..35c60a2a 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,14 @@ +2011-09-20 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/annacat.spad.pamphlet: Remove. + * algebra/routines.spad.pamphlet: Likewise. + * algebra/functions.spad.pamphlet: Likewise. + * algebra/tools.spad.pamphlet: Likewise. + * algebra/cont.spad.pamphlet: Likewise. + * algebra/fortran.spad.pamphlet: Likewise. + * algebra/fortmac.spad.pamphlet: Likewise. + * algebra/fortpak.spad.pamphlet: Likewise. + 2011-09-19 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/asp.spad.pamphlet: Remove. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index cb018420..dcd03071 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -949,7 +949,7 @@ $(OUT)/DMEXT.$(FASLEXT): $(OUT)/DSEXT.$(FASLEXT) $(OUT)/DIFFMOD.$(FASLEXT) \ $(OUT)/STREAM.$(FASLEXT): $(OUT)/LZSTAGG.$(FASLEXT) axiom_algebra_layer_1 = \ - ABELGRP ABELGRP- ABELMON ABELMON- FORTCAT ITUPLE \ + ABELGRP ABELGRP- ABELMON ABELMON- ITUPLE \ CABMON MONOID MONOID- RING RING- COMRING \ DIFRING ENTIRER INTDOM INTDOM- OINTDOM \ GCDDOM GCDDOM- UFD UFD- ES ES- \ @@ -1005,9 +1005,9 @@ $(OUT)/PALETTE.$(FASLEXT): $(OUT)/COLOR.$(FASLEXT) axiom_algebra_layer_4 = \ - ANON OSI COMM COMPPROP ESCONT1 EXIT \ - FAMONC FORMULA1 IDPC NONE NUMINT \ - ODECAT COLOR ONECOMP2 OPTCAT \ + ANON OSI COMM COMPPROP EXIT \ + FAMONC FORMULA1 IDPC NONE \ + COLOR ONECOMP2 \ PALETTE PARPCURV PARPC2 PARSCURV PARSC2 PARSURF \ PARSU2 PATRES2 PATTERN1 PDECAT \ REPSQ REPDB RFDIST RIDIST SPACEC SPLNODE \ @@ -1028,7 +1028,7 @@ $(OUT)/PDRING.$(FASLEXT): $(OUT)/PDSPC.$(FASLEXT) axiom_algebra_layer_5 = \ CHARNZ DVARCAT DVARCAT- ELEMFUN \ - ELEMFUN- ESTOOLS2 FCOMP FPATMAB IDPAM IDPO \ + ELEMFUN- FCOMP FPATMAB IDPAM IDPO \ INCRMAPS KERNEL2 MODMONOM MONADWU MONADWU- \ MRF2 NARNG NARNG- NSUP2 ODVAR OPQUERY \ ORDMON PATMATCH PERMCAT PDRING \ @@ -1081,7 +1081,7 @@ $(OUT)/BSTREE.$(FASLEXT): $(OUT)/BTREE.$(FASLEXT) $(OUT)/ITAYLOR.$(FASLEXT): $(OUT)/STREAM.$(FASLEXT) axiom_algebra_layer_8 = \ - BSTREE BTOURN CARD DRAWHACK FACTFUNC FMTC \ + BSTREE BTOURN CARD DRAWHACK FACTFUNC \ FR2 FRAC2 FRUTIL ITAYLOR MLO NAALG \ NAALG- OP ORDCOMP2 RANDSRC UNISEG2 XALG \ BTREE ARR2CAT ARR2CAT- @@ -1095,14 +1095,13 @@ axiom_algebra_layer_8_objects = \ $(OUT)/FT.$(FASLEXT): $(OUT)/FST.$(FASLEXT) axiom_algebra_layer_9 = \ - AMR AMR- DEGRED DLP EAB ESTOOLS1 \ + AMR AMR- DEGRED DLP EAB \ FAGROUP FAMONOID FLINEXP FLINEXP- FRETRCT FRETRCT- \ FSERIES FT IDPAG IDPOAMS INFINITY LA \ OMLO ORTHPOL PRODUCT PADICCT PMPRED PMASS \ PTFUNC2 RATRET RADUTIL UPXS2 \ XFALG ZLINDEP BBTREE TABLE INTABL \ - NIPROB ODEPROB OPTPROB \ - PDEPROB SIG FMONCAT FST + SIG FMONCAT FST axiom_algebra_layer_9_nrlibs = \ @@ -1129,7 +1128,7 @@ $(OUT)/BTAGG.$(FASLEXT): $(OUT)/BOOLE.$(FASLEXT) $(OUT)/PATLRES.$(FASLEXT): $(OUT)/PATRES.$(FASLEXT) axiom_algebra_layer_10 = \ - RESULT BFUNCT BPADIC ANY \ + BPADIC ANY \ SEXOF CRAPACK DEQUEUE DLIST \ DRAWCX \ DRAWPT FAMR FAMR- FLASORT \ @@ -1209,7 +1208,7 @@ axiom_algebra_layer_13 = \ COORDSYS DBASE DHMATRIX DIOSP \ FAXF FAXF- FFPOLY2 \ FNLA GRAY HB IRSN \ - MCALCFN MHROWRED NUMODE NUMQUAD \ + MHROWRED NUMODE NUMQUAD \ ODESYS ODETOOLS ORDFUNS PERMAN \ PFECAT PFECAT- POINT PSEUDLIN \ PTPACK REP2 SETMN \ @@ -1223,7 +1222,6 @@ axiom_algebra_layer_13_objects = \ $(addprefix $(OUT)/, \ $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_13))) $(OUT)/FS.$(FASLEXT): $(OUT)/UPOLYC.$(FASLEXT) -$(OUT)/FTEM.$(FASLEXT): $(OUT)/TEXTFILE.$(FASLEXT) $(OUT)/FILE.$(FASLEXT): $(OUT)/FNAME.$(FASLEXT) axiom_algebra_layer_14 = \ @@ -1238,8 +1236,8 @@ axiom_algebra_layer_14 = \ FFPOLY FFX FFSLPE FGLMICPK \ FILE FINAALG FINAALG- FINRALG \ FINRALG- FLOATRP FNAME \ - FOP FORMULA FORT FRAC \ - FTEM GENEEZ GENMFACT GENPGCD \ + FORMULA FRAC \ + GENEEZ GENMFACT GENPGCD \ GALFACTU GALPOLYU GB GBEUCLID \ GBF GBINTERN GHENSEL GMODPOL \ GOSPER GRIMAGE GROEBSOL HDMP \ @@ -1251,7 +1249,7 @@ axiom_algebra_layer_14 = \ ISUMP LAUPOL LEADCDET LGROBP \ LIMITRF LINDEP LO LPEFRAC \ LSPP MATLIN MCDEN MDDFACT \ - MFINFACT MFLOAT MINT MLIFT \ + MFINFACT MLIFT \ MMAP MODMON MONOTOOL MPCPF \ MPC2 MPC3 MPOLY MPRFF \ MRATFAC MULTSQFR NORMRETR NPCOEF \ @@ -1272,7 +1270,7 @@ axiom_algebra_layer_14 = \ SMITH SMP SMTS SOLVEFOR \ SPLTREE STINPROD STTFNC SUBRESP \ SUMRF SUP SUPFRACF TANEXP \ - TEMUTL TEX TEXTFILE \ + TEX TEXTFILE \ TWOFACT UNIFACT UP UPCDEN \ UPDECOMP UPDIVP UPMP UPOLYC2 \ UPXSCAT UPSQFREE VIEWDEF VIEW2D \ @@ -1355,13 +1353,12 @@ axiom_algebra_layer_18_objects = \ $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_18))) $(OUT)/TSETCAT.$(FASLEXT): $(OUT)/PSETCAT.$(FASLEXT) $(OUT)/RPOLCAT.$(FASLEXT) $(OUT)/FPARFRAC.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) -$(OUT)/FEXPR.$(FASLEXT): $(OUT)/EXPR.$(FASLEXT) axiom_algebra_layer_19 = \ - ACPLOT ANTISYM ATTRBUT \ + ACPLOT ANTISYM \ COMPCAT \ COMPCAT- DRAW DRAWCFUN DROPT \ - DROPT0 EP FCPAK1 FEXPR \ + DROPT0 EP \ FFCAT FFCAT- FFCGP FFNBP \ FFP FLOAT FPARFRAC FR \ FRNAALG FRNAALG- EXPR \ @@ -1369,16 +1366,16 @@ axiom_algebra_layer_19 = \ IDEAL INFORM INFORM1 IPRNTPK \ IR ISUPS LIB \ LMDICT LODOOPS MKFLCFN \ - MSET M3D \ + MSET \ NREP NUMFMT OC OC- \ ODERAT \ PATTERN OVAR \ PMKERNEL PMSYM PRIMELT \ QALGSET2 QEQUAT RECLOS REP1 \ QUATCAT QUATCAT- RFFACT \ - ROMAN ROUTINE RNGBIND \ + ROMAN RNGBIND \ RULECOLD SAOS SEGBIND \ - SET SPECOUT SWITCH \ + SET SPECOUT \ SYSSOLP \ VARIABLE WFFINTBS SPADPRSR \ PARSER TSETCAT TSETCAT- @@ -1401,10 +1398,10 @@ axiom_algebra_layer_20 = \ CTRIGMNP \ DBLRESP DERHAM DFSFUN DRAWCURV \ EF EFSTRUC \ - ELFUTS ESTOOLS EXPEXPAN EXPRODE \ - EXPRTUBE EXPR2 FC FDIVCAT \ + ELFUTS EXPEXPAN EXPRODE \ + EXPRTUBE EXPR2 FDIVCAT \ FDIVCAT- FDIV2 FFCAT2 FLOATCP \ - FORDER FORTRAN FSRED FSUPFACT \ + FORDER FSRED FSUPFACT \ FRNAAF2 FSPECF FS2 FS2UPS \ GAUSSFAC GCNAALG GENUFACT GENUPS \ GTSET GPOLSET IAN INEP \ @@ -1413,7 +1410,7 @@ axiom_algebra_layer_20 = \ INTHERAL INTPAF INTPM INTTOOLS \ ITRIGMNP JORDAN KOVACIC LF \ LIE LODOF LSQM \ - MCMPLX MULTFACT NCEP \ + MULTFACT NCEP \ NLINSOL NSMP NUMERIC OCT \ OCTCT2 ODEPAL ODERTRIC PADE \ PAN2EXPR PFO PFOQ \ @@ -1421,7 +1418,7 @@ axiom_algebra_layer_20 = \ PSETPK QUAT QUATCT2 RADFF \ RDEEF RDEEFS RDIV RSETCAT \ RSETCAT- RULE RULESET SIMPAN \ - SFORT SOLVESER SUMFS SUTS \ + SOLVESER SUMFS SUTS \ TOOLSIGN TRIGMNIP TRMANIP ULSCCAT \ ULSCCAT- UPXSSING UTSODE UTSODETL \ UTS2 WUTSET @@ -1439,7 +1436,7 @@ $(OUT)/SUPXS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_21 = \ DEFINTEF DFINTTLS DEFINTRF \ - EFULS ESCONT EXPR2UPS \ + EFULS EXPR2UPS \ FDIV FSCINT FSINT FS2EXPXP \ GSERIES HELLFDIV INVLAPLA IR2F \ IRRF2F LAPLACE LIMITPS LODEEF \ @@ -1488,7 +1485,7 @@ axiom_algebra_layer_user = \ QQUTAST DEFAST MACROAST SPADXPT SPADAST PARAMAST \ INBFILE OUTBFILE IOBFILE RGBCMDL RGBCSPC STEPAST \ CTOR IP4ADDR NETCLT INETCLTS \ - FMC FMFUN FORTFN FVC FVFUN IRFORM COMPILER \ + IRFORM COMPILER \ ITFORM ELABOR TALGOP YDIAGRAM LINELT DBASIS \ LINFORM LINBASIS JVMOP JVMCFACC JVMFDACC JVMMDACC \ JVMCSTTG diff --git a/src/algebra/annacat.spad.pamphlet b/src/algebra/annacat.spad.pamphlet deleted file mode 100644 index 1c92b907..00000000 --- a/src/algebra/annacat.spad.pamphlet +++ /dev/null @@ -1,496 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra annacat.spad} -\author{Brian Dupee} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{domain NIPROB NumericalIntegrationProblem} -<<domain NIPROB NumericalIntegrationProblem>>= -)abbrev domain NIPROB NumericalIntegrationProblem -++ Author: Brian Dupee -++ Date Created: December 1997 -++ Date Last Updated: December 1997 -++ Basic Operations: coerce, retract -++ Related Constructors: Union -++ Description: -++ \axiomType{NumericalIntegrationProblem} is a \axiom{domain} -++ for the representation of Numerical Integration problems for use -++ by ANNA. -++ -++ The representation is a Union of two record types - one for integration of -++ a function of one variable: -++ -++ \axiomType{Record}(var:\axiomType{Symbol}, -++ fn:\axiomType{Expression DoubleFloat}, -++ range:\axiomType{Segment OrderedCompletion DoubleFloat}, -++ abserr:\axiomType{DoubleFloat}, -++ relerr:\axiomType{DoubleFloat},) -++ -++ and one for multivariate integration: -++ -++ \axiomType{Record}(fn:\axiomType{Expression DoubleFloat}, -++ range:\axiomType{List Segment OrderedCompletion DoubleFloat}, -++ abserr:\axiomType{DoubleFloat}, -++ relerr:\axiomType{DoubleFloat},). -++ - -EDFA ==> Expression DoubleFloat -SOCDFA ==> Segment OrderedCompletion DoubleFloat -DFA ==> DoubleFloat -NIAA ==> Record(var:Symbol,fn:EDFA,range:SOCDFA,abserr:DFA,relerr:DFA) -MDNIAA ==> Record(fn:EDFA,range:List SOCDFA,abserr:DFA,relerr:DFA) - -NumericalIntegrationProblem():SetCategory with - coerce: NIAA -> % - ++ coerce(x) \undocumented{} - coerce: MDNIAA -> % - ++ coerce(x) \undocumented{} - coerce: Union(nia:NIAA,mdnia:MDNIAA) -> % - ++ coerce(x) \undocumented{} - retract: % -> Union(nia:NIAA,mdnia:MDNIAA) - ++ retract(x) \undocumented{} - - == - - add - Rep := Union(nia:NIAA,mdnia:MDNIAA) - - coerce(s:NIAA) == [s] - coerce(s:MDNIAA) == [s] - coerce(s:Union(nia:NIAA,mdnia:MDNIAA)) == s - coerce(x:%):OutputForm == - (x) case nia => (x.nia)::OutputForm - (x.mdnia)::OutputForm - retract(x:%):Union(nia:NIAA,mdnia:MDNIAA) == - (x) case nia => [x.nia] - [x.mdnia] - -@ -\section{domain ODEPROB NumericalODEProblem} -<<domain ODEPROB NumericalODEProblem>>= -)abbrev domain ODEPROB NumericalODEProblem -++ Author: Brian Dupee -++ Date Created: December 1997 -++ Date Last Updated: December 1997 -++ Basic Operations: coerce, retract -++ Related Constructors: Union -++ Description: -++ \axiomType{NumericalODEProblem} is a \axiom{domain} -++ for the representation of Numerical ODE problems for use -++ by ANNA. -++ -++ The representation is of type: -++ -++ \axiomType{Record}(xinit:\axiomType{DoubleFloat}, -++ xend:\axiomType{DoubleFloat}, -++ fn:\axiomType{Vector Expression DoubleFloat}, -++ yinit:\axiomType{List DoubleFloat},intvals:\axiomType{List DoubleFloat}, -++ g:\axiomType{Expression DoubleFloat},abserr:\axiomType{DoubleFloat}, -++ relerr:\axiomType{DoubleFloat}) -++ - -DFB ==> DoubleFloat -VEDFB ==> Vector Expression DoubleFloat -LDFB ==> List DoubleFloat -EDFB ==> Expression DoubleFloat -ODEAB ==> Record(xinit:DFB,xend:DFB,fn:VEDFB,yinit:LDFB,intvals:LDFB,g:EDFB,abserr:DFB,relerr:DFB) -NumericalODEProblem():SetCategory with - - coerce: ODEAB -> % - ++ coerce(x) \undocumented{} - retract: % -> ODEAB - ++ retract(x) \undocumented{} - - == - - add - Rep := ODEAB - - coerce(s:ODEAB) == s - coerce(x:%):OutputForm == - (retract(x))::OutputForm - retract(x:%):ODEAB == x :: Rep - -@ -\section{domain PDEPROB NumericalPDEProblem} -<<domain PDEPROB NumericalPDEProblem>>= -)abbrev domain PDEPROB NumericalPDEProblem -++ Author: Brian Dupee -++ Date Created: December 1997 -++ Date Last Updated: December 1997 -++ Basic Operations: coerce, retract -++ Related Constructors: Union -++ Description: -++ \axiomType{NumericalPDEProblem} is a \axiom{domain} -++ for the representation of Numerical PDE problems for use -++ by ANNA. -++ -++ The representation is of type: -++ -++ \axiomType{Record}(pde:\axiomType{List Expression DoubleFloat}, -++ constraints:\axiomType{List PDEC}, -++ f:\axiomType{List List Expression DoubleFloat}, -++ st:\axiomType{String}, -++ tol:\axiomType{DoubleFloat}) -++ -++ where \axiomType{PDEC} is of type: -++ -++ \axiomType{Record}(start:\axiomType{DoubleFloat}, -++ finish:\axiomType{DoubleFloat}, -++ grid:\axiomType{NonNegativeInteger}, -++ boundaryType:\axiomType{Integer}, -++ dStart:\axiomType{Matrix DoubleFloat}, -++ dFinish:\axiomType{Matrix DoubleFloat}) -++ - -DFC ==> DoubleFloat -NNIC ==> NonNegativeInteger -INTC ==> Integer -MDFC ==> Matrix DoubleFloat -PDECC ==> Record(start:DFC, finish:DFC, grid:NNIC, boundaryType:INTC, - dStart:MDFC, dFinish:MDFC) -LEDFC ==> List Expression DoubleFloat -PDEBC ==> Record(pde:LEDFC, constraints:List PDECC, f:List LEDFC, - st:String, tol:DFC) -NumericalPDEProblem():SetCategory with - - coerce: PDEBC -> % - ++ coerce(x) \undocumented{} - retract: % -> PDEBC - ++ retract(x) \undocumented{} - - == - - add - Rep := PDEBC - - coerce(s:PDEBC) == s - coerce(x:%):OutputForm == - (retract(x))::OutputForm - retract(x:%):PDEBC == x :: Rep - -@ -\section{domain OPTPROB NumericalOptimizationProblem} -<<domain OPTPROB NumericalOptimizationProblem>>= -)abbrev domain OPTPROB NumericalOptimizationProblem -++ Author: Brian Dupee -++ Date Created: December 1997 -++ Date Last Updated: December 1997 -++ Basic Operations: coerce, retract -++ Related Constructors: Union -++ Description: -++ \axiomType{NumericalOptimizationProblem} is a \axiom{domain} -++ for the representation of Numerical Optimization problems for use -++ by ANNA. -++ -++ The representation is a Union of two record types - one for otimization of -++ a single function of one or more variables: -++ -++ \axiomType{Record}( -++ fn:\axiomType{Expression DoubleFloat}, -++ init:\axiomType{List DoubleFloat}, -++ lb:\axiomType{List OrderedCompletion DoubleFloat}, -++ cf:\axiomType{List Expression DoubleFloat}, -++ ub:\axiomType{List OrderedCompletion DoubleFloat}) -++ -++ and one for least-squares problems i.e. optimization of a set of -++ observations of a data set: -++ -++ \axiomType{Record}(lfn:\axiomType{List Expression DoubleFloat}, -++ init:\axiomType{List DoubleFloat}). -++ - -LDFD ==> List DoubleFloat -LEDFD ==> List Expression DoubleFloat -LSAD ==> Record(lfn:LEDFD, init:LDFD) -UNOALSAD ==> Union(noa:NOAD,lsa:LSAD) -EDFD ==> Expression DoubleFloat -LOCDFD ==> List OrderedCompletion DoubleFloat -NOAD ==> Record(fn:EDFD, init:LDFD, lb:LOCDFD, cf:LEDFD, ub:LOCDFD) -NumericalOptimizationProblem():SetCategory with - - coerce: NOAD -> % - ++ coerce(x) \undocumented{} - coerce: LSAD -> % - ++ coerce(x) \undocumented{} - coerce: UNOALSAD -> % - ++ coerce(x) \undocumented{} - retract: % -> UNOALSAD - ++ retract(x) \undocumented{} - - == - - add - Rep := UNOALSAD - - coerce(s:NOAD) == [s] - coerce(s:LSAD) == [s] - coerce(x:UNOALSAD) == x - coerce(x:%):OutputForm == - (x) case noa => (x.noa)::OutputForm - (x.lsa)::OutputForm - retract(x:%):UNOALSAD == - (x) case noa => [x.noa] - [x.lsa] - -@ -\section{category NUMINT NumericalIntegrationCategory} -<<category NUMINT NumericalIntegrationCategory>>= -)abbrev category NUMINT NumericalIntegrationCategory -++ Author: Brian Dupee -++ Date Created: February 1994 -++ Date Last Updated: March 1996 -++ Description: -++ \axiomType{NumericalIntegrationCategory} is the \axiom{category} for -++ describing the set of Numerical Integration \axiom{domains} with -++ \axiomFun{measure} and \axiomFun{numericalIntegration}. - -EDFE ==> Expression DoubleFloat -SOCDFE ==> Segment OrderedCompletion DoubleFloat -DFE ==> DoubleFloat -NIAE ==> Record(var:Symbol,fn:EDFE,range:SOCDFE,abserr:DFE,relerr:DFE) -MDNIAE ==> Record(fn:EDFE,range:List SOCDFE,abserr:DFE,relerr:DFE) -NumericalIntegrationCategory(): Category == SetCategory with - - measure:(RoutinesTable,NIAE)->Record(measure:Float,explanations:String,extra:Result) - ++ measure(R,args) calculates an estimate of the ability of a particular - ++ method to solve a problem. - ++ - ++ 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). - ++ - ++ 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. - - numericalIntegration: (NIAE, Result) -> Result - ++ numericalIntegration(args,hints) performs the integration of the - ++ function given the strategy or method returned by \axiomFun{measure}. - - measure:(RoutinesTable,MDNIAE)->Record(measure:Float,explanations:String,extra:Result) - ++ measure(R,args) calculates an estimate of the ability of a particular - ++ method to solve a problem. - ++ - ++ 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). - ++ - ++ 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. - - numericalIntegration: (MDNIAE, Result) -> Result - ++ numericalIntegration(args,hints) performs the integration of the - ++ function given the strategy or method returned by \axiomFun{measure}. - -@ -\section{category ODECAT OrdinaryDifferentialEquationsSolverCategory} -<<category ODECAT OrdinaryDifferentialEquationsSolverCategory>>= -)abbrev category ODECAT OrdinaryDifferentialEquationsSolverCategory -++ Author: Brian Dupee -++ Date Created: February 1995 -++ Date Last Updated: June 1995 -++ Basic Operations: -++ Description: -++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} is the -++ \axiom{category} for describing the set of ODE solver \axiom{domains} -++ with \axiomFun{measure} and \axiomFun{ODEsolve}. - -DFF ==> DoubleFloat -VEDFF ==> Vector Expression DoubleFloat -LDFF ==> List DoubleFloat -EDFF ==> Expression DoubleFloat -ODEAF ==> Record(xinit:DFF,xend:DFF,fn:VEDFF,yinit:LDFF,intvals:LDFF,g:EDFF,abserr:DFF,relerr:DFF) -OrdinaryDifferentialEquationsSolverCategory(): Category == SetCategory with - - measure:(RoutinesTable,ODEAF) -> Record(measure:Float,explanations:String) - ++ measure(R,args) calculates an estimate of the ability of a particular - ++ method to solve a problem. - ++ - ++ 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). - ++ - ++ 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. - - ODESolve: ODEAF -> Result - ++ ODESolve(args) performs the integration of the - ++ function given the strategy or method returned by \axiomFun{measure}. - -@ -\section{category PDECAT PartialDifferentialEquationsSolverCategory} -<<category PDECAT PartialDifferentialEquationsSolverCategory>>= -)abbrev category PDECAT PartialDifferentialEquationsSolverCategory -++ Author: Brian Dupee -++ Date Created: February 1995 -++ Date Last Updated: June 1995 -++ Basic Operations: -++ Description: -++ \axiomType{PartialDifferentialEquationsSolverCategory} is the -++ \axiom{category} for describing the set of PDE solver \axiom{domains} -++ with \axiomFun{measure} and \axiomFun{PDEsolve}. - --- PDEA ==> Record(xmin:F,xmax:F,ymin:F,ymax:F,ngx:NNI,ngy:NNI,_ --- pde:List Expression Float, bounds:List List Expression Float,_ --- st:String, tol:DF) - --- measure:(RoutinesTable,PDEA) -> Record(measure:F,explanations:String) --- ++ measure(R,args) calculates an estimate of the ability of a particular --- ++ method to solve a problem. --- ++ --- ++ 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). --- ++ --- ++ 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. - --- PDESolve: PDEA -> Result --- ++ PDESolve(args) performs the integration of the --- ++ function given the strategy or method returned by \axiomFun{measure}. - -DFG ==> DoubleFloat -NNIG ==> NonNegativeInteger -INTG ==> Integer -MDFG ==> Matrix DoubleFloat -PDECG ==> Record(start:DFG, finish:DFG, grid:NNIG, boundaryType:INTG, - dStart:MDFG, dFinish:MDFG) -LEDFG ==> List Expression DoubleFloat -PDEBG ==> Record(pde:LEDFG, constraints:List PDECG, f:List LEDFG, - st:String, tol:DFG) -PartialDifferentialEquationsSolverCategory(): Category == SetCategory with - - measure:(RoutinesTable,PDEBG) -> Record(measure:Float,explanations:String) - ++ measure(R,args) calculates an estimate of the ability of a particular - ++ method to solve a problem. - ++ - ++ 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). - ++ - ++ 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. - - PDESolve: PDEBG -> Result - ++ PDESolve(args) performs the integration of the - ++ function given the strategy or method returned by \axiomFun{measure}. - -@ -\section{category OPTCAT NumericalOptimizationCategory} -<<category OPTCAT NumericalOptimizationCategory>>= -)abbrev category OPTCAT NumericalOptimizationCategory -++ Author: Brian Dupee -++ Date Created: January 1996 -++ Date Last Updated: March 1996 -++ Description: -++ \axiomType{NumericalOptimizationCategory} is the \axiom{category} for -++ describing the set of Numerical Optimization \axiom{domains} with -++ \axiomFun{measure} and \axiomFun{optimize}. - -LDFH ==> List DoubleFloat -LEDFH ==> List Expression DoubleFloat -LSAH ==> Record(lfn:LEDFH, init:LDFH) -EDFH ==> Expression DoubleFloat -LOCDFH ==> List OrderedCompletion DoubleFloat -NOAH ==> Record(fn:EDFH, init:LDFH, lb:LOCDFH, cf:LEDFH, ub:LOCDFH) -NumericalOptimizationCategory(): Category == SetCategory with - measure:(RoutinesTable,NOAH)->Record(measure:Float,explanations:String) - ++ measure(R,args) calculates an estimate of the ability of a particular - ++ method to solve an optimization problem. - ++ - ++ 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). - ++ - ++ 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. - - measure:(RoutinesTable,LSAH)->Record(measure:Float,explanations:String) - ++ measure(R,args) calculates an estimate of the ability of a particular - ++ method to solve an optimization problem. - ++ - ++ 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). - ++ - ++ 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. - - numericalOptimization:LSAH -> Result - ++ numericalOptimization(args) performs the optimization of the - ++ function given the strategy or method returned by \axiomFun{measure}. - - numericalOptimization:NOAH -> Result - ++ numericalOptimization(args) performs the optimization of the - ++ function given the strategy or method returned by \axiomFun{measure}. - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain NIPROB NumericalIntegrationProblem>> -<<domain ODEPROB NumericalODEProblem>> -<<domain PDEPROB NumericalPDEProblem>> -<<domain OPTPROB NumericalOptimizationProblem>> -<<category NUMINT NumericalIntegrationCategory>> -<<category ODECAT OrdinaryDifferentialEquationsSolverCategory>> -<<category PDECAT PartialDifferentialEquationsSolverCategory>> -<<category OPTCAT NumericalOptimizationCategory>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/asp.spad.pamphlet b/src/algebra/asp.spad.pamphlet deleted file mode 100644 index d95211a8..00000000 --- a/src/algebra/asp.spad.pamphlet +++ /dev/null @@ -1,4282 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra asp.spad} -\author{Mike Dewar, Grant Keady, Godfrey Nolan} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{domain ASP1 Asp1} -<<domain ASP1 Asp1>>= -)abbrev domain ASP1 Asp1 -++ Author: Mike Dewar, Grant Keady, Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 18 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranFunctionCategory, FortranProgramCategory. -++ Description: -++\spadtype{Asp1} produces Fortran for Type 1 ASPs, needed for various -++NAG routines. Type 1 ASPs take a univariate expression (in the symbol -++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} - - -Asp1(name): Exports == Implementation where - name : Symbol - - FEXPR ==> FortranExpression - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - - Exports ==> FortranFunctionCategory with - coerce : FEXPR(['X],[],MachineFloat) -> $ - ++coerce(f) takes an object from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns it into an ASP. - - Implementation ==> add - - -- Build Symbol Table for Rep - syms : SYMTAB := empty()$SYMTAB - declare!(X,fortranReal()$FT,syms)$SYMTAB - real : FST := "real"::FST - - Rep := FortranProgram(name,[real]$Union(fst:FST,void:"void"),[X],syms) - - retract(u:FRAC POLY INT):$ == (retract(u)@FEXPR(['X],[],MachineFloat))::$ - retractIfCan(u:FRAC POLY INT):Union($,"failed") == - foo : Union(FEXPR(['X],[],MachineFloat),"failed") - foo := retractIfCan(u)$FEXPR(['X],[],MachineFloat) - foo case "failed" => "failed" - foo::FEXPR(['X],[],MachineFloat)::$ - - retract(u:FRAC POLY FLOAT):$ == (retract(u)@FEXPR(['X],[],MachineFloat))::$ - retractIfCan(u:FRAC POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR(['X],[],MachineFloat),"failed") - foo := retractIfCan(u)$FEXPR(['X],[],MachineFloat) - foo case "failed" => "failed" - foo::FEXPR(['X],[],MachineFloat)::$ - - retract(u:EXPR FLOAT):$ == (retract(u)@FEXPR(['X],[],MachineFloat))::$ - retractIfCan(u:EXPR FLOAT):Union($,"failed") == - foo : Union(FEXPR(['X],[],MachineFloat),"failed") - foo := retractIfCan(u)$FEXPR(['X],[],MachineFloat) - foo case "failed" => "failed" - foo::FEXPR(['X],[],MachineFloat)::$ - - retract(u:EXPR INT):$ == (retract(u)@FEXPR(['X],[],MachineFloat))::$ - retractIfCan(u:EXPR INT):Union($,"failed") == - foo : Union(FEXPR(['X],[],MachineFloat),"failed") - foo := retractIfCan(u)$FEXPR(['X],[],MachineFloat) - foo case "failed" => "failed" - foo::FEXPR(['X],[],MachineFloat)::$ - - retract(u:POLY FLOAT):$ == (retract(u)@FEXPR(['X],[],MachineFloat))::$ - retractIfCan(u:POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR(['X],[],MachineFloat),"failed") - foo := retractIfCan(u)$FEXPR(['X],[],MachineFloat) - foo case "failed" => "failed" - foo::FEXPR(['X],[],MachineFloat)::$ - - retract(u:POLY INT):$ == (retract(u)@FEXPR(['X],[],MachineFloat))::$ - retractIfCan(u:POLY INT):Union($,"failed") == - foo : Union(FEXPR(['X],[],MachineFloat),"failed") - foo := retractIfCan(u)$FEXPR(['X],[],MachineFloat) - foo case "failed" => "failed" - foo::FEXPR(['X],[],MachineFloat)::$ - - coerce(u:FEXPR(['X],[],MachineFloat)):$ == - coerce((u::Expression(MachineFloat))$FEXPR(['X],[],MachineFloat))$Rep - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP10 Asp10} -<<domain ASP10 Asp10>>= -)abbrev domain ASP10 Asp10 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 18 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp10(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - EXF ==> Expression Float - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FEXPR ==> FortranExpression(['JINT,'X,'ELAM],[],MFLOAT) - MFLOAT ==> MachineFloat - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - - Exports ==> FortranVectorFunctionCategory with - coerce : Vector FEXPR -> % - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : FST := "real"::FST - syms : SYMTAB := empty()$SYMTAB - declare!(P,fortranReal()$FT,syms)$SYMTAB - declare!(Q,fortranReal()$FT,syms)$SYMTAB - declare!(DQDL,fortranReal()$FT,syms)$SYMTAB - declare!(X,fortranReal()$FT,syms)$SYMTAB - declare!(ELAM,fortranReal()$FT,syms)$SYMTAB - declare!(JINT,fortranInteger()$FT,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$Union(fst:FST,void:"void"), - [P,Q,DQDL,X,ELAM,JINT],syms) - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - coerce(c:FortranCode):% == coerce(c)$Rep - - coerce(r:RSFC):% == coerce(r)$Rep - - coerce(c:List FortranCode):% == coerce(c)$Rep - - -- To help the poor old compiler! - localAssign(s:Symbol,u:Expression MFLOAT):FortranCode == - assign(s,u)$FortranCode - - coerce(u:Vector FEXPR):% == - import Vector FEXPR - not (#u = 3) => error "Incorrect Dimension For Vector" - ([localAssign(P,elt(u,1)::Expression MFLOAT),_ - localAssign(Q,elt(u,2)::Expression MFLOAT),_ - localAssign(DQDL,elt(u,3)::Expression MFLOAT),_ - returns()$FortranCode ]$List(FortranCode))::Rep - - coerce(u:%):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP12 Asp12} -<<domain ASP12 Asp12>>= -)abbrev domain ASP12 Asp12 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Oct 1993 -++ Date Last Updated: 18 March 1994 -++ 21 June 1994 Changed print to printStatement -++ Related Constructors: -++ Description: -++\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} -Asp12(name): Exports == Implementation where - name : Symbol - - O ==> OutputForm - S ==> Symbol - FST ==> FortranScalarType - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - EXI ==> Expression Integer - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - U ==> Union(I: Expression Integer,F: Expression Float,_ - CF: Expression Complex Float,switch:Switch) - UFST ==> Union(fst:FST,void:"void") - - Exports ==> FortranProgramCategory with - outputAsFortran:() -> Void - ++outputAsFortran() generates the default code for \spadtype{ASP12}. - - Implementation ==> add - - import FC - import Switch - - real : FST := "real"::FST - syms : SYMTAB := empty()$SYMTAB - declare!(MAXIT,fortranInteger()$FT,syms)$SYMTAB - declare!(IFLAG,fortranInteger()$FT,syms)$SYMTAB - declare!(ELAM,fortranReal()$FT,syms)$SYMTAB - fType : FT := construct([real]$UFST,["15"::Symbol],false)$FT - declare!(FINFO,fType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST,[MAXIT,IFLAG,ELAM,FINFO],syms) - - -- eqn : O := (I::O)=(1@Integer::EXI::O) - code:=([cond(EQ([MAXIT@S::EXI]$U,[-1::EXI]$U), - printStatement(["_"Output from Monit_""::O])), - printStatement([MAXIT::O,IFLAG::O,ELAM::O,subscript("(FINFO"::S,[I::O])::O,"I=1"::S::O,"4)"::S::O]), -- YUCK! - returns()]$List(FortranCode))::Rep - - coerce(u:%):OutputForm == coerce(u)$Rep - - outputAsFortran(u:%):Void == outputAsFortran(u)$Rep - outputAsFortran():Void == outputAsFortran(code)$Rep - -@ -\section{domain ASP19 Asp19} -<<domain ASP19 Asp19>>= -)abbrev domain ASP19 Asp19 -++ Author: Mike Dewar, Godfrey Nolan, Grant Keady -++ Date Created: Mar 1993 -++ Date Last Updated: 18 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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)=0.0D0 -++25004 CONTINUE -++25003 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} - -Asp19(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FC)) - FSTU ==> Union(fst:FST,void:"void") - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - MFLOAT ==> MachineFloat - VEC ==> Vector - VF2 ==> VectorFunctions2 - MF2 ==> MatrixCategoryFunctions2(FEXPR,VEC FEXPR,VEC FEXPR,Matrix FEXPR,EXPR MFLOAT,VEC EXPR MFLOAT,VEC EXPR MFLOAT,Matrix EXPR MFLOAT) - FEXPR ==> FortranExpression([],['XC],MFLOAT) - S ==> Symbol - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : FSTU := ["real"::FST]$FSTU - syms : SYMTAB := empty()$SYMTAB - declare!(M,fortranInteger()$FT,syms)$SYMTAB - declare!(N,fortranInteger()$FT,syms)$SYMTAB - declare!(LJC,fortranInteger()$FT,syms)$SYMTAB - xcType : FT := construct(real,[N],false)$FT - declare!(XC,xcType,syms)$SYMTAB - fveccType : FT := construct(real,[M],false)$FT - declare!(FVECC,fveccType,syms)$SYMTAB - fjaccType : FT := construct(real,[LJC,N],false)$FT - declare!(FJACC,fjaccType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$FSTU,[M,N,XC,FVECC,FJACC,LJC],syms) - - coerce(c:List FC):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FC):$ == coerce(c)$Rep - - -- Take a symbol, pull of the script and turn it into an integer!! - o2int(u:S):Integer == - o : OutputForm := first elt(scripts(u)$S,sub) - o pretend Integer - - -- To help the poor old compiler! - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign1(s:S,j:Matrix FEXPR):FC == - j' : Matrix EXPR MFLOAT := map(fexpr2expr,j)$MF2 - assign(s,j')$FC - - localAssign2(s:S,j:VEC FEXPR):FC == - j' : VEC EXPR MFLOAT := map(fexpr2expr,j)$VF2(FEXPR,EXPR MFLOAT) - assign(s,j')$FC - - coerce(u:VEC FEXPR):$ == - -- First zero the Jacobian matrix in case we miss some derivatives which - -- are zero. - import POLY INT - seg1 : Segment (POLY INT) := segment(1::(POLY INT),LJC@S::(POLY INT)) - seg2 : Segment (POLY INT) := segment(1::(POLY INT),N@S::(POLY INT)) - s1 : SegmentBinding POLY INT := equation(I@S,seg1) - s2 : SegmentBinding POLY INT := equation(J@S,seg2) - as : FC := assign(FJACC,[I@S::(POLY INT),J@S::(POLY INT)],0.0::EXPR FLOAT) - clear : FC := forLoop(s1,forLoop(s2,as)) - x:S := XC::S - pu:List(S) := [] - -- Work out which variables appear in the expressions - for e in entries(u) repeat - pu := setUnion(pu,variables(e)$FEXPR) - scriptList : List Integer := map(o2int,pu)$ListFunctions2(S,Integer) - -- This should be the maximum XC_n which occurs (there may be others - -- which don't): - n:Integer := reduce(max,scriptList)$List(Integer) - p:List(S) := [] - for j in 1..n repeat p:= cons(subscript(x,[j::OutputForm])$S,p) - p:= reverse(p) - jac:Matrix(FEXPR) := _ - jacobian(u,p)$MultiVariableCalculusFunctions(S,FEXPR,VEC FEXPR,List(S)) - c1:FC := localAssign2(FVECC,u) - c2:FC := localAssign1(FJACC,jac) - [clear,c1,c2,returns()]$List(FC)::$ - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - -@ -\section{domain ASP20 Asp20} -<<domain ASP20 Asp20>>= -)abbrev domain ASP20 Asp20 -++ Author: Mike Dewar and Godfrey Nolan and Grant Keady -++ Date Created: Dec 1993 -++ Date Last Updated: 21 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp20(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - PI ==> PositiveInteger - UFST ==> Union(fst:FST,void:"void") - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - MAT ==> Matrix - VF2 ==> VectorFunctions2 - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression([],['X,'HESS],MFLOAT) - O ==> OutputForm - M2 ==> MatrixCategoryFunctions2 - MF2a ==> M2(FRAC POLY INT,VEC FRAC POLY INT,VEC FRAC POLY INT, - MAT FRAC POLY INT,FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2b ==> M2(FRAC POLY FLOAT,VEC FRAC POLY FLOAT,VEC FRAC POLY FLOAT, - MAT FRAC POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2c ==> M2(POLY INT,VEC POLY INT,VEC POLY INT,MAT POLY INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2d ==> M2(POLY FLOAT,VEC POLY FLOAT,VEC POLY FLOAT, - MAT POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2e ==> M2(EXPR INT,VEC EXPR INT,VEC EXPR INT,MAT EXPR INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2f ==> M2(EXPR FLOAT,VEC EXPR FLOAT,VEC EXPR FLOAT, - MAT EXPR FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - - - Exports == Join(FortranMatrixFunctionCategory, CoercibleFrom MAT FEXPR) - Implementation == add - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty() - declare!(N,fortranInteger(),syms)$SYMTAB - declare!(NROWH,fortranInteger(),syms)$SYMTAB - declare!(NCOLH,fortranInteger(),syms)$SYMTAB - declare!(JTHCOL,fortranInteger(),syms)$SYMTAB - hessType : FT := construct(real,[NROWH,NCOLH],false)$FT - declare!(HESS,hessType,syms)$SYMTAB - xType : FT := construct(real,[N],false)$FT - declare!(X,xType,syms)$SYMTAB - declare!(HX,xType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST, - [N,NROWH,NCOLH,JTHCOL,HESS,X,HX],syms) - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - -- To help the poor old compiler! - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign(s:Symbol,j:VEC FEXPR):FortranCode == - j' : VEC EXPR MFLOAT := map(fexpr2expr,j)$VF2(FEXPR,EXPR MFLOAT) - assign(s,j')$FortranCode - - coerce(u:MAT FEXPR):$ == - x:Symbol := X::Symbol - n := nrows(u)::PI - p:VEC FEXPR := [retract(subscript(x,[j::O])$Symbol)@FEXPR for j in 1..n] - prod:VEC FEXPR := u*p - ([localAssign(HX,prod),returns()$FortranCode]$List(FortranCode))::$ - - retract(u:MAT FRAC POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2a - v::$ - - retractIfCan(u:MAT FRAC POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2a - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT FRAC POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2b - v::$ - - retractIfCan(u:MAT FRAC POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2b - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR INT):$ == - v : MAT FEXPR := map(retract,u)$MF2e - v::$ - - retractIfCan(u:MAT EXPR INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2e - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2f - v::$ - - retractIfCan(u:MAT EXPR FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2f - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2c - v::$ - - retractIfCan(u:MAT POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2c - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2d - v::$ - - retractIfCan(u:MAT POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2d - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - coerce(u:$):O == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP24 Asp24} -<<domain ASP24 Asp24>>= -)abbrev domain ASP24 Asp24 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 21 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp24(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FSTU ==> Union(fst:FST,void:"void") - FEXPR ==> FortranExpression([],['XC],MachineFloat) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - - Exports ==> FortranFunctionCategory with - coerce : FEXPR -> $ - ++ coerce(f) takes an object from the appropriate instantiation of - ++ \spadtype{FortranExpression} and turns it into an ASP. - - - Implementation ==> add - - - real : FSTU := ["real"::FST]$FSTU - syms : SYMTAB := empty() - declare!(N,fortranInteger(),syms)$SYMTAB - xcType : FT := construct(real,[N::Symbol],false)$FT - declare!(XC,xcType,syms)$SYMTAB - declare!(FC,fortranReal(),syms)$SYMTAB - Rep := FortranProgram(name,["void"]$FSTU,[N,XC,FC],syms) - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:FEXPR):$ == - coerce(assign(FC,u::Expression(MachineFloat))$FortranCode)$Rep - - retract(u:FRAC POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:FRAC POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:EXPR FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:EXPR INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP27 Asp27} -<<domain ASP27 Asp27>>= -)abbrev domain ASP27 Asp27 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Nov 1993 -++ Date Last Updated: 27 April 1994 -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\spadtype{Asp27} produces Fortran for Type 27 ASPs, needed for NAG routine -++\axiomOpFrom{f02fjf}{f02Package} ,for example: -++\begin{verbatim} -++ FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) -++ DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) -++ INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) -++ DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 -++ &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( -++ &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 -++ &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( -++ &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) -++ &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) -++ &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. -++ &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 -++ &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( -++ &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) -++ RETURN -++ END -++\end{verbatim} - -Asp27(name): Exports == Implementation where - name : Symbol - - O ==> OutputForm - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - UFST ==> Union(fst:FST,void:"void") - FC ==> FortranCode - PI ==> PositiveInteger - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - EXPR ==> Expression - MAT ==> Matrix - MFLOAT ==> MachineFloat - - - - Exports == FortranMatrixCategory - - Implementation == add - - - real : UFST := ["real"::FST]$UFST - integer : UFST := ["integer"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!(IFLAG,fortranInteger(),syms)$SYMTAB - declare!(N,fortranInteger(),syms)$SYMTAB - declare!(LRWORK,fortranInteger(),syms)$SYMTAB - declare!(LIWORK,fortranInteger(),syms)$SYMTAB - zType : FT := construct(real,[N],false)$FT - declare!(Z,zType,syms)$SYMTAB - declare!(W,zType,syms)$SYMTAB - rType : FT := construct(real,[LRWORK],false)$FT - declare!(RWORK,rType,syms)$SYMTAB - iType : FT := construct(integer,[LIWORK],false)$FT - declare!(IWORK,iType,syms)$SYMTAB - Rep := FortranProgram(name,real, - [IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK],syms) - - -- To help the poor old compiler! - localCoerce(u:Symbol):EXPR(MFLOAT) == coerce(u)$EXPR(MFLOAT) - - coerce (u:MAT MFLOAT):$ == - Ws: Symbol := W - Zs: Symbol := Z - code : List FC - l:EXPR MFLOAT := "+"/ _ - [("+"/[localCoerce(elt(Ws,[j::O])$Symbol) * u(j,i)_ - for j in 1..nrows(u)::PI])_ - *localCoerce(elt(Zs,[i::O])$Symbol) for i in 1..ncols(u)::PI] - c := assign(name,l)$FC - code := [c,returns()]$List(FC) - code::$ - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP28 Asp28} -<<domain ASP28 Asp28>>= -)abbrev domain ASP28 Asp28 -++ Author: Mike Dewar -++ Date Created: 21 March 1994 -++ Date Last Updated: 28 April 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp28(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - FC ==> FortranCode - PI ==> PositiveInteger - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - EXPR ==> Expression - MFLOAT ==> MachineFloat - VEC ==> Vector - UFST ==> Union(fst:FST,void:"void") - MAT ==> Matrix - - Exports == FortranMatrixCategory - - Implementation == add - - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty() - declare!(IFLAG,fortranInteger(),syms)$SYMTAB - declare!(N,fortranInteger(),syms)$SYMTAB - declare!(LRWORK,fortranInteger(),syms)$SYMTAB - declare!(LIWORK,fortranInteger(),syms)$SYMTAB - xType : FT := construct(real,[N],false)$FT - declare!(Z,xType,syms)$SYMTAB - declare!(W,xType,syms)$SYMTAB - rType : FT := construct(real,[LRWORK],false)$FT - declare!(RWORK,rType,syms)$SYMTAB - iType : FT := construct(real,[LIWORK],false)$FT - declare!(IWORK,rType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST, - [IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK],syms) - - -- To help the poor old compiler! - localCoerce(u:Symbol):EXPR(MFLOAT) == coerce(u)$EXPR(MFLOAT) - - coerce (u:MAT MFLOAT):$ == - Zs: Symbol := Z - code : List FC - r: List EXPR MFLOAT - r := ["+"/[u(j,i)*localCoerce(elt(Zs,[i::OutputForm])$Symbol)_ - for i in 1..ncols(u)$MAT(MFLOAT)::PI]_ - for j in 1..nrows(u)$MAT(MFLOAT)::PI] - code := [assign(W@Symbol,vector(r)$VEC(EXPR MFLOAT)),returns()]$List(FC) - code::$ - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP29 Asp29} -<<domain ASP29 Asp29>>= -)abbrev domain ASP29 Asp29 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Nov 1993 -++ Date Last Updated: 18 March 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp29(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - FSTU ==> Union(fst:FST,void:"void") - SYMTAB ==> SymbolTable - FC ==> FortranCode - PI ==> PositiveInteger - EXF ==> Expression Float - EXI ==> Expression Integer - VEF ==> Vector Expression Float - VEI ==> Vector Expression Integer - MEI ==> Matrix Expression Integer - MEF ==> Matrix Expression Float - UEXPR ==> Union(I: Expression Integer,F: Expression Float,_ - CF: Expression Complex Float) - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - - Exports == FortranProgramCategory with - outputAsFortran:() -> Void - ++outputAsFortran() generates the default code for \spadtype{ASP29}. - - - Implementation == add - - import FST - import FT - import FC - import SYMTAB - - real : FSTU := ["real"::FST]$FSTU - integer : FSTU := ["integer"::FST]$FSTU - syms : SYMTAB := empty() - declare!(ISTATE,fortranInteger(),syms) - declare!(NEXTIT,fortranInteger(),syms) - declare!(NEVALS,fortranInteger(),syms) - declare!(NVECS,fortranInteger(),syms) - declare!(K,fortranInteger(),syms) - kType : FT := construct(real,[K],false)$FT - declare!(F,kType,syms) - declare!(D,kType,syms) - Rep := FortranProgram(name,["void"]$FSTU, - [ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D],syms) - - - outputAsFortran():Void == - callOne := call("F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)") - code : List FC := [callOne,returns()]$List(FC) - outputAsFortran(coerce(code)@Rep)$Rep - -@ -\section{domain ASP30 Asp30} -<<domain ASP30 Asp30>>= -)abbrev domain ASP30 Asp30 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Nov 1993 -++ Date Last Updated: 28 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp30(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - FC ==> FortranCode - PI ==> PositiveInteger - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - UFST ==> Union(fst:FST,void:"void") - MAT ==> Matrix - MFLOAT ==> MachineFloat - EXI ==> Expression Integer - UEXPR ==> Union(I:Expression Integer,F:Expression Float,_ - CF:Expression Complex Float,switch:Switch) - S ==> Symbol - - Exports == FortranMatrixCategory - - Implementation == add - - import FC - import FT - import Switch - - real : UFST := ["real"::FST]$UFST - integer : UFST := ["integer"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!(MODE,fortranInteger()$FT,syms)$SYMTAB - declare!(M,fortranInteger()$FT,syms)$SYMTAB - declare!(N,fortranInteger()$FT,syms)$SYMTAB - declare!(LRWORK,fortranInteger()$FT,syms)$SYMTAB - declare!(LIWORK,fortranInteger()$FT,syms)$SYMTAB - xType : FT := construct(real,[N],false)$FT - declare!(X,xType,syms)$SYMTAB - yType : FT := construct(real,[M],false)$FT - declare!(Y,yType,syms)$SYMTAB - rType : FT := construct(real,[LRWORK],false)$FT - declare!(RWORK,rType,syms)$SYMTAB - iType : FT := construct(integer,[LIWORK],false)$FT - declare!(IWORK,iType,syms)$SYMTAB - declare!(IFAIL,fortranInteger()$FT,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST, - [MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK],syms) - - coerce(a:MAT MFLOAT):$ == - locals : SYMTAB := empty() - numRows := nrows(a) :: Polynomial Integer - numCols := ncols(a) :: Polynomial Integer - declare!(A,[real,[numRows,numCols],false]$FT,locals) - declare!(F06PAF@S,construct(["void"]$UFST,[]@List(S),true)$FT,locals) - ptA:UEXPR := [("MODE"::S)::EXI] - ptB:UEXPR := [1::EXI] - ptC:UEXPR := [2::EXI] - sw1 : Switch := EQ(ptA,ptB)$Switch - sw2 : Switch := EQ(ptA,ptC)$Switch - callOne := call("F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)") - callTwo := call("F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)") - c : FC := cond(sw1,callOne,cond(sw2,callTwo)) - code' : List FC := [assign(A,a),c,returns()] - ([locals,code']$RSFC)::$ - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP31 Asp31} -<<domain ASP31 Asp31>>= -)abbrev domain ASP31 Asp31 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 22 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranMatrixFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp31(name): Exports == Implementation where - name : Symbol - - O ==> OutputForm - FST ==> FortranScalarType - UFST ==> Union(fst:FST,void:"void") - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['X],['Y],MFLOAT) - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - MAT ==> Matrix - VF2 ==> VectorFunctions2 - MF2 ==> MatrixCategoryFunctions2(FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR, - EXPR MFLOAT,VEC EXPR MFLOAT,VEC EXPR MFLOAT,MAT EXPR MFLOAT) - - - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty() - declare!(X,fortranReal(),syms)$SYMTAB - yType : FT := construct(real,["*"::Symbol],false)$FT - declare!(Y,yType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST,[X,Y,PW],syms) - - -- To help the poor old compiler! - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign(s:Symbol,j:MAT FEXPR):FC == - j' : MAT EXPR MFLOAT := map(fexpr2expr,j)$MF2 - assign(s,j')$FC - - makeXList(n:Integer):List(Symbol) == - y:Symbol := Y::Symbol - p:List(Symbol) := [] - for j in 1 .. n repeat p:= cons(subscript(y,[j::OutputForm])$Symbol,p) - p:= reverse(p) - - coerce(u:VEC FEXPR):$ == - dimension := #u::Polynomial Integer - locals : SYMTAB := empty() - declare!(PW,[real,[dimension,dimension],false]$FT,locals)$SYMTAB - n:Integer := maxIndex(u)$VEC(FEXPR) - p:List(Symbol) := makeXList(n) - jac: MAT FEXPR := jacobian(u,p)$MultiVariableCalculusFunctions(_ - Symbol,FEXPR ,VEC FEXPR,List(Symbol)) - code' : List FC := [localAssign(PW,jac),returns()$FC]$List(FC) - ([locals,code']$RSFC)::$ - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - coerce(c:List FC):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FC):$ == coerce(c)$Rep - - coerce(u:$):O == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP33 Asp33} -<<domain ASP33 Asp33>>= -)abbrev domain ASP33 Asp33 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Nov 1993 -++ Date Last Updated: 30 March 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory. -++ Description: -++\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} - -Asp33(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - UFST ==> Union(fst:FST,void:"void") - FT ==> FortranType - SYMTAB ==> SymbolTable - FC ==> FortranCode - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - - Exports ==> FortranProgramCategory with - outputAsFortran:() -> Void - ++outputAsFortran() generates the default code for \spadtype{ASP33}. - - - Implementation ==> add - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty() - declare!(JINT,fortranInteger(),syms)$SYMTAB - declare!(X,fortranReal(),syms)$SYMTAB - vType : FT := construct(real,["3"::Symbol],false)$FT - declare!(V,vType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST,[X,V,JINT],syms) - - outputAsFortran():Void == - outputAsFortran( (returns()$FortranCode)::Rep )$Rep - - outputAsFortran(u):Void == outputAsFortran(u)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - -@ -\section{domain ASP34 Asp34} -<<domain ASP34 Asp34>>= -)abbrev domain ASP34 Asp34 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Nov 1993 -++ Date Last Updated: 14 June 1994 (Themos Tsikas) -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\spadtype{Asp34} produces Fortran for Type 34 ASPs, needed for NAG routine -++\axiomOpFrom{f04mbf}{f04Package}, for example: -++\begin{verbatim} -++ SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) -++ DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) -++ INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) -++ DOUBLE PRECISION W1(3),W2(3),MS(3,3) -++ IFLAG=-1 -++ MS(1,1)=2.0D0 -++ MS(1,2)=1.0D0 -++ MS(1,3)=0.0D0 -++ MS(2,1)=1.0D0 -++ MS(2,2)=2.0D0 -++ MS(2,3)=1.0D0 -++ MS(3,1)=0.0D0 -++ MS(3,2)=1.0D0 -++ MS(3,3)=2.0D0 -++ CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) -++ IFLAG=-IFLAG -++ RETURN -++ END -++\end{verbatim} - -Asp34(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - UFST ==> Union(fst:FST,void:"void") - SYMTAB ==> SymbolTable - FC ==> FortranCode - PI ==> PositiveInteger - EXI ==> Expression Integer - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - - Exports == FortranMatrixCategory - - Implementation == add - - real : UFST := ["real"::FST]$UFST - integer : UFST := ["integer"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!('IFLAG,fortranInteger(),syms)$SYMTAB - declare!('N,fortranInteger(),syms)$SYMTAB - xType : FT := construct(real,['N],false)$FT - declare!('X,xType,syms)$SYMTAB - declare!('Y,xType,syms)$SYMTAB - declare!('LRWORK,fortranInteger(),syms)$SYMTAB - declare!('LIWORK,fortranInteger(),syms)$SYMTAB - rType : FT := construct(real,['LRWORK],false)$FT - declare!('RWORK,rType,syms)$SYMTAB - iType : FT := construct(integer,['LIWORK],false)$FT - declare!('IWORK,iType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST, - ['IFLAG,'N,'X,'Y,'RWORK,'LRWORK,'IWORK,'LIWORK],syms) - - -- To help the poor old compiler - localAssign(s:Symbol,u:EXI):FC == assign(s,u)$FC - - coerce(u:Matrix MachineFloat):$ == - dimension := nrows(u) ::Polynomial Integer - locals : SYMTAB := empty()$SYMTAB - declare!('I,fortranInteger(),syms)$SYMTAB - declare!('J,fortranInteger(),syms)$SYMTAB - declare!('W1,[real,[dimension],false]$FT,locals)$SYMTAB - declare!('W2,[real,[dimension],false]$FT,locals)$SYMTAB - declare!('MS,[real,[dimension,dimension],false]$FT,locals)$SYMTAB - assign1 : FC := localAssign('IFLAG,(-1)@EXI) - call : FC := call("F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)")$FC - assign2 : FC := localAssign('IFLAG,-('IFLAG::EXI)) - assign3 : FC := assign('MS,u)$FC - code' : List FC := [assign1,assign3,call,assign2,returns()]$List(FC) - ([locals,code']$RSFC)::$ - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP35 Asp35} -<<domain ASP35 Asp35>>= -)abbrev domain ASP35 Asp35 -++ Author: Mike Dewar, Godfrey Nolan, Grant Keady -++ Date Created: Mar 1993 -++ Date Last Updated: 22 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp35(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - UFST ==> Union(fst:FST,void:"void") - SYMTAB ==> SymbolTable - FC ==> FortranCode - PI ==> PositiveInteger - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - MAT ==> Matrix - VF2 ==> VectorFunctions2 - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression([],['X],MFLOAT) - MF2 ==> MatrixCategoryFunctions2(FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR, - EXPR MFLOAT,VEC EXPR MFLOAT,VEC EXPR MFLOAT,MAT EXPR MFLOAT) - SWU ==> Union(I:Expression Integer,F:Expression Float, - CF:Expression Complex Float,switch:Switch) - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!(N,fortranInteger(),syms)$SYMTAB - xType : FT := construct(real,[N],false)$FT - declare!(X,xType,syms)$SYMTAB - declare!(FVEC,xType,syms)$SYMTAB - declare!(LDFJAC,fortranInteger(),syms)$SYMTAB - jType : FT := construct(real,[LDFJAC,N],false)$FT - declare!(FJAC,jType,syms)$SYMTAB - declare!(IFLAG,fortranInteger(),syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST,[N,X,FVEC,FJAC,LDFJAC,IFLAG],syms) - - coerce(u:$):OutputForm == coerce(u)$Rep - - makeXList(n:Integer):List(Symbol) == - x:Symbol := X::Symbol - [subscript(x,[j::OutputForm])$Symbol for j in 1..n] - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign1(s:Symbol,j:MAT FEXPR):FC == - j' : MAT EXPR MFLOAT := map(fexpr2expr,j)$MF2 - assign(s,j')$FC - - localAssign2(s:Symbol,j:VEC FEXPR):FC == - j' : VEC EXPR MFLOAT := map(fexpr2expr,j)$VF2(FEXPR,EXPR MFLOAT) - assign(s,j')$FC - - coerce(u:VEC FEXPR):$ == - n:Integer := maxIndex(u) - p:List(Symbol) := makeXList(n) - jac: MAT FEXPR := jacobian(u,p)$MultiVariableCalculusFunctions(_ - Symbol,FEXPR,VEC FEXPR,List(Symbol)) - assf:FC := localAssign2(FVEC,u) - assj:FC := localAssign1(FJAC,jac) - iflag:SWU := [IFLAG@Symbol::EXPR(INT)]$SWU - sw1:Switch := EQ(iflag,[1::EXPR(INT)]$SWU) - sw2:Switch := EQ(iflag,[2::EXPR(INT)]$SWU) - cond(sw1,assf,cond(sw2,assj)$FC)$FC::$ - - coerce(c:List FC):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FC):$ == coerce(c)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - -@ -\section{domain ASP4 Asp4} -<<domain ASP4 Asp4>>= -)abbrev domain ASP4 Asp4 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 18 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\spadtype{Asp4} produces Fortran for Type 4 ASPs, which take an expression -++in X(1) .. 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} - -Asp4(name): Exports == Implementation where - name : Symbol - - FEXPR ==> FortranExpression([],['X],MachineFloat) - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FSTU ==> Union(fst:FST,void:"void") - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - - Exports ==> FortranFunctionCategory with - coerce : FEXPR -> $ - ++coerce(f) takes an object from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns it into an ASP. - - Implementation ==> add - - real : FSTU := ["real"::FST]$FSTU - syms : SYMTAB := empty()$SYMTAB - declare!(NDIM,fortranInteger(),syms)$SYMTAB - xType : FT := construct(real,[NDIM],false)$FT - declare!(X,xType,syms)$SYMTAB - Rep := FortranProgram(name,real,[NDIM,X],syms) - - retract(u:FRAC POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - foo::FEXPR::$ - - retract(u:FRAC POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - foo::FEXPR::$ - - retract(u:EXPR FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - foo::FEXPR::$ - - retract(u:EXPR INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - foo::FEXPR::$ - - retract(u:POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - foo::FEXPR::$ - - retract(u:POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - foo::FEXPR::$ - - coerce(u:FEXPR):$ == - coerce((u::Expression(MachineFloat))$FEXPR)$Rep - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP41 Asp41} -<<domain ASP41 Asp41>>= -)abbrev domain ASP41 Asp41 -++ Author: Mike Dewar, Godfrey Nolan -++ Date Created: -++ Date Last Updated: 29 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranFunctionCategory, FortranProgramCategory. -++ Description: -++\spadtype{Asp41} produces Fortran for Type 41 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 Y(i) and also a continuation parameter EPS, for example: -++\begin{verbatim} -++ SUBROUTINE FCN(X,EPS,Y,F,N) -++ DOUBLE PRECISION EPS,F(N),X,Y(N) -++ INTEGER N -++ F(1)=Y(2) -++ F(2)=Y(3) -++ F(3)=(-1.0D0*Y(1)*Y(3))+2.0D0*EPS*Y(2)**2+(-2.0D0*EPS) -++ RETURN -++ END -++ SUBROUTINE JACOBF(X,EPS,Y,F,N) -++ DOUBLE PRECISION EPS,F(N,N),X,Y(N) -++ INTEGER N -++ F(1,1)=0.0D0 -++ F(1,2)=1.0D0 -++ F(1,3)=0.0D0 -++ F(2,1)=0.0D0 -++ F(2,2)=0.0D0 -++ F(2,3)=1.0D0 -++ F(3,1)=-1.0D0*Y(3) -++ F(3,2)=4.0D0*EPS*Y(2) -++ F(3,3)=-1.0D0*Y(1) -++ RETURN -++ END -++ SUBROUTINE JACEPS(X,EPS,Y,F,N) -++ DOUBLE PRECISION EPS,F(N),X,Y(N) -++ INTEGER N -++ F(1)=0.0D0 -++ F(2)=0.0D0 -++ F(3)=2.0D0*Y(2)**2-2.0D0 -++ RETURN -++ END -++\end{verbatim} - -Asp41(nameOne,nameTwo,nameThree): Exports == Implementation where - nameOne : Symbol - nameTwo : Symbol - nameThree : Symbol - - D ==> differentiate - FST ==> FortranScalarType - UFST ==> Union(fst:FST,void:"void") - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['X,'EPS],['Y],MFLOAT) - S ==> Symbol - MF2 ==> MatrixCategoryFunctions2(FEXPR,VEC FEXPR,VEC FEXPR,Matrix FEXPR, - EXPR MFLOAT,VEC EXPR MFLOAT,VEC EXPR MFLOAT,Matrix EXPR MFLOAT) - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - real : UFST := ["real"::FST]$UFST - - symOne : SYMTAB := empty()$SYMTAB - declare!(N,fortranInteger(),symOne)$SYMTAB - declare!(X,fortranReal(),symOne)$SYMTAB - declare!(EPS,fortranReal(),symOne)$SYMTAB - yType : FT := construct(real,[N],false)$FT - declare!(Y,yType,symOne)$SYMTAB - declare!(F,yType,symOne)$SYMTAB - - symTwo : SYMTAB := empty()$SYMTAB - declare!(N,fortranInteger(),symTwo)$SYMTAB - declare!(X,fortranReal(),symTwo)$SYMTAB - declare!(EPS,fortranReal(),symTwo)$SYMTAB - declare!(Y,yType,symTwo)$SYMTAB - fType : FT := construct(real,[N,N],false)$FT - declare!(F,fType,symTwo)$SYMTAB - - symThree : SYMTAB := empty()$SYMTAB - declare!(N,fortranInteger(),symThree)$SYMTAB - declare!(X,fortranReal(),symThree)$SYMTAB - declare!(EPS,fortranReal(),symThree)$SYMTAB - declare!(Y,yType,symThree)$SYMTAB - declare!(F,yType,symThree)$SYMTAB - - R1:=FortranProgram(nameOne,["void"]$UFST,[X,EPS,Y,F,N],symOne) - R2:=FortranProgram(nameTwo,["void"]$UFST,[X,EPS,Y,F,N],symTwo) - R3:=FortranProgram(nameThree,["void"]$UFST,[X,EPS,Y,F,N],symThree) - Rep := Record(f:R1,fJacob:R2,eJacob:R3) - Fsym:Symbol:=coerce "F" - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign1(s:S,j:Matrix FEXPR):FC == - j' : Matrix EXPR MFLOAT := map(fexpr2expr,j)$MF2 - assign(s,j')$FC - - localAssign2(s:S,j:VEC FEXPR):FC == - j' : VEC EXPR MFLOAT := map(fexpr2expr,j)$VF2(FEXPR,EXPR MFLOAT) - assign(s,j')$FC - - makeCodeOne(u:VEC FEXPR):FortranCode == - -- simple assign - localAssign2(Fsym,u) - - makeCodeThree(u:VEC FEXPR):FortranCode == - -- compute jacobian wrt to eps - jacEps:VEC FEXPR := [D(v,EPS) for v in entries(u)]$VEC(FEXPR) - makeCodeOne(jacEps) - - makeYList(n:Integer):List(Symbol) == - y:Symbol := Y::Symbol - p:List(Symbol) := [] - [subscript(y,[j::OutputForm])$Symbol for j in 1..n] - - makeCodeTwo(u:VEC FEXPR):FortranCode == - -- compute jacobian wrt to f - n:Integer := maxIndex(u)$VEC(FEXPR) - p:List(Symbol) := makeYList(n) - jac:Matrix(FEXPR) := _ - jacobian(u,p)$MultiVariableCalculusFunctions(S,FEXPR,VEC FEXPR,List(S)) - localAssign1(Fsym,jac) - - coerce(u:VEC FEXPR):$ == - aF:FortranCode := makeCodeOne(u) - bF:FortranCode := makeCodeTwo(u) - cF:FortranCode := makeCodeThree(u) - -- add returns() to complete subroutines - aLF:List(FortranCode) := [aF,returns()$FortranCode]$List(FortranCode) - bLF:List(FortranCode) := [bF,returns()$FortranCode]$List(FortranCode) - cLF:List(FortranCode) := [cF,returns()$FortranCode]$List(FortranCode) - [coerce(aLF)$R1,coerce(bLF)$R2,coerce(cLF)$R3] - - coerce(u:$):OutputForm == - bracket commaSeparate - [nameOne::OutputForm,nameTwo::OutputForm,nameThree::OutputForm] - - outputAsFortran(u:$):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran elt(u,f)$Rep - outputAsFortran elt(u,fJacob)$Rep - outputAsFortran elt(u,eJacob)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - -@ -\section{domain ASP42 Asp42} -<<domain ASP42 Asp42>>= -)abbrev domain ASP42 Asp42 -++ Author: Mike Dewar, Godfrey Nolan -++ Date Created: -++ Date Last Updated: 29 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranFunctionCategory, FortranProgramCategory. -++ Description: -++\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 Y(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} - -Asp42(nameOne,nameTwo,nameThree): Exports == Implementation where - nameOne : Symbol - nameTwo : Symbol - nameThree : Symbol - - D ==> differentiate - FST ==> FortranScalarType - FT ==> FortranType - FP ==> FortranProgram - FC ==> FortranCode - PI ==> PositiveInteger - NNI ==> NonNegativeInteger - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - UFST ==> Union(fst:FST,void:"void") - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['EPS],['YA,'YB],MFLOAT) - S ==> Symbol - MF2 ==> MatrixCategoryFunctions2(FEXPR,VEC FEXPR,VEC FEXPR,Matrix FEXPR, - EXPR MFLOAT,VEC EXPR MFLOAT,VEC EXPR MFLOAT,Matrix EXPR MFLOAT) - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - real : UFST := ["real"::FST]$UFST - - symOne : SYMTAB := empty()$SYMTAB - declare!(EPS,fortranReal(),symOne)$SYMTAB - declare!(N,fortranInteger(),symOne)$SYMTAB - yType : FT := construct(real,[N],false)$FT - declare!(YA,yType,symOne)$SYMTAB - declare!(YB,yType,symOne)$SYMTAB - declare!(BC,yType,symOne)$SYMTAB - - symTwo : SYMTAB := empty()$SYMTAB - declare!(EPS,fortranReal(),symTwo)$SYMTAB - declare!(N,fortranInteger(),symTwo)$SYMTAB - declare!(YA,yType,symTwo)$SYMTAB - declare!(YB,yType,symTwo)$SYMTAB - ajType : FT := construct(real,[N,N],false)$FT - declare!(AJ,ajType,symTwo)$SYMTAB - declare!(BJ,ajType,symTwo)$SYMTAB - - symThree : SYMTAB := empty()$SYMTAB - declare!(EPS,fortranReal(),symThree)$SYMTAB - declare!(N,fortranInteger(),symThree)$SYMTAB - declare!(YA,yType,symThree)$SYMTAB - declare!(YB,yType,symThree)$SYMTAB - declare!(BCEP,yType,symThree)$SYMTAB - - rt := ["void"]$UFST - R1:=FortranProgram(nameOne,rt,[EPS,YA,YB,BC,N],symOne) - R2:=FortranProgram(nameTwo,rt,[EPS,YA,YB,AJ,BJ,N],symTwo) - R3:=FortranProgram(nameThree,rt,[EPS,YA,YB,BCEP,N],symThree) - Rep := Record(g:R1,gJacob:R2,geJacob:R3) - BCsym:Symbol:=coerce "BC" - AJsym:Symbol:=coerce "AJ" - BJsym:Symbol:=coerce "BJ" - BCEPsym:Symbol:=coerce "BCEP" - - makeList(n:Integer,s:Symbol):List(Symbol) == - p:List(Symbol) := [] - for j in 1 .. n repeat p:= cons(subscript(s,[j::OutputForm])$Symbol,p) - reverse(p) - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign1(s:S,j:Matrix FEXPR):FC == - j' : Matrix EXPR MFLOAT := map(fexpr2expr,j)$MF2 - assign(s,j')$FC - - localAssign2(s:S,j:VEC FEXPR):FC == - j' : VEC EXPR MFLOAT := map(fexpr2expr,j)$VF2(FEXPR,EXPR MFLOAT) - assign(s,j')$FC - - makeCodeOne(u:VEC FEXPR):FortranCode == - -- simple assign - localAssign2(BCsym,u) - - makeCodeTwo(u:VEC FEXPR):List(FortranCode) == - -- compute jacobian wrt to ya - n:Integer := maxIndex(u) - p:List(Symbol) := makeList(n,YA::Symbol) - jacYA:Matrix(FEXPR) := _ - jacobian(u,p)$MultiVariableCalculusFunctions(S,FEXPR,VEC FEXPR,List(S)) - -- compute jacobian wrt to yb - p:List(Symbol) := makeList(n,YB::Symbol) - jacYB: Matrix(FEXPR) := _ - jacobian(u,p)$MultiVariableCalculusFunctions(S,FEXPR,VEC FEXPR,List(S)) - -- assign jacobians to AJ & BJ - [localAssign1(AJsym,jacYA),localAssign1(BJsym,jacYB),returns()$FC]$List(FC) - - makeCodeThree(u:VEC FEXPR):FortranCode == - -- compute jacobian wrt to eps - jacEps:VEC FEXPR := [D(v,EPS) for v in entries u]$VEC(FEXPR) - localAssign2(BCEPsym,jacEps) - - coerce(u:VEC FEXPR):$ == - aF:FortranCode := makeCodeOne(u) - bF:List(FortranCode) := makeCodeTwo(u) - cF:FortranCode := makeCodeThree(u) - -- add returns() to complete subroutines - aLF:List(FortranCode) := [aF,returns()$FC]$List(FortranCode) - cLF:List(FortranCode) := [cF,returns()$FC]$List(FortranCode) - [coerce(aLF)$R1,coerce(bF)$R2,coerce(cLF)$R3] - - coerce(u:$) : OutputForm == - bracket commaSeparate - [nameOne::OutputForm,nameTwo::OutputForm,nameThree::OutputForm] - - outputAsFortran(u:$):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran elt(u,g)$Rep - outputAsFortran elt(u,gJacob)$Rep - outputAsFortran elt(u,geJacob)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - -@ -\section{domain ASP49 Asp49} -<<domain ASP49 Asp49>>= -)abbrev domain ASP49 Asp49 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 23 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp49(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - UFST ==> Union(fst:FST,void:"void") - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FC)) - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression([],['X],MFLOAT) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - S ==> Symbol - - Exports ==> FortranFunctionCategory with - coerce : FEXPR -> $ - ++coerce(f) takes an object from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns it into an ASP. - - Implementation ==> add - - real : UFST := ["real"::FST]$UFST - integer : UFST := ["integer"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!(MODE,fortranInteger(),syms)$SYMTAB - declare!(N,fortranInteger(),syms)$SYMTAB - xType : FT := construct(real,[N::S],false)$FT - declare!(X,xType,syms)$SYMTAB - declare!(OBJF,fortranReal(),syms)$SYMTAB - declare!(OBJGRD,xType,syms)$SYMTAB - declare!(NSTATE,fortranInteger(),syms)$SYMTAB - iuType : FT := construct(integer,["*"::S],false)$FT - declare!(IUSER,iuType,syms)$SYMTAB - uType : FT := construct(real,["*"::S],false)$FT - declare!(USER,uType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST, - [MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER],syms) - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign(s:S,j:VEC FEXPR):FC == - j' : VEC EXPR MFLOAT := map(fexpr2expr,j)$VF2(FEXPR,EXPR MFLOAT) - assign(s,j')$FC - - coerce(u:FEXPR):$ == - vars:List(S) := variables(u) - grd:VEC FEXPR := gradient(u,vars)$MultiVariableCalculusFunctions(_ - S,FEXPR,VEC FEXPR,List(S)) - code : List(FC) := [assign(OBJF@S,fexpr2expr u)$FC,_ - localAssign(OBJGRD@S,grd),_ - returns()$FC] - code::$ - - coerce(u:$):OutputForm == coerce(u)$Rep - - coerce(c:List FC):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FC):$ == coerce(c)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:FRAC POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:FRAC POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:EXPR FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:EXPR INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - -@ -\section{domain ASP50 Asp50} -<<domain ASP50 Asp50>>= -)abbrev domain ASP50 Asp50 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 23 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp50(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - UFST ==> Union(fst:FST,void:"void") - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - FEXPR ==> FortranExpression([],['XC],MFLOAT) - MFLOAT ==> MachineFloat - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!(M,fortranInteger(),syms)$SYMTAB - declare!(N,fortranInteger(),syms)$SYMTAB - xcType : FT := construct(real,[N],false)$FT - declare!(XC,xcType,syms)$SYMTAB - fveccType : FT := construct(real,[M],false)$FT - declare!(FVECC,fveccType,syms)$SYMTAB - declare!(I,fortranInteger(),syms)$SYMTAB - tType : FT := construct(real,[M,N],false)$FT --- declare!(TC,tType,syms)$SYMTAB --- declare!(Y,fveccType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST, [M,N,XC,FVECC],syms) - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - coerce(u:VEC FEXPR):$ == - u' : VEC EXPR MFLOAT := map(fexpr2expr,u)$VF2(FEXPR,EXPR MFLOAT) - assign(FVECC,u')$FortranCode::$ - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP55 Asp55} -<<domain ASP55 Asp55>>= -)abbrev domain ASP55 Asp55 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: June 1993 -++ Date Last Updated: 23 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp55(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - FSTU ==> Union(fst:FST,void:"void") - SYMTAB ==> SymbolTable - FC ==> FortranCode - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - S ==> Symbol - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - MAT ==> Matrix - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression([],['X],MFLOAT) - MF2 ==> MatrixCategoryFunctions2(FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR, - EXPR MFLOAT,VEC EXPR MFLOAT,VEC EXPR MFLOAT,MAT EXPR MFLOAT) - SWU ==> Union(I:Expression Integer,F:Expression Float, - CF:Expression Complex Float,switch:Switch) - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : FSTU := ["real"::FST]$FSTU - integer : FSTU := ["integer"::FST]$FSTU - syms : SYMTAB := empty()$SYMTAB - declare!(MODE,fortranInteger(),syms)$SYMTAB - declare!(NCNLN,fortranInteger(),syms)$SYMTAB - declare!(N,fortranInteger(),syms)$SYMTAB - declare!(NROWJ,fortranInteger(),syms)$SYMTAB - needcType : FT := construct(integer,[NCNLN::Symbol],false)$FT - declare!(NEEDC,needcType,syms)$SYMTAB - xType : FT := construct(real,[N::Symbol],false)$FT - declare!(X,xType,syms)$SYMTAB - cType : FT := construct(real,[NCNLN::Symbol],false)$FT - declare!(C,cType,syms)$SYMTAB - cjacType : FT := construct(real,[NROWJ::Symbol,N::Symbol],false)$FT - declare!(CJAC,cjacType,syms)$SYMTAB - declare!(NSTATE,fortranInteger(),syms)$SYMTAB - iuType : FT := construct(integer,["*"::Symbol],false)$FT - declare!(IUSER,iuType,syms)$SYMTAB - uType : FT := construct(real,["*"::Symbol],false)$FT - declare!(USER,uType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$FSTU, - [MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER,USER],syms) - - -- Take a symbol, pull of the script and turn it into an integer!! - o2int(u:S):Integer == - o : OutputForm := first elt(scripts(u)$S,sub) - o pretend Integer - - localAssign(s:Symbol,dim:List POLY INT,u:FEXPR):FC == - assign(s,dim,(u::EXPR MFLOAT)$FEXPR)$FC - - makeCond(index:INT,fun:FEXPR,jac:VEC FEXPR):FC == - needc : EXPR INT := (subscript(NEEDC,[index::OutputForm])$S)::EXPR(INT) - sw : Switch := GT([needc]$SWU,[0::EXPR(INT)]$SWU)$Switch - ass : List FC := [localAssign(CJAC,[index::POLY INT,i::POLY INT],jac.i)_ - for i in 1..maxIndex(jac)] - cond(sw,block([localAssign(C,[index::POLY INT],fun),:ass])$FC)$FC - - coerce(u:VEC FEXPR):$ == - ncnln:Integer := maxIndex(u) - x:S := X::S - pu:List(S) := [] - -- Work out which variables appear in the expressions - for e in entries(u) repeat - pu := setUnion(pu,variables(e)$FEXPR) - scriptList : List Integer := map(o2int,pu)$ListFunctions2(S,Integer) - -- This should be the maximum X_n which occurs (there may be others - -- which don't): - n:Integer := reduce(max,scriptList)$List(Integer) - p:List(S) := [] - for j in 1..n repeat p:= cons(subscript(x,[j::OutputForm])$S,p) - p:= reverse(p) - jac:MAT FEXPR := _ - jacobian(u,p)$MultiVariableCalculusFunctions(S,FEXPR,VEC FEXPR,List(S)) - code : List FC := [makeCond(j,u.j,row(jac,j)) for j in 1..ncnln] - [:code,returns()$FC]::$ - - coerce(c:List FC):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FC):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - -@ -\section{domain ASP6 Asp6} -<<domain ASP6 Asp6>>= -)abbrev domain ASP6 Asp6 -++ Author: Mike Dewar and Godfrey Nolan and Grant Keady -++ Date Created: Mar 1993 -++ Date Last Updated: 18 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\spadtype{Asp6} produces Fortran for Type 6 ASPs, needed for NAG routines -++\axiomOpFrom{c05nbf}{c05Package}, \axiomOpFrom{c05ncf}{c05Package}. -++These represent vectors of functions of X(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} - -Asp6(name): Exports == Implementation where - name : Symbol - - FEXPR ==> FortranExpression([],['X],MFLOAT) - MFLOAT ==> MachineFloat - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - UFST ==> Union(fst:FST,void:"void") - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - - Exports == Join(FortranVectorFunctionCategory, CoercibleFrom Vector FEXPR) - Implementation == add - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!(N,fortranInteger()$FT,syms)$SYMTAB - xType : FT := construct(real,[N],false)$FT - declare!(X,xType,syms)$SYMTAB - declare!(FVEC,xType,syms)$SYMTAB - declare!(IFLAG,fortranInteger()$FT,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$Union(fst:FST,void:"void"), - [N,X,FVEC,IFLAG],syms) - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VectorFunctions2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VectorFunctions2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VectorFunctions2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VectorFunctions2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VectorFunctions2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - fexpr2expr(u:FEXPR):EXPR MFLOAT == - (u::EXPR MFLOAT)$FEXPR - - coerce(u:VEC FEXPR):% == - v : VEC EXPR MFLOAT - v := map(fexpr2expr,u)$VF2(FEXPR,EXPR MFLOAT) - ([assign(FVEC,v)$FortranCode,returns()$FortranCode]$List(FortranCode))::$ - - coerce(c:List FortranCode):% == coerce(c)$Rep - - coerce(r:RSFC):% == coerce(r)$Rep - - coerce(c:FortranCode):% == coerce(c)$Rep - - coerce(u:%):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP7 Asp7} -<<domain ASP7 Asp7>>= -)abbrev domain ASP7 Asp7 -++ Author: Mike Dewar and Godfrey Nolan and Grant Keady -++ Date Created: Mar 1993 -++ Date Last Updated: 18 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\spadtype{Asp7} produces Fortran for Type 7 ASPs, needed for NAG routines -++\axiomOpFrom{d02bbf}{d02Package}, \axiomOpFrom{d02gaf}{d02Package}. -++These represent a vector of functions of the scalar X and -++the array Z, and look like: -++\begin{verbatim} -++ SUBROUTINE FCN(X,Z,F) -++ DOUBLE PRECISION F(*),X,Z(*) -++ F(1)=DTAN(Z(3)) -++ F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) -++ &**2))/(Z(2)*DCOS(Z(3))) -++ F(3)=-0.03199999999999999D0/(X*Z(2)**2) -++ RETURN -++ END -++\end{verbatim} - -Asp7(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['X],['Y],MFLOAT) - UFST ==> Union(fst:FST,void:"void") - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - - Exports ==> FortranVectorFunctionCategory with - coerce : Vector FEXPR -> % - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!(X,fortranReal(),syms)$SYMTAB - yType : FT := construct(real,["*"::Symbol],false)$FT - declare!(Y,yType,syms)$SYMTAB - declare!(F,yType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST,[X,Y,F],syms) - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - fexpr2expr(u:FEXPR):EXPR MFLOAT == - (u::EXPR MFLOAT)$FEXPR - - coerce(u:Vector FEXPR ):% == - v : Vector EXPR MFLOAT - v:=map(fexpr2expr,u)$VF2(FEXPR,EXPR MFLOAT) - ([assign(F,v)$FortranCode,returns()$FortranCode]$List(FortranCode))::% - - coerce(c:List FortranCode):% == coerce(c)$Rep - - coerce(r:RSFC):% == coerce(r)$Rep - - coerce(c:FortranCode):% == coerce(c)$Rep - - coerce(u:%):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{domain ASP73 Asp73} -<<domain ASP73 Asp73>>= -)abbrev domain ASP73 Asp73 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 30 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp73(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FSTU ==> Union(fst:FST,void:"void") - FEXPR ==> FortranExpression(['X,'Y],[],MachineFloat) - FT ==> FortranType - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - syms : SYMTAB := empty()$SYMTAB - declare!(X,fortranReal(),syms) $SYMTAB - declare!(Y,fortranReal(),syms) $SYMTAB - declare!(ALPHA,fortranReal(),syms)$SYMTAB - declare!(BETA,fortranReal(),syms) $SYMTAB - declare!(GAMMA,fortranReal(),syms) $SYMTAB - declare!(DELTA,fortranReal(),syms) $SYMTAB - declare!(EPSOLN,fortranReal(),syms) $SYMTAB - declare!(PHI,fortranReal(),syms) $SYMTAB - declare!(PSI,fortranReal(),syms) $SYMTAB - Rep := FortranProgram(name,["void"]$FSTU, - [X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI],syms) - - -- To help the poor compiler! - localAssign(u:Symbol,v:FEXPR):FortranCode == - assign(u,(v::EXPR MachineFloat)$FEXPR)$FortranCode - - coerce(u:VEC FEXPR):$ == - maxIndex(u) ~= 7 => error "Vector is not of dimension 7" - [localAssign(ALPHA@Symbol,elt(u,1)),_ - localAssign(BETA@Symbol,elt(u,2)),_ - localAssign(GAMMA@Symbol,elt(u,3)),_ - localAssign(DELTA@Symbol,elt(u,4)),_ - localAssign(EPSOLN@Symbol,elt(u,5)),_ - localAssign(PHI@Symbol,elt(u,6)),_ - localAssign(PSI@Symbol,elt(u,7)),_ - returns()$FortranCode]$List(FortranCode)::$ - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - -@ -\section{domain ASP74 Asp74} -<<domain ASP74 Asp74>>= -)abbrev domain ASP74 Asp74 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Oct 1993 -++ Date Last Updated: 30 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranScalarFunctionCategory, FortranProgramCategory. -++ Description: -++\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} - -Asp74(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FSTU ==> Union(fst:FST,void:"void") - FT ==> FortranType - SYMTAB ==> SymbolTable - FC ==> FortranCode - PI ==> PositiveInteger - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['X,'Y],[],MFLOAT) - U ==> Union(I: Expression Integer,F: Expression Float,_ - CF: Expression Complex Float,switch:Switch) - VEC ==> Vector - MAT ==> Matrix - M2 ==> MatrixCategoryFunctions2 - MF2a ==> M2(FRAC POLY INT,VEC FRAC POLY INT,VEC FRAC POLY INT, - MAT FRAC POLY INT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2b ==> M2(FRAC POLY FLOAT,VEC FRAC POLY FLOAT,VEC FRAC POLY FLOAT, - MAT FRAC POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2c ==> M2(POLY INT,VEC POLY INT,VEC POLY INT,MAT POLY INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2d ==> M2(POLY FLOAT,VEC POLY FLOAT,VEC POLY FLOAT, - MAT POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2e ==> M2(EXPR INT,VEC EXPR INT,VEC EXPR INT,MAT EXPR INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2f ==> M2(EXPR FLOAT,VEC EXPR FLOAT,VEC EXPR FLOAT, - MAT EXPR FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - - Exports ==> FortranMatrixFunctionCategory with - coerce : MAT FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - syms : SYMTAB := empty()$SYMTAB - declare!(X,fortranReal(),syms)$SYMTAB - declare!(Y,fortranReal(),syms)$SYMTAB - declare!(A,fortranReal(),syms)$SYMTAB - declare!(B,fortranReal(),syms)$SYMTAB - declare!(C,fortranReal(),syms)$SYMTAB - declare!(IBND,fortranInteger(),syms)$SYMTAB - Rep := FortranProgram(name,["void"]$FSTU,[X,Y,A,B,C,IBND],syms) - - -- To help the poor compiler! - localAssign(u:Symbol,v:FEXPR):FC == assign(u,(v::EXPR MFLOAT)$FEXPR)$FC - - coerce(u:MAT FEXPR):$ == - (nrows(u) ~= 4 or ncols(u) ~= 3) => error "Not a 4X3 matrix" - flag:U := [IBND@Symbol::EXPR INT]$U - pt0:U := [0::EXPR INT]$U - pt1:U := [1::EXPR INT]$U - pt2:U := [2::EXPR INT]$U - pt3:U := [3::EXPR INT]$U - sw1: Switch := EQ(flag,pt0)$Switch - sw2: Switch := EQ(flag,pt1)$Switch - sw3: Switch := EQ(flag,pt2)$Switch - sw4: Switch := EQ(flag,pt3)$Switch - a11 : FC := localAssign(A,u(1,1)) - a12 : FC := localAssign(B,u(1,2)) - a13 : FC := localAssign(C,u(1,3)) - a21 : FC := localAssign(A,u(2,1)) - a22 : FC := localAssign(B,u(2,2)) - a23 : FC := localAssign(C,u(2,3)) - a31 : FC := localAssign(A,u(3,1)) - a32 : FC := localAssign(B,u(3,2)) - a33 : FC := localAssign(C,u(3,3)) - a41 : FC := localAssign(A,u(4,1)) - a42 : FC := localAssign(B,u(4,2)) - a43 : FC := localAssign(C,u(4,3)) - c : FC := cond(sw1,block([a11,a12,a13])$FC, - cond(sw2,block([a21,a22,a23])$FC, - cond(sw3,block([a31,a32,a33])$FC, - cond(sw4,block([a41,a42,a43])$FC)$FC)$FC)$FC)$FC - c::$ - - coerce(u:$):OutputForm == coerce(u)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:MAT FRAC POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2a - v::$ - - retractIfCan(u:MAT FRAC POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2a - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT FRAC POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2b - v::$ - - retractIfCan(u:MAT FRAC POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2b - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR INT):$ == - v : MAT FEXPR := map(retract,u)$MF2e - v::$ - - retractIfCan(u:MAT EXPR INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2e - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2f - v::$ - - retractIfCan(u:MAT EXPR FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2f - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2c - v::$ - - retractIfCan(u:MAT POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2c - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2d - v::$ - - retractIfCan(u:MAT POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2d - v case "failed" => "failed" - (v::MAT FEXPR)::$ - -@ -\section{domain ASP77 Asp77} -<<domain ASP77 Asp77>>= -)abbrev domain ASP77 Asp77 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 30 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranMatrixFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp77(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FSTU ==> Union(fst:FST,void:"void") - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FC)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['X],[],MFLOAT) - VEC ==> Vector - MAT ==> Matrix - M2 ==> MatrixCategoryFunctions2 - MF2 ==> M2(FEXPR,VEC FEXPR,VEC FEXPR,Matrix FEXPR,EXPR MFLOAT, - VEC EXPR MFLOAT,VEC EXPR MFLOAT,Matrix EXPR MFLOAT) - MF2a ==> M2(FRAC POLY INT,VEC FRAC POLY INT,VEC FRAC POLY INT, - MAT FRAC POLY INT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2b ==> M2(FRAC POLY FLOAT,VEC FRAC POLY FLOAT,VEC FRAC POLY FLOAT, - MAT FRAC POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2c ==> M2(POLY INT,VEC POLY INT,VEC POLY INT,MAT POLY INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2d ==> M2(POLY FLOAT,VEC POLY FLOAT,VEC POLY FLOAT, - MAT POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2e ==> M2(EXPR INT,VEC EXPR INT,VEC EXPR INT,MAT EXPR INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2f ==> M2(EXPR FLOAT,VEC EXPR FLOAT,VEC EXPR FLOAT, - MAT EXPR FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - - - Exports ==> FortranMatrixFunctionCategory with - coerce : MAT FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : FSTU := ["real"::FST]$FSTU - syms : SYMTAB := empty()$SYMTAB - declare!(X,fortranReal(),syms)$SYMTAB - Rep := FortranProgram(name,["void"]$FSTU,[X,F],syms) - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - localAssign(s:Symbol,j:MAT FEXPR):FortranCode == - j' : MAT EXPR MFLOAT := map(fexpr2expr,j)$MF2 - assign(s,j')$FortranCode - - coerce(u:MAT FEXPR):$ == - dimension := nrows(u)::POLY(INT) - locals : SYMTAB := empty() - declare!(F,[real,[dimension,dimension]$List(POLY(INT)),false]$FT,locals) - code' : List FC := [localAssign(F,u),returns()$FC] - ([locals,code']$RSFC)::$ - - coerce(c:List FC):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FC):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:MAT FRAC POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2a - v::$ - - retractIfCan(u:MAT FRAC POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2a - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT FRAC POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2b - v::$ - - retractIfCan(u:MAT FRAC POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2b - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR INT):$ == - v : MAT FEXPR := map(retract,u)$MF2e - v::$ - - retractIfCan(u:MAT EXPR INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2e - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2f - v::$ - - retractIfCan(u:MAT EXPR FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2f - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2c - v::$ - - retractIfCan(u:MAT POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2c - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2d - v::$ - - retractIfCan(u:MAT POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2d - v case "failed" => "failed" - (v::MAT FEXPR)::$ - -@ -\section{domain ASP78 Asp78} -<<domain ASP78 Asp78>>= -)abbrev domain ASP78 Asp78 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 30 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp78(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FSTU ==> Union(fst:FST,void:"void") - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FC)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - VEC ==> Vector - VF2 ==> VectorFunctions2 - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['X],[],MFLOAT) - - Exports ==> FortranVectorFunctionCategory with - coerce : VEC FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : FSTU := ["real"::FST]$FSTU - syms : SYMTAB := empty()$SYMTAB - declare!(X,fortranReal(),syms)$SYMTAB - gType : FT := construct(real,["*"::Symbol],false)$FT - declare!(G,gType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$FSTU,[X,G],syms) - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - coerce(u:VEC FEXPR):$ == - u' : VEC EXPR MFLOAT := map(fexpr2expr,u)$VF2(FEXPR,EXPR MFLOAT) - (assign(G,u')$FC)::$ - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - coerce(c:List FC):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FC):$ == coerce(c)$Rep - - retract(u:VEC FRAC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC FRAC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(FRAC POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC FRAC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(FRAC POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR INT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC EXPR FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(EXPR FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC EXPR FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(EXPR FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY INT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY INT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY INT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY INT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - - retract(u:VEC POLY FLOAT):$ == - v : VEC FEXPR := map(retract,u)$VF2(POLY FLOAT,FEXPR) - v::$ - - retractIfCan(u:VEC POLY FLOAT):Union($,"failed") == - v:Union(VEC FEXPR,"failed"):=map(retractIfCan,u)$VF2(POLY FLOAT,FEXPR) - v case "failed" => "failed" - (v::VEC FEXPR)::$ - -@ -\section{domain ASP8 Asp8} -<<domain ASP8 Asp8>>= -)abbrev domain ASP8 Asp8 -++ Author: Godfrey Nolan and Mike Dewar -++ Date Created: 11 February 1994 -++ Date Last Updated: 18 March 1994 -++ 31 May 1994 to use alternative interface. MCD -++ 30 June 1994 to handle the end condition correctly. MCD -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp8(name): Exports == Implementation where - name : Symbol - - O ==> OutputForm - S ==> Symbol - FST ==> FortranScalarType - UFST ==> Union(fst:FST,void:"void") - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - EX ==> Expression Integer - MFLOAT ==> MachineFloat - EXPR ==> Expression - PI ==> Polynomial Integer - EXU ==> Union(I: EXPR Integer,F: EXPR Float,CF: EXPR Complex Float, - switch: Switch) - - Exports ==> FortranVectorCategory - - Implementation ==> add - - real : UFST := ["real"::FST]$UFST - syms : SYMTAB := empty()$SYMTAB - declare!([COUNT,M,N],fortranInteger(),syms)$SYMTAB - declare!(XSOL,fortranReal(),syms)$SYMTAB - yType : FT := construct(real,[N],false)$FT - declare!(Y,yType,syms)$SYMTAB - declare!(FORWRD,fortranLogical(),syms)$SYMTAB - declare!(RESULT,construct(real,[M,N],false)$FT,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$UFST,[XSOL,Y,COUNT,M,N,RESULT,FORWRD],syms) - - coerce(c:List FC):% == coerce(c)$Rep - - coerce(r:RSFC):% == coerce(r)$Rep - - coerce(c:FC):% == coerce(c)$Rep - - coerce(u:%):O == coerce(u)$Rep - - outputAsFortran(u:%):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - - f2ex(u:MFLOAT):EXPR MFLOAT == (u::EXPR MFLOAT)$EXPR(MFLOAT) - - coerce(points:Vector MFLOAT):% == - import PI - import EXPR Integer - -- Create some extra declarations - locals : SYMTAB := empty()$SYMTAB - nPol : PI := "N"::S::PI - iPol : PI := "I"::S::PI - countPol : PI := "COUNT"::S::PI - pointsDim : PI := max(#points,1)::PI - declare!(POINTS,[real,[pointsDim],false]$FT,locals)$SYMTAB - declare!(X02ALF,[real,[],true]$FT,locals)$SYMTAB - -- Now build up the code fragments - index : SegmentBinding PI := equation(I@S,1::PI..nPol)$SegmentBinding(PI) - ySym : EX := (subscript("Y"::S,[I::O])$S)::EX - loop := forLoop(index,assign(RESULT,[countPol,iPol],ySym)$FC)$FC - v:Vector EXPR MFLOAT - v := map(f2ex,points)$VectorFunctions2(MFLOAT,EXPR MFLOAT) - assign1 : FC := assign(POINTS,v)$FC - countExp: EX := COUNT@S::EX - newValue: EX := 1 + countExp - assign2 : FC := assign(COUNT,newValue)$FC - newSymbol : S := subscript(POINTS,[COUNT]@List(O))$S - assign3 : FC := assign(XSOL, newSymbol::EX )$FC - fphuge : EX := kernel(operator X02ALF,empty()$List(EX)) - assign4 : FC := assign(XSOL, fphuge)$FC - assign5 : FC := assign(XSOL, -fphuge)$FC - innerCond : FC := cond("FORWRD"::Symbol::Switch,assign4,assign5) - mExp : EX := M@S::EX - endCase : FC := cond(EQ([countExp]$EXU,[mExp]$EXU)$Switch,innerCond,assign3) - code' := [assign1, assign2, loop, endCase]$List(FC) - ([locals,code']$RSFC)::% - -@ -\section{domain ASP80 Asp80} -<<domain ASP80 Asp80>>= -)abbrev domain ASP80 Asp80 -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: Oct 1993 -++ Date Last Updated: 30 March 1994 -++ 6 October 1994 -++ Related Constructors: FortranMatrixFunctionCategory, FortranProgramCategory -++ Description: -++\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} - -Asp80(name): Exports == Implementation where - name : Symbol - - FST ==> FortranScalarType - FSTU ==> Union(fst:FST,void:"void") - FT ==> FortranType - FC ==> FortranCode - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - MFLOAT ==> MachineFloat - FEXPR ==> FortranExpression(['XL,'XR,'ELAM],[],MFLOAT) - VEC ==> Vector - MAT ==> Matrix - VF2 ==> VectorFunctions2 - M2 ==> MatrixCategoryFunctions2 - MF2a ==> M2(FRAC POLY INT,VEC FRAC POLY INT,VEC FRAC POLY INT, - MAT FRAC POLY INT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2b ==> M2(FRAC POLY FLOAT,VEC FRAC POLY FLOAT,VEC FRAC POLY FLOAT, - MAT FRAC POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2c ==> M2(POLY INT,VEC POLY INT,VEC POLY INT,MAT POLY INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2d ==> M2(POLY FLOAT,VEC POLY FLOAT,VEC POLY FLOAT, - MAT POLY FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2e ==> M2(EXPR INT,VEC EXPR INT,VEC EXPR INT,MAT EXPR INT, - FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - MF2f ==> M2(EXPR FLOAT,VEC EXPR FLOAT,VEC EXPR FLOAT, - MAT EXPR FLOAT, FEXPR,VEC FEXPR,VEC FEXPR,MAT FEXPR) - - Exports ==> FortranMatrixFunctionCategory with - coerce : MAT FEXPR -> $ - ++coerce(f) takes objects from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns them into an ASP. - - Implementation ==> add - - real : FSTU := ["real"::FST]$FSTU - syms : SYMTAB := empty()$SYMTAB - declare!(XL,fortranReal(),syms)$SYMTAB - declare!(XR,fortranReal(),syms)$SYMTAB - declare!(ELAM,fortranReal(),syms)$SYMTAB - yType : FT := construct(real,["3"::Symbol],false)$FT - declare!(YL,yType,syms)$SYMTAB - declare!(YR,yType,syms)$SYMTAB - Rep := FortranProgram(name,["void"]$FSTU, [XL,XR,ELAM,YL,YR],syms) - - fexpr2expr(u:FEXPR):EXPR MFLOAT == coerce(u)$FEXPR - - vecAssign(s:Symbol,u:VEC FEXPR):FC == - u' : VEC EXPR MFLOAT := map(fexpr2expr,u)$VF2(FEXPR,EXPR MFLOAT) - assign(s,u')$FC - - coerce(u:MAT FEXPR):$ == - [vecAssign(YL,row(u,1)),vecAssign(YR,row(u,2)),returns()$FC]$List(FC)::$ - - coerce(c:List FortranCode):$ == coerce(c)$Rep - - coerce(r:RSFC):$ == coerce(r)$Rep - - coerce(c:FortranCode):$ == coerce(c)$Rep - - coerce(u:$):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - - retract(u:MAT FRAC POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2a - v::$ - - retractIfCan(u:MAT FRAC POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2a - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT FRAC POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2b - v::$ - - retractIfCan(u:MAT FRAC POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2b - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR INT):$ == - v : MAT FEXPR := map(retract,u)$MF2e - v::$ - - retractIfCan(u:MAT EXPR INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2e - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT EXPR FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2f - v::$ - - retractIfCan(u:MAT EXPR FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2f - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY INT):$ == - v : MAT FEXPR := map(retract,u)$MF2c - v::$ - - retractIfCan(u:MAT POLY INT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2c - v case "failed" => "failed" - (v::MAT FEXPR)::$ - - retract(u:MAT POLY FLOAT):$ == - v : MAT FEXPR := map(retract,u)$MF2d - v::$ - - retractIfCan(u:MAT POLY FLOAT):Union($,"failed") == - v:Union(MAT FEXPR,"failed"):=map(retractIfCan,u)$MF2d - v case "failed" => "failed" - (v::MAT FEXPR)::$ - -@ -\section{domain ASP9 Asp9} -<<domain ASP9 Asp9>>= -)abbrev domain ASP9 Asp9 -++ Author: Mike Dewar, Grant Keady and Godfrey Nolan -++ Date Created: Mar 1993 -++ Date Last Updated: 18 March 1994 -++ 12 July 1994 added COMMON blocks for d02cjf, d02ejf -++ 6 October 1994 -++ Related Constructors: FortranVectorFunctionCategory, FortranProgramCategory -++ Description: -++\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 X and a vector 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 G, then extra information is added -++via COMMON blocks used by certain routines. This specifies that the value -++returned by G in this case is to be ignored. - -Asp9(name): Exports == Implementation where - name : Symbol - - FEXPR ==> FortranExpression(['X],['Y],MFLOAT) - MFLOAT ==> MachineFloat - FC ==> FortranCode - FST ==> FortranScalarType - FT ==> FortranType - SYMTAB ==> SymbolTable - RSFC ==> Record(localSymbols:SymbolTable,code:List(FortranCode)) - UFST ==> Union(fst:FST,void:"void") - FRAC ==> Fraction - POLY ==> Polynomial - EXPR ==> Expression - INT ==> Integer - FLOAT ==> Float - - Exports ==> FortranFunctionCategory with - coerce : FEXPR -> % - ++coerce(f) takes an object from the appropriate instantiation of - ++\spadtype{FortranExpression} and turns it into an ASP. - - Implementation ==> add - - real : FST := "real"::FST - syms : SYMTAB := empty()$SYMTAB - declare!(X,fortranReal()$FT,syms)$SYMTAB - yType : FT := construct([real]$UFST,["*"::Symbol],false)$FT - declare!(Y,yType,syms)$SYMTAB - Rep := FortranProgram(name,[real]$UFST,[X,Y],syms) - - retract(u:FRAC POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:FRAC POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:FRAC POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:EXPR FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:EXPR INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:EXPR INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:POLY FLOAT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY FLOAT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - retract(u:POLY INT):$ == (retract(u)@FEXPR)::$ - retractIfCan(u:POLY INT):Union($,"failed") == - foo : Union(FEXPR,"failed") - foo := retractIfCan(u)$FEXPR - foo case "failed" => "failed" - (foo::FEXPR)::$ - - coerce(u:FEXPR):% == - expr : Expression MachineFloat := (u::Expression(MachineFloat))$FEXPR - (retractIfCan(u)@Union(MFLOAT,"failed"))$FEXPR case "failed" => - coerce(expr)$Rep - locals : SYMTAB := empty() - charType : FT := construct(["character"::FST]$UFST,[6::POLY(INT)],false)$FT - declare!([CHDUM1,CHDUM2,GOPT1,CHDUM,GOPT2],charType,locals)$SYMTAB - common1 := common(CD02EJ,[CHDUM1,CHDUM2,GOPT1] )$FC - common2 := common(AD02CJ,[CHDUM,GOPT2] )$FC - assign1 := assign(GOPT1,"NOGOPT")$FC - assign2 := assign(GOPT2,"NOGOPT")$FC - result := assign(name,expr)$FC - code' : List FC := [common1,common2,assign1,assign2,result] - ([locals,code']$RSFC)::Rep - - coerce(c:List FortranCode):% == coerce(c)$Rep - - coerce(r:RSFC):% == coerce(r)$Rep - - coerce(c:FortranCode):% == coerce(c)$Rep - - coerce(u:%):OutputForm == coerce(u)$Rep - - outputAsFortran(u):Void == - p := checkPrecision()$NAGLinkSupportPackage - outputAsFortran(u)$Rep - p => restorePrecision()$NAGLinkSupportPackage - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain ASP1 Asp1>> -<<domain ASP10 Asp10>> -<<domain ASP12 Asp12>> -<<domain ASP19 Asp19>> -<<domain ASP20 Asp20>> -<<domain ASP24 Asp24>> -<<domain ASP27 Asp27>> -<<domain ASP28 Asp28>> -<<domain ASP29 Asp29>> -<<domain ASP30 Asp30>> -<<domain ASP31 Asp31>> -<<domain ASP33 Asp33>> -<<domain ASP34 Asp34>> -<<domain ASP35 Asp35>> -<<domain ASP4 Asp4>> -<<domain ASP41 Asp41>> -<<domain ASP42 Asp42>> -<<domain ASP49 Asp49>> -<<domain ASP50 Asp50>> -<<domain ASP55 Asp55>> -<<domain ASP6 Asp6>> -<<domain ASP7 Asp7>> -<<domain ASP73 Asp73>> -<<domain ASP74 Asp74>> -<<domain ASP77 Asp77>> -<<domain ASP78 Asp78>> -<<domain ASP8 Asp8>> -<<domain ASP80 Asp80>> -<<domain ASP9 Asp9>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/cont.spad.pamphlet b/src/algebra/cont.spad.pamphlet deleted file mode 100644 index 9444f58f..00000000 --- a/src/algebra/cont.spad.pamphlet +++ /dev/null @@ -1,354 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra cont.spad} -\author{Brian Dupee} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{package ESCONT ExpertSystemContinuityPackage} -<<package ESCONT ExpertSystemContinuityPackage>>= -)abbrev package ESCONT ExpertSystemContinuityPackage -++ Author: Brian Dupee -++ Date Created: May 1994 -++ Date Last Updated: June 1995 -++ Basic Operations: problemPoints, singularitiesOf, zerosOf -++ Related Constructors: -++ Description: -++ ExpertSystemContinuityPackage is a package of functions for the use of domains -++ belonging to the category \axiomType{NumericalIntegration}. - -ExpertSystemContinuityPackage(): E == I where - EF2 ==> ExpressionFunctions2 - FI ==> Fraction Integer - EFI ==> Expression Fraction Integer - PFI ==> Polynomial Fraction Integer - DF ==> DoubleFloat - LDF ==> List DoubleFloat - EDF ==> Expression DoubleFloat - VEDF ==> Vector Expression DoubleFloat - SDF ==> Stream DoubleFloat - SS ==> Stream String - EEDF ==> Equation Expression DoubleFloat - LEDF ==> List Expression DoubleFloat - KEDF ==> Kernel Expression DoubleFloat - LKEDF ==> List Kernel Expression DoubleFloat - PDF ==> Polynomial DoubleFloat - FPDF ==> Fraction Polynomial DoubleFloat - OCDF ==> OrderedCompletion DoubleFloat - SOCDF ==> Segment OrderedCompletion DoubleFloat - NIA ==> Record(var:Symbol,fn:EDF,range:SOCDF,abserr:DF,relerr:DF) - UP ==> UnivariatePolynomial - BO ==> BasicOperator - RS ==> Record(zeros: SDF,ones: SDF,singularities: SDF) - - E ==> with - - getlo : SOCDF -> DF - ++ getlo(u) gets the \axiomType{DoubleFloat} equivalent of - ++ the first endpoint of the range \axiom{u} - gethi : SOCDF -> DF - ++ gethi(u) gets the \axiomType{DoubleFloat} equivalent of - ++ the second endpoint of the range \axiom{u} - functionIsFracPolynomial?: NIA -> Boolean - ++ functionIsFracPolynomial?(args) tests whether the function - ++ can be retracted to \axiomType{Fraction(Polynomial(DoubleFloat))} - problemPoints:(EDF,Symbol,SOCDF) -> List DF - ++ problemPoints(f,var,range) returns a list of possible problem points - ++ by looking at the zeros of the denominator of the function \spad{f} - ++ if it can be retracted to \axiomType{Polynomial(DoubleFloat)}. - zerosOf:(EDF,List Symbol,SOCDF) -> SDF - ++ zerosOf(e,vars,range) returns a list of points - ++ (\axiomType{Doublefloat}) at which a NAG fortran version of \spad{e} - ++ will most likely produce an error. - singularitiesOf: (EDF,List Symbol,SOCDF) -> SDF - ++ singularitiesOf(e,vars,range) returns a list of points - ++ (\axiomType{Doublefloat}) at which a NAG fortran - ++ version of \spad{e} will most likely produce - ++ an error. This includes those points which evaluate to 0/0. - singularitiesOf: (Vector EDF,List Symbol,SOCDF) -> SDF - ++ singularitiesOf(v,vars,range) returns a list of points - ++ (\axiomType{Doublefloat}) at which a NAG fortran - ++ version of \spad{v} will most likely produce - ++ an error. This includes those points which evaluate to 0/0. - polynomialZeros:(PFI,Symbol,SOCDF) -> LDF - ++ polynomialZeros(fn,var,range) calculates the real zeros of the - ++ polynomial which are contained in the given interval. It returns - ++ a list of points (\axiomType{Doublefloat}) for which the univariate - ++ polynomial \spad{fn} is zero. - df2st:DF -> String - ++ df2st(n) coerces a \axiomType{DoubleFloat} to \axiomType{String} - ldf2lst:LDF -> List String - ++ ldf2lst(ln) coerces a List of \axiomType{DoubleFloat} to - ++ \axiomType{List}(\axiomType{String}) - sdf2lst:SDF -> List String - ++ sdf2lst(ln) coerces a Stream of \axiomType{DoubleFloat} to - ++ \axiomType{List}(\axiomType{String}) - - I ==> ExpertSystemToolsPackage add - - import ExpertSystemToolsPackage - - functionIsPolynomial?(args:NIA):Boolean == - -- tests whether the function can be retracted to a polynomial - (retractIfCan(args.fn)@Union(PDF,"failed"))$EDF case PDF - - isPolynomial?(f:EDF):Boolean == - -- tests whether the function can be retracted to a polynomial - (retractIfCan(f)@Union(PDF,"failed"))$EDF case PDF - - isConstant?(f:EDF):Boolean == - -- tests whether the function can be retracted to a constant (DoubleFloat) - (retractIfCan(f)@Union(DF,"failed"))$EDF case DF - - denominatorIsPolynomial?(args:NIA):Boolean == - -- tests if the denominator can be retracted to polynomial - a:= copy args - a.fn:=denominator(args.fn) - (functionIsPolynomial?(a))@Boolean - - denIsPolynomial?(f:EDF):Boolean == - -- tests if the denominator can be retracted to polynomial - (isPolynomial?(denominator f))@Boolean - - listInRange(l:LDF,range:SOCDF):LDF == - -- returns a list with only those elements internal to the range range - [t for t in l | in?(t,range)] - - loseUntil(l:SDF,a:DF):SDF == - empty?(l)$SDF => l - f := first(l)$SDF - (abs(f) <= abs(a)) => loseUntil(rest(l)$SDF,a) - l - - retainUntil(l:SDF,a:DF,b:DF,flag:Boolean):SDF == - empty?(l)$SDF => l - f := first(l)$SDF - (in?(f)$ExpertSystemContinuityPackage1(a,b)) => - concat(f,retainUntil(rest(l),a,b,false)) - flag => empty()$SDF - retainUntil(rest(l),a,b,true) - - streamInRange(l:SDF,range:SOCDF):SDF == - -- returns a stream with only those elements internal to the range range - a := getlo(range := dfRange(range)) - b := gethi(range) - explicitlyFinite?(l) => - select(in?$ExpertSystemContinuityPackage1(a,b),l)$SDF - negative?(a*b) => retainUntil(l,a,b,false) - negative?(a) => - l := loseUntil(l,b) - retainUntil(l,a,b,false) - l := loseUntil(l,a) - retainUntil(l,a,b,false) - - getStream(n:Symbol,s:String):SDF == - import RS - entry?(n,bfKeys()$BasicFunctions)$(List(Symbol)) => - c := bfEntry(n)$BasicFunctions - (s = "zeros")@Boolean => c.zeros - (s = "singularities")@Boolean => c.singularities - (s = "ones")@Boolean => c.ones - empty()$SDF - - polynomialZeros(fn:PFI,var:Symbol,range:SOCDF):LDF == - up := unmakeSUP(univariate(fn)$PFI)$UP(var,FI) - range := dfRange(range) - r:Record(left:FI,right:FI) := [df2fi(getlo(range)), df2fi(gethi(range))] - ans:List(Record(left:FI,right:FI)) := - realZeros(up,r,1/1000000000000000000)$RealZeroPackageQ(UP(var,FI)) - listInRange(dflist(ans),range) - - functionIsFracPolynomial?(args:NIA):Boolean == - -- tests whether the function can be retracted to a fraction - -- where both numerator and denominator are polynomial - (retractIfCan(args.fn)@Union(FPDF,"failed"))$EDF case FPDF - - problemPoints(f:EDF,var:Symbol,range:SOCDF):LDF == - (denIsPolynomial?(f))@Boolean => - c := retract(edf2efi(denominator(f)))@PFI - polynomialZeros(c,var,range) - empty()$LDF - - zerosOf(e:EDF,vars:List Symbol,range:SOCDF):SDF == - (u := isQuotient(e)) case EDF => - singularitiesOf(u,vars,range) - k := kernels(e)$EDF - ((nk := # k) = 0)@Boolean => empty()$SDF -- constant found. - (nk = 1)@Boolean => -- single expression found. - ker := first(k)$LKEDF - n := name(operator(ker)$KEDF)$BO - entry?(n,vars) => -- polynomial found. - c := retract(edf2efi(e))@PFI - coerce(polynomialZeros(c,n,range))$SDF - a := first(argument(ker)$KEDF)$LEDF - (not (n = log :: Symbol)@Boolean) and ((w := isPlus a) case LEDF) => - var:Symbol := first(variables(a)) - c:EDF := w.2 - c1:EDF := w.1 - entry?(c1,[b::EDF for b in vars]) and (one?(# vars)) => - c2:DF := edf2df c - c3 := c2 :: OCDF - varEdf := var :: EDF - varEqn := equation(varEdf,c1-c)$EEDF - range2 := (lo(range)+c3)..(hi(range)+c3) - s := zerosOf(subst(e,varEqn)$EDF,vars,range2) - st := map(#1-c2,s)$StreamFunctions2(DF,DF) - streamInRange(st,range) - zerosOf(a,vars,range) - (t := isPlus(e)$EDF) case LEDF => -- constant + expression - # t > 2 => empty()$SDF - entry?(a,[b::EDF for b in vars]) => -- finds entries like sqrt(x) - st := getStream(n,"ones") - o := edf2df(second(t)$LEDF) - one?(o) or one?(-o) => -- is it like (f(x) -/+ 1) - st := map(-#1/o,st)$StreamFunctions2(DF,DF) - streamInRange(st,range) - empty()$SDF - empty()$SDF - entry?(a,[b::EDF for b in vars]) => -- finds entries like sqrt(x) - st := getStream(n,"zeros") - streamInRange(st,range) - (n = tan :: Symbol)@Boolean => - concat([zerosOf(a,vars,range),singularitiesOf(a,vars,range)]) - (n = sin :: Symbol)@Boolean => - concat([zerosOf(a,vars,range),singularitiesOf(a,vars,range)]) - empty()$SDF - (t := isPlus(e)$EDF) case LEDF => empty()$SDF -- INCOMPLETE!!! - (v := isTimes(e)$EDF) case LEDF => - concat([zerosOf(u,vars,range) for u in v]) - empty()$SDF - - singularitiesOf(e:EDF,vars:List Symbol,range:SOCDF):SDF == - (u := isQuotient(e)) case EDF => - zerosOf(u,vars,range) - (t := isPlus e) case LEDF => - concat([singularitiesOf(u,vars,range) for u in t]) - (v := isTimes e) case LEDF => - concat([singularitiesOf(u,vars,range) for u in v]) - (k := mainKernel e) case KEDF => - n := name(operator k) - entry?(n,vars) => coerce(problemPoints(e,n,range))$SDF - a:EDF := (argument k).1 - (not (n = log :: Symbol)@Boolean) and ((w := isPlus a) case LEDF) => - var:Symbol := first(variables(a)) - c:EDF := w.2 - c1:EDF := w.1 - entry?(c1,[b::EDF for b in vars]) and (one?(# vars)) => - c2:DF := edf2df c - c3 := c2 :: OCDF - varEdf := var :: EDF - varEqn := equation(varEdf,c1-c)$EEDF - range2 := (lo(range)+c3)..(hi(range)+c3) - s := singularitiesOf(subst(e,varEqn)$EDF,vars,range2) - st := map(#1-c2,s)$StreamFunctions2(DF,DF) - streamInRange(st,range) - singularitiesOf(a,vars,range) - entry?(a,[b::EDF for b in vars]) => - st := getStream(n,"singularities") - streamInRange(st,range) - (n = log :: Symbol)@Boolean => - concat([zerosOf(a,vars,range),singularitiesOf(a,vars,range)]) - singularitiesOf(a,vars,range) - empty()$SDF - - singularitiesOf(v:VEDF,vars:List Symbol,range:SOCDF):SDF == - ls := [singularitiesOf(u,vars,range) for u in entries(v)$VEDF] - concat(ls)$SDF - -@ -\section{package ESCONT1 ExpertSystemContinuityPackage1} -<<package ESCONT1 ExpertSystemContinuityPackage1>>= -)abbrev package ESCONT1 ExpertSystemContinuityPackage1 -++ Author: Brian Dupee -++ Date Created: May 1994 -++ Date Last Updated: June 1995 -++ Basic Operations: problemPoints, singularitiesOf, zerosOf -++ Related Constructors: -++ Description: -++ ExpertSystemContinuityPackage1 exports a function to check range inclusion - -ExpertSystemContinuityPackage1(A:DF,B:DF): E == I where - EF2 ==> ExpressionFunctions2 - FI ==> Fraction Integer - EFI ==> Expression Fraction Integer - PFI ==> Polynomial Fraction Integer - DF ==> DoubleFloat - LDF ==> List DoubleFloat - EDF ==> Expression DoubleFloat - VEDF ==> Vector Expression DoubleFloat - SDF ==> Stream DoubleFloat - SS ==> Stream String - EEDF ==> Equation Expression DoubleFloat - LEDF ==> List Expression DoubleFloat - KEDF ==> Kernel Expression DoubleFloat - LKEDF ==> List Kernel Expression DoubleFloat - PDF ==> Polynomial DoubleFloat - FPDF ==> Fraction Polynomial DoubleFloat - OCDF ==> OrderedCompletion DoubleFloat - SOCDF ==> Segment OrderedCompletion DoubleFloat - NIA ==> Record(var:Symbol,fn:EDF,range:SOCDF,abserr:DF,relerr:DF) - UP ==> UnivariatePolynomial - BO ==> BasicOperator - RS ==> Record(zeros: SDF,ones: SDF,singularities: SDF) - - E ==> with - - in?:DF -> Boolean - ++ in?(p) tests whether point p is internal to the range [\spad{A..B}] - - I ==> add - - in?(p:DF):Boolean == - a:Boolean := (p < B)$DF - b:Boolean := (A < p)$DF - (a and b)@Boolean - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<package ESCONT ExpertSystemContinuityPackage>> -<<package ESCONT1 ExpertSystemContinuityPackage1>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index 5108f68d..0e75f115 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -49,7 +49,7 @@ (in-package "BOOT") (defparameter |$globalExposureGroupAlist| '( -;;define the groups |basic| |naglink| |anna| |categories| |Hidden| |defaults| +;;define the groups |basic| |naglink| |categories| |Hidden| |defaults| (|basic| (|AddAst| . ADDAST) (|AlgebraicManipulations| . ALGMANIP) @@ -452,51 +452,11 @@ (|WuWenTsunTriangularSet| . WUTSET) ) (|naglink| - (|FortranCode| . FC) - (|FortranCodePackage1| . FCPAK1) - (|FortranExpression| . FEXPR) - (|FortranMachineTypeCategory| . FMTC) - (|FortranMatrixCategory| . FMC) - (|FortranMatrixFunctionCategory| . FMFUN) - (|FortranOutputStackPackage| . FOP) - (|FortranPackage| . FORT) - (|FortranProgramCategory| . FORTCAT) - (|FortranProgram| . FORTRAN) - (|FortranFunctionCategory| . FORTFN) (|FortranScalarType| . FST) (|FortranType| . FT) - (|FortranTemplate| . FTEM) - (|FortranVectorFunctionCategory| . FVFUN) - (|FortranVectorCategory| . FVC) - (|MachineComplex| . MCMPLX) - (|MachineFloat| . MFLOAT) - (|MachineInteger| . MINT) - (|MultiVariableCalculusFunctions| . MCALCFN) - (|PackedHermitianSequence| . PACKED) - (|Result| . RESULT) - (|SimpleFortranProgram| . SFORT) - (|Switch| . SWITCH) (|SymbolTable| . SYMTAB) - (|TemplateUtilities| . TEMUTL) (|TheSymbolTable| . SYMS) - (|ThreeDimensionalMatrix| . M3D)) -(|anna| - (|AttributeButtons| . ATTRBUT) - (|BasicFunctions| . BFUNCT) - (|ExpertSystemContinuityPackage| . ESCONT) - (|ExpertSystemContinuityPackage1| . ESCONT1) - (|ExpertSystemToolsPackage| . ESTOOLS) - (|ExpertSystemToolsPackage1| . ESTOOLS1) - (|ExpertSystemToolsPackage2| . ESTOOLS2) - (|NumericalIntegrationCategory| . NUMINT) - (|NumericalIntegrationProblem| . NIPROB) - (|NumericalODEProblem| . ODEPROB) - (|NumericalOptimizationCategory| . OPTCAT) - (|NumericalOptimizationProblem| . OPTPROB) - (|NumericalPDEProblem| . PDEPROB) - (|OrdinaryDifferentialEquationsSolverCategory| . ODECAT) - (|PartialDifferentialEquationsSolverCategory| . PDECAT) - (|RoutinesTable| . ROUTINE)) +) (|categories| (|AbelianGroup| . ABELGRP) (|AbelianMonoid| . ABELMON) @@ -1243,7 +1203,6 @@ '|basic| '|categories| '|naglink| -'|anna| ) (LIST ;;These constructors will be explicitly exposed diff --git a/src/algebra/fortcat.spad.pamphlet b/src/algebra/fortcat.spad.pamphlet deleted file mode 100644 index 84c2fd5c..00000000 --- a/src/algebra/fortcat.spad.pamphlet +++ /dev/null @@ -1,345 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra fortcat.spad} -\author{Mike Dewar} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{category FORTFN FortranFunctionCategory} -<<category FORTFN FortranFunctionCategory>>= -)abbrev category FORTFN FortranFunctionCategory -++ Author: Mike Dewar -++ Date Created: 13 January 1994 -++ Date Last Updated: 18 March 1994 -++ Related Constructors: FortranProgramCategory. -++ Description: -++ \axiomType{FortranFunctionCategory} is the category of arguments to -++ NAG Library routines which return (sets of) function values. -FortranFunctionCategory():Category == FortranProgramCategory with - coerce : List FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{List FortranCode} and - ++ uses it as the body of an ASP. - coerce : FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{FortranCode} and - ++ uses it as the body of an ASP. - coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $ - ++ 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. - retract : Expression Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Expression Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Expression Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Expression Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Polynomial Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Polynomial Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Polynomial Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Polynomial Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Fraction Polynomial Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Fraction Polynomial Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Fraction Polynomial Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Fraction Polynomial Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - - -- NB: These ASPs also have a coerce from an appropriate instantiation - -- of FortranExpression. - - -@ -\section{category FMC FortranMatrixCategory} -<<category FMC FortranMatrixCategory>>= -)abbrev category FMC FortranMatrixCategory -++ Author: Mike Dewar -++ Date Created: 21 March 1994 -++ Date Last Updated: -++ Related Constructors: FortranProgramCategory. -++ Description: -++ \axiomType{FortranMatrixCategory} provides support for -++ producing Functions and Subroutines when the input to these -++ is an AXIOM object of type \axiomType{Matrix} or in domains -++ involving \axiomType{FortranCode}. -FortranMatrixCategory():Category == FortranProgramCategory with - coerce : Matrix MachineFloat -> $ - ++ coerce(v) produces an ASP which returns the value of \spad{v}. - coerce : List FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{List FortranCode} and - ++ uses it as the body of an ASP. - coerce : FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{FortranCode} and - ++ uses it as the body of an ASP. - coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $ - ++ 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. - -@ -\section{category FORTCAT FortranProgramCategory} -<<category FORTCAT FortranProgramCategory>>= -)abbrev category FORTCAT FortranProgramCategory -++ Author: Mike Dewar -++ Date Created: November 1992 -++ Date Last Updated: -++ Basic Operations: -++ Related Constructors: FortranType, FortranCode, Switch -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: -++ \axiomType{FortranProgramCategory} provides various models of -++ FORTRAN subprograms. These can be transformed into actual FORTRAN -++ code. -FortranProgramCategory():Category == Join(Type,CoercibleTo OutputForm) with - outputAsFortran : $ -> Void - ++ \axiom{outputAsFortran(u)} translates \axiom{u} into a legal FORTRAN - ++ subprogram. - -@ -\section{category FVC FortranVectorCategory} -<<category FVC FortranVectorCategory>>= -)abbrev category FVC FortranVectorCategory -++ Author: Mike Dewar -++ Date Created: October 1993 -++ Date Last Updated: 18 March 1994 -++ Related Constructors: FortranProgramCategory. -++ Description: -++ \axiomType{FortranVectorCategory} provides support for -++ producing Functions and Subroutines when the input to these -++ is an AXIOM object of type \axiomType{Vector} or in domains -++ involving \axiomType{FortranCode}. -FortranVectorCategory():Category == FortranProgramCategory with - coerce : Vector MachineFloat -> $ - ++ coerce(v) produces an ASP which returns the value of \spad{v}. - coerce : List FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{List FortranCode} and - ++ uses it as the body of an ASP. - coerce : FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{FortranCode} and - ++ uses it as the body of an ASP. - coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $ - ++ 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. - -@ -\section{category FMTC FortranMachineTypeCategory} -<<category FMTC FortranMachineTypeCategory>>= -)abbrev category FMTC FortranMachineTypeCategory -++ Author: Mike Dewar -++ Date Created: December 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: FortranExpression, MachineInteger, MachineFloat, MachineComplex -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A category of domains which model machine arithmetic -++ used by machines in the AXIOM-NAG link. -FortranMachineTypeCategory():Category == Join(IntegralDomain,OrderedSet, - RetractableTo(Integer) ) - -@ -\section{category FMFUN FortranMatrixFunctionCategory} -<<category FMFUN FortranMatrixFunctionCategory>>= -)abbrev category FMFUN FortranMatrixFunctionCategory -++ Author: Mike Dewar -++ Date Created: March 18 1994 -++ Date Last Updated: -++ Related Constructors: FortranProgramCategory. -++ Description: -++ \axiomType{FortranMatrixFunctionCategory} provides support for -++ producing Functions and Subroutines representing matrices of -++ expressions. - -FortranMatrixFunctionCategory():Category == FortranProgramCategory with - coerce : List FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{List FortranCode} and - ++ uses it as the body of an ASP. - coerce : FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{FortranCode} and - ++ uses it as the body of an ASP. - coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $ - ++ 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. - retract : Matrix Expression Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Matrix Expression Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Matrix Expression Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Matrix Expression Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Matrix Polynomial Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Matrix Polynomial Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Matrix Polynomial Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Matrix Polynomial Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Matrix Fraction Polynomial Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Matrix Fraction Polynomial Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Matrix Fraction Polynomial Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Matrix Fraction Polynomial Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - - -- NB: These ASPs also have a coerce from an appropriate instantiation - -- of Matrix FortranExpression. - -@ -\section{category FVFUN FortranVectorFunctionCategory} -<<category FVFUN FortranVectorFunctionCategory>>= -)abbrev category FVFUN FortranVectorFunctionCategory -++ Author: Mike Dewar -++ Date Created: 11 March 1994 -++ Date Last Updated: 18 March 1994 -++ Related Constructors: FortranProgramCategory. -++ Description: -++ \axiomType{FortranVectorFunctionCategory} is the catagory of arguments -++ to NAG Library routines which return the values of vectors of functions. -FortranVectorFunctionCategory():Category == FortranProgramCategory with - coerce : List FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{List FortranCode} and - ++ uses it as the body of an ASP. - coerce : FortranCode -> $ - ++ coerce(e) takes an object from \spadtype{FortranCode} and - ++ uses it as the body of an ASP. - coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $ - ++ 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. - retract : Vector Expression Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Vector Expression Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Vector Expression Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Vector Expression Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Vector Polynomial Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Vector Polynomial Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Vector Polynomial Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Vector Polynomial Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Vector Fraction Polynomial Float -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Vector Fraction Polynomial Float -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retract : Vector Fraction Polynomial Integer -> $ - ++ retract(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - retractIfCan : Vector Fraction Polynomial Integer -> Union($,"failed") - ++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that - ++ legal Fortran-77 is produced. - - -- NB: These ASPs also have a coerce from an appropriate instantiation - -- of Vector FortranExpression. - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<category FORTFN FortranFunctionCategory>> -<<category FMC FortranMatrixCategory>> -<<category FORTCAT FortranProgramCategory>> -<<category FVC FortranVectorCategory>> -<<category FMTC FortranMachineTypeCategory>> -<<category FMFUN FortranMatrixFunctionCategory>> -<<category FVFUN FortranVectorFunctionCategory>> - -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/fortmac.spad.pamphlet b/src/algebra/fortmac.spad.pamphlet deleted file mode 100644 index 5684244c..00000000 --- a/src/algebra/fortmac.spad.pamphlet +++ /dev/null @@ -1,458 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra fortmac.spad} -\author{Mike Dewar} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{domain MINT MachineInteger} -<<domain MINT MachineInteger>>= -)abbrev domain MINT MachineInteger -++ Author: Mike Dewar -++ Date Created: December 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: FortranExpression, FortranMachineTypeCategory, MachineFloat, -++ MachineComplex -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A domain which models the integer representation -++ used by machines in the AXIOM-NAG link. -MachineInteger(): Exports == Implementation where - - S ==> String - - Exports ==> Join(FortranMachineTypeCategory,IntegerNumberSystem) with - maxint : PositiveInteger -> PositiveInteger - ++ maxint(u) sets the maximum integer in the model to u - maxint : () -> PositiveInteger - ++ maxint() returns the maximum integer in the model - coerce : Expression Integer -> Expression $ - ++ coerce(x) returns x with coefficients in the domain - - Implementation ==> Integer add - - MAXINT : PositiveInteger := 2**32 - - maxint():PositiveInteger == MAXINT - - maxint(new:PositiveInteger):PositiveInteger == - old := MAXINT - MAXINT := new - old - - coerce(u:Expression Integer):Expression($) == - map(coerce,u)$ExpressionFunctions2(Integer,$) - - coerce(u:Integer):$ == - import S - abs(u) > MAXINT => - message: S := concat [string u," > MAXINT(",string MAXINT,")"] - error message - per u - - retract(u:$):Integer == rep u - - retractIfCan(u:$):Union(Integer,"failed") == rep u - -@ -\section{domain MFLOAT MachineFloat} -<<domain MFLOAT MachineFloat>>= -)abbrev domain MFLOAT MachineFloat -++ Author: Mike Dewar -++ Date Created: December 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: FortranExpression, FortranMachineTypeCategory, MachineInteger, -++ MachineComplex -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A domain which models the floating point representation -++ used by machines in the AXIOM-NAG link. -MachineFloat(): Exports == Implementation where - - PI ==> PositiveInteger - NNI ==> NonNegativeInteger - F ==> Float - I ==> Integer - S ==> String - FI ==> Fraction Integer - SUP ==> SparseUnivariatePolynomial - SF ==> DoubleFloat - - Exports ==> Join(FloatingPointSystem,FortranMachineTypeCategory,Field, - RetractableTo(Float),RetractableTo(Fraction(Integer)),CharacteristicZero) with - precision : PI -> PI - ++ precision(p) sets the number of digits in the model to p - precision : () -> PI - ++ precision() returns the number of digits in the model - base : PI -> PI - ++ base(b) sets the base of the model to b - maximumExponent : I -> I - ++ maximumExponent(e) sets the maximum exponent in the model to e - maximumExponent : () -> I - ++ maximumExponent() returns the maximum exponent in the model - minimumExponent : I -> I - ++ minimumExponent(e) sets the minimum exponent in the model to e - minimumExponent : () -> I - ++ minimumExponent() returns the minimum exponent in the model - coerce : $ -> F - ++ coerce(u) transforms a MachineFloat to a standard Float - coerce : MachineInteger -> $ - ++ coerce(u) transforms a MachineInteger into a MachineFloat - mantissa : $ -> I - ++ mantissa(u) returns the mantissa of u - exponent : $ -> I - ++ exponent(u) returns the exponent of u - changeBase : (I,I,PI) -> $ - ++ changeBase(exp,man,base) \undocumented{} - - Implementation ==> add - - import F - import FI - - Rep := Record(mantissa:I,exponent:I) - - -- Parameters of the Floating Point Representation - P : PI := 16 -- Precision - B : PI := 2 -- Base - EMIN : I := -1021 -- Minimum Exponent - EMAX : I := 1024 -- Maximum Exponent - - -- Useful constants - POWER : PI := 53 -- The maximum power of B which will yield P - -- decimal digits. - MMAX : PI := B**POWER - - - -- locals - locRound:(FI)->I - checkExponent:($)->$ - normalise:($)->$ - newPower:(PI,PI)->Void - - retractIfCan(u:$):Union(FI,"failed") == - mantissa(u)*(B/1)**(exponent(u)) - - wholePart(u:$):Integer == - man:I:=mantissa u - exp:I:=exponent u - f:= - positive? exp => man*B**(exp pretend PI) - zero? exp => man - wholePart(man/B**((-exp) pretend PI)) - normalise(u:$):$ == - -- We want the largest possible mantissa, to ensure a canonical - -- representation. - exp : I := exponent u - man : I := mantissa u - BB : I := B pretend I - sgn : I := sign man ; man := abs man - zero? man => [0,0]$Rep - if man < MMAX then - while man < MMAX repeat - exp := exp - 1 - man := man * BB - if man > MMAX then - q1:FI:= man/1 - BBF:FI:=BB/1 - while wholePart(q1) > MMAX repeat - q1:= q1 / BBF - exp:=exp + 1 - man := locRound(q1) - positive?(sgn) => checkExponent [man,exp]$Rep - checkExponent [-man,exp]$Rep - - mantissa(u:$):I == elt(u,mantissa)$Rep - exponent(u:$):I == elt(u,exponent)$Rep - - newPower(base:PI,prec:PI):Void == - power : PI := 1 - target : PI := 10**prec - current : PI := base - while (current := current*base) < target repeat power := power+1 - POWER := power - MMAX := B**POWER - - changeBase(exp:I,man:I,base:PI):$ == - newExp : I := 0 - f : FI := man*(base pretend I)::FI**exp - sign : I := sign f - f : FI := abs f - newMan : I := wholePart f - zero? f => [0,0]$Rep - BB : FI := (B pretend I)::FI - if newMan < MMAX then - while newMan < MMAX repeat - newExp := newExp - 1 - f := f*BB - newMan := wholePart f - if newMan > MMAX then - while newMan > MMAX repeat - newExp := newExp + 1 - f := f/BB - newMan := wholePart f - [sign*newMan,newExp]$Rep - - checkExponent(u:$):$ == - exponent(u) < EMIN or exponent(u) > EMAX => - message :S := concat(["Exponent out of range: ", - string EMIN, "..", string EMAX])$S - error message - u - - coerce(u:$):OutputForm == - coerce(u::F) - - coerce(u:MachineInteger):$ == - checkExponent changeBase(0,retract(u)@Integer,10) - - coerce(u:$):F == - oldDigits : PI := digits(P)$F - r : F := float(mantissa u,exponent u,B)$Float - digits(oldDigits)$F - r - - coerce(u:F):$ == - checkExponent changeBase(exponent(u)$F,mantissa(u)$F,base()$F) - - coerce(u:I):$ == - checkExponent changeBase(0,u,10) - - coerce(u:FI):$ == (numer u)::$/(denom u)::$ - - retract(u:$):FI == - value : Union(FI,"failed") := retractIfCan(u) - value case "failed" => error "Cannot retract to a Fraction Integer" - value::FI - - retract(u:$):F == u::F - - retractIfCan(u:$):Union(F,"failed") == u::F::Union(F,"failed") - - retractIfCan(u:$):Union(I,"failed") == - value:FI := mantissa(u)*(B pretend I)::FI**exponent(u) - zero? fractionPart(value) => wholePart(value)::Union(I,"failed") - "failed"::Union(I,"failed") - - retract(u:$):I == - result : Union(I,"failed") := retractIfCan u - result = "failed" => error "Not an Integer" - result::I - - precision(p: PI):PI == - old : PI := P - newPower(B,p) - P := p - old - - precision():PI == P - - base(b:PI):PI == - old : PI := b - newPower(b,P) - B := b - old - - base():PI == B - - maximumExponent(u:I):I == - old : I := EMAX - EMAX := u - old - - maximumExponent():I == EMAX - - minimumExponent(u:I):I == - old : I := EMIN - EMIN := u - old - - minimumExponent():I == EMIN - - 0 == [0,0]$Rep - 1 == changeBase(0,1,10) - - zero?(u:$):Boolean == u=[0,0]$Rep - - - - f1:$ - f2:$ - - - locRound(x:FI):I == - abs(fractionPart(x)) >= 1/2 => wholePart(x)+sign(x) - wholePart(x) - - recip f1 == - zero? f1 => "failed" - normalise [ locRound(B**(2*POWER)/mantissa f1),-(exponent f1 + 2*POWER)] - - f1 * f2 == - normalise [mantissa(f1)*mantissa(f2),exponent(f1)+exponent(f2)]$Rep - - f1 **(p:FI) == - ((f1::F)**p)::% - ---inline - f1 / f2 == - zero? f2 => error "division by zero" - zero? f1 => 0 - f1=f2 => 1 - normalise [locRound(mantissa(f1)*B**(2*POWER)/mantissa(f2)), - exponent(f1)-(exponent f2 + 2*POWER)] - - inv(f1) == 1/f1 - - f1 exquo f2 == f1/f2 - - divide(f1,f2) == [ f1/f2,0] - - f1 quo f2 == f1/f2 - f1 rem f2 == 0 - u:I * f1 == - normalise [u*mantissa(f1),exponent(f1)]$Rep - - f1 = f2 == mantissa(f1)=mantissa(f2) and exponent(f1)=exponent(f2) - - f1 + f2 == - m1 : I := mantissa f1 - m2 : I := mantissa f2 - e1 : I := exponent f1 - e2 : I := exponent f2 - e1 > e2 => ---insignificance - e1 > e2 + POWER + 2 => - zero? f1 => f2 - f1 - normalise [m1*(B pretend I)**((e1-e2) pretend NNI)+m2,e2]$Rep - e2 > e1 + POWER +2 => - zero? f2 => f1 - f2 - normalise [m2*(B pretend I)**((e2-e1) pretend NNI)+m1,e1]$Rep - - - f1 == [- mantissa f1,exponent f1]$Rep - - f1 - f2 == f1 + (-f2) - - f1 < f2 == - m1 : I := mantissa f1 - m2 : I := mantissa f2 - e1 : I := exponent f1 - e2 : I := exponent f2 - sign(m1) = sign(m2) => - e1 < e2 => true - e1 = e2 and m1 < m2 => true - false - sign(m1) = 1 => false - sign(m1) = 0 and sign(m2) = -1 => false - true - - characteristic:NNI == 0 - -@ -\section{domain MCMPLX MachineComplex} -<<domain MCMPLX MachineComplex>>= -)abbrev domain MCMPLX MachineComplex -++ Date Created: December 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: FortranExpression, FortranMachineTypeCategory, MachineInteger, -++ MachineFloat -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A domain which models the complex number representation -++ used by machines in the AXIOM-NAG link. -MachineComplex():Exports == Implementation where - - Exports ==> Join (FortranMachineTypeCategory, - ComplexCategory(MachineFloat)) with - coerce : Complex Float -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : Complex Integer -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : Complex MachineFloat -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : Complex MachineInteger -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : $ -> Complex Float - ++ coerce(u) transforms u into a COmplex Float - - Implementation ==> Complex MachineFloat add - - coerce(u:Complex Float):$ == - complex(real(u)::MachineFloat,imag(u)::MachineFloat) - - coerce(u:Complex Integer):$ == - complex(real(u)::MachineFloat,imag(u)::MachineFloat) - - coerce(u:Complex MachineInteger):$ == - complex(real(u)::MachineFloat,imag(u)::MachineFloat) - - coerce(u:Complex MachineFloat):$ == - complex(real(u),imag(u)) - - coerce(u:$):Complex Float == - complex(real(u)::Float,imag(u)::Float) - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain MINT MachineInteger>> -<<domain MFLOAT MachineFloat>> -<<domain MCMPLX MachineComplex>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/fortpak.spad.pamphlet b/src/algebra/fortpak.spad.pamphlet deleted file mode 100644 index 05d33441..00000000 --- a/src/algebra/fortpak.spad.pamphlet +++ /dev/null @@ -1,641 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra fortpak.spad} -\author{Grant Keady, Godfrey Nolan, Mike Dewar, Themos Tsikas} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{package FCPAK1 FortranCodePackage1} -<<package FCPAK1 FortranCodePackage1>>= -)abbrev package FCPAK1 FortranCodePackage1 -++ Author: Grant Keady and Godfrey Nolan -++ Date Created: April 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Constructors: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: -++ \spadtype{FortranCodePackage1} provides some utilities for -++ producing useful objects in FortranCode domain. -++ The Package may be used with the FortranCode domain and its -++ \spad{printCode} or possibly via an outputAsFortran. -++ (The package provides items of use in connection with ASPs -++ in the AXIOM-NAG link and, where appropriate, naming accords -++ with that in IRENA.) -++ The easy-to-use functions use Fortran loop variables I1, I2, -++ and it is users' responsibility to check that this is sensible. -++ The advanced functions use SegmentBinding to allow users control -++ over Fortran loop variable names. --- Later might add functions to build --- diagonalMatrix from List, i.e. the FC version of the corresponding --- AXIOM function from MatrixCategory; --- bandedMatrix, i.e. the full-matrix-FC version of the corresponding --- AXIOM function in BandedMatrix Domain --- bandedSymmetricMatrix, i.e. the full-matrix-FC version of the corresponding --- AXIOM function in BandedSymmetricMatrix Domain - -FortranCodePackage1: Exports == Implementation where - - NNI ==> NonNegativeInteger - PI ==> PositiveInteger - PIN ==> Polynomial(Integer) - SBINT ==> SegmentBinding(Integer) - SEGINT ==> Segment(Integer) - LSBINT ==> List(SegmentBinding(Integer)) - SBPIN ==> SegmentBinding(Polynomial(Integer)) - SEGPIN ==> Segment(Polynomial(Integer)) - LSBPIN ==> List(SegmentBinding(Polynomial(Integer))) - FC ==> FortranCode - EXPRESSION ==> Union(Expression Integer,Expression Float,Expression Complex Integer,Expression Complex Float) - - Exports == with - - zeroVector: (Symbol,PIN) -> FC - ++ zeroVector(s,p) \undocumented{} - - zeroMatrix: (Symbol,PIN,PIN) -> FC - ++ zeroMatrix(s,p,q) uses loop variables in the Fortran, I1 and I2 - - zeroMatrix: (Symbol,SBPIN,SBPIN) -> FC - ++ zeroMatrix(s,b,d) in this version gives the user control - ++ over names of Fortran variables used in loops. - - zeroSquareMatrix: (Symbol,PIN) -> FC - ++ zeroSquareMatrix(s,p) \undocumented{} - - identitySquareMatrix: (Symbol,PIN) -> FC - ++ identitySquareMatrix(s,p) \undocumented{} - - Implementation ==> add - import FC - - zeroVector(fname:Symbol,n:PIN):FC == - ue:Expression(Integer) := 0 - i1:Symbol := "I1"::Symbol - lp1:PIN := 1::PIN - hp1:PIN := n - segp1:SEGPIN:= segment(lp1,hp1)$SEGPIN - segbp1:SBPIN := equation(i1,segp1)$SBPIN - ip1:PIN := i1::PIN - indices:List(PIN) := [ip1] - fa:FC := forLoop(segbp1,assign(fname,indices,ue)$FC)$FC - fa - - zeroMatrix(fname:Symbol,m:PIN,n:PIN):FC == - ue:Expression(Integer) := 0 - i1:Symbol := "I1"::Symbol - lp1:PIN := 1::PIN - hp1:PIN := m - segp1:SEGPIN:= segment(lp1,hp1)$SEGPIN - segbp1:SBPIN := equation(i1,segp1)$SBPIN - i2:Symbol := "I2"::Symbol - hp2:PIN := n - segp2:SEGPIN:= segment(lp1,hp2)$SEGPIN - segbp2:SBPIN := equation(i2,segp2)$SBPIN - ip1:PIN := i1::PIN - ip2:PIN := i2::PIN - indices:List(PIN) := [ip1,ip2] - fa:FC :=forLoop(segbp1,forLoop(segbp2,assign(fname,indices,ue)$FC)$FC)$FC - fa - - zeroMatrix(fname:Symbol,segbp1:SBPIN,segbp2:SBPIN):FC == - ue:Expression(Integer) := 0 - i1:Symbol := variable(segbp1)$SBPIN - i2:Symbol := variable(segbp2)$SBPIN - ip1:PIN := i1::PIN - ip2:PIN := i2::PIN - indices:List(PIN) := [ip1,ip2] - fa:FC :=forLoop(segbp1,forLoop(segbp2,assign(fname,indices,ue)$FC)$FC)$FC - fa - - zeroSquareMatrix(fname:Symbol,n:PIN):FC == - ue:Expression(Integer) := 0 - i1:Symbol := "I1"::Symbol - lp1:PIN := 1::PIN - hp1:PIN := n - segp1:SEGPIN:= segment(lp1,hp1)$SEGPIN - segbp1:SBPIN := equation(i1,segp1)$SBPIN - i2:Symbol := "I2"::Symbol - segbp2:SBPIN := equation(i2,segp1)$SBPIN - ip1:PIN := i1::PIN - ip2:PIN := i2::PIN - indices:List(PIN) := [ip1,ip2] - fa:FC :=forLoop(segbp1,forLoop(segbp2,assign(fname,indices,ue)$FC)$FC)$FC - fa - - identitySquareMatrix(fname:Symbol,n:PIN):FC == - ue:Expression(Integer) := 0 - u1:Expression(Integer) := 1 - i1:Symbol := "I1"::Symbol - lp1:PIN := 1::PIN - hp1:PIN := n - segp1:SEGPIN:= segment(lp1,hp1)$SEGPIN - segbp1:SBPIN := equation(i1,segp1)$SBPIN - i2:Symbol := "I2"::Symbol - segbp2:SBPIN := equation(i2,segp1)$SBPIN - ip1:PIN := i1::PIN - ip2:PIN := i2::PIN - indice1:List(PIN) := [ip1,ip1] - indices:List(PIN) := [ip1,ip2] - fc:FC := forLoop(segbp2,assign(fname,indices,ue)$FC)$FC - f1:FC := assign(fname,indice1,u1)$FC - fl:List(FC) := [fc,f1] - fa:FC := forLoop(segbp1,block(fl)$FC)$FC - fa - -@ -\section{package NAGSP NAGLinkSupportPackage} -<<package NAGSP NAGLinkSupportPackage>>= -)abbrev package NAGSP NAGLinkSupportPackage -++ Author: Mike Dewar and Godfrey Nolan -++ Date Created: March 1993 -++ Date Last Updated: March 4 1994 -++ October 6 1994 -++ Basic Operations: -++ Related Domains: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: Support functions for the NAG Library Link functions -NAGLinkSupportPackage() : exports == implementation where - - exports ==> with - fortranCompilerName : () -> String - ++ fortranCompilerName() returns the name of the currently selected - ++ Fortran compiler - fortranLinkerArgs : () -> String - ++ fortranLinkerArgs() returns the current linker arguments - aspFilename : String -> String - ++ aspFilename("f") returns a String consisting of "f" suffixed with - ++ an extension identifying the current AXIOM session. - dimensionsOf : (Symbol, Matrix DoubleFloat) -> SExpression - ++ dimensionsOf(s,m) \undocumented{} - dimensionsOf : (Symbol, Matrix Integer) -> SExpression - ++ dimensionsOf(s,m) \undocumented{} - checkPrecision : () -> Boolean - ++ checkPrecision() \undocumented{} - restorePrecision : () -> Void - ++ restorePrecision() \undocumented{} - - implementation ==> add - makeAs: (Symbol,Symbol) -> Symbol - changeVariables: (Expression Integer,Symbol) -> Expression Integer - changeVariablesF: (Expression Float,Symbol) -> Expression Float - - import String - import Symbol - - checkPrecision():Boolean == - (_$fortranPrecision$Lisp = "single"::Symbol) and (_$nagEnforceDouble$Lisp) => - systemCommand("set fortran precision double")$MoreSystemCommands - if _$nagMessages$Lisp then - print("*** Warning: Resetting fortran precision to double")$PrintPackage - true - false - - restorePrecision():Void == - systemCommand("set fortran precision single")$MoreSystemCommands - if _$nagMessages$Lisp then - print("** Warning: Restoring fortran precision to single")$PrintPackage - - uniqueId : String := "" - counter : Integer := 0 - getUniqueId():String == - if uniqueId = "" then - uniqueId := concat(getEnv("HOST")$Lisp,getEnv("SPADNUM")$Lisp) - concat(uniqueId,string (counter:=counter+1)) - - fortranCompilerName() == string _$fortranCompilerName$Lisp - fortranLinkerArgs() == string _$fortranLibraries$Lisp - - aspFilename(f:String):String == concat ["/tmp/",f,getUniqueId(),".f"] - - dimensionsOf(u:Symbol,m:Matrix DoubleFloat):SExpression == - [u,nrows m,ncols m]$Lisp - dimensionsOf(u:Symbol,m:Matrix Integer):SExpression == - [u,nrows m,ncols m]$Lisp - -@ -\section{package FORT FortranPackage} -<<package FORT FortranPackage>>= -)abbrev package FORT FortranPackage - -++ Author: Mike Dewar -++ Date Created: October 6 1991 -++ Date Last Updated: 13 July 1994 -++ Basic Operations: linkToFortran -++ Related Constructors: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: provides an interface to the boot code for calling Fortran -FortranPackage(): Exports == Implementation where - FST ==> FortranScalarType - SEX ==> SExpression - L ==> List - S ==> Symbol - FOP ==> FortranOutputStackPackage - U ==> Union(array:L S,scalar:S) - - Exports ==> with - linkToFortran: (S, L U, L L U, L S) -> SEX - ++ linkToFortran(s,l,ll,lv) \undocumented{} - linkToFortran: (S, L U, L L U, L S, S) -> SEX - ++ linkToFortran(s,l,ll,lv,t) \undocumented{} - linkToFortran: (S,L S,TheSymbolTable,L S) -> SEX - ++ linkToFortran(s,l,t,lv) \undocumented{} - outputAsFortran: FileName -> Void - ++ outputAsFortran(fn) \undocumented{} - setLegalFortranSourceExtensions: List String -> List String - ++ setLegalFortranSourceExtensions(l) \undocumented{} - - Implementation ==> add - - legalFortranSourceExtensions : List String := ["f"] - - setLegalFortranSourceExtensions(l:List String):List String == - legalFortranSourceExtensions := l - - checkExtension(fn : FileName) : String == - -- Does it end in a legal extension ? - stringFn := fn::String - not member?(extension fn,legalFortranSourceExtensions) => - error [stringFn,"is not a legal Fortran Source File."] - stringFn - - outputAsFortran(fn:FileName):Void == --- source : String := checkExtension fn - source : String := fn::String - not readable? fn => - popFortranOutputStack()$FOP - error([source,"is not readable"]@List(String)) - target : String := topFortranOutputStack()$FOP - command : String := - concat(["sys rm -f ",target," ; cp ",source," ",target])$String - systemCommand(command)$MoreSystemCommands - - linkToFortran(name:S,args:L U, decls:L L U, res:L(S)):SEX == - makeFort(name,args,decls,res,NIL$Lisp,NIL$Lisp)$Lisp - - linkToFortran(name:S,args:L U, decls:L L U, res:L(S),returnType:S):SEX == - makeFort(name,args,decls,res,returnType,NIL$Lisp)$Lisp - - dimensions(type:FortranType):SEX == - convert([convert(convert(u)@InputForm)@SEX _ - for u in dimensionsOf(type)])@SEX - - ftype(name:S,type:FortranType):SEX == - [name,scalarTypeOf(type),dimensions(type),external? type]$Lisp - - makeAspList(asp:S,syms:TheSymbolTable):SExpression== - symtab : SymbolTable := symbolTableOf(asp,syms) - [asp,returnTypeOf(asp,syms),argumentListOf(asp,syms), _ - [ftype(u,fortranTypeOf(u,symtab)) for u in parametersOf symtab]]$Lisp - - linkToFortran(name:S,aArgs:L S,syms:TheSymbolTable,res:L S):SEX == - arguments : L S := argumentListOf(name,syms)$TheSymbolTable - dummies : L S := setDifference(arguments,aArgs) - symbolTable:SymbolTable := symbolTableOf(name,syms) - symbolList := newTypeLists(symbolTable) - rt:Union(fst: FST,void: "void") := returnTypeOf(name,syms)$TheSymbolTable - - -- Look for arguments which are subprograms - asps :=[makeAspList(u,syms) for u in externalList(symbolTable)$SymbolTable] - rt case fst => - makeFort1(name,arguments,aArgs,dummies,symbolList,res,(rt.fst)::S,asps)$Lisp - makeFort1(name,arguments,aArgs,dummies,symbolList,res,NIL$Lisp,asps)$Lisp - -@ -\section{package FOP FortranOutputStackPackage} -<<package FOP FortranOutputStackPackage>>= -)abbrev package FOP FortranOutputStackPackage - -++ Author: Mike Dewar -++ Date Created: October 1992 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: Code to manipulate Fortran Output Stack -FortranOutputStackPackage() : specification == implementation where - - specification == with - - clearFortranOutputStack : () -> Stack String - ++ clearFortranOutputStack() clears the Fortran output stack - showFortranOutputStack : () -> Stack String - ++ showFortranOutputStack() returns the Fortran output stack - popFortranOutputStack : () -> Void - ++ popFortranOutputStack() pops the Fortran output stack - pushFortranOutputStack : FileName -> Void - ++ pushFortranOutputStack(f) pushes f onto the Fortran output stack - pushFortranOutputStack : String -> Void - ++ pushFortranOutputStack(f) pushes f onto the Fortran output stack - topFortranOutputStack : () -> String - ++ topFortranOutputStack() returns the top element of the Fortran - ++ output stack - - implementation == add - - import MoreSystemCommands - - -- A stack of filenames for Fortran output. We are sharing this with - -- the standard Fortran output code, so want to be a bit careful about - -- how we interact with what the user does independently. We get round - -- potential problems by always examining the top element of the stack - -- before we push. If the user has redirected output then we alter our - -- top value accordingly. - fortranOutputStack : Stack String := empty()@(Stack String) - - topFortranOutputStack():String == string(_$fortranOutputFile$Lisp) - - pushFortranOutputStack(fn:FileName):Void == - if empty? fortranOutputStack then - push!(string(_$fortranOutputFile$Lisp),fortranOutputStack) - else if not(top(fortranOutputStack)=string(_$fortranOutputFile$Lisp)) then - pop! fortranOutputStack - push!(string(_$fortranOutputFile$Lisp),fortranOutputStack) - push!( fn::String,fortranOutputStack) - systemCommand concat(["set output fortran quiet ", fn::String])$String - - pushFortranOutputStack(fn:String):Void == - if empty? fortranOutputStack then - push!(string(_$fortranOutputFile$Lisp),fortranOutputStack) - else if not(top(fortranOutputStack)=string(_$fortranOutputFile$Lisp)) then - pop! fortranOutputStack - push!(string(_$fortranOutputFile$Lisp),fortranOutputStack) - push!( fn,fortranOutputStack) - systemCommand concat(["set output fortran quiet ", fn])$String - - popFortranOutputStack():Void == - if not empty? fortranOutputStack then pop! fortranOutputStack - if empty? fortranOutputStack then push!("CONSOLE",fortranOutputStack) - systemCommand concat(["set output fortran quiet append ",_ - top fortranOutputStack])$String - - clearFortranOutputStack():Stack String == - fortranOutputStack := empty()@(Stack String) - - showFortranOutputStack():Stack String == - fortranOutputStack - -@ -\section{package TEMUTL TemplateUtilities} -<<package TEMUTL TemplateUtilities>>= -)abbrev package TEMUTL TemplateUtilities -++ Author: Mike Dewar -++ Date Created: October 1992 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: This package provides functions for template manipulation -TemplateUtilities(): Exports == Implementation where - - Exports == with - interpretString : String -> Any - ++ interpretString(s) treats a string as a piece of AXIOM input, by - ++ parsing and interpreting it. - stripCommentsAndBlanks : String -> String - ++ stripCommentsAndBlanks(s) treats s as a piece of AXIOM input, and - ++ removes comments, and leading and trailing blanks. - - Implementation == add - - import InputForm - - stripC(s:String,u:String):String == - i : Integer := position(u,s,1) - i = 0 => s - delete(s,i..) - - stripCommentsAndBlanks(s:String):String == - trim(stripC(stripC(s,"++"),"--"),char " ") - - parse(s:String):InputForm == - ncParseFromString(s)$Lisp::InputForm - - interpretString(s:String):Any == - interpret parse s - -@ -\section{package MCALCFN MultiVariableCalculusFunctions} -<<package MCALCFN MultiVariableCalculusFunctions>>= -)abbrev package MCALCFN MultiVariableCalculusFunctions -++ Author: Themos Tsikas, Grant Keady -++ Date Created: December 1992 -++ Date Last Updated: June 1993 -++ Basic Operations: -++ Related Constructors: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: -++ \spadtype{MultiVariableCalculusFunctions} Package provides several -++ functions for multivariable calculus. -++ These include gradient, hessian and jacobian, -++ divergence and laplacian. -++ Various forms for banded and sparse storage of matrices are -++ included. -MultiVariableCalculusFunctions(S,F,FLAF,FLAS) : Exports == Implementation where - PI ==> PositiveInteger - NNI ==> NonNegativeInteger - - S: SetCategory - F: PartialDifferentialRing(S) - FLAS: FiniteLinearAggregate(S) - with finiteAggregate - FLAF: FiniteLinearAggregate(F) - - Exports ==> with - gradient: (F,FLAS) -> Vector F - ++ \spad{gradient(v,xlist)} - ++ computes the gradient, the vector of first partial derivatives, - ++ of the scalar field v, - ++ v a function of the variables listed in xlist. - divergence: (FLAF,FLAS) -> F - ++ \spad{divergence(vf,xlist)} - ++ computes the divergence of the vector field vf, - ++ vf a vector function of the variables listed in xlist. - laplacian: (F,FLAS) -> F - ++ \spad{laplacian(v,xlist)} - ++ computes the laplacian of the scalar field v, - ++ v a function of the variables listed in xlist. - hessian: (F,FLAS) -> Matrix F - ++ \spad{hessian(v,xlist)} - ++ computes the hessian, the matrix of second partial derivatives, - ++ of the scalar field v, - ++ v a function of the variables listed in xlist. - bandedHessian: (F,FLAS,NNI) -> Matrix F - ++ \spad{bandedHessian(v,xlist,k)} - ++ computes the hessian, the matrix of second partial derivatives, - ++ of the scalar field v, - ++ v a function of the variables listed in xlist, - ++ 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 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-F07 conventions.) - -- At one stage it seemed a good idea to help the ASP<n> domains - -- with the types of their input arguments and this led to the - -- standard Gradient|Hessian|Jacobian functions. - --standardJacobian: (Vector(F),List(S)) -> Matrix F - -- ++ \spad{jacobian(vf,xlist)} - -- ++ computes the jacobian, the matrix of first partial derivatives, - -- ++ of the vector field vf, - -- ++ vf a vector function of the variables listed in xlist. - jacobian: (FLAF,FLAS) -> Matrix F - ++ \spad{jacobian(vf,xlist)} - ++ computes the jacobian, the matrix of first partial derivatives, - ++ of the vector field vf, - ++ vf a vector function of the variables listed in xlist. - bandedJacobian: (FLAF,FLAS,NNI,NNI) -> Matrix F - ++ \spad{bandedJacobian(vf,xlist,kl,ku)} - ++ computes the jacobian, the matrix of first partial derivatives, - ++ of the vector field vf, - ++ vf a vector function of the variables listed in xlist, - ++ kl is the number of nonzero subdiagonals, - ++ ku is the number of nonzero superdiagonals, - ++ kl+ku+1 being actual bandwidth. - ++ Stores the nonzero band in a matrix, - ++ dimensions kl+ku+1 by #xlist. - ++ The upper triangle is in the top ku rows, - ++ the diagonal is in row ku+1, - ++ the lower triangle in the last 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-F07 conventions.) - - Implementation ==> add - localGradient(v:F,xlist:List(S)):Vector(F) == - vector([D(v,x) for x in xlist]) - gradient(v,xflas) == - --xlist:List(S) := [xflas(i) for i in 1 .. maxIndex(xflas)] - xlist:List(S) := parts(xflas) - localGradient(v,xlist) - localDivergence(vf:Vector(F),xlist:List(S)):F == - n: NNI - ans: F - -- Perhaps should report error if two args of min different - n:= min(#(xlist),((maxIndex(vf))::NNI))$NNI - ans:= 0 - for i in 1 .. n repeat ans := ans + D(vf(i),xlist(i)) - ans - divergence(vf,xflas) == - xlist:List(S) := parts(xflas) - n: NNI - ans: F - -- Perhaps should report error if two args of min different - n:= min(#(xlist),((maxIndex(vf))::NNI))$NNI - ans:= 0 - for i in 1 .. n repeat ans := ans + D(vf(i),xlist(i)) - ans - laplacian(v,xflas) == - xlist:List(S) := parts(xflas) - gv:Vector(F) := localGradient(v,xlist) - localDivergence(gv,xlist) - hessian(v,xflas) == - xlist:List(S) := parts(xflas) - matrix([[D(v,[x,y]) for x in xlist] for y in xlist]) - --standardJacobian(vf,xlist) == - -- i: PI - -- matrix([[D(vf(i),x) for x in xlist] for i in 1 .. maxIndex(vf)]) - jacobian(vf,xflas) == - xlist:List(S) := parts(xflas) - matrix([[D(vf(i),x) for x in xlist] for i in 1 .. maxIndex(vf)]) - bandedHessian(v,xflas,k) == - xlist:List(S) := parts(xflas) - n: NNI - bandM: Matrix F - n:= #(xlist) - bandM:= new(k+1,n,0) - for j in 1 .. n repeat setelt(bandM,1,j,D(v,xlist(j),2)) - for iw in 2 .. (k+1) repeat (_ - for j in 1 .. (n-iw+1) repeat (_ - setelt(bandM,iw,j,D(v,[xlist(j),xlist(j+iw-1)])) ) ) - bandM - bandedJacobian(vf,xflas,kl,ku) == - xlist:List(S) := parts(xflas) - n: NNI - bandM: Matrix F - n:= #(xlist) - bandM:= new(kl+ku+1,n,0) - for j in 1 .. n repeat setelt(bandM,ku+1,j,D(vf(j),xlist(j))) - for iw in (ku+2) .. (ku+kl+1) repeat (_ - for j in 1 .. (n-iw+ku+1) repeat (_ - setelt(bandM,iw,j,D(vf(j+iw-1-ku),xlist(j))) ) ) - for iw in 1 .. ku repeat (_ - for j in (ku+2-iw) .. n repeat (_ - setelt(bandM,iw,j,D(vf(j+iw-1-ku),xlist(j))) ) ) - bandM - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<package FCPAK1 FortranCodePackage1>> -<<package NAGSP NAGLinkSupportPackage>> -<<package FORT FortranPackage>> -<<package FOP FortranOutputStackPackage>> -<<package TEMUTL TemplateUtilities>> -<<package MCALCFN MultiVariableCalculusFunctions>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/fortran.spad.pamphlet b/src/algebra/fortran.spad.pamphlet deleted file mode 100644 index 050960e0..00000000 --- a/src/algebra/fortran.spad.pamphlet +++ /dev/null @@ -1,1784 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{src/algebra fortran.spad} -\author{Didier Pinchon, Mike Dewar, William Naylor} -\maketitle - -\begin{abstract} -\end{abstract} -\tableofcontents -\eject - -\section{domain RESULT Result} - -<<domain RESULT Result>>= -import Boolean -import Symbol -import OutputForm -import Any -import TableAggregate -)abbrev domain RESULT Result -++ Author: Didier Pinchon and Mike Dewar -++ Date Created: 8 April 1994 -++ Date Last Updated: 28 June 1994 -++ Basic Operations: -++ Related Domains: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: 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. -Result():Exports==Implementation where - - O ==> OutputForm - - Exports ==> TableAggregate(Symbol,Any) with - showScalarValues : Boolean -> Boolean - ++ showScalarValues(true) forces the values of scalar components to be - ++ displayed rather than just their types. - showArrayValues : Boolean -> Boolean - ++ showArrayValues(true) forces the values of array components to be - ++ displayed rather than just their types. - finiteAggregate - - Implementation ==> Table(Symbol,Any) add - import SExpression - - -- Constant - colon := ": "::Symbol::O - elide := "..."::Symbol::O - - -- Flags - showScalarValuesFlag : Boolean := false - showArrayValuesFlag : Boolean := false - - cleanUpDomainForm(d:SExpression):O == - not list? d => d::O - #d=1 => (car d)::O - -- If the car is an atom then we have a domain constructor, if not - -- then we have some kind of value. Since we often can't print these - -- ****ers we just elide them. - not atom? car d => elide - prefix((car d)::O,[cleanUpDomainForm(u) for u in destruct cdr(d)]$List(O)) - - display(v:Any,d:SExpression):O == - not list? d => error "Domain form is non-list" - #d=1 => - showScalarValuesFlag => v::OutputForm - cleanUpDomainForm d - car(d) = convert("Complex"::Symbol)@SExpression => - showScalarValuesFlag => v::OutputForm - cleanUpDomainForm d - showArrayValuesFlag => v::OutputForm - cleanUpDomainForm d - - makeEntry(k:Symbol,v:Any):O == - hconcat [k::O,colon,display(v,dom v)] - - coerce(r:%):O == - bracket [makeEntry(key,r.key) for key in reverse! keys(r)] - - showArrayValues(b:Boolean):Boolean == showArrayValuesFlag := b - showScalarValues(b:Boolean):Boolean == showScalarValuesFlag := b - -@ - -\section{domain FC FortranCode} - -<<domain FC FortranCode>>= -import Void -import List -import Fraction -)abbrev domain FC FortranCode --- The FortranCode domain is used to represent operations which are to be --- translated into FORTRAN. -++ Author: Mike Dewar -++ Date Created: April 1991 -++ Date Last Updated: 22 March 1994 -++ 26 May 1994 Added common, MCD -++ 21 June 1994 Changed print to printStatement, MCD -++ 30 June 1994 Added stop, MCD -++ 12 July 1994 Added assign for String, MCD -++ 9 January 1995 Added fortran2Lines to getCall, MCD -++ Basic Operations: -++ Related Constructors: FortranProgram, Switch, FortranType -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: -++ This domain builds representations of program code segments for use with -++ the FortranProgram domain. -FortranCode(): public == private where - L ==> List - PI ==> PositiveInteger - PIN ==> Polynomial Integer - SEX ==> SExpression - O ==> OutputForm - OP ==> Union(Null:"null", - Assignment:"assignment", - Conditional:"conditional", - Return:"return", - Block:"block", - Comment:"comment", - Call:"call", - For:"for", - While:"while", - Repeat:"repeat", - Goto:"goto", - Continue:"continue", - ArrayAssignment:"arrayAssignment", - Save:"save", - Stop:"stop", - Common:"common", - Print:"print") - ARRAYASS ==> Record(var:Symbol, rand:O, ints2Floats?:Boolean) - EXPRESSION ==> Record(ints2Floats?:Boolean,expr:O) - ASS ==> Record(var:Symbol, - arrayIndex:L PIN, - rand:EXPRESSION - ) - COND ==> Record(switch: Switch(), - thenClause: $, - elseClause: $ - ) - RETURN ==> Record(empty?:Boolean,value:EXPRESSION) - BLOCK ==> List $ - COMMENT ==> List String - COMMON ==> Record(name:Symbol,contents:List Symbol) - CALL ==> String - FOR ==> Record(range:SegmentBinding PIN, span:PIN, body:$) - LABEL ==> SingleInteger - LOOP ==> Record(switch:Switch(),body:$) - PRINTLIST ==> List O - OPREC ==> Union(nullBranch:"null", assignmentBranch:ASS, - arrayAssignmentBranch:ARRAYASS, - conditionalBranch:COND, returnBranch:RETURN, - blockBranch:BLOCK, commentBranch:COMMENT, callBranch:CALL, - forBranch:FOR, labelBranch:LABEL, loopBranch:LOOP, - commonBranch:COMMON, printBranch:PRINTLIST) - - public == SetCategory with - forLoop: (SegmentBinding PIN,$) -> $ - ++ forLoop(i=1..10,c) creates a representation of a FORTRAN DO loop with - ++ \spad{i} ranging over the values 1 to 10. - forLoop: (SegmentBinding PIN,PIN,$) -> $ - ++ forLoop(i=1..10,n,c) creates a representation of a FORTRAN DO loop with - ++ \spad{i} ranging over the values 1 to 10 by n. - whileLoop: (Switch,$) -> $ - ++ whileLoop(s,c) creates a while loop in FORTRAN. - repeatUntilLoop: (Switch,$) -> $ - ++ repeatUntilLoop(s,c) creates a repeat ... until loop in FORTRAN. - goto: SingleInteger -> $ - ++ goto(l) creates a representation of a FORTRAN GOTO statement - continue: SingleInteger -> $ - ++ continue(l) creates a representation of a FORTRAN CONTINUE labelled - ++ with l - comment: String -> $ - ++ comment(s) creates a representation of the String s as a single FORTRAN - ++ comment. - comment: List String -> $ - ++ comment(s) creates a representation of the Strings s as a multi-line - ++ FORTRAN comment. - call: String -> $ - ++ call(s) creates a representation of a FORTRAN CALL statement - returns: () -> $ - ++ returns() creates a representation of a FORTRAN RETURN statement. - returns: Expression MachineFloat -> $ - ++ returns(e) creates a representation of a FORTRAN RETURN statement - ++ with a returned value. - returns: Expression MachineInteger -> $ - ++ returns(e) creates a representation of a FORTRAN RETURN statement - ++ with a returned value. - returns: Expression MachineComplex -> $ - ++ returns(e) creates a representation of a FORTRAN RETURN statement - ++ with a returned value. - returns: Expression Float -> $ - ++ returns(e) creates a representation of a FORTRAN RETURN statement - ++ with a returned value. - returns: Expression Integer -> $ - ++ returns(e) creates a representation of a FORTRAN RETURN statement - ++ with a returned value. - returns: Expression Complex Float -> $ - ++ returns(e) creates a representation of a FORTRAN RETURN statement - ++ with a returned value. - cond: (Switch,$) -> $ - ++ cond(s,e) creates a representation of the FORTRAN expression - ++ IF (s) THEN e. - cond: (Switch,$,$) -> $ - ++ cond(s,e,f) creates a representation of the FORTRAN expression - ++ IF (s) THEN e ELSE f. - assign: (Symbol,String) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Expression MachineInteger) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Expression MachineFloat) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Expression MachineComplex) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix MachineInteger) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix MachineFloat) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix MachineComplex) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector MachineInteger) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector MachineFloat) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector MachineComplex) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix Expression MachineInteger) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix Expression MachineFloat) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix Expression MachineComplex) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector Expression MachineInteger) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector Expression MachineFloat) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector Expression MachineComplex) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,L PIN,Expression MachineInteger) -> $ - ++ assign(x,l,y) creates a representation of the assignment of \spad{y} - ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of - ++ indices). - assign: (Symbol,L PIN,Expression MachineFloat) -> $ - ++ assign(x,l,y) creates a representation of the assignment of \spad{y} - ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of - ++ indices). - assign: (Symbol,L PIN,Expression MachineComplex) -> $ - ++ assign(x,l,y) creates a representation of the assignment of \spad{y} - ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of - ++ indices). - assign: (Symbol,Expression Integer) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Expression Float) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Expression Complex Float) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix Expression Integer) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix Expression Float) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Matrix Expression Complex Float) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector Expression Integer) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector Expression Float) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,Vector Expression Complex Float) -> $ - ++ assign(x,y) creates a representation of the FORTRAN expression - ++ x=y. - assign: (Symbol,L PIN,Expression Integer) -> $ - ++ assign(x,l,y) creates a representation of the assignment of \spad{y} - ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of - ++ indices). - assign: (Symbol,L PIN,Expression Float) -> $ - ++ assign(x,l,y) creates a representation of the assignment of \spad{y} - ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of - ++ indices). - assign: (Symbol,L PIN,Expression Complex Float) -> $ - ++ assign(x,l,y) creates a representation of the assignment of \spad{y} - ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of - ++ indices). - block: List($) -> $ - ++ block(l) creates a representation of the statements in l as a block. - stop: () -> $ - ++ stop() creates a representation of a STOP statement. - save: () -> $ - ++ save() creates a representation of a SAVE statement. - printStatement: List O -> $ - ++ printStatement(l) creates a representation of a PRINT statement. - common: (Symbol,List Symbol) -> $ - ++ common(name,contents) creates a representation a named common block. - operation: $ -> OP - ++ operation(f) returns the name of the operation represented by \spad{f}. - code: $ -> OPREC - ++ code(f) returns the internal representation of the object represented - ++ by \spad{f}. - printCode: $ -> Void - ++ printCode(f) prints out \spad{f} in FORTRAN notation. - getCode: $ -> SEX - ++ getCode(f) returns a Lisp list of strings representing \spad{f} - ++ in Fortran notation. This is used by the FortranProgram domain. - setLabelValue:SingleInteger -> SingleInteger - ++ setLabelValue(i) resets the counter which produces labels to i - - private == add - import Void - import ASS - import COND - import RETURN - import L PIN - import O - import SEX - import FortranType - import TheSymbolTable - - Rep := Record(op: OP, data: OPREC) - - -- We need to be able to generate unique labels - labelValue:SingleInteger := 25000::SingleInteger - setLabelValue(u:SingleInteger):SingleInteger == labelValue := u - newLabel():SingleInteger == - labelValue := labelValue + 1$SingleInteger - labelValue - - commaSep(l:List String):List(String) == - [(l.1),:[:[",",u] for u in rest(l)]] - - getReturn(rec:RETURN):SEX == - returnToken : SEX := convert("RETURN"::Symbol::O)$SEX - elt(rec,empty?)$RETURN => - getStatement(returnToken,NIL$Lisp)$Lisp - rt : EXPRESSION := elt(rec,value)$RETURN - rv : O := elt(rt,expr)$EXPRESSION - getStatement([returnToken,convert(rv)$SEX]$Lisp, - elt(rt,ints2Floats?)$EXPRESSION )$Lisp - - getStop():SEX == - fortran2Lines(LIST("STOP")$Lisp)$Lisp - - getSave():SEX == - fortran2Lines(LIST("SAVE")$Lisp)$Lisp - - getCommon(u:COMMON):SEX == - fortran2Lines(APPEND(LIST("COMMON"," /",string (u.name),"/ ")$Lisp,_ - addCommas(u.contents)$Lisp)$Lisp)$Lisp - - getPrint(l:PRINTLIST):SEX == - ll : SEX := LIST("PRINT*")$Lisp - for i in l repeat - ll := APPEND(ll,CONS(",",expression2Fortran(i)$Lisp)$Lisp)$Lisp - fortran2Lines(ll)$Lisp - - getBlock(rec:BLOCK):SEX == - indentFortLevel(convert(1@Integer)$SEX)$Lisp - expr : SEX := LIST()$Lisp - for u in rec repeat - expr := APPEND(expr,getCode(u))$Lisp - indentFortLevel(convert(-1@Integer)$SEX)$Lisp - expr - - getBody(f:$):SEX == - operation(f) case Block => getCode f - indentFortLevel(convert(1@Integer)$SEX)$Lisp - expr := getCode f - indentFortLevel(convert(-1@Integer)$SEX)$Lisp - expr - - getElseIf(f:$):SEX == - rec := code f - expr := - fortFormatElseIf(elt(rec.conditionalBranch,switch)$COND::O)$Lisp - expr := - APPEND(expr,getBody elt(rec.conditionalBranch,thenClause)$COND)$Lisp - elseBranch := elt(rec.conditionalBranch,elseClause)$COND - not(operation(elseBranch) case Null) => - operation(elseBranch) case Conditional => - APPEND(expr,getElseIf elseBranch)$Lisp - expr := APPEND(expr, getStatement(ELSE::O,NIL$Lisp)$Lisp)$Lisp - expr := APPEND(expr, getBody elseBranch)$Lisp - expr - - getContinue(label:SingleInteger):SEX == - lab : O := label::O - if (width(lab) > 6) then error "Label too big" - cnt : O := "CONTINUE"::O - --sp : O := hspace(6-width lab) - sp : O := hspace(_$fortIndent$Lisp -width lab) - LIST(STRCONC(string(label)$String,sp,cnt)$Lisp)$Lisp - - getGoto(label:SingleInteger):SEX == - fortran2Lines( - LIST(STRCONC("GOTO ",string(label)$String)$Lisp)$Lisp)$Lisp - - getRepeat(repRec:LOOP):SEX == - sw : Switch := NOT elt(repRec,switch)$LOOP - lab := newLabel() - bod := elt(repRec,body)$LOOP - APPEND(getContinue lab,getBody bod, - fortFormatIfGoto(sw::O,lab)$Lisp)$Lisp - - getWhile(whileRec:LOOP):SEX == - sw := NOT elt(whileRec,switch)$LOOP - lab1 := newLabel() - lab2 := newLabel() - bod := elt(whileRec,body)$LOOP - APPEND(fortFormatLabelledIfGoto(sw::O,lab1,lab2)$Lisp, - getBody bod, getBody goto(lab1), getContinue lab2)$Lisp - - getArrayAssign(rec:ARRAYASS):SEX == - getfortarrayexp((rec.var)::O,rec.rand,rec.ints2Floats?)$Lisp - - getAssign(rec:ASS):SEX == - indices : L PIN := elt(rec,arrayIndex)$ASS - if indices = []::(L PIN) then - lhs := elt(rec,var)$ASS::O - else - lhs := cons(elt(rec,var)$ASS::PIN,indices)::O - -- Must get the index brackets correct: - lhs := (cdr car cdr convert(lhs)$SEX::SEX)::O -- Yuck! - elt(elt(rec,rand)$ASS,ints2Floats?)$EXPRESSION => - assignment2Fortran1(lhs,elt(elt(rec,rand)$ASS,expr)$EXPRESSION)$Lisp - integerAssignment2Fortran1(lhs,elt(elt(rec,rand)$ASS,expr)$EXPRESSION)$Lisp - - getCond(rec:COND):SEX == - expr := APPEND(fortFormatIf(elt(rec,switch)$COND::O)$Lisp, - getBody elt(rec,thenClause)$COND)$Lisp - elseBranch := elt(rec,elseClause)$COND - if not(operation(elseBranch) case Null) then - operation(elseBranch) case Conditional => - expr := APPEND(expr,getElseIf elseBranch)$Lisp - expr := APPEND(expr,getStatement(ELSE::O,NIL$Lisp)$Lisp, - getBody elseBranch)$Lisp - APPEND(expr,getStatement(ENDIF::O,NIL$Lisp)$Lisp)$Lisp - - getComment(rec:COMMENT):SEX == - convert([convert(concat("C ",c)$String)@SEX for c in rec])@SEX - - getCall(rec:CALL):SEX == - expr := concat("CALL ",rec)$String - #expr > 1320 => error "Fortran CALL too large" - fortran2Lines(convert([convert(expr)@SEX ])@SEX)$Lisp - - getFor(rec:FOR):SEX == - rnge : SegmentBinding PIN := elt(rec,range)$FOR - increment : PIN := elt(rec,span)$FOR - lab : SingleInteger := newLabel() - declare!(variable rnge,fortranInteger()) - expr := fortFormatDo(variable rnge, (lo segment rnge)::O,_ - (hi segment rnge)::O,increment::O,lab)$Lisp - APPEND(expr, getBody elt(rec,body)$FOR, getContinue(lab))$Lisp - - getCode(f:$):SEX == - opp:OP := operation f - rec:OPREC:= code f - opp case Assignment => getAssign(rec.assignmentBranch) - opp case ArrayAssignment => getArrayAssign(rec.arrayAssignmentBranch) - opp case Conditional => getCond(rec.conditionalBranch) - opp case Return => getReturn(rec.returnBranch) - opp case Block => getBlock(rec.blockBranch) - opp case Comment => getComment(rec.commentBranch) - opp case Call => getCall(rec.callBranch) - opp case For => getFor(rec.forBranch) - opp case Continue => getContinue(rec.labelBranch) - opp case Goto => getGoto(rec.labelBranch) - opp case Repeat => getRepeat(rec.loopBranch) - opp case While => getWhile(rec.loopBranch) - opp case Save => getSave() - opp case Stop => getStop() - opp case Print => getPrint(rec.printBranch) - opp case Common => getCommon(rec.commonBranch) - error "Unsupported program construct." - convert(0)@SEX - - printCode(f:$):Void == - displayLines1$Lisp getCode f - - code (f:$):OPREC == - elt(f,data)$Rep - - operation (f:$):OP == - elt(f,op)$Rep - - common(name':Symbol,contents':List Symbol):$ == - [["common"]$OP,[[name',contents']$COMMON]$OPREC]$Rep - - stop():$ == - [["stop"]$OP,["null"]$OPREC]$Rep - - save():$ == - [["save"]$OP,["null"]$OPREC]$Rep - - printStatement(l:List O):$ == - [["print"]$OP,[l]$OPREC]$Rep - - comment(s:List String):$ == - [["comment"]$OP,[s]$OPREC]$Rep - - comment(s:String):$ == - [["comment"]$OP,[list s]$OPREC]$Rep - - forLoop(r:SegmentBinding PIN,body':$):$ == - [["for"]$OP,[[r,(incr segment r)::PIN,body']$FOR]$OPREC]$Rep - - forLoop(r:SegmentBinding PIN,increment:PIN,body':$):$ == - [["for"]$OP,[[r,increment,body']$FOR]$OPREC]$Rep - - goto(l:SingleInteger):$ == - [["goto"]$OP,[l]$OPREC]$Rep - - continue(l:SingleInteger):$ == - [["continue"]$OP,[l]$OPREC]$Rep - - whileLoop(sw:Switch,b:$):$ == - [["while"]$OP,[[sw,b]$LOOP]$OPREC]$Rep - - repeatUntilLoop(sw:Switch,b:$):$ == - [["repeat"]$OP,[[sw,b]$LOOP]$OPREC]$Rep - - returns():$ == - v := [false,0::O]$EXPRESSION - [["return"]$OP,[[true,v]$RETURN]$OPREC]$Rep - - returns(v:Expression MachineInteger):$ == - [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep - - returns(v:Expression MachineFloat):$ == - [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep - - returns(v:Expression MachineComplex):$ == - [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep - - returns(v:Expression Integer):$ == - [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep - - returns(v:Expression Float):$ == - [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep - - returns(v:Expression Complex Float):$ == - [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep - - block(l:List $):$ == - [["block"]$OP,[l]$OPREC]$Rep - - cond(sw:Switch,thenC:$):$ == - [["conditional"]$OP, - [[sw,thenC,[["null"]$OP,["null"]$OPREC]$Rep]$COND]$OPREC]$Rep - - cond(sw:Switch,thenC:$,elseC:$):$ == - [["conditional"]$OP,[[sw,thenC,elseC]$COND]$OPREC]$Rep - - coerce(f : $):O == - (f.op)::O - - assign(v:Symbol,rhs:String):$ == - [["assignment"]$OP,[[v,nil()::L PIN,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix MachineInteger):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix MachineFloat):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix MachineComplex):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector MachineInteger):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector MachineFloat):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector MachineComplex):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix Expression MachineInteger):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix Expression MachineFloat):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix Expression MachineComplex):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector Expression MachineInteger):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector Expression MachineFloat):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector Expression MachineComplex):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,index:L PIN,rhs:Expression MachineInteger):$ == - [["assignment"]$OP,[[v,index,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,index:L PIN,rhs:Expression MachineFloat):$ == - [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,index:L PIN,rhs:Expression MachineComplex):$ == - [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Expression MachineInteger):$ == - [["assignment"]$OP,[[v,nil()::L PIN,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Expression MachineFloat):$ == - [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Expression MachineComplex):$ == - [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix Expression Integer):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix Expression Float):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Matrix Expression Complex Float):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector Expression Integer):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector Expression Float):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Vector Expression Complex Float):$ == - [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep - - assign(v:Symbol,index:L PIN,rhs:Expression Integer):$ == - [["assignment"]$OP,[[v,index,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,index:L PIN,rhs:Expression Float):$ == - [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,index:L PIN,rhs:Expression Complex Float):$ == - [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Expression Integer):$ == - [["assignment"]$OP,[[v,nil()::L PIN,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Expression Float):$ == - [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - assign(v:Symbol,rhs:Expression Complex Float):$ == - [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep - - call(s:String):$ == - [["call"]$OP,[s]$OPREC]$Rep - -@ -\section{domain FORTRAN FortranProgram} -<<domain FORTRAN FortranProgram>>= -)abbrev domain FORTRAN FortranProgram -++ Author: Mike Dewar -++ Date Created: October 1992 -++ Date Last Updated: 13 January 1994 -++ 23 January 1995 Added support for intrinsic functions -++ Basic Operations: -++ Related Constructors: FortranType, FortranCode, Switch -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: \axiomType{FortranProgram} allows the user to build and manipulate simple -++ models of FORTRAN subprograms. These can then be transformed into actual FORTRAN -++ notation. -FortranProgram(name,returnType,arguments,symbols): Exports == Implement where - name : Symbol - returnType : Union(fst:FortranScalarType,void:"void") - arguments : List Symbol - symbols : SymbolTable - - FC ==> FortranCode - EXPR ==> Expression - INT ==> Integer - CMPX ==> Complex - MINT ==> MachineInteger - MFLOAT ==> MachineFloat - MCMPLX ==> MachineComplex - REP ==> Record(localSymbols : SymbolTable, code : List FortranCode) - - Exports ==> FortranProgramCategory with - coerce : FortranCode -> $ - ++ coerce(fc) \undocumented{} - coerce : List FortranCode -> $ - ++ coerce(lfc) \undocumented{} - coerce : REP -> $ - ++ coerce(r) \undocumented{} - coerce : EXPR MINT -> $ - ++ coerce(e) \undocumented{} - coerce : EXPR MFLOAT -> $ - ++ coerce(e) \undocumented{} - coerce : EXPR MCMPLX -> $ - ++ coerce(e) \undocumented{} - coerce : Equation EXPR MINT -> $ - ++ coerce(eq) \undocumented{} - coerce : Equation EXPR MFLOAT -> $ - ++ coerce(eq) \undocumented{} - coerce : Equation EXPR MCMPLX -> $ - ++ coerce(eq) \undocumented{} - coerce : EXPR INT -> $ - ++ coerce(e) \undocumented{} - coerce : EXPR Float -> $ - ++ coerce(e) \undocumented{} - coerce : EXPR CMPX Float -> $ - ++ coerce(e) \undocumented{} - coerce : Equation EXPR INT -> $ - ++ coerce(eq) \undocumented{} - coerce : Equation EXPR Float -> $ - ++ coerce(eq) \undocumented{} - coerce : Equation EXPR CMPX Float -> $ - ++ coerce(eq) \undocumented{} - - Implement ==> add - - Rep := REP - - import SExpression - import TheSymbolTable - import FortranCode - - makeRep(b:List FortranCode):$ == - construct(empty()$SymbolTable,b)$REP - - codeFrom(u:$):List FortranCode == - elt(u::Rep,code)$REP - - outputAsFortran(p:$):Void == - setLabelValue(25000::SingleInteger)$FC - -- Do this first to catch any extra type declarations: - tempName := "FPTEMP"::Symbol - newSubProgram(tempName) - initialiseIntrinsicList()$Lisp - body : List SExpression := [getCode(l)$FortranCode for l in codeFrom(p)] - intrinsics : SExpression := getIntrinsicList()$Lisp - endSubProgram() - fortFormatHead(returnType::OutputForm, name::OutputForm, _ - arguments::OutputForm)$Lisp - printTypes(symbols)$SymbolTable - printTypes((p::Rep).localSymbols)$SymbolTable - printTypes(tempName)$TheSymbolTable - fortFormatIntrinsics(intrinsics)$Lisp - clearTheSymbolTable(tempName) - for expr in body repeat displayLines1(expr)$Lisp - dispStatement(END::OutputForm)$Lisp - - mkString(l:List Symbol):String == - unparse(convert(l::OutputForm)@InputForm)$InputForm - - checkVariables(user:List Symbol,target:List Symbol):Void == - -- We don't worry about whether the user has subscripted the - -- variables or not. - setDifference(map(name$Symbol,user),target) ~= empty()$List(Symbol) => - s1 : String := mkString(user) - s2 : String := mkString(target) - error ["Incompatible variable lists:", s1, s2] - - coerce(u:EXPR MINT) : $ == - checkVariables(variables(u)$EXPR(MINT),arguments) - l : List(FC) := [assign(name,u)$FC,returns()$FC] - makeRep l - - coerce(u:Equation EXPR MINT) : $ == - retractIfCan(lhs u)@Union(Kernel(EXPR MINT),"failed") case "failed" => - error "left hand side is not a kernel" - vList : List Symbol := variables lhs u - #vList ~= #arguments => - error "Incorrect number of arguments" - veList : List EXPR MINT := [w::EXPR(MINT) for w in vList] - aeList : List EXPR MINT := [w::EXPR(MINT) for w in arguments] - eList : List Equation EXPR MINT := - [equation(w,v) for w in veList for v in aeList] - (subst(rhs u,eList))::$ - - coerce(u:EXPR MFLOAT) : $ == - checkVariables(variables(u)$EXPR(MFLOAT),arguments) - l : List(FC) := [assign(name,u)$FC,returns()$FC] - makeRep l - - coerce(u:Equation EXPR MFLOAT) : $ == - retractIfCan(lhs u)@Union(Kernel(EXPR MFLOAT),"failed") case "failed" => - error "left hand side is not a kernel" - vList : List Symbol := variables lhs u - #vList ~= #arguments => - error "Incorrect number of arguments" - veList : List EXPR MFLOAT := [w::EXPR(MFLOAT) for w in vList] - aeList : List EXPR MFLOAT := [w::EXPR(MFLOAT) for w in arguments] - eList : List Equation EXPR MFLOAT := - [equation(w,v) for w in veList for v in aeList] - (subst(rhs u,eList))::$ - - coerce(u:EXPR MCMPLX) : $ == - checkVariables(variables(u)$EXPR(MCMPLX),arguments) - l : List(FC) := [assign(name,u)$FC,returns()$FC] - makeRep l - - coerce(u:Equation EXPR MCMPLX) : $ == - retractIfCan(lhs u)@Union(Kernel EXPR MCMPLX,"failed") case "failed"=> - error "left hand side is not a kernel" - vList : List Symbol := variables lhs u - #vList ~= #arguments => - error "Incorrect number of arguments" - veList : List EXPR MCMPLX := [w::EXPR(MCMPLX) for w in vList] - aeList : List EXPR MCMPLX := [w::EXPR(MCMPLX) for w in arguments] - eList : List Equation EXPR MCMPLX := - [equation(w,v) for w in veList for v in aeList] - (subst(rhs u,eList))::$ - - - coerce(u:REP):$ == - u@Rep - - coerce(u:$):OutputForm == - coerce(name)$Symbol - - coerce(c:List FortranCode):$ == - makeRep c - - coerce(c:FortranCode):$ == - makeRep [c] - - coerce(u:EXPR INT) : $ == - checkVariables(variables(u)$EXPR(INT),arguments) - l : List(FC) := [assign(name,u)$FC,returns()$FC] - makeRep l - - coerce(u:Equation EXPR INT) : $ == - retractIfCan(lhs u)@Union(Kernel(EXPR INT),"failed") case "failed" => - error "left hand side is not a kernel" - vList : List Symbol := variables lhs u - #vList ~= #arguments => - error "Incorrect number of arguments" - veList : List EXPR INT := [w::EXPR(INT) for w in vList] - aeList : List EXPR INT := [w::EXPR(INT) for w in arguments] - eList : List Equation EXPR INT := - [equation(w,v) for w in veList for v in aeList] - (subst(rhs u,eList))::$ - - coerce(u:EXPR Float) : $ == - checkVariables(variables(u)$EXPR(Float),arguments) - l : List(FC) := [assign(name,u)$FC,returns()$FC] - makeRep l - - coerce(u:Equation EXPR Float) : $ == - retractIfCan(lhs u)@Union(Kernel(EXPR Float),"failed") case "failed" => - error "left hand side is not a kernel" - vList : List Symbol := variables lhs u - #vList ~= #arguments => - error "Incorrect number of arguments" - veList : List EXPR Float := [w::EXPR(Float) for w in vList] - aeList : List EXPR Float := [w::EXPR(Float) for w in arguments] - eList : List Equation EXPR Float := - [equation(w,v) for w in veList for v in aeList] - (subst(rhs u,eList))::$ - - coerce(u:EXPR Complex Float) : $ == - checkVariables(variables(u)$EXPR(Complex Float),arguments) - l : List(FC) := [assign(name,u)$FC,returns()$FC] - makeRep l - - coerce(u:Equation EXPR CMPX Float) : $ == - retractIfCan(lhs u)@Union(Kernel EXPR CMPX Float,"failed") case "failed"=> - error "left hand side is not a kernel" - vList : List Symbol := variables lhs u - #vList ~= #arguments => - error "Incorrect number of arguments" - veList : List EXPR CMPX Float := [w::EXPR(CMPX Float) for w in vList] - aeList : List EXPR CMPX Float := [w::EXPR(CMPX Float) for w in arguments] - eList : List Equation EXPR CMPX Float := - [equation(w,v) for w in veList for v in aeList] - (subst(rhs u,eList))::$ - -@ -\section{domain M3D ThreeDimensionalMatrix} -<<domain M3D ThreeDimensionalMatrix>>= -)abbrev domain M3D ThreeDimensionalMatrix -++ Author: William Naylor -++ Date Created: 20 October 1993 -++ Date Last Updated: 20 May 1994 -++ BasicFunctions: -++ Related Constructors: Matrix -++ Also See: PrimitiveArray -++ AMS Classification: -++ Keywords: -++ References: -++ Description: -++ This domain represents three dimensional matrices over a general object type -ThreeDimensionalMatrix(R) : Exports == Implementation where - - R : SetCategory - L ==> List - NNI ==> NonNegativeInteger - A1AGG ==> OneDimensionalArrayAggregate - ARRAY1 ==> OneDimensionalArray - PA ==> PrimitiveArray - INT ==> Integer - PI ==> PositiveInteger - - Exports ==> HomogeneousAggregate(R) with - - if R has Ring then - zeroMatrix : (NNI,NNI,NNI) -> $ - ++ zeroMatrix(i,j,k) create a matrix with all zero terms - identityMatrix : (NNI) -> $ - ++ identityMatrix(n) create an identity matrix - ++ we note that this must be square - plus : ($,$) -> $ - ++ plus(x,y) adds two matrices, term by term - ++ we note that they must be the same size - construct : (L L L R) -> $ - ++ construct(lll) creates a 3-D matrix from a List List List R lll - elt : ($,NNI,NNI,NNI) -> R - ++ elt(x,i,j,k) extract an element from the matrix x - setelt! :($,NNI,NNI,NNI,R) -> R - ++ setelt!(x,i,j,k,s) (or x.i.j.k:=s) sets a specific element of the array to some value of type R - coerce : (PA PA PA R) -> $ - ++ coerce(p) moves from the representation type - ++ (PrimitiveArray PrimitiveArray PrimitiveArray R) - ++ to the domain - coerce : $ -> (PA PA PA R) - ++ coerce(x) moves from the domain to the representation type - matrixConcat3D : (Symbol,$,$) -> $ - ++ matrixConcat3D(s,x,y) concatenates two 3-D matrices along a specified axis - matrixDimensions : $ -> Vector NNI - ++ matrixDimensions(x) returns the dimensions of a matrix - - Implementation ==> (PA PA PA R) add - - import (PA PA PA R) - import (PA PA R) - import (PA R) - import R - - matrix1,matrix2,resultMatrix : $ - - -- function to concatenate two matrices - -- the first argument must be a symbol, which is either i,j or k - -- to specify the direction in which the concatenation is to take place - matrixConcat3D(dir : Symbol,mat1 : $,mat2 : $) : $ == - not ((dir = (i::Symbol)) or (dir = (j::Symbol)) or (dir = (k::Symbol)))_ - => error "the axis of concatenation must be i,j or k" - mat1Dim := matrixDimensions(mat1) - mat2Dim := matrixDimensions(mat2) - iDim1 := mat1Dim.1 - jDim1 := mat1Dim.2 - kDim1 := mat1Dim.3 - iDim2 := mat2Dim.1 - jDim2 := mat2Dim.2 - kDim2 := mat2Dim.3 - matRep1 : (PA PA PA R) := copy(mat1 :: (PA PA PA R))$(PA PA PA R) - matRep2 : (PA PA PA R) := copy(mat2 :: (PA PA PA R))$(PA PA PA R) - retVal : $ - - if (dir = (i::Symbol)) then - -- j,k dimensions must agree - if (not ((jDim1 = jDim2) and (kDim1=kDim2))) - then - error "jxk do not agree" - else - retVal := (coerce(concat(matRep1,matRep2)$(PA PA PA R))$$)@$ - - if (dir = (j::Symbol)) then - -- i,k dimensions must agree - if (not ((iDim1 = iDim2) and (kDim1=kDim2))) - then - error "ixk do not agree" - else - for i in 0..(iDim1-1) repeat - setelt(matRep1,i,(concat(elt(matRep1,i)$(PA PA PA R)_ - ,elt(matRep2,i)$(PA PA PA R))$(PA PA R))@(PA PA R))$(PA PA PA R) - retVal := (coerce(matRep1)$$)@$ - - if (dir = (k::Symbol)) then - temp : (PA PA R) - -- i,j dimensions must agree - if (not ((iDim1 = iDim2) and (jDim1=jDim2))) - then - error "ixj do not agree" - else - for i in 0..(iDim1-1) repeat - temp := copy(elt(matRep1,i)$(PA PA PA R))$(PA PA R) - for j in 0..(jDim1-1) repeat - setelt(temp,j,concat(elt(elt(matRep1,i)$(PA PA PA R)_ - ,j)$(PA PA R),elt(elt(matRep2,i)$(PA PA PA R),j)$(PA PA R)_ - )$(PA R))$(PA PA R) - setelt(matRep1,i,temp)$(PA PA PA R) - retVal := (coerce(matRep1)$$)@$ - - retVal - - matrixDimensions(mat : $) : Vector NNI == - matRep : (PA PA PA R) := mat :: (PA PA PA R) - iDim : NNI := (#matRep)$(PA PA PA R) - matRep2 : PA PA R := elt(matRep,0)$(PA PA PA R) - jDim : NNI := (#matRep2)$(PA PA R) - matRep3 : (PA R) := elt(matRep2,0)$(PA PA R) - kDim : NNI := (#matRep3)$(PA R) - retVal : Vector NNI := new(3,0)$(Vector NNI) - retVal.1 := iDim - retVal.2 := jDim - retVal.3 := kDim - retVal - - coerce(matrixRep : (PA PA PA R)) : $ == matrixRep pretend $ - - coerce(mat : $) : (PA PA PA R) == mat pretend (PA PA PA R) - - -- i,j,k must be with in the bounds of the matrix - elt(mat : $,i : NNI,j : NNI,k : NNI) : R == - matDims := matrixDimensions(mat) - iLength := matDims.1 - jLength := matDims.2 - kLength := matDims.3 - ((i > iLength) or (j > jLength) or (k > kLength) or (i=0) or (j=0) or_ -(k=0)) => error "coordinates must be within the bounds of the matrix" - matrixRep : PA PA PA R := mat :: (PA PA PA R) - elt(elt(elt(matrixRep,i-1)$(PA PA PA R),j-1)$(PA PA R),k-1)$(PA R) - - setelt!(mat : $,i : NNI,j : NNI,k : NNI,val : R)_ - : R == - matDims := matrixDimensions(mat) - iLength := matDims.1 - jLength := matDims.2 - kLength := matDims.3 - ((i > iLength) or (j > jLength) or (k > kLength) or (i=0) or (j=0) or_ -(k=0)) => error "coordinates must be within the bounds of the matrix" - matrixRep : PA PA PA R := mat :: (PA PA PA R) - row2 : PA PA R := copy(elt(matrixRep,i-1)$(PA PA PA R))$(PA PA R) - row1 : PA R := copy(elt(row2,j-1)$(PA PA R))$(PA R) - setelt(row1,k-1,val)$(PA R) - setelt(row2,j-1,row1)$(PA PA R) - setelt(matrixRep,i-1,row2)$(PA PA PA R) - val - - if R has Ring then - zeroMatrix(iLength:NNI,jLength:NNI,kLength:NNI) : $ == - (new(iLength,new(jLength,new(kLength,(0$R))$(PA R))$(PA PA R))$(PA PA PA R)) :: $ - - identityMatrix(iLength:NNI) : $ == - retValueRep : PA PA PA R := zeroMatrix(iLength,iLength,iLength)$$ :: (PA PA PA R) - row1 : PA R - row2 : PA PA R - row1empty : PA R := new(iLength,0$R)$(PA R) - row2empty : PA PA R := new(iLength,copy(row1empty)$(PA R))$(PA PA R) - for count in 0..(iLength-1) repeat - row1 := copy(row1empty)$(PA R) - setelt(row1,count,1$R)$(PA R) - row2 := copy(row2empty)$(PA PA R) - setelt(row2,count,copy(row1)$(PA R))$(PA PA R) - setelt(retValueRep,count,copy(row2)$(PA PA R))$(PA PA PA R) - retValueRep :: $ - - - plus(mat1 : $,mat2 :$) : $ == - - mat1Dims := matrixDimensions(mat1) - iLength1 := mat1Dims.1 - jLength1 := mat1Dims.2 - kLength1 := mat1Dims.3 - - mat2Dims := matrixDimensions(mat2) - iLength2 := mat2Dims.1 - jLength2 := mat2Dims.2 - kLength2 := mat2Dims.3 - - -- check that the dimensions are the same - (not (iLength1 = iLength2) or not (jLength1 = jLength2) or not(kLength1 = kLength2))_ - => error "error the matrices are different sizes" - - sum : R - row1 : (PA R) := new(kLength1,0$R)$(PA R) - row2 : (PA PA R) := new(jLength1,copy(row1)$(PA R))$(PA PA R) - row3 : (PA PA PA R) := new(iLength1,copy(row2)$(PA PA R))$(PA PA PA R) - - for i in 1..iLength1 repeat - for j in 1..jLength1 repeat - for k in 1..kLength1 repeat - sum := (elt(mat1,i,j,k)::R +$R_ - elt(mat2,i,j,k)::R) - setelt(row1,k-1,sum)$(PA R) - setelt(row2,j-1,copy(row1)$(PA R))$(PA PA R) - setelt(row3,i-1,copy(row2)$(PA PA R))$(PA PA PA R) - - resultMatrix := (row3 pretend $) - - resultMatrix - - construct(listRep : L L L R) : $ == - - (#listRep)$(L L L R) = 0 => error "empty list" - (#(listRep.1))$(L L R) = 0 => error "empty list" - (#((listRep.1).1))$(L R) = 0 => error "empty list" - iLength := (#listRep)$(L L L R) - jLength := (#(listRep.1))$(L L R) - kLength := (#((listRep.1).1))$(L R) - - --first check that the matrix is in the correct form - for subList in listRep repeat - not((#subList)$(L L R) = jLength) => error_ - "can not have an irregular shaped matrix" - for subSubList in subList repeat - not((#(subSubList))$(L R) = kLength) => error_ - "can not have an irregular shaped matrix" - - row1 : (PA R) := new(kLength,((listRep.1).1).1)$(PA R) - row2 : (PA PA R) := new(jLength,copy(row1)$(PA R))$(PA PA R) - row3 : (PA PA PA R) := new(iLength,copy(row2)$(PA PA R))$(PA PA PA R) - - for i in 1..iLength repeat - for j in 1..jLength repeat - for k in 1..kLength repeat - - element := elt(elt(elt(listRep,i)$(L L L R),j)$(L L R),k)$(L R) - setelt(row1,k-1,element)$(PA R) - setelt(row2,j-1,copy(row1)$(PA R))$(PA PA R) - setelt(row3,i-1,copy(row2)$(PA PA R))$(PA PA PA R) - - resultMatrix := (row3 pretend $) - - resultMatrix - -@ -\section{domain SFORT SimpleFortranProgram} -<<domain SFORT SimpleFortranProgram>>= -)abbrev domain SFORT SimpleFortranProgram - -++ Author: Mike Dewar -++ Date Created: November 1992 -++ Date Last Updated: -++ Basic Operations: -++ Related Constructors: FortranType, FortranCode, Switch -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: -++ \axiomType{SimpleFortranProgram(f,type)} provides a simple model of some -++ FORTRAN subprograms, making it possible to coerce objects of various -++ domains into a FORTRAN subprogram called \axiom{f}. -++ These can then be translated into legal FORTRAN code. -SimpleFortranProgram(R,FS): Exports == Implementation where - R : SetCategory - FS : FunctionSpace(R) - - FST ==> FortranScalarType - - Exports ==> FortranProgramCategory with - fortran : (Symbol,FST,FS) -> $ - ++fortran(fname,ftype,body) builds an object of type - ++\axiomType{FortranProgramCategory}. The three arguments specify - ++the name, the type and the body of the program. - - Implementation ==> add - - Rep := Record(name : Symbol, type : FST, body : FS ) - - fortran(fname, ftype, res) == - construct(fname,ftype,res)$Rep - - nameOf(u:$):Symbol == u . name - - typeOf(u:$):Union(FST,"void") == u . type - - bodyOf(u:$):FS == u . body - - argumentsOf(u:$):List Symbol == variables(bodyOf u)$FS - - coerce(u:$):OutputForm == - coerce(nameOf u)$Symbol - - outputAsFortran(u:$):Void == - ftype := (checkType(typeOf(u)::OutputForm)$Lisp)::OutputForm - fname := nameOf(u)::OutputForm - args := argumentsOf(u) - nargs:=args::OutputForm - val := bodyOf(u)::OutputForm - fortFormatHead(ftype,fname,nargs)$Lisp - fortFormatTypes(ftype,args)$Lisp - dispfortexp1$Lisp ["="::OutputForm, fname, val]@List(OutputForm) - dispfortexp1$Lisp "RETURN"::OutputForm - dispfortexp1$Lisp "END"::OutputForm - -@ -\section{domain SWITCH Switch} -<<domain SWITCH Switch>>= -)abbrev domain SWITCH Switch - -++ Author: Mike Dewar -++ Date Created: April 1991 -++ Date Last Updated: March 1994 -++ 30.6.94 Added coercion from Symbol MCD -++ Basic Operations: -++ Related Constructors: FortranProgram, FortranCode, FortranTypes -++ Also See: -++ AMS Classifications: -++ Keywords: -++ References: -++ Description: -++ This domain builds representations of boolean expressions for use with -++ the \axiomType{FortranCode} domain. -Switch():public == private where - EXPR ==> Union(I:Expression Integer,F:Expression Float, - CF:Expression Complex Float,switch:%) - - public == CoercibleTo OutputForm with - coerce : Symbol -> $ - ++ coerce(s) \undocumented{} - LT : (EXPR,EXPR) -> $ - ++ LT(x,y) returns the \axiomType{Switch} expression representing \spad{x<y}. - GT : (EXPR,EXPR) -> $ - ++ GT(x,y) returns the \axiomType{Switch} expression representing \spad{x>y}. - LE : (EXPR,EXPR) -> $ - ++ LE(x,y) returns the \axiomType{Switch} expression representing \spad{x<=y}. - GE : (EXPR,EXPR) -> $ - ++ GE(x,y) returns the \axiomType{Switch} expression representing \spad{x>=y}. - OR : (EXPR,EXPR) -> $ - ++ OR(x,y) returns the \axiomType{Switch} expression representing \spad{x or y}. - EQ : (EXPR,EXPR) -> $ - ++ EQ(x,y) returns the \axiomType{Switch} expression representing \spad{x = y}. - AND : (EXPR,EXPR) -> $ - ++ AND(x,y) returns the \axiomType{Switch} expression representing \spad{x and y}. - NOT : EXPR -> $ - ++ NOT(x) returns the \axiomType{Switch} expression representing \spad{\~~x}. - NOT : $ -> $ - ++ NOT(x) returns the \axiomType{Switch} expression representing \spad{\~~x}. - - private == add - Rep := Record(op:BasicOperator,rands:List EXPR) - - -- Public function definitions - - nullOp : BasicOperator := operator NULL - - coerce(s:%):OutputForm == - rat := (s . op)::OutputForm - ran := [u::OutputForm for u in s.rands] - (s . op) = nullOp => first ran - #ran = 1 => - prefix(rat,ran) - infix(rat,ran) - - coerce(s:Symbol):$ == [nullOp,[[s::Expression(Integer)]$EXPR]$List(EXPR)]$Rep - - NOT(r:EXPR):% == - [operator("~"::Symbol),[r]$List(EXPR)]$Rep - - NOT(r:%):% == - [operator("~"::Symbol),[[r]$EXPR]$List(EXPR)]$Rep - - LT(r1:EXPR,r2:EXPR):% == - [operator("<"::Symbol),[r1,r2]$List(EXPR)]$Rep - - GT(r1:EXPR,r2:EXPR):% == - [operator(">"::Symbol),[r1,r2]$List(EXPR)]$Rep - - LE(r1:EXPR,r2:EXPR):% == - [operator("<="::Symbol),[r1,r2]$List(EXPR)]$Rep - - GE(r1:EXPR,r2:EXPR):% == - [operator(">="::Symbol),[r1,r2]$List(EXPR)]$Rep - - AND(r1:EXPR,r2:EXPR):% == - [operator("and"::Symbol),[r1,r2]$List(EXPR)]$Rep - - OR(r1:EXPR,r2:EXPR):% == - [operator("or"::Symbol),[r1,r2]$List(EXPR)]$Rep - - EQ(r1:EXPR,r2:EXPR):% == - [operator("EQ"::Symbol),[r1,r2]$List(EXPR)]$Rep - -@ -\section{domain FTEM FortranTemplate} -<<domain FTEM FortranTemplate>>= -)abbrev domain FTEM FortranTemplate -++ Author: Mike Dewar -++ Date Created: October 1992 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: Code to manipulate Fortran templates -FortranTemplate() : specification == implementation where - - specification == FileCategory(FileName, String) with - - processTemplate : (FileName, FileName) -> FileName - ++ processTemplate(tp,fn) processes the template tp, writing the - ++ result out to fn. - processTemplate : (FileName) -> FileName - ++ processTemplate(tp) processes the template tp, writing the - ++ result to the current FORTRAN output stream. - fortranLiteralLine : String -> Void - ++ fortranLiteralLine(s) writes s to the current Fortran output stream, - ++ followed by a carriage return - fortranLiteral : String -> Void - ++ fortranLiteral(s) writes s to the current Fortran output stream - fortranCarriageReturn : () -> Void - ++ fortranCarriageReturn() produces a carriage return on the current - ++ Fortran output stream - - implementation == TextFile add - - import TemplateUtilities - import FortranOutputStackPackage - - Rep := TextFile - - fortranLiteralLine(s:String):Void == - %writeLine(s,_$fortranOutputStream$Lisp)$Foreign(Builtin) - - fortranLiteral(s:String):Void == - %writeString(s,_$fortranOutputStream$Lisp)$Foreign(Builtin) - - fortranCarriageReturn():Void == - %writeNewline(_$fortranOutputStream$Lisp)$Foreign(Builtin) - - writePassiveLine!(line:String):Void == - -- We might want to be a bit clever here and look for new SubPrograms etc. - fortranLiteralLine line - - processTemplate(tp:FileName, fn:FileName):FileName == - pushFortranOutputStack(fn) - processTemplate(tp) - popFortranOutputStack() - fn - - getLine(fp:TextFile):String == - line : String := stripCommentsAndBlanks readLine!(fp) - while not empty?(line) and elt(line,maxIndex line) = char "__" repeat - setelt(line,maxIndex line,char " ") - line := concat(line, stripCommentsAndBlanks readLine!(fp))$String - line - - processTemplate(tp:FileName):FileName == - fp : TextFile := open(tp,"input") - active : Boolean := true - line : String - endInput : Boolean := false - while not (endInput or endOfFile? fp) repeat - if active then - line := getLine fp - line = "endInput" => endInput := true - if line = "beginVerbatim" then - active := false - else - not empty? line => interpretString line - else - line := readLine!(fp) - if line = "endVerbatim" then - active := true - else - writePassiveLine! line - close!(fp) - if not active then - error concat(["Missing `endVerbatim' line in ",tp::String])$String - string(_$fortranOutputFile$Lisp)::FileName - -@ -\section{domain FEXPR FortranExpression} -<<domain FEXPR FortranExpression>>= -)abbrev domain FEXPR FortranExpression -++ Author: Mike Dewar -++ Date Created: December 1993 -++ Date Last Updated: 19 May 1994 -++ 7 July 1994 added %power to f77Functions -++ 12 July 1994 added RetractableTo(R) -++ Basic Operations: -++ Related Domains: -++ Also See: FortranMachineTypeCategory, MachineInteger, MachineFloat, -++ MachineComplex -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A domain of expressions involving functions which can be -++ translated into standard Fortran-77, with some extra extensions from -++ the NAG Fortran Library. -FortranExpression(basicSymbols,subscriptedSymbols,R): - Exports==Implementation where - basicSymbols : List Symbol - subscriptedSymbols : List Symbol - R : FortranMachineTypeCategory - - EXPR ==> Expression - EXF2 ==> ExpressionFunctions2 - S ==> Symbol - L ==> List - BO ==> BasicOperator - FRAC ==> Fraction - POLY ==> Polynomial - - Exports ==> Join(ExpressionSpace,Algebra(R),RetractableTo(R), - PartialDifferentialRing(Symbol)) with - retract : EXPR R -> $ - ++ retract(e) takes e and transforms it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : EXPR R -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retract : S -> $ - ++ retract(e) takes e and transforms it into a FortranExpression - ++ checking that it is one of the given basic symbols - ++ or subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : S -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a FortranExpression - ++ checking that it is one of the given basic symbols - ++ or subscripted symbols which correspond to scalar and array - ++ parameters respectively. - coerce : $ -> EXPR R - ++ coerce(x) \undocumented{} - if (R has RetractableTo(Integer)) then - retract : EXPR Integer -> $ - ++ retract(e) takes e and transforms it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : EXPR Integer -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retract : FRAC POLY Integer -> $ - ++ retract(e) takes e and transforms it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : FRAC POLY Integer -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retract : POLY Integer -> $ - ++ retract(e) takes e and transforms it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : POLY Integer -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - if (R has RetractableTo(Float)) then - retract : EXPR Float -> $ - ++ retract(e) takes e and transforms it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : EXPR Float -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retract : FRAC POLY Float -> $ - ++ retract(e) takes e and transforms it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : FRAC POLY Float -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retract : POLY Float -> $ - ++ retract(e) takes e and transforms it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - retractIfCan : POLY Float -> Union($,"failed") - ++ retractIfCan(e) takes e and tries to transform it into a - ++ FortranExpression checking that it contains no non-Fortran - ++ functions, and that it only contains the given basic symbols - ++ and subscripted symbols which correspond to scalar and array - ++ parameters respectively. - abs : $ -> $ - ++ abs(x) represents the Fortran intrinsic function ABS - sqrt : $ -> $ - ++ sqrt(x) represents the Fortran intrinsic function SQRT - exp : $ -> $ - ++ exp(x) represents the Fortran intrinsic function EXP - log : $ -> $ - ++ log(x) represents the Fortran intrinsic function LOG - log10 : $ -> $ - ++ log10(x) represents the Fortran intrinsic function LOG10 - sin : $ -> $ - ++ sin(x) represents the Fortran intrinsic function SIN - cos : $ -> $ - ++ cos(x) represents the Fortran intrinsic function COS - tan : $ -> $ - ++ tan(x) represents the Fortran intrinsic function TAN - asin : $ -> $ - ++ asin(x) represents the Fortran intrinsic function ASIN - acos : $ -> $ - ++ acos(x) represents the Fortran intrinsic function ACOS - atan : $ -> $ - ++ atan(x) represents the Fortran intrinsic function ATAN - sinh : $ -> $ - ++ sinh(x) represents the Fortran intrinsic function SINH - cosh : $ -> $ - ++ cosh(x) represents the Fortran intrinsic function COSH - tanh : $ -> $ - ++ tanh(x) represents the Fortran intrinsic function TANH - pi : () -> $ - ++ pi(x) represents the NAG Library function X01AAF which returns - ++ an approximation to the value of pi - variables : $ -> L S - ++ variables(e) return a list of all the variables in \spad{e}. - useNagFunctions : () -> Boolean - ++ useNagFunctions() indicates whether NAG functions are being used - ++ for mathematical and machine constants. - useNagFunctions : Boolean -> Boolean - ++ useNagFunctions(v) sets the flag which controls whether NAG functions - ++ are being used for mathematical and machine constants. The previous - ++ value is returned. - - Implementation ==> EXPR R add - - -- The standard FORTRAN-77 intrinsic functions, plus nthRoot which - -- can be translated into an arithmetic expression: - f77Functions : L S := [abs,sqrt,exp,log,log10,sin,cos,tan,asin,acos, - atan,sinh,cosh,tanh,nthRoot,%power] - nagFunctions : L S := [pi, X01AAF] - useNagFunctionsFlag : Boolean := true - - -- Local functions to check for "unassigned" symbols etc. - - mkEqn(s1:Symbol,s2:Symbol):Equation EXPR(R) == - equation(s2::EXPR(R),script(s1,scripts(s2))::EXPR(R)) - - fixUpSymbols(u:EXPR R):Union(EXPR R,"failed") == - -- If its a univariate expression then just fix it up: - syms : L S := variables(u) - one?(#basicSymbols) and zero?(#subscriptedSymbols) => - not one?(#syms) => "failed" - subst(u,equation(first(syms)::EXPR(R),first(basicSymbols)::EXPR(R))) - -- We have one variable but it is subscripted: - zero?(#basicSymbols) and one?(#subscriptedSymbols) => - -- Make sure we don't have both X and X_i - for s in syms repeat - not scripted?(s) => return "failed" - not one?(#(syms:=removeDuplicates! [name(s) for s in syms]))=> "failed" - sym : Symbol := first subscriptedSymbols - subst(u,[mkEqn(sym,i) for i in variables(u)]) - "failed" - - extraSymbols?(u:EXPR R):Boolean == - syms : L S := [name(v) for v in variables(u)] - extras : L S := setDifference(syms, - setUnion(basicSymbols,subscriptedSymbols)) - not empty? extras - - checkSymbols(u:EXPR R):EXPR(R) == - syms : L S := [name(v) for v in variables(u)] - extras : L S := setDifference(syms, - setUnion(basicSymbols,subscriptedSymbols)) - not empty? extras => - m := fixUpSymbols(u) - m case EXPR(R) => m::EXPR(R) - error ["Extra symbols detected:",[string(v) for v in extras]$L(String)] - u - - notSymbol?(v:BO):Boolean == - s : S := name v - member?(s,basicSymbols) or - scripted?(s) and member?(name s,subscriptedSymbols) => false - true - - extraOperators?(u:EXPR R):Boolean == - ops : L S := [name v for v in operators(u) | notSymbol?(v)] - if useNagFunctionsFlag then - fortranFunctions : L S := append(f77Functions,nagFunctions) - else - fortranFunctions : L S := f77Functions - extras : L S := setDifference(ops,fortranFunctions) - not empty? extras - - checkOperators(u:EXPR R):Void == - ops : L S := [name v for v in operators(u) | notSymbol?(v)] - if useNagFunctionsFlag then - fortranFunctions : L S := append(f77Functions,nagFunctions) - else - fortranFunctions : L S := f77Functions - extras : L S := setDifference(ops,fortranFunctions) - not empty? extras => - error ["Non FORTRAN-77 functions detected:",[string(v) for v in extras]] - - checkForNagOperators(u:EXPR R):$ == - useNagFunctionsFlag => - import Pi - import PiCoercions(R) - piOp : BasicOperator := operator X01AAF - piSub : Equation EXPR R := - equation(pi()$Pi::EXPR(R),kernel(piOp,0::EXPR(R))$EXPR(R)) - per subst(u,piSub) - per u - - -- Conditional retractions: - - if R has RetractableTo(Integer) then - - retractIfCan(u:POLY Integer):Union($,"failed") == - retractIfCan((u::EXPR Integer)$EXPR(Integer))@Union($,"failed") - - retract(u:POLY Integer):$ == - retract((u::EXPR Integer)$EXPR(Integer))@$ - - retractIfCan(u:FRAC POLY Integer):Union($,"failed") == - retractIfCan((u::EXPR Integer)$EXPR(Integer))@Union($,"failed") - - retract(u:FRAC POLY Integer):$ == - retract((u::EXPR Integer)$EXPR(Integer))@$ - - int2R(u:Integer):R == u::R - - retractIfCan(u:EXPR Integer):Union($,"failed") == - retractIfCan(map(int2R,u)$EXF2(Integer,R))@Union($,"failed") - - retract(u:EXPR Integer):$ == - retract(map(int2R,u)$EXF2(Integer,R))@$ - - if R has RetractableTo(Float) then - - retractIfCan(u:POLY Float):Union($,"failed") == - retractIfCan((u::EXPR Float)$EXPR(Float))@Union($,"failed") - - retract(u:POLY Float):$ == - retract((u::EXPR Float)$EXPR(Float))@$ - - retractIfCan(u:FRAC POLY Float):Union($,"failed") == - retractIfCan((u::EXPR Float)$EXPR(Float))@Union($,"failed") - - retract(u:FRAC POLY Float):$ == - retract((u::EXPR Float)$EXPR(Float))@$ - - float2R(u:Float):R == (u::R) - - retractIfCan(u:EXPR Float):Union($,"failed") == - retractIfCan(map(float2R,u)$EXF2(Float,R))@Union($,"failed") - - retract(u:EXPR Float):$ == - retract(map(float2R,u)$EXF2(Float,R))@$ - - -- Exported Functions - - useNagFunctions():Boolean == useNagFunctionsFlag - useNagFunctions(v:Boolean):Boolean == - old := useNagFunctionsFlag - useNagFunctionsFlag := v - old - - log10(x:$):$ == - kernel(operator log10,x) - - pi():$ == kernel(operator X01AAF,0) - - coerce(u:$):EXPR R == rep u - - retractIfCan(u:EXPR R):Union($,"failed") == - if (extraSymbols? u) then - m := fixUpSymbols(u) - m case "failed" => return "failed" - u := m::EXPR(R) - extraOperators? u => "failed" - checkForNagOperators(u) - - retract(u:EXPR R):$ == - u:=checkSymbols(u) - checkOperators(u) - checkForNagOperators(u) - - retractIfCan(u:Symbol):Union($,"failed") == - not (member?(u,basicSymbols) or - scripted?(u) and member?(name u,subscriptedSymbols)) => "failed" - per (u::EXPR(R)) - - retract(u:Symbol):$ == - res : Union($,"failed") := retractIfCan(u) - res case "failed" => error ["Illegal Symbol Detected:",u::String] - res - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain RESULT Result>> -<<domain FC FortranCode>> -<<domain FORTRAN FortranProgram>> -<<domain M3D ThreeDimensionalMatrix>> -<<domain SFORT SimpleFortranProgram>> -<<domain SWITCH Switch>> -<<domain FTEM FortranTemplate>> -<<domain FEXPR FortranExpression>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/functions.spad.pamphlet b/src/algebra/functions.spad.pamphlet deleted file mode 100644 index 63b0e5ea..00000000 --- a/src/algebra/functions.spad.pamphlet +++ /dev/null @@ -1,120 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra functions.spad} -\author{Brian Dupee} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{domain BFUNCT BasicFunctions} -<<domain BFUNCT BasicFunctions>>= -)abbrev domain BFUNCT BasicFunctions -++ Author: Brian Dupee -++ Date Created: August 1994 -++ Date Last Updated: April 1996 -++ Basic Operations: bfKeys, bfEntry -++ Description: A Domain which implements a table containing details of -++ points at which particular functions have evaluation problems. -DF ==> DoubleFloat -SDF ==> Stream DoubleFloat -RS ==> Record(zeros: SDF, ones: SDF, singularities: SDF) - -BasicFunctions(): E == I where - E ==> SetCategory with - bfKeys:() -> List Symbol - ++ bfKeys() returns the names of each function in the - ++ \axiomType{BasicFunctions} table - bfEntry:Symbol -> RS - ++ bfEntry(k) returns the entry in the \axiomType{BasicFunctions} table - ++ corresponding to \spad{k} - finiteAggregate - - I ==> add - - Rep := Table(Symbol,RS) - import Rep, SDF - - f(x:DF):DF == - positive?(x) => -x - -x+1 - - bf():$ == - import RS - dpi := pi()$DF - ndpi:SDF := map(#1*dpi,(z := generate(f,0))) -- [n pi for n in Z] - n1dpi:SDF := map(-(2*(#1)-1)*dpi/2,z) -- [(n+1) pi /2] - n2dpi:SDF := map(2*#1*dpi,z) -- [2 n pi for n in Z] - n3dpi:SDF := map(-(4*(#1)-1)*dpi/4,z) - n4dpi:SDF := map(-(4*(#1)-1)*dpi/2,z) - sinEntry:RS := [ndpi, n4dpi, empty()$SDF] - cosEntry:RS := [n1dpi, n2dpi, esdf := empty()$SDF] - tanEntry:RS := [ndpi, n3dpi, n1dpi] - asinEntry:RS := [construct([0$DF])$SDF, - construct([float(8414709848078965,-16,10)$DF]), esdf] - acosEntry:RS := [construct([1$DF])$SDF, - construct([float(54030230586813977,-17,10)$DF]), esdf] - atanEntry:RS := [construct([0$DF])$SDF, - construct([float(15574077246549023,-16,10)$DF]), esdf] - secEntry:RS := [esdf, n2dpi, n1dpi] - cscEntry:RS := [esdf, n4dpi, ndpi] - cotEntry:RS := [n1dpi, n3dpi, ndpi] - logEntry:RS := [construct([1$DF])$SDF,esdf, construct([0$DF])$SDF] - entryList:List(Record(key:Symbol,entry:RS)) := - [['sin, sinEntry], ['cos, cosEntry], - ['tan, tanEntry], ['sec, secEntry], - ['csc, cscEntry], ['cot, cotEntry], - ['asin, asinEntry], ['acos, acosEntry], - ['atan, atanEntry], ['log, logEntry]] - construct(entryList)$Rep - - bfKeys():List Symbol == keys(bf())$Rep - - bfEntry(k:Symbol):RS == qelt(bf(),k)$Rep - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain BFUNCT BasicFunctions>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/algebra/routines.spad.pamphlet b/src/algebra/routines.spad.pamphlet deleted file mode 100644 index 5b67f754..00000000 --- a/src/algebra/routines.spad.pamphlet +++ /dev/null @@ -1,647 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra routines.spad} -\author{Brian Dupee} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{domain ROUTINE RoutinesTable} -<<domain ROUTINE RoutinesTable>>= -)abbrev domain ROUTINE RoutinesTable -++ Author: Brian Dupee -++ Date Created: August 1994 -++ Date Last Updated: December 1997 -++ Basic Operations: routines, getMeasure -++ Related Constructors: TableAggregate(Symbol,Any) -++ Description: -++ \axiomType{RoutinesTable} implements a database and associated tuning -++ mechanisms for a set of known NAG routines -RoutinesTable(): E == I where - F ==> Float - ST ==> String - LST ==> List String - Rec ==> Record(key:Symbol,entry:Any) - RList ==> List(Record(key:Symbol,entry:Any)) - IFL ==> List(Record(ifail:Integer,instruction:ST)) - Entry ==> Record(chapter:ST, type:ST, domainName: ST, - defaultMin:F, measure:F, failList:IFL, explList:LST) - - E ==> TableAggregate(Symbol,Any) with - - concat:(%,%) -> % - ++ concat(x,y) merges two tables x and y - routines:() -> % - ++ routines() initialises a database of known NAG routines - selectIntegrationRoutines:% -> % - ++ selectIntegrationRoutines(R) chooses only those routines from - ++ the database which are for integration - selectOptimizationRoutines:% -> % - ++ selectOptimizationRoutines(R) chooses only those routines from - ++ the database which are for integration - selectPDERoutines:% -> % - ++ selectPDERoutines(R) chooses only those routines from the - ++ database which are for the solution of PDE's - selectODEIVPRoutines:% -> % - ++ selectODEIVPRoutines(R) chooses only those routines from the - ++ database which are for the solution of ODE's - selectFiniteRoutines:% -> % - ++ selectFiniteRoutines(R) chooses only those routines from the - ++ database which are designed for use with finite expressions - selectSumOfSquaresRoutines:% -> % - ++ selectSumOfSquaresRoutines(R) chooses only those routines from the - ++ database which are designed for use with sums of squares - selectNonFiniteRoutines:% -> % - ++ selectNonFiniteRoutines(R) chooses only those routines from the - ++ database which are designed for use with non-finite expressions. - selectMultiDimensionalRoutines:% -> % - ++ selectMultiDimensionalRoutines(R) chooses only those routines from - ++ the database which are designed for use with multi-dimensional - ++ expressions - changeThreshhold:(%,Symbol,F) -> % - ++ 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. - changeMeasure:(%,Symbol,F) -> % - ++ changeMeasure(R,s,newValue) changes the maximum value for a - ++ measure of the given NAG routine. - getMeasure:(%,Symbol) -> F - ++ getMeasure(R,s) gets the current value of the maximum measure for - ++ the given NAG routine. - getExplanations:(%,ST) -> LST - ++ getExplanations(R,s) gets the explanations of the output parameters for - ++ the given NAG routine. - deleteRoutine!:(%,Symbol) -> % - ++ deleteRoutine!(R,s) destructively deletes the given routine from - ++ the current database of NAG routines - showTheRoutinesTable:() -> % - ++ showTheRoutinesTable() returns the current table of NAG routines. - recoverAfterFail:(%,ST,Integer) -> Union(ST,"failed") - ++ recoverAfterFail(routs,routineName,ifailValue) acts on the - ++ instructions given by the ifail list - finiteAggregate - - I ==> Result add - - Rep := Result - import Rep - - theRoutinesTable:% := routines() - - showTheRoutinesTable():% == theRoutinesTable - - integrationRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,chapter) = "Integration" - false - - selectIntegrationRoutines(R:%):% == select(integrationRoutine?,R) - - optimizationRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,chapter) = "Optimization" - false - - selectOptimizationRoutines(R:%):% == select(optimizationRoutine?,R) - - PDERoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,chapter) = "PDE" - false - - selectPDERoutines(R:%):% == select(PDERoutine?,R) - - ODERoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,chapter) = "ODE" - false - - selectODEIVPRoutines(R:%):% == select(ODERoutine?,R) - - sumOfSquaresRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,type) = "SS" - false - - selectSumOfSquaresRoutines(R:%):% == select(sumOfSquaresRoutine?,R) - - finiteRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,type) = "One-dimensional finite" - false - - selectFiniteRoutines(R:%):% == select(finiteRoutine?,R) - - infiniteRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,type) = "One-dimensional infinite" - false - - semiInfiniteRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,type) = "One-dimensional semi-infinite" - false - - nonFiniteRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (semiInfiniteRoutine?(r) or infiniteRoutine?(r)) - - selectNonFiniteRoutines(R:%):% == select(nonFiniteRoutine?,R) - - multiDimensionalRoutine?(r:Record(key:Symbol,entry:Any)):Boolean == - (a := retractIfCan(r.entry)$AnyFunctions1(Entry)) case Entry => - elt(a,type) = "Multi-dimensional" - false - - selectMultiDimensionalRoutines(R:%):% == select(multiDimensionalRoutine?,R) - - concat(a:%,b:%):% == - membersOfa := (members(a)@List(Record(key:Symbol,entry:Any))) - membersOfb := (members(b)@List(Record(key:Symbol,entry:Any))) - allMembers:= - concat(membersOfa,membersOfb)$List(Record(key:Symbol,entry:Any)) - construct(allMembers) - - changeThreshhold(R:%,s:Symbol,newValue:F):% == - (a := search(s,R)) case Any => - e := retract(a)$AnyFunctions1(Entry) - e.defaultMin := newValue - a := coerce(e)$AnyFunctions1(Entry) - insert!([s,a],R) - error("changeThreshhold","Cannot find routine of that name")$ErrorFunctions - - changeMeasure(R:%,s:Symbol,newValue:F):% == - (a := search(s,R)) case Any => - e := retract(a)$AnyFunctions1(Entry) - e.measure := newValue - a := coerce(e)$AnyFunctions1(Entry) - insert!([s,a],R) - error("changeMeasure","Cannot find routine of that name")$ErrorFunctions - - getMeasure(R:%,s:Symbol):F == - (a := search(s,R)) case Any => - e := retract(a)$AnyFunctions1(Entry) - e.measure - error("getMeasure","Cannot find routine of that name")$ErrorFunctions - - deleteRoutine!(R:%,s:Symbol):% == - (a := search(s,R)) case Any => - e:Record(key:Symbol,entry:Any) := [s,a] - remove!(e,R) - error("deleteRoutine!","Cannot find routine of that name")$ErrorFunctions - - routines():% == - f := "One-dimensional finite" - s := "One-dimensional semi-infinite" - i := "One-dimensional infinite" - m := "Multi-dimensional" - int := "Integration" - ode := "ODE" - pde := "PDE" - opt := "Optimization" - d01ajfExplList:LST := ["result: Calculated value of the integral", - "iw: iw(1) contains the actual number of sub-intervals used, the rest is workspace", - "w: contains the end-points of the sub-intervals used along with the integral contributions and error estimates over the sub-intervals", - "abserr: the estimate of the absolute error of the result", - "ifail: the error warning parameter", - "method: details of the method used and measures of all methods", - "attributes: a list of the attributes pertaining to the integrand which had some bearing on the choice of method"] - d01asfExplList:LST := ["result: Calculated value of the integral", - "iw: iw(1) contains the actual number of sub-intervals used, the rest is workspace", - "lst: contains the actual number of sub-intervals used", - "erlst: contains the error estimates over the sub-intervals", - "rslst: contains the integral contributions of the sub-intervals", - "ierlst: contains the error flags corresponding to the values in rslst", - "abserr: the estimate of the absolute error of the result", - "ifail: the error warning parameter", - "method: details of the method used and measures of all methods", - "attributes: a list of the attributes pertaining to the integrand which had some bearing on the choice of method"] - d01fcfExplList:LST := ["result: Calculated value of the integral", - "acc: the estimate of the relative error of the result", - "minpts: the number of integrand evaluations", - "ifail: the error warning parameter", - "method: details of the method used and measures of all methods", - "attributes: a list of the attributes pertaining to the integrand which had some bearing on the choice of method"] - d01transExplList:LST := ["result: Calculated value of the integral", - "abserr: the estimate of the absolute error of the result", - "method: details of the method and transformation used and measures of all methods", - "d01***AnnaTypeAnswer: the individual results from the routines", - "attributes: a list of the attributes pertaining to the integrand which had some bearing on the choice of method"] - d02bhfExplList:LST := ["x: the value of x at the end of the calculation", - "y: the computed values of Y\[1\]..Y\[n\] at x", - "tol: the (possible) estimate of the error; this is not guarunteed", - "ifail: the error warning parameter", - "method: details of the method used and measures of all methods", - "intensityFunctions: a list of the attributes and values pertaining to the ODE which had some bearing on the choice of method"] - d02bbfExplList:LST := concat(["result: the computed values of the solution at the required points"],d02bhfExplList)$LST - d03eefExplList:LST := ["See the NAG On-line Documentation for D03EEF/D03EDF", - "u: the computed solution u[i][j] is returned in u(i+(j-1)*ngx),for i = 1,2,..ngx; j = 1,2,..ngy"] - e04fdfExplList:LST := ["x: the position of the minimum", - "objf: the value of the objective function at x", - "ifail: the error warning parameter", - "method: details of the method used and measures of all methods", - "attributes: a list of the attributes pertaining to the function or functions which had some bearing on the choice of method"] - e04dgfExplList:LST := concat(e04fdfExplList, - ["objgrd: the values of the derivatives at x", - "iter: the number of iterations performed"])$LST - e04jafExplList:LST := concat(e04fdfExplList, - ["bu: the values of the upper bounds used", - "bl: the values of the lower bounds used"])$LST - e04ucfExplList:LST := concat(e04dgfExplList, - ["istate: the status of every constraint at x", - "clamda: the QP multipliers for the last QP sub-problem", - "For other output parameters see the NAG On-line Documentation for E04UCF"])$LST - e04mbfExplList:LST := concat(e04fdfExplList, - ["istate: the status of every constraint at x", - "clamda: the Lagrange multipliers for each constraint"])$LST - d01ajfIfail:IFL := [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"delete"], [6,"delete"]] - d01akfIfail:IFL := [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"]] - d01alfIfail:IFL := [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"delete"], [6,"delete"], [7,"delete"]] - d01amfIfail:IFL := [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"delete"], [6,"delete"]] - d01anfIfail:IFL := [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"delete"], [6,"delete"], [7,"delete"]] - d01apfIfail:IFL := - [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"], [5,"delete"]] - d01aqfIfail:IFL := - [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"], [5,"delete"]] - d01asfIfail:IFL := [[1,"incrFunEvals"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"delete"], [6,"delete"], [7,"delete"], [8,"delete"], [9,"delete"]] - d01fcfIfail:IFL := [[1,"delete"], [2,"incrFunEvals"], [3,"delete"]] - d01gbfIfail:IFL := [[1,"delete"], [2,"incrFunEvals"]] - d02bbfIfail:IFL := - [[1,"delete"], [2,"decrease tolerance"], [3,"increase tolerance"], - [4,"delete"], [5,"delete"], [6,"delete"], [7,"delete"]] - d02bhfIfail:IFL := - [[1,"delete"], [2,"decrease tolerance"], [3,"increase tolerance"], - [4,"no action"], [5,"delete"], [6,"delete"], [7,"delete"]] - d02cjfIfail:IFL := - [[1,"delete"], [2,"decrease tolerance"], [3,"increase tolerance"], - [4,"delete"], [5,"delete"], [6,"no action"], [7,"delete"]] - d02ejfIfail:IFL := - [[1,"delete"], [2,"decrease tolerance"], [3,"increase tolerance"], - [4,"delete"], [5,"delete"], [6,"no action"], [7,"delete"], [8,"delete"], - [9,"delete"]] - e04dgfIfail:IFL := [[3,"delete"], [4,"no action"], [6,"delete"], - [7,"delete"], [8,"delete"], [9,"delete"]] - e04fdfIfail:IFL := - [[1,"delete"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"no action"], [6,"no action"], [7,"delete"], [8,"delete"]] - e04gcfIfail:IFL := [[1,"delete"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"no action"], [6,"no action"], [7,"delete"], [8,"delete"], [9,"delete"]] - e04jafIfail:IFL := [[1,"delete"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"no action"], [6,"no action"], [7,"delete"], [8,"delete"], [9,"delete"]] - e04mbfIfail:IFL := - [[1,"delete"], [2,"delete"], [3,"delete"], [4,"delete"], [5,"delete"]] - e04nafIfail:IFL := - [[1,"delete"], [2,"delete"], [3,"delete"], [4,"delete"], [5,"delete"], - [6,"delete"], [7,"delete"], [8,"delete"], [9,"delete"]] - e04ucfIfail:IFL := [[1,"delete"], [2,"delete"], [3,"delete"], [4,"delete"], - [5,"delete"], [6,"delete"], [7,"delete"], [8,"delete"], [9,"delete"]] - d01ajfEntry:Entry := [int, f, "d01ajfAnnaType",0.4,0.4,d01ajfIfail,d01ajfExplList] - d01akfEntry:Entry := [int, f, "d01akfAnnaType",0.6,1.0,d01akfIfail,d01ajfExplList] - d01alfEntry:Entry := [int, f, "d01alfAnnaType",0.6,0.6,d01alfIfail,d01ajfExplList] - d01amfEntry:Entry := [int, i, "d01amfAnnaType",0.5,0.5,d01amfIfail,d01ajfExplList] - d01anfEntry:Entry := [int, f, "d01anfAnnaType",0.6,0.9,d01anfIfail,d01ajfExplList] - d01apfEntry:Entry := [int, f, "d01apfAnnaType",0.7,0.7,d01apfIfail,d01ajfExplList] - d01aqfEntry:Entry := [int, f, "d01aqfAnnaType",0.6,0.7,d01aqfIfail,d01ajfExplList] - d01asfEntry:Entry := [int, s, "d01asfAnnaType",0.6,0.9,d01asfIfail,d01asfExplList] - d01transEntry:Entry:=[int, i, "d01TransformFunctionType",0.6,0.9,[],d01transExplList] - d01gbfEntry:Entry := [int, m, "d01gbfAnnaType",0.6,0.6,d01gbfIfail,d01fcfExplList] - d01fcfEntry:Entry := [int, m, "d01fcfAnnaType",0.5,0.5,d01fcfIfail,d01fcfExplList] - d02bbfEntry:Entry := [ode, "IVP", "d02bbfAnnaType",0.7,0.5,d02bbfIfail,d02bbfExplList] - d02bhfEntry:Entry := [ode, "IVP", "d02bhfAnnaType",0.7,0.49,d02bhfIfail,d02bhfExplList] - d02cjfEntry:Entry := [ode, "IVP", "d02cjfAnnaType",0.7,0.5,d02cjfIfail,d02bbfExplList] - d02ejfEntry:Entry := [ode, "IVP", "d02ejfAnnaType",0.7,0.5,d02ejfIfail,d02bbfExplList] - d03eefEntry:Entry := [pde, "2", "d03eefAnnaType",0.6,0.5,[],d03eefExplList] - --d03fafEntry:Entry := [pde, "3", "d03fafAnnaType",0.6,0.5,[],[]] - e04dgfEntry:Entry := [opt, "CGA", "e04dgfAnnaType",0.4,0.4,e04dgfIfail,e04dgfExplList] - e04fdfEntry:Entry := [opt, "SS", "e04fdfAnnaType",0.7,0.7,e04fdfIfail,e04fdfExplList] - e04gcfEntry:Entry := [opt, "SS", "e04gcfAnnaType",0.8,0.8,e04gcfIfail,e04fdfExplList] - e04jafEntry:Entry := [opt, "QNA", "e04jafAnnaType",0.5,0.5,e04jafIfail,e04jafExplList] - e04mbfEntry:Entry := [opt, "LP", "e04mbfAnnaType",0.7,0.7,e04mbfIfail,e04mbfExplList] - e04nafEntry:Entry := [opt, "QP", "e04nafAnnaType",0.7,0.7,e04nafIfail,e04mbfExplList] - e04ucfEntry:Entry := [opt, "SQP", "e04ucfAnnaType",0.6,0.6,e04ucfIfail,e04ucfExplList] - rl:RList := - [["d01apf" :: Symbol, coerce(d01apfEntry)$AnyFunctions1(Entry)],_ - ["d01aqf" :: Symbol, coerce(d01aqfEntry)$AnyFunctions1(Entry)],_ - ["d01alf" :: Symbol, coerce(d01alfEntry)$AnyFunctions1(Entry)],_ - ["d01anf" :: Symbol, coerce(d01anfEntry)$AnyFunctions1(Entry)],_ - ["d01akf" :: Symbol, coerce(d01akfEntry)$AnyFunctions1(Entry)],_ - ["d01ajf" :: Symbol, coerce(d01ajfEntry)$AnyFunctions1(Entry)],_ - ["d01asf" :: Symbol, coerce(d01asfEntry)$AnyFunctions1(Entry)],_ - ["d01amf" :: Symbol, coerce(d01amfEntry)$AnyFunctions1(Entry)],_ - ["d01transform" :: Symbol, coerce(d01transEntry)$AnyFunctions1(Entry)],_ - ["d01gbf" :: Symbol, coerce(d01gbfEntry)$AnyFunctions1(Entry)],_ - ["d01fcf" :: Symbol, coerce(d01fcfEntry)$AnyFunctions1(Entry)],_ - ["d02bbf" :: Symbol, coerce(d02bbfEntry)$AnyFunctions1(Entry)],_ - ["d02bhf" :: Symbol, coerce(d02bhfEntry)$AnyFunctions1(Entry)],_ - ["d02cjf" :: Symbol, coerce(d02cjfEntry)$AnyFunctions1(Entry)],_ - ["d02ejf" :: Symbol, coerce(d02ejfEntry)$AnyFunctions1(Entry)],_ - ["d03eef" :: Symbol, coerce(d03eefEntry)$AnyFunctions1(Entry)],_ - --["d03faf" :: Symbol, coerce(d03fafEntry)$AnyFunctions1(Entry)], - ["e04dgf" :: Symbol, coerce(e04dgfEntry)$AnyFunctions1(Entry)],_ - ["e04fdf" :: Symbol, coerce(e04fdfEntry)$AnyFunctions1(Entry)],_ - ["e04gcf" :: Symbol, coerce(e04gcfEntry)$AnyFunctions1(Entry)],_ - ["e04jaf" :: Symbol, coerce(e04jafEntry)$AnyFunctions1(Entry)],_ - ["e04mbf" :: Symbol, coerce(e04mbfEntry)$AnyFunctions1(Entry)],_ - ["e04naf" :: Symbol, coerce(e04nafEntry)$AnyFunctions1(Entry)],_ - ["e04ucf" :: Symbol, coerce(e04ucfEntry)$AnyFunctions1(Entry)]] - construct(rl) - - getIFL(s:Symbol,l:%):Union(IFL,"failed") == - o := search(s,l)$% - o case "failed" => "failed" - e := retractIfCan(o)$AnyFunctions1(Entry) - e case "failed" => "failed" - e.failList - - getInstruction(l:IFL,ifailValue:Integer):Union(ST,"failed") == - output := empty()$ST - for i in 1..#l repeat - if ((l.i).ifail=ifailValue)@Boolean then - output := (l.i).instruction - empty?(output)$ST => "failed" - output - - recoverAfterFail(routs:%,routineName:ST, - ifailValue:Integer):Union(ST,"failed") == - name := routineName :: Symbol - failedList := getIFL(name,routs) - failedList case "failed" => "failed" - empty? failedList => "failed" - instr := getInstruction(failedList,ifailValue) - instr case "failed" => concat(routineName," failed")$ST - (instr = "delete")@Boolean => - deleteRoutine!(routs,name) - concat(routineName," failed - trying alternatives")$ST - instr - - getExplanations(R:%,routineName:ST):LST == - name := routineName :: Symbol - (a := search(name,R)) case Any => - e := retract(a)$AnyFunctions1(Entry) - e.explList - empty()$LST - -@ -\section{domain ATTRBUT AttributeButtons} -<<domain ATTRBUT AttributeButtons>>= -)abbrev domain ATTRBUT AttributeButtons -++ Author: Brian Dupee -++ Date Created: April 1996 -++ Date Last Updated: December 1997 -++ Basic Operations: increase, decrease, getButtonValue, setButtonValue -++ Related Constructors: Table(String,Float) -++ Description: -++ \axiomType{AttributeButtons} implements a database and associated -++ adjustment mechanisms for a set of attributes. -++ -++ For ODEs these attributes are "stiffness", "stability" (i.e. how much -++ affect the cosine or sine component of the solution has on the stability of -++ the result), "accuracy" and "expense" (i.e. how expensive is the evaluation -++ of the ODE). All these have bearing on the cost of calculating the -++ solution given that reducing the step-length to achieve greater accuracy -++ requires considerable number of evaluations and calculations. -++ -++ The effect of each of these attributes can be altered by increasing or -++ decreasing the button value. -++ -++ For Integration there is a button for increasing and decreasing the preset -++ number of function evaluations for each method. This is automatically used -++ by ANNA when a method fails due to insufficient workspace or where the -++ limit of function evaluations has been reached before the required -++ accuracy is achieved. -++ -AttributeButtons(): E == I where - F ==> Float - ST ==> String - LST ==> List String - Rec ==> Record(key:Symbol,entry:Any) - RList ==> List(Record(key:Symbol,entry:Any)) - IFL ==> List(Record(ifail:Integer,instruction:ST)) - Entry ==> Record(chapter:ST, type:ST, domainName: ST, - defaultMin:F, measure:F, failList:IFL, explList:LST) - - - E ==> SetCategory with - - increase:(ST,ST) -> F - ++ \axiom{increase(routineName,attributeName)} increases the value - ++ for the effect of the attribute \axiom{attributeName} with routine - ++ \axiom{routineName}. - ++ - ++ \axiom{attributeName} should be one of the values - ++ "stiffness", "stability", "accuracy", "expense" or - ++ "functionEvaluations". - increase:(ST) -> F - ++ \axiom{increase(attributeName)} increases the value for the - ++ effect of the attribute \axiom{attributeName} with all routines. - ++ - ++ \axiom{attributeName} should be one of the values - ++ "stiffness", "stability", "accuracy", "expense" or - ++ "functionEvaluations". - decrease:(ST,ST) -> F - ++ \axiom{decrease(routineName,attributeName)} decreases the value - ++ for the effect of the attribute \axiom{attributeName} with routine - ++ \axiom{routineName}. - ++ - ++ \axiom{attributeName} should be one of the values - ++ "stiffness", "stability", "accuracy", "expense" or - ++ "functionEvaluations". - decrease:(ST) -> F - ++ \axiom{decrease(attributeName)} decreases the value for the - ++ effect of the attribute \axiom{attributeName} with all routines. - ++ - ++ \axiom{attributeName} should be one of the values - ++ "stiffness", "stability", "accuracy", "expense" or - ++ "functionEvaluations". - getButtonValue:(ST,ST) -> F - ++ \axiom{getButtonValue(routineName,attributeName)} returns the - ++ current value for the effect of the attribute \axiom{attributeName} - ++ with routine \axiom{routineName}. - ++ - ++ \axiom{attributeName} should be one of the values - ++ "stiffness", "stability", "accuracy", "expense" or - ++ "functionEvaluations". - resetAttributeButtons:() -> Void - ++ \axiom{resetAttributeButtons()} resets the Attribute buttons to a - ++ neutral level. - setAttributeButtonStep:(F) -> F - ++ \axiom{setAttributeButtonStep(n)} sets the value of the steps for - ++ increasing and decreasing the button values. \axiom{n} must be - ++ greater than 0 and less than 1. The preset value is 0.5. - setButtonValue:(ST,F) -> F - ++ \axiom{setButtonValue(attributeName,n)} sets the - ++ value of all buttons of attribute \spad{attributeName} - ++ to \spad{n}. \spad{n} must be in the range [0..1]. - ++ - ++ \axiom{attributeName} should be one of the values - ++ "stiffness", "stability", "accuracy", "expense" or - ++ "functionEvaluations". - setButtonValue:(ST,ST,F) -> F - ++ \axiom{setButtonValue(attributeName,routineName,n)} sets the - ++ value of the button of attribute \spad{attributeName} to routine - ++ \spad{routineName} to \spad{n}. \spad{n} must be in the range [0..1]. - ++ - ++ \axiom{attributeName} should be one of the values - ++ "stiffness", "stability", "accuracy", "expense" or - ++ "functionEvaluations". - finiteAggregate - - I ==> add - - Rep := StringTable(F) - import Rep - - buttons:() -> $ - - buttons():$ == - eList := empty()$List(Record(key:ST,entry:F)) - l1:List String := ["stability","stiffness","accuracy","expense"] - l2:List String := ["functionEvaluations"] - ro1 := selectODEIVPRoutines(r := routines()$RoutinesTable)$RoutinesTable - ro2 := selectIntegrationRoutines(r)$RoutinesTable - k1:List String := [string(i)$Symbol for i in keys(ro1)$RoutinesTable] - k2:List String := [string(i)$Symbol for i in keys(ro2)$RoutinesTable] - for i in k1 repeat - for j in l1 repeat - e:Record(key:ST,entry:F) := [i j,0.5] - eList := cons(e,eList)$List(Record(key:ST,entry:F)) - for i in k2 repeat - for j in l2 repeat - e:Record(key:ST,entry:F) := [i j,0.5] - eList := cons(e,eList)$List(Record(key:ST,entry:F)) - construct(eList)$Rep - - attributeButtons:$ := buttons() - - attributeStep:F := 0.5 - - setAttributeButtonStep(n:F):F == - positive?(n)$F and (n<1$F) => attributeStep:F := n - error("setAttributeButtonStep","New value must be in (0..1)")$ErrorFunctions - - resetAttributeButtons():Void == - attributeButtons := buttons() - - setButtonValue(routineName:ST,attributeName:ST,n:F):F == - f := search(routineName attributeName,attributeButtons)$Rep - f case Float => - n>=0$F and n<=1$F => - setelt(attributeButtons,routineName attributeName,n)$Rep - error("setAttributeButtonStep","New value must be in [0..1]")$ErrorFunctions - error("setButtonValue","attribute name " attributeName - " not found for routine " routineName)$ErrorFunctions - - setButtonValue(attributeName:ST,n:F):F == - ro1 := selectODEIVPRoutines(r := routines()$RoutinesTable)$RoutinesTable - ro2 := selectIntegrationRoutines(r)$RoutinesTable - l1:List String := ["stability","stiffness","accuracy","expense"] - l2:List String := ["functionEvaluations"] - if attributeName="functionEvaluations" then - for i in keys(ro2)$RoutinesTable repeat - setButtonValue(string(i)$Symbol,attributeName,n) - else - for i in keys(ro1)$RoutinesTable repeat - setButtonValue(string(i)$Symbol,attributeName,n) - n - - increase(routineName:ST,attributeName:ST):F == - f := search(routineName attributeName,attributeButtons)$Rep - f case Float => - newValue:F := (1$F-attributeStep)*f+attributeStep - setButtonValue(routineName,attributeName,newValue) - error("increase","attribute name " attributeName - " not found for routine " routineName)$ErrorFunctions - - increase(attributeName:ST):F == - ro1 := selectODEIVPRoutines(r := routines()$RoutinesTable)$RoutinesTable - ro2 := selectIntegrationRoutines(r)$RoutinesTable - l1:List String := ["stability","stiffness","accuracy","expense"] - l2:List String := ["functionEvaluations"] - if attributeName="functionEvaluations" then - for i in keys(ro2)$RoutinesTable repeat - increase(string(i)$Symbol,attributeName) - else - for i in keys(ro1)$RoutinesTable repeat - increase(string(i)$Symbol,attributeName) - getButtonValue(string(i)$Symbol,attributeName) - - decrease(routineName:ST,attributeName:ST):F == - f := search(routineName attributeName,attributeButtons)$Rep - f case Float => - newValue:F := (1$F-attributeStep)*f - setButtonValue(routineName,attributeName,newValue) - error("increase","attribute name " attributeName - " not found for routine " routineName)$ErrorFunctions - - decrease(attributeName:ST):F == - ro1 := selectODEIVPRoutines(r := routines()$RoutinesTable)$RoutinesTable - ro2 := selectIntegrationRoutines(r)$RoutinesTable - l1:List String := ["stability","stiffness","accuracy","expense"] - l2:List String := ["functionEvaluations"] - if attributeName="functionEvaluations" then - for i in keys(ro2)$RoutinesTable repeat - decrease(string(i)$Symbol,attributeName) - else - for i in keys(ro1)$RoutinesTable repeat - decrease(string(i)$Symbol,attributeName) - getButtonValue(string(i)$Symbol,attributeName) - - - getButtonValue(routineName:ST,attributeName:ST):F == - f := search(routineName attributeName,attributeButtons)$Rep - f case Float => f - error("getButtonValue","attribute name " attributeName - " not found for routine " routineName)$ErrorFunctions - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain ROUTINE RoutinesTable>> -<<domain ATTRBUT AttributeButtons>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 5bbe29bd..83134acf 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2094401 . 3525483391) +(2005181 . 3525500984) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4142 . T) (-4140 . T) (-4139 . T) ((-4147 "*") . T) (-4138 . T) (-4143 . T) (-4137 . T)) +((-3976 . T) (-3974 . T) (-3973 . T) ((-3981 "*") . T) (-3972 . T) (-3977 . T) (-3971 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3215) +(-32 R -3076) ((|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 -978) (QUOTE (-499))))) +((|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4145))) +((|HasAttribute| |#1| (QUOTE -3979))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -3215 UP UPUP -2733) +(-40 -3076 UP UPUP -2598) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4138 |has| (-361 |#2|) (-318)) (-4143 |has| (-361 |#2|) (-318)) (-4137 |has| (-361 |#2|) (-318)) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-361 |#2|) (QUOTE (-118))) (|HasCategory| (-361 |#2|) (QUOTE (-120))) (|HasCategory| (-361 |#2|) (QUOTE (-305))) (-3677 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (QUOTE (-305)))) (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (QUOTE (-323))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-190))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (|HasCategory| (-361 |#2|) (QUOTE (-305)))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-190))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-189))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (|HasCategory| (-361 |#2|) (QUOTE (-305)))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117))))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-305))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117)))))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117))))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -838) (QUOTE (-1117)))))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -596) (QUOTE (-499)))) (-3677 (|HasCategory| (-361 |#2|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-323))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-189))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -838) (QUOTE (-1117))))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-190))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117)))))) -(-41 R -3215) +((-3972 |has| (-343 |#2|) (-308)) (-3977 |has| (-343 |#2|) (-308)) (-3971 |has| (-343 |#2|) (-308)) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-343 |#2|) (QUOTE (-116))) (|HasCategory| (-343 |#2|) (QUOTE (-118))) (|HasCategory| (-343 |#2|) (QUOTE (-295))) (OR (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (QUOTE (-295)))) (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (QUOTE (-313))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-188))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (|HasCategory| (-343 |#2|) (QUOTE (-295)))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-188))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-187))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (|HasCategory| (-343 |#2|) (QUOTE (-295)))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079))))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-295))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079)))))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079))))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -804) (QUOTE (-1079)))))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -575) (QUOTE (-478)))) (OR (|HasCategory| (-343 |#2|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-313))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-187))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -804) (QUOTE (-1079))))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-188))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079)))))) +(-41 R -3076) ((|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 (-406))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -375) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -357) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -103,34 +103,34 @@ NIL (-43 R A) ((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,a) = 0} and \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,x,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,b,x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,a,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis."))) NIL -((|HasCategory| |#1| (QUOTE (-261)))) +((|HasCategory| |#1| (QUOTE (-254)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4142 |has| |#1| (-510)) (-4140 . T) (-4139 . T)) -((|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510)))) +((-3976 |has| |#1| (-489)) (-3974 . T) (-3973 . T)) +((|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (-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."))) -((-4145 . T) (-4146 . T)) -((-3677 (-12 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-781)))) (-12 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041))))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-781))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-3677 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-781))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-781))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-781))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041))) (-3677 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73))) (-12 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041))))) +((-3979 . T) (-3980 . T)) +((OR (-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-749)))) (-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005))))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-749))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-749))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-749))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-749))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005))) (OR (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-318)))) +((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-308)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| $ (QUOTE (-989))) (|HasCategory| $ (|%list| (QUOTE -978) (QUOTE (-499))))) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| $ (QUOTE (-954))) (|HasCategory| $ (|%list| (QUOTE -943) (QUOTE (-478))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4142 . T)) +((-3976 . T)) NIL (-51) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -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 -3215) +(-54 |Base| R -3076) ((|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 @@ -158,28 +158,28 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) 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}"))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|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 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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) (-61 R L) ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) NIL -((|HasCategory| |#1| (QUOTE (-318)))) +((|HasCategory| |#1| (QUOTE (-308)))) (-62 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}."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) (-63 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -201,4684 +201,4528 @@ NIL NIL NIL (-68) -((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4145 . T)) -NIL -(-69) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4145 . T) ((-4147 "*") . T) (-4146 . T) (-4142 . T) (-4140 . T) (-4139 . T) (-4138 . T) (-4143 . T) (-4137 . T) (-4136 . T) (-4135 . T) (-4134 . T) (-4133 . T) (-4141 . T) (-4144 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4132 . T)) +((-3979 . T) ((-3981 "*") . T) (-3980 . T) (-3976 . T) (-3974 . T) (-3973 . T) (-3972 . T) (-3977 . T) (-3971 . T) (-3970 . T) (-3969 . T) (-3968 . T) (-3967 . T) (-3975 . T) (-3978 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3966 . T)) NIL -(-70 R) +(-69 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4142 . T)) +((-3976 . T)) NIL -(-71 R UP) +(-70 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) NIL NIL -(-72 S) +(-71 S) ((|constructor| (NIL "\\spadtype{BasicType} is the basic category for describing a collection of elements with \\spadop{=} (equality).")) (|before?| (((|Boolean|) $ $) "\\spad{before?(x,y)} holds if the system representation of \\spad{x} comes before that of \\spad{y} in a an implementation defined manner.")) (~= (((|Boolean|) $ $) "\\spad{x~=y} tests if \\spad{x} and \\spad{y} are not equal.")) (= (((|Boolean|) $ $) "\\spad{x=y} tests if \\spad{x} and \\spad{y} are equal."))) NIL NIL -(-73) +(-72) ((|constructor| (NIL "\\spadtype{BasicType} is the basic category for describing a collection of elements with \\spadop{=} (equality).")) (|before?| (((|Boolean|) $ $) "\\spad{before?(x,y)} holds if the system representation of \\spad{x} comes before that of \\spad{y} in a an implementation defined manner.")) (~= (((|Boolean|) $ $) "\\spad{x~=y} tests if \\spad{x} and \\spad{y} are not equal.")) (= (((|Boolean|) $ $) "\\spad{x=y} tests if \\spad{x} and \\spad{y} are equal."))) NIL NIL -(-74 S) +(-73 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#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}."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-75 R UP M |Row| |Col|) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-74 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4147 "*")))) -(-76) -((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4145 . T)) -NIL -(-77 A S) +((|HasAttribute| |#1| (QUOTE (-3981 "*")))) +(-75 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) NIL NIL -(-78 S) +(-76 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4146 . T)) +((-3980 . T)) NIL -(-79) +(-77) ((|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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-499) (QUOTE (-848))) (|HasCategory| (-499) (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| (-499) (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-120))) (|HasCategory| (-499) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-499) (QUOTE (-960))) (|HasCategory| (-499) (QUOTE (-763))) (|HasCategory| (-499) (QUOTE (-781))) (-3677 (|HasCategory| (-499) (QUOTE (-763))) (|HasCategory| (-499) (QUOTE (-781)))) (|HasCategory| (-499) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-499) (QUOTE (-1092))) (|HasCategory| (-499) (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| (-499) (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| (-499) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| (-499) (QUOTE (-189))) (|HasCategory| (-499) (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| (-499) (QUOTE (-190))) (|HasCategory| (-499) (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| (-499) (|%list| (QUOTE -468) (QUOTE (-1117)) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -263) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -240) (QUOTE (-499)) (QUOTE (-499)))) (|HasCategory| (-499) (QUOTE (-261))) (|HasCategory| (-499) (QUOTE (-498))) (|HasCategory| (-499) (|%list| (QUOTE -596) (QUOTE (-499)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-848)))) (-3677 (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-848)))) (|HasCategory| (-499) (QUOTE (-118))))) -(-80) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-478) (QUOTE (-814))) (|HasCategory| (-478) (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| (-478) (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-118))) (|HasCategory| (-478) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-478) (QUOTE (-926))) (|HasCategory| (-478) (QUOTE (-733))) (|HasCategory| (-478) (QUOTE (-749))) (OR (|HasCategory| (-478) (QUOTE (-733))) (|HasCategory| (-478) (QUOTE (-749)))) (|HasCategory| (-478) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-478) (QUOTE (-1055))) (|HasCategory| (-478) (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-478) (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-478) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-478) (QUOTE (-187))) (|HasCategory| (-478) (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| (-478) (QUOTE (-188))) (|HasCategory| (-478) (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| (-478) (|%list| (QUOTE -447) (QUOTE (-1079)) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -256) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -238) (QUOTE (-478)) (QUOTE (-478)))) (|HasCategory| (-478) (QUOTE (-254))) (|HasCategory| (-478) (QUOTE (-477))) (|HasCategory| (-478) (|%list| (QUOTE -575) (QUOTE (-478)))) (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-814)))) (OR (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-814)))) (|HasCategory| (-478) (QUOTE (-116))))) +(-78) ((|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL -(-81) +(-79) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-1041))) (|HasCategory| (-85) (|%list| (QUOTE -263) (QUOTE (-85))))) (|HasCategory| (-85) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-85) (QUOTE (-781))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| (-85) (QUOTE (-1041))) (|HasCategory| (-85) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-85) (QUOTE (-73)))) -(-82 R S) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| (-83) (QUOTE (-1005))) (|HasCategory| (-83) (|%list| (QUOTE -256) (QUOTE (-83))))) (|HasCategory| (-83) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-83) (QUOTE (-749))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| (-83) (QUOTE (-1005))) (|HasCategory| (-83) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-83) (QUOTE (-72)))) +(-80 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-83 S) +(-81 S) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) NIL NIL -(-84) +(-82) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) NIL NIL -(-85) +(-83) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) NIL NIL -(-86) +(-84) ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Maybe| (|Mapping| (|InputForm|) (|List| (|InputForm|)))) $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \\spad{nothing} otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Maybe| (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \\spad{nothing} otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1} and \\spad{op2} should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-87 A) +(-85 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\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 -(-88 -3215 UP) +(-86 -3076 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 -(-89 |p|) +(-87 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-90 |p|) +(-88 |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}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-89 |#1|) (QUOTE (-848))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-89 |#1|) (QUOTE (-960))) (|HasCategory| (-89 |#1|) (QUOTE (-763))) (|HasCategory| (-89 |#1|) (QUOTE (-781))) (-3677 (|HasCategory| (-89 |#1|) (QUOTE (-763))) (|HasCategory| (-89 |#1|) (QUOTE (-781)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-89 |#1|) (QUOTE (-1092))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -468) (QUOTE (-1117)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -263) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -240) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-261))) (|HasCategory| (-89 |#1|) (QUOTE (-498))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-848)))) (-3677 (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-848)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) -(-91 A S) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-87 |#1|) (QUOTE (-814))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| (-87 |#1|) (QUOTE (-116))) (|HasCategory| (-87 |#1|) (QUOTE (-118))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-87 |#1|) (QUOTE (-926))) (|HasCategory| (-87 |#1|) (QUOTE (-733))) (|HasCategory| (-87 |#1|) (QUOTE (-749))) (OR (|HasCategory| (-87 |#1|) (QUOTE (-733))) (|HasCategory| (-87 |#1|) (QUOTE (-749)))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-87 |#1|) (QUOTE (-1055))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| (-87 |#1|) (QUOTE (-187))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| (-87 |#1|) (QUOTE (-188))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -447) (QUOTE (-1079)) (|%list| (QUOTE -87) (|devaluate| |#1|)))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -256) (|%list| (QUOTE -87) (|devaluate| |#1|)))) (|HasCategory| (-87 |#1|) (|%list| (QUOTE -238) (|%list| (QUOTE -87) (|devaluate| |#1|)) (|%list| (QUOTE -87) (|devaluate| |#1|)))) (|HasCategory| (-87 |#1|) (QUOTE (-254))) (|HasCategory| (-87 |#1|) (QUOTE (-477))) (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-87 |#1|) (QUOTE (-814)))) (OR (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-87 |#1|) (QUOTE (-814)))) (|HasCategory| (-87 |#1|) (QUOTE (-116))))) +(-89 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4146))) -(-92 S) +((|HasAttribute| |#1| (QUOTE -3980))) +(-90 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 NIL -(-93 UP) +(-91 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} pp. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) NIL NIL -(-94 S) +(-92 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"))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-95 S) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-93 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL -(-96) +(-94) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-97 A S) +(-95 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) NIL NIL -(-98 S) +(-96 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) NIL -(-99 S) +(-97 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-100 S) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-98 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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-101) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-99) ((|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 NIL -(-102) +(-100) ((|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."))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| (-101) (QUOTE (-781))) (|HasCategory| (-101) (|%list| (QUOTE -263) (QUOTE (-101))))) (-12 (|HasCategory| (-101) (QUOTE (-1041))) (|HasCategory| (-101) (|%list| (QUOTE -263) (QUOTE (-101)))))) (-3677 (-12 (|HasCategory| (-101) (QUOTE (-1041))) (|HasCategory| (-101) (|%list| (QUOTE -263) (QUOTE (-101))))) (|HasCategory| (-101) (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| (-101) (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| (-101) (QUOTE (-781))) (|HasCategory| (-101) (QUOTE (-1041)))) (|HasCategory| (-101) (QUOTE (-781))) (-3677 (|HasCategory| (-101) (QUOTE (-73))) (|HasCategory| (-101) (QUOTE (-781))) (|HasCategory| (-101) (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| (-101) (QUOTE (-1041))) (|HasCategory| (-101) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-101) (QUOTE (-73))) (-12 (|HasCategory| (-101) (QUOTE (-1041))) (|HasCategory| (-101) (|%list| (QUOTE -263) (QUOTE (-101)))))) -(-103) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| (-99) (QUOTE (-749))) (|HasCategory| (-99) (|%list| (QUOTE -256) (QUOTE (-99))))) (-12 (|HasCategory| (-99) (QUOTE (-1005))) (|HasCategory| (-99) (|%list| (QUOTE -256) (QUOTE (-99)))))) (OR (-12 (|HasCategory| (-99) (QUOTE (-1005))) (|HasCategory| (-99) (|%list| (QUOTE -256) (QUOTE (-99))))) (|HasCategory| (-99) (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| (-99) (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| (-99) (QUOTE (-749))) (|HasCategory| (-99) (QUOTE (-1005)))) (|HasCategory| (-99) (QUOTE (-749))) (OR (|HasCategory| (-99) (QUOTE (-72))) (|HasCategory| (-99) (QUOTE (-749))) (|HasCategory| (-99) (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| (-99) (QUOTE (-1005))) (|HasCategory| (-99) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-99) (QUOTE (-72))) (-12 (|HasCategory| (-99) (QUOTE (-1005))) (|HasCategory| (-99) (|%list| (QUOTE -256) (QUOTE (-99)))))) +(-101) ((|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 NIL -(-104) +(-102) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x, y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL NIL -(-105) +(-103) ((|constructor| (NIL "A cachable set is a set whose elements keep an integer as part of their structure.")) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) "\\spad{setPosition(x, n)} associates the integer \\spad{n} to \\spad{x}.")) (|position| (((|NonNegativeInteger|) $) "\\spad{position(x)} returns the integer \\spad{n} associated to \\spad{x}."))) NIL NIL -(-106) +(-104) ((|constructor| (NIL "This domain represents the capsule of a domain definition.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of top level expressions appearing in `c'."))) NIL NIL -(-107) +(-105) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4147 "*") . T)) +(((-3981 "*") . T)) NIL -(-108 |minix| -2740 R) +(-106 |minix| -2605 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) NIL NIL -(-109 |minix| -2740 S T$) +(-107 |minix| -2605 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 -(-110) +(-108) ((|constructor| (NIL "This domain represents a `case' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the case expression `e'."))) NIL NIL -(-111) +(-109) ((|constructor| (NIL "This domain represents the unnamed category defined \\indented{2}{by a list of exported signatures}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of exports in category syntax `c'.")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(c)} returns the kind of unnamed category,{} either 'domain' or 'package'."))) NIL NIL -(-112) +(-110) ((|constructor| (NIL "This domain provides representations for category constructors."))) NIL NIL -(-113) +(-111) ((|parents| (((|List| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{parents(c)} returns the list of all category forms directly extended by the category `c'.")) (|principalAncestors| (((|List| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{principalAncestors(c)} returns the list of all category forms that are principal ancestors of the the category `c'.")) (|exportedOperators| (((|List| (|OperatorSignature|)) $) "\\spad{exportedOperators(c)} returns the list of all operator signatures exported by the category `c',{} along with their predicates.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: December 20,{} 2008. Date Last Updated: February 16,{} 2008. Basic Operations: coerce Related Constructors: Also See: Type") (((|CategoryConstructor|) $) "\\spad{constructor(c)} returns the category constructor used to instantiate the category object `c'."))) NIL NIL -(-114) +(-112) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}."))) -((-4145 . T) (-4135 . T) (-4146 . T)) -((-3677 (-12 (|HasCategory| (-117) (QUOTE (-323))) (|HasCategory| (-117) (|%list| (QUOTE -263) (QUOTE (-117))))) (-12 (|HasCategory| (-117) (QUOTE (-1041))) (|HasCategory| (-117) (|%list| (QUOTE -263) (QUOTE (-117)))))) (|HasCategory| (-117) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-117) (QUOTE (-323))) (|HasCategory| (-117) (QUOTE (-781))) (|HasCategory| (-117) (QUOTE (-1041))) (|HasCategory| (-117) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-117) (QUOTE (-73))) (-12 (|HasCategory| (-117) (QUOTE (-1041))) (|HasCategory| (-117) (|%list| (QUOTE -263) (QUOTE (-117)))))) -(-115 R Q A) +((-3979 . T) (-3969 . T) (-3980 . T)) +((OR (-12 (|HasCategory| (-115) (QUOTE (-313))) (|HasCategory| (-115) (|%list| (QUOTE -256) (QUOTE (-115))))) (-12 (|HasCategory| (-115) (QUOTE (-1005))) (|HasCategory| (-115) (|%list| (QUOTE -256) (QUOTE (-115)))))) (|HasCategory| (-115) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-115) (QUOTE (-313))) (|HasCategory| (-115) (QUOTE (-749))) (|HasCategory| (-115) (QUOTE (-1005))) (|HasCategory| (-115) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-115) (QUOTE (-72))) (-12 (|HasCategory| (-115) (QUOTE (-1005))) (|HasCategory| (-115) (|%list| (QUOTE -256) (QUOTE (-115)))))) +(-113 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 NIL -(-116) +(-114) ((|constructor| (NIL "Category for the usual combinatorial functions.")) (|permutation| (($ $ $) "\\spad{permutation(n, m)} returns the number of permutations of \\spad{n} objects taken \\spad{m} at a time. Note: \\spad{permutation(n,m) = n!/(n-m)!}.")) (|factorial| (($ $) "\\spad{factorial(n)} computes the factorial of \\spad{n} (denoted in the literature by \\spad{n!}) Note: \\spad{n! = n (n-1)! when n > 0}; also,{} \\spad{0! = 1}.")) (|binomial| (($ $ $) "\\spad{binomial(n,r)} returns the \\spad{(n,r)} binomial coefficient (often denoted in the literature by \\spad{C(n,r)}). Note: \\spad{C(n,r) = n!/(r!(n-r)!)} where \\spad{n >= r >= 0}."))) NIL NIL -(-117) +(-115) ((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|escape| (($) "\\spad{escape} designate the escape character.")) (|verticalTab| (($) "\\spad{verticalTab} designates vertical tab.")) (|horizontalTab| (($) "\\spad{horizontalTab} designates horizontal tab.")) (|backspace| (($) "\\spad{backspace} designates the backspace character.")) (|formfeed| (($) "\\spad{formfeed} designates the form feed character.")) (|linefeed| (($) "\\spad{linefeed} designates the line feed character.")) (|carriageReturn| (($) "\\spad{carriageReturn} designates carriage return.")) (|newline| (($) "\\spad{newline} designates the new line character.")) (|underscore| (($) "\\spad{underscore} designates the underbar character.")) (|quote| (($) "\\spad{quote} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|NonNegativeInteger|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|NonNegativeInteger|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}."))) NIL NIL -(-118) +(-116) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4142 . T)) +((-3976 . T)) NIL -(-119 R) +(-117 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) NIL NIL -(-120) +(-118) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4142 . T)) +((-3976 . T)) NIL -(-121 -3215 UP UPUP) +(-119 -3076 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 -(-122 R CR) +(-120 R CR) ((|constructor| (NIL "This package provides the generalized euclidean algorithm which is needed as the basic step for factoring polynomials.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} where (\\spad{fi} relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g} = sum \\spad{ai} prod fj (\\spad{j} \\= \\spad{i}) or equivalently g/prod fj = sum (ai/fi) or returns \"failed\" if no such list exists"))) NIL NIL -(-123 A S) +(-121 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasAttribute| |#1| (QUOTE -4145))) -(-124 S) +((|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasAttribute| |#1| (QUOTE -3979))) +(-122 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL -(-125 |n| K Q) +(-123 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4140 . T) (-4139 . T) (-4142 . T)) +((-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-126) +(-124) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) NIL NIL -(-127) +(-125) ((|constructor| (NIL "This domain represents list comprehension syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the expression being collected by the list comprehension `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of the iterators of the list comprehension `e'."))) NIL NIL -(-128 UP |Par|) +(-126 UP |Par|) ((|complexZeros| (((|List| (|Complex| |#2|)) |#1| |#2|) "\\spad{complexZeros(poly, eps)} finds the complex zeros of the univariate polynomial \\spad{poly} to precision eps with solutions returned as complex floats or rationals depending on the type of eps."))) NIL NIL -(-129) +(-127) ((|constructor| (NIL "This domain represents type specification \\indented{2}{for an identifier or expression.}")) (|rhs| (((|TypeAst|) $) "\\spad{rhs(e)} returns the right hand side of the colon expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the colon expression `e'."))) NIL NIL -(-130) +(-128) ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|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 -(-131 R -3215) +(-129 R -3076) ((|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 -(-132 I) +(-130 I) ((|stirling2| ((|#1| |#1| |#1|) "\\spad{stirling2(n,m)} returns the Stirling number of the second kind denoted \\spad{SS[n,m]}.")) (|stirling1| ((|#1| |#1| |#1|) "\\spad{stirling1(n,m)} returns the Stirling number of the first kind denoted \\spad{S[n,m]}.")) (|permutation| ((|#1| |#1| |#1|) "\\spad{permutation(n)} returns \\spad{!P(n,r) = n!/(n-r)!}. This is the number of permutations of \\spad{n} objects taken \\spad{r} at a time.")) (|partition| ((|#1| |#1|) "\\spad{partition(n)} returns the number of partitions of the integer \\spad{n}. This is the number of distinct ways that \\spad{n} can be written as a sum of positive integers.")) (|multinomial| ((|#1| |#1| (|List| |#1|)) "\\spad{multinomial(n,[m1,m2,...,mk])} returns the multinomial coefficient \\spad{n!/(m1! m2! ... mk!)}.")) (|factorial| ((|#1| |#1|) "\\spad{factorial(n)} returns \\spad{n!}. this is the product of all integers between 1 and \\spad{n} (inclusive). Note: \\spad{0!} is defined to be 1.")) (|binomial| ((|#1| |#1| |#1|) "\\spad{binomial(n,r)} returns the binomial coefficient \\spad{C(n,r) = n!/(r! (n-r)!)},{} where \\spad{n >= r >= 0}. This is the number of combinations of \\spad{n} objects taken \\spad{r} at a time."))) NIL NIL -(-133) +(-131) ((|constructor| (NIL "CombinatorialOpsCategory is the category obtaining by adjoining summations and products to the usual combinatorial operations.")) (|product| (($ $ (|SegmentBinding| $)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") (($ $ (|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| (($ $ (|SegmentBinding| $)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") (($ $ (|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| (($ $ (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") (($ $) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials."))) NIL NIL -(-134) +(-132) ((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) NIL NIL -(-135) +(-133) ((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) NIL NIL -(-136) +(-134) ((|constructor| (NIL "This package exports the elementary operators,{} with some semantics already attached to them. The semantics that is attached here is not dependent on the set in which the operators will be applied.")) (|operator| (((|BasicOperator|) (|Symbol|)) "\\spad{operator(s)} returns an operator with name \\spad{s},{} with the appropriate semantics if \\spad{s} is known. If \\spad{s} is not known,{} the result has no semantics."))) NIL NIL -(-137 R UP UPUP) +(-135 R UP UPUP) ((|constructor| (NIL "A package for swapping the order of two variables in a tower of two UnivariatePolynomialCategory extensions.")) (|swap| ((|#3| |#3|) "\\spad{swap(p(x,y))} returns \\spad{p}(\\spad{y},{}\\spad{x})."))) NIL NIL -(-138 S R) +(-136 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-498))) (|HasCategory| |#2| (QUOTE (-942))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (QUOTE (-1000))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (QUOTE (-318))) (|HasAttribute| |#2| (QUOTE -4141)) (|HasAttribute| |#2| (QUOTE -4144)) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (QUOTE (-510)))) -(-139 R) +((|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-477))) (|HasCategory| |#2| (QUOTE (-908))) (|HasCategory| |#2| (QUOTE (-1104))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasAttribute| |#2| (QUOTE -3975)) (|HasAttribute| |#2| (QUOTE -3978)) (|HasCategory| |#2| (QUOTE (-254))) (|HasCategory| |#2| (QUOTE (-489)))) +(-137 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})).")) 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T)) +((-3972 OR (|has| |#1| (-489)) (-12 (|has| |#1| (-254)) (|has| |#1| (-814)))) (-3977 |has| |#1| (-308)) (-3971 |has| |#1| (-308)) (-3975 |has| |#1| (-6 -3975)) (-3978 |has| |#1| (-6 -3978)) (-1363 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-140 RR PR) +(-138 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."))) NIL NIL -(-141) +(-139) ((|constructor| (NIL "This package implements a Spad compiler.")) (|elaborate| (((|Maybe| (|Elaboration|)) (|SpadAst|)) "\\spad{elaborate(s)} returns the elaboration of the syntax object \\spad{s} in the empty environement.")) (|macroExpand| (((|SpadAst|) (|SpadAst|) (|Environment|)) "\\spad{macroExpand(s,e)} traverses the syntax object \\spad{s} replacing all (niladic) macro invokations with the corresponding substitution."))) NIL NIL -(-142 R) +(-140 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}."))) -((-4138 -3677 (|has| |#1| (-510)) (-12 (|has| |#1| (-261)) (|has| |#1| (-848)))) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) (-4141 |has| |#1| (-6 -4141)) (-4144 |has| |#1| (-6 -4144)) (-1409 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . 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T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL NIL -(-144 R S CS) +(-142 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL NIL -(-145) +(-143) ((|constructor| (NIL "This domain implements some global properties of subspaces.")) (|copy| (($ $) "\\spad{copy(x)} \\undocumented")) (|solid| (((|Boolean|) $ (|Boolean|)) "\\spad{solid(x,b)} \\undocumented")) (|close| (((|Boolean|) $ (|Boolean|)) "\\spad{close(x,b)} \\undocumented")) (|solid?| (((|Boolean|) $) "\\spad{solid?(x)} \\undocumented")) (|closed?| (((|Boolean|) $) "\\spad{closed?(x)} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented"))) NIL NIL -(-146) +(-144) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-147) +(-145) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) NIL NIL -(-148 R) +(-146 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4147 "*") . T) (-4138 . T) (-4143 . T) (-4137 . T) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") . T) (-3972 . T) (-3977 . T) (-3971 . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-149) +(-147) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) NIL NIL -(-150 R) +(-148 R) ((|constructor| (NIL "CoordinateSystems provides coordinate transformation functions for plotting. Functions in this package return conversion functions which take points expressed in other coordinate systems and return points with the corresponding Cartesian coordinates.")) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) "\\spad{conical(a,b)} transforms from conical coordinates to Cartesian coordinates: \\spad{conical(a,b)} is a function which will map the point \\spad{(lambda,mu,nu)} to \\spad{x = lambda*mu*nu/(a*b)},{} \\spad{y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))},{} \\spad{z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))}.")) (|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{toroidal(a)} transforms from toroidal coordinates to Cartesian coordinates: \\spad{toroidal(a)} is a function which will map the point \\spad{(u,v,phi)} to \\spad{x = a*sinh(v)*cos(phi)/(cosh(v)-cos(u))},{} \\spad{y = a*sinh(v)*sin(phi)/(cosh(v)-cos(u))},{} \\spad{z = a*sin(u)/(cosh(v)-cos(u))}.")) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolarCylindrical(a)} transforms from bipolar cylindrical coordinates to Cartesian coordinates: \\spad{bipolarCylindrical(a)} is a function which will map the point \\spad{(u,v,z)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))},{} \\spad{z}.")) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolar(a)} transforms from bipolar coordinates to Cartesian coordinates: \\spad{bipolar(a)} is a function which will map the point \\spad{(u,v)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))}.")) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{oblateSpheroidal(a)} transforms from oblate spheroidal coordinates to Cartesian coordinates: \\spad{oblateSpheroidal(a)} is a function which will map the point \\spad{(xi,eta,phi)} to \\spad{x = a*sinh(xi)*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(xi)*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(xi)*cos(eta)}.")) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{prolateSpheroidal(a)} transforms from prolate spheroidal coordinates to Cartesian coordinates: \\spad{prolateSpheroidal(a)} is a function which will map the point \\spad{(xi,eta,phi)} to \\spad{x = a*sinh(xi)*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(xi)*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(xi)*cos(eta)}.")) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{ellipticCylindrical(a)} transforms from elliptic cylindrical coordinates to Cartesian coordinates: \\spad{ellipticCylindrical(a)} is a function which will map the point \\spad{(u,v,z)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)},{} \\spad{z}.")) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{elliptic(a)} transforms from elliptic coordinates to Cartesian coordinates: \\spad{elliptic(a)} is a function which will map the point \\spad{(u,v)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)}.")) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) "\\spad{paraboloidal(pt)} transforms \\spad{pt} from paraboloidal coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,v,phi)} to \\spad{x = u*v*cos(phi)},{} \\spad{y = u*v*sin(phi)},{} \\spad{z = 1/2 * (u**2 - v**2)}.")) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolicCylindrical(pt)} transforms \\spad{pt} from parabolic cylindrical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,v,z)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v},{} \\spad{z}.")) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolic(pt)} transforms \\spad{pt} from parabolic coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,v)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v}.")) (|spherical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{spherical(pt)} transforms \\spad{pt} from spherical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,theta,phi)} to \\spad{x = r*sin(phi)*cos(theta)},{} \\spad{y = r*sin(phi)*sin(theta)},{} \\spad{z = r*cos(phi)}.")) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cylindrical(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,theta,z)} to \\spad{x = r * cos(theta)},{} \\spad{y = r * sin(theta)},{} \\spad{z}.")) (|polar| (((|Point| |#1|) (|Point| |#1|)) "\\spad{polar(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,theta)} to \\spad{x = r * cos(theta)} ,{} \\spad{y = r * sin(theta)}.")) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cartesian(pt)} returns the Cartesian coordinates of point \\spad{pt}."))) NIL NIL -(-151 R |PolR| E) +(-149 R |PolR| E) ((|constructor| (NIL "This package implements characteristicPolynomials for monogenic algebras using resultants")) (|characteristicPolynomial| ((|#2| |#3|) "\\spad{characteristicPolynomial(e)} returns the characteristic polynomial of \\spad{e} using resultants"))) NIL NIL -(-152 R S CS) +(-150 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-884 |#2|) (|%list| (QUOTE -821) (|devaluate| |#1|)))) -(-153 R) +((|HasCategory| (-850 |#2|) (|%list| (QUOTE -789) (|devaluate| |#1|)))) +(-151 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL NIL -(-154) +(-152) ((|constructor| (NIL "This domain represents `coerce' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-155 R UP) +(-153 R UP) ((|constructor| (NIL "\\spadtype{ComplexRootFindingPackage} provides functions to find all roots of a polynomial \\spad{p} over the complex number by using Plesken's idea to calculate in the polynomial ring modulo \\spad{f} and employing the Chinese Remainder Theorem. In this first version,{} the precision (see \\spadfunFrom{digits}{Float}) is not increased when this is necessary to avoid rounding errors. Hence it is the user's responsibility to increase the precision if necessary. Note also,{} if this package is called with \\spadignore{e.g.} \\spadtype{Fraction Integer},{} the precise calculations could require a lot of time. Also note that evaluating the zeros is not necessarily a good check whether the result is correct: already evaluation can cause rounding errors.")) (|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|) "\\spad{startPolynomial(p)} uses the ideas of Schoenhage's variant of Graeffe's method to construct circles which separate roots to get a good start polynomial,{} \\spadignore{i.e.} one whose image under the Chinese Remainder Isomorphism has both entries of norm smaller and greater or equal to 1. In case the roots are found during internal calculations. The corresponding factors are in {\\em factors} which are otherwise 1.")) (|setErrorBound| ((|#1| |#1|) "\\spad{setErrorBound(eps)} changes the internal error bound,{} by default being {\\em 10 ** (-3)} to \\spad{eps},{} if \\spad{R} is a member in the category \\spadtype{QuotientFieldCategory Integer}. The internal {\\em globalDigits} is set to {\\em ceiling(1/r)**2*10} being {\\em 10**7} by default.")) (|schwerpunkt| (((|Complex| |#1|) |#2|) "\\spad{schwerpunkt(p)} determines the 'Schwerpunkt' of the roots of the polynomial \\spad{p} of degree \\spad{n},{} \\spadignore{i.e.} the center of gravity,{} which is {\\em coeffient of \\spad{x**(n-1)}} divided by {\\em n times coefficient of \\spad{x**n}}.")) (|rootRadius| ((|#1| |#2|) "\\spad{rootRadius(p)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em 1+globalEps},{} where {\\em globalEps} is the internal error bound,{} which can be set by {\\em setErrorBound}.") ((|#1| |#2| |#1|) "\\spad{rootRadius(p,errQuot)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em errQuot}.")) (|reciprocalPolynomial| ((|#2| |#2|) "\\spad{reciprocalPolynomial(p)} calulates a polynomial which has exactly the inverses of the non-zero roots of \\spad{p} as roots,{} and the same number of 0-roots.")) (|pleskenSplit| (((|Factored| |#2|) |#2| |#1|) "\\spad{pleskenSplit(poly, eps)} determines a start polynomial {\\em start}\\\\ by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} -1\". Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{pleskenSplit(poly,eps,info)} determines a start polynomial {\\em start} by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} -1\". Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough. If {\\em info} is {\\em true},{} then information messages are issued.")) (|norm| ((|#1| |#2|) "\\spad{norm(p)} determines sum of absolute values of coefficients Note: this function depends on \\spadfunFrom{abs}{Complex}.")) (|graeffe| ((|#2| |#2|) "\\spad{graeffe p} determines \\spad{q} such that \\spad{q(-z**2) = p(z)*p(-z)}. Note that the roots of \\spad{q} are the squares of the roots of \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} tries to factor \\spad{p} into linear factors with error atmost {\\em globalEps},{} the internal error bound,{} which can be set by {\\em setErrorBound}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1|) "\\spad{factor(p, eps)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{factor(p, eps, info)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization. If {\\em info} is {\\em true},{} then information messages are given.")) (|divisorCascade| (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) "\\spad{divisorCascade(p,tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions is calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial.") (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|)) "\\spad{divisorCascade(p,tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions are calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial. If {\\em info} is {\\em true},{} then information messages are issued.")) (|complexZeros| (((|List| (|Complex| |#1|)) |#2| |#1|) "\\spad{complexZeros(p, eps)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by {\\em eps}.") (((|List| (|Complex| |#1|)) |#2|) "\\spad{complexZeros(p)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by the package constant {\\em globalEps} which you may change by {\\em setErrorBound}."))) NIL NIL -(-156 S ST) +(-154 S ST) ((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) NIL NIL -(-157) +(-155) ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-158 C) +(-156 C) ((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") ((|#1| $) "\\spad{constructor(t)} returns the name of the constructor used to make the call."))) NIL NIL -(-159 S) +(-157 S) ((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(\\spad{i+1}) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL -(-160) +(-158) ((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(\\spad{i+1}) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL -(-161) +(-159) ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 -(-162 R -3215) +(-160 R -3076) ((|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 -(-163 R) +(-161 R) ((|constructor| (NIL "CoerceVectorMatrixPackage: an unexposed,{} technical package for data conversions")) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) "\\spad{coerce(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Fraction Polynomial R}")) (|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) "\\spad{coerceP(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Polynomial R}"))) NIL NIL -(-164) +(-162) ((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{SFunction(li)} is the \\spad{S}-function of the partition \\spad{li} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}"))) NIL NIL -(-165) +(-163) ((|constructor| (NIL "This package \\undocumented{}")) (|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicFactorization(n)} \\undocumented{}")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} \\undocumented{}")) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicDecomposition(n)} \\undocumented{}"))) NIL NIL -(-166 N T$) +(-164 N T$) ((|constructor| (NIL "This domain provides for a fixed-sized homogeneous data buffer.")) (|qsetelt| ((|#2| $ (|NonNegativeInteger|) |#2|) "setelt(\\spad{b},{}\\spad{i},{}\\spad{x}) sets the \\spad{i}th entry of data buffer `b' to `x'. Indexing is 0-based.")) (|qelt| ((|#2| $ (|NonNegativeInteger|)) "elt(\\spad{b},{}\\spad{i}) returns the \\spad{i}th element in buffer `b'. Indexing is 0-based.")) (|new| (($) "\\spad{new()} returns a fresly allocated data buffer or length \\spad{N}."))) NIL NIL -(-167 S) +(-165 S) ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-168 |vars|) +(-166 |vars|) ((|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 -(-169 -3215 UP UPUP R) +(-167 -3076 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 -(-170 -3215 FP) +(-168 -3076 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 -(-171) +(-169) ((|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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-499) (QUOTE (-848))) (|HasCategory| (-499) (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| (-499) (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-120))) (|HasCategory| (-499) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-499) (QUOTE (-960))) (|HasCategory| (-499) (QUOTE (-763))) (|HasCategory| (-499) (QUOTE (-781))) (-3677 (|HasCategory| (-499) (QUOTE (-763))) (|HasCategory| (-499) (QUOTE (-781)))) (|HasCategory| (-499) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-499) (QUOTE (-1092))) (|HasCategory| (-499) (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| (-499) (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| (-499) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| (-499) (QUOTE (-189))) (|HasCategory| (-499) (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| (-499) (QUOTE (-190))) (|HasCategory| (-499) (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| (-499) (|%list| (QUOTE -468) (QUOTE (-1117)) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -263) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -240) (QUOTE (-499)) (QUOTE (-499)))) (|HasCategory| (-499) (QUOTE (-261))) (|HasCategory| (-499) (QUOTE (-498))) (|HasCategory| (-499) (|%list| (QUOTE -596) (QUOTE (-499)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-848)))) (-3677 (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-848)))) (|HasCategory| (-499) (QUOTE (-118))))) -(-172) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-478) (QUOTE (-814))) (|HasCategory| (-478) (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| (-478) (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-118))) (|HasCategory| (-478) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-478) (QUOTE (-926))) (|HasCategory| (-478) (QUOTE (-733))) (|HasCategory| (-478) (QUOTE (-749))) (OR (|HasCategory| (-478) (QUOTE (-733))) (|HasCategory| (-478) (QUOTE (-749)))) (|HasCategory| (-478) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-478) (QUOTE (-1055))) (|HasCategory| (-478) (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-478) (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-478) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-478) (QUOTE (-187))) (|HasCategory| (-478) (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| (-478) (QUOTE (-188))) (|HasCategory| (-478) (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| (-478) (|%list| (QUOTE -447) (QUOTE (-1079)) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -256) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -238) (QUOTE (-478)) (QUOTE (-478)))) (|HasCategory| (-478) (QUOTE (-254))) (|HasCategory| (-478) (QUOTE (-477))) (|HasCategory| (-478) (|%list| (QUOTE -575) (QUOTE (-478)))) (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-814)))) (OR (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-814)))) (|HasCategory| (-478) (QUOTE (-116))))) +(-170) ((|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 -(-173 R -3215) +(-171 R -3076) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="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| #1#) (|:| |pole| #2#)) |#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| #1#) (|:| |pole| #2#)) |#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 -(-174 R) +(-172 R) ((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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 -(-175 R1 R2) +(-173 R1 R2) ((|constructor| (NIL "This package \\undocumented{}")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}"))) NIL NIL -(-176 S) +(-174 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}."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-177 |CoefRing| |listIndVar|) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-175 |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}."))) -((-4142 . T)) +((-3976 . T)) NIL -(-178 R -3215) +(-176 R -3076) ((|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 -(-179) +(-177) ((|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.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|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}."))) -((-3920 . T) (-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3754 . T) (-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-180) +(-178) ((|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)}.}"))) NIL NIL -(-181 R) +(-179 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}"))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-261))) (|HasCategory| |#1| (QUOTE (-510))) (|HasAttribute| |#1| (QUOTE (-4147 "*"))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-182 A S) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (QUOTE (-254))) (|HasCategory| |#1| (QUOTE (-489))) (|HasAttribute| |#1| (QUOTE (-3981 "*"))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-180 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL -(-183 S) +(-181 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."))) -((-4146 . T)) +((-3980 . T)) NIL -(-184 R) +(-182 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4142 . T)) +((-3976 . T)) NIL -(-185 S T$) +(-183 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) NIL NIL -(-186 T$) +(-184 T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#1| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#1| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) NIL NIL -(-187 R) +(-185 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-188 S) +(-186 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) NIL NIL -(-189) +(-187) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) NIL NIL -(-190) +(-188) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4142 . T)) +((-3976 . T)) NIL -(-191 A S) +(-189 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4145))) -(-192 S) +((|HasAttribute| |#1| (QUOTE -3979))) +(-190 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4146 . T)) +((-3980 . T)) NIL -(-193) +(-191) ((|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 -(-194 S -2740 R) +(-192 S -2605 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 (-318))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-781))) (|HasAttribute| |#3| (QUOTE -4142)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-323))) (|HasCategory| |#3| (QUOTE (-684))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-989))) (|HasCategory| |#3| (QUOTE (-1041)))) -(-195 -2740 R) +((|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-710))) (|HasCategory| |#3| (QUOTE (-749))) (|HasAttribute| |#3| (QUOTE -3976)) (|HasCategory| |#3| (QUOTE (-144))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#3| (QUOTE (-658))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (QUOTE (-1005)))) +(-193 -2605 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"))) -((-4139 |has| |#2| (-989)) (-4140 |has| |#2| (-989)) (-4142 |has| |#2| (-6 -4142)) (-4145 . T)) +((-3973 |has| |#2| (-954)) (-3974 |has| |#2| (-954)) (-3976 |has| |#2| (-6 -3976)) (-3979 . T)) NIL -(-196 -2740 R) +(-194 -2605 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."))) -((-4139 |has| |#2| (-989)) (-4140 |has| |#2| (-989)) (-4142 |has| |#2| (-6 -4142)) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-323))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-684))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-738))) 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NIL NIL -(-199 S) +(-197 S) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) NIL NIL -(-200) +(-198) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4138 . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) (-3973 . T) (-3974 . T) (-3976 . 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T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-201 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) 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(|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (|HasCategory| |#3| (QUOTE (-954)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-144))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-658))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-710))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-749))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478)))))) (|HasCategory| (-478) (QUOTE (-749))) (-12 (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (|%list| (QUOTE -575) (QUOTE (-478))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (|%list| (QUOTE -802) (QUOTE (-1079))))) (-12 (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (|%list| (QUOTE -804) (QUOTE (-1079)))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (QUOTE (-954)))) (-12 (|HasCategory| |#3| (QUOTE (-187))) (|HasCategory| |#3| (QUOTE (-954))))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (|HasCategory| |#3| (QUOTE (-954)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (|%list| (QUOTE -802) (QUOTE (-1079))))) (|HasAttribute| |#3| (QUOTE -3976)) (-12 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (QUOTE (-954))))) (-12 (|HasCategory| |#3| (QUOTE (-187))) (|HasCategory| |#3| (QUOTE (-954)))) (-12 (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (|%list| (QUOTE -804) (QUOTE (-1079))))) (|HasCategory| |#3| (QUOTE (-144))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -256) (|devaluate| |#3|))))) +(-209 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL -((|HasCategory| |#2| (QUOTE (-190)))) -(-212 R S V E) +((|HasCategory| |#2| (QUOTE (-188)))) +(-210 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-6 -3977)) (-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-213 S) +(-211 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) NIL -(-214 |Ex|) +(-212 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-215) +(-213) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-216 R |Ex|) +(-214 R |Ex|) ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,y) = g(x,y),x,y,l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) NIL NIL -(-217) +(-215) ((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,rRange,iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f, -2..2, -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,rRange,iRange,arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f, 0.3..3, 0..2*\\%pi, false)}} Parameter descriptions: \\indented{2}{f:\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) NIL NIL -(-218 R) +(-216 R) ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) NIL NIL -(-219) +(-217) ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,lz,l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly,lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL NIL -(-220) +(-218) ((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,y,z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,y,z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) NIL NIL -(-221) +(-219) ((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn't exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) NIL NIL -(-222 S) +(-220 S) ((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) NIL NIL -(-223 S R) +(-221 S R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#2| (QUOTE (-189)))) -(-224 R) +((|HasCategory| |#2| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-187)))) +(-222 R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) 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T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-814))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| |#3| (|%list| (QUOTE -789) (QUOTE (-323))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#3| (|%list| (QUOTE -789) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| |#3| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#3| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#3| (|%list| (QUOTE -548) (QUOTE (-467))))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasAttribute| |#1| (QUOTE -3977)) (|HasCategory| |#1| (QUOTE (-385))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#1| (QUOTE (-116))))) +(-224 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|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 NIL -(-227 S) +(-225 S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL NIL -(-228) +(-226) ((|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 -(-229 R -3215) +(-227 R -3076) ((|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 -(-230 R -3215) +(-228 R -3076) ((|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 -(-231 |Coef| UTS ULS) +(-229 |Coef| UTS ULS) ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-318)))) -(-232 |Coef| ULS UPXS EFULS) +((|HasCategory| |#1| (QUOTE (-308)))) +(-230 |Coef| ULS UPXS EFULS) ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-318)))) -(-233) +((|HasCategory| |#1| (QUOTE (-308)))) +(-231) ((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Identifier|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Identifier|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|Syntax|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter."))) NIL NIL -(-234) +(-232) ((|environment| (((|Environment|) $) "\\spad{environment(x)} returns the environment of the elaboration \\spad{x}.")) (|typeForm| (((|InternalTypeForm|) $) "\\spad{typeForm(x)} returns the type form of the elaboration \\spad{x}.")) (|irForm| (((|InternalRepresentationForm|) $) "\\spad{irForm(x)} returns the internal representation form of the elaboration \\spad{x}.")) (|elaboration| (($ (|InternalRepresentationForm|) (|InternalTypeForm|) (|Environment|)) "\\spad{elaboration(ir,ty,env)} construct an elaboration object for for the internal representation form \\spad{ir},{} with type \\spad{ty},{} and environment \\spad{env}."))) NIL NIL -(-235 A S) +(-233 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-1041)))) -(-236 S) +((|HasCategory| |#2| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-1005)))) +(-234 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4146 . T)) +((-3980 . T)) NIL -(-237 S) +(-235 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) NIL NIL -(-238) +(-236) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) NIL NIL -(-239 |Coef| UTS) +(-237 |Coef| UTS) ((|constructor| (NIL "The elliptic functions sn,{} sc and dn are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function dn as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function cn as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function sn as a Taylor \\indented{1}{series.}"))) NIL NIL -(-240 S T$) +(-238 S T$) ((|constructor| (NIL "An eltable over domains \\spad{S} and \\spad{T} is a structure which can be viewed as a function from \\spad{S} to \\spad{T}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,s)} (also written: \\spad{u.s}) returns the value of \\spad{u} at \\spad{s}. Error: if \\spad{u} is not defined at \\spad{s}."))) NIL NIL -(-241 S |Dom| |Im|) +(-239 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4146))) -(-242 |Dom| |Im|) +((|HasAttribute| |#1| (QUOTE -3980))) +(-240 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-243 S R |Mod| -2138 -3658 |exactQuo|) +(-241 S R |Mod| -2023 -3502 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-244) +(-242) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4138 . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-245) +(-243) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) NIL NIL -(-246 R) +(-244 R) ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,m,k,g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) NIL NIL -(-247 S) +(-245 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."))) -((-4142 -3677 (|has| |#1| (-989)) (|has| |#1| (-427))) (-4139 |has| |#1| (-989)) (-4140 |has| |#1| (-989))) -((|HasCategory| |#1| (QUOTE (-318))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-989)))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (-3677 (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117))))) (-3677 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117))))) (-3677 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117))))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-989)))) (-3677 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-684)))) (|HasCategory| |#1| (QUOTE (-427))) (-3677 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-684))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117))))) (-3677 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-684))) (|HasCategory| |#1| (QUOTE (-1052)))) (|HasCategory| |#1| (|%list| (QUOTE -468) (QUOTE (-1117)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-252))) (-3677 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-427)))) (-3677 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-684)))) (-3677 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-989)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-684)))) -(-248 S R) +((-3976 OR (|has| |#1| (-954)) (|has| |#1| (-406))) (-3973 |has| |#1| (-954)) (-3974 |has| |#1| (-954))) +((|HasCategory| |#1| (QUOTE (-308))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-954)))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (OR (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079))))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-954)))) (OR (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-658)))) (|HasCategory| |#1| (QUOTE (-406))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079))))) (OR (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (|%list| (QUOTE -447) (QUOTE (-1079)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-250))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-406)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-658)))) (OR (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-954)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-658)))) +(-246 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 NIL -(-249 |Key| |Entry|) +(-247 |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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-1041))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) -(-250) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-1005))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) +(-248) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-251 S) +(-249 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|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 -((|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-989)))) -(-252) +((|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-954)))) +(-250) ((|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 -(-253 -3215 S) +(-251 -3076 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 -(-254 E -3215) +(-252 E -3076) ((|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 -(-255) -((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,var,range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,var,range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) -NIL -NIL -(-256 A B) -((|constructor| (NIL "\\spad{ExpertSystemContinuityPackage1} exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) -NIL -NIL -(-257) -((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|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{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' -> 0.75 200 `operation units' -> 0.5 83 `operation units' -> 0.25 ** = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) -NIL -NIL -(-258 R1) -((|constructor| (NIL "\\axiom{\\spad{ExpertSystemToolsPackage1}} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) -NIL -NIL -(-259 R1 R2) -((|constructor| (NIL "\\axiom{\\spad{ExpertSystemToolsPackage2}} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,m)} applies a mapping \\spad{f:R1} -> \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) -NIL -NIL -(-260 S) +(-253 S) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) NIL NIL -(-261) +(-254) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-262 S R) +(-255 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-263 R) +(-256 R) ((|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 -(-264 -3215) +(-257 -3076) ((|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 -(-265) +(-258) ((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) NIL NIL -(-266) +(-259) ((|constructor| (NIL "This domain represents exit expressions.")) 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|#1| (|%list| (QUOTE -943) (QUOTE (-478))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-954)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-954)))) (OR (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-954)))) (-12 (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489)))) (OR (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1015)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-954)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| $ (QUOTE (-954))) (|HasCategory| $ (|%list| (QUOTE -943) (QUOTE (-478))))) +(-262 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 NIL -(-270 R FE) +(-263 R FE) ((|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 -(-271 R -3215) +(-264 R -3076) ((|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 -(-272) +(-265) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}."))) NIL NIL -(-273 FE |var| |cen|) +(-266 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."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-146))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499))) (|devaluate| |#1|)))) (|HasCategory| (-361 (-499)) (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-318))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510)))) (-3677 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasSignature| |#1| (|%list| (QUOTE -4096) (|%list| (|devaluate| |#1|) (QUOTE (-1117)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499)))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-898))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-499))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasSignature| |#1| (|%list| (QUOTE -3962) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1117))))) (|HasSignature| |#1| (|%list| (QUOTE -3204) (|%list| (|%list| (QUOTE -599) (QUOTE (-1117))) (|devaluate| |#1|))))))) -(-274 M) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-308)) (-3971 |has| |#1| (-308)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|)))) (|HasCategory| (-343 (-478)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-308))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasSignature| |#1| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#1|) (QUOTE (-1079)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasSignature| |#1| (|%list| (QUOTE -3796) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1079))))) (|HasSignature| |#1| (|%list| (QUOTE -3065) (|%list| (|%list| (QUOTE -578) (QUOTE (-1079))) (|devaluate| |#1|))))))) +(-267 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 NIL -(-275 E OV R P) +(-268 E OV R P) ((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between -k and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly, lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly, lvar, lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}."))) NIL NIL -(-276 S) +(-269 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) -((-4140 . T) (-4139 . T)) -((|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| (-499) (QUOTE (-737)))) -(-277 S E) +((-3974 . T) (-3973 . T)) +((|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| (-478) (QUOTE (-709)))) +(-270 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL NIL -(-278 S) +(-271 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-714) (QUOTE (-737)))) -(-279 S R E) +((|HasCategory| (-687) (QUOTE (-709)))) +(-272 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-146)))) -(-280 R E) +((|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-144)))) +(-273 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-281 S) +(-274 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."))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-282 S -3215) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-275 S -3076) ((|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 (-323)))) -(-283 -3215) +((|HasCategory| |#2| (QUOTE (-313)))) +(-276 -3076) ((|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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -NIL -(-284) -((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -NIL -(-285 E) +(-277 E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) NIL NIL -(-286) -((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables \\spad{I1},{} \\spad{I2},{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,b,d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,p,q)} uses loop variables in the Fortran,{} \\spad{I1} and \\spad{I2}")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,p)} \\undocumented{}"))) -NIL -NIL -(-287) +(-278) ((|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 -(-288 -3215 UP UPUP R) +(-279 -3076 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 -(-289 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-280 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|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 -(-290 S -3215 UP UPUP R) +(-281 S -3076 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 -(-291 -3215 UP UPUP R) +(-282 -3076 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|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-292 S R) +(-283 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -468) (QUOTE (-1117)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -240) (|devaluate| |#2|) (|devaluate| |#2|)))) -(-293 R) +((|HasCategory| |#2| (|%list| (QUOTE -447) (QUOTE (-1079)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -238) (|devaluate| |#2|) (|devaluate| |#2|)))) +(-284 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL -(-294 |basicSymbols| |subscriptedSymbols| R) -((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function \\spad{LOG10}")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#3| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#3| (|%list| (QUOTE -978) (QUOTE (-333)))) (|HasCategory| $ (QUOTE (-989))) (|HasCategory| $ (|%list| (QUOTE -978) (QUOTE (-499))))) -(-295 |p| |n|) +(-285 |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}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| (-844 |#1|) (QUOTE (-118))) (|HasCategory| (-844 |#1|) (QUOTE (-323)))) (|HasCategory| (-844 |#1|) (QUOTE (-120))) (|HasCategory| (-844 |#1|) (QUOTE (-323))) (|HasCategory| (-844 |#1|) (QUOTE (-118)))) -(-296 S -3215 UP UPUP) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| (-810 |#1|) (QUOTE (-116))) (|HasCategory| (-810 |#1|) (QUOTE (-313)))) (|HasCategory| (-810 |#1|) (QUOTE (-118))) (|HasCategory| (-810 |#1|) (QUOTE (-313))) (|HasCategory| (-810 |#1|) (QUOTE (-116)))) +(-286 S -3076 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 (-323))) (|HasCategory| |#2| (QUOTE (-318)))) -(-297 -3215 UP UPUP) +((|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-308)))) +(-287 -3076 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."))) -((-4138 |has| (-361 |#2|) (-318)) (-4143 |has| (-361 |#2|) (-318)) (-4137 |has| (-361 |#2|) (-318)) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 |has| (-343 |#2|) (-308)) (-3977 |has| (-343 |#2|) (-308)) (-3971 |has| (-343 |#2|) (-308)) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-298 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-288 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-299 |p| |extdeg|) +(-289 |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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| (-844 |#1|) (QUOTE (-118))) (|HasCategory| (-844 |#1|) (QUOTE (-323)))) (|HasCategory| (-844 |#1|) (QUOTE (-120))) (|HasCategory| (-844 |#1|) (QUOTE (-323))) (|HasCategory| (-844 |#1|) (QUOTE (-118)))) -(-300 GF |defpol|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| (-810 |#1|) (QUOTE (-116))) (|HasCategory| (-810 |#1|) (QUOTE (-313)))) (|HasCategory| (-810 |#1|) (QUOTE (-118))) (|HasCategory| (-810 |#1|) (QUOTE (-313))) (|HasCategory| (-810 |#1|) (QUOTE (-116)))) +(-290 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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-118)))) -(-301 GF |extdeg|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-116)))) +(-291 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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-118)))) -(-302 GF) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-116)))) +(-292 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 NIL -(-303 F1 GF F2) +(-293 F1 GF F2) ((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}GF,{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn't divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn't divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL NIL -(-304 S) +(-294 S) ((|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."))) NIL NIL -(-305) +(-295) ((|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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-306 R UP -3215) +(-296 R UP -3076) ((|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 -(-307 |p| |extdeg|) +(-297 |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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| (-844 |#1|) (QUOTE (-118))) (|HasCategory| (-844 |#1|) (QUOTE (-323)))) (|HasCategory| (-844 |#1|) (QUOTE (-120))) (|HasCategory| (-844 |#1|) (QUOTE (-323))) (|HasCategory| (-844 |#1|) (QUOTE (-118)))) -(-308 GF |uni|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| (-810 |#1|) (QUOTE (-116))) (|HasCategory| (-810 |#1|) (QUOTE (-313)))) (|HasCategory| (-810 |#1|) (QUOTE (-118))) (|HasCategory| (-810 |#1|) (QUOTE (-313))) (|HasCategory| (-810 |#1|) (QUOTE (-116)))) +(-298 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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-118)))) -(-309 GF |extdeg|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-116)))) +(-299 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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-118)))) -(-310 GF |defpol|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-116)))) +(-300 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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-118)))) -(-311 GF) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-116)))) +(-301 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 -(-312 -3215 GF) +(-302 -3076 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 -(-313 -3215 FP FPP) +(-303 -3076 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 -(-314 GF |n|) +(-304 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}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-118)))) -(-315 R |ls|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-116)))) +(-305 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 NIL -(-316 S) +(-306 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4142 . T)) +((-3976 . T)) NIL -(-317 S) +(-307 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) NIL NIL -(-318) +(-308) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-319 S) +(-309 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL -(-320 |Name| S) +(-310 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer's file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) NIL NIL -(-321 S R) +(-311 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-510)))) -(-322 R) +((|HasCategory| |#2| (QUOTE (-489)))) +(-312 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4142 |has| |#1| (-510)) (-4140 . T) (-4139 . T)) +((-3976 |has| |#1| (-489)) (-3974 . T) (-3973 . T)) NIL -(-323) +(-313) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) NIL NIL -(-324 S R UP) +(-314 S R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) NIL -((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-318)))) -(-325 R UP) +((|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-308)))) +(-315 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-326 A S) +(-316 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4146)) (|HasCategory| |#2| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-1041)))) -(-327 S) +((|HasAttribute| |#1| (QUOTE -3980)) (|HasCategory| |#2| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-1005)))) +(-317 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4145 . T)) +((-3979 . T)) NIL -(-328 S A R B) +(-318 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) NIL NIL -(-329 |VarSet| R) +(-319 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4140 . T) (-4139 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3974 . T) (-3973 . T)) NIL -(-330 S V) +(-320 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) NIL NIL -(-331 S R) +(-321 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -596) (QUOTE (-499))))) -(-332 R) +((|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478))))) +(-322 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL NIL -(-333) +(-323) ((|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}."))) -((-4128 . T) (-4136 . T) (-3920 . T) (-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3962 . T) (-3970 . T) (-3754 . T) (-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-334 |Par|) +(-324 |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}."))) NIL NIL -(-335 |Par|) +(-325 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in lp,{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) NIL NIL -(-336 R S) +(-326 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4140 . T) (-4139 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-1041))))) -(-337 R S) +((-3974 . T) (-3973 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005))))) +(-327 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4140 . T) (-4139 . T)) -((|HasCategory| |#1| (QUOTE (-146)))) -(-338) -((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -NIL -NIL -(-339 R |Basis|) +((-3974 . T) (-3973 . T)) +((|HasCategory| |#1| (QUOTE (-144)))) +(-328 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4140 . T) (-4139 . T)) -NIL -(-340) -((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) +((-3974 . T) (-3973 . T)) NIL -NIL -(-341 S) +(-329 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL NIL -(-342 S) +(-330 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) NIL -((|HasCategory| |#1| (QUOTE (-781)))) -(-343) -((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -NIL -(-344) +((|HasCategory| |#1| (QUOTE (-749)))) +(-331) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) NIL NIL -(-345) +(-332) ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,pref,e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,n,e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used."))) NIL NIL -(-346 |n| |class| R) +(-333 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4140 . T) (-4139 . T)) -NIL -(-347) -((|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"))) +((-3974 . T) (-3973 . T)) NIL -NIL -(-348 -3215 UP UPUP R) +(-334 -3076 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 -(-349) -((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) -NIL -NIL -(-350) -((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -NIL -NIL -(-351) -((|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 -(-352 -3690 |returnType| -1456 |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 -(-353 -3215 UP) +(-335 -3076 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL -(-354 R) +(-336 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) NIL NIL -(-355 S) +(-337 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) NIL NIL -(-356) +(-338) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-357 S) +(-339 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4128)) (|HasAttribute| |#1| (QUOTE -4136))) -(-358) +((|HasAttribute| |#1| (QUOTE -3962)) (|HasAttribute| |#1| (QUOTE -3970))) +(-340) ((|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\"."))) -((-3920 . T) (-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3754 . T) (-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-359 R) +(-341 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| #1="nil" #2="sqfr" #3="irred" #4="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| #1# #2# #3# #4#) $ (|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| #1# #2# #3# #4#)) (|:| |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| #1# #2# #3# #4#)) (|:| |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."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -468) (QUOTE (-1117)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -263) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -240) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (QUOTE (-1162))) (-3677 (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-1162)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (|%list| (QUOTE -468) (QUOTE (-1117)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-498))) (|HasCategory| |#1| (QUOTE (-406)))) -(-360 R S) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -447) (QUOTE (-1079)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -256) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -238) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (QUOTE (-1123))) (OR (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-1123)))) (|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (|%list| (QUOTE -447) (QUOTE (-1079)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -238) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-477))) (|HasCategory| |#1| (QUOTE (-385)))) +(-342 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 NIL -(-361 S) +(-343 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."))) -((-4132 -12 (|has| |#1| (-6 -4143)) (|has| |#1| (-406)) (|has| |#1| (-6 -4132))) (-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-763))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-763))) (|HasCategory| |#1| (QUOTE (-781)))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| |#1| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| |#1| (|%list| (QUOTE -468) (QUOTE (-1117)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-261))) (|HasCategory| |#1| (QUOTE (-498))) (-12 (|HasAttribute| |#1| (QUOTE -4132)) (|HasAttribute| |#1| (QUOTE -4143)) (|HasCategory| |#1| (QUOTE (-406)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-362 A B) +((-3966 -12 (|has| |#1| (-6 -3977)) (|has| |#1| (-385)) (|has| |#1| (-6 -3966))) (-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-733))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-733))) (|HasCategory| |#1| (QUOTE (-749)))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -447) (QUOTE (-1079)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -238) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-254))) (|HasCategory| |#1| (QUOTE (-477))) (-12 (|HasAttribute| |#1| (QUOTE -3966)) (|HasAttribute| |#1| (QUOTE -3977)) (|HasCategory| |#1| (QUOTE (-385)))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#1| (QUOTE (-116))))) +(-344 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 NIL -(-363 S R UP) +(-345 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} 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{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL -(-364 R UP) +(-346 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} 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{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-365 A S) +(-347 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499))))) -(-366 S) +((|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478))))) +(-348 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-367 R -3215 UP A) +(-349 R -3076 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4142 . T)) +((-3976 . T)) NIL -(-368 R1 F1 U1 A1 R2 F2 U2 A2) +(-350 R1 F1 U1 A1 R2 F2 U2 A2) ((|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 -(-369 R -3215 UP A |ibasis|) +(-351 R -3076 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (|%list| (QUOTE -978) (|devaluate| |#2|)))) -(-370 AR R AS S) +((|HasCategory| |#4| (|%list| (QUOTE -943) (|devaluate| |#2|)))) +(-352 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL NIL -(-371 S R) +(-353 S R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-318)))) -(-372 R) +((|HasCategory| |#2| (QUOTE (-308)))) +(-354 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4142 |has| |#1| (-510)) (-4140 . T) (-4139 . T)) +((-3976 |has| |#1| (-489)) (-3974 . T) (-3973 . T)) NIL -(-373 R) +(-355 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL NIL -(-374 S R) +(-356 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|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| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488))))) -(-375 R) +((|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-954))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467))))) +(-357 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}."))) -((-4142 -3677 (|has| |#1| (-989)) (|has| |#1| (-427))) (-4140 |has| |#1| (-146)) (-4139 |has| |#1| (-146)) ((-4147 "*") |has| |#1| (-510)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-510)) (-4137 |has| |#1| (-510))) +((-3976 OR (|has| |#1| (-954)) (|has| |#1| (-406))) (-3974 |has| |#1| (-144)) (-3973 |has| |#1| (-144)) ((-3981 "*") |has| |#1| (-489)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-489)) (-3971 |has| |#1| (-489))) NIL -(-376 R A S B) +(-358 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}."))) NIL NIL -(-377 R FE |x| |cen|) +(-359 R FE |x| |cen|) ((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) NIL NIL -(-378 R FE |Expon| UPS TRAN |x|) +(-360 R FE |Expon| UPS TRAN |x|) ((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) NIL NIL -(-379 A S) +(-361 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL -((|HasCategory| |#2| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-323)))) -(-380 S) +((|HasCategory| |#2| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-313)))) +(-362 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4145 . T) (-4135 . T) (-4146 . T)) +((-3979 . T) (-3969 . T) (-3980 . T)) NIL -(-381 S A R B) +(-363 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -(-382 R -3215) +(-364 R -3076) ((|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 -(-383 R E) +(-365 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4132 -12 (|has| |#1| (-6 -4132)) (|has| |#2| (-6 -4132))) (-4139 . T) (-4140 . T) (-4142 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4132)) (|HasAttribute| |#2| (QUOTE -4132)))) -(-384 R -3215) +((-3966 -12 (|has| |#1| (-6 -3966)) (|has| |#2| (-6 -3966))) (-3973 . T) (-3974 . T) (-3976 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -3966)) (|HasAttribute| |#2| (QUOTE -3966)))) +(-366 R -3076) ((|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 -(-385 R -3215) +(-367 R -3076) ((|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 -(-386 R -3215) +(-368 R -3076) ((|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)))) -(-387 R -3215) +(-369 R -3076) ((|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 -(-388) +(-370) ((|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 -(-389 R -3215 UP) +(-371 R -3076 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 -978) (QUOTE (-48))))) -(-390) +((|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-48))))) +(-372) ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) NIL NIL -(-391) -((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) -NIL -NIL -(-392 |f|) +(-373 |f|) ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-393) +(-374) ((|constructor| (NIL "This is the datatype for exported function descriptor. A function descriptor consists of: (1) a signature; (2) a predicate; and (3) a slot into the scope object.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}."))) NIL NIL -(-394) -((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -NIL -NIL -(-395) -((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -NIL -NIL -(-396 UP) +(-375 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein'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 -(-397 R UP -3215) +(-376 R UP -3076) ((|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 -(-398 R UP) +(-377 R UP) ((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1)."))) NIL NIL -(-399 R) +(-378 R) ((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,r)} returns the binomial coefficient \\spad{C(n,r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation."))) NIL -((|HasCategory| |#1| (QUOTE (-358)))) -(-400) +((|HasCategory| |#1| (QUOTE (-340)))) +(-379) ((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(zi)} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(zi)} produces the complete factorization of the complex integer \\spad{zi}."))) NIL NIL -(-401 |Dom| |Expon| |VarSet| |Dpol|) +(-380 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp, infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) NIL -((|HasCategory| |#1| (QUOTE (-318)))) -(-402 |Dom| |Expon| |VarSet| |Dpol|) +((|HasCategory| |#1| (QUOTE (-308)))) +(-381 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp, infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL NIL -(-403 |Dom| |Expon| |VarSet| |Dpol|) +(-382 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions, info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) NIL NIL -(-404 |Dom| |Expon| |VarSet| |Dpol|) +(-383 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) NIL NIL -(-405 S) +(-384 S) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) NIL NIL -(-406) +(-385) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-407 R |n| |ls| |gamma|) +(-386 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4142 |has| (-361 (-884 |#1|)) (-510)) (-4140 . T) (-4139 . T)) -((|HasCategory| (-361 (-884 |#1|)) (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| (-361 (-884 |#1|)) (QUOTE (-510)))) -(-408 |vl| R E) +((-3976 |has| (-343 (-850 |#1|)) (-489)) (-3974 . T) (-3973 . T)) +((|HasCategory| (-343 (-850 |#1|)) (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| (-343 (-850 |#1|)) (QUOTE (-489)))) +(-387 |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"))) -(((-4147 "*") |has| |#2| (-146)) (-4138 |has| |#2| (-510)) (-4143 |has| |#2| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . 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T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#2| (QUOTE (-814))) (OR (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-814)))) (OR (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-814)))) (OR (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-814)))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-144))) (OR (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-489)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -789) (QUOTE (-323))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -789) (QUOTE (-478))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -548) (QUOTE (-467))))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasAttribute| |#2| (QUOTE -3977)) (|HasCategory| |#2| (QUOTE (-385))) (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#2| (QUOTE (-116))))) +(-388 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 NIL -(-410 OV E S R P) +(-389 OV E S R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|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 -(-411 E OV R P) +(-390 E OV R P) ((|constructor| (NIL "This package provides operations for GCD computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,q)} returns the GCD of \\spad{p} and \\spad{q}"))) NIL NIL -(-412 R) +(-391 R) ((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}"))) NIL NIL -(-413 R FE) +(-392 R FE) ((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),n,x = a,n0..)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}; \\spad{taylor(a(n),n,x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),x = a,n0..)} returns \\spad{sum(n=n0..,a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}."))) NIL NIL -(-414 RP TP) +(-393 RP TP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,lfact,prime,bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,lfacts,prime,bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done ."))) NIL NIL -(-415 |vl| R IS E |ff| P) +(-394 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-416 E V R P Q) +(-395 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) NIL NIL -(-417 R E |VarSet| P) +(-396 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#4| (|%list| (QUOTE -263) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#4| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#4| (QUOTE (-73)))) -(-418 S R E) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (|%list| (QUOTE -256) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#4| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-397 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL NIL -(-419 R E) +(-398 R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL NIL -(-420) +(-399) ((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n+1} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(vv) if {\\em vv.2.1 = n+1}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect."))) NIL NIL -(-421) +(-400) ((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done."))) NIL NIL -(-422) +(-401) ((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(gi)} returns the indicated graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{gi} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) NIL NIL -(-423 S R E) +(-402 S R E) ((|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.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-424 R E) +(-403 R E) ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-425 |lv| -3215 R) +(-404 |lv| -3076 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL -(-426 S) +(-405 S) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) NIL NIL -(-427) +(-406) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) 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T)) +((-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) +(-409 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. 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T)) -((-12 (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#4| (|%list| (QUOTE -263) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#3| (QUOTE (-323))) (|HasCategory| |#4| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#4| (QUOTE (-73)))) -(-431) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (|%list| (QUOTE -256) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#4| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-410) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-432) +(-411) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) NIL NIL -(-433 |Key| |Entry| |hashfn|) +(-412 |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."))) -((-4145 . T) (-4146 . 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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 NIL -(-435 |vl| R) +(-414 |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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For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4145)) (|HasAttribute| |#1| (QUOTE -4146)) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797))))) -(-443 S) +((|HasAttribute| |#1| (QUOTE -3979)) (|HasAttribute| |#1| (QUOTE -3980)) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) +(-422 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL NIL -(-444 S) +(-423 S) ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) NIL NIL -(-445) +(-424) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name `n'."))) NIL NIL -(-446 S) +(-425 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-447) +(-426) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-448 -3215 UP |AlExt| |AlPol|) +(-427 -3076 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL -(-449) +(-428) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| $ (QUOTE (-989))) (|HasCategory| $ (|%list| (QUOTE -978) (QUOTE (-499))))) -(-450 S |mn|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| $ (QUOTE (-954))) (|HasCategory| $ (|%list| (QUOTE -943) (QUOTE (-478))))) +(-429 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-451 R |mnRow| |mnCol|) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-430 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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-452 K R UP) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-431 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 -(-453 R UP -3215) +(-432 R UP -3076) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL -(-454 |mn|) +(-433 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-1041))) (|HasCategory| (-85) (|%list| (QUOTE -263) (QUOTE (-85))))) (|HasCategory| (-85) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-85) (QUOTE (-781))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| (-85) (QUOTE (-1041))) (|HasCategory| (-85) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-85) (QUOTE (-73)))) -(-455 K R UP L) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| (-83) (QUOTE (-1005))) (|HasCategory| (-83) (|%list| (QUOTE -256) (QUOTE (-83))))) (|HasCategory| (-83) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-83) (QUOTE (-749))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| (-83) (QUOTE (-1005))) (|HasCategory| (-83) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-83) (QUOTE (-72)))) +(-434 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL NIL -(-456) +(-435) ((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) NIL NIL -(-457 R Q A B) +(-436 R Q A B) ((|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 -(-458 -3215 |Expon| |VarSet| |DPoly|) +(-437 -3076 |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 -569) (QUOTE (-1117))))) -(-459 |vl| |nv|) +((|HasCategory| |#3| (|%list| (QUOTE -548) (QUOTE (-1079))))) +(-438 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL NIL -(-460) +(-439) ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) NIL NIL -(-461 A S) +(-440 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-1041))))) -(-462 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005))))) +(-441 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-1041))))) -(-463 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005))))) +(-442 A S) ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL NIL -(-464 A S) +(-443 A S) ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-1041))))) -(-465 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005))))) +(-444 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-1041))))) -(-466 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005))))) +(-445 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-1041))))) -(-467 S A B) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005))))) +(-446 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-468 A B) +(-447 A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-469 S E |un|) +(-448 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-737)))) -(-470 S |mn|) +((|HasCategory| |#2| (QUOTE (-709)))) +(-449 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}"))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-471) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-450) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL -(-472 |p| |n|) +(-451 |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}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((-3677 (|HasCategory| (-532 |#1|) (QUOTE (-118))) (|HasCategory| (-532 |#1|) (QUOTE (-323)))) (|HasCategory| (-532 |#1|) (QUOTE (-120))) (|HasCategory| (-532 |#1|) (QUOTE (-323))) (|HasCategory| (-532 |#1|) (QUOTE (-118)))) -(-473 R |mnRow| |mnCol| |Row| |Col|) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((OR (|HasCategory| (-511 |#1|) (QUOTE (-116))) (|HasCategory| (-511 |#1|) (QUOTE (-313)))) (|HasCategory| (-511 |#1|) (QUOTE (-118))) (|HasCategory| (-511 |#1|) (QUOTE (-313))) (|HasCategory| (-511 |#1|) (QUOTE (-116)))) +(-452 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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-474 R |Row| |Col| M) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-453 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 -((|HasAttribute| |#3| (QUOTE -4146))) -(-475 R |Row| |Col| M QF |Row2| |Col2| M2) +((|HasAttribute| |#3| (QUOTE -3980))) +(-454 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4146))) -(-476 R |mnRow| |mnCol|) +((|HasAttribute| |#7| (QUOTE -3980))) +(-455 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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-261))) (|HasCategory| |#1| (QUOTE (-510))) (|HasAttribute| |#1| (QUOTE (-4147 "*"))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-477) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (QUOTE (-254))) (|HasCategory| |#1| (QUOTE (-489))) (|HasAttribute| |#1| (QUOTE (-3981 "*"))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-456) ((|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 NIL -(-478) +(-457) ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) NIL NIL -(-479 S) +(-458 S) ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL -(-480) +(-459) ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL -(-481 GF) +(-460 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(GF) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{**}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,e,d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\",{} Information and Computation 78,{} pp.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,n,k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} pp.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,...,vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field GF."))) NIL NIL -(-482) +(-461) ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file."))) NIL NIL -(-483 R) +(-462 R) ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}."))) NIL NIL -(-484 |Varset|) +(-463 |Varset|) ((|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| |#1| (QUOTE (-1041))) (|HasCategory| (-714) (QUOTE (-1041))))) -(-485 K -3215 |Par|) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| (-687) (QUOTE (-1005))))) +(-464 K -3076 |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 -(-486) +(-465) NIL NIL NIL -(-487) +(-466) ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL NIL -(-488) +(-467) ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) NIL NIL -(-489 R) +(-468 R) ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) NIL NIL -(-490 |Coef| UTS) +(-469 |Coef| UTS) ((|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 -(-491 K -3215 |Par|) +(-470 K -3076 |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 -(-492 R BP |pMod| |nextMod|) +(-471 R BP |pMod| |nextMod|) ((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) NIL NIL -(-493 OV E R P) +(-472 OV E R P) ((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) NIL NIL -(-494 K UP |Coef| UTS) +(-473 K UP |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|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| ((|#4| |#4|) "\\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| ((|#4| |#4|) "\\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| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-495 |Coef| UTS) +(-474 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|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 -(-496 R UP) +(-475 R UP) ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) NIL NIL -(-497 S) +(-476 S) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) NIL NIL -(-498) +(-477) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4143 . T) (-4144 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3977 . T) (-3978 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-499) +(-478) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4133 . T) (-4137 . T) (-4132 . T) (-4143 . T) (-4144 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3967 . T) (-3971 . T) (-3966 . T) (-3977 . T) (-3978 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-500) +(-479) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) NIL NIL -(-501) +(-480) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) NIL NIL -(-502) +(-481) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) NIL NIL -(-503) +(-482) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) NIL NIL -(-504 |Key| |Entry| |addDom|) +(-483 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-1041))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) -(-505 R -3215) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-1005))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) +(-484 R -3076) ((|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 -(-506 R0 -3215 UP UPUP R) +(-485 R0 -3076 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 -(-507) +(-486) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-508 R) +(-487 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."))) -((-3920 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3754 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-509 S) +(-488 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."))) NIL NIL -(-510) +(-489) ((|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."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-511 R -3215) +(-490 R -3076) ((|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|)) #1="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|)) #1#) |#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 -(-512 I) +(-491 I) ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-513 R -3215 L) +(-492 R -3076 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| #1="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| #1#)) (|:| |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| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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|))))) #3="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|))))) #3#) |#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|)) #4="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|)) #4#) |#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 -616) (|devaluate| |#2|)))) -(-514) +((|HasCategory| |#3| (|%list| (QUOTE -595) (|devaluate| |#2|)))) +(-493) ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-515 -3215 UP UPUP R) +(-494 -3076 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-516 -3215 UP) +(-495 -3076 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL -(-517 R -3215 L) +(-496 R -3076 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| #1="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| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#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 -616) (|devaluate| |#2|)))) -(-518 R -3215) +((|HasCategory| |#3| (|%list| (QUOTE -595) (|devaluate| |#2|)))) +(-497 R -3076) ((|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 -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-1079)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-585))))) -(-519 -3215 UP) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-1042)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-564))))) +(-498 -3076 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 -(-520 S) +(-499 S) ((|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 -(-521 -3215) +(-500 -3076) ((|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 -(-522 R) +(-501 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."))) -((-3920 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3754 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-523) +(-502) ((|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 -(-524 R -3215) +(-503 R -3076) ((|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| (QUOTE (-406))) (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-585))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-1117))))) (-12 (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#1| (QUOTE (-510)))) -(-525 -3215 UP) +((-12 (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-236))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-1079))))) (-12 (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-236)))) (|HasCategory| |#1| (QUOTE (-489)))) +(-504 -3076 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|)) #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|)) #1#) |#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|)) #1#) |#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|)) #1#) |#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 -(-526 R -3215) +(-505 R -3076) ((|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 -(-527) +(-506) ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) NIL NIL -(-528) +(-507) ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file."))) NIL NIL -(-529) +(-508) ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) NIL NIL -(-530) +(-509) ((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) NIL NIL -(-531 |p| |unBalanced?|) +(-510 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-532 |p|) +(-511 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-323)))) -(-533) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-116))) (|HasCategory| $ (QUOTE (-313)))) +(-512) ((|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 -(-534 -3215) +(-513 -3076) ((|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}."))) -((-4140 . T) (-4139 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-1117))))) -(-535 E -3215) +((-3974 . T) (-3973 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-1079))))) +(-514 E -3076) ((|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 -(-536 R -3215) +(-515 R -3076) ((|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 -(-537) +(-516) ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-538 I) +(-517 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL NIL -(-539 GF) +(-518 GF) ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) NIL NIL -(-540 R) +(-519 R) ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\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 -((|HasCategory| |#1| (QUOTE (-120)))) -(-541) +((|HasCategory| |#1| (QUOTE (-118)))) +(-520) ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) NIL NIL -(-542 R E V P TS) +(-521 R E V P TS) ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) NIL NIL -(-543) +(-522) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) NIL NIL -(-544 E V R P) +(-523 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL -(-545 |Coef|) +(-524 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-510))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-499)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-499)) (|devaluate| |#1|)))) (|HasCategory| (-499) (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-499))))) (|HasSignature| |#1| (|%list| (QUOTE -4096) (|%list| (|devaluate| |#1|) (QUOTE (-1117)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-499)))))) -(-546 |Coef|) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-478)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-478)) (|devaluate| |#1|)))) (|HasCategory| (-478) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-308))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-478))))) (|HasSignature| |#1| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#1|) (QUOTE (-1079)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-478)))))) +(-525 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4147 "*") |has| |#1| (-510)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-510)))) -(-547) +(((-3981 "*") |has| |#1| (-489)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-489)))) +(-526) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) NIL NIL -(-548 A B) +(-527 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-549 A B C) +(-528 A B C) ((|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 -(-550 R -3215 FG) +(-529 R -3076 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 -(-551 S) +(-530 S) ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) NIL NIL -(-552 R |mn|) +(-531 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4146 . T) (-4145 . 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T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#1| (QUOTE (-954))) (-12 (|HasCategory| |#1| (QUOTE (-908))) (|HasCategory| |#1| (QUOTE (-954)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-532 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4146)) (|HasCategory| |#2| (QUOTE (-781))) (|HasAttribute| |#1| (QUOTE -4145)) (|HasCategory| |#3| (QUOTE (-1041)))) -(-554 |Index| |Entry|) +((|HasAttribute| |#1| (QUOTE -3980)) (|HasCategory| |#2| (QUOTE (-749))) (|HasAttribute| |#1| (QUOTE -3979)) (|HasCategory| |#3| (QUOTE (-1005)))) +(-533 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL NIL -(-555) +(-534) ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) NIL NIL -(-556 R A) +(-535 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. 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(|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) NIL NIL -(-562) +(-541) ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) NIL NIL -(-563 |Entry|) +(-542 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (QUOTE (-1099))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| (-1099) (QUOTE (-781))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-73)))) -(-564 S |Key| |Entry|) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (QUOTE (-1062))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| (-1062) (QUOTE (-749))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-72)))) +(-543 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL -(-565 |Key| |Entry|) +(-544 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4146 . T)) +((-3980 . T)) NIL -(-566 S) +(-545 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499)))))) -(-567 R S) +((|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) +(-546 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL NIL -(-568 S) +(-547 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-569 S) +(-548 S) ((|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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-570 -3215 UP) +(-549 -3076 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -(-571 S) +(-550 S) ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-572) +(-551) ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) NIL NIL -(-573 S) +(-552 S) ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-574 A R S) +(-553 A R S) ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-780)))) -(-575 S R) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-748)))) +(-554 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-576 R) +(-555 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4142 . T)) +((-3976 . T)) NIL -(-577 R -3215) +(-556 R -3076) ((|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 -(-578 R UP) +(-557 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4140 . T) (-4139 . T) ((-4147 "*") . T) (-4138 . T) (-4142 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| |#2| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499))))) -(-579 R E V P TS ST) +((-3974 . T) (-3973 . T) ((-3981 "*") . T) (-3972 . T) (-3976 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#2| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (QUOTE (-187))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478))))) +(-558 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) NIL NIL -(-580 OV E Z P) +(-559 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-581) +(-560) ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) NIL NIL -(-582 |VarSet| R |Order|) +(-561 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4142 . T)) +((-3976 . T)) NIL -(-583 R |ls|) +(-562 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(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.")) 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((|#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 -(-585) +(-564) ((|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 -(-586 |lv| -3215) +(-565 |lv| -3076) ((|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.")) 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(|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."))) -((-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (QUOTE (-1099))) (|%list| (QUOTE |:|) (QUOTE |entry|) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-51) (|%list| (QUOTE -263) (QUOTE (-51))))) (|HasCategory| (-1099) (QUOTE (-781))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-73)))) (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| (-51))) (QUOTE (-1041)))) -(-588 R A) +((-3980 . 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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)."))) -((-4142 -3677 (-2681 (|has| |#2| (-322 |#1|)) (|has| |#1| (-510))) (-12 (|has| |#2| (-372 |#1|)) (|has| |#1| (-510)))) (-4140 . T) (-4139 . T)) -((-3677 (|HasCategory| |#2| (|%list| (QUOTE -322) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -372) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -372) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (|%list| (QUOTE -372) (|devaluate| |#1|)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#2| (|%list| (QUOTE -322) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#2| (|%list| (QUOTE -372) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -322) (|devaluate| |#1|)))) -(-589 S R) +((-3976 OR (-2546 (|has| |#2| (-312 |#1|)) (|has| |#1| (-489))) (-12 (|has| |#2| (-354 |#1|)) (|has| |#1| (-489)))) (-3974 . T) (-3973 . T)) +((OR (|HasCategory| |#2| (|%list| (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -354) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -354) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#2| (|%list| (QUOTE -354) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#2| (|%list| (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#2| (|%list| (QUOTE -354) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -312) (|devaluate| |#1|)))) +(-568 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL -((|HasCategory| |#2| (QUOTE (-318)))) -(-590 R) +((|HasCategory| |#2| (QUOTE (-308)))) +(-569 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4140 . T) (-4139 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3974 . T) (-3973 . T)) NIL -(-591 R FE) +(-570 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL NIL -(-592 R) +(-571 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-593 |vars|) +(-572 |vars|) ((|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 vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) NIL NIL -(-594 S R) +(-573 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 -((-2679 (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-318)))) -(-595 K B) +((-2544 (|HasCategory| |#1| (QUOTE (-308)))) (|HasCategory| |#1| (QUOTE (-308)))) +(-574 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}."))) -((-4140 . T) (-4139 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| (-593 |#2|) (QUOTE (-1041))))) -(-596 R) +((-3974 . T) (-3973 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| (-572 |#2|) (QUOTE (-1005))))) +(-575 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL NIL -(-597 K B) +(-576 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-598 S) +(-577 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) NIL NIL -(-599 S) +(-578 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. 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."))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-600 A B) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-579 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL NIL -(-601 A B) +(-580 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-602 A B C) +(-581 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-603 T$) +(-582 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-604 S) +(-583 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-605 S) +(-584 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-606 R) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-585 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL NIL -(-607 S E |un|) +(-586 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) NIL NIL -(-608 A S) +(-587 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4146))) -(-609 S) +((|HasAttribute| |#1| (QUOTE -3980))) +(-588 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-610 M R S) +(-589 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4140 . T) (-4139 . T)) -((|HasCategory| |#1| (QUOTE (-735)))) -(-611 R -3215 L) +((-3974 . T) (-3973 . T)) +((|HasCategory| |#1| (QUOTE (-707)))) +(-590 R -3076 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 -(-612 A -2610) +(-591 A -2476) ((|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}}"))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-318)))) -(-613 A) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-308)))) +(-592 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-318)))) -(-614 A M) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-308)))) +(-593 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-318)))) -(-615 S A) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-308)))) +(-594 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL -((|HasCategory| |#2| (QUOTE (-318)))) -(-616 A) +((|HasCategory| |#2| (QUOTE (-308)))) +(-595 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-617 -3215 UP) +(-596 -3076 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)))) -(-618 A L) +(-597 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-619 S) +(-598 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-620) +(-599) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-621 R) +(-600 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-622 |VarSet| R) +(-601 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4140 . T) (-4139 . T)) -((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-146)))) -(-623 A S) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3974 . T) (-3973 . T)) +((|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-144)))) +(-602 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) NIL NIL -(-624 S) +(-603 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-625 -3215 |Row| |Col| M) +(-604 -3076 |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| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |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| #1#)) (|:| |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 -(-626 -3215) +(-605 -3076) ((|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|) #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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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 -(-627 R E OV P) +(-606 R E OV P) ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) NIL NIL -(-628 |n| R) +(-607 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) -((-4142 . T) (-4145 . T) (-4139 . T) (-4140 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| |#2| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-4147 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (-3677 (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -596) (QUOTE (-499))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117)))))) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-510))) (-3677 (|HasAttribute| |#2| (QUOTE (-4147 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117))))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-73))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-629) +((-3976 . T) (-3979 . T) (-3973 . T) (-3974 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#2| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (QUOTE (-187))) (|HasAttribute| |#2| (QUOTE (-3981 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))))) (|HasCategory| |#2| (QUOTE (-254))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-489))) (OR (|HasAttribute| |#2| (QUOTE (-3981 #1#))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079))))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-144)))) +(-608) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL NIL -(-630 |VarSet|) +(-609 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-631 A S) +(-610 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-632 S) +(-611 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-633 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 -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-634) +(-612) ((|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 NIL -(-635 |VarSet|) +(-613 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL NIL -(-636 A) +(-614 A) ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) NIL NIL -(-637 A C) +(-615 A C) ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) NIL NIL -(-638 A B C) +(-616 A B C) ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) NIL NIL -(-639) +(-617) ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) NIL NIL -(-640 A) +(-618 A) ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-641 A C) +(-619 A C) ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-642 A B C) +(-620 A B C) ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) NIL NIL -(-643 S R |Row| |Col|) +(-621 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4147 "*"))) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-510)))) -(-644 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-3981 "*"))) (|HasCategory| |#2| (QUOTE (-254))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-489)))) +(-622 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) NIL -(-645 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-623 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-646 R |Row| |Col| M) +(-624 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that m*n = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL -((|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-261))) (|HasCategory| |#1| (QUOTE (-510)))) -(-647 R) +((|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-254))) (|HasCategory| |#1| (QUOTE (-489)))) +(-625 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."))) -((-4145 . T) (-4146 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (QUOTE (-261))) (|HasCategory| |#1| (QUOTE (-510))) (|HasAttribute| |#1| (QUOTE (-4147 "*"))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-648 R) +((-3979 . T) (-3980 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (QUOTE (-254))) (|HasCategory| |#1| (QUOTE (-489))) (|HasAttribute| |#1| (QUOTE (-3981 "*"))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-626 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 NIL -(-649 T$) +(-627 T$) ((|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 -(-650 S -3215 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}."))) -NIL -NIL -(-651 R Q) +(-628 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL NIL -(-652) -((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4138 . T) (-4143 |has| (-657) (-318)) (-4137 |has| (-657) (-318)) (-1409 . T) (-4144 |has| (-657) (-6 -4144)) (-4141 |has| (-657) (-6 -4141)) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-657) (QUOTE (-120))) (|HasCategory| (-657) (QUOTE (-118))) (|HasCategory| (-657) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-657) (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| (-657) (QUOTE (-323))) (|HasCategory| (-657) (QUOTE (-318))) (-3677 (|HasCategory| (-657) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-657) (QUOTE (-318)))) (|HasCategory| (-657) (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| (-657) (QUOTE (-190))) (|HasCategory| (-657) (QUOTE (-189))) (-3677 (-12 (|HasCategory| (-657) (QUOTE (-318))) (|HasCategory| (-657) (|%list| (QUOTE -836) (QUOTE (-1117))))) (|HasCategory| (-657) (|%list| (QUOTE -838) (QUOTE (-1117))))) (-3677 (|HasCategory| (-657) (QUOTE (-318))) (|HasCategory| (-657) (QUOTE (-305)))) (|HasCategory| (-657) (QUOTE (-305))) (|HasCategory| (-657) (|%list| (QUOTE -240) (QUOTE (-657)) (QUOTE (-657)))) (|HasCategory| (-657) (|%list| (QUOTE -263) (QUOTE (-657)))) (|HasCategory| (-657) (|%list| (QUOTE -468) (QUOTE (-1117)) (QUOTE (-657)))) (|HasCategory| (-657) (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| (-657) (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| (-657) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| (-657) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (-3677 (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-318))) (|HasCategory| (-657) (QUOTE (-305)))) (|HasCategory| (-657) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-657) (QUOTE (-960))) (|HasCategory| (-657) (QUOTE (-1143))) (-12 (|HasCategory| (-657) (QUOTE (-942))) (|HasCategory| (-657) (QUOTE (-1143)))) (-3677 (-12 (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848)))) (-12 (|HasCategory| (-657) (QUOTE (-305))) (|HasCategory| (-657) (QUOTE (-848)))) (|HasCategory| (-657) (QUOTE (-318)))) (-3677 (-12 (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848)))) (-12 (|HasCategory| (-657) (QUOTE (-318))) (|HasCategory| (-657) (QUOTE (-848)))) (-12 (|HasCategory| (-657) (QUOTE (-305))) (|HasCategory| (-657) (QUOTE (-848))))) (|HasCategory| (-657) (QUOTE (-498))) (-12 (|HasCategory| (-657) (QUOTE (-1000))) (|HasCategory| (-657) (QUOTE (-1143)))) (|HasCategory| (-657) (QUOTE (-1000))) (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848))) (-3677 (-12 (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848)))) (|HasCategory| (-657) (QUOTE (-318)))) (-3677 (-12 (|HasCategory| (-657) (QUOTE (-190))) (|HasCategory| (-657) (QUOTE (-318)))) (|HasCategory| (-657) (QUOTE (-189)))) (-3677 (-12 (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848)))) (|HasCategory| (-657) (QUOTE (-510)))) (-12 (|HasCategory| (-657) (QUOTE (-189))) (|HasCategory| (-657) (QUOTE (-318)))) (-12 (|HasCategory| (-657) (QUOTE (-318))) (|HasCategory| (-657) (|%list| (QUOTE -838) (QUOTE (-1117))))) (-12 (|HasCategory| (-657) (QUOTE (-190))) (|HasCategory| (-657) (QUOTE (-318)))) (-12 (|HasCategory| (-657) (QUOTE (-318))) (|HasCategory| (-657) (|%list| (QUOTE -836) (QUOTE (-1117))))) (|HasCategory| (-657) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-657) (QUOTE (-510))) (|HasAttribute| (-657) (QUOTE -4144)) (|HasAttribute| (-657) (QUOTE -4141)) (-12 (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848)))) (|HasCategory| (-657) (|%list| (QUOTE -838) (QUOTE (-1117)))) (-3677 (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848)))) (|HasCategory| (-657) (QUOTE (-118)))) (-3677 (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-657) (QUOTE (-261))) (|HasCategory| (-657) (QUOTE (-848)))) (|HasCategory| (-657) (QUOTE (-305))))) -(-653 S) +(-629 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4146 . T)) +((-3980 . T)) NIL -(-654 U) +(-630 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL -(-655) +(-631) ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-656 OV E -3215 PG) +(-632 OV E -3076 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL -(-657) -((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3920 . T) (-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -NIL -(-658 R) +(-633 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) NIL NIL -(-659) -((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4144 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -NIL -(-660 S D1 D2 I) +(-634 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-661 S) +(-635 S) ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-662 S) +(-636 S) ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) NIL NIL -(-663 S T$) +(-637 S T$) ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-664 S -2790 I) +(-638 S -2653 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL -(-665 E OV R P) +(-639 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) NIL NIL -(-666 R) +(-640 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-667 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-641 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) NIL NIL -(-668) +(-642) ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-669 R |Mod| -2138 -3658 |exactQuo|) +(-643 R |Mod| -2023 -3502 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-670 R |Rep|) +(-644 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4141 |has| |#1| (-318)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . 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(|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4140 |has| |#1| (-146)) (-4139 |has| |#1| (-146)) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-673 R |Mod| -2138 -3658 |exactQuo|) +((-3974 |has| |#1| (-144)) (-3973 |has| |#1| (-144)) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118)))) +(-647 R |Mod| -2023 -3502 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4142 . T)) +((-3976 . T)) NIL -(-674 S R) +(-648 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-675 R) +(-649 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-676 -3215) +(-650 -3076) ((|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]]}."))) -((-4142 . T)) +((-3976 . T)) NIL -(-677 S) +(-651 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-678) +(-652) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-679 S) +(-653 S) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-680) +(-654) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-681 S R UP) +(-655 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL -((|HasCategory| |#2| (QUOTE (-305))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-323)))) -(-682 R UP) +((|HasCategory| |#2| (QUOTE (-295))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-313)))) +(-656 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4138 |has| |#1| (-318)) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 |has| |#1| (-308)) (-3977 |has| |#1| (-308)) (-3971 |has| |#1| (-308)) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-683 S) +(-657 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-684) +(-658) ((|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 -(-685 -3215 UP) +(-659 -3076 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 -(-686 |VarSet| E1 E2 R S PR PS) +(-660 |VarSet| E1 E2 R S PR PS) ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented "))) NIL NIL -(-687 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-661 |Vars1| |Vars2| E1 E2 R PR1 PR2) ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-688 E OV R PPR) +(-662 E OV R PPR) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-689 |vl| R) +(-663 |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."))) -(((-4147 "*") |has| |#2| (-146)) (-4138 |has| |#2| (-510)) (-4143 |has| |#2| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . T)) -((|HasCategory| |#2| (QUOTE (-848))) (-3677 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-848)))) (-3677 (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-848)))) (-3677 (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-848)))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-146))) (-3677 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-510)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| (-798 |#1|) (|%list| (QUOTE -821) (QUOTE (-333))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| (-798 |#1|) (|%list| (QUOTE -821) (QUOTE (-499))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| (-798 |#1|) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| (-798 |#1|) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-798 |#1|) (|%list| (QUOTE -569) (QUOTE (-488))))) (|HasCategory| |#2| (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (-3677 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-318))) (|HasAttribute| |#2| (QUOTE -4143)) (|HasCategory| |#2| (QUOTE (-406))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (-3677 (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-690 E OV R PRF) +(((-3981 "*") |has| |#2| (-144)) (-3972 |has| |#2| (-489)) (-3977 |has| |#2| (-6 -3977)) (-3974 . T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#2| (QUOTE (-814))) (OR (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-814)))) (OR (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-814)))) (OR (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-814)))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-144))) (OR (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-489)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -789) (QUOTE (-323))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -789) (QUOTE (-478))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-766 |#1|) (|%list| (QUOTE -548) (QUOTE (-467))))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasAttribute| |#2| (QUOTE -3977)) (|HasCategory| |#2| (QUOTE (-385))) (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#2| (QUOTE (-116))))) +(-664 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-691 E OV R P) +(-665 E OV R P) ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-692 R S M) +(-666 R S M) ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-693 R M) +(-667 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4140 |has| |#1| (-146)) (-4139 |has| |#1| (-146)) (-4142 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#2| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-781)))) -(-694 S) +((-3974 |has| |#1| (-144)) (-3973 |has| |#1| (-144)) (-3976 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-749)))) +(-668 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4145 . T) (-4135 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-695 S) +((-3979 . T) (-3969 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-669 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4135 . T) (-4146 . T)) +((-3969 . T) (-3980 . T)) NIL -(-696) +(-670) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL NIL -(-697 S) +(-671 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) NIL NIL -(-698 |Coef| |Var|) +(-672 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4140 . T) (-4139 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-699 OV E R P) +(-673 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) NIL NIL -(-700 E OV R P) +(-674 E OV R P) ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) NIL NIL -(-701 S R) +(-675 S R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) NIL NIL -(-702 R) +(-676 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-703 S) +(-677 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-704) +(-678) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-705 S) +(-679 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-706) +(-680) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-707 |Par|) +(-681 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-708 -3215) +(-682 -3076) ((|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 -(-709 P -3215) +(-683 P -3076) ((|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 -(-710 T$) +(-684 T$) NIL NIL NIL -(-711 UP -3215) +(-685 UP -3076) ((|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 -(-712) -((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) -NIL -NIL -(-713 R) +(-686 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-714) +(-687) ((|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."))) -(((-4147 "*") . T)) +(((-3981 "*") . T)) NIL -(-715 R -3215) +(-688 R -3076) ((|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 -(-716) +(-689) ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-717 S) +(-690 S) ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-718 R |PolR| E |PolE|) +(-691 R |PolR| E |PolE|) ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) NIL NIL -(-719 R E V P TS) +(-692 R E V P TS) ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of 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 -(-720 -3215 |ExtF| |SUEx| |ExtP| |n|) +(-693 -3076 |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 -(-721 BP E OV R P) +(-694 BP E OV R P) ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) NIL NIL -(-722 |Par|) +(-695 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) NIL NIL -(-723 R |VarSet|) +(-696 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."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . 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(|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)}"))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4141 |has| |#1| (-318)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . 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T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-986) (|%list| (QUOTE -789) (QUOTE (-323))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-986) (|%list| (QUOTE -789) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-986) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-986) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-986) (|%list| (QUOTE -548) (QUOTE (-467))))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (QUOTE (-188))) (|HasAttribute| |#1| (QUOTE -3977)) (|HasCategory| |#1| (QUOTE (-385))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#1| (QUOTE (-116))))) +(-698 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 NIL -(-726 R) +(-699 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499)))))) -(-727 R E V P) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478)))))) +(-700 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-728 S) +(-701 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-781)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-146)))) -(-729) +((-12 (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-749)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-144)))) +(-702) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL NIL -(-730) -((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) -NIL -NIL -(-731) +(-703) ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-732) +(-704) ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-733 |Curve|) +(-705 |Curve|) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) NIL NIL -(-734 S) +(-706 S) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-735) +(-707) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-736 S) +(-708 S) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-737) +(-709) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-738) +(-710) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-739) +(-711) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-740 S R) +(-712 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-498))) (|HasCategory| |#2| (QUOTE (-1000))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-323)))) -(-741 R) +((|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-477))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-313)))) +(-713 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-742) +(-714) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-743 R) +(-715 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (|%list| (QUOTE -468) (QUOTE (-1117)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (-3677 (|HasCategory| (-936 |#1|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499)))))) (-3677 (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-936 |#1|) (|%list| (QUOTE -978) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-498))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| (-936 |#1|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-936 |#1|) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499))))) -(-744 -3677 R OS S) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (|%list| (QUOTE -447) (QUOTE (-1079)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -238) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| (-902 |#1|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (OR (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-902 |#1|) (|%list| (QUOTE -943) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-477))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| (-902 |#1|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-902 |#1|) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478))))) +(-716 OR 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 -(-745) -((|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 -(-746 R -3215 L) +(-717 R -3076 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 -(-747 R -3215) +(-718 R -3076) ((|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| #1="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| #1#) (|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| #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| #2#) (|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 -(-748 R -3215) +(-719 R -3076) ((|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 -(-749 -3215 UP UPUP R) +(-720 -3076 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 -(-750 -3215 UP L LQ) +(-721 -3076 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 -(-751) -((|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 -(-752 -3215 UP L LQ) +(-722 -3076 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 -(-753 -3215 UP) +(-723 -3076 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|) #1="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|) #1#)) (|:| |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 -(-754 -3215 L UP A LO) +(-724 -3076 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 -(-755 -3215 UP) +(-725 -3076 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)))) -(-756 -3215 LO) +(-726 -3076 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 -(-757 -3215 LODO) +(-727 -3076 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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T) (-4140 . T) (-4139 . T)) -((|HasCategory| |#2| (QUOTE (-318)))) -(-761 S) +(((-3981 "*") |has| |#2| (-308)) (-3972 |has| |#2| (-308)) (-3977 |has| |#2| (-308)) (-3971 |has| |#2| (-308)) (-3976 . T) (-3974 . T) (-3973 . T)) +((|HasCategory| |#2| (QUOTE (-308)))) +(-731 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) NIL NIL -(-762 S) +(-732 S) ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-781)))) -(-763) +((|HasCategory| |#1| (QUOTE (-749)))) +(-733) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-764 P R) +(-734 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) -(-765 S) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-188)))) +(-735 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4145 . T) (-4135 . T) (-4146 . T)) +((-3979 . T) (-3969 . T) (-3980 . T)) NIL -(-766 R) +(-736 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."))) -((-4142 |has| |#1| (-780))) -((|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#1| (QUOTE (-21))) (-3677 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-780)))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (-3677 (|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-498)))) -(-767 R S) +((-3976 |has| |#1| (-748))) +((|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (OR (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-477)))) +(-737 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-768 R) +(-738 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4140 |has| |#1| (-146)) (-4139 |has| |#1| (-146)) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-769 A S) +((-3974 |has| |#1| (-144)) (-3973 |has| |#1| (-144)) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118)))) +(-739 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-770 S) +(-740 S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-771) +(-741) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) NIL NIL -(-772) +(-742) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) NIL NIL -(-773) -((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) -NIL -NIL -(-774) -((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) -NIL -NIL -(-775 R) +(-743 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4142 |has| |#1| (-780))) -((|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#1| (QUOTE (-21))) (-3677 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-780)))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (-3677 (|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-498)))) -(-776 R S) +((-3976 |has| |#1| (-748))) +((|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (OR (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-477)))) +(-744 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-777) +(-745) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-778 -2740 S) +(-746 -2605 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-779) +(-747) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-780) +(-748) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-4142 . T)) +((-3976 . T)) NIL -(-781) +(-749) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-782 T$ |f|) +(-750 T$ |f|) ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) -(-783 S) +((|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) +(-751 S) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-784) +(-752) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-785 S R) +(-753 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-146)))) -(-786 R) +((|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-144)))) +(-754 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-787 R C) +(-755 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\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 (-318))) (|HasCategory| |#1| (QUOTE (-510)))) -(-788 R |sigma| -3382) +((|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) +(-756 R |sigma| -3227) ((|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."))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-318)))) -(-789 |x| R |sigma| -3382) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-308)))) +(-757 |x| R |sigma| -3227) ((|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}."))) -((-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-318)))) -(-790 R) +((-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-308)))) +(-758 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) NIL -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499)))))) -(-791) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478)))))) +(-759) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-792) +(-760) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-793) +(-761) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-794 S) +(-762 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-795) +(-763) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-796) +(-764) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) NIL NIL -(-797) +(-765) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-798 |VariableList|) +(-766 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-799) +(-767) ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) NIL NIL -(-800 R |vl| |wl| |wtlevel|) +(-768 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4140 |has| |#1| (-146)) (-4139 |has| |#1| (-146)) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318)))) -(-801 R PS UP) +((-3974 |has| |#1| (-144)) (-3973 |has| |#1| (-144)) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308)))) +(-769 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-802 R |x| |pt|) +(-770 R |x| |pt|) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-803 |p|) +(-771 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-804 |p|) +(-772 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-805 |p|) +(-773 |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)."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-803 |#1|) (QUOTE (-848))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| (-803 |#1|) (QUOTE (-118))) (|HasCategory| (-803 |#1|) (QUOTE (-120))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-803 |#1|) (QUOTE (-960))) (|HasCategory| (-803 |#1|) (QUOTE (-763))) (|HasCategory| (-803 |#1|) (QUOTE (-781))) (-3677 (|HasCategory| (-803 |#1|) (QUOTE (-763))) (|HasCategory| (-803 |#1|) (QUOTE (-781)))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-803 |#1|) (QUOTE (-1092))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| (-803 |#1|) (QUOTE (-189))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| (-803 |#1|) (QUOTE (-190))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -468) (QUOTE (-1117)) (|%list| (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -263) (|%list| (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (|%list| (QUOTE -240) (|%list| (QUOTE -803) (|devaluate| |#1|)) (|%list| (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (QUOTE (-261))) (|HasCategory| (-803 |#1|) (QUOTE (-498))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-803 |#1|) (QUOTE (-848)))) (-3677 (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-803 |#1|) (QUOTE (-848)))) (|HasCategory| (-803 |#1|) (QUOTE (-118))))) -(-806 |p| PADIC) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-771 |#1|) (QUOTE (-814))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| (-771 |#1|) (QUOTE (-116))) (|HasCategory| (-771 |#1|) (QUOTE (-118))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-771 |#1|) (QUOTE (-926))) (|HasCategory| (-771 |#1|) (QUOTE (-733))) (|HasCategory| (-771 |#1|) (QUOTE (-749))) (OR (|HasCategory| (-771 |#1|) (QUOTE (-733))) (|HasCategory| (-771 |#1|) (QUOTE (-749)))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-771 |#1|) (QUOTE (-1055))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| (-771 |#1|) (QUOTE (-187))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| (-771 |#1|) (QUOTE (-188))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -447) (QUOTE (-1079)) (|%list| (QUOTE -771) (|devaluate| |#1|)))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -256) (|%list| (QUOTE -771) (|devaluate| |#1|)))) (|HasCategory| (-771 |#1|) (|%list| (QUOTE -238) (|%list| (QUOTE -771) (|devaluate| |#1|)) (|%list| (QUOTE -771) (|devaluate| |#1|)))) (|HasCategory| (-771 |#1|) (QUOTE (-254))) (|HasCategory| (-771 |#1|) (QUOTE (-477))) (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-771 |#1|) (QUOTE (-814)))) (OR (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-771 |#1|) (QUOTE (-814)))) (|HasCategory| (-771 |#1|) (QUOTE (-116))))) +(-774 |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)}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-763))) (|HasCategory| |#2| (QUOTE (-781))) (-3677 (|HasCategory| |#2| (QUOTE (-763))) (|HasCategory| |#2| (QUOTE (-781)))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| |#2| (|%list| (QUOTE -468) (QUOTE (-1117)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -240) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (QUOTE (-498))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (-3677 (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-807 S T$) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-733))) (|HasCategory| |#2| (QUOTE (-749))) (OR (|HasCategory| |#2| (QUOTE (-733))) (|HasCategory| |#2| (QUOTE (-749)))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-187))) (|HasCategory| |#2| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#2| (|%list| (QUOTE -447) (QUOTE (-1079)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -238) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-254))) (|HasCategory| |#2| (QUOTE (-477))) (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#2| (QUOTE (-116))))) +(-775 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 (-1041))) (|HasCategory| |#2| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797))))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-1041))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))))) -(-808) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-1005))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))))) +(-776) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|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 NIL -(-809) +(-777) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-810) +(-778) ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) NIL NIL -(-811 CF1 CF2) +(-779 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-812 |ComponentFunction|) +(-780 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-813 CF1 CF2) +(-781 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-814 |ComponentFunction|) +(-782 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-815) +(-783) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-816 CF1 CF2) +(-784 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-817 |ComponentFunction|) +(-785 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-818) +(-786) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) NIL NIL -(-819 R) +(-787 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-820 R S L) +(-788 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-821 S) +(-789 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-822 |Base| |Subject| |Pat|) +(-790 |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 (-2679 (|HasCategory| |#2| (QUOTE (-989)))) (-2679 (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-1117)))))) (-12 (|HasCategory| |#2| (QUOTE (-989))) (-2679 (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-1117)))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-1117))))) -(-823 R S) +((-12 (-2544 (|HasCategory| |#2| (QUOTE (-954)))) (-2544 (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-1079)))))) (-12 (|HasCategory| |#2| (QUOTE (-954))) (-2544 (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-1079)))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-1079))))) +(-791 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 NIL -(-824 R A B) +(-792 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) NIL NIL -(-825 R) +(-793 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and 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 -(-826 R -2790) +(-794 R -2653) ((|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 -(-827 R S) +(-795 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-828 |VarSet|) +(-796 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-829 UP R) +(-797 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-830 A T$ S) +(-798 A T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-831 T$ S) +(-799 T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-832) -((|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 -(-833 UP -3215) +(-800 UP -3076) ((|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 -(-834) -((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) -NIL -NIL -(-835 R S) +(-801 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-836 S) +(-802 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4142 . T)) +((-3976 . T)) NIL -(-837 A S) +(-803 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-838 S) +(-804 S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-839 S) +(-805 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 (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-840 S) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-806 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4142 . T)) -((-3677 (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-781)))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-781)))) -(-841 |n| R) +((-3976 . T)) +((OR (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-749)))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-749)))) +(-807 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 NIL -(-842 S) +(-808 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4142 . T)) +((-3976 . T)) NIL -(-843 S) +(-809 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-844 |p|) +(-810 |p|) ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-323)))) -(-845 R E |VarSet| S) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-116))) (|HasCategory| $ (QUOTE (-313)))) +(-811 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-846 R S) +(-812 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-847 S) +(-813 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|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}."))) NIL -((|HasCategory| |#1| (QUOTE (-118)))) -(-848) +((|HasCategory| |#1| (QUOTE (-116)))) +(-814) ((|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}."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-849 R0 -3215 UP UPUP R) +(-815 R0 -3076 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 -(-850 UP UPUP R) +(-816 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-851 UP UPUP) +(-817 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-852 R) +(-818 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-853 R) +(-819 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL NIL -(-854 E OV R P) +(-820 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-855) +(-821) ((|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 -(-856 -3215) +(-822 -3076) ((|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 -(-857) +(-823) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4147 "*") . T)) +(((-3981 "*") . T)) NIL -(-858 R) +(-824 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-859) +(-825) ((|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)}"))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-860 |xx| -3215) +(-826 |xx| -3076) ((|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 -(-861 -3215 P) +(-827 -3076 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-862 R |Var| |Expon| GR) +(-828 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-863) +(-829) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) NIL NIL -(-864 S) +(-830 S) ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-865) +(-831) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-866) +(-832) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-867) +(-833) ((|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 -(-868 R -3215) +(-834 R -3076) ((|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 -(-869 S A B) +(-835 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-870 S R -3215) +(-836 S R -3076) ((|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 -(-871 I) +(-837 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-872 S E) +(-838 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-873 S R L) +(-839 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-874 S E V R P) +(-840 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (|%list| (QUOTE -821) (|devaluate| |#1|)))) -(-875 -2790) +((|HasCategory| |#3| (|%list| (QUOTE -789) (|devaluate| |#1|)))) +(-841 -2653) ((|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 -(-876 R -3215 -2790) +(-842 R -3076 -2653) ((|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 -(-877 S R Q) +(-843 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-878 S) +(-844 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-879 S R P) +(-845 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-880) +(-846) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) NIL NIL -(-881 R) +(-847 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4146 . T) (-4145 . 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T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#1| (QUOTE (-954))) (-12 (|HasCategory| |#1| (QUOTE (-908))) (|HasCategory| |#1| (QUOTE (-954)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-848 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-883 |TheField| |ThePols|) +(-849 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn,{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL -((|HasCategory| |#1| (QUOTE (-780)))) -(-884 R) +((|HasCategory| |#1| (QUOTE (-748)))) +(-850 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}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . 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(|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-886 |x| R) +(-852 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-887 S R E |VarSet|) +(-853 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the 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| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-848))) (|HasAttribute| |#2| (QUOTE -4143)) (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| |#4| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#4| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| |#4| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#4| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488))))) -(-888 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-814))) (|HasAttribute| |#2| (QUOTE -3977)) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#4| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| |#4| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#4| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| |#4| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#4| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467))))) +(-854 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the 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}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-6 -3977)) (-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-889 E V R P -3215) +(-855 E V R P -3076) ((|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 -(-890 E |Vars| R P S) +(-856 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-891 E V R P -3215) +(-857 E V R P -3076) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL -((|HasCategory| |#3| (QUOTE (-406)))) -(-892) +((|HasCategory| |#3| (QUOTE (-385)))) +(-858) ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) NIL NIL -(-893) +(-859) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-894 R E) +(-860 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-510))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-3677 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-406))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -4143))) -(-895 R L) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-6 -3977)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-385))) (-12 (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasAttribute| |#1| (QUOTE -3977))) +(-861 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-896 S) +(-862 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"))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-897 A B) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-863 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL -(-898) +(-864) ((|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 -(-899 -3215) +(-865 -3076) ((|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 -(-900 I) +(-866 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-901) +(-867) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-902 A B) +(-868 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"))) -((-4142 -12 (|has| |#2| (-427)) (|has| |#1| (-427)))) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-781))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-427)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-427)))) (-12 (|HasCategory| |#1| (QUOTE (-684))) (|HasCategory| |#2| (QUOTE (-684))))) (-12 (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#2| (QUOTE (-323)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-427)))) (-12 (|HasCategory| |#1| (QUOTE (-684))) (|HasCategory| |#2| (QUOTE (-684))))) (-12 (|HasCategory| |#1| (QUOTE (-684))) (|HasCategory| |#2| (QUOTE (-684)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-781))))) -(-903) +((-3976 -12 (|has| |#2| (-406)) (|has| |#1| (-406)))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-710))) (|HasCategory| |#2| (QUOTE (-710)))) (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-749))))) (-12 (|HasCategory| |#1| (QUOTE (-710))) (|HasCategory| |#2| (QUOTE (-710)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-12 (|HasCategory| |#1| (QUOTE (-710))) (|HasCategory| |#2| (QUOTE (-710)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-12 (|HasCategory| |#1| (QUOTE (-710))) (|HasCategory| |#2| (QUOTE (-710)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-406)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-406)))) (-12 (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#2| (QUOTE (-658))))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-313)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-12 (|HasCategory| |#1| (QUOTE (-710))) (|HasCategory| |#2| (QUOTE (-710)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-406)))) (-12 (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#2| (QUOTE (-658))))) (-12 (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#2| (QUOTE (-658)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-749))))) +(-869) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-904 T$) +(-870 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-905 T$) +(-871 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-906 S T$) +(-872 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-907) +(-873) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-908 S) +(-874 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) NIL -(-909 R |polR|) +(-875 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL -((|HasCategory| |#1| (QUOTE (-406)))) -(-910) +((|HasCategory| |#1| (QUOTE (-385)))) +(-876) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-911) +(-877) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-912 S |Coef| |Expon| |Var|) +(-878 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) NIL NIL -(-913 |Coef| |Expon| |Var|) +(-879 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-914) +(-880) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-915 S R E |VarSet| P) +(-881 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-510)))) -(-916 R E |VarSet| P) +((|HasCategory| |#2| (QUOTE (-489)))) +(-882 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4145 . T)) +((-3979 . T)) NIL -(-917 R E V P) +(-883 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-261)))) (|HasCategory| |#1| (QUOTE (-406)))) -(-918 K) +((-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-254)))) (|HasCategory| |#1| (QUOTE (-385)))) +(-884 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-919 |VarSet| E RC P) +(-885 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-920 R) +(-886 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-921 R1 R2) +(-887 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-922 R) +(-888 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-923 K) +(-889 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-924 R E OV PPR) +(-890 R E OV PPR) ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-925 K R UP -3215) +(-891 K R UP -3076) ((|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 -(-926 R |Var| |Expon| |Dpoly|) +(-892 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-261))))) -(-927 |vl| |nv|) +((-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-254))))) +(-893 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-928 R E V P TS) +(-894 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-929) +(-895) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) NIL NIL -(-930 A S) +(-896 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-498))) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-763))) (|HasCategory| |#2| (QUOTE (-781))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-1092)))) -(-931 S) +((|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-477))) (|HasCategory| |#2| (QUOTE (-254))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-733))) (|HasCategory| |#2| (QUOTE (-749))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-1055)))) +(-897 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-932 A B R S) +(-898 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-933 |n| K) +(-899 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-934) +(-900) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-935 S) +(-901 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) NIL -(-936 R) +(-902 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.}"))) -((-4138 |has| |#1| (-244)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (QUOTE (-318))) (-3677 (|HasCategory| |#1| (QUOTE (-244))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-244))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| |#1| (|%list| (QUOTE -468) (QUOTE (-1117)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (-3677 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-498)))) -(-937 S R) +((-3972 |has| |#1| (-242)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (QUOTE (-308))) (OR (|HasCategory| |#1| (QUOTE (-242))) (|HasCategory| |#1| (QUOTE (-308)))) (|HasCategory| |#1| (QUOTE (-242))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#1| (|%list| (QUOTE -447) (QUOTE (-1079)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -238) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-477)))) +(-903 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-498))) (|HasCategory| |#2| (QUOTE (-1000))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-244)))) -(-938 R) +((|HasCategory| |#2| (QUOTE (-477))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-242)))) +(-904 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4138 |has| |#1| (-244)) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 |has| |#1| (-242)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-939 QR R QS S) +(-905 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-940 S) +(-906 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-941 S) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-907 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-942) +(-908) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-943 -3215 UP UPUP |radicnd| |n|) +(-909 -3076 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4138 |has| (-361 |#2|) (-318)) (-4143 |has| (-361 |#2|) (-318)) (-4137 |has| (-361 |#2|) (-318)) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-361 |#2|) (QUOTE (-118))) (|HasCategory| (-361 |#2|) (QUOTE (-120))) (|HasCategory| (-361 |#2|) (QUOTE (-305))) (-3677 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (QUOTE (-305)))) (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (QUOTE (-323))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-190))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (|HasCategory| (-361 |#2|) (QUOTE (-305)))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-190))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-189))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (|HasCategory| (-361 |#2|) (QUOTE (-305)))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117))))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-305))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117)))))) (-3677 (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117))))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -838) (QUOTE (-1117)))))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -596) (QUOTE (-499)))) (-3677 (|HasCategory| (-361 |#2|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-323))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-189))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -838) (QUOTE (-1117))))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-190))) (|HasCategory| (-361 |#2|) (QUOTE (-318)))) (-12 (|HasCategory| (-361 |#2|) (QUOTE (-318))) (|HasCategory| (-361 |#2|) (|%list| (QUOTE -836) (QUOTE (-1117)))))) -(-944 |bb|) +((-3972 |has| (-343 |#2|) (-308)) (-3977 |has| (-343 |#2|) (-308)) (-3971 |has| (-343 |#2|) (-308)) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-343 |#2|) (QUOTE (-116))) (|HasCategory| (-343 |#2|) (QUOTE (-118))) (|HasCategory| (-343 |#2|) (QUOTE (-295))) (OR (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (QUOTE (-295)))) (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (QUOTE (-313))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-188))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (|HasCategory| (-343 |#2|) (QUOTE (-295)))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-188))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-187))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (|HasCategory| (-343 |#2|) (QUOTE (-295)))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079))))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-295))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079)))))) (OR (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079))))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -804) (QUOTE (-1079)))))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -575) (QUOTE (-478)))) (OR (|HasCategory| (-343 |#2|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-313))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-187))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -804) (QUOTE (-1079))))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-188))) (|HasCategory| (-343 |#2|) (QUOTE (-308)))) (-12 (|HasCategory| (-343 |#2|) (QUOTE (-308))) (|HasCategory| (-343 |#2|) (|%list| (QUOTE -802) (QUOTE (-1079)))))) +(-910 |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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-499) (QUOTE (-848))) (|HasCategory| (-499) (|%list| (QUOTE -978) (QUOTE (-1117)))) (|HasCategory| (-499) (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-120))) (|HasCategory| (-499) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-499) (QUOTE (-960))) (|HasCategory| (-499) (QUOTE (-763))) (|HasCategory| (-499) (QUOTE (-781))) (-3677 (|HasCategory| (-499) (QUOTE (-763))) (|HasCategory| (-499) (QUOTE (-781)))) (|HasCategory| (-499) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-499) (QUOTE (-1092))) (|HasCategory| (-499) (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| (-499) (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| (-499) (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| (-499) (QUOTE (-189))) (|HasCategory| (-499) (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| (-499) (QUOTE (-190))) (|HasCategory| (-499) (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| (-499) (|%list| (QUOTE -468) (QUOTE (-1117)) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -263) (QUOTE (-499)))) (|HasCategory| (-499) (|%list| (QUOTE -240) (QUOTE (-499)) (QUOTE (-499)))) (|HasCategory| (-499) (QUOTE (-261))) (|HasCategory| (-499) (QUOTE (-498))) (|HasCategory| (-499) (|%list| (QUOTE -596) (QUOTE (-499)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-848)))) (-3677 (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-499) (QUOTE (-848)))) (|HasCategory| (-499) (QUOTE (-118))))) -(-945) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-478) (QUOTE (-814))) (|HasCategory| (-478) (|%list| (QUOTE -943) (QUOTE (-1079)))) (|HasCategory| (-478) (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-118))) (|HasCategory| (-478) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-478) (QUOTE (-926))) (|HasCategory| (-478) (QUOTE (-733))) (|HasCategory| (-478) (QUOTE (-749))) (OR (|HasCategory| (-478) (QUOTE (-733))) (|HasCategory| (-478) (QUOTE (-749)))) (|HasCategory| (-478) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-478) (QUOTE (-1055))) (|HasCategory| (-478) (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-478) (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-478) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-478) (QUOTE (-187))) (|HasCategory| (-478) (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| (-478) (QUOTE (-188))) (|HasCategory| (-478) (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| (-478) (|%list| (QUOTE -447) (QUOTE (-1079)) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -256) (QUOTE (-478)))) (|HasCategory| (-478) (|%list| (QUOTE -238) (QUOTE (-478)) (QUOTE (-478)))) (|HasCategory| (-478) (QUOTE (-254))) (|HasCategory| (-478) (QUOTE (-477))) (|HasCategory| (-478) (|%list| (QUOTE -575) (QUOTE (-478)))) (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-814)))) (OR (-12 (|HasCategory| $ (QUOTE (-116))) (|HasCategory| (-478) (QUOTE (-814)))) (|HasCategory| (-478) (QUOTE (-116))))) +(-911) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL NIL -(-946) +(-912) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-947 RP) +(-913 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-948 S) +(-914 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-949 A S) +(-915 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4146)) (|HasCategory| |#2| (QUOTE (-1041)))) -(-950 S) +((|HasAttribute| |#1| (QUOTE -3980)) (|HasCategory| |#2| (QUOTE (-1005)))) +(-916 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-951 S) +(-917 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (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}}"))) NIL NIL -(-952) +(-918) ((|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}}"))) -((-4138 . T) (-4143 . T) (-4137 . T) (-4140 . T) (-4139 . T) ((-4147 "*") . T) (-4142 . T)) +((-3972 . T) (-3977 . T) (-3971 . T) (-3974 . T) (-3973 . T) ((-3981 "*") . T) (-3976 . T)) NIL -(-953 R -3215) +(-919 R -3076) ((|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 -(-954 R -3215) +(-920 R -3076) ((|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 -(-955 -3215 UP) +(-921 -3076 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 -(-956 -3215 UP) +(-922 -3076 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 -(-957 S) +(-923 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-958 F1 UP UPUP R F2) +(-924 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) NIL NIL -(-959) +(-925) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-960) +(-926) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-961 |Pol|) +(-927 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-962 |Pol|) +(-928 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-963) +(-929) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-964 |TheField|) +(-930 |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"))) -((-4138 . T) (-4143 . T) (-4137 . T) (-4140 . T) (-4139 . T) ((-4147 "*") . T) (-4142 . T)) -((-3677 (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-361 (-499)) (|%list| (QUOTE -978) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-361 (-499)) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-361 (-499)) (|%list| (QUOTE -978) (QUOTE (-499))))) -(-965 -3215 L) +((-3972 . T) (-3977 . T) (-3971 . T) (-3974 . T) (-3973 . T) ((-3981 "*") . T) (-3976 . T)) +((OR (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-343 (-478)) (|%list| (QUOTE -943) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-343 (-478)) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-343 (-478)) (|%list| (QUOTE -943) (QUOTE (-478))))) +(-931 -3076 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 -(-966 S) +(-932 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1041)))) -(-967 R E V P) +((|HasCategory| |#1| (QUOTE (-1005)))) +(-933 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#4| (|%list| (QUOTE -263) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#3| (QUOTE (-323))) (|HasCategory| |#4| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#4| (QUOTE (-73)))) -(-968) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (|%list| (QUOTE -256) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#4| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-934) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-969 R) +(-935 R) ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4147 "*")))) -(-970 R) +((|HasAttribute| |#1| (QUOTE (-3981 "*")))) +(-936 R) ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-261)))) -(-971 S) +((-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-254)))) +(-937 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-972 S) +(-938 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-973 S) +(-939 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-974 -3215 |Expon| |VarSet| |FPol| |LFPol|) +(-940 -3076 |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"))) -(((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-975) -((|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.}"))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (QUOTE (-1117))) (|%list| (QUOTE |:|) (QUOTE |entry|) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-51) (|%list| (QUOTE -263) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041))) (|HasCategory| (-1117) (QUOTE (-781))) (|HasCategory| (-51) (QUOTE (-1041))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-73)))) (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-73)))) -(-976) +(-941) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-977 A S) +(-942 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-978 S) +(-943 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-979 Q R) +(-944 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-980 R) +(-945 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-981) +(-946) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-982 UP) +(-947 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-983 R) +(-948 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-984 T$) +(-949 T$) ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) NIL NIL -(-985 T$) +(-950 T$) ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-986 R |ls|) +(-951 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| (-723 |#1| (-798 |#2|)) (QUOTE (-1041))) (|HasCategory| (-723 |#1| (-798 |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -723) (|devaluate| |#1|) (|%list| (QUOTE -798) (|devaluate| |#2|)))))) (|HasCategory| (-723 |#1| (-798 |#2|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-723 |#1| (-798 |#2|)) (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| (-798 |#2|) (QUOTE (-323))) (|HasCategory| (-723 |#1| (-798 |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-723 |#1| (-798 |#2|)) (QUOTE (-73)))) -(-987) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| (-696 |#1| (-766 |#2|)) (QUOTE (-1005))) (|HasCategory| (-696 |#1| (-766 |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -696) (|devaluate| |#1|) (|%list| (QUOTE -766) (|devaluate| |#2|)))))) (|HasCategory| (-696 |#1| (-766 |#2|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-696 |#1| (-766 |#2|)) (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| (-766 |#2|) (QUOTE (-313))) (|HasCategory| (-696 |#1| (-766 |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-696 |#1| (-766 |#2|)) (QUOTE (-72)))) +(-952) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-988 S) +(-953 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL -(-989) +(-954) ((|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."))) -((-4142 . T)) +((-3976 . T)) NIL -(-990 |xx| -3215) +(-955 |xx| -3076) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-991 S) +(-956 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-992 S |m| |n| R |Row| |Col|) +(-957 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL -((|HasCategory| |#4| (QUOTE (-261))) (|HasCategory| |#4| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-510))) (|HasCategory| |#4| (QUOTE (-146)))) -(-993 |m| |n| R |Row| |Col|) +((|HasCategory| |#4| (QUOTE (-254))) (|HasCategory| |#4| (QUOTE (-308))) (|HasCategory| |#4| (QUOTE (-489))) (|HasCategory| |#4| (QUOTE (-144)))) +(-958 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4145 . T) (-4140 . T) (-4139 . T)) +((-3979 . T) (-3974 . T) (-3973 . T)) NIL -(-994 |m| |n| R) +(-959 |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}."))) -((-4145 . T) (-4140 . T) (-4139 . T)) -((|HasCategory| |#3| (QUOTE (-146))) (-3677 (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1041))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-318)))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-1041))) (|HasCategory| |#3| (QUOTE (-261))) (|HasCategory| |#3| (QUOTE (-510))) (-12 (|HasCategory| |#3| (QUOTE (-1041))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-73))) (|HasCategory| |#3| (|%list| (QUOTE -568) (QUOTE (-797))))) -(-995 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-3979 . T) (-3974 . T) (-3973 . T)) +((|HasCategory| |#3| (QUOTE (-144))) (OR (-12 (|HasCategory| |#3| (QUOTE (-144))) (|HasCategory| |#3| (|%list| (QUOTE -256) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (|%list| (QUOTE -256) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -256) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#3| (QUOTE (-144))) (|HasCategory| |#3| (QUOTE (-308)))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (QUOTE (-254))) (|HasCategory| |#3| (QUOTE (-489))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -256) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (|%list| (QUOTE -547) (QUOTE (-765))))) +(-960 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-996 R) +(-961 R) ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) NIL NIL -(-997) +(-962) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) NIL NIL -(-998 S T$) +(-963 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1041)))) -(-999 S) +((|HasCategory| |#1| (QUOTE (-1005)))) +(-964 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.")) (|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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1000) +(-965) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1001 |TheField| |ThePolDom|) +(-966 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1002) +(-967) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4133 . T) (-4137 . T) (-4132 . T) (-4143 . T) (-4144 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3967 . T) (-3971 . T) (-3966 . T) (-3977 . T) (-3978 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1003) -((|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}"))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (QUOTE (-1117))) (|%list| (QUOTE |:|) (QUOTE |entry|) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| (-51) (QUOTE (-1041))) (|HasCategory| (-51) (|%list| (QUOTE -263) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-1041))) (|HasCategory| (-1117) (QUOTE (-781))) (|HasCategory| (-51) (QUOTE (-1041))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-73)))) (|HasCategory| (-51) (QUOTE (-73))) (|HasCategory| (-51) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1117)) (|:| |entry| (-51))) (QUOTE (-73)))) -(-1004 S R E V) +(-968 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-498))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -931) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#4| (|%list| (QUOTE -569) (QUOTE (-1117))))) -(-1005 R E V) +((|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-477))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -897) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#4| (|%list| (QUOTE -548) (QUOTE (-1079))))) +(-969 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|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| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}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|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-6 -3977)) (-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-1006) +(-970) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-1007 S |TheField| |ThePols|) +(-971 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1008 |TheField| |ThePols|) +(-972 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1009 R E V P TS) +(-973 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1010 S R E V P) +(-974 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-1011 R E V P) +(-975 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-1012 R E V P TS) +(-976 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1013) +(-977) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1014) +(-978) ((|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 -(-1015 |Base| R -3215) +(-979 |Base| R -3076) ((|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 -(-1016 |f|) +(-980 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1017 |Base| R -3215) +(-981 |Base| R -3076) ((|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 -(-1018 R |ls|) +(-982 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1019 R UP M) +(-983 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."))) -((-4138 |has| |#1| (-318)) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . 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T) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-295))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-295)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-313))) (OR (-12 (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-308)))) (|HasCategory| |#1| (QUOTE (-295)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-308)))) (-12 (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (QUOTE (-308)))) (|HasCategory| |#1| (QUOTE (-295)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079))))) (-12 (|HasCategory| |#1| (QUOTE (-295))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079))))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079)))))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (QUOTE (-308)))) (|HasCategory| |#1| (QUOTE (-295)))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079))))) (-12 (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (QUOTE (-308)))) (-12 (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-308)))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))))) +(-984 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1021 UP SAE UPA) +(-985 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1022) +(-986) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1023) +(-987) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1024 S) +(-988 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-1025) +(-989) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1026 R) +(-990 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-1027 R) +(-991 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. 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T)) +((|HasCategory| |#1| (QUOTE (-814))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-992 (-1079)) (|%list| (QUOTE -789) (QUOTE (-323))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-992 (-1079)) (|%list| (QUOTE -789) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-992 (-1079)) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-992 (-1079)) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-992 (-1079)) (|%list| (QUOTE -548) (QUOTE (-467))))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-187))) (|HasCategory| |#1| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasAttribute| |#1| (QUOTE -3977)) (|HasCategory| |#1| (QUOTE (-385))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#1| (QUOTE (-116))))) +(-992 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1029 S) +(-993 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#1| (QUOTE (-1041)))) -(-1030 R S) +((|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1005)))) +(-994 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -((|HasCategory| |#1| (QUOTE (-780)))) -(-1031) +((|HasCategory| |#1| (QUOTE (-748)))) +(-995) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1032 S) +(-996 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1029 |#1|) (QUOTE (-1041)))) -(-1033 R S) +((|HasCategory| (-993 |#1|) (QUOTE (-1005)))) +(-997 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1034 S) +(-998 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1035 S L) +(-999 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) NIL NIL -(-1036) +(-1000) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1037 S) +(-1001 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)}}"))) -((-4145 . T) (-4135 . T) (-4146 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-1038 A S) +((-3979 . T) (-3969 . T) (-3980 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-1002 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1039 S) +(-1003 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4135 . T)) +((-3969 . T)) NIL -(-1040 S) +(-1004 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1041) +(-1005) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1042 |m| |n|) +(-1006 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1043) +(-1007) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1044 |Str| |Sym| |Int| |Flt| |Expr|) +(-1008 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Flt.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1045 |Str| |Sym| |Int| |Flt| |Expr|) +(-1009 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1046 R FS) -((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) -NIL -NIL -(-1047 R E V P TS) +(-1010 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1048 R E V P TS) +(-1011 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1049 R E V P) +(-1012 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-1050) +(-1013) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1051 S) +(-1014 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1052) +(-1015) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1053 |dimtot| |dim1| S) +(-1016 |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. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4139 |has| |#3| (-989)) (-4140 |has| |#3| (-989)) (-4142 |has| |#3| (-6 -4142)) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-323))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-684))) (|HasCategory| |#3| (|%list| (QUOTE -263) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-738))) 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(-1079))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (|HasCategory| |#3| (QUOTE (-954)))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (QUOTE (-478))))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasAttribute| |#3| (QUOTE -3976)) (-12 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (QUOTE (-954)))) (-12 (|HasCategory| |#3| (QUOTE (-954))) (|HasCategory| |#3| (|%list| (QUOTE -802) (QUOTE (-1079))))) (|HasCategory| |#3| (QUOTE (-144))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1005))) (|HasCategory| |#3| (|%list| (QUOTE -256) (|devaluate| |#3|))))) +(-1017 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 -((|HasCategory| |#1| (QUOTE (-406)))) -(-1055) +((|HasCategory| |#1| (QUOTE (-385)))) +(-1018) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) NIL NIL -(-1056) +(-1019) ((|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 -(-1057 R -3215) +(-1020 R -3076) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="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|) #1#) |#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|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1058 R) +(-1021 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1059) +(-1022) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1060) +(-1023) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4133 . T) (-4137 . T) (-4132 . T) (-4143 . T) (-4144 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3967 . T) (-3971 . T) (-3966 . T) (-3977 . T) (-3978 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1061 S) +(-1024 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4145 . T) (-4146 . T)) +((-3979 . T) (-3980 . T)) NIL -(-1062 S |ndim| R |Row| |Col|) +(-1025 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-318))) (|HasAttribute| |#3| (QUOTE (-4147 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) -(-1063 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-308))) (|HasAttribute| |#3| (QUOTE (-3981 "*"))) (|HasCategory| |#3| (QUOTE (-144)))) +(-1026 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) -((-4145 . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3979 . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1064 R |Row| |Col| M) +(-1027 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1065 R |VarSet|) +(-1028 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."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-848))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-848)))) (-3677 (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-848)))) (-3677 (|HasCategory| |#1| (QUOTE (-406))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-146))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -821) (QUOTE (-333)))) (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-333))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -821) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -821) (QUOTE (-499))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333))))) (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-333)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (QUOTE (-499)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488))))) (|HasCategory| |#1| (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (-3677 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasAttribute| |#1| (QUOTE -4143)) (|HasCategory| |#1| (QUOTE (-406))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1066 |Coef| |Var| SMP) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-6 -3977)) (-3974 . T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-814))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-814)))) (OR (|HasCategory| |#1| (QUOTE (-385))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-323))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467))))) (|HasCategory| |#1| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasAttribute| |#1| (QUOTE -3977)) (|HasCategory| |#1| (QUOTE (-385))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#1| (QUOTE (-116))))) +(-1029 |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}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4140 . T) (-4139 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-318)))) -(-1067 R E V P) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3974 . T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-116))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-308)))) +(-1030 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}"))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-1068 UP -3215) +(-1031 UP -3076) ((|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 -(-1069 R) +(-1032 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1070 R) +(-1033 R) ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1071 R) +(-1034 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1072 S A) +(-1035 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-781)))) -(-1073 R) +((|HasCategory| |#1| (QUOTE (-749)))) +(-1036 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1074 R) +(-1037 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1075) +(-1038) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1076) +(-1039) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1077) +(-1040) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) NIL NIL -(-1078) +(-1041) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1079) +(-1042) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1080 V C) +(-1043 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1081 V C) +(-1044 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."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-1080 |#1| |#2|) (|%list| (QUOTE -263) (|%list| (QUOTE -1080) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1080 |#1| |#2|) (QUOTE (-1041)))) (|HasCategory| (-1080 |#1| |#2|) (QUOTE (-1041))) (-3677 (|HasCategory| (-1080 |#1| |#2|) (QUOTE (-73))) (|HasCategory| (-1080 |#1| |#2|) (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| (-1080 |#1| |#2|) (|%list| (QUOTE -263) (|%list| (QUOTE -1080) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1080 |#1| |#2|) (QUOTE (-1041)))) (|HasCategory| (-1080 |#1| |#2|) (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| (-1080 |#1| |#2|) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-1080 |#1| |#2|) (QUOTE (-73)))) -(-1082 |ndim| R) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| (-1043 |#1| |#2|) (|%list| (QUOTE -256) (|%list| (QUOTE -1043) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1043 |#1| |#2|) (QUOTE (-1005)))) (|HasCategory| (-1043 |#1| |#2|) (QUOTE (-1005))) (OR (|HasCategory| (-1043 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1043 |#1| |#2|) (QUOTE (-1005)))) (OR (-12 (|HasCategory| (-1043 |#1| |#2|) (|%list| (QUOTE -256) (|%list| (QUOTE -1043) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1043 |#1| |#2|) (QUOTE (-1005)))) (|HasCategory| (-1043 |#1| |#2|) (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| (-1043 |#1| |#2|) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-1043 |#1| |#2|) (QUOTE (-72)))) +(-1045 |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}."))) -((-4142 . T) (-4134 |has| |#2| (-6 (-4147 "*"))) (-4145 . T) (-4139 . T) (-4140 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasCategory| |#2| (|%list| (QUOTE -838) (QUOTE (-1117)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-4147 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -596) (QUOTE (-499)))) (|HasCategory| |#2| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (|%list| (QUOTE -978) (QUOTE (-499)))) (-3677 (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -596) (QUOTE (-499))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117)))))) (|HasCategory| |#2| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-318))) (-3677 (|HasAttribute| |#2| (QUOTE (-4147 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -836) (QUOTE (-1117))))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-73))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1083 S) +((-3976 . T) (-3968 |has| |#2| (-6 (-3981 "*"))) (-3979 . T) (-3973 . T) (-3974 . T)) +((|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#2| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (QUOTE (-187))) (|HasAttribute| |#2| (QUOTE (-3981 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))))) (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#2| (QUOTE (-254))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-308))) (OR (|HasAttribute| |#2| (QUOTE (-3981 #1#))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079))))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-144)))) +(-1046 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1084) +(-1047) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-1085 R E V P TS) +(-1048 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1086 R E V P) +(-1049 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#4| (|%list| (QUOTE -263) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#3| (QUOTE (-323))) (|HasCategory| |#4| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#4| (QUOTE (-73)))) -(-1087) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (|%list| (QUOTE -256) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#4| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-1050) ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) NIL NIL -(-1088 S) +(-1051 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}."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-1089 A S) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1052 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}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1090 S) +(-1053 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}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1091 |Key| |Ent| |dent|) +(-1054 |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."))) -((-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) -(-1092) +((-3980 . T)) +((-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) +(-1055) ((|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 non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|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 NIL -(-1093) +(-1056) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1094 |Coef|) +(-1057 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1095 S) +(-1058 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4146 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-1096 S) +((-3980 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1059 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL NIL -(-1097 A B) +(-1060 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-1098 A B C) +(-1061 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) NIL NIL -(-1099) +(-1062) ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|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"))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| (-117) (QUOTE (-781))) (|HasCategory| (-117) (|%list| (QUOTE -263) (QUOTE (-117))))) (-12 (|HasCategory| (-117) (QUOTE (-1041))) (|HasCategory| (-117) (|%list| (QUOTE -263) (QUOTE (-117)))))) (-3677 (-12 (|HasCategory| (-117) (QUOTE (-1041))) (|HasCategory| (-117) (|%list| (QUOTE -263) (QUOTE (-117))))) (|HasCategory| (-117) (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| (-117) (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| (-117) (QUOTE (-781))) (|HasCategory| (-117) (QUOTE (-1041)))) (|HasCategory| (-117) (QUOTE (-781))) (-3677 (|HasCategory| (-117) (QUOTE (-73))) (|HasCategory| (-117) (QUOTE (-781))) (|HasCategory| (-117) (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| (-117) (QUOTE (-1041))) (|HasCategory| (-117) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-117) (QUOTE (-73))) (-12 (|HasCategory| (-117) (QUOTE (-1041))) (|HasCategory| (-117) (|%list| (QUOTE -263) (QUOTE (-117)))))) -(-1100 |Entry|) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| (-115) (QUOTE (-749))) (|HasCategory| (-115) (|%list| (QUOTE -256) (QUOTE (-115))))) (-12 (|HasCategory| (-115) (QUOTE (-1005))) (|HasCategory| (-115) (|%list| (QUOTE -256) (QUOTE (-115)))))) (OR (-12 (|HasCategory| (-115) (QUOTE (-1005))) (|HasCategory| (-115) (|%list| (QUOTE -256) (QUOTE (-115))))) (|HasCategory| (-115) (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| (-115) (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| (-115) (QUOTE (-749))) (|HasCategory| (-115) (QUOTE (-1005)))) (|HasCategory| (-115) (QUOTE (-749))) (OR (|HasCategory| (-115) (QUOTE (-72))) (|HasCategory| (-115) (QUOTE (-749))) (|HasCategory| (-115) (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| (-115) (QUOTE (-1005))) (|HasCategory| (-115) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-115) (QUOTE (-72))) (-12 (|HasCategory| (-115) (QUOTE (-1005))) (|HasCategory| (-115) (|%list| (QUOTE -256) (QUOTE (-115)))))) +(-1063 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (QUOTE (-1099))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-1041))) (|HasCategory| (-1099) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-73)))) (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 (-1099)) (|:| |entry| |#1|)) (QUOTE (-73)))) -(-1101 A) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (QUOTE (-1062))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-1005)))) (OR (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-1005)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-1005)))) (OR (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-1005))) (|HasCategory| (-1062) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 (-1062)) (|:| |entry| |#1|)) (QUOTE (-72)))) +(-1064 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 -((|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499)))))) -(-1102 |Coef|) +((|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478)))))) +(-1065 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1103 |Coef|) +(-1066 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1104 R UP) +(-1067 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) NIL -((|HasCategory| |#1| (QUOTE (-261)))) -(-1105 |n| R) +((|HasCategory| |#1| (QUOTE (-254)))) +(-1068 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) NIL NIL -(-1106 S1 S2) +(-1069 S1 S2) ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form s:t"))) NIL NIL -(-1107) +(-1070) ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) NIL NIL -(-1108 |Coef| |var| |cen|) +(-1071 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4147 "*") -3677 (-2681 (|has| |#1| (-318)) (|has| (-1115 |#1| |#2| |#3|) (-763))) (|has| |#1| (-146)) (-2681 (|has| |#1| (-318)) (|has| (-1115 |#1| |#2| |#3|) (-848)))) (-4138 -3677 (-2681 (|has| |#1| (-318)) (|has| (-1115 |#1| |#2| |#3|) (-763))) (|has| |#1| (-510)) (-2681 (|has| |#1| (-318)) (|has| (-1115 |#1| |#2| |#3|) (-848)))) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) (-4139 . T) (-4140 . T) (-4142 . 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(|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 -(-1110 R) +(-1073 R) ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) NIL NIL -(-1111 R) +(-1074 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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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 NIL -(-1113 E OV R P) +(-1076 E OV R P) ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) NIL NIL -(-1114 |Coef| |var| |cen|) +(-1077 |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."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) (-4139 . T) (-4140 . T) (-4142 . 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T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|)))) (|HasCategory| (-343 (-478)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-308))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasSignature| |#1| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#1|) (QUOTE (-1079)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasSignature| |#1| (|%list| (QUOTE -3796) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1079))))) (|HasSignature| |#1| (|%list| (QUOTE -3065) (|%list| (|%list| (QUOTE -578) (QUOTE (-1079))) (|devaluate| |#1|))))))) +(-1078 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-510))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-714)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-714)) (|devaluate| |#1|)))) (|HasCategory| (-714) (QUOTE (-1052))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-714))))) (|HasSignature| |#1| (|%list| (QUOTE -4096) (|%list| (|devaluate| |#1|) (QUOTE (-1117)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-714))))) (|HasCategory| |#1| (QUOTE (-318))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-898))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-499))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasSignature| |#1| (|%list| (QUOTE -3962) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1117))))) (|HasSignature| |#1| (|%list| (QUOTE -3204) (|%list| (|%list| (QUOTE -599) (QUOTE (-1117))) (|devaluate| |#1|))))))) -(-1116) -((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) -NIL -NIL -(-1117) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-687)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-687)) (|devaluate| |#1|)))) (|HasCategory| (-687) (QUOTE (-1015))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-687))))) (|HasSignature| |#1| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#1|) (QUOTE (-1079)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-687))))) (|HasCategory| |#1| (QUOTE (-308))) (OR (-12 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasSignature| |#1| (|%list| (QUOTE -3796) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1079))))) (|HasSignature| |#1| (|%list| (QUOTE -3065) (|%list| (|%list| (QUOTE -578) (QUOTE (-1079))) (|devaluate| |#1|))))))) +(-1079) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1118 R) +(-1080 R) ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1119 R) +(-1081 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-6 -4143)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-510))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-3677 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-406))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| (-911) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -4143))) -(-1120) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-6 -3977)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-385))) (-12 (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| (-877) (QUOTE (-102)))) (|HasAttribute| |#1| (QUOTE -3977))) +(-1082) ((|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| #1="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| #1#))) "\\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| #1#))) "\\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| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1121) +(-1083) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1122) +(-1084) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1123 N) +(-1085 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1124 N) +(-1086 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) NIL NIL -(-1125) +(-1087) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1126 R) +(-1088 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1127) +(-1089) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1128 S) +(-1090 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1129 |Key| |Entry|) +(-1091 |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}"))) -((-4145 . T) (-4146 . T)) -((-12 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -263) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4010) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -569) (QUOTE (-488)))) (-12 (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (|%list| (QUOTE -263) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#2| (QUOTE (-1041))) (-3677 (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797))))) (-3677 (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) (|HasCategory| |#2| (QUOTE (-73))) (|HasCategory| |#2| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| (-2 (|:| -4010 |#1|) (|:| |entry| |#2|)) (QUOTE (-73)))) -(-1130 S) +((-3979 . T) (-3980 . T)) +((-12 (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -256) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3844) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -548) (QUOTE (-467)))) (-12 (|HasCategory| |#2| (QUOTE (-1005))) (|HasCategory| |#2| (|%list| (QUOTE -256) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#2| (QUOTE (-1005))) (OR (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765))))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| (-2 (|:| -3844 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) +(-1092 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1131 S) +(-1093 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL NIL -(-1132 R) +(-1094 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1133 S |Key| |Entry|) +(-1095 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1134 |Key| |Entry|) +(-1096 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4146 . T)) +((-3980 . T)) NIL -(-1135 |Key| |Entry|) +(-1097 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1136) -((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) -NIL -NIL -(-1137) +(-1098) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1138 S) +(-1099 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1139) +(-1100) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1140 R) +(-1101 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1141) +(-1102) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1142 S) +(-1103 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1143) +(-1104) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1144 S) +(-1105 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1041))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-1041)))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73)))) -(-1145 S) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1005))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1005)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1106 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1146) +(-1107) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1147 R -3215) +(-1108 R -3076) ((|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 -(-1148 R |Row| |Col| M) +(-1109 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1149 R -3215) +(-1110 R -3076) ((|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 -569) (|%list| (QUOTE -825) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -821) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -569) (|%list| (QUOTE -825) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -821) (|devaluate| |#1|))))) -(-1150 |Coef|) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -789) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -789) (|devaluate| |#1|))))) +(-1111 |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}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4140 . T) (-4139 . T) (-4142 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-318)))) -(-1151 S R E V P) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3974 . T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-116))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-308)))) +(-1112 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 -((|HasCategory| |#4| (QUOTE (-323)))) -(-1152 R E V P) +((|HasCategory| |#4| (QUOTE (-313)))) +(-1113 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| (($ $ |#4|) "\\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") $ |#4|) "\\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| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\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| |#4| "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| |#4| "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| |#4|)))) (|List| |#4|)) "\\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| |#4|)) "\\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| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\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| ((|#4| |#4| $) "\\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| ((|#4| |#4| $) "\\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| ((|#4| |#4| $) "\\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| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\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| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\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|) |#4| (|List| |#4|))) "\\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|) |#4| $) "\\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|) |#4| $) "\\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|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\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|) |#4| $) "\\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| |#4|)) (|:| |open| (|List| |#4|))) $) "\\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| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\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| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-1153 |Curve|) +(-1114 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1154) +(-1115) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1155 S) +(-1116 S) ((|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 (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) -(-1156 -3215) +((|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) +(-1117 -3076) ((|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 -(-1157) +(-1118) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1158) +(-1119) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1159 S) +(-1120 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) NIL -((|HasCategory| |#1| (QUOTE (-781)))) -(-1160) +((|HasCategory| |#1| (QUOTE (-749)))) +(-1121) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1161 S) +(-1122 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) NIL NIL -(-1162) +(-1123) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1163) +(-1124) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1164) +(-1125) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1165) +(-1126) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1166) +(-1127) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1167 |Coef| |var| |cen|) +(-1128 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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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NIL NIL -(-1169 |Coef|) +(-1130 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-308)) (-3971 |has| |#1| (-308)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1170 S |Coef| UTS) +(-1131 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL -((|HasCategory| |#2| (QUOTE (-318)))) -(-1171 |Coef| UTS) +((|HasCategory| |#2| (QUOTE (-308)))) +(-1132 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. 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T)) +((|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-144))) (OR (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-489)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-323)))) (|HasCategory| (-986) (|%list| (QUOTE -789) (QUOTE (-323))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -789) (QUOTE (-478)))) (|HasCategory| (-986) (|%list| (QUOTE -789) (QUOTE (-478))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323))))) (|HasCategory| (-986) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-323)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478))))) (|HasCategory| (-986) (|%list| (QUOTE -548) (|%list| (QUOTE -793) (QUOTE (-478)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| (-986) (|%list| (QUOTE -548) (QUOTE (-467))))) (|HasCategory| |#2| (|%list| (QUOTE -575) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (QUOTE (-478)))) (OR (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| |#2| (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (OR (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-814)))) (OR (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-814)))) (OR (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-814)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (|%list| (QUOTE -804) (QUOTE (-1079)))) (|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasCategory| |#2| (QUOTE (-187))) (|HasCategory| |#2| (QUOTE (-188))) (|HasAttribute| |#2| (QUOTE -3977)) (|HasCategory| |#2| (QUOTE (-385))) (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| $ (QUOTE (-116)))) (|HasCategory| |#2| (QUOTE (-116))))) +(-1138 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1178 R Q UP) +(-1139 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1179 R UP) +(-1140 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1180 R UP) +(-1141 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1181 R U) +(-1142 R U) ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) NIL NIL -(-1182 S R) +(-1143 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-406))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1092)))) -(-1183 R) +((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-385))) (|HasCategory| |#2| (QUOTE (-489))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-1055)))) +(-1144 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4141 |has| |#1| (-318)) (-4143 |has| |#1| (-6 -4143)) (-4140 . T) (-4139 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3975 |has| |#1| (-308)) (-3977 |has| |#1| (-6 -3977)) (-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-1184 R PR S PS) +(-1145 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1185 S |Coef| |Expon|) +(-1146 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 -836) (QUOTE (-1117)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1052))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4096) (|%list| (|devaluate| |#2|) (QUOTE (-1117)))))) -(-1186 |Coef| |Expon|) +((|HasCategory| |#2| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#2|) (QUOTE (-1079)))))) +(-1147 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1187 RC P) +(-1148 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1188 |Coef| |var| |cen|) +(-1149 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) (-4139 . 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T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-146))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499))) (|devaluate| |#1|)))) (|HasCategory| (-361 (-499)) (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-318))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510)))) (-3677 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasSignature| |#1| (|%list| (QUOTE -4096) (|%list| (|devaluate| |#1|) (QUOTE (-1117)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499)))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-898))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-499))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasSignature| |#1| (|%list| (QUOTE -3962) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1117))))) (|HasSignature| |#1| (|%list| (QUOTE -3204) (|%list| (|%list| (QUOTE -599) (QUOTE (-1117))) (|devaluate| |#1|))))))) -(-1189 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-308)) (-3971 |has| |#1| (-308)) (-3973 . 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T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|)))) (|HasCategory| (-343 (-478)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-308))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasSignature| |#1| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#1|) (QUOTE (-1079)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasSignature| |#1| (|%list| (QUOTE -3796) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1079))))) (|HasSignature| |#1| (|%list| (QUOTE -3065) (|%list| (|%list| (QUOTE -578) (QUOTE (-1079))) (|devaluate| |#1|))))))) +(-1150 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1190 |Coef|) +(-1151 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4143 |has| |#1| (-318)) (-4137 |has| |#1| (-318)) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-308)) (-3971 |has| |#1| (-308)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1191 S |Coef| ULS) +(-1152 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1192 |Coef| ULS) +(-1153 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) 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T)) -((|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-146))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499))) (|devaluate| |#1|)))) (|HasCategory| (-361 (-499)) (QUOTE (-1052))) (|HasCategory| |#1| (QUOTE (-318))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510)))) (-3677 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-510)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasSignature| |#1| (|%list| (QUOTE -4096) (|%list| (|devaluate| |#1|) (QUOTE (-1117)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -361) (QUOTE (-499)))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-898))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-499))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasSignature| |#1| (|%list| (QUOTE -3962) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1117))))) (|HasSignature| |#1| (|%list| (QUOTE -3204) (|%list| (|%list| (QUOTE -599) (QUOTE (-1117))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499)))))) -(-1194 R FE |var| |cen|) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3977 |has| |#1| (-308)) (-3971 |has| |#1| (-308)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#1| (QUOTE (-144))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478))) (|devaluate| |#1|)))) (|HasCategory| (-343 (-478)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-308))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (OR (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-489)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasSignature| |#1| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#1|) (QUOTE (-1079)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -343) (QUOTE (-478)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasSignature| |#1| (|%list| (QUOTE -3796) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1079))))) (|HasSignature| |#1| (|%list| (QUOTE -3065) (|%list| (|%list| (QUOTE -578) (QUOTE (-1079))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478)))))) +(-1155 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))}."))) -(((-4147 "*") |has| (-1188 |#2| |#3| |#4|) (-146)) (-4138 |has| (-1188 |#2| |#3| |#4|) (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) -((|HasCategory| (-1188 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-1188 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1188 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1188 |#2| |#3| |#4|) (QUOTE (-146))) (-3677 (|HasCategory| (-1188 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-1188 |#2| |#3| |#4|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499)))))) (|HasCategory| (-1188 |#2| |#3| |#4|) (|%list| (QUOTE -978) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| (-1188 |#2| |#3| |#4|) (|%list| (QUOTE -978) (QUOTE (-499)))) (|HasCategory| (-1188 |#2| |#3| |#4|) (QUOTE (-318))) (|HasCategory| (-1188 |#2| |#3| |#4|) (QUOTE (-406))) (|HasCategory| (-1188 |#2| |#3| |#4|) (QUOTE (-510)))) -(-1195 A S) +(((-3981 "*") |has| (-1149 |#2| |#3| |#4|) (-144)) (-3972 |has| (-1149 |#2| |#3| |#4|) (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| (-1149 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-1149 |#2| |#3| |#4|) (QUOTE (-116))) (|HasCategory| (-1149 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1149 |#2| |#3| |#4|) (QUOTE (-144))) (OR (|HasCategory| (-1149 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-1149 |#2| |#3| |#4|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478)))))) (|HasCategory| (-1149 |#2| |#3| |#4|) (|%list| (QUOTE -943) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| (-1149 |#2| |#3| |#4|) (|%list| (QUOTE -943) (QUOTE (-478)))) (|HasCategory| (-1149 |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1149 |#2| |#3| |#4|) (QUOTE (-385))) (|HasCategory| (-1149 |#2| |#3| |#4|) (QUOTE (-489)))) +(-1156 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4146))) -(-1196 S) +((|HasAttribute| |#1| (QUOTE -3980))) +(-1157 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{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})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1197 |Coef| |var| |cen|) +(-1158 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . 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T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-510))) (-3677 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-510)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -836) (QUOTE (-1117)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-714)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-714)) (|devaluate| |#1|)))) (|HasCategory| (-714) (QUOTE (-1052))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-714))))) (|HasSignature| |#1| (|%list| (QUOTE -4096) (|%list| (|devaluate| |#1|) (QUOTE (-1117)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-714))))) (|HasCategory| |#1| (QUOTE (-318))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-898))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-499))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasSignature| |#1| (|%list| (QUOTE -3962) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1117))))) (|HasSignature| |#1| (|%list| (QUOTE -3204) (|%list| (|%list| (QUOTE -599) (QUOTE (-1117))) (|devaluate| |#1|))))))) -(-1198 |Coef1| |Coef2| UTS1 UTS2) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (QUOTE (-489))) (OR (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-489)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-116))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -802) (QUOTE (-1079)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-687)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-687)) (|devaluate| |#1|)))) (|HasCategory| (-687) (QUOTE (-1015))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-687))))) (|HasSignature| |#1| (|%list| (QUOTE -3930) (|%list| (|devaluate| |#1|) (QUOTE (-1079)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-687))))) (|HasCategory| |#1| (QUOTE (-308))) (OR (-12 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-478))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasSignature| |#1| (|%list| (QUOTE -3796) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1079))))) (|HasSignature| |#1| (|%list| (QUOTE -3065) (|%list| (|%list| (QUOTE -578) (QUOTE (-1079))) (|devaluate| |#1|))))))) +(-1159 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1199 S |Coef|) +(-1160 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 (-499)))) (|HasCategory| |#2| (QUOTE (-898))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE -3204) (|%list| (|%list| (QUOTE -599) (QUOTE (-1117))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3962) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1117))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-318)))) -(-1200 |Coef|) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-478)))) (|HasCategory| |#2| (QUOTE (-864))) (|HasCategory| |#2| (QUOTE (-1104))) (|HasSignature| |#2| (|%list| (QUOTE -3065) (|%list| (|%list| (QUOTE -578) (QUOTE (-1079))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3796) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1079))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasCategory| |#2| (QUOTE (-308)))) +(-1161 |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."))) -(((-4147 "*") |has| |#1| (-146)) (-4138 |has| |#1| (-510)) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") |has| |#1| (-144)) (-3972 |has| |#1| (-489)) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1201 |Coef| UTS) +(-1162 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1202 -3215 UP L UTS) +(-1163 -3076 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 (-510)))) -(-1203) +((|HasCategory| |#1| (QUOTE (-489)))) +(-1164) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1204 |sym|) +(-1165 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1205 S R) +(-1166 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-942))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-684))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1206 R) +((|HasCategory| |#2| (QUOTE (-908))) (|HasCategory| |#2| (QUOTE (-954))) (|HasCategory| |#2| (QUOTE (-658))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1167 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4146 . T) (-4145 . T)) +((-3980 . T) (-3979 . T)) NIL -(-1207 R) +(-1168 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4146 . T) (-4145 . T)) -((-3677 (-12 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) (-3677 (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797))))) (|HasCategory| |#1| (|%list| (QUOTE -569) (QUOTE (-488)))) (-3677 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| |#1| (QUOTE (-781))) (-3677 (|HasCategory| |#1| (QUOTE (-73))) (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041)))) (|HasCategory| (-499) (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-684))) (|HasCategory| |#1| (QUOTE (-989))) (-12 (|HasCategory| |#1| (QUOTE (-942))) (|HasCategory| |#1| (QUOTE (-989)))) (|HasCategory| |#1| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#1| (QUOTE (-73))) (-12 (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -263) (|devaluate| |#1|))))) -(-1208 A B) +((-3980 . T) (-3979 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765))))) (|HasCategory| |#1| (|%list| (QUOTE -548) (QUOTE (-467)))) (OR (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| |#1| (QUOTE (-749))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005)))) (|HasCategory| (-478) (QUOTE (-749))) (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-658))) (|HasCategory| |#1| (QUOTE (-954))) (-12 (|HasCategory| |#1| (QUOTE (-908))) (|HasCategory| |#1| (QUOTE (-954)))) (|HasCategory| |#1| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1005))) (|HasCategory| |#1| (|%list| (QUOTE -256) (|devaluate| |#1|))))) +(-1169 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1209) +(-1170) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1210) +(-1171) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1211) +(-1172) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1212) +(-1173) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1213) +(-1174) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1214 A S) +(-1175 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1215 S) +(-1176 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4140 . T) (-4139 . T)) +((-3974 . T) (-3973 . T)) NIL -(-1216 R) +(-1177 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*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 -(-1217 K R UP -3215) +(-1178 K R UP -3076) ((|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 -(-1218) +(-1179) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1219) +(-1180) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1220 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1181 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4140 |has| |#1| (-146)) (-4139 |has| |#1| (-146)) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318)))) -(-1221 R E V P) +((-3974 |has| |#1| (-144)) (-3973 |has| |#1| (-144)) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308)))) +(-1182 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) -((-4146 . T) (-4145 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#4| (|%list| (QUOTE -263) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -569) (QUOTE (-488)))) (|HasCategory| |#4| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#3| (QUOTE (-323))) (|HasCategory| |#4| (|%list| (QUOTE -568) (QUOTE (-797)))) (|HasCategory| |#4| (QUOTE (-73)))) -(-1222 R) +((-3980 . T) (-3979 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#4| (|%list| (QUOTE -256) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -548) (QUOTE (-467)))) (|HasCategory| |#4| (QUOTE (-1005))) (|HasCategory| |#1| (QUOTE (-489))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#4| (|%list| (QUOTE -547) (QUOTE (-765)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-1183 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) -((-4139 . T) (-4140 . T) (-4142 . T)) +((-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1223 |vl| R) +(-1184 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4142 . T) (-4138 |has| |#2| (-6 -4138)) (-4140 . T) (-4139 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -4138))) -(-1224 R |VarSet| XPOLY) +((-3976 . T) (-3972 |has| |#2| (-6 -3972)) (-3974 . T) (-3973 . T)) +((|HasCategory| |#2| (QUOTE (-144))) (|HasAttribute| |#2| (QUOTE -3972))) +(-1185 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.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 -(-1225 S -3215) +(-1186 S -3076) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL -((|HasCategory| |#2| (QUOTE (-323))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) -(-1226 -3215) +((|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-116))) (|HasCategory| |#2| (QUOTE (-118)))) +(-1187 -3076) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-4137 . T) (-4143 . T) (-4138 . T) ((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +((-3971 . T) (-3977 . T) (-3972 . T) ((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL -(-1227 |vl| R) +(-1188 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4138 |has| |#2| (-6 -4138)) (-4140 . T) (-4139 . T) (-4142 . T)) +((-3972 |has| |#2| (-6 -3972)) (-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-1228 |VarSet| R) +(-1189 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4138 |has| |#2| (-6 -4138)) (-4140 . T) (-4139 . T) (-4142 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -675) (|%list| (QUOTE -361) (QUOTE (-499))))) (|HasAttribute| |#2| (QUOTE -4138))) -(-1229 R) +((-3972 |has| |#2| (-6 -3972)) (-3974 . T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (|%list| (QUOTE -649) (|%list| (QUOTE -343) (QUOTE (-478))))) (|HasAttribute| |#2| (QUOTE -3972))) +(-1190 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4138 |has| |#1| (-6 -4138)) (-4140 . T) (-4139 . T) (-4142 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -4138))) -(-1230 |vl| R) +((-3972 |has| |#1| (-6 -3972)) (-3974 . T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasAttribute| |#1| (QUOTE -3972))) +(-1191 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4138 |has| |#2| (-6 -4138)) (-4140 . T) (-4139 . T) (-4142 . T)) +((-3972 |has| |#2| (-6 -3972)) (-3974 . T) (-3973 . T) (-3976 . T)) NIL -(-1231 R E) +(-1192 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4142 . T) (-4143 |has| |#1| (-6 -4143)) (-4138 |has| |#1| (-6 -4138)) (-4140 . T) (-4139 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasAttribute| |#1| (QUOTE -4142)) (|HasAttribute| |#1| (QUOTE -4143)) (|HasAttribute| |#1| (QUOTE -4138))) -(-1232 |VarSet| R) +((-3976 . T) (-3977 |has| |#1| (-6 -3977)) (-3972 |has| |#1| (-6 -3972)) (-3974 . T) (-3973 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-308))) (|HasAttribute| |#1| (QUOTE -3976)) (|HasAttribute| |#1| (QUOTE -3977)) (|HasAttribute| |#1| (QUOTE -3972))) +(-1193 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4138 |has| |#2| (-6 -4138)) (-4140 . T) (-4139 . T) (-4142 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -4138))) -(-1233) +((-3972 |has| |#2| (-6 -3972)) (-3974 . T) (-3973 . T) (-3976 . T)) +((|HasCategory| |#2| (QUOTE (-144))) (|HasAttribute| |#2| (QUOTE -3972))) +(-1194) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL NIL -(-1234 A) +(-1195 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1235 R |ls| |ls2|) +(-1196 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}. ") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1236 R) +(-1197 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1237 |p|) +(-1198 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4147 "*") . T) (-4139 . T) (-4140 . T) (-4142 . T)) +(((-3981 "*") . T) (-3973 . T) (-3974 . T) (-3976 . T)) NIL NIL NIL @@ -4896,4 +4740,4 @@ NIL NIL NIL NIL -((-3 NIL 2094381 2094386 2094391 2094396) (-2 NIL 2094361 2094366 2094371 2094376) (-1 NIL 2094341 2094346 2094351 2094356) (0 NIL 2094321 2094326 2094331 2094336) (-1237 "ZMOD.spad" 2094130 2094143 2094259 2094316) (-1236 "ZLINDEP.spad" 2093228 2093239 2094120 2094125) (-1235 "ZDSOLVE.spad" 2083188 2083210 2093218 2093223) (-1234 "YSTREAM.spad" 2082683 2082694 2083178 2083183) (-1233 "YDIAGRAM.spad" 2082317 2082326 2082673 2082678) (-1232 "XRPOLY.spad" 2081537 2081557 2082173 2082242) (-1231 "XPR.spad" 2079332 2079345 2081255 2081354) (-1230 "XPOLYC.spad" 2078651 2078667 2079258 2079327) (-1229 "XPOLY.spad" 2078206 2078217 2078507 2078576) (-1228 "XPBWPOLY.spad" 2076645 2076665 2077980 2078049) (-1227 "XFALG.spad" 2073693 2073709 2076571 2076640) (-1226 "XF.spad" 2072156 2072171 2073595 2073688) (-1225 "XF.spad" 2070599 2070616 2072040 2072045) (-1224 "XEXPPKG.spad" 2069858 2069884 2070589 2070594) (-1223 "XDPOLY.spad" 2069472 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1937863) (-1167 "ULS.spad" 1926960 1926988 1927905 1928334) (-1166 "UINT8.spad" 1926837 1926846 1926950 1926955) (-1165 "UINT64.spad" 1926713 1926722 1926827 1926832) (-1164 "UINT32.spad" 1926589 1926598 1926703 1926708) (-1163 "UINT16.spad" 1926465 1926474 1926579 1926584) (-1162 "UFD.spad" 1925530 1925539 1926391 1926460) (-1161 "UFD.spad" 1924657 1924668 1925520 1925525) (-1160 "UDVO.spad" 1923538 1923547 1924647 1924652) (-1159 "UDPO.spad" 1921119 1921130 1923494 1923499) (-1158 "TYPEAST.spad" 1921038 1921047 1921109 1921114) (-1157 "TYPE.spad" 1920970 1920979 1921028 1921033) (-1156 "TWOFACT.spad" 1919622 1919637 1920960 1920965) (-1155 "TUPLE.spad" 1919113 1919124 1919518 1919523) (-1154 "TUBETOOL.spad" 1915980 1915989 1919103 1919108) (-1153 "TUBE.spad" 1914627 1914644 1915970 1915975) (-1152 "TSETCAT.spad" 1902698 1902715 1914595 1914622) (-1151 "TSETCAT.spad" 1890755 1890774 1902654 1902659) (-1150 "TS.spad" 1889348 1889364 1890314 1890411) (-1149 "TRMANIP.spad" 1883712 1883729 1889036 1889041) (-1148 "TRIMAT.spad" 1882675 1882700 1883702 1883707) (-1147 "TRIGMNIP.spad" 1881202 1881219 1882665 1882670) (-1146 "TRIGCAT.spad" 1880714 1880723 1881192 1881197) (-1145 "TRIGCAT.spad" 1880224 1880235 1880704 1880709) (-1144 "TREE.spad" 1878672 1878683 1879704 1879731) (-1143 "TRANFUN.spad" 1878511 1878520 1878662 1878667) (-1142 "TRANFUN.spad" 1878348 1878359 1878501 1878506) (-1141 "TOPSP.spad" 1878022 1878031 1878338 1878343) (-1140 "TOOLSIGN.spad" 1877685 1877696 1878012 1878017) (-1139 "TEXTFILE.spad" 1876246 1876255 1877675 1877680) (-1138 "TEX1.spad" 1875802 1875813 1876236 1876241) (-1137 "TEX.spad" 1872996 1873005 1875792 1875797) (-1136 "TEMUTL.spad" 1872551 1872560 1872986 1872991) (-1135 "TBCMPPK.spad" 1870652 1870675 1872541 1872546) (-1134 "TBAGG.spad" 1869710 1869733 1870632 1870647) (-1133 "TBAGG.spad" 1868776 1868801 1869700 1869705) (-1132 "TANEXP.spad" 1868184 1868195 1868766 1868771) (-1131 "TALGOP.spad" 1867908 1867919 1868174 1868179) (-1130 "TABLEAU.spad" 1867389 1867400 1867898 1867903) (-1129 "TABLE.spad" 1865300 1865323 1865570 1865597) (-1128 "TABLBUMP.spad" 1862079 1862090 1865290 1865295) (-1127 "SYSTEM.spad" 1861307 1861316 1862069 1862074) (-1126 "SYSSOLP.spad" 1858790 1858801 1861297 1861302) (-1125 "SYSPTR.spad" 1858689 1858698 1858780 1858785) (-1124 "SYSNNI.spad" 1857912 1857923 1858679 1858684) (-1123 "SYSINT.spad" 1857316 1857327 1857902 1857907) (-1122 "SYNTAX.spad" 1853650 1853659 1857306 1857311) (-1121 "SYMTAB.spad" 1851718 1851727 1853640 1853645) (-1120 "SYMS.spad" 1847747 1847756 1851708 1851713) (-1119 "SYMPOLY.spad" 1846730 1846741 1846812 1846939) (-1118 "SYMFUNC.spad" 1846231 1846242 1846720 1846725) (-1117 "SYMBOL.spad" 1843726 1843735 1846221 1846226) (-1116 "SWITCH.spad" 1840497 1840506 1843716 1843721) (-1115 "SUTS.spad" 1837476 1837504 1838895 1838992) (-1114 "SUPXS.spad" 1834678 1834706 1835527 1835676) (-1113 "SUPFRACF.spad" 1833783 1833801 1834668 1834673) (-1112 "SUP2.spad" 1833175 1833188 1833773 1833778) (-1111 "SUP.spad" 1829820 1829831 1830593 1830746) (-1110 "SUMRF.spad" 1828794 1828805 1829810 1829815) (-1109 "SUMFS.spad" 1828423 1828440 1828784 1828789) (-1108 "SULS.spad" 1817988 1818016 1818946 1819375) (-1107 "SUCHTAST.spad" 1817757 1817766 1817978 1817983) (-1106 "SUCH.spad" 1817447 1817462 1817747 1817752) (-1105 "SUBSPACE.spad" 1809578 1809593 1817437 1817442) (-1104 "SUBRESP.spad" 1808748 1808762 1809534 1809539) (-1103 "STTFNC.spad" 1805216 1805232 1808738 1808743) (-1102 "STTF.spad" 1801315 1801331 1805206 1805211) (-1101 "STTAYLOR.spad" 1793960 1793971 1801190 1801195) (-1100 "STRTBL.spad" 1791953 1791970 1792102 1792129) (-1099 "STRING.spad" 1790557 1790566 1790942 1790969) (-1098 "STREAM3.spad" 1790130 1790145 1790547 1790552) (-1097 "STREAM2.spad" 1789258 1789271 1790120 1790125) (-1096 "STREAM1.spad" 1788964 1788975 1789248 1789253) (-1095 "STREAM.spad" 1785752 1785763 1788359 1788374) (-1094 "STINPROD.spad" 1784688 1784704 1785742 1785747) (-1093 "STEPAST.spad" 1783922 1783931 1784678 1784683) (-1092 "STEP.spad" 1783239 1783248 1783912 1783917) (-1091 "STBL.spad" 1781265 1781293 1781432 1781447) (-1090 "STAGG.spad" 1779964 1779975 1781255 1781260) (-1089 "STAGG.spad" 1778661 1778674 1779954 1779959) (-1088 "STACK.spad" 1777891 1777902 1778141 1778168) (-1087 "SRING.spad" 1777651 1777660 1777881 1777886) (-1086 "SREGSET.spad" 1775351 1775368 1777253 1777280) (-1085 "SRDCMPK.spad" 1773928 1773948 1775341 1775346) (-1084 "SRAGG.spad" 1769111 1769120 1773896 1773923) (-1083 "SRAGG.spad" 1764314 1764325 1769101 1769106) (-1082 "SQMATRIX.spad" 1761809 1761827 1762725 1762812) (-1081 "SPLTREE.spad" 1756277 1756290 1761073 1761100) (-1080 "SPLNODE.spad" 1752897 1752910 1756267 1756272) (-1079 "SPFCAT.spad" 1751706 1751715 1752887 1752892) (-1078 "SPECOUT.spad" 1750258 1750267 1751696 1751701) (-1077 "SPADXPT.spad" 1742349 1742358 1750248 1750253) (-1076 "spad-parser.spad" 1741814 1741823 1742339 1742344) (-1075 "SPADAST.spad" 1741515 1741524 1741804 1741809) (-1074 "SPACEC.spad" 1725730 1725741 1741505 1741510) (-1073 "SPACE3.spad" 1725506 1725517 1725720 1725725) (-1072 "SORTPAK.spad" 1725055 1725068 1725462 1725467) (-1071 "SOLVETRA.spad" 1722818 1722829 1725045 1725050) (-1070 "SOLVESER.spad" 1721274 1721285 1722808 1722813) (-1069 "SOLVERAD.spad" 1717300 1717311 1721264 1721269) (-1068 "SOLVEFOR.spad" 1715762 1715780 1717290 1717295) (-1067 "SNTSCAT.spad" 1715362 1715379 1715730 1715757) (-1066 "SMTS.spad" 1713644 1713670 1714921 1715018) (-1065 "SMP.spad" 1711050 1711070 1711440 1711567) (-1064 "SMITH.spad" 1709895 1709920 1711040 1711045) (-1063 "SMATCAT.spad" 1708013 1708043 1709839 1709890) (-1062 "SMATCAT.spad" 1706063 1706095 1707891 1707896) (-1061 "SKAGG.spad" 1705032 1705043 1706031 1706058) (-1060 "SINT.spad" 1703972 1703981 1704898 1705027) (-1059 "SIMPAN.spad" 1703700 1703709 1703962 1703967) (-1058 "SIGNRF.spad" 1702825 1702836 1703690 1703695) (-1057 "SIGNEF.spad" 1702111 1702128 1702815 1702820) (-1056 "SIGAST.spad" 1701528 1701537 1702101 1702106) (-1055 "SIG.spad" 1700890 1700899 1701518 1701523) (-1054 "SHP.spad" 1698834 1698849 1700846 1700851) (-1053 "SHDP.spad" 1686264 1686291 1686781 1686878) (-1052 "SGROUP.spad" 1685872 1685881 1686254 1686259) (-1051 "SGROUP.spad" 1685478 1685489 1685862 1685867) (-1050 "SGCF.spad" 1678617 1678626 1685468 1685473) (-1049 "SFRTCAT.spad" 1677563 1677580 1678585 1678612) (-1048 "SFRGCD.spad" 1676626 1676646 1677553 1677558) (-1047 "SFQCMPK.spad" 1671439 1671459 1676616 1676621) (-1046 "SFORT.spad" 1670878 1670892 1671429 1671434) (-1045 "SEXOF.spad" 1670721 1670761 1670868 1670873) (-1044 "SEXCAT.spad" 1668549 1668589 1670711 1670716) (-1043 "SEX.spad" 1668441 1668450 1668539 1668544) (-1042 "SETMN.spad" 1666901 1666918 1668431 1668436) (-1041 "SETCAT.spad" 1666386 1666395 1666891 1666896) (-1040 "SETCAT.spad" 1665869 1665880 1666376 1666381) (-1039 "SETAGG.spad" 1662418 1662429 1665849 1665864) (-1038 "SETAGG.spad" 1658975 1658988 1662408 1662413) (-1037 "SET.spad" 1657249 1657260 1658346 1658385) (-1036 "SEQAST.spad" 1656952 1656961 1657239 1657244) (-1035 "SEGXCAT.spad" 1656108 1656121 1656942 1656947) (-1034 "SEGCAT.spad" 1655033 1655044 1656098 1656103) (-1033 "SEGBIND2.spad" 1654731 1654744 1655023 1655028) (-1032 "SEGBIND.spad" 1654489 1654500 1654678 1654683) (-1031 "SEGAST.spad" 1654219 1654228 1654479 1654484) (-1030 "SEG2.spad" 1653654 1653667 1654175 1654180) (-1029 "SEG.spad" 1653467 1653478 1653573 1653578) (-1028 "SDVAR.spad" 1652743 1652754 1653457 1653462) (-1027 "SDPOL.spad" 1650001 1650012 1650292 1650419) (-1026 "SCPKG.spad" 1648090 1648101 1649991 1649996) (-1025 "SCOPE.spad" 1647267 1647276 1648080 1648085) (-1024 "SCACHE.spad" 1645963 1645974 1647257 1647262) (-1023 "SASTCAT.spad" 1645872 1645881 1645953 1645958) (-1022 "SAOS.spad" 1645744 1645753 1645862 1645867) (-1021 "SAERFFC.spad" 1645457 1645477 1645734 1645739) (-1020 "SAEFACT.spad" 1645158 1645178 1645447 1645452) (-1019 "SAE.spad" 1642595 1642611 1643206 1643341) (-1018 "RURPK.spad" 1640254 1640270 1642585 1642590) (-1017 "RULESET.spad" 1639707 1639731 1640244 1640249) (-1016 "RULECOLD.spad" 1639559 1639572 1639697 1639702) (-1015 "RULE.spad" 1637807 1637831 1639549 1639554) (-1014 "RTVALUE.spad" 1637542 1637551 1637797 1637802) (-1013 "RSTRCAST.spad" 1637259 1637268 1637532 1637537) (-1012 "RSETGCD.spad" 1633701 1633721 1637249 1637254) (-1011 "RSETCAT.spad" 1623669 1623686 1633669 1633696) (-1010 "RSETCAT.spad" 1613657 1613676 1623659 1623664) (-1009 "RSDCMPK.spad" 1612157 1612177 1613647 1613652) (-1008 "RRCC.spad" 1610541 1610571 1612147 1612152) (-1007 "RRCC.spad" 1608923 1608955 1610531 1610536) (-1006 "RPTAST.spad" 1608625 1608634 1608913 1608918) (-1005 "RPOLCAT.spad" 1588129 1588144 1608493 1608620) (-1004 "RPOLCAT.spad" 1567330 1567347 1587696 1587701) (-1003 "ROUTINE.spad" 1562709 1562718 1565457 1565484) (-1002 "ROMAN.spad" 1562037 1562046 1562575 1562704) (-1001 "ROIRC.spad" 1561117 1561149 1562027 1562032) (-1000 "RNS.spad" 1560093 1560102 1561019 1561112) (-999 "RNS.spad" 1559156 1559166 1560083 1560088) (-998 "RNGBIND.spad" 1558317 1558330 1559111 1559116) (-997 "RNG.spad" 1558053 1558061 1558307 1558312) (-996 "RMODULE.spad" 1557835 1557845 1558043 1558048) (-995 "RMCAT2.spad" 1557256 1557312 1557825 1557830) (-994 "RMATRIX.spad" 1556028 1556046 1556370 1556409) (-993 "RMATCAT.spad" 1551608 1551638 1555984 1556023) (-992 "RMATCAT.spad" 1547078 1547110 1551456 1551461) (-991 "RLINSET.spad" 1546783 1546793 1547068 1547073) (-990 "RINTERP.spad" 1546672 1546691 1546773 1546778) (-989 "RING.spad" 1546143 1546151 1546652 1546667) (-988 "RING.spad" 1545622 1545632 1546133 1546138) (-987 "RIDIST.spad" 1545015 1545023 1545612 1545617) (-986 "RGCHAIN.spad" 1543538 1543553 1544431 1544458) (-985 "RGBCSPC.spad" 1543328 1543339 1543528 1543533) (-984 "RGBCMDL.spad" 1542891 1542902 1543318 1543323) (-983 "RFFACTOR.spad" 1542354 1542364 1542881 1542886) (-982 "RFFACT.spad" 1542090 1542101 1542344 1542349) (-981 "RFDIST.spad" 1541087 1541095 1542080 1542085) (-980 "RF.spad" 1538762 1538772 1541077 1541082) (-979 "RETSOL.spad" 1538182 1538194 1538752 1538757) (-978 "RETRACT.spad" 1537611 1537621 1538172 1538177) (-977 "RETRACT.spad" 1537038 1537050 1537601 1537606) (-976 "RETAST.spad" 1536851 1536859 1537028 1537033) (-975 "RESULT.spad" 1534392 1534400 1534978 1535005) (-974 "RESRING.spad" 1533740 1533786 1534330 1534387) (-973 "RESLATC.spad" 1533065 1533075 1533730 1533735) (-972 "REPSQ.spad" 1532797 1532807 1533055 1533060) (-971 "REPDB.spad" 1532505 1532515 1532787 1532792) (-970 "REP2.spad" 1522220 1522230 1532347 1532352) (-969 "REP1.spad" 1516441 1516451 1522170 1522175) (-968 "REP.spad" 1513996 1514004 1516431 1516436) (-967 "REGSET.spad" 1511790 1511806 1513598 1513625) (-966 "REF.spad" 1511126 1511136 1511745 1511750) (-965 "REDORDER.spad" 1510333 1510349 1511116 1511121) (-964 "RECLOS.spad" 1509099 1509118 1509802 1509895) (-963 "REALSOLV.spad" 1508240 1508248 1509089 1509094) (-962 "REAL0Q.spad" 1505539 1505553 1508230 1508235) (-961 "REAL0.spad" 1502384 1502398 1505529 1505534) (-960 "REAL.spad" 1502257 1502265 1502374 1502379) (-959 "RDUCEAST.spad" 1501979 1501987 1502247 1502252) (-958 "RDIV.spad" 1501635 1501659 1501969 1501974) (-957 "RDIST.spad" 1501203 1501213 1501625 1501630) (-956 "RDETRS.spad" 1500068 1500085 1501193 1501198) (-955 "RDETR.spad" 1498208 1498225 1500058 1500063) (-954 "RDEEFS.spad" 1497308 1497324 1498198 1498203) (-953 "RDEEF.spad" 1496319 1496335 1497298 1497303) (-952 "RCFIELD.spad" 1493538 1493546 1496221 1496314) (-951 "RCFIELD.spad" 1490843 1490853 1493528 1493533) (-950 "RCAGG.spad" 1488780 1488790 1490833 1490838) (-949 "RCAGG.spad" 1486644 1486656 1488699 1488704) (-948 "RATRET.spad" 1486005 1486015 1486634 1486639) (-947 "RATFACT.spad" 1485698 1485709 1485995 1486000) (-946 "RANDSRC.spad" 1485018 1485026 1485688 1485693) (-945 "RADUTIL.spad" 1484775 1484783 1485008 1485013) (-944 "RADIX.spad" 1481558 1481571 1483103 1483196) (-943 "RADFF.spad" 1479265 1479301 1479383 1479539) (-942 "RADCAT.spad" 1478861 1478869 1479255 1479260) (-941 "RADCAT.spad" 1478455 1478465 1478851 1478856) (-940 "QUEUE.spad" 1477677 1477687 1477935 1477962) (-939 "QUATCT2.spad" 1477298 1477316 1477667 1477672) (-938 "QUATCAT.spad" 1475469 1475479 1477228 1477293) (-937 "QUATCAT.spad" 1473388 1473400 1475149 1475154) (-936 "QUAT.spad" 1471844 1471854 1472186 1472251) (-935 "QUAGG.spad" 1470678 1470688 1471812 1471839) (-934 "QQUTAST.spad" 1470447 1470455 1470668 1470673) (-933 "QFORM.spad" 1470066 1470080 1470437 1470442) (-932 "QFCAT2.spad" 1469759 1469775 1470056 1470061) (-931 "QFCAT.spad" 1468462 1468472 1469661 1469754) (-930 "QFCAT.spad" 1466750 1466762 1467951 1467956) (-929 "QEQUAT.spad" 1466309 1466317 1466740 1466745) (-928 "QCMPACK.spad" 1461224 1461243 1466299 1466304) (-927 "QALGSET2.spad" 1459220 1459238 1461214 1461219) (-926 "QALGSET.spad" 1455325 1455357 1459134 1459139) (-925 "PWFFINTB.spad" 1452741 1452762 1455315 1455320) (-924 "PUSHVAR.spad" 1452080 1452099 1452731 1452736) (-923 "PTRANFN.spad" 1448216 1448226 1452070 1452075) (-922 "PTPACK.spad" 1445304 1445314 1448206 1448211) (-921 "PTFUNC2.spad" 1445127 1445141 1445294 1445299) (-920 "PTCAT.spad" 1444382 1444392 1445095 1445122) (-919 "PSQFR.spad" 1443697 1443721 1444372 1444377) (-918 "PSEUDLIN.spad" 1442583 1442593 1443687 1443692) (-917 "PSETPK.spad" 1429288 1429304 1442461 1442466) (-916 "PSETCAT.spad" 1423688 1423711 1429268 1429283) (-915 "PSETCAT.spad" 1418062 1418087 1423644 1423649) (-914 "PSCURVE.spad" 1417061 1417069 1418052 1418057) (-913 "PSCAT.spad" 1415844 1415873 1416959 1417056) (-912 "PSCAT.spad" 1414717 1414748 1415834 1415839) (-911 "PRTITION.spad" 1413415 1413423 1414707 1414712) (-910 "PRTDAST.spad" 1413134 1413142 1413405 1413410) (-909 "PRS.spad" 1402752 1402769 1413090 1413095) (-908 "PRQAGG.spad" 1402187 1402197 1402720 1402747) (-907 "PROPLOG.spad" 1401791 1401799 1402177 1402182) (-906 "PROPFUN2.spad" 1401414 1401427 1401781 1401786) (-905 "PROPFUN1.spad" 1400820 1400831 1401404 1401409) (-904 "PROPFRML.spad" 1399388 1399399 1400810 1400815) (-903 "PROPERTY.spad" 1398884 1398892 1399378 1399383) (-902 "PRODUCT.spad" 1396566 1396578 1396850 1396905) (-901 "PRINT.spad" 1396318 1396326 1396556 1396561) (-900 "PRIMES.spad" 1394579 1394589 1396308 1396313) (-899 "PRIMELT.spad" 1392700 1392714 1394569 1394574) (-898 "PRIMCAT.spad" 1392343 1392351 1392690 1392695) (-897 "PRIMARR2.spad" 1391110 1391122 1392333 1392338) (-896 "PRIMARR.spad" 1389951 1389961 1390121 1390148) (-895 "PREASSOC.spad" 1389333 1389345 1389941 1389946) (-894 "PR.spad" 1387701 1387713 1388400 1388527) (-893 "PPCURVE.spad" 1386838 1386846 1387691 1387696) (-892 "PORTNUM.spad" 1386629 1386637 1386828 1386833) (-891 "POLYROOT.spad" 1385478 1385500 1386585 1386590) (-890 "POLYLIFT.spad" 1384743 1384766 1385468 1385473) (-889 "POLYCATQ.spad" 1382869 1382891 1384733 1384738) (-888 "POLYCAT.spad" 1376371 1376392 1382737 1382864) (-887 "POLYCAT.spad" 1369169 1369192 1375537 1375542) (-886 "POLY2UP.spad" 1368621 1368635 1369159 1369164) (-885 "POLY2.spad" 1368218 1368230 1368611 1368616) (-884 "POLY.spad" 1365484 1365494 1365999 1366126) (-883 "POLUTIL.spad" 1364449 1364478 1365440 1365445) (-882 "POLTOPOL.spad" 1363197 1363212 1364439 1364444) (-881 "POINT.spad" 1361866 1361876 1361953 1361980) (-880 "PNTHEORY.spad" 1358568 1358576 1361856 1361861) (-879 "PMTOOLS.spad" 1357343 1357357 1358558 1358563) (-878 "PMSYM.spad" 1356892 1356902 1357333 1357338) (-877 "PMQFCAT.spad" 1356483 1356497 1356882 1356887) (-876 "PMPREDFS.spad" 1355945 1355967 1356473 1356478) (-875 "PMPRED.spad" 1355432 1355446 1355935 1355940) (-874 "PMPLCAT.spad" 1354509 1354527 1355361 1355366) (-873 "PMLSAGG.spad" 1354094 1354108 1354499 1354504) (-872 "PMKERNEL.spad" 1353673 1353685 1354084 1354089) (-871 "PMINS.spad" 1353253 1353263 1353663 1353668) (-870 "PMFS.spad" 1352830 1352848 1353243 1353248) (-869 "PMDOWN.spad" 1352120 1352134 1352820 1352825) (-868 "PMASSFS.spad" 1351095 1351111 1352110 1352115) (-867 "PMASS.spad" 1350113 1350121 1351085 1351090) (-866 "PLOTTOOL.spad" 1349893 1349901 1350103 1350108) (-865 "PLOT3D.spad" 1346357 1346365 1349883 1349888) (-864 "PLOT1.spad" 1345530 1345540 1346347 1346352) (-863 "PLOT.spad" 1340453 1340461 1345520 1345525) (-862 "PLEQN.spad" 1327855 1327882 1340443 1340448) (-861 "PINTERPA.spad" 1327639 1327655 1327845 1327850) (-860 "PINTERP.spad" 1327261 1327280 1327629 1327634) (-859 "PID.spad" 1326235 1326243 1327187 1327256) (-858 "PICOERCE.spad" 1325892 1325902 1326225 1326230) (-857 "PI.spad" 1325509 1325517 1325866 1325887) (-856 "PGROEB.spad" 1324118 1324132 1325499 1325504) (-855 "PGE.spad" 1315791 1315799 1324108 1324113) (-854 "PGCD.spad" 1314745 1314762 1315781 1315786) (-853 "PFRPAC.spad" 1313894 1313904 1314735 1314740) (-852 "PFR.spad" 1310597 1310607 1313796 1313889) (-851 "PFOTOOLS.spad" 1309855 1309871 1310587 1310592) (-850 "PFOQ.spad" 1309225 1309243 1309845 1309850) (-849 "PFO.spad" 1308644 1308671 1309215 1309220) (-848 "PFECAT.spad" 1306354 1306362 1308570 1308639) (-847 "PFECAT.spad" 1304092 1304102 1306310 1306315) (-846 "PFBRU.spad" 1301980 1301992 1304082 1304087) (-845 "PFBR.spad" 1299540 1299563 1301970 1301975) (-844 "PF.spad" 1299114 1299126 1299345 1299438) (-843 "PERMGRP.spad" 1293884 1293894 1299104 1299109) (-842 "PERMCAT.spad" 1292545 1292555 1293864 1293879) (-841 "PERMAN.spad" 1291101 1291115 1292535 1292540) (-840 "PERM.spad" 1286908 1286918 1290931 1290946) (-839 "PENDTREE.spad" 1286130 1286140 1286410 1286415) (-838 "PDSPC.spad" 1284943 1284953 1286120 1286125) (-837 "PDSPC.spad" 1283754 1283766 1284933 1284938) (-836 "PDRING.spad" 1283596 1283606 1283734 1283749) (-835 "PDMOD.spad" 1283412 1283424 1283564 1283591) (-834 "PDEPROB.spad" 1282427 1282435 1283402 1283407) (-833 "PDECOMP.spad" 1281897 1281914 1282417 1282422) (-832 "PDECAT.spad" 1280253 1280261 1281887 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(-194 "DIRPCAT.spad" 220240 220258 220945 220950) (-193 "DIOSP.spad" 219065 219073 220230 220235) (-192 "DIOPS.spad" 218061 218071 219045 219060) (-191 "DIOPS.spad" 217031 217043 218017 218022) (-190 "DIFRING.spad" 216869 216877 217011 217026) (-189 "DIFFSPC.spad" 216448 216456 216859 216864) (-188 "DIFFSPC.spad" 216025 216035 216438 216443) (-187 "DIFFMOD.spad" 215514 215524 215993 216020) (-186 "DIFFDOM.spad" 214679 214690 215504 215509) (-185 "DIFFDOM.spad" 213842 213855 214669 214674) (-184 "DIFEXT.spad" 213661 213671 213822 213837) (-183 "DIAGG.spad" 213291 213301 213641 213656) (-182 "DIAGG.spad" 212929 212941 213281 213286) (-181 "DHMATRIX.spad" 211114 211124 212259 212286) (-180 "DFSFUN.spad" 204754 204762 211104 211109) (-179 "DFLOAT.spad" 201361 201369 204644 204749) (-178 "DFINTTLS.spad" 199592 199608 201351 201356) (-177 "DERHAM.spad" 197506 197538 199572 199587) (-176 "DEQUEUE.spad" 196703 196713 196986 197013) (-175 "DEGRED.spad" 196320 196334 196693 196698) (-174 "DEFINTRF.spad" 193902 193912 196310 196315) (-173 "DEFINTEF.spad" 192440 192456 193892 193897) (-172 "DEFAST.spad" 191824 191832 192430 192435) (-171 "DECIMAL.spad" 189791 189799 190152 190245) (-170 "DDFACT.spad" 187612 187629 189781 189786) (-169 "DBLRESP.spad" 187212 187236 187602 187607) (-168 "DBASIS.spad" 186838 186853 187202 187207) (-167 "DBASE.spad" 185502 185512 186828 186833) (-166 "DATAARY.spad" 184988 185001 185492 185497) (-165 "CYCLOTOM.spad" 184494 184502 184978 184983) (-164 "CYCLES.spad" 181286 181294 184484 184489) (-163 "CVMP.spad" 180703 180713 181276 181281) (-162 "CTRIGMNP.spad" 179203 179219 180693 180698) (-161 "CTORKIND.spad" 178806 178814 179193 179198) (-160 "CTORCAT.spad" 178047 178055 178796 178801) (-159 "CTORCAT.spad" 177286 177296 178037 178042) (-158 "CTORCALL.spad" 176875 176885 177276 177281) (-157 "CTOR.spad" 176566 176574 176865 176870) (-156 "CSTTOOLS.spad" 175811 175824 176556 176561) (-155 "CRFP.spad" 169583 169596 175801 175806) (-154 "CRCEAST.spad" 169303 169311 169573 169578) (-153 "CRAPACK.spad" 168370 168380 169293 169298) (-152 "CPMATCH.spad" 167871 167886 168292 168297) (-151 "CPIMA.spad" 167576 167595 167861 167866) (-150 "COORDSYS.spad" 162585 162595 167566 167571) (-149 "CONTOUR.spad" 162012 162020 162575 162580) (-148 "CONTFRAC.spad" 157762 157772 161914 162007) (-147 "CONDUIT.spad" 157520 157528 157752 157757) (-146 "COMRING.spad" 157194 157202 157458 157515) (-145 "COMPPROP.spad" 156712 156720 157184 157189) (-144 "COMPLPAT.spad" 156479 156494 156702 156707) (-143 "COMPLEX2.spad" 156194 156206 156469 156474) (-142 "COMPLEX.spad" 151546 151556 151790 152051) (-141 "COMPILER.spad" 151095 151103 151536 151541) (-140 "COMPFACT.spad" 150697 150711 151085 151090) (-139 "COMPCAT.spad" 148769 148779 150431 150692) (-138 "COMPCAT.spad" 146568 146580 148232 148237) (-137 "COMMUPC.spad" 146316 146334 146558 146563) (-136 "COMMONOP.spad" 145849 145857 146306 146311) (-135 "COMMAAST.spad" 145612 145620 145839 145844) (-134 "COMM.spad" 145423 145431 145602 145607) (-133 "COMBOPC.spad" 144346 144354 145413 145418) (-132 "COMBINAT.spad" 143113 143123 144336 144341) (-131 "COMBF.spad" 140535 140551 143103 143108) (-130 "COLOR.spad" 139372 139380 140525 140530) (-129 "COLONAST.spad" 139038 139046 139362 139367) (-128 "CMPLXRT.spad" 138749 138766 139028 139033) (-127 "CLLCTAST.spad" 138411 138419 138739 138744) (-126 "CLIP.spad" 134519 134527 138401 138406) (-125 "CLIF.spad" 133174 133190 134475 134514) (-124 "CLAGG.spad" 129711 129721 133164 133169) (-123 "CLAGG.spad" 126116 126128 129571 129576) (-122 "CINTSLPE.spad" 125471 125484 126106 126111) (-121 "CHVAR.spad" 123609 123631 125461 125466) (-120 "CHARZ.spad" 123524 123532 123589 123604) (-119 "CHARPOL.spad" 123050 123060 123514 123519) (-118 "CHARNZ.spad" 122812 122820 123030 123045) (-117 "CHAR.spad" 120180 120188 122802 122807) (-116 "CFCAT.spad" 119508 119516 120170 120175) (-115 "CDEN.spad" 118728 118742 119498 119503) (-114 "CCLASS.spad" 116825 116833 118087 118126) (-113 "CATEGORY.spad" 115899 115907 116815 116820) (-112 "CATCTOR.spad" 115790 115798 115889 115894) (-111 "CATAST.spad" 115416 115424 115780 115785) (-110 "CASEAST.spad" 115130 115138 115406 115411) (-109 "CARTEN2.spad" 114520 114547 115120 115125) (-108 "CARTEN.spad" 110272 110296 114510 114515) (-107 "CARD.spad" 107567 107575 110246 110267) (-106 "CAPSLAST.spad" 107349 107357 107557 107562) (-105 "CACHSET.spad" 106973 106981 107339 107344) (-104 "CABMON.spad" 106528 106536 106963 106968) (-103 "BYTEORD.spad" 106203 106211 106518 106523) (-102 "BYTEBUF.spad" 103906 103914 105192 105219) (-101 "BYTE.spad" 103381 103389 103896 103901) (-100 "BTREE.spad" 102327 102337 102861 102888) (-99 "BTOURN.spad" 101206 101215 101807 101834) (-98 "BTCAT.spad" 100599 100608 101174 101201) (-97 "BTCAT.spad" 100012 100023 100589 100594) (-96 "BTAGG.spad" 99479 99486 99980 100007) (-95 "BTAGG.spad" 98966 98975 99469 99474) (-94 "BSTREE.spad" 97581 97590 98446 98473) (-93 "BRILL.spad" 95787 95797 97571 97576) (-92 "BRAGG.spad" 94744 94753 95777 95782) (-91 "BRAGG.spad" 93665 93676 94700 94705) (-90 "BPADICRT.spad" 91527 91538 91773 91866) (-89 "BPADIC.spad" 91200 91211 91453 91522) (-88 "BOUNDZRO.spad" 90857 90873 91190 91195) (-87 "BOP1.spad" 88316 88325 90847 90852) (-86 "BOP.spad" 83459 83466 88306 88311) (-85 "BOOLEAN.spad" 83008 83015 83449 83454) (-84 "BOOLE.spad" 82659 82666 82998 83003) (-83 "BOOLE.spad" 82308 82317 82649 82654) (-82 "BMODULE.spad" 82021 82032 82276 82303) (-81 "BITS.spad" 81405 81412 81619 81646) (-80 "BINDING.spad" 80827 80834 81395 81400) (-79 "BINARY.spad" 78800 78807 79155 79248) (-78 "BGAGG.spad" 78006 78015 78780 78795) (-77 "BGAGG.spad" 77220 77231 77996 78001) (-76 "BFUNCT.spad" 76785 76792 77200 77215) (-75 "BEZOUT.spad" 75926 75952 76735 76740) (-74 "BBTREE.spad" 72677 72686 75406 75433) (-73 "BASTYPE.spad" 72177 72184 72667 72672) (-72 "BASTYPE.spad" 71675 71684 72167 72172) (-71 "BALFACT.spad" 71135 71147 71665 71670) (-70 "AUTOMOR.spad" 70586 70595 71115 71130) (-69 "ATTREG.spad" 67309 67316 70338 70581) (-68 "ATTRBUT.spad" 63332 63339 67289 67304) (-67 "ATTRAST.spad" 63049 63056 63322 63327) (-66 "ATRIG.spad" 62519 62526 63039 63044) (-65 "ATRIG.spad" 61987 61996 62509 62514) (-64 "ASTCAT.spad" 61891 61898 61977 61982) (-63 "ASTCAT.spad" 61793 61802 61881 61886) (-62 "ASTACK.spad" 61005 61014 61273 61300) (-61 "ASSOCEQ.spad" 59839 59850 60961 60966) (-60 "ARRAY2.spad" 59080 59089 59319 59346) (-59 "ARRAY12.spad" 57793 57804 59070 59075) (-58 "ARRAY1.spad" 56458 56467 56804 56831) (-57 "ARR2CAT.spad" 52240 52261 56426 56453) (-56 "ARR2CAT.spad" 48042 48065 52230 52235) (-55 "ARITY.spad" 47414 47421 48032 48037) (-54 "APPRULE.spad" 46698 46720 47404 47409) (-53 "APPLYORE.spad" 46317 46330 46688 46693) (-52 "ANY1.spad" 45388 45397 46307 46312) (-51 "ANY.spad" 44239 44246 45378 45383) (-50 "ANTISYM.spad" 42684 42700 44219 44234) (-49 "ANON.spad" 42393 42400 42674 42679) (-48 "AN.spad" 40845 40852 42208 42301) (-47 "AMR.spad" 39030 39041 40743 40840) (-46 "AMR.spad" 37046 37059 38761 38766) (-45 "ALIST.spad" 33842 33863 34192 34219) (-44 "ALGSC.spad" 32977 33003 33714 33767) (-43 "ALGPKG.spad" 28760 28771 32933 32938) (-42 "ALGMFACT.spad" 27953 27967 28750 28755) (-41 "ALGMANIP.spad" 25438 25453 27781 27786) (-40 "ALGFF.spad" 23046 23073 23263 23419) (-39 "ALGFACT.spad" 22165 22175 23036 23041) (-38 "ALGEBRA.spad" 21998 22007 22121 22160) (-37 "ALGEBRA.spad" 21863 21874 21988 21993) (-36 "ALAGG.spad" 21375 21396 21831 21858) (-35 "AHYP.spad" 20756 20763 21365 21370) (-34 "AGG.spad" 19465 19472 20746 20751) (-33 "AGG.spad" 18138 18147 19421 19426) (-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 2005161 2005166 2005171 2005176) (-2 NIL 2005141 2005146 2005151 2005156) (-1 NIL 2005121 2005126 2005131 2005136) (0 NIL 2005101 2005106 2005111 2005116) (-1198 "ZMOD.spad" 2004910 2004923 2005039 2005096) (-1197 "ZLINDEP.spad" 2004008 2004019 2004900 2004905) (-1196 "ZDSOLVE.spad" 1993968 1993990 2003998 2004003) (-1195 "YSTREAM.spad" 1993463 1993474 1993958 1993963) (-1194 "YDIAGRAM.spad" 1993097 1993106 1993453 1993458) (-1193 "XRPOLY.spad" 1992317 1992337 1992953 1993022) (-1192 "XPR.spad" 1990112 1990125 1992035 1992134) (-1191 "XPOLYC.spad" 1989431 1989447 1990038 1990107) (-1190 "XPOLY.spad" 1988986 1988997 1989287 1989356) (-1189 "XPBWPOLY.spad" 1987425 1987445 1988760 1988829) (-1188 "XFALG.spad" 1984473 1984489 1987351 1987420) (-1187 "XF.spad" 1982936 1982951 1984375 1984468) (-1186 "XF.spad" 1981379 1981396 1982820 1982825) (-1185 "XEXPPKG.spad" 1980638 1980664 1981369 1981374) (-1184 "XDPOLY.spad" 1980252 1980268 1980494 1980563) (-1183 "XALG.spad" 1979920 1979931 1980208 1980247) (-1182 "WUTSET.spad" 1975891 1975908 1979522 1979549) (-1181 "WP.spad" 1975098 1975142 1975749 1975816) (-1180 "WHILEAST.spad" 1974896 1974905 1975088 1975093) (-1179 "WHEREAST.spad" 1974567 1974576 1974886 1974891) (-1178 "WFFINTBS.spad" 1972230 1972252 1974557 1974562) (-1177 "WEIER.spad" 1970452 1970463 1972220 1972225) (-1176 "VSPACE.spad" 1970125 1970136 1970420 1970447) (-1175 "VSPACE.spad" 1969818 1969831 1970115 1970120) (-1174 "VOID.spad" 1969495 1969504 1969808 1969813) (-1173 "VIEWDEF.spad" 1964696 1964705 1969485 1969490) (-1172 "VIEW3D.spad" 1948657 1948666 1964686 1964691) (-1171 "VIEW2D.spad" 1936556 1936565 1948647 1948652) (-1170 "VIEW.spad" 1934276 1934285 1936546 1936551) (-1169 "VECTOR2.spad" 1932915 1932928 1934266 1934271) (-1168 "VECTOR.spad" 1931432 1931443 1931683 1931710) (-1167 "VECTCAT.spad" 1929344 1929355 1931400 1931427) (-1166 "VECTCAT.spad" 1927065 1927078 1929123 1929128) (-1165 "VARIABLE.spad" 1926845 1926860 1927055 1927060) (-1164 "UTYPE.spad" 1926489 1926498 1926835 1926840) (-1163 "UTSODETL.spad" 1925784 1925808 1926445 1926450) (-1162 "UTSODE.spad" 1924000 1924020 1925774 1925779) (-1161 "UTSCAT.spad" 1921479 1921495 1923898 1923995) (-1160 "UTSCAT.spad" 1918578 1918596 1920999 1921004) (-1159 "UTS2.spad" 1918173 1918208 1918568 1918573) (-1158 "UTS.spad" 1913057 1913085 1916577 1916674) (-1157 "URAGG.spad" 1907778 1907789 1913047 1913052) (-1156 "URAGG.spad" 1902463 1902476 1907734 1907739) (-1155 "UPXSSING.spad" 1900087 1900113 1901523 1901656) (-1154 "UPXSCONS.spad" 1897777 1897797 1898150 1898299) (-1153 "UPXSCCA.spad" 1896348 1896368 1897623 1897772) (-1152 "UPXSCCA.spad" 1895061 1895083 1896338 1896343) (-1151 "UPXSCAT.spad" 1893650 1893666 1894907 1895056) (-1150 "UPXS2.spad" 1893193 1893246 1893640 1893645) (-1149 "UPXS.spad" 1890420 1890448 1891256 1891405) (-1148 "UPSQFREE.spad" 1888835 1888849 1890410 1890415) (-1147 "UPSCAT.spad" 1886630 1886654 1888733 1888830) (-1146 "UPSCAT.spad" 1884110 1884136 1886215 1886220) (-1145 "UPOLYC2.spad" 1883581 1883600 1884100 1884105) (-1144 "UPOLYC.spad" 1878661 1878672 1883423 1883576) (-1143 "UPOLYC.spad" 1873627 1873640 1878391 1878396) (-1142 "UPMP.spad" 1872559 1872572 1873617 1873622) (-1141 "UPDIVP.spad" 1872124 1872138 1872549 1872554) (-1140 "UPDECOMP.spad" 1870385 1870399 1872114 1872119) (-1139 "UPCDEN.spad" 1869602 1869618 1870375 1870380) (-1138 "UP2.spad" 1868966 1868987 1869592 1869597) (-1137 "UP.spad" 1866020 1866035 1866407 1866560) (-1136 "UNISEG2.spad" 1865517 1865530 1865976 1865981) (-1135 "UNISEG.spad" 1864870 1864881 1865436 1865441) (-1134 "UNIFACT.spad" 1863973 1863985 1864860 1864865) (-1133 "ULSCONS.spad" 1854942 1854962 1855312 1855461) (-1132 "ULSCCAT.spad" 1852679 1852699 1854788 1854937) (-1131 "ULSCCAT.spad" 1850524 1850546 1852635 1852640) (-1130 "ULSCAT.spad" 1848764 1848780 1850370 1850519) (-1129 "ULS2.spad" 1848278 1848331 1848754 1848759) (-1128 "ULS.spad" 1837910 1837938 1838855 1839278) (-1127 "UINT8.spad" 1837787 1837796 1837900 1837905) (-1126 "UINT64.spad" 1837663 1837672 1837777 1837782) (-1125 "UINT32.spad" 1837539 1837548 1837653 1837658) (-1124 "UINT16.spad" 1837415 1837424 1837529 1837534) (-1123 "UFD.spad" 1836480 1836489 1837341 1837410) (-1122 "UFD.spad" 1835607 1835618 1836470 1836475) (-1121 "UDVO.spad" 1834488 1834497 1835597 1835602) (-1120 "UDPO.spad" 1832069 1832080 1834444 1834449) (-1119 "TYPEAST.spad" 1831988 1831997 1832059 1832064) (-1118 "TYPE.spad" 1831920 1831929 1831978 1831983) (-1117 "TWOFACT.spad" 1830572 1830587 1831910 1831915) (-1116 "TUPLE.spad" 1830063 1830074 1830468 1830473) (-1115 "TUBETOOL.spad" 1826930 1826939 1830053 1830058) (-1114 "TUBE.spad" 1825577 1825594 1826920 1826925) (-1113 "TSETCAT.spad" 1813648 1813665 1825545 1825572) (-1112 "TSETCAT.spad" 1801705 1801724 1813604 1813609) (-1111 "TS.spad" 1800301 1800317 1801267 1801364) (-1110 "TRMANIP.spad" 1794665 1794682 1799989 1799994) (-1109 "TRIMAT.spad" 1793628 1793653 1794655 1794660) (-1108 "TRIGMNIP.spad" 1792155 1792172 1793618 1793623) (-1107 "TRIGCAT.spad" 1791667 1791676 1792145 1792150) (-1106 "TRIGCAT.spad" 1791177 1791188 1791657 1791662) (-1105 "TREE.spad" 1789631 1789642 1790663 1790690) (-1104 "TRANFUN.spad" 1789470 1789479 1789621 1789626) (-1103 "TRANFUN.spad" 1789307 1789318 1789460 1789465) (-1102 "TOPSP.spad" 1788981 1788990 1789297 1789302) (-1101 "TOOLSIGN.spad" 1788644 1788655 1788971 1788976) (-1100 "TEXTFILE.spad" 1787205 1787214 1788634 1788639) (-1099 "TEX1.spad" 1786761 1786772 1787195 1787200) (-1098 "TEX.spad" 1783955 1783964 1786751 1786756) (-1097 "TBCMPPK.spad" 1782056 1782079 1783945 1783950) (-1096 "TBAGG.spad" 1781114 1781137 1782036 1782051) (-1095 "TBAGG.spad" 1780180 1780205 1781104 1781109) (-1094 "TANEXP.spad" 1779588 1779599 1780170 1780175) (-1093 "TALGOP.spad" 1779312 1779323 1779578 1779583) (-1092 "TABLEAU.spad" 1778793 1778804 1779302 1779307) (-1091 "TABLE.spad" 1776719 1776742 1776989 1777016) (-1090 "TABLBUMP.spad" 1773498 1773509 1776709 1776714) (-1089 "SYSTEM.spad" 1772726 1772735 1773488 1773493) (-1088 "SYSSOLP.spad" 1770209 1770220 1772716 1772721) (-1087 "SYSPTR.spad" 1770108 1770117 1770199 1770204) (-1086 "SYSNNI.spad" 1769331 1769342 1770098 1770103) (-1085 "SYSINT.spad" 1768735 1768746 1769321 1769326) (-1084 "SYNTAX.spad" 1765069 1765078 1768725 1768730) (-1083 "SYMTAB.spad" 1763137 1763146 1765059 1765064) (-1082 "SYMS.spad" 1759166 1759175 1763127 1763132) (-1081 "SYMPOLY.spad" 1758155 1758166 1758237 1758364) (-1080 "SYMFUNC.spad" 1757656 1757667 1758145 1758150) (-1079 "SYMBOL.spad" 1755151 1755160 1757646 1757651) (-1078 "SUTS.spad" 1752136 1752164 1753555 1753652) (-1077 "SUPXS.spad" 1749350 1749378 1750199 1750348) (-1076 "SUPFRACF.spad" 1748455 1748473 1749340 1749345) (-1075 "SUP2.spad" 1747847 1747860 1748445 1748450) (-1074 "SUP.spad" 1744515 1744526 1745288 1745441) (-1073 "SUMRF.spad" 1743489 1743500 1744505 1744510) (-1072 "SUMFS.spad" 1743118 1743135 1743479 1743484) (-1071 "SULS.spad" 1732737 1732765 1733695 1734118) (-1070 "SUCHTAST.spad" 1732506 1732515 1732727 1732732) (-1069 "SUCH.spad" 1732196 1732211 1732496 1732501) (-1068 "SUBSPACE.spad" 1724327 1724342 1732186 1732191) (-1067 "SUBRESP.spad" 1723497 1723511 1724283 1724288) (-1066 "STTFNC.spad" 1719965 1719981 1723487 1723492) (-1065 "STTF.spad" 1716064 1716080 1719955 1719960) (-1064 "STTAYLOR.spad" 1708709 1708720 1715939 1715944) (-1063 "STRTBL.spad" 1706717 1706734 1706866 1706893) (-1062 "STRING.spad" 1705333 1705342 1705718 1705745) (-1061 "STREAM3.spad" 1704906 1704921 1705323 1705328) (-1060 "STREAM2.spad" 1704034 1704047 1704896 1704901) (-1059 "STREAM1.spad" 1703740 1703751 1704024 1704029) (-1058 "STREAM.spad" 1700534 1700545 1703141 1703156) (-1057 "STINPROD.spad" 1699470 1699486 1700524 1700529) (-1056 "STEPAST.spad" 1698704 1698713 1699460 1699465) (-1055 "STEP.spad" 1698021 1698030 1698694 1698699) (-1054 "STBL.spad" 1696062 1696090 1696229 1696244) (-1053 "STAGG.spad" 1694761 1694772 1696052 1696057) (-1052 "STAGG.spad" 1693458 1693471 1694751 1694756) (-1051 "STACK.spad" 1692694 1692705 1692944 1692971) (-1050 "SRING.spad" 1692454 1692463 1692684 1692689) (-1049 "SREGSET.spad" 1690154 1690171 1692056 1692083) (-1048 "SRDCMPK.spad" 1688731 1688751 1690144 1690149) (-1047 "SRAGG.spad" 1683914 1683923 1688699 1688726) (-1046 "SRAGG.spad" 1679117 1679128 1683904 1683909) (-1045 "SQMATRIX.spad" 1676618 1676636 1677534 1677621) (-1044 "SPLTREE.spad" 1671092 1671105 1675888 1675915) (-1043 "SPLNODE.spad" 1667712 1667725 1671082 1671087) (-1042 "SPFCAT.spad" 1666521 1666530 1667702 1667707) (-1041 "SPECOUT.spad" 1665073 1665082 1666511 1666516) (-1040 "SPADXPT.spad" 1657164 1657173 1665063 1665068) (-1039 "spad-parser.spad" 1656629 1656638 1657154 1657159) (-1038 "SPADAST.spad" 1656330 1656339 1656619 1656624) (-1037 "SPACEC.spad" 1640545 1640556 1656320 1656325) (-1036 "SPACE3.spad" 1640321 1640332 1640535 1640540) (-1035 "SORTPAK.spad" 1639870 1639883 1640277 1640282) (-1034 "SOLVETRA.spad" 1637633 1637644 1639860 1639865) (-1033 "SOLVESER.spad" 1636089 1636100 1637623 1637628) (-1032 "SOLVERAD.spad" 1632115 1632126 1636079 1636084) (-1031 "SOLVEFOR.spad" 1630577 1630595 1632105 1632110) (-1030 "SNTSCAT.spad" 1630177 1630194 1630545 1630572) (-1029 "SMTS.spad" 1628462 1628488 1629739 1629836) (-1028 "SMP.spad" 1625886 1625906 1626276 1626403) (-1027 "SMITH.spad" 1624731 1624756 1625876 1625881) (-1026 "SMATCAT.spad" 1622849 1622879 1624675 1624726) (-1025 "SMATCAT.spad" 1620899 1620931 1622727 1622732) (-1024 "SKAGG.spad" 1619868 1619879 1620867 1620894) (-1023 "SINT.spad" 1618808 1618817 1619734 1619863) (-1022 "SIMPAN.spad" 1618536 1618545 1618798 1618803) (-1021 "SIGNRF.spad" 1617661 1617672 1618526 1618531) (-1020 "SIGNEF.spad" 1616947 1616964 1617651 1617656) (-1019 "SIGAST.spad" 1616364 1616373 1616937 1616942) (-1018 "SIG.spad" 1615726 1615735 1616354 1616359) (-1017 "SHP.spad" 1613670 1613685 1615682 1615687) (-1016 "SHDP.spad" 1601157 1601184 1601674 1601771) (-1015 "SGROUP.spad" 1600765 1600774 1601147 1601152) (-1014 "SGROUP.spad" 1600371 1600382 1600755 1600760) (-1013 "SGCF.spad" 1593510 1593519 1600361 1600366) (-1012 "SFRTCAT.spad" 1592456 1592473 1593478 1593505) (-1011 "SFRGCD.spad" 1591519 1591539 1592446 1592451) (-1010 "SFQCMPK.spad" 1586332 1586352 1591509 1591514) (-1009 "SEXOF.spad" 1586175 1586215 1586322 1586327) (-1008 "SEXCAT.spad" 1584003 1584043 1586165 1586170) (-1007 "SEX.spad" 1583895 1583904 1583993 1583998) (-1006 "SETMN.spad" 1582355 1582372 1583885 1583890) (-1005 "SETCAT.spad" 1581840 1581849 1582345 1582350) (-1004 "SETCAT.spad" 1581323 1581334 1581830 1581835) (-1003 "SETAGG.spad" 1577872 1577883 1581303 1581318) (-1002 "SETAGG.spad" 1574429 1574442 1577862 1577867) (-1001 "SET.spad" 1572706 1572717 1573803 1573842) (-1000 "SEQAST.spad" 1572409 1572418 1572696 1572701) (-999 "SEGXCAT.spad" 1571566 1571578 1572399 1572404) (-998 "SEGCAT.spad" 1570492 1570502 1571556 1571561) (-997 "SEGBIND2.spad" 1570191 1570203 1570482 1570487) (-996 "SEGBIND.spad" 1569951 1569961 1570139 1570144) (-995 "SEGAST.spad" 1569682 1569690 1569941 1569946) (-994 "SEG2.spad" 1569118 1569130 1569638 1569643) (-993 "SEG.spad" 1568932 1568942 1569037 1569042) (-992 "SDVAR.spad" 1568209 1568219 1568922 1568927) (-991 "SDPOL.spad" 1565491 1565501 1565781 1565908) (-990 "SCPKG.spad" 1563581 1563591 1565481 1565486) (-989 "SCOPE.spad" 1562759 1562767 1563571 1563576) (-988 "SCACHE.spad" 1561456 1561466 1562749 1562754) (-987 "SASTCAT.spad" 1561366 1561374 1561446 1561451) (-986 "SAOS.spad" 1561239 1561247 1561356 1561361) (-985 "SAERFFC.spad" 1560953 1560972 1561229 1561234) (-984 "SAEFACT.spad" 1560655 1560674 1560943 1560948) (-983 "SAE.spad" 1558114 1558129 1558724 1558859) (-982 "RURPK.spad" 1555774 1555789 1558104 1558109) (-981 "RULESET.spad" 1555228 1555251 1555764 1555769) (-980 "RULECOLD.spad" 1555081 1555093 1555218 1555223) (-979 "RULE.spad" 1553330 1553353 1555071 1555076) (-978 "RTVALUE.spad" 1553066 1553074 1553320 1553325) (-977 "RSTRCAST.spad" 1552784 1552792 1553056 1553061) (-976 "RSETGCD.spad" 1549227 1549246 1552774 1552779) (-975 "RSETCAT.spad" 1539196 1539212 1549195 1549222) (-974 "RSETCAT.spad" 1529185 1529203 1539186 1539191) (-973 "RSDCMPK.spad" 1527686 1527705 1529175 1529180) (-972 "RRCC.spad" 1526071 1526100 1527676 1527681) (-971 "RRCC.spad" 1524454 1524485 1526061 1526066) (-970 "RPTAST.spad" 1524157 1524165 1524444 1524449) (-969 "RPOLCAT.spad" 1503662 1503676 1524025 1524152) (-968 "RPOLCAT.spad" 1482864 1482880 1503229 1503234) (-967 "ROMAN.spad" 1482193 1482201 1482730 1482859) (-966 "ROIRC.spad" 1481274 1481305 1482183 1482188) (-965 "RNS.spad" 1480251 1480259 1481176 1481269) (-964 "RNS.spad" 1479314 1479324 1480241 1480246) (-963 "RNGBIND.spad" 1478475 1478488 1479269 1479274) (-962 "RNG.spad" 1478211 1478219 1478465 1478470) (-961 "RMODULE.spad" 1477993 1478003 1478201 1478206) (-960 "RMCAT2.spad" 1477414 1477470 1477983 1477988) (-959 "RMATRIX.spad" 1476192 1476210 1476534 1476573) (-958 "RMATCAT.spad" 1471772 1471802 1476148 1476187) (-957 "RMATCAT.spad" 1467242 1467274 1471620 1471625) (-956 "RLINSET.spad" 1466947 1466957 1467232 1467237) (-955 "RINTERP.spad" 1466836 1466855 1466937 1466942) (-954 "RING.spad" 1466307 1466315 1466816 1466831) (-953 "RING.spad" 1465786 1465796 1466297 1466302) (-952 "RIDIST.spad" 1465179 1465187 1465776 1465781) (-951 "RGCHAIN.spad" 1463702 1463717 1464595 1464622) (-950 "RGBCSPC.spad" 1463492 1463503 1463692 1463697) (-949 "RGBCMDL.spad" 1463055 1463066 1463482 1463487) (-948 "RFFACTOR.spad" 1462518 1462528 1463045 1463050) (-947 "RFFACT.spad" 1462254 1462265 1462508 1462513) (-946 "RFDIST.spad" 1461251 1461259 1462244 1462249) (-945 "RF.spad" 1458926 1458936 1461241 1461246) (-944 "RETSOL.spad" 1458346 1458358 1458916 1458921) (-943 "RETRACT.spad" 1457775 1457785 1458336 1458341) (-942 "RETRACT.spad" 1457202 1457214 1457765 1457770) (-941 "RETAST.spad" 1457015 1457023 1457192 1457197) (-940 "RESRING.spad" 1456363 1456409 1456953 1457010) (-939 "RESLATC.spad" 1455688 1455698 1456353 1456358) (-938 "REPSQ.spad" 1455420 1455430 1455678 1455683) (-937 "REPDB.spad" 1455128 1455138 1455410 1455415) (-936 "REP2.spad" 1444843 1444853 1454970 1454975) (-935 "REP1.spad" 1439064 1439074 1444793 1444798) (-934 "REP.spad" 1436619 1436627 1439054 1439059) (-933 "REGSET.spad" 1434413 1434429 1436221 1436248) (-932 "REF.spad" 1433749 1433759 1434368 1434373) (-931 "REDORDER.spad" 1432956 1432972 1433739 1433744) (-930 "RECLOS.spad" 1431725 1431744 1432428 1432521) (-929 "REALSOLV.spad" 1430866 1430874 1431715 1431720) (-928 "REAL0Q.spad" 1428165 1428179 1430856 1430861) (-927 "REAL0.spad" 1425010 1425024 1428155 1428160) (-926 "REAL.spad" 1424883 1424891 1425000 1425005) (-925 "RDUCEAST.spad" 1424605 1424613 1424873 1424878) (-924 "RDIV.spad" 1424261 1424285 1424595 1424600) (-923 "RDIST.spad" 1423829 1423839 1424251 1424256) (-922 "RDETRS.spad" 1422694 1422711 1423819 1423824) (-921 "RDETR.spad" 1420834 1420851 1422684 1422689) (-920 "RDEEFS.spad" 1419934 1419950 1420824 1420829) (-919 "RDEEF.spad" 1418945 1418961 1419924 1419929) (-918 "RCFIELD.spad" 1416164 1416172 1418847 1418940) (-917 "RCFIELD.spad" 1413469 1413479 1416154 1416159) (-916 "RCAGG.spad" 1411406 1411416 1413459 1413464) (-915 "RCAGG.spad" 1409270 1409282 1411325 1411330) (-914 "RATRET.spad" 1408631 1408641 1409260 1409265) (-913 "RATFACT.spad" 1408324 1408335 1408621 1408626) (-912 "RANDSRC.spad" 1407644 1407652 1408314 1408319) (-911 "RADUTIL.spad" 1407401 1407409 1407634 1407639) (-910 "RADIX.spad" 1404190 1404203 1405735 1405828) (-909 "RADFF.spad" 1401915 1401951 1402033 1402189) (-908 "RADCAT.spad" 1401511 1401519 1401905 1401910) (-907 "RADCAT.spad" 1401105 1401115 1401501 1401506) (-906 "QUEUE.spad" 1400333 1400343 1400591 1400618) (-905 "QUATCT2.spad" 1399954 1399972 1400323 1400328) (-904 "QUATCAT.spad" 1398125 1398135 1399884 1399949) (-903 "QUATCAT.spad" 1396045 1396057 1397806 1397811) (-902 "QUAT.spad" 1394508 1394518 1394850 1394915) (-901 "QUAGG.spad" 1393342 1393352 1394476 1394503) (-900 "QQUTAST.spad" 1393111 1393119 1393332 1393337) (-899 "QFORM.spad" 1392730 1392744 1393101 1393106) (-898 "QFCAT2.spad" 1392423 1392439 1392720 1392725) (-897 "QFCAT.spad" 1391126 1391136 1392325 1392418) (-896 "QFCAT.spad" 1389414 1389426 1390615 1390620) (-895 "QEQUAT.spad" 1388973 1388981 1389404 1389409) (-894 "QCMPACK.spad" 1383888 1383907 1388963 1388968) (-893 "QALGSET2.spad" 1381884 1381902 1383878 1383883) (-892 "QALGSET.spad" 1377989 1378021 1381798 1381803) (-891 "PWFFINTB.spad" 1375405 1375426 1377979 1377984) (-890 "PUSHVAR.spad" 1374744 1374763 1375395 1375400) (-889 "PTRANFN.spad" 1370880 1370890 1374734 1374739) (-888 "PTPACK.spad" 1367968 1367978 1370870 1370875) (-887 "PTFUNC2.spad" 1367791 1367805 1367958 1367963) (-886 "PTCAT.spad" 1367046 1367056 1367759 1367786) (-885 "PSQFR.spad" 1366361 1366385 1367036 1367041) (-884 "PSEUDLIN.spad" 1365247 1365257 1366351 1366356) (-883 "PSETPK.spad" 1351952 1351968 1365125 1365130) (-882 "PSETCAT.spad" 1346352 1346375 1351932 1351947) (-881 "PSETCAT.spad" 1340726 1340751 1346308 1346313) (-880 "PSCURVE.spad" 1339725 1339733 1340716 1340721) (-879 "PSCAT.spad" 1338508 1338537 1339623 1339720) (-878 "PSCAT.spad" 1337381 1337412 1338498 1338503) (-877 "PRTITION.spad" 1336079 1336087 1337371 1337376) (-876 "PRTDAST.spad" 1335798 1335806 1336069 1336074) (-875 "PRS.spad" 1325416 1325433 1335754 1335759) (-874 "PRQAGG.spad" 1324851 1324861 1325384 1325411) (-873 "PROPLOG.spad" 1324455 1324463 1324841 1324846) (-872 "PROPFUN2.spad" 1324078 1324091 1324445 1324450) (-871 "PROPFUN1.spad" 1323484 1323495 1324068 1324073) (-870 "PROPFRML.spad" 1322052 1322063 1323474 1323479) (-869 "PROPERTY.spad" 1321548 1321556 1322042 1322047) (-868 "PRODUCT.spad" 1319245 1319257 1319529 1319584) (-867 "PRINT.spad" 1318997 1319005 1319235 1319240) (-866 "PRIMES.spad" 1317258 1317268 1318987 1318992) (-865 "PRIMELT.spad" 1315379 1315393 1317248 1317253) (-864 "PRIMCAT.spad" 1315022 1315030 1315369 1315374) (-863 "PRIMARR2.spad" 1313789 1313801 1315012 1315017) (-862 "PRIMARR.spad" 1312642 1312652 1312812 1312839) (-861 "PREASSOC.spad" 1312024 1312036 1312632 1312637) (-860 "PR.spad" 1310398 1310410 1311097 1311224) (-859 "PPCURVE.spad" 1309535 1309543 1310388 1310393) (-858 "PORTNUM.spad" 1309326 1309334 1309525 1309530) (-857 "POLYROOT.spad" 1308175 1308197 1309282 1309287) (-856 "POLYLIFT.spad" 1307440 1307463 1308165 1308170) (-855 "POLYCATQ.spad" 1305566 1305588 1307430 1307435) (-854 "POLYCAT.spad" 1299068 1299089 1305434 1305561) (-853 "POLYCAT.spad" 1291866 1291889 1298234 1298239) (-852 "POLY2UP.spad" 1291318 1291332 1291856 1291861) (-851 "POLY2.spad" 1290915 1290927 1291308 1291313) (-850 "POLY.spad" 1288199 1288209 1288714 1288841) (-849 "POLUTIL.spad" 1287164 1287193 1288155 1288160) (-848 "POLTOPOL.spad" 1285912 1285927 1287154 1287159) (-847 "POINT.spad" 1284593 1284603 1284680 1284707) (-846 "PNTHEORY.spad" 1281295 1281303 1284583 1284588) (-845 "PMTOOLS.spad" 1280070 1280084 1281285 1281290) (-844 "PMSYM.spad" 1279619 1279629 1280060 1280065) (-843 "PMQFCAT.spad" 1279210 1279224 1279609 1279614) (-842 "PMPREDFS.spad" 1278672 1278694 1279200 1279205) (-841 "PMPRED.spad" 1278159 1278173 1278662 1278667) (-840 "PMPLCAT.spad" 1277236 1277254 1278088 1278093) (-839 "PMLSAGG.spad" 1276821 1276835 1277226 1277231) (-838 "PMKERNEL.spad" 1276400 1276412 1276811 1276816) (-837 "PMINS.spad" 1275980 1275990 1276390 1276395) (-836 "PMFS.spad" 1275557 1275575 1275970 1275975) (-835 "PMDOWN.spad" 1274847 1274861 1275547 1275552) (-834 "PMASSFS.spad" 1273822 1273838 1274837 1274842) (-833 "PMASS.spad" 1272840 1272848 1273812 1273817) (-832 "PLOTTOOL.spad" 1272620 1272628 1272830 1272835) (-831 "PLOT3D.spad" 1269084 1269092 1272610 1272615) (-830 "PLOT1.spad" 1268257 1268267 1269074 1269079) (-829 "PLOT.spad" 1263180 1263188 1268247 1268252) (-828 "PLEQN.spad" 1250582 1250609 1263170 1263175) (-827 "PINTERPA.spad" 1250366 1250382 1250572 1250577) (-826 "PINTERP.spad" 1249988 1250007 1250356 1250361) (-825 "PID.spad" 1248962 1248970 1249914 1249983) (-824 "PICOERCE.spad" 1248619 1248629 1248952 1248957) (-823 "PI.spad" 1248236 1248244 1248593 1248614) (-822 "PGROEB.spad" 1246845 1246859 1248226 1248231) (-821 "PGE.spad" 1238518 1238526 1246835 1246840) (-820 "PGCD.spad" 1237472 1237489 1238508 1238513) (-819 "PFRPAC.spad" 1236621 1236631 1237462 1237467) (-818 "PFR.spad" 1233324 1233334 1236523 1236616) (-817 "PFOTOOLS.spad" 1232582 1232598 1233314 1233319) (-816 "PFOQ.spad" 1231952 1231970 1232572 1232577) (-815 "PFO.spad" 1231371 1231398 1231942 1231947) (-814 "PFECAT.spad" 1229081 1229089 1231297 1231366) (-813 "PFECAT.spad" 1226819 1226829 1229037 1229042) (-812 "PFBRU.spad" 1224707 1224719 1226809 1226814) (-811 "PFBR.spad" 1222267 1222290 1224697 1224702) (-810 "PF.spad" 1221841 1221853 1222072 1222165) (-809 "PERMGRP.spad" 1216611 1216621 1221831 1221836) (-808 "PERMCAT.spad" 1215272 1215282 1216591 1216606) (-807 "PERMAN.spad" 1213828 1213842 1215262 1215267) (-806 "PERM.spad" 1209638 1209648 1213661 1213676) (-805 "PENDTREE.spad" 1208866 1208876 1209146 1209151) (-804 "PDSPC.spad" 1207679 1207689 1208856 1208861) (-803 "PDSPC.spad" 1206490 1206502 1207669 1207674) (-802 "PDRING.spad" 1206332 1206342 1206470 1206485) (-801 "PDMOD.spad" 1206148 1206160 1206300 1206327) (-800 "PDECOMP.spad" 1205618 1205635 1206138 1206143) (-799 "PDDOM.spad" 1205056 1205069 1205608 1205613) (-798 "PDDOM.spad" 1204492 1204507 1205046 1205051) (-797 "PCOMP.spad" 1204345 1204358 1204482 1204487) (-796 "PBWLB.spad" 1202941 1202958 1204335 1204340) (-795 "PATTERN2.spad" 1202679 1202691 1202931 1202936) (-794 "PATTERN1.spad" 1201023 1201039 1202669 1202674) (-793 "PATTERN.spad" 1195594 1195604 1201013 1201018) (-792 "PATRES2.spad" 1195266 1195280 1195584 1195589) (-791 "PATRES.spad" 1192849 1192861 1195256 1195261) (-790 "PATMATCH.spad" 1191042 1191073 1192553 1192558) (-789 "PATMAB.spad" 1190471 1190481 1191032 1191037) (-788 "PATLRES.spad" 1189557 1189571 1190461 1190466) (-787 "PATAB.spad" 1189321 1189331 1189547 1189552) (-786 "PARTPERM.spad" 1187377 1187385 1189311 1189316) (-785 "PARSURF.spad" 1186811 1186839 1187367 1187372) (-784 "PARSU2.spad" 1186608 1186624 1186801 1186806) (-783 "script-parser.spad" 1186128 1186136 1186598 1186603) (-782 "PARSCURV.spad" 1185562 1185590 1186118 1186123) (-781 "PARSC2.spad" 1185353 1185369 1185552 1185557) (-780 "PARPCURV.spad" 1184815 1184843 1185343 1185348) (-779 "PARPC2.spad" 1184606 1184622 1184805 1184810) (-778 "PARAMAST.spad" 1183734 1183742 1184596 1184601) (-777 "PAN2EXPR.spad" 1183146 1183154 1183724 1183729) (-776 "PALETTE.spad" 1182260 1182268 1183136 1183141) (-775 "PAIR.spad" 1181270 1181283 1181839 1181844) (-774 "PADICRC.spad" 1178483 1178501 1179646 1179739) (-773 "PADICRAT.spad" 1176351 1176363 1176564 1176657) (-772 "PADICCT.spad" 1174900 1174912 1176277 1176346) (-771 "PADIC.spad" 1174603 1174615 1174826 1174895) (-770 "PADEPAC.spad" 1173292 1173311 1174593 1174598) (-769 "PADE.spad" 1172044 1172060 1173282 1173287) (-768 "OWP.spad" 1171292 1171322 1171902 1171969) (-767 "OVERSET.spad" 1170865 1170873 1171282 1171287) (-766 "OVAR.spad" 1170646 1170669 1170855 1170860) (-765 "OUTFORM.spad" 1160054 1160062 1170636 1170641) (-764 "OUTBFILE.spad" 1159488 1159496 1160044 1160049) (-763 "OUTBCON.spad" 1158558 1158566 1159478 1159483) (-762 "OUTBCON.spad" 1157626 1157636 1158548 1158553) (-761 "OUT.spad" 1156744 1156752 1157616 1157621) (-760 "OSI.spad" 1156219 1156227 1156734 1156739) (-759 "OSGROUP.spad" 1156137 1156145 1156209 1156214) (-758 "ORTHPOL.spad" 1154616 1154626 1156048 1156053) (-757 "OREUP.spad" 1154062 1154090 1154289 1154328) (-756 "ORESUP.spad" 1153356 1153380 1153735 1153774) (-755 "OREPCTO.spad" 1151245 1151257 1153276 1153281) (-754 "OREPCAT.spad" 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T)) -(((-3) T) ((-2) T) ((-1) T) ((0) T) ((-1237 . -146) T) ((-1237 . -571) 205294) ((-1237 . -684) T) ((-1237 . -1052) T) ((-1237 . -997) T) ((-1237 . -989) T) ((-1237 . -606) 205281) ((-1237 . -604) 205253) ((-1237 . -104) T) ((-1237 . -25) T) ((-1237 . -73) T) ((-1237 . -1157) T) ((-1237 . -568) 205235) ((-1237 . -1041) T) ((-1237 . -23) T) ((-1237 . -21) T) ((-1237 . -996) 205222) ((-1237 . -991) 205209) ((-1237 . -82) 205194) ((-1237 . -323) T) ((-1237 . -569) 205176) ((-1237 . -1092) T) ((-1233 . -1041) T) ((-1233 . -568) 205143) ((-1233 . -1157) T) ((-1233 . -73) T) ((-1233 . -444) 205125) ((-1233 . -571) 205107) ((-1232 . -1230) 205086) ((-1232 . -978) 205063) ((-1232 . -571) 205012) ((-1232 . -989) T) ((-1232 . -997) T) ((-1232 . -1052) T) ((-1232 . -684) T) ((-1232 . -21) T) ((-1232 . -604) 204971) ((-1232 . -23) T) ((-1232 . -1041) T) ((-1232 . -568) 204953) ((-1232 . -1157) T) ((-1232 . -73) T) ((-1232 . -25) T) ((-1232 . -104) T) ((-1232 . -606) 204927) ((-1232 . -1222) 204911) ((-1232 . -675) 204881) ((-1232 . -598) 204851) ((-1232 . -996) 204835) ((-1232 . -991) 204819) ((-1232 . -82) 204798) ((-1232 . -38) 204768) ((-1232 . -1227) 204747) ((-1231 . -989) T) ((-1231 . -997) T) ((-1231 . -1052) T) ((-1231 . -684) T) ((-1231 . -21) T) ((-1231 . -604) 204706) ((-1231 . -23) T) ((-1231 . -1041) T) ((-1231 . -568) 204688) ((-1231 . -1157) T) ((-1231 . -73) T) ((-1231 . -25) T) ((-1231 . -104) T) ((-1231 . -606) 204662) ((-1231 . -571) 204618) ((-1231 . -1222) 204602) ((-1231 . -675) 204572) ((-1231 . -598) 204542) ((-1231 . -996) 204526) ((-1231 . -991) 204510) ((-1231 . -82) 204489) ((-1231 . -38) 204459) ((-1231 . -339) 204438) ((-1231 . -978) 204422) ((-1229 . -1230) 204398) ((-1229 . -978) 204372) ((-1229 . -571) 204318) ((-1229 . -989) T) ((-1229 . -997) T) ((-1229 . -1052) T) ((-1229 . -684) T) ((-1229 . -21) T) ((-1229 . -604) 204277) ((-1229 . -23) T) ((-1229 . -1041) T) ((-1229 . -568) 204259) ((-1229 . -1157) T) ((-1229 . -73) T) ((-1229 . -25) T) ((-1229 . -104) T) ((-1229 . -606) 204233) ((-1229 . -1222) 204217) ((-1229 . -675) 204187) ((-1229 . -598) 204157) ((-1229 . -996) 204141) ((-1229 . -991) 204125) ((-1229 . -82) 204104) ((-1229 . -38) 204074) ((-1229 . -1227) 204050) ((-1228 . -1230) 204029) ((-1228 . -978) 203986) ((-1228 . -571) 203915) ((-1228 . -989) T) ((-1228 . -997) T) ((-1228 . -1052) T) ((-1228 . -684) T) ((-1228 . -21) T) ((-1228 . -604) 203874) ((-1228 . -23) T) ((-1228 . -1041) T) ((-1228 . -568) 203856) ((-1228 . -1157) T) ((-1228 . -73) T) ((-1228 . -25) T) ((-1228 . -104) T) ((-1228 . -606) 203830) ((-1228 . -1222) 203814) ((-1228 . -675) 203784) ((-1228 . -598) 203754) ((-1228 . -996) 203738) ((-1228 . -991) 203722) ((-1228 . -82) 203701) ((-1228 . -38) 203671) ((-1228 . -1227) 203650) ((-1228 . -339) 203622) ((-1223 . -339) 203594) ((-1223 . -571) 203543) ((-1223 . -978) 203520) ((-1223 . -598) 203490) ((-1223 . -675) 203460) ((-1223 . -606) 203434) ((-1223 . -604) 203393) ((-1223 . -104) T) ((-1223 . -25) T) ((-1223 . -73) T) ((-1223 . -1157) T) ((-1223 . -568) 203375) ((-1223 . -1041) T) ((-1223 . -23) T) ((-1223 . -21) T) ((-1223 . -996) 203359) ((-1223 . -991) 203343) ((-1223 . -82) 203322) ((-1223 . -1230) 203301) ((-1223 . -989) T) ((-1223 . -997) T) ((-1223 . -1052) T) ((-1223 . -684) T) ((-1223 . -1222) 203285) ((-1223 . -38) 203255) ((-1223 . -1227) 203234) ((-1221 . -1152) 203203) ((-1221 . -568) 203165) ((-1221 . -124) 203149) ((-1221 . -34) T) ((-1221 . -1157) T) ((-1221 . -73) T) ((-1221 . -263) 203087) ((-1221 . -468) 203020) ((-1221 . -1041) T) ((-1221 . -443) 203004) ((-1221 . -569) 202965) ((-1221 . -916) 202934) ((-1220 . -989) T) ((-1220 . -997) T) ((-1220 . -1052) T) ((-1220 . -684) T) ((-1220 . -21) T) ((-1220 . -604) 202879) ((-1220 . -23) T) ((-1220 . -1041) T) ((-1220 . -568) 202848) ((-1220 . -1157) T) ((-1220 . -73) T) ((-1220 . -25) T) ((-1220 . -104) T) ((-1220 . -606) 202808) ((-1220 . -571) 202750) ((-1220 . -444) 202734) ((-1220 . -38) 202704) ((-1220 . -82) 202669) ((-1220 . -991) 202639) ((-1220 . -996) 202609) ((-1220 . -598) 202579) ((-1220 . -675) 202549) ((-1219 . -1023) T) ((-1219 . -444) 202530) ((-1219 . -568) 202496) ((-1219 . -571) 202477) ((-1219 . -1041) T) ((-1219 . -1157) T) ((-1219 . -73) T) ((-1219 . -64) T) ((-1218 . -1023) T) ((-1218 . -444) 202458) ((-1218 . -568) 202424) ((-1218 . -571) 202405) ((-1218 . -1041) T) ((-1218 . -1157) T) ((-1218 . -73) T) ((-1218 . -64) T) ((-1213 . -568) 202387) ((-1211 . -1041) T) ((-1211 . -568) 202369) ((-1211 . -1157) T) ((-1211 . -73) T) ((-1210 . -1041) T) ((-1210 . -568) 202351) ((-1210 . -1157) T) ((-1210 . -73) T) ((-1207 . -1206) 202335) ((-1207 . -327) 202319) ((-1207 . -784) 202298) ((-1207 . -781) 202277) ((-1207 . -124) 202261) ((-1207 . -34) T) ((-1207 . -1157) T) ((-1207 . -73) 202192) ((-1207 . -568) 202104) ((-1207 . -263) 202042) ((-1207 . -468) 201975) ((-1207 . -1041) 201925) ((-1207 . -443) 201909) ((-1207 . -569) 201870) ((-1207 . -240) 201822) ((-1207 . -554) 201799) ((-1207 . -242) 201776) ((-1207 . -609) 201760) ((-1207 . -19) 201744) ((-1204 . -1041) T) ((-1204 . -568) 201710) ((-1204 . -1157) T) ((-1204 . -73) T) ((-1197 . -1200) 201694) ((-1197 . -190) 201653) ((-1197 . -571) 201535) ((-1197 . -606) 201460) ((-1197 . -604) 201370) ((-1197 . -104) T) ((-1197 . -25) T) ((-1197 . -73) T) ((-1197 . -568) 201352) ((-1197 . -1041) T) ((-1197 . -23) T) ((-1197 . -21) T) ((-1197 . -684) T) ((-1197 . -1052) T) ((-1197 . -997) T) ((-1197 . -989) T) ((-1197 . -186) 201305) ((-1197 . -1157) T) ((-1197 . -189) 201264) ((-1197 . -240) 201229) ((-1197 . -836) 201142) ((-1197 . -831) 201030) ((-1197 . -838) 200943) ((-1197 . -913) 200912) ((-1197 . -38) 200809) ((-1197 . -82) 200671) ((-1197 . -991) 200554) ((-1197 . -996) 200437) ((-1197 . -598) 200334) ((-1197 . -675) 200231) ((-1197 . -118) 200210) ((-1197 . -120) 200189) ((-1197 . -146) 200140) ((-1197 . -510) 200119) ((-1197 . -244) 200098) ((-1197 . -47) 200075) ((-1197 . -1186) 200052) ((-1197 . -35) 200018) ((-1197 . -66) 199984) ((-1197 . -238) 199950) ((-1197 . -447) 199916) ((-1197 . -1146) 199882) ((-1197 . -1143) 199848) ((-1197 . -942) 199814) ((-1194 . -280) 199758) ((-1194 . -978) 199724) ((-1194 . -366) 199690) ((-1194 . -38) 199547) ((-1194 . -571) 199421) ((-1194 . -606) 199310) ((-1194 . -604) 199184) ((-1194 . -684) T) ((-1194 . -1052) T) ((-1194 . -997) T) ((-1194 . -989) T) ((-1194 . -82) 199034) ((-1194 . -991) 198923) ((-1194 . -996) 198812) ((-1194 . -21) T) ((-1194 . -23) T) ((-1194 . -1041) T) ((-1194 . -568) 198794) ((-1194 . -1157) T) ((-1194 . -73) T) ((-1194 . -25) T) ((-1194 . -104) T) ((-1194 . -598) 198651) ((-1194 . -675) 198508) ((-1194 . -118) 198469) ((-1194 . -120) 198430) ((-1194 . -146) T) ((-1194 . -510) T) ((-1194 . -244) T) ((-1194 . -47) 198374) ((-1193 . -1192) 198353) ((-1193 . -318) 198332) ((-1193 . -1162) 198311) ((-1193 . -859) 198290) ((-1193 . -510) 198241) ((-1193 . -146) 198172) ((-1193 . -571) 197985) ((-1193 . -675) 197826) ((-1193 . -598) 197667) ((-1193 . -38) 197508) ((-1193 . -406) 197487) ((-1193 . -261) 197466) ((-1193 . -606) 197363) ((-1193 . -604) 197245) ((-1193 . -684) T) ((-1193 . -1052) T) ((-1193 . -997) T) ((-1193 . -989) T) ((-1193 . -82) 197059) ((-1193 . -991) 196894) ((-1193 . -996) 196729) ((-1193 . -21) T) ((-1193 . -23) T) ((-1193 . -1041) T) ((-1193 . -568) 196711) ((-1193 . -1157) T) ((-1193 . -73) T) ((-1193 . -25) T) ((-1193 . -104) T) ((-1193 . -244) 196662) ((-1193 . -200) 196641) ((-1193 . -942) 196607) ((-1193 . -1143) 196573) ((-1193 . -1146) 196539) ((-1193 . -447) 196505) ((-1193 . -238) 196471) ((-1193 . -66) 196437) ((-1193 . -35) 196403) ((-1193 . -1186) 196373) ((-1193 . -47) 196343) ((-1193 . -120) 196322) ((-1193 . -118) 196301) ((-1193 . -913) 196263) ((-1193 . -838) 196169) ((-1193 . -831) 196073) ((-1193 . -836) 195979) ((-1193 . -240) 195937) ((-1193 . -189) 195889) ((-1193 . -186) 195835) ((-1193 . -190) 195787) ((-1193 . -1190) 195771) ((-1193 . -978) 195755) ((-1188 . -1192) 195716) ((-1188 . -318) 195695) ((-1188 . -1162) 195674) ((-1188 . -859) 195653) ((-1188 . -510) 195604) ((-1188 . -146) 195535) ((-1188 . -571) 195278) ((-1188 . -675) 195119) ((-1188 . -598) 194960) ((-1188 . -38) 194801) ((-1188 . -406) 194780) ((-1188 . -261) 194759) ((-1188 . -606) 194656) ((-1188 . -604) 194538) ((-1188 . -684) T) ((-1188 . -1052) T) ((-1188 . -997) T) ((-1188 . -989) T) ((-1188 . -82) 194352) ((-1188 . -991) 194187) ((-1188 . -996) 194022) ((-1188 . -21) T) ((-1188 . -23) T) ((-1188 . -1041) T) ((-1188 . -568) 194004) ((-1188 . -1157) T) ((-1188 . -73) T) ((-1188 . -25) T) ((-1188 . -104) T) ((-1188 . -244) 193955) ((-1188 . -200) 193934) ((-1188 . -942) 193900) ((-1188 . -1143) 193866) ((-1188 . -1146) 193832) ((-1188 . -447) 193798) ((-1188 . -238) 193764) ((-1188 . -66) 193730) ((-1188 . -35) 193696) ((-1188 . -1186) 193666) ((-1188 . -47) 193636) ((-1188 . -120) 193615) ((-1188 . -118) 193594) ((-1188 . -913) 193556) ((-1188 . -838) 193462) ((-1188 . -831) 193343) ((-1188 . -836) 193249) ((-1188 . -240) 193207) ((-1188 . -189) 193159) ((-1188 . -186) 193105) ((-1188 . -190) 193057) ((-1188 . -1190) 193041) ((-1188 . -978) 192976) ((-1176 . -1183) 192960) ((-1176 . -1092) 192938) ((-1176 . -569) NIL) ((-1176 . -263) 192925) ((-1176 . -468) 192871) ((-1176 . -280) 192848) ((-1176 . -978) 192730) ((-1176 . -366) 192714) ((-1176 . -38) 192543) ((-1176 . -82) 192345) ((-1176 . -991) 192168) ((-1176 . -996) 191991) ((-1176 . -604) 191901) ((-1176 . -606) 191790) ((-1176 . -598) 191619) ((-1176 . -675) 191448) ((-1176 . -571) 191197) ((-1176 . -118) 191176) ((-1176 . -120) 191155) ((-1176 . -47) 191132) ((-1176 . -332) 191116) ((-1176 . -596) 191064) ((-1176 . -836) 191007) ((-1176 . -831) 190910) ((-1176 . -838) 190817) ((-1176 . -821) NIL) ((-1176 . -848) 190796) ((-1176 . -1162) 190775) ((-1176 . -888) 190744) ((-1176 . -859) 190723) ((-1176 . -510) 190634) ((-1176 . -244) 190545) ((-1176 . -146) 190436) ((-1176 . -406) 190367) ((-1176 . -261) 190346) ((-1176 . -240) 190273) ((-1176 . -190) T) ((-1176 . -104) T) ((-1176 . -25) T) ((-1176 . -73) T) ((-1176 . -568) 190255) ((-1176 . -1041) T) ((-1176 . -23) T) ((-1176 . -21) T) ((-1176 . -684) T) ((-1176 . -1052) T) ((-1176 . -997) T) ((-1176 . -989) T) ((-1176 . -186) 190242) ((-1176 . -1157) T) ((-1176 . -189) T) ((-1176 . -224) 190226) ((-1176 . -184) 190210) ((-1174 . -1034) 190194) ((-1174 . -573) 190178) ((-1174 . -1041) 190156) ((-1174 . -568) 190123) ((-1174 . -1157) 190101) ((-1174 . -73) 190079) ((-1174 . -1035) 190036) ((-1172 . -1171) 190015) ((-1172 . -942) 189981) ((-1172 . -1143) 189947) ((-1172 . -1146) 189913) ((-1172 . -447) 189879) ((-1172 . -238) 189845) ((-1172 . -66) 189811) ((-1172 . -35) 189777) ((-1172 . -1186) 189754) ((-1172 . -47) 189731) ((-1172 . -571) 189480) ((-1172 . -675) 189294) ((-1172 . -598) 189108) ((-1172 . -606) 188916) ((-1172 . -604) 188771) ((-1172 . -996) 188579) ((-1172 . -991) 188387) ((-1172 . -82) 188169) ((-1172 . -38) 187983) ((-1172 . -913) 187952) ((-1172 . -240) 187852) ((-1172 . -1169) 187836) ((-1172 . -684) T) ((-1172 . -1052) T) ((-1172 . -997) T) ((-1172 . -989) T) ((-1172 . -21) T) ((-1172 . -23) T) ((-1172 . -1041) T) ((-1172 . -568) 187818) ((-1172 . -1157) T) ((-1172 . -73) T) ((-1172 . -25) T) ((-1172 . -104) T) ((-1172 . -118) 187743) ((-1172 . -120) 187668) ((-1172 . -569) 187341) ((-1172 . -184) 187311) ((-1172 . -836) 187162) ((-1172 . -838) 186959) ((-1172 . -831) 186754) ((-1172 . -224) 186724) ((-1172 . -189) 186583) ((-1172 . -186) 186436) ((-1172 . -190) 186341) ((-1172 . -318) 186320) ((-1172 . -1162) 186299) ((-1172 . -859) 186278) ((-1172 . -510) 186229) ((-1172 . -146) 186160) ((-1172 . -406) 186139) ((-1172 . -261) 186118) ((-1172 . -244) 186069) ((-1172 . -200) 186048) ((-1172 . -293) 186018) ((-1172 . -468) 185878) ((-1172 . -263) 185817) ((-1172 . -332) 185787) ((-1172 . -596) 185695) ((-1172 . -354) 185665) ((-1172 . -821) 185538) ((-1172 . -763) 185491) ((-1172 . -735) 185444) ((-1172 . -737) 185397) ((-1172 . -781) 185296) ((-1172 . -784) 185195) ((-1172 . -739) 185148) ((-1172 . -742) 185101) ((-1172 . -780) 185054) ((-1172 . -819) 185024) ((-1172 . -848) 184977) ((-1172 . -960) 184930) ((-1172 . -978) 184719) ((-1172 . -1092) 184671) ((-1172 . -931) 184641) ((-1167 . -1171) 184602) ((-1167 . -942) 184568) ((-1167 . -1143) 184534) ((-1167 . -1146) 184500) ((-1167 . -447) 184466) ((-1167 . -238) 184432) ((-1167 . -66) 184398) ((-1167 . -35) 184364) ((-1167 . -1186) 184341) ((-1167 . -47) 184318) ((-1167 . -571) 184113) ((-1167 . -675) 183909) ((-1167 . -598) 183705) ((-1167 . -606) 183557) ((-1167 . -604) 183394) ((-1167 . -996) 183184) ((-1167 . -991) 182974) ((-1167 . -82) 182720) ((-1167 . -38) 182516) ((-1167 . -913) 182485) ((-1167 . -240) 182313) ((-1167 . -1169) 182297) ((-1167 . -684) T) ((-1167 . -1052) T) ((-1167 . -997) T) ((-1167 . -989) T) ((-1167 . -21) T) ((-1167 . -23) T) ((-1167 . -1041) T) ((-1167 . -568) 182279) ((-1167 . -1157) T) ((-1167 . -73) T) ((-1167 . -25) T) ((-1167 . -104) T) ((-1167 . -118) 182186) ((-1167 . -120) 182093) ((-1167 . -569) NIL) ((-1167 . -184) 182045) ((-1167 . -836) 181878) ((-1167 . -838) 181639) ((-1167 . -831) 181375) ((-1167 . -224) 181327) ((-1167 . -189) 181150) ((-1167 . -186) 180967) ((-1167 . -190) 180854) ((-1167 . -318) 180833) ((-1167 . -1162) 180812) ((-1167 . -859) 180791) ((-1167 . -510) 180742) ((-1167 . -146) 180673) ((-1167 . -406) 180652) ((-1167 . -261) 180631) ((-1167 . -244) 180582) ((-1167 . -200) 180561) ((-1167 . -293) 180513) ((-1167 . -468) 180247) ((-1167 . -263) 180132) ((-1167 . -332) 180084) ((-1167 . -596) 180036) ((-1167 . -354) 179988) ((-1167 . -821) NIL) ((-1167 . -763) NIL) ((-1167 . -735) NIL) ((-1167 . -737) NIL) ((-1167 . -781) NIL) ((-1167 . -784) NIL) ((-1167 . -739) NIL) ((-1167 . -742) NIL) ((-1167 . -780) NIL) ((-1167 . -819) 179940) ((-1167 . -848) NIL) ((-1167 . -960) NIL) ((-1167 . -978) 179906) ((-1167 . -1092) NIL) ((-1167 . -931) 179858) ((-1166 . -777) T) ((-1166 . -784) T) ((-1166 . -781) T) ((-1166 . -1041) T) ((-1166 . -568) 179840) ((-1166 . -1157) T) ((-1166 . -73) T) ((-1166 . -323) T) ((-1166 . -620) T) ((-1165 . -777) T) ((-1165 . -784) T) ((-1165 . -781) T) ((-1165 . -1041) T) ((-1165 . -568) 179822) ((-1165 . -1157) T) ((-1165 . -73) T) ((-1165 . -323) T) ((-1165 . -620) T) ((-1164 . -777) T) ((-1164 . -784) T) ((-1164 . -781) T) ((-1164 . -1041) T) ((-1164 . -568) 179804) ((-1164 . -1157) T) ((-1164 . -73) T) ((-1164 . -323) T) ((-1164 . -620) T) ((-1163 . -777) T) ((-1163 . -784) T) ((-1163 . -781) T) ((-1163 . -1041) T) ((-1163 . -568) 179786) ((-1163 . -1157) T) ((-1163 . -73) T) ((-1163 . -323) T) ((-1163 . -620) T) ((-1158 . -1023) T) ((-1158 . -444) 179767) ((-1158 . -568) 179733) ((-1158 . -571) 179714) ((-1158 . -1041) T) ((-1158 . -1157) T) ((-1158 . -73) T) ((-1158 . -64) T) ((-1155 . -444) 179691) ((-1155 . -568) 179632) ((-1155 . -571) 179609) ((-1155 . -1041) 179587) ((-1155 . -1157) 179565) ((-1155 . -73) 179543) ((-1150 . -698) 179519) ((-1150 . -35) 179485) ((-1150 . -66) 179451) ((-1150 . -238) 179417) ((-1150 . -447) 179383) ((-1150 . -1146) 179349) ((-1150 . -1143) 179315) ((-1150 . -942) 179281) ((-1150 . -47) 179250) ((-1150 . -38) 179147) ((-1150 . -598) 179044) ((-1150 . -675) 178941) ((-1150 . -571) 178823) ((-1150 . -244) 178802) ((-1150 . -510) 178781) ((-1150 . -82) 178643) ((-1150 . -991) 178526) ((-1150 . -996) 178409) ((-1150 . -146) 178360) ((-1150 . -120) 178339) ((-1150 . -118) 178318) ((-1150 . -606) 178243) ((-1150 . -604) 178153) ((-1150 . -913) 178114) ((-1150 . -838) 178095) ((-1150 . -1157) T) ((-1150 . -831) 178074) ((-1150 . -989) T) ((-1150 . -997) T) ((-1150 . -1052) T) ((-1150 . -684) T) ((-1150 . -21) T) ((-1150 . -23) T) ((-1150 . -1041) T) ((-1150 . -568) 178056) ((-1150 . -73) T) ((-1150 . -25) T) ((-1150 . -104) T) ((-1150 . -836) 178037) ((-1150 . -468) 178004) ((-1150 . -263) 177991) ((-1144 . -950) 177975) ((-1144 . -34) T) ((-1144 . -1157) T) ((-1144 . -73) 177926) ((-1144 . -568) 177858) ((-1144 . -263) 177796) ((-1144 . -468) 177729) ((-1144 . -1041) 177707) ((-1144 . -443) 177691) ((-1139 . -320) 177665) ((-1139 . -73) T) ((-1139 . -1157) T) ((-1139 . -568) 177647) ((-1139 . -1041) T) ((-1137 . -1041) T) ((-1137 . -568) 177629) ((-1137 . -1157) T) ((-1137 . -73) T) ((-1137 . -571) 177611) ((-1131 . -770) 177595) ((-1131 . -73) T) ((-1131 . -1157) T) ((-1131 . -568) 177577) ((-1131 . -1041) T) ((-1129 . -1134) 177556) ((-1129 . -183) 177504) ((-1129 . -78) 177452) ((-1129 . -263) 177250) ((-1129 . -468) 177002) ((-1129 . -443) 176937) ((-1129 . -124) 176885) ((-1129 . -569) NIL) ((-1129 . -192) 176833) ((-1129 . -565) 176812) ((-1129 . -242) 176791) ((-1129 . -1157) T) ((-1129 . -240) 176770) ((-1129 . -1041) T) ((-1129 . -568) 176752) ((-1129 . -73) T) ((-1129 . -34) T) ((-1129 . -554) 176731) ((-1125 . -1041) T) ((-1125 . -568) 176713) ((-1125 . -1157) T) ((-1125 . -73) T) ((-1124 . -777) T) ((-1124 . -784) T) ((-1124 . -781) T) ((-1124 . -1041) T) ((-1124 . -568) 176695) ((-1124 . -1157) T) ((-1124 . -73) T) ((-1124 . -323) T) ((-1124 . -620) T) ((-1123 . -777) T) ((-1123 . -784) T) ((-1123 . -781) T) ((-1123 . -1041) T) ((-1123 . -568) 176677) ((-1123 . -1157) T) ((-1123 . -73) T) ((-1123 . -323) T) ((-1122 . -1203) T) ((-1122 . -1041) T) ((-1122 . -568) 176644) ((-1122 . -1157) T) ((-1122 . -73) T) ((-1122 . -978) 176580) ((-1122 . -571) 176516) ((-1121 . -568) 176498) ((-1120 . -568) 176480) ((-1119 . -280) 176457) ((-1119 . -978) 176355) ((-1119 . -366) 176339) ((-1119 . -38) 176236) ((-1119 . -571) 176090) ((-1119 . -606) 176015) ((-1119 . -604) 175925) ((-1119 . -684) T) ((-1119 . -1052) T) ((-1119 . -997) T) ((-1119 . -989) T) ((-1119 . -82) 175787) ((-1119 . -991) 175670) ((-1119 . -996) 175553) ((-1119 . -21) T) ((-1119 . -23) T) ((-1119 . -1041) T) ((-1119 . -568) 175535) ((-1119 . -1157) T) ((-1119 . -73) T) ((-1119 . -25) T) ((-1119 . -104) T) ((-1119 . -598) 175432) ((-1119 . -675) 175329) ((-1119 . -118) 175308) ((-1119 . -120) 175287) ((-1119 . -146) 175238) ((-1119 . -510) 175217) ((-1119 . -244) 175196) ((-1119 . -47) 175173) ((-1117 . -781) T) ((-1117 . -568) 175155) ((-1117 . -1041) T) ((-1117 . -73) T) ((-1117 . -1157) T) ((-1117 . -784) T) ((-1117 . -569) 175077) ((-1117 . -571) 175043) ((-1117 . -978) 175025) ((-1117 . -821) 174992) ((-1116 . -568) 174974) ((-1115 . -1200) 174958) ((-1115 . -190) 174917) ((-1115 . -571) 174799) ((-1115 . -606) 174724) ((-1115 . -604) 174634) ((-1115 . -104) T) ((-1115 . -25) T) ((-1115 . -73) T) ((-1115 . -568) 174616) ((-1115 . -1041) T) ((-1115 . -23) T) ((-1115 . -21) T) ((-1115 . -684) T) ((-1115 . -1052) T) ((-1115 . -997) T) ((-1115 . -989) T) ((-1115 . -186) 174569) ((-1115 . -1157) T) ((-1115 . -189) 174528) ((-1115 . -240) 174493) ((-1115 . -836) 174406) ((-1115 . -831) 174294) ((-1115 . -838) 174207) ((-1115 . -913) 174176) ((-1115 . -38) 174073) ((-1115 . -82) 173935) ((-1115 . -991) 173818) ((-1115 . -996) 173701) ((-1115 . -598) 173598) ((-1115 . -675) 173495) ((-1115 . -118) 173474) ((-1115 . -120) 173453) ((-1115 . -146) 173404) ((-1115 . -510) 173383) ((-1115 . -244) 173362) ((-1115 . -47) 173339) ((-1115 . -1186) 173316) ((-1115 . -35) 173282) ((-1115 . -66) 173248) ((-1115 . -238) 173214) ((-1115 . -447) 173180) ((-1115 . -1146) 173146) ((-1115 . -1143) 173112) ((-1115 . -942) 173078) ((-1114 . -1192) 173039) ((-1114 . -318) 173018) ((-1114 . -1162) 172997) ((-1114 . -859) 172976) ((-1114 . -510) 172927) ((-1114 . -146) 172858) ((-1114 . -571) 172601) ((-1114 . -675) 172442) ((-1114 . -598) 172283) ((-1114 . -38) 172124) ((-1114 . -406) 172103) ((-1114 . -261) 172082) ((-1114 . -606) 171979) ((-1114 . -604) 171861) ((-1114 . -684) T) ((-1114 . -1052) T) ((-1114 . -997) T) ((-1114 . -989) T) ((-1114 . -82) 171675) ((-1114 . -991) 171510) ((-1114 . -996) 171345) ((-1114 . -21) T) ((-1114 . -23) T) ((-1114 . -1041) T) ((-1114 . -568) 171327) ((-1114 . -1157) T) ((-1114 . -73) T) ((-1114 . -25) T) ((-1114 . -104) T) ((-1114 . -244) 171278) ((-1114 . -200) 171257) ((-1114 . -942) 171223) ((-1114 . -1143) 171189) ((-1114 . -1146) 171155) ((-1114 . -447) 171121) ((-1114 . -238) 171087) ((-1114 . -66) 171053) ((-1114 . -35) 171019) ((-1114 . -1186) 170989) ((-1114 . -47) 170959) ((-1114 . -120) 170938) ((-1114 . -118) 170917) ((-1114 . -913) 170879) ((-1114 . -838) 170785) ((-1114 . -831) 170666) ((-1114 . -836) 170572) ((-1114 . -240) 170530) ((-1114 . -189) 170482) ((-1114 . -186) 170428) ((-1114 . -190) 170380) ((-1114 . -1190) 170364) ((-1114 . -978) 170299) ((-1111 . -1183) 170283) ((-1111 . -1092) 170261) ((-1111 . -569) NIL) ((-1111 . -263) 170248) ((-1111 . -468) 170194) ((-1111 . -280) 170171) ((-1111 . -978) 170053) ((-1111 . -366) 170037) ((-1111 . -38) 169866) ((-1111 . -82) 169668) ((-1111 . -991) 169491) ((-1111 . -996) 169314) ((-1111 . -604) 169224) ((-1111 . -606) 169113) ((-1111 . -598) 168942) ((-1111 . -675) 168771) ((-1111 . -571) 168541) ((-1111 . -118) 168520) ((-1111 . -120) 168499) ((-1111 . -47) 168476) ((-1111 . -332) 168460) ((-1111 . -596) 168408) ((-1111 . -836) 168351) ((-1111 . -831) 168254) ((-1111 . -838) 168161) ((-1111 . -821) NIL) ((-1111 . -848) 168140) ((-1111 . -1162) 168119) ((-1111 . -888) 168088) ((-1111 . -859) 168067) ((-1111 . -510) 167978) ((-1111 . -244) 167889) ((-1111 . -146) 167780) ((-1111 . -406) 167711) ((-1111 . -261) 167690) ((-1111 . -240) 167617) ((-1111 . -190) T) ((-1111 . -104) T) ((-1111 . -25) T) ((-1111 . -73) T) ((-1111 . -568) 167599) ((-1111 . -1041) T) ((-1111 . -23) T) ((-1111 . -21) T) ((-1111 . -684) T) ((-1111 . -1052) T) ((-1111 . -997) T) ((-1111 . -989) T) ((-1111 . -186) 167586) ((-1111 . -1157) T) ((-1111 . -189) T) ((-1111 . -224) 167570) ((-1111 . -184) 167554) ((-1108 . -1171) 167515) ((-1108 . -942) 167481) ((-1108 . -1143) 167447) ((-1108 . -1146) 167413) ((-1108 . -447) 167379) ((-1108 . -238) 167345) ((-1108 . -66) 167311) ((-1108 . -35) 167277) ((-1108 . -1186) 167254) ((-1108 . -47) 167231) ((-1108 . -571) 167026) ((-1108 . -675) 166822) ((-1108 . -598) 166618) ((-1108 . -606) 166470) ((-1108 . -604) 166307) ((-1108 . -996) 166097) ((-1108 . -991) 165887) ((-1108 . -82) 165633) ((-1108 . -38) 165429) ((-1108 . -913) 165398) ((-1108 . -240) 165226) ((-1108 . -1169) 165210) ((-1108 . -684) T) ((-1108 . -1052) T) ((-1108 . -997) T) ((-1108 . -989) T) ((-1108 . -21) T) ((-1108 . -23) T) ((-1108 . -1041) T) ((-1108 . -568) 165192) ((-1108 . -1157) T) ((-1108 . -73) T) ((-1108 . -25) T) ((-1108 . -104) T) ((-1108 . -118) 165099) ((-1108 . -120) 165006) ((-1108 . -569) NIL) ((-1108 . -184) 164958) ((-1108 . -836) 164791) ((-1108 . -838) 164552) ((-1108 . -831) 164288) ((-1108 . -224) 164240) ((-1108 . -189) 164063) ((-1108 . -186) 163880) ((-1108 . -190) 163767) ((-1108 . -318) 163746) ((-1108 . -1162) 163725) ((-1108 . -859) 163704) ((-1108 . -510) 163655) ((-1108 . -146) 163586) ((-1108 . -406) 163565) ((-1108 . -261) 163544) ((-1108 . -244) 163495) ((-1108 . -200) 163474) ((-1108 . -293) 163426) ((-1108 . -468) 163160) ((-1108 . -263) 163045) ((-1108 . -332) 162997) ((-1108 . -596) 162949) ((-1108 . -354) 162901) ((-1108 . -821) NIL) ((-1108 . -763) NIL) ((-1108 . -735) NIL) ((-1108 . -737) NIL) ((-1108 . -781) NIL) ((-1108 . -784) NIL) ((-1108 . -739) NIL) ((-1108 . -742) NIL) ((-1108 . -780) NIL) ((-1108 . -819) 162853) ((-1108 . -848) NIL) ((-1108 . -960) NIL) ((-1108 . -978) 162819) ((-1108 . -1092) NIL) ((-1108 . -931) 162771) ((-1107 . -1023) T) ((-1107 . -444) 162752) ((-1107 . -568) 162718) ((-1107 . -571) 162699) ((-1107 . -1041) T) ((-1107 . -1157) T) ((-1107 . -73) T) ((-1107 . -64) T) ((-1106 . -1041) T) ((-1106 . -568) 162681) ((-1106 . -1157) T) ((-1106 . -73) T) ((-1105 . -1041) T) ((-1105 . -568) 162663) ((-1105 . -1157) T) ((-1105 . -73) T) ((-1100 . -1134) 162639) ((-1100 . -183) 162584) ((-1100 . -78) 162529) ((-1100 . -263) 162318) ((-1100 . -468) 162058) ((-1100 . -443) 161990) ((-1100 . -124) 161935) ((-1100 . -569) NIL) ((-1100 . -192) 161880) ((-1100 . -565) 161856) ((-1100 . -242) 161832) ((-1100 . -1157) T) ((-1100 . -240) 161808) ((-1100 . -1041) T) ((-1100 . -568) 161790) ((-1100 . -73) T) ((-1100 . -34) T) ((-1100 . -554) 161766) ((-1099 . -1084) T) ((-1099 . -327) 161748) ((-1099 . -784) T) ((-1099 . -781) T) ((-1099 . -124) 161730) ((-1099 . -34) T) ((-1099 . -1157) T) ((-1099 . -73) T) ((-1099 . -568) 161712) ((-1099 . -263) NIL) ((-1099 . -468) NIL) ((-1099 . -1041) T) ((-1099 . -443) 161694) ((-1099 . -569) NIL) ((-1099 . -240) 161644) ((-1099 . -554) 161619) ((-1099 . -242) 161594) ((-1099 . -609) 161576) ((-1099 . -19) 161558) ((-1095 . -632) 161542) ((-1095 . -609) 161526) ((-1095 . -242) 161503) ((-1095 . -240) 161455) ((-1095 . -554) 161432) ((-1095 . -569) 161393) ((-1095 . -443) 161377) ((-1095 . -1041) 161355) ((-1095 . -468) 161288) ((-1095 . -263) 161226) ((-1095 . -568) 161158) ((-1095 . -73) 161109) ((-1095 . -1157) T) ((-1095 . -34) T) ((-1095 . -124) 161093) ((-1095 . -1196) 161077) ((-1095 . -950) 161061) ((-1095 . -1090) 161045) ((-1095 . -571) 161022) ((-1093 . -1023) T) ((-1093 . -444) 161003) ((-1093 . -568) 160969) ((-1093 . -571) 160950) ((-1093 . -1041) T) ((-1093 . -1157) T) ((-1093 . -73) T) ((-1093 . -64) T) ((-1091 . -1134) 160929) ((-1091 . -183) 160877) ((-1091 . -78) 160825) ((-1091 . -263) 160623) ((-1091 . -468) 160375) ((-1091 . -443) 160310) ((-1091 . -124) 160258) ((-1091 . -569) NIL) ((-1091 . -192) 160206) ((-1091 . -565) 160185) ((-1091 . -242) 160164) ((-1091 . -1157) T) ((-1091 . -240) 160143) ((-1091 . -1041) T) ((-1091 . -568) 160125) ((-1091 . -73) T) ((-1091 . -34) T) ((-1091 . -554) 160104) ((-1088 . -1061) 160088) ((-1088 . -443) 160072) ((-1088 . -1041) 160050) ((-1088 . -468) 159983) ((-1088 . -263) 159921) ((-1088 . -568) 159853) ((-1088 . -73) 159804) ((-1088 . -1157) T) ((-1088 . -34) T) ((-1088 . -78) 159788) ((-1086 . -1049) 159757) ((-1086 . -1152) 159726) ((-1086 . -568) 159688) ((-1086 . -124) 159672) ((-1086 . -34) T) ((-1086 . -1157) T) ((-1086 . -73) T) ((-1086 . -263) 159610) ((-1086 . -468) 159543) ((-1086 . -1041) T) ((-1086 . -443) 159527) ((-1086 . -569) 159488) ((-1086 . -916) 159457) ((-1086 . -1011) 159426) ((-1082 . -1063) 159371) ((-1082 . -443) 159355) ((-1082 . -468) 159288) ((-1082 . -263) 159226) ((-1082 . -34) T) ((-1082 . -993) 159166) ((-1082 . -978) 159064) ((-1082 . -571) 158983) ((-1082 . -366) 158967) ((-1082 . -596) 158915) ((-1082 . -606) 158853) ((-1082 . -332) 158837) ((-1082 . -190) 158816) ((-1082 . -186) 158761) ((-1082 . -189) 158712) ((-1082 . -224) 158696) ((-1082 . -831) 158617) ((-1082 . -838) 158540) ((-1082 . -836) 158499) ((-1082 . -184) 158483) ((-1082 . -675) 158415) ((-1082 . -598) 158347) ((-1082 . -604) 158306) ((-1082 . -104) T) ((-1082 . -25) T) ((-1082 . -73) T) ((-1082 . -1157) T) ((-1082 . -568) 158268) ((-1082 . -1041) T) ((-1082 . -23) T) ((-1082 . -21) T) ((-1082 . -996) 158252) ((-1082 . -991) 158236) ((-1082 . -82) 158215) ((-1082 . -989) T) ((-1082 . -997) T) ((-1082 . -1052) T) ((-1082 . -684) T) ((-1082 . -38) 158175) ((-1082 . -569) 158136) ((-1081 . -950) 158107) ((-1081 . -34) T) ((-1081 . -1157) T) ((-1081 . -73) T) ((-1081 . -568) 158089) ((-1081 . -263) 158015) ((-1081 . -468) 157923) ((-1081 . -1041) T) ((-1081 . -443) 157894) ((-1080 . -1041) T) ((-1080 . -568) 157876) ((-1080 . -1157) T) ((-1080 . -73) T) ((-1075 . -1077) T) ((-1075 . -1203) T) ((-1075 . -64) T) ((-1075 . -73) T) ((-1075 . -1157) T) ((-1075 . -568) 157842) ((-1075 . -1041) T) ((-1075 . -571) 157823) ((-1075 . -444) 157804) ((-1075 . -1023) T) ((-1073 . -1074) 157788) ((-1073 . -73) T) ((-1073 . -1157) T) ((-1073 . -568) 157770) ((-1073 . -1041) T) ((-1066 . -698) 157749) ((-1066 . -35) 157715) ((-1066 . -66) 157681) ((-1066 . -238) 157647) ((-1066 . -447) 157613) ((-1066 . -1146) 157579) ((-1066 . -1143) 157545) ((-1066 . -942) 157511) ((-1066 . -47) 157483) ((-1066 . -38) 157380) ((-1066 . -598) 157277) ((-1066 . -675) 157174) ((-1066 . -571) 157056) ((-1066 . -244) 157035) ((-1066 . -510) 157014) ((-1066 . -82) 156876) ((-1066 . -991) 156759) ((-1066 . -996) 156642) ((-1066 . -146) 156593) ((-1066 . -120) 156572) ((-1066 . -118) 156551) ((-1066 . -606) 156476) ((-1066 . -604) 156386) ((-1066 . -913) 156353) ((-1066 . -838) 156337) ((-1066 . -1157) T) ((-1066 . -831) 156319) ((-1066 . -989) T) ((-1066 . -997) T) ((-1066 . -1052) T) ((-1066 . -684) T) ((-1066 . -21) T) ((-1066 . -23) T) ((-1066 . -1041) T) ((-1066 . -568) 156301) ((-1066 . -73) T) ((-1066 . -25) T) ((-1066 . -104) T) ((-1066 . -836) 156285) ((-1066 . -468) 156255) ((-1066 . -263) 156242) ((-1065 . -888) 156209) ((-1065 . -571) 156002) ((-1065 . -978) 155887) ((-1065 . -1162) 155866) ((-1065 . -848) 155845) ((-1065 . -821) 155704) ((-1065 . -838) 155688) ((-1065 . -831) 155670) ((-1065 . -836) 155654) ((-1065 . -468) 155606) ((-1065 . -406) 155557) ((-1065 . -596) 155505) ((-1065 . -606) 155394) ((-1065 . -332) 155378) ((-1065 . -47) 155350) ((-1065 . -38) 155199) ((-1065 . -598) 155048) ((-1065 . -675) 154897) ((-1065 . -244) 154828) ((-1065 . -510) 154759) ((-1065 . -82) 154581) ((-1065 . -991) 154424) ((-1065 . -996) 154267) ((-1065 . -146) 154178) ((-1065 . -120) 154157) ((-1065 . -118) 154136) ((-1065 . -604) 154046) ((-1065 . -104) T) ((-1065 . -25) T) ((-1065 . -73) T) ((-1065 . -1157) T) ((-1065 . -568) 154028) ((-1065 . -1041) T) ((-1065 . -23) T) ((-1065 . -21) T) ((-1065 . -989) T) ((-1065 . -997) T) ((-1065 . -1052) T) ((-1065 . -684) T) ((-1065 . -366) 154012) ((-1065 . -280) 153984) ((-1065 . -263) 153971) ((-1065 . -569) 153719) ((-1060 . -498) T) ((-1060 . -1162) T) ((-1060 . -1092) T) ((-1060 . -978) 153701) ((-1060 . -569) 153616) ((-1060 . -960) T) ((-1060 . -821) 153598) ((-1060 . -780) T) ((-1060 . -742) T) ((-1060 . -739) T) ((-1060 . -784) T) ((-1060 . -781) T) ((-1060 . -737) T) ((-1060 . -735) T) ((-1060 . -763) T) ((-1060 . -606) 153570) ((-1060 . -596) 153552) ((-1060 . -859) T) ((-1060 . -510) T) ((-1060 . -244) T) ((-1060 . -146) T) ((-1060 . -571) 153524) ((-1060 . -675) 153511) ((-1060 . -598) 153498) ((-1060 . -996) 153485) ((-1060 . -991) 153472) ((-1060 . -82) 153457) ((-1060 . -38) 153444) ((-1060 . -406) T) ((-1060 . -261) T) ((-1060 . -189) T) ((-1060 . -186) 153431) ((-1060 . -190) T) ((-1060 . -116) T) ((-1060 . -989) T) ((-1060 . -997) T) ((-1060 . -1052) T) ((-1060 . -684) T) ((-1060 . -21) T) ((-1060 . -604) 153403) ((-1060 . -23) T) ((-1060 . -1041) T) ((-1060 . -568) 153385) ((-1060 . -1157) T) ((-1060 . -73) T) ((-1060 . -25) T) ((-1060 . -104) T) ((-1060 . -120) T) ((-1060 . -777) T) ((-1060 . -323) T) ((-1060 . -84) T) ((-1060 . -620) T) ((-1056 . -1023) T) ((-1056 . -444) 153366) ((-1056 . -568) 153332) ((-1056 . -571) 153313) ((-1056 . -1041) T) ((-1056 . -1157) T) ((-1056 . -73) T) ((-1056 . -64) T) ((-1055 . -1041) T) ((-1055 . -568) 153295) ((-1055 . -1157) T) ((-1055 . -73) T) ((-1053 . -195) 153274) ((-1053 . -1215) 153244) ((-1053 . -742) 153223) ((-1053 . -739) 153202) ((-1053 . -784) 153153) ((-1053 . -781) 153104) ((-1053 . -737) 153083) ((-1053 . -738) 153062) ((-1053 . -675) 153004) ((-1053 . -598) 152926) ((-1053 . -242) 152903) ((-1053 . -240) 152880) ((-1053 . -443) 152864) ((-1053 . -468) 152797) ((-1053 . -263) 152735) ((-1053 . -34) T) ((-1053 . -554) 152712) ((-1053 . -978) 152541) ((-1053 . -571) 152342) ((-1053 . -366) 152311) ((-1053 . -596) 152219) ((-1053 . -606) 152055) ((-1053 . -332) 152025) ((-1053 . -323) 152004) ((-1053 . -190) 151957) ((-1053 . -604) 151739) ((-1053 . -684) 151718) ((-1053 . -1052) 151697) ((-1053 . -997) 151676) ((-1053 . -989) 151655) ((-1053 . -186) 151548) ((-1053 . -189) 151447) ((-1053 . -224) 151417) ((-1053 . -831) 151286) ((-1053 . -838) 151157) ((-1053 . -836) 151090) ((-1053 . -184) 151060) ((-1053 . -568) 150754) ((-1053 . -996) 150676) ((-1053 . -991) 150578) ((-1053 . -82) 150495) ((-1053 . -104) 150367) ((-1053 . -25) 150201) ((-1053 . -73) 149935) ((-1053 . -1157) T) ((-1053 . -1041) 149688) ((-1053 . -23) 149541) ((-1053 . -21) 149453) ((-1046 . -350) T) ((-1046 . -1157) T) ((-1046 . -568) 149435) ((-1045 . -1044) 149399) ((-1045 . -73) T) ((-1045 . -568) 149381) ((-1045 . -1041) T) ((-1045 . -240) 149337) ((-1045 . -1157) T) ((-1045 . -573) 149252) ((-1043 . -1044) 149204) ((-1043 . -73) T) ((-1043 . -568) 149186) ((-1043 . -1041) T) ((-1043 . -240) 149142) ((-1043 . -1157) T) ((-1043 . -573) 149045) ((-1042 . -323) T) ((-1042 . -73) T) ((-1042 . -1157) T) ((-1042 . -568) 149027) ((-1042 . -1041) T) ((-1037 . -380) 149011) ((-1037 . -1039) 148995) ((-1037 . -323) 148974) ((-1037 . -192) 148958) ((-1037 . -569) 148919) ((-1037 . -124) 148903) ((-1037 . -443) 148887) ((-1037 . -1041) T) ((-1037 . -468) 148820) ((-1037 . -263) 148758) ((-1037 . -568) 148740) ((-1037 . -73) T) ((-1037 . -1157) T) ((-1037 . -34) T) ((-1037 . -78) 148724) ((-1037 . -183) 148708) ((-1036 . -1023) T) ((-1036 . -444) 148689) ((-1036 . -568) 148655) ((-1036 . -571) 148636) ((-1036 . -1041) T) ((-1036 . -1157) T) ((-1036 . -73) T) ((-1036 . -64) T) ((-1032 . -1157) T) ((-1032 . -1041) 148606) ((-1032 . -568) 148565) ((-1032 . -73) 148535) ((-1031 . -1023) T) ((-1031 . -444) 148516) ((-1031 . -568) 148482) ((-1031 . -571) 148463) ((-1031 . -1041) T) ((-1031 . -1157) T) ((-1031 . -73) T) ((-1031 . -64) T) ((-1029 . -1034) 148447) ((-1029 . -573) 148431) ((-1029 . -1041) 148409) ((-1029 . -568) 148376) ((-1029 . -1157) 148354) ((-1029 . -73) 148332) ((-1029 . -1035) 148290) ((-1028 . -227) 148274) ((-1028 . -571) 148258) ((-1028 . -978) 148242) ((-1028 . -784) T) ((-1028 . -73) T) ((-1028 . -1041) T) ((-1028 . -568) 148224) ((-1028 . -781) T) ((-1028 . -186) 148211) ((-1028 . -1157) T) ((-1028 . -189) T) ((-1027 . -212) 148148) ((-1027 . -571) 147885) ((-1027 . -978) 147714) ((-1027 . -569) NIL) ((-1027 . -280) 147675) ((-1027 . -366) 147659) ((-1027 . -38) 147508) ((-1027 . -82) 147330) ((-1027 . -991) 147173) ((-1027 . -996) 147016) ((-1027 . -604) 146926) ((-1027 . -606) 146815) ((-1027 . -598) 146664) ((-1027 . -675) 146513) ((-1027 . -118) 146492) ((-1027 . -120) 146471) ((-1027 . -146) 146382) ((-1027 . -510) 146313) ((-1027 . -244) 146244) ((-1027 . -47) 146205) ((-1027 . -332) 146189) ((-1027 . -596) 146137) ((-1027 . -406) 146088) ((-1027 . -468) 145951) ((-1027 . -836) 145886) ((-1027 . -831) 145781) ((-1027 . -838) 145680) ((-1027 . -821) NIL) ((-1027 . -848) 145659) ((-1027 . -1162) 145638) ((-1027 . -888) 145583) ((-1027 . -263) 145570) ((-1027 . -190) 145549) ((-1027 . -104) T) ((-1027 . -25) T) ((-1027 . -73) T) ((-1027 . -568) 145531) ((-1027 . -1041) T) ((-1027 . -23) T) ((-1027 . -21) T) ((-1027 . -684) T) ((-1027 . -1052) T) ((-1027 . -997) T) ((-1027 . -989) T) ((-1027 . -186) 145476) ((-1027 . -1157) T) ((-1027 . -189) 145427) ((-1027 . -224) 145411) ((-1027 . -184) 145395) ((-1025 . -568) 145377) ((-1022 . -781) T) ((-1022 . -568) 145359) ((-1022 . -1041) T) ((-1022 . -73) T) ((-1022 . -1157) T) ((-1022 . -784) T) ((-1022 . -569) 145340) ((-1019 . -682) 145319) ((-1019 . -978) 145217) ((-1019 . -366) 145201) ((-1019 . -596) 145149) ((-1019 . -606) 145023) ((-1019 . -332) 145007) ((-1019 . -325) 144986) ((-1019 . -120) 144965) ((-1019 . -571) 144784) ((-1019 . -675) 144652) ((-1019 . -598) 144520) ((-1019 . -604) 144415) ((-1019 . -996) 144325) ((-1019 . -991) 144235) ((-1019 . -82) 144124) ((-1019 . -38) 143992) ((-1019 . -364) 143971) ((-1019 . -356) 143950) ((-1019 . -118) 143901) ((-1019 . -1092) 143880) ((-1019 . -305) 143859) ((-1019 . -323) 143810) ((-1019 . -200) 143761) ((-1019 . -244) 143712) ((-1019 . -261) 143663) ((-1019 . -406) 143614) ((-1019 . -510) 143565) ((-1019 . -859) 143516) ((-1019 . -1162) 143467) ((-1019 . -318) 143418) ((-1019 . -190) 143343) ((-1019 . -186) 143216) ((-1019 . -189) 143095) ((-1019 . -224) 143065) ((-1019 . -831) 142934) ((-1019 . -838) 142805) ((-1019 . -836) 142738) ((-1019 . -184) 142708) ((-1019 . -569) 142692) ((-1019 . -21) T) ((-1019 . -23) T) ((-1019 . -1041) T) ((-1019 . -568) 142674) ((-1019 . -1157) T) ((-1019 . -73) T) ((-1019 . -25) T) ((-1019 . -104) T) ((-1019 . -989) T) ((-1019 . -997) T) ((-1019 . -1052) T) ((-1019 . -684) T) ((-1019 . -146) T) ((-1017 . -1041) T) ((-1017 . -568) 142656) ((-1017 . -1157) T) ((-1017 . -73) T) ((-1017 . -240) 142635) ((-1016 . -1041) T) ((-1016 . -568) 142617) ((-1016 . -1157) T) ((-1016 . -73) T) ((-1015 . -1041) T) ((-1015 . -568) 142599) ((-1015 . -1157) T) ((-1015 . -73) T) ((-1015 . -240) 142578) ((-1015 . -978) 142555) ((-1015 . -571) 142532) ((-1014 . -1157) T) ((-1013 . -1023) T) ((-1013 . -444) 142513) ((-1013 . -568) 142479) ((-1013 . -571) 142460) ((-1013 . -1041) T) ((-1013 . -1157) T) ((-1013 . -73) T) ((-1013 . -64) T) ((-1006 . -1023) T) ((-1006 . -444) 142441) ((-1006 . -568) 142407) ((-1006 . -571) 142388) ((-1006 . -1041) T) ((-1006 . -1157) T) ((-1006 . -73) T) ((-1006 . -64) T) ((-1003 . -1134) 142363) ((-1003 . -183) 142307) ((-1003 . -78) 142251) ((-1003 . -263) 142096) ((-1003 . -468) 141896) ((-1003 . -443) 141826) ((-1003 . -124) 141770) ((-1003 . -569) NIL) ((-1003 . -192) 141714) ((-1003 . -565) 141689) ((-1003 . -242) 141664) ((-1003 . -1157) T) ((-1003 . -240) 141639) ((-1003 . -1041) T) ((-1003 . -568) 141621) ((-1003 . -73) T) ((-1003 . -34) T) ((-1003 . -554) 141596) ((-1002 . -498) T) ((-1002 . -1162) T) ((-1002 . -1092) T) ((-1002 . -978) 141578) ((-1002 . -569) 141493) ((-1002 . -960) T) ((-1002 . -821) 141475) ((-1002 . -780) T) ((-1002 . -742) T) ((-1002 . -739) T) ((-1002 . -784) T) ((-1002 . -781) T) ((-1002 . -737) T) ((-1002 . -735) T) ((-1002 . -763) T) ((-1002 . -606) 141447) ((-1002 . -596) 141429) ((-1002 . -859) T) ((-1002 . -510) T) ((-1002 . -244) T) ((-1002 . -146) T) ((-1002 . -571) 141401) ((-1002 . -675) 141388) ((-1002 . -598) 141375) ((-1002 . -996) 141362) ((-1002 . -991) 141349) ((-1002 . -82) 141334) ((-1002 . -38) 141321) ((-1002 . -406) T) ((-1002 . -261) T) ((-1002 . -189) T) ((-1002 . -186) 141308) ((-1002 . -190) T) ((-1002 . -116) T) ((-1002 . -989) T) ((-1002 . -997) T) ((-1002 . -1052) T) ((-1002 . -684) T) ((-1002 . -21) T) ((-1002 . -604) 141280) ((-1002 . -23) T) ((-1002 . -1041) T) ((-1002 . -568) 141262) ((-1002 . -1157) T) ((-1002 . -73) T) ((-1002 . -25) T) ((-1002 . -104) T) ((-1002 . -120) T) ((-1002 . -573) 141243) ((-1001 . -1008) 141222) ((-1001 . -73) T) ((-1001 . -1157) T) ((-1001 . -568) 141204) ((-1001 . -1041) T) ((-998 . -1157) T) ((-998 . -1041) 141182) ((-998 . -568) 141149) ((-998 . -73) 141127) ((-994 . -993) 141067) ((-994 . -598) 141009) ((-994 . -675) 140951) ((-994 . -34) T) ((-994 . -263) 140889) ((-994 . -468) 140822) ((-994 . -443) 140806) ((-994 . -606) 140790) ((-994 . -604) 140759) ((-994 . -104) T) ((-994 . -25) T) ((-994 . -73) T) ((-994 . -1157) T) ((-994 . -568) 140721) ((-994 . -1041) T) ((-994 . -23) T) ((-994 . -21) T) ((-994 . -996) 140705) ((-994 . -991) 140689) ((-994 . -82) 140668) ((-994 . -1215) 140638) ((-994 . -569) 140599) ((-986 . -1011) 140528) ((-986 . -916) 140457) ((-986 . -569) 140399) ((-986 . -443) 140364) ((-986 . -1041) T) ((-986 . -468) 140248) ((-986 . -263) 140156) ((-986 . -568) 140099) ((-986 . -73) T) ((-986 . -1157) T) ((-986 . -34) T) ((-986 . -124) 140064) ((-986 . -1152) 139993) ((-976 . -1023) T) ((-976 . -444) 139974) ((-976 . -568) 139940) ((-976 . -571) 139921) ((-976 . -1041) T) ((-976 . -1157) T) ((-976 . -73) T) ((-976 . -64) T) ((-975 . -1134) 139896) ((-975 . -183) 139840) ((-975 . -78) 139784) ((-975 . -263) 139629) ((-975 . -468) 139429) ((-975 . -443) 139359) ((-975 . -124) 139303) ((-975 . -569) NIL) ((-975 . -192) 139247) ((-975 . -565) 139222) ((-975 . -242) 139197) ((-975 . -1157) T) ((-975 . -240) 139172) ((-975 . -1041) T) ((-975 . -568) 139154) ((-975 . -73) T) ((-975 . -34) T) ((-975 . -554) 139129) ((-974 . -146) T) ((-974 . -571) 139098) ((-974 . -684) T) ((-974 . -1052) T) ((-974 . -997) T) ((-974 . -989) T) ((-974 . -606) 139072) ((-974 . -604) 139031) ((-974 . -104) T) ((-974 . -25) T) ((-974 . -73) T) ((-974 . -1157) T) ((-974 . -568) 139013) ((-974 . -1041) T) ((-974 . -23) T) ((-974 . -21) T) ((-974 . -996) 138987) ((-974 . -991) 138961) ((-974 . -82) 138928) ((-974 . -38) 138912) ((-974 . -598) 138896) ((-974 . -675) 138880) ((-967 . -1011) 138849) ((-967 . -916) 138818) ((-967 . -569) 138779) ((-967 . -443) 138763) ((-967 . -1041) T) ((-967 . -468) 138696) ((-967 . -263) 138634) ((-967 . -568) 138596) ((-967 . -73) T) ((-967 . -1157) T) ((-967 . -34) T) ((-967 . -124) 138580) ((-967 . -1152) 138549) ((-966 . -1157) T) ((-966 . -1041) 138527) ((-966 . -568) 138494) ((-966 . -73) 138472) ((-964 . -952) T) ((-964 . -942) T) ((-964 . -735) T) ((-964 . -737) T) ((-964 . -781) T) ((-964 . -784) T) ((-964 . -739) T) ((-964 . -742) T) ((-964 . -780) T) ((-964 . -978) 138354) ((-964 . -366) 138316) ((-964 . -200) T) ((-964 . -244) T) ((-964 . -261) T) ((-964 . -406) T) ((-964 . -38) 138253) ((-964 . -598) 138190) ((-964 . -675) 138127) ((-964 . -571) 138064) ((-964 . -510) T) ((-964 . -859) T) ((-964 . -1162) T) ((-964 . -318) T) ((-964 . -82) 137973) ((-964 . -991) 137910) ((-964 . -996) 137847) ((-964 . -146) T) ((-964 . -120) T) ((-964 . -606) 137784) ((-964 . -604) 137721) ((-964 . -104) T) ((-964 . -25) T) ((-964 . -73) T) ((-964 . -1157) T) ((-964 . -568) 137703) ((-964 . -1041) T) ((-964 . -23) T) ((-964 . -21) T) ((-964 . -989) T) ((-964 . -997) T) ((-964 . -1052) T) ((-964 . -684) T) ((-959 . -1023) T) ((-959 . -444) 137684) ((-959 . -568) 137650) ((-959 . -571) 137631) ((-959 . -1041) T) ((-959 . -1157) T) ((-959 . -73) T) ((-959 . -64) T) ((-944 . -931) 137613) ((-944 . -1092) T) ((-944 . -571) 137563) ((-944 . -978) 137523) ((-944 . -569) 137453) ((-944 . -960) T) ((-944 . -848) NIL) ((-944 . -819) 137435) ((-944 . -780) T) ((-944 . -742) T) ((-944 . -739) T) ((-944 . -784) T) ((-944 . -781) T) ((-944 . -737) T) ((-944 . -735) T) ((-944 . -763) T) ((-944 . -821) 137417) ((-944 . -354) 137399) ((-944 . -596) 137381) ((-944 . -332) 137363) ((-944 . -240) NIL) ((-944 . -263) NIL) ((-944 . -468) NIL) ((-944 . -293) 137345) ((-944 . -200) T) ((-944 . -82) 137272) ((-944 . -991) 137222) ((-944 . -996) 137172) ((-944 . -244) T) ((-944 . -675) 137122) ((-944 . -598) 137072) ((-944 . -606) 137022) ((-944 . -604) 136972) ((-944 . -38) 136922) ((-944 . -261) T) ((-944 . -406) T) ((-944 . -146) T) ((-944 . -510) T) ((-944 . -859) T) ((-944 . -1162) T) ((-944 . -318) T) ((-944 . -190) T) ((-944 . -186) 136909) ((-944 . -189) T) ((-944 . -224) 136891) ((-944 . -831) NIL) ((-944 . -838) NIL) ((-944 . -836) NIL) ((-944 . -184) 136873) ((-944 . -120) T) ((-944 . -118) NIL) ((-944 . -104) T) ((-944 . -25) T) ((-944 . -73) T) ((-944 . -1157) T) ((-944 . -568) 136833) ((-944 . -1041) T) ((-944 . -23) T) ((-944 . -21) T) ((-944 . -989) T) ((-944 . -997) T) ((-944 . -1052) T) ((-944 . -684) T) ((-943 . -297) 136807) ((-943 . -146) T) ((-943 . -571) 136737) ((-943 . -684) T) ((-943 . -1052) T) ((-943 . -997) T) ((-943 . -989) T) ((-943 . -606) 136639) ((-943 . -604) 136569) ((-943 . -104) T) ((-943 . -25) T) ((-943 . -73) T) ((-943 . -1157) T) ((-943 . -568) 136551) ((-943 . -1041) T) ((-943 . -23) T) ((-943 . -21) T) ((-943 . -996) 136496) ((-943 . -991) 136441) ((-943 . -82) 136358) ((-943 . -569) 136342) ((-943 . -184) 136319) ((-943 . -836) 136271) ((-943 . -838) 136180) ((-943 . -831) 136087) ((-943 . -224) 136064) ((-943 . -189) 136001) ((-943 . -186) 135932) ((-943 . -190) 135904) ((-943 . -318) T) ((-943 . -1162) T) ((-943 . -859) T) ((-943 . -510) T) ((-943 . -675) 135849) ((-943 . -598) 135794) ((-943 . -38) 135739) ((-943 . -406) T) ((-943 . -261) T) ((-943 . -244) T) ((-943 . -200) T) ((-943 . -323) NIL) ((-943 . -305) NIL) ((-943 . -1092) NIL) ((-943 . -118) 135711) ((-943 . -356) NIL) ((-943 . -364) 135683) ((-943 . -120) 135655) ((-943 . -325) 135627) ((-943 . -332) 135604) ((-943 . -596) 135538) 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. -739) T) ((-659 . -737) T) ((-659 . -735) T) ((-659 . -763) T) ((-659 . -596) 95947) ((-659 . -859) T) ((-659 . -406) T) ((-659 . -261) T) ((-659 . -189) T) ((-659 . -186) 95934) ((-659 . -190) T) ((-659 . -116) T) ((-659 . -120) T) ((-657 . -358) T) ((-657 . -120) T) ((-657 . -571) 95869) ((-657 . -606) 95834) ((-657 . -604) 95784) ((-657 . -104) T) ((-657 . -25) T) ((-657 . -73) T) ((-657 . -1157) T) ((-657 . -568) 95766) ((-657 . -1041) T) ((-657 . -23) T) ((-657 . -21) T) ((-657 . -684) T) ((-657 . -1052) T) ((-657 . -997) T) ((-657 . -989) T) ((-657 . -569) 95711) ((-657 . -318) T) ((-657 . -1162) T) ((-657 . -859) T) ((-657 . -510) T) ((-657 . -146) T) ((-657 . -675) 95676) ((-657 . -598) 95641) ((-657 . -38) 95606) ((-657 . -406) T) ((-657 . -261) T) ((-657 . -82) 95555) ((-657 . -991) 95520) ((-657 . -996) 95485) ((-657 . -244) T) ((-657 . -200) T) ((-657 . -780) T) ((-657 . -742) T) ((-657 . -739) T) ((-657 . -784) T) ((-657 . -781) T) ((-657 . -737) T) ((-657 . -735) T) 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. -1041) 75240) ((-450 . -468) 75173) ((-450 . -263) 75111) ((-450 . -568) 75023) ((-450 . -73) 74954) ((-450 . -1157) T) ((-450 . -34) T) ((-450 . -124) 74938) ((-450 . -781) 74917) ((-450 . -784) 74896) ((-450 . -327) 74880) ((-449 . -252) T) ((-449 . -73) T) ((-449 . -1157) T) ((-449 . -568) 74862) ((-449 . -1041) T) ((-449 . -571) 74763) ((-449 . -978) 74706) ((-449 . -468) 74672) ((-449 . -263) 74659) ((-449 . -27) T) ((-449 . -942) T) ((-449 . -200) T) ((-449 . -82) 74608) ((-449 . -991) 74573) ((-449 . -996) 74538) ((-449 . -244) T) ((-449 . -675) 74503) ((-449 . -598) 74468) ((-449 . -606) 74418) ((-449 . -604) 74368) ((-449 . -104) T) ((-449 . -25) T) ((-449 . -23) T) ((-449 . -21) T) ((-449 . -989) T) ((-449 . -997) T) ((-449 . -1052) T) ((-449 . -684) T) ((-449 . -38) 74333) ((-449 . -261) T) ((-449 . -406) T) ((-449 . -146) T) ((-449 . -510) T) ((-449 . -859) T) ((-449 . -1162) T) ((-449 . -318) T) ((-449 . -596) 74293) ((-449 . -960) T) ((-449 . -569) 74238) ((-449 . -120) 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72848) ((-436 . -739) 72827) ((-436 . -784) 72778) ((-436 . -781) 72729) ((-436 . -737) 72708) ((-436 . -738) 72687) ((-436 . -675) 72629) ((-436 . -598) 72551) ((-436 . -242) 72528) ((-436 . -240) 72505) ((-436 . -443) 72489) ((-436 . -468) 72422) ((-436 . -263) 72360) ((-436 . -34) T) ((-436 . -554) 72337) ((-436 . -978) 72166) ((-436 . -571) 71967) ((-436 . -366) 71936) ((-436 . -596) 71844) ((-436 . -606) 71680) ((-436 . -332) 71650) ((-436 . -323) 71629) ((-436 . -190) 71582) ((-436 . -604) 71364) ((-436 . -684) 71343) ((-436 . -1052) 71322) ((-436 . -997) 71301) ((-436 . -989) 71280) ((-436 . -186) 71173) ((-436 . -189) 71072) ((-436 . -224) 71042) ((-436 . -831) 70911) ((-436 . -838) 70782) ((-436 . -836) 70715) ((-436 . -184) 70685) ((-436 . -568) 70379) ((-436 . -996) 70301) ((-436 . -991) 70203) ((-436 . -82) 70120) ((-436 . -104) 69992) ((-436 . -25) 69826) ((-436 . -73) 69560) ((-436 . -1157) T) ((-436 . -1041) 69313) ((-436 . -23) 69166) ((-436 . -21) 69078) ((-435 . -888) 69023) ((-435 . -571) 68809) ((-435 . -978) 68687) ((-435 . -1162) 68666) ((-435 . -848) 68645) ((-435 . -821) NIL) ((-435 . -838) 68622) ((-435 . -831) 68597) ((-435 . -836) 68574) ((-435 . -468) 68512) ((-435 . -406) 68463) ((-435 . -596) 68411) ((-435 . -606) 68300) ((-435 . -332) 68284) ((-435 . -47) 68241) ((-435 . -38) 68090) ((-435 . -598) 67939) ((-435 . -675) 67788) ((-435 . -244) 67719) ((-435 . -510) 67650) ((-435 . -82) 67472) ((-435 . -991) 67315) ((-435 . -996) 67158) ((-435 . -146) 67069) ((-435 . -120) 67048) ((-435 . -118) 67027) ((-435 . -604) 66937) ((-435 . -104) T) ((-435 . -25) T) ((-435 . -73) T) ((-435 . -1157) T) ((-435 . -568) 66919) ((-435 . -1041) T) ((-435 . -23) T) ((-435 . -21) T) ((-435 . -989) T) ((-435 . -997) T) ((-435 . -1052) T) ((-435 . -684) T) ((-435 . -366) 66903) ((-435 . -280) 66860) ((-435 . -263) 66847) ((-435 . -569) 66708) ((-433 . -1134) 66687) ((-433 . -183) 66635) ((-433 . -78) 66583) ((-433 . -263) 66381) ((-433 . -468) 66133) ((-433 . -443) 66068) ((-433 . -124) 66016) ((-433 . -569) NIL) ((-433 . -192) 65964) ((-433 . -565) 65943) ((-433 . -242) 65922) ((-433 . -1157) T) ((-433 . -240) 65901) ((-433 . -1041) T) ((-433 . -568) 65883) ((-433 . -73) T) ((-433 . -34) T) ((-433 . -554) 65862) ((-432 . -1023) T) ((-432 . -444) 65843) ((-432 . -568) 65809) ((-432 . -571) 65790) ((-432 . -1041) T) ((-432 . -1157) T) ((-432 . -73) T) ((-432 . -64) T) ((-431 . -318) T) ((-431 . -1162) T) ((-431 . -859) T) ((-431 . -510) T) ((-431 . -146) T) ((-431 . -571) 65740) ((-431 . -675) 65705) ((-431 . -598) 65670) ((-431 . -38) 65635) ((-431 . -406) T) ((-431 . -261) T) ((-431 . -606) 65600) ((-431 . -604) 65550) ((-431 . -684) T) ((-431 . -1052) T) ((-431 . -997) T) ((-431 . -989) T) ((-431 . -82) 65499) ((-431 . -991) 65464) ((-431 . -996) 65429) ((-431 . -21) T) ((-431 . -23) T) ((-431 . -1041) T) ((-431 . -568) 65381) ((-431 . -1157) T) ((-431 . -73) T) ((-431 . -25) T) ((-431 . -104) T) ((-431 . -244) T) ((-431 . -200) T) ((-431 . -120) T) ((-431 . -978) 65341) ((-431 . -960) T) ((-431 . -569) 65263) ((-430 . -1152) 65232) ((-430 . -568) 65194) ((-430 . -124) 65178) ((-430 . -34) T) ((-430 . -1157) T) ((-430 . -73) T) ((-430 . -263) 65116) ((-430 . -468) 65049) ((-430 . -1041) T) ((-430 . -443) 65033) ((-430 . -569) 64994) ((-430 . -916) 64963) ((-429 . -1134) 64942) ((-429 . -183) 64890) ((-429 . -78) 64838) ((-429 . -263) 64636) ((-429 . -468) 64388) ((-429 . -443) 64323) ((-429 . -124) 64271) ((-429 . -569) NIL) ((-429 . -192) 64219) ((-429 . -565) 64198) ((-429 . -242) 64177) ((-429 . -1157) T) ((-429 . -240) 64156) ((-429 . -1041) T) ((-429 . -568) 64138) ((-429 . -73) T) ((-429 . -34) T) ((-429 . -554) 64117) ((-428 . -1190) 64101) ((-428 . -190) 64053) ((-428 . -186) 63999) ((-428 . -189) 63951) ((-428 . -240) 63909) ((-428 . -836) 63815) ((-428 . -831) 63696) ((-428 . -838) 63602) ((-428 . -913) 63564) ((-428 . -38) 63405) ((-428 . -82) 63219) ((-428 . -991) 63054) ((-428 . -996) 62889) ((-428 . -604) 62771) ((-428 . -606) 62668) ((-428 . -598) 62509) ((-428 . -675) 62350) ((-428 . -571) 62176) ((-428 . -118) 62155) ((-428 . -120) 62134) ((-428 . -47) 62104) ((-428 . -1186) 62074) ((-428 . -35) 62040) ((-428 . -66) 62006) ((-428 . -238) 61972) ((-428 . -447) 61938) ((-428 . -1146) 61904) ((-428 . -1143) 61870) ((-428 . -942) 61836) ((-428 . -200) 61815) ((-428 . -244) 61766) ((-428 . -104) T) ((-428 . -25) T) ((-428 . -73) T) ((-428 . -1157) T) ((-428 . -568) 61748) ((-428 . -1041) T) ((-428 . -23) T) ((-428 . -21) T) ((-428 . -989) T) ((-428 . -997) T) ((-428 . -1052) T) ((-428 . -684) T) ((-428 . -261) 61727) ((-428 . -406) 61706) ((-428 . -146) 61637) ((-428 . -510) 61588) ((-428 . -859) 61567) ((-428 . -1162) 61546) ((-428 . -318) 61525) ((-422 . -1041) T) ((-422 . -568) 61507) ((-422 . -1157) T) ((-422 . -73) T) ((-417 . -916) 61476) ((-417 . -569) 61437) ((-417 . -443) 61421) ((-417 . -1041) T) ((-417 . -468) 61354) ((-417 . -263) 61292) ((-417 . -568) 61254) ((-417 . -73) T) 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((-408 . -1157) T) ((-408 . -568) 58877) ((-408 . -1041) T) ((-408 . -23) T) ((-408 . -21) T) ((-408 . -989) T) ((-408 . -997) T) ((-408 . -1052) T) ((-408 . -684) T) ((-408 . -366) 58861) ((-408 . -280) 58840) ((-408 . -263) 58827) ((-408 . -569) 58688) ((-407 . -372) 58658) ((-407 . -702) 58628) ((-407 . -678) T) ((-407 . -704) T) ((-407 . -82) 58579) ((-407 . -991) 58549) ((-407 . -996) 58519) ((-407 . -21) T) ((-407 . -604) 58434) ((-407 . -23) T) ((-407 . -1041) T) ((-407 . -568) 58416) ((-407 . -73) T) ((-407 . -25) T) ((-407 . -104) T) ((-407 . -606) 58346) ((-407 . -598) 58316) ((-407 . -675) 58286) ((-407 . -322) 58256) ((-407 . -1157) T) ((-407 . -240) 58219) ((-393 . -1041) T) ((-393 . -568) 58201) ((-393 . -1157) T) ((-393 . -73) T) ((-392 . -1041) T) ((-392 . -568) 58183) ((-392 . -1157) T) ((-392 . -73) T) ((-391 . -320) 58157) ((-391 . -73) T) ((-391 . -1157) T) ((-391 . -568) 58139) ((-391 . -1041) T) ((-390 . -1041) T) ((-390 . -568) 58121) ((-390 . -1157) T) ((-390 . 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T) ((-202 . -124) 21464) ((-202 . -236) 21448) ((-202 . -444) 21425) ((-202 . -571) 21402) ((-196 . -195) 21381) ((-196 . -1215) 21351) ((-196 . -742) 21330) ((-196 . -739) 21309) ((-196 . -784) 21260) ((-196 . -781) 21211) ((-196 . -737) 21190) ((-196 . -738) 21169) ((-196 . -675) 21111) ((-196 . -598) 21033) ((-196 . -242) 21010) ((-196 . -240) 20987) ((-196 . -443) 20971) ((-196 . -468) 20904) ((-196 . -263) 20842) ((-196 . -34) T) ((-196 . -554) 20819) ((-196 . -978) 20648) ((-196 . -571) 20449) ((-196 . -366) 20418) ((-196 . -596) 20326) ((-196 . -606) 20162) ((-196 . -332) 20132) ((-196 . -323) 20111) ((-196 . -190) 20064) ((-196 . -604) 19846) ((-196 . -684) 19825) ((-196 . -1052) 19804) ((-196 . -997) 19783) ((-196 . -989) 19762) ((-196 . -186) 19655) ((-196 . -189) 19554) ((-196 . -224) 19524) ((-196 . -831) 19393) ((-196 . -838) 19264) ((-196 . -836) 19197) ((-196 . -184) 19167) ((-196 . -568) 18861) ((-196 . -996) 18783) ((-196 . -991) 18685) ((-196 . -82) 18602) ((-196 . 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198276) ((-1193 . -649) 198246) ((-1193 . -577) 198216) ((-1193 . -961) 198200) ((-1193 . -956) 198184) ((-1193 . -80) 198163) ((-1193 . -38) 198133) ((-1193 . -1188) 198112) ((-1192 . -954) T) ((-1192 . -962) T) ((-1192 . -1015) T) ((-1192 . -658) T) ((-1192 . -21) T) ((-1192 . -583) 198071) ((-1192 . -23) T) ((-1192 . -1005) T) ((-1192 . -547) 198053) ((-1192 . -1118) T) ((-1192 . -72) T) ((-1192 . -25) T) ((-1192 . -102) T) ((-1192 . -585) 198027) ((-1192 . -550) 197983) ((-1192 . -1183) 197967) ((-1192 . -649) 197937) ((-1192 . -577) 197907) ((-1192 . -961) 197891) ((-1192 . -956) 197875) ((-1192 . -80) 197854) ((-1192 . -38) 197824) ((-1192 . -328) 197803) ((-1192 . -943) 197787) ((-1190 . -1191) 197763) ((-1190 . -943) 197737) ((-1190 . -550) 197683) ((-1190 . -954) T) ((-1190 . -962) T) ((-1190 . -1015) T) ((-1190 . -658) T) ((-1190 . -21) T) ((-1190 . -583) 197642) ((-1190 . -23) T) ((-1190 . -1005) T) ((-1190 . -547) 197624) ((-1190 . -1118) T) ((-1190 . -72) T) ((-1190 . -25) T) ((-1190 . -102) T) ((-1190 . -585) 197598) ((-1190 . -1183) 197582) ((-1190 . -649) 197552) ((-1190 . -577) 197522) ((-1190 . -961) 197506) ((-1190 . -956) 197490) ((-1190 . -80) 197469) ((-1190 . -38) 197439) ((-1190 . -1188) 197415) ((-1189 . -1191) 197394) ((-1189 . -943) 197351) ((-1189 . -550) 197280) ((-1189 . -954) T) ((-1189 . -962) T) ((-1189 . -1015) T) ((-1189 . -658) T) ((-1189 . -21) T) ((-1189 . -583) 197239) ((-1189 . -23) T) ((-1189 . -1005) T) ((-1189 . -547) 197221) ((-1189 . -1118) T) ((-1189 . -72) T) ((-1189 . -25) T) ((-1189 . -102) T) ((-1189 . -585) 197195) ((-1189 . -1183) 197179) ((-1189 . -649) 197149) ((-1189 . -577) 197119) ((-1189 . -961) 197103) ((-1189 . -956) 197087) ((-1189 . -80) 197066) ((-1189 . -38) 197036) ((-1189 . -1188) 197015) ((-1189 . -328) 196987) ((-1184 . -328) 196959) ((-1184 . -550) 196908) ((-1184 . -943) 196885) ((-1184 . -577) 196855) ((-1184 . -649) 196825) ((-1184 . -585) 196799) ((-1184 . -583) 196758) ((-1184 . -102) T) ((-1184 . -25) T) ((-1184 . -72) T) ((-1184 . -1118) T) ((-1184 . -547) 196740) ((-1184 . -1005) T) ((-1184 . -23) T) ((-1184 . -21) T) ((-1184 . -961) 196724) ((-1184 . -956) 196708) ((-1184 . -80) 196687) ((-1184 . -1191) 196666) ((-1184 . -954) T) ((-1184 . -962) T) ((-1184 . -1015) T) ((-1184 . -658) T) ((-1184 . -1183) 196650) ((-1184 . -38) 196620) ((-1184 . -1188) 196599) ((-1182 . -1113) 196568) ((-1182 . -547) 196530) ((-1182 . -122) 196514) ((-1182 . -34) T) ((-1182 . -1118) T) ((-1182 . -72) T) ((-1182 . -256) 196452) ((-1182 . -447) 196385) ((-1182 . -1005) T) ((-1182 . -422) 196369) ((-1182 . -548) 196330) ((-1182 . -882) 196299) ((-1181 . -954) T) ((-1181 . -962) T) ((-1181 . -1015) T) ((-1181 . -658) T) ((-1181 . -21) T) ((-1181 . -583) 196244) ((-1181 . -23) T) ((-1181 . -1005) T) ((-1181 . -547) 196213) ((-1181 . -1118) T) ((-1181 . -72) T) ((-1181 . -25) T) ((-1181 . -102) T) ((-1181 . -585) 196173) ((-1181 . -550) 196115) ((-1181 . -423) 196099) ((-1181 . -38) 196069) ((-1181 . -80) 196034) ((-1181 . -956) 196004) ((-1181 . -961) 195974) ((-1181 . -577) 195944) ((-1181 . -649) 195914) ((-1180 . -987) T) ((-1180 . -423) 195895) ((-1180 . -547) 195861) ((-1180 . -550) 195842) ((-1180 . -1005) T) ((-1180 . -1118) T) ((-1180 . -72) T) ((-1180 . -64) T) ((-1179 . -987) T) ((-1179 . -423) 195823) ((-1179 . -547) 195789) ((-1179 . -550) 195770) ((-1179 . -1005) T) ((-1179 . -1118) T) ((-1179 . -72) T) ((-1179 . -64) T) ((-1174 . -547) 195752) ((-1172 . -1005) T) ((-1172 . -547) 195734) ((-1172 . -1118) T) ((-1172 . -72) T) ((-1171 . -1005) T) ((-1171 . -547) 195716) ((-1171 . -1118) T) ((-1171 . -72) T) ((-1168 . -1167) 195700) ((-1168 . -317) 195684) ((-1168 . -752) 195663) ((-1168 . -749) 195642) ((-1168 . -122) 195626) ((-1168 . -34) T) ((-1168 . -1118) T) ((-1168 . -72) 195560) ((-1168 . -547) 195475) ((-1168 . -256) 195413) ((-1168 . -447) 195346) ((-1168 . -1005) 195299) ((-1168 . -422) 195283) ((-1168 . -548) 195244) ((-1168 . -238) 195196) ((-1168 . -533) 195173) ((-1168 . -240) 195150) ((-1168 . -588) 195134) ((-1168 . -19) 195118) ((-1165 . -1005) T) ((-1165 . -547) 195084) ((-1165 . -1118) T) ((-1165 . -72) T) ((-1158 . -1161) 195068) ((-1158 . -188) 195027) ((-1158 . -550) 194909) ((-1158 . -585) 194834) ((-1158 . -583) 194744) ((-1158 . -102) T) ((-1158 . -25) T) ((-1158 . -72) T) ((-1158 . -547) 194726) ((-1158 . -1005) T) ((-1158 . -23) T) ((-1158 . -21) T) ((-1158 . -658) T) ((-1158 . -1015) T) ((-1158 . -962) T) ((-1158 . -954) T) ((-1158 . -184) 194679) ((-1158 . -1118) T) ((-1158 . -187) 194638) ((-1158 . -238) 194603) ((-1158 . -802) 194516) ((-1158 . -799) 194404) ((-1158 . -804) 194317) ((-1158 . -879) 194287) ((-1158 . -38) 194184) ((-1158 . -80) 194049) ((-1158 . -956) 193935) ((-1158 . -961) 193821) ((-1158 . -577) 193718) ((-1158 . -649) 193615) ((-1158 . -116) 193594) ((-1158 . -118) 193573) ((-1158 . -144) 193527) ((-1158 . -489) 193506) ((-1158 . -242) 193485) ((-1158 . -47) 193462) ((-1158 . -1147) 193439) ((-1158 . -35) 193405) ((-1158 . -66) 193371) ((-1158 . -236) 193337) ((-1158 . -426) 193303) ((-1158 . -1107) 193269) ((-1158 . -1104) 193235) ((-1158 . -908) 193201) ((-1155 . -273) 193145) ((-1155 . -943) 193111) ((-1155 . -348) 193077) ((-1155 . -38) 192934) ((-1155 . -550) 192808) ((-1155 . -585) 192697) ((-1155 . -583) 192571) ((-1155 . -658) T) ((-1155 . -1015) T) ((-1155 . -962) T) ((-1155 . -954) T) ((-1155 . -80) 192421) ((-1155 . -956) 192310) ((-1155 . -961) 192199) ((-1155 . -21) T) ((-1155 . -23) T) ((-1155 . -1005) T) ((-1155 . -547) 192181) ((-1155 . -1118) T) ((-1155 . -72) T) ((-1155 . -25) T) ((-1155 . -102) T) ((-1155 . -577) 192038) ((-1155 . -649) 191895) ((-1155 . -116) 191856) ((-1155 . -118) 191817) ((-1155 . -144) T) ((-1155 . -489) T) ((-1155 . -242) T) ((-1155 . -47) 191761) ((-1154 . -1153) 191740) ((-1154 . -308) 191719) ((-1154 . -1123) 191698) ((-1154 . -825) 191677) ((-1154 . -489) 191631) ((-1154 . -144) 191565) ((-1154 . -550) 191384) ((-1154 . -649) 191231) ((-1154 . -577) 191078) ((-1154 . -38) 190925) ((-1154 . -385) 190904) ((-1154 . -254) 190883) ((-1154 . -585) 190783) ((-1154 . -583) 190668) ((-1154 . -658) T) ((-1154 . -1015) T) ((-1154 . -962) T) ((-1154 . -954) T) ((-1154 . -80) 190488) ((-1154 . -956) 190329) ((-1154 . -961) 190170) ((-1154 . -21) T) ((-1154 . -23) T) ((-1154 . -1005) T) ((-1154 . -547) 190152) ((-1154 . -1118) T) ((-1154 . -72) T) ((-1154 . -25) T) ((-1154 . -102) T) ((-1154 . -242) 190106) ((-1154 . -198) 190085) ((-1154 . -908) 190051) ((-1154 . -1104) 190017) ((-1154 . -1107) 189983) ((-1154 . -426) 189949) ((-1154 . -236) 189915) ((-1154 . -66) 189881) ((-1154 . -35) 189847) ((-1154 . -1147) 189817) ((-1154 . -47) 189787) ((-1154 . -118) 189766) ((-1154 . -116) 189745) ((-1154 . -879) 189708) ((-1154 . -804) 189614) ((-1154 . -799) 189518) ((-1154 . -802) 189424) ((-1154 . -238) 189382) ((-1154 . -187) 189334) ((-1154 . -184) 189280) ((-1154 . -188) 189232) ((-1154 . -1151) 189216) ((-1154 . -943) 189200) ((-1149 . -1153) 189161) ((-1149 . -308) 189140) ((-1149 . -1123) 189119) ((-1149 . -825) 189098) ((-1149 . -489) 189052) ((-1149 . -144) 188986) ((-1149 . -550) 188735) ((-1149 . -649) 188582) ((-1149 . -577) 188429) ((-1149 . -38) 188276) ((-1149 . -385) 188255) ((-1149 . -254) 188234) ((-1149 . -585) 188134) ((-1149 . -583) 188019) ((-1149 . -658) T) ((-1149 . -1015) T) ((-1149 . -962) T) ((-1149 . -954) T) ((-1149 . -80) 187839) ((-1149 . -956) 187680) ((-1149 . -961) 187521) ((-1149 . -21) T) ((-1149 . -23) T) ((-1149 . -1005) T) ((-1149 . -547) 187503) ((-1149 . -1118) T) ((-1149 . -72) T) ((-1149 . -25) T) ((-1149 . -102) T) ((-1149 . -242) 187457) ((-1149 . -198) 187436) ((-1149 . -908) 187402) ((-1149 . -1104) 187368) ((-1149 . -1107) 187334) ((-1149 . -426) 187300) ((-1149 . -236) 187266) ((-1149 . -66) 187232) ((-1149 . -35) 187198) ((-1149 . -1147) 187168) ((-1149 . -47) 187138) ((-1149 . -118) 187117) ((-1149 . -116) 187096) ((-1149 . -879) 187059) ((-1149 . -804) 186965) ((-1149 . -799) 186846) ((-1149 . -802) 186752) ((-1149 . -238) 186710) ((-1149 . -187) 186662) ((-1149 . -184) 186608) ((-1149 . -188) 186560) ((-1149 . -1151) 186544) ((-1149 . -943) 186479) ((-1137 . -1144) 186463) ((-1137 . -1055) 186441) ((-1137 . -548) NIL) ((-1137 . -256) 186428) ((-1137 . -447) 186376) ((-1137 . -273) 186353) ((-1137 . -943) 186236) ((-1137 . -348) 186220) ((-1137 . -38) 186052) ((-1137 . -80) 185857) ((-1137 . -956) 185683) ((-1137 . -961) 185509) ((-1137 . -583) 185419) ((-1137 . -585) 185308) ((-1137 . -577) 185140) ((-1137 . -649) 184972) ((-1137 . -550) 184728) ((-1137 . -116) 184707) ((-1137 . -118) 184686) ((-1137 . -47) 184663) ((-1137 . -322) 184647) ((-1137 . -575) 184595) ((-1137 . -802) 184539) ((-1137 . -799) 184446) ((-1137 . -804) 184357) ((-1137 . -789) NIL) ((-1137 . -814) 184336) ((-1137 . -1123) 184315) ((-1137 . -854) 184285) ((-1137 . -825) 184264) ((-1137 . -489) 184178) ((-1137 . -242) 184092) ((-1137 . -144) 183986) ((-1137 . -385) 183920) ((-1137 . -254) 183899) ((-1137 . -238) 183826) ((-1137 . -188) T) ((-1137 . -102) T) ((-1137 . -25) T) ((-1137 . -72) T) ((-1137 . -547) 183808) ((-1137 . -1005) T) ((-1137 . -23) T) ((-1137 . -21) T) ((-1137 . -658) T) ((-1137 . -1015) T) ((-1137 . -962) T) ((-1137 . -954) T) ((-1137 . -184) 183795) ((-1137 . -1118) T) ((-1137 . -187) T) ((-1137 . -222) 183779) ((-1137 . -182) 183763) ((-1135 . -998) 183747) ((-1135 . -552) 183731) ((-1135 . -1005) 183709) ((-1135 . -547) 183676) ((-1135 . -1118) 183654) ((-1135 . -72) 183632) ((-1135 . -999) 183589) ((-1133 . -1132) 183568) ((-1133 . -908) 183534) ((-1133 . -1104) 183500) ((-1133 . -1107) 183466) ((-1133 . -426) 183432) ((-1133 . -236) 183398) ((-1133 . -66) 183364) ((-1133 . -35) 183330) ((-1133 . -1147) 183307) ((-1133 . -47) 183284) ((-1133 . -550) 183039) ((-1133 . -649) 182859) ((-1133 . -577) 182679) ((-1133 . -585) 182490) ((-1133 . -583) 182348) ((-1133 . -961) 182162) ((-1133 . -956) 181976) ((-1133 . -80) 181764) ((-1133 . -38) 181584) ((-1133 . -879) 181554) ((-1133 . -238) 181454) ((-1133 . -1130) 181438) ((-1133 . -658) T) ((-1133 . -1015) T) ((-1133 . -962) T) ((-1133 . -954) T) ((-1133 . -21) T) ((-1133 . -23) T) ((-1133 . -1005) T) ((-1133 . -547) 181420) ((-1133 . -1118) T) ((-1133 . -72) T) ((-1133 . -25) T) ((-1133 . -102) T) ((-1133 . -116) 181348) ((-1133 . -118) 181276) ((-1133 . -548) 180949) ((-1133 . -182) 180919) ((-1133 . -802) 180773) ((-1133 . -804) 180573) ((-1133 . -799) 180371) ((-1133 . -222) 180341) ((-1133 . -187) 180203) ((-1133 . -184) 180059) ((-1133 . -188) 179967) ((-1133 . -308) 179946) ((-1133 . -1123) 179925) ((-1133 . -825) 179904) ((-1133 . -489) 179858) ((-1133 . -144) 179792) ((-1133 . -385) 179771) ((-1133 . -254) 179750) ((-1133 . -242) 179704) ((-1133 . -198) 179683) ((-1133 . -284) 179653) ((-1133 . -447) 179513) ((-1133 . -256) 179452) ((-1133 . -322) 179422) ((-1133 . -575) 179330) ((-1133 . -336) 179300) ((-1133 . -789) 179173) ((-1133 . -733) 179126) ((-1133 . -707) 179079) ((-1133 . -709) 179032) ((-1133 . -749) 178934) ((-1133 . -752) 178836) ((-1133 . -711) 178789) ((-1133 . -714) 178742) ((-1133 . -748) 178695) ((-1133 . -787) 178665) ((-1133 . -814) 178618) ((-1133 . -926) 178571) ((-1133 . -943) 178360) ((-1133 . -1055) 178312) ((-1133 . -897) 178282) ((-1128 . -1132) 178243) ((-1128 . -908) 178209) ((-1128 . -1104) 178175) ((-1128 . -1107) 178141) ((-1128 . -426) 178107) ((-1128 . -236) 178073) ((-1128 . -66) 178039) ((-1128 . -35) 178005) ((-1128 . -1147) 177982) ((-1128 . -47) 177959) ((-1128 . -550) 177760) ((-1128 . -649) 177562) ((-1128 . -577) 177364) ((-1128 . -585) 177219) ((-1128 . -583) 177059) ((-1128 . -961) 176855) ((-1128 . -956) 176651) ((-1128 . -80) 176403) ((-1128 . -38) 176205) ((-1128 . -879) 176175) ((-1128 . -238) 176003) ((-1128 . -1130) 175987) ((-1128 . -658) T) ((-1128 . -1015) T) ((-1128 . -962) T) ((-1128 . -954) T) ((-1128 . -21) T) ((-1128 . -23) T) ((-1128 . -1005) T) ((-1128 . -547) 175969) ((-1128 . -1118) T) ((-1128 . -72) T) ((-1128 . -25) T) ((-1128 . -102) T) ((-1128 . -116) 175879) ((-1128 . -118) 175789) ((-1128 . -548) NIL) ((-1128 . -182) 175741) ((-1128 . -802) 175577) ((-1128 . -804) 175341) ((-1128 . -799) 175080) ((-1128 . -222) 175032) ((-1128 . -187) 174858) ((-1128 . -184) 174678) ((-1128 . -188) 174568) ((-1128 . -308) 174547) ((-1128 . -1123) 174526) ((-1128 . -825) 174505) ((-1128 . -489) 174459) ((-1128 . -144) 174393) ((-1128 . -385) 174372) ((-1128 . -254) 174351) ((-1128 . -242) 174305) ((-1128 . -198) 174284) ((-1128 . -284) 174236) ((-1128 . -447) 173970) ((-1128 . -256) 173855) ((-1128 . -322) 173807) ((-1128 . -575) 173759) ((-1128 . -336) 173711) ((-1128 . -789) NIL) ((-1128 . -733) NIL) ((-1128 . -707) NIL) ((-1128 . -709) NIL) ((-1128 . -749) NIL) ((-1128 . -752) NIL) ((-1128 . -711) NIL) ((-1128 . -714) NIL) ((-1128 . -748) NIL) ((-1128 . -787) 173663) ((-1128 . -814) NIL) ((-1128 . -926) NIL) ((-1128 . -943) 173629) ((-1128 . -1055) NIL) ((-1128 . -897) 173581) ((-1127 . -745) T) ((-1127 . -752) T) ((-1127 . -749) T) ((-1127 . -1005) T) ((-1127 . -547) 173563) ((-1127 . -1118) T) ((-1127 . -72) T) ((-1127 . -313) T) ((-1127 . -599) T) ((-1126 . -745) T) ((-1126 . -752) T) ((-1126 . -749) T) ((-1126 . -1005) T) ((-1126 . -547) 173545) ((-1126 . -1118) T) ((-1126 . -72) T) ((-1126 . -313) T) ((-1126 . -599) T) ((-1125 . -745) T) ((-1125 . -752) T) ((-1125 . -749) T) ((-1125 . -1005) T) ((-1125 . -547) 173527) ((-1125 . -1118) T) ((-1125 . -72) T) ((-1125 . -313) T) ((-1125 . -599) T) ((-1124 . -745) T) ((-1124 . -752) T) ((-1124 . -749) T) ((-1124 . -1005) T) ((-1124 . -547) 173509) ((-1124 . -1118) T) ((-1124 . -72) T) ((-1124 . -313) T) ((-1124 . -599) T) ((-1119 . -987) T) ((-1119 . -423) 173490) ((-1119 . -547) 173456) ((-1119 . -550) 173437) ((-1119 . -1005) T) ((-1119 . -1118) T) ((-1119 . -72) T) ((-1119 . -64) T) ((-1116 . -423) 173414) ((-1116 . -547) 173355) ((-1116 . -550) 173332) ((-1116 . -1005) 173310) ((-1116 . -1118) 173288) ((-1116 . -72) 173266) ((-1111 . -672) 173242) ((-1111 . -35) 173208) ((-1111 . -66) 173174) ((-1111 . -236) 173140) ((-1111 . -426) 173106) ((-1111 . -1107) 173072) ((-1111 . -1104) 173038) ((-1111 . -908) 173004) ((-1111 . -47) 172973) ((-1111 . -38) 172870) ((-1111 . -577) 172767) ((-1111 . -649) 172664) ((-1111 . -550) 172546) ((-1111 . -242) 172525) ((-1111 . -489) 172504) ((-1111 . -80) 172369) ((-1111 . -956) 172255) ((-1111 . -961) 172141) ((-1111 . -144) 172095) ((-1111 . -118) 172074) ((-1111 . -116) 172053) ((-1111 . -585) 171978) ((-1111 . -583) 171888) ((-1111 . -879) 171849) ((-1111 . -804) 171830) ((-1111 . -1118) T) ((-1111 . -799) 171809) ((-1111 . -954) T) ((-1111 . -962) T) ((-1111 . -1015) T) ((-1111 . -658) T) ((-1111 . -21) T) ((-1111 . -23) T) ((-1111 . -1005) T) ((-1111 . -547) 171791) ((-1111 . -72) T) ((-1111 . -25) T) ((-1111 . -102) T) ((-1111 . -802) 171772) ((-1111 . -447) 171739) ((-1111 . -256) 171726) ((-1105 . -916) 171710) ((-1105 . -34) T) ((-1105 . -1118) T) ((-1105 . -72) 171664) ((-1105 . -547) 171599) ((-1105 . -256) 171537) ((-1105 . -447) 171470) ((-1105 . -1005) 171448) ((-1105 . -422) 171432) ((-1100 . -310) 171406) ((-1100 . -72) T) ((-1100 . -1118) T) ((-1100 . -547) 171388) ((-1100 . -1005) T) ((-1098 . -1005) T) ((-1098 . -547) 171370) ((-1098 . -1118) T) ((-1098 . -72) T) ((-1098 . -550) 171352) ((-1093 . -740) 171336) ((-1093 . -72) T) ((-1093 . -1118) T) ((-1093 . -547) 171318) ((-1093 . -1005) T) ((-1091 . -1096) 171297) ((-1091 . -181) 171245) ((-1091 . -76) 171193) ((-1091 . -256) 170991) ((-1091 . -447) 170743) ((-1091 . -422) 170678) ((-1091 . -122) 170626) ((-1091 . -548) NIL) ((-1091 . -190) 170574) ((-1091 . -544) 170553) ((-1091 . -240) 170532) ((-1091 . -1118) T) ((-1091 . -238) 170511) ((-1091 . -1005) T) ((-1091 . -547) 170493) ((-1091 . -72) T) ((-1091 . -34) T) ((-1091 . -533) 170472) ((-1087 . -1005) T) ((-1087 . -547) 170454) ((-1087 . -1118) T) ((-1087 . -72) T) ((-1086 . -745) T) ((-1086 . -752) T) ((-1086 . -749) T) ((-1086 . -1005) T) ((-1086 . -547) 170436) ((-1086 . -1118) T) ((-1086 . -72) T) ((-1086 . -313) T) ((-1086 . -599) T) ((-1085 . -745) T) ((-1085 . -752) T) ((-1085 . -749) T) ((-1085 . -1005) T) ((-1085 . -547) 170418) ((-1085 . -1118) T) ((-1085 . -72) T) ((-1085 . -313) T) ((-1084 . -1164) T) ((-1084 . -1005) T) ((-1084 . -547) 170385) ((-1084 . -1118) T) ((-1084 . -72) T) ((-1084 . -943) 170321) ((-1084 . -550) 170257) ((-1083 . -547) 170239) ((-1082 . -547) 170221) ((-1081 . -273) 170198) ((-1081 . -943) 170096) ((-1081 . -348) 170080) ((-1081 . -38) 169977) ((-1081 . -550) 169834) ((-1081 . -585) 169759) ((-1081 . -583) 169669) ((-1081 . -658) T) ((-1081 . -1015) T) ((-1081 . -962) T) ((-1081 . -954) T) ((-1081 . -80) 169534) ((-1081 . -956) 169420) ((-1081 . -961) 169306) ((-1081 . -21) T) ((-1081 . -23) T) ((-1081 . -1005) T) ((-1081 . -547) 169288) ((-1081 . -1118) T) ((-1081 . -72) T) ((-1081 . -25) T) ((-1081 . -102) T) ((-1081 . -577) 169185) ((-1081 . -649) 169082) ((-1081 . -116) 169061) ((-1081 . -118) 169040) ((-1081 . -144) 168994) ((-1081 . -489) 168973) ((-1081 . -242) 168952) ((-1081 . -47) 168929) ((-1079 . -749) T) ((-1079 . -547) 168911) ((-1079 . -1005) T) ((-1079 . -72) T) ((-1079 . -1118) T) ((-1079 . -752) T) ((-1079 . -548) 168833) ((-1079 . -550) 168799) ((-1079 . -943) 168781) ((-1079 . -789) 168748) ((-1078 . -1161) 168732) ((-1078 . -188) 168691) ((-1078 . -550) 168573) ((-1078 . -585) 168498) ((-1078 . -583) 168408) ((-1078 . -102) T) ((-1078 . -25) T) ((-1078 . -72) T) ((-1078 . -547) 168390) ((-1078 . -1005) T) ((-1078 . -23) T) ((-1078 . -21) T) ((-1078 . -658) T) ((-1078 . -1015) T) ((-1078 . -962) T) ((-1078 . -954) T) ((-1078 . -184) 168343) ((-1078 . -1118) T) ((-1078 . -187) 168302) ((-1078 . -238) 168267) ((-1078 . -802) 168180) ((-1078 . -799) 168068) ((-1078 . -804) 167981) ((-1078 . -879) 167951) ((-1078 . -38) 167848) ((-1078 . -80) 167713) ((-1078 . -956) 167599) ((-1078 . -961) 167485) ((-1078 . -577) 167382) ((-1078 . -649) 167279) ((-1078 . -116) 167258) ((-1078 . -118) 167237) ((-1078 . -144) 167191) ((-1078 . -489) 167170) ((-1078 . -242) 167149) ((-1078 . -47) 167126) ((-1078 . -1147) 167103) ((-1078 . -35) 167069) ((-1078 . -66) 167035) ((-1078 . -236) 167001) ((-1078 . -426) 166967) ((-1078 . -1107) 166933) ((-1078 . -1104) 166899) ((-1078 . -908) 166865) ((-1077 . -1153) 166826) ((-1077 . -308) 166805) ((-1077 . -1123) 166784) ((-1077 . -825) 166763) ((-1077 . -489) 166717) ((-1077 . -144) 166651) ((-1077 . -550) 166400) ((-1077 . -649) 166247) ((-1077 . -577) 166094) ((-1077 . -38) 165941) ((-1077 . -385) 165920) ((-1077 . -254) 165899) ((-1077 . -585) 165799) ((-1077 . -583) 165684) ((-1077 . -658) T) ((-1077 . -1015) T) ((-1077 . -962) T) ((-1077 . -954) T) ((-1077 . -80) 165504) ((-1077 . -956) 165345) ((-1077 . -961) 165186) ((-1077 . -21) T) ((-1077 . -23) T) ((-1077 . -1005) T) ((-1077 . -547) 165168) ((-1077 . -1118) T) ((-1077 . -72) T) ((-1077 . -25) T) ((-1077 . -102) T) ((-1077 . -242) 165122) ((-1077 . -198) 165101) ((-1077 . -908) 165067) ((-1077 . -1104) 165033) ((-1077 . -1107) 164999) ((-1077 . -426) 164965) ((-1077 . -236) 164931) ((-1077 . -66) 164897) ((-1077 . -35) 164863) ((-1077 . -1147) 164833) ((-1077 . -47) 164803) ((-1077 . -118) 164782) ((-1077 . -116) 164761) ((-1077 . -879) 164724) ((-1077 . -804) 164630) ((-1077 . -799) 164511) ((-1077 . -802) 164417) ((-1077 . -238) 164375) ((-1077 . -187) 164327) ((-1077 . -184) 164273) ((-1077 . -188) 164225) ((-1077 . -1151) 164209) ((-1077 . -943) 164144) ((-1074 . -1144) 164128) ((-1074 . -1055) 164106) ((-1074 . -548) NIL) ((-1074 . -256) 164093) ((-1074 . -447) 164041) ((-1074 . -273) 164018) ((-1074 . -943) 163901) ((-1074 . -348) 163885) ((-1074 . -38) 163717) ((-1074 . -80) 163522) ((-1074 . -956) 163348) ((-1074 . -961) 163174) ((-1074 . -583) 163084) ((-1074 . -585) 162973) ((-1074 . -577) 162805) ((-1074 . -649) 162637) ((-1074 . -550) 162414) ((-1074 . -116) 162393) ((-1074 . -118) 162372) ((-1074 . -47) 162349) ((-1074 . -322) 162333) ((-1074 . -575) 162281) ((-1074 . -802) 162225) ((-1074 . -799) 162132) ((-1074 . -804) 162043) ((-1074 . -789) NIL) ((-1074 . -814) 162022) ((-1074 . -1123) 162001) ((-1074 . -854) 161971) ((-1074 . -825) 161950) ((-1074 . -489) 161864) ((-1074 . -242) 161778) ((-1074 . -144) 161672) ((-1074 . -385) 161606) ((-1074 . -254) 161585) ((-1074 . -238) 161512) ((-1074 . -188) T) ((-1074 . -102) T) ((-1074 . -25) T) ((-1074 . -72) T) ((-1074 . -547) 161494) ((-1074 . -1005) T) ((-1074 . -23) T) ((-1074 . -21) T) ((-1074 . -658) T) ((-1074 . -1015) T) ((-1074 . -962) T) ((-1074 . -954) T) ((-1074 . -184) 161481) ((-1074 . -1118) T) ((-1074 . -187) T) ((-1074 . -222) 161465) ((-1074 . -182) 161449) ((-1071 . -1132) 161410) ((-1071 . -908) 161376) ((-1071 . -1104) 161342) ((-1071 . -1107) 161308) ((-1071 . -426) 161274) ((-1071 . -236) 161240) ((-1071 . -66) 161206) ((-1071 . -35) 161172) ((-1071 . -1147) 161149) ((-1071 . -47) 161126) ((-1071 . -550) 160927) ((-1071 . -649) 160729) ((-1071 . -577) 160531) ((-1071 . -585) 160386) ((-1071 . -583) 160226) ((-1071 . -961) 160022) ((-1071 . -956) 159818) ((-1071 . -80) 159570) ((-1071 . -38) 159372) ((-1071 . -879) 159342) ((-1071 . -238) 159170) ((-1071 . -1130) 159154) ((-1071 . -658) T) ((-1071 . -1015) T) ((-1071 . -962) T) ((-1071 . -954) T) ((-1071 . -21) T) ((-1071 . -23) T) ((-1071 . -1005) T) ((-1071 . -547) 159136) ((-1071 . -1118) T) ((-1071 . -72) T) ((-1071 . -25) T) ((-1071 . -102) T) ((-1071 . -116) 159046) ((-1071 . -118) 158956) ((-1071 . -548) NIL) ((-1071 . -182) 158908) ((-1071 . -802) 158744) ((-1071 . -804) 158508) ((-1071 . -799) 158247) ((-1071 . -222) 158199) ((-1071 . -187) 158025) ((-1071 . -184) 157845) ((-1071 . -188) 157735) ((-1071 . -308) 157714) ((-1071 . -1123) 157693) ((-1071 . -825) 157672) ((-1071 . -489) 157626) ((-1071 . -144) 157560) ((-1071 . -385) 157539) ((-1071 . -254) 157518) ((-1071 . 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155912) ((-1063 . -548) NIL) ((-1063 . -190) 155857) ((-1063 . -544) 155833) ((-1063 . -240) 155809) ((-1063 . -1118) T) ((-1063 . -238) 155785) ((-1063 . -1005) T) ((-1063 . -547) 155767) ((-1063 . -72) T) ((-1063 . -34) T) ((-1063 . -533) 155743) ((-1062 . -1047) T) ((-1062 . -317) 155725) ((-1062 . -752) T) ((-1062 . -749) T) ((-1062 . -122) 155707) ((-1062 . -34) T) ((-1062 . -1118) T) ((-1062 . -72) T) ((-1062 . -547) 155689) ((-1062 . -256) NIL) ((-1062 . -447) NIL) ((-1062 . -1005) T) ((-1062 . -422) 155671) ((-1062 . -548) NIL) ((-1062 . -238) 155621) ((-1062 . -533) 155596) ((-1062 . -240) 155571) ((-1062 . -588) 155553) ((-1062 . -19) 155535) ((-1058 . -611) 155519) ((-1058 . -588) 155503) ((-1058 . -240) 155480) ((-1058 . -238) 155432) ((-1058 . -533) 155409) ((-1058 . -548) 155370) ((-1058 . -422) 155354) ((-1058 . -1005) 155332) ((-1058 . -447) 155265) ((-1058 . -256) 155203) ((-1058 . -547) 155138) ((-1058 . -72) 155092) ((-1058 . -1118) T) ((-1058 . -34) T) ((-1058 . -122) 155076) ((-1058 . -1157) 155060) ((-1058 . -916) 155044) ((-1058 . -1053) 155028) ((-1058 . -550) 155005) ((-1056 . -987) T) ((-1056 . -423) 154986) ((-1056 . -547) 154952) ((-1056 . -550) 154933) ((-1056 . -1005) T) ((-1056 . -1118) T) ((-1056 . -72) T) ((-1056 . -64) T) ((-1054 . -1096) 154912) ((-1054 . -181) 154860) ((-1054 . -76) 154808) ((-1054 . -256) 154606) ((-1054 . -447) 154358) ((-1054 . -422) 154293) ((-1054 . -122) 154241) ((-1054 . -548) NIL) ((-1054 . -190) 154189) ((-1054 . -544) 154168) ((-1054 . -240) 154147) ((-1054 . -1118) T) ((-1054 . -238) 154126) ((-1054 . -1005) T) ((-1054 . -547) 154108) ((-1054 . -72) T) ((-1054 . -34) T) ((-1054 . -533) 154087) ((-1051 . -1024) 154071) ((-1051 . -422) 154055) ((-1051 . -1005) 154033) ((-1051 . -447) 153966) ((-1051 . -256) 153904) ((-1051 . -547) 153839) ((-1051 . -72) 153793) ((-1051 . -1118) T) ((-1051 . -34) T) ((-1051 . -76) 153777) ((-1049 . -1012) 153746) ((-1049 . -1113) 153715) ((-1049 . -547) 153677) ((-1049 . -122) 153661) ((-1049 . -34) T) ((-1049 . -1118) T) ((-1049 . -72) T) ((-1049 . -256) 153599) ((-1049 . -447) 153532) ((-1049 . -1005) T) ((-1049 . -422) 153516) ((-1049 . -548) 153477) ((-1049 . -882) 153446) ((-1049 . -975) 153415) ((-1045 . -1026) 153360) ((-1045 . -422) 153344) ((-1045 . -447) 153277) ((-1045 . -256) 153215) ((-1045 . -34) T) ((-1045 . -958) 153155) ((-1045 . -943) 153053) ((-1045 . -550) 152972) ((-1045 . -348) 152956) ((-1045 . -575) 152904) ((-1045 . -585) 152842) ((-1045 . -322) 152826) ((-1045 . -188) 152805) ((-1045 . -184) 152753) ((-1045 . -187) 152707) ((-1045 . -222) 152691) ((-1045 . -799) 152615) ((-1045 . -804) 152541) ((-1045 . -802) 152500) ((-1045 . -182) 152484) ((-1045 . -649) 152419) ((-1045 . -577) 152354) ((-1045 . -583) 152313) ((-1045 . -102) T) ((-1045 . -25) T) ((-1045 . -72) T) ((-1045 . -1118) T) ((-1045 . -547) 152275) ((-1045 . -1005) T) ((-1045 . -23) T) ((-1045 . -21) T) ((-1045 . -961) 152259) ((-1045 . -956) 152243) ((-1045 . -80) 152222) ((-1045 . -954) T) ((-1045 . -962) T) ((-1045 . -1015) T) ((-1045 . -658) T) ((-1045 . -38) 152182) ((-1045 . -548) 152143) ((-1044 . -916) 152114) ((-1044 . -34) T) ((-1044 . -1118) T) ((-1044 . -72) T) ((-1044 . -547) 152096) ((-1044 . -256) 152022) ((-1044 . -447) 151930) ((-1044 . -1005) T) ((-1044 . -422) 151901) ((-1043 . -1005) T) ((-1043 . -547) 151883) ((-1043 . -1118) T) ((-1043 . -72) T) ((-1038 . -1040) T) ((-1038 . -1164) T) ((-1038 . -64) T) ((-1038 . -72) T) ((-1038 . -1118) T) ((-1038 . -547) 151849) ((-1038 . -1005) T) ((-1038 . -550) 151830) ((-1038 . -423) 151811) ((-1038 . -987) T) ((-1036 . -1037) 151795) ((-1036 . -72) T) ((-1036 . -1118) T) ((-1036 . -547) 151777) ((-1036 . -1005) T) ((-1029 . -672) 151756) ((-1029 . -35) 151722) ((-1029 . -66) 151688) ((-1029 . -236) 151654) ((-1029 . -426) 151620) ((-1029 . -1107) 151586) ((-1029 . -1104) 151552) ((-1029 . -908) 151518) ((-1029 . -47) 151490) ((-1029 . -38) 151387) ((-1029 . -577) 151284) ((-1029 . -649) 151181) ((-1029 . -550) 151063) ((-1029 . -242) 151042) ((-1029 . -489) 151021) ((-1029 . -80) 150886) ((-1029 . -956) 150772) ((-1029 . -961) 150658) ((-1029 . -144) 150612) ((-1029 . -118) 150591) ((-1029 . -116) 150570) ((-1029 . -585) 150495) ((-1029 . -583) 150405) ((-1029 . -879) 150372) ((-1029 . -804) 150356) ((-1029 . -1118) T) ((-1029 . -799) 150338) ((-1029 . -954) T) ((-1029 . -962) T) ((-1029 . -1015) T) ((-1029 . -658) T) ((-1029 . -21) T) ((-1029 . -23) T) ((-1029 . -1005) T) ((-1029 . -547) 150320) ((-1029 . -72) T) ((-1029 . -25) T) ((-1029 . -102) T) ((-1029 . -802) 150304) ((-1029 . -447) 150274) ((-1029 . -256) 150261) ((-1028 . -854) 150228) ((-1028 . -550) 150027) ((-1028 . -943) 149912) ((-1028 . -1123) 149891) ((-1028 . -814) 149870) ((-1028 . -789) 149729) ((-1028 . -804) 149713) ((-1028 . -799) 149695) ((-1028 . -802) 149679) ((-1028 . -447) 149631) ((-1028 . -385) 149585) ((-1028 . -575) 149533) ((-1028 . -585) 149422) ((-1028 . -322) 149406) ((-1028 . -47) 149378) ((-1028 . -38) 149230) ((-1028 . -577) 149082) ((-1028 . -649) 148934) ((-1028 . -242) 148868) ((-1028 . -489) 148802) ((-1028 . -80) 148627) ((-1028 . -956) 148473) ((-1028 . -961) 148319) ((-1028 . -144) 148233) ((-1028 . -118) 148212) ((-1028 . -116) 148191) ((-1028 . -583) 148101) ((-1028 . -102) T) ((-1028 . -25) T) ((-1028 . -72) T) ((-1028 . -1118) T) ((-1028 . -547) 148083) ((-1028 . -1005) T) ((-1028 . -23) T) ((-1028 . -21) T) ((-1028 . -954) T) ((-1028 . -962) T) ((-1028 . -1015) T) ((-1028 . -658) T) ((-1028 . -348) 148067) ((-1028 . -273) 148039) ((-1028 . -256) 148026) ((-1028 . -548) 147774) ((-1023 . -477) T) ((-1023 . -1123) T) ((-1023 . -1055) T) ((-1023 . -943) 147756) ((-1023 . -548) 147671) ((-1023 . -926) T) ((-1023 . -789) 147653) ((-1023 . -748) T) ((-1023 . -714) T) ((-1023 . -711) T) ((-1023 . -752) T) ((-1023 . -749) T) ((-1023 . -709) T) ((-1023 . -707) T) ((-1023 . -733) T) ((-1023 . -585) 147625) ((-1023 . -575) 147607) ((-1023 . -825) T) 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T) ((-810 . -825) T) ((-810 . -489) T) ((-810 . -144) T) ((-810 . -550) 122117) ((-810 . -649) 122082) ((-810 . -577) 122047) ((-810 . -38) 122012) ((-810 . -385) T) ((-810 . -254) T) ((-810 . -80) 121961) ((-810 . -956) 121926) ((-810 . -961) 121891) ((-810 . -583) 121841) ((-810 . -585) 121806) ((-810 . -242) T) ((-810 . -198) T) ((-810 . -338) T) ((-810 . -187) T) ((-810 . -1118) T) ((-810 . -184) 121793) ((-810 . -954) T) ((-810 . -962) T) ((-810 . -1015) T) ((-810 . -658) T) ((-810 . -21) T) ((-810 . -23) T) ((-810 . -1005) T) ((-810 . -547) 121775) ((-810 . -72) T) ((-810 . -25) T) ((-810 . -102) T) ((-810 . -188) T) ((-810 . -276) 121762) ((-810 . -118) 121744) ((-810 . -943) 121731) ((-810 . -1176) 121718) ((-810 . -1187) 121705) ((-810 . -548) 121687) ((-809 . -1005) T) ((-809 . -547) 121669) ((-809 . -1118) T) ((-809 . -72) T) ((-806 . -808) 121653) ((-806 . -752) 121607) ((-806 . -749) 121561) ((-806 . -658) T) ((-806 . -1005) T) ((-806 . -547) 121543) ((-806 . -72) T) ((-806 . -1015) T) ((-806 . -406) T) ((-806 . -1118) T) ((-806 . -238) 121522) ((-805 . -90) 121506) ((-805 . -422) 121490) ((-805 . -1005) 121468) ((-805 . -447) 121401) ((-805 . -256) 121339) ((-805 . -547) 121253) ((-805 . -72) 121207) ((-805 . -1118) T) ((-805 . -34) T) ((-805 . -916) 121191) ((-796 . -749) T) ((-796 . -547) 121173) ((-796 . -1005) T) ((-796 . -72) T) ((-796 . -1118) T) ((-796 . -752) T) ((-796 . -943) 121150) ((-796 . -550) 121127) ((-793 . -1005) T) ((-793 . -547) 121109) ((-793 . -1118) T) ((-793 . -72) T) ((-793 . -943) 121077) ((-793 . -550) 121045) ((-791 . -1005) T) ((-791 . -547) 121027) ((-791 . -1118) T) ((-791 . -72) T) ((-788 . -1005) T) ((-788 . -547) 121009) ((-788 . -1118) T) ((-788 . -72) T) ((-778 . -987) T) ((-778 . -423) 120990) ((-778 . -547) 120956) ((-778 . -550) 120937) ((-778 . -1005) T) ((-778 . -1118) T) ((-778 . -72) T) ((-778 . -64) T) ((-778 . -1164) T) ((-776 . -1005) T) ((-776 . -547) 120919) ((-776 . -1118) T) ((-776 . -72) T) ((-776 . -550) 120901) ((-775 . -1118) T) ((-775 . -547) 120776) ((-775 . -1005) 120727) ((-775 . -72) 120678) ((-774 . -897) 120662) ((-774 . -1055) 120640) ((-774 . -943) 120507) ((-774 . -550) 120406) ((-774 . -548) 120209) ((-774 . -926) 120188) ((-774 . -814) 120167) ((-774 . -787) 120151) ((-774 . -748) 120130) ((-774 . -714) 120109) ((-774 . -711) 120088) ((-774 . -752) 120042) ((-774 . -749) 119996) ((-774 . -709) 119975) ((-774 . -707) 119954) ((-774 . -733) 119933) ((-774 . -789) 119858) ((-774 . -336) 119842) ((-774 . -575) 119790) ((-774 . -585) 119706) ((-774 . -322) 119690) ((-774 . -238) 119648) ((-774 . -256) 119613) ((-774 . -447) 119525) ((-774 . -284) 119509) ((-774 . -198) T) ((-774 . -80) 119440) ((-774 . -956) 119392) ((-774 . -961) 119344) ((-774 . -242) T) ((-774 . -649) 119296) ((-774 . -577) 119248) ((-774 . -583) 119185) ((-774 . -38) 119137) ((-774 . -254) T) ((-774 . -385) T) ((-774 . -144) T) ((-774 . -489) T) ((-774 . -825) T) ((-774 . -1123) T) ((-774 . -308) T) ((-774 . -188) 119116) ((-774 . -184) 119064) ((-774 . -187) 119018) ((-774 . -222) 119002) ((-774 . -799) 118926) ((-774 . -804) 118852) ((-774 . -802) 118811) ((-774 . -182) 118795) ((-774 . -118) 118774) ((-774 . -116) 118753) ((-774 . -102) T) ((-774 . -25) T) ((-774 . -72) T) ((-774 . -1118) T) ((-774 . -547) 118735) ((-774 . -1005) T) ((-774 . -23) T) ((-774 . -21) T) ((-774 . -954) T) ((-774 . -962) T) ((-774 . -1015) T) ((-774 . -658) T) ((-773 . -897) 118712) ((-773 . -1055) NIL) ((-773 . -943) 118689) ((-773 . -550) 118619) ((-773 . -548) NIL) ((-773 . -926) NIL) ((-773 . -814) NIL) ((-773 . -787) 118596) ((-773 . -748) NIL) ((-773 . -714) NIL) ((-773 . -711) NIL) ((-773 . -752) NIL) ((-773 . -749) NIL) ((-773 . -709) NIL) ((-773 . -707) NIL) ((-773 . -733) NIL) ((-773 . -789) NIL) ((-773 . -336) 118573) ((-773 . -575) 118550) ((-773 . -585) 118495) ((-773 . -322) 118472) ((-773 . -238) 118402) ((-773 . -256) 118346) ((-773 . -447) 118209) ((-773 . -284) 118186) ((-773 . -198) T) ((-773 . -80) 118103) ((-773 . -956) 118048) ((-773 . -961) 117993) ((-773 . -242) T) ((-773 . -649) 117938) ((-773 . -577) 117883) ((-773 . -583) 117813) ((-773 . -38) 117758) ((-773 . -254) T) ((-773 . -385) T) ((-773 . -144) T) ((-773 . -489) T) ((-773 . -825) T) ((-773 . -1123) T) ((-773 . -308) T) ((-773 . -188) NIL) ((-773 . -184) NIL) ((-773 . -187) NIL) ((-773 . -222) 117735) ((-773 . -799) NIL) ((-773 . -804) NIL) ((-773 . -802) NIL) ((-773 . -182) 117712) ((-773 . -118) T) ((-773 . -116) NIL) ((-773 . -102) T) ((-773 . -25) T) ((-773 . -72) T) ((-773 . -1118) T) ((-773 . -547) 117694) ((-773 . -1005) T) ((-773 . -23) T) ((-773 . -21) T) ((-773 . -954) T) ((-773 . -962) T) ((-773 . -1015) T) ((-773 . -658) T) ((-771 . -772) 117678) ((-771 . -825) T) ((-771 . -489) T) ((-771 . -242) T) ((-771 . -144) T) ((-771 . -550) 117650) ((-771 . -649) 117637) ((-771 . -577) 117624) ((-771 . -961) 117611) ((-771 . -956) 117598) ((-771 . -80) 117583) ((-771 . -38) 117570) ((-771 . -385) T) ((-771 . -254) T) ((-771 . -954) T) ((-771 . -962) T) ((-771 . -1015) T) ((-771 . -658) T) ((-771 . -21) T) ((-771 . -583) 117542) ((-771 . -23) T) ((-771 . -1005) T) ((-771 . -547) 117524) ((-771 . -1118) T) ((-771 . -72) T) ((-771 . -25) T) ((-771 . -102) T) ((-771 . -585) 117511) ((-771 . -118) T) ((-768 . -954) T) ((-768 . -962) T) ((-768 . -1015) T) ((-768 . -658) T) ((-768 . -21) T) ((-768 . -583) 117456) ((-768 . -23) T) ((-768 . -1005) T) ((-768 . -547) 117418) ((-768 . -1118) T) ((-768 . -72) T) ((-768 . -25) T) ((-768 . -102) T) ((-768 . -585) 117378) ((-768 . -550) 117313) ((-768 . -423) 117290) ((-768 . -38) 117260) ((-768 . -80) 117225) ((-768 . -956) 117195) ((-768 . -961) 117165) ((-768 . -577) 117135) ((-768 . -649) 117105) ((-767 . -1005) T) ((-767 . -547) 117087) ((-767 . -1118) T) ((-767 . -72) T) ((-766 . -745) T) ((-766 . -752) T) ((-766 . -749) T) ((-766 . -1005) T) ((-766 . -547) 117069) ((-766 . -1118) T) ((-766 . -72) T) ((-766 . -313) T) ((-766 . -548) 116991) ((-765 . -1005) T) ((-765 . -547) 116973) ((-765 . -1118) T) ((-765 . -72) T) ((-764 . -763) T) ((-764 . -145) T) ((-764 . -547) 116955) ((-760 . -749) T) ((-760 . -547) 116937) ((-760 . -1005) T) ((-760 . -72) T) ((-760 . -1118) T) ((-760 . -752) T) ((-757 . -754) 116921) ((-757 . -943) 116819) ((-757 . -550) 116717) ((-757 . -348) 116701) ((-757 . -649) 116671) ((-757 . -577) 116641) ((-757 . -585) 116615) ((-757 . -583) 116574) ((-757 . -102) T) ((-757 . -25) T) ((-757 . -72) T) ((-757 . -1118) T) ((-757 . -547) 116556) ((-757 . -1005) T) ((-757 . -23) T) ((-757 . -21) T) ((-757 . -961) 116540) ((-757 . -956) 116524) ((-757 . -80) 116503) ((-757 . -954) T) ((-757 . -962) T) ((-757 . -1015) T) ((-757 . -658) T) ((-757 . -38) 116473) ((-756 . -754) 116457) ((-756 . -943) 116355) ((-756 . -550) 116274) ((-756 . -348) 116258) ((-756 . -649) 116228) ((-756 . -577) 116198) ((-756 . -585) 116172) ((-756 . -583) 116131) ((-756 . -102) T) ((-756 . -25) T) ((-756 . -72) T) ((-756 . -1118) T) ((-756 . -547) 116113) ((-756 . -1005) T) ((-756 . -23) T) ((-756 . -21) T) ((-756 . -961) 116097) ((-756 . -956) 116081) ((-756 . -80) 116060) ((-756 . -954) T) ((-756 . -962) T) ((-756 . -1015) T) ((-756 . -658) T) ((-756 . -38) 116030) ((-750 . -752) T) ((-750 . -1118) T) ((-750 . -72) T) ((-750 . -423) 116014) ((-750 . -547) 115962) ((-750 . -550) 115946) ((-743 . -1005) T) ((-743 . -547) 115928) ((-743 . -1118) T) ((-743 . -72) T) ((-743 . -348) 115912) ((-743 . -550) 115785) ((-743 . -943) 115683) ((-743 . -21) 115638) ((-743 . -583) 115558) ((-743 . -23) 115513) ((-743 . -25) 115468) ((-743 . -102) 115423) ((-743 . -748) 115402) ((-743 . -585) 115375) ((-743 . -962) 115354) ((-743 . -954) 115333) ((-743 . -714) 115312) ((-743 . -711) 115291) ((-743 . -752) 115270) ((-743 . -749) 115249) ((-743 . -709) 115228) ((-743 . -707) 115207) ((-743 . -1015) 115186) ((-743 . -658) 115165) ((-742 . -740) 115147) ((-742 . -72) T) ((-742 . -1118) T) ((-742 . -547) 115129) ((-742 . -1005) T) ((-738 . -954) T) ((-738 . -962) T) ((-738 . -1015) T) ((-738 . -658) T) ((-738 . -21) T) ((-738 . -583) 115074) ((-738 . -23) T) ((-738 . -1005) T) ((-738 . -547) 115056) ((-738 . -1118) T) ((-738 . -72) T) ((-738 . -25) T) ((-738 . -102) T) ((-738 . -585) 115016) ((-738 . -550) 114971) ((-738 . -943) 114941) ((-738 . -238) 114920) ((-738 . -118) 114899) ((-738 . -116) 114878) ((-738 . -38) 114848) ((-738 . -80) 114813) ((-738 . -956) 114783) ((-738 . -961) 114753) ((-738 . -577) 114723) ((-738 . -649) 114693) ((-736 . -1005) T) ((-736 . -547) 114675) ((-736 . -1118) T) ((-736 . -72) T) ((-736 . -348) 114659) ((-736 . -550) 114532) ((-736 . -943) 114430) ((-736 . -21) 114385) ((-736 . -583) 114305) ((-736 . -23) 114260) ((-736 . -25) 114215) ((-736 . -102) 114170) ((-736 . -748) 114149) ((-736 . -585) 114122) ((-736 . -962) 114101) ((-736 . -954) 114080) ((-736 . -714) 114059) ((-736 . -711) 114038) ((-736 . -752) 114017) ((-736 . -749) 113996) ((-736 . -709) 113975) ((-736 . -707) 113954) ((-736 . -1015) 113933) ((-736 . -658) 113912) ((-734 . -640) 113896) ((-734 . -550) 113851) ((-734 . -649) 113821) ((-734 . -577) 113791) ((-734 . -585) 113765) ((-734 . -583) 113724) ((-734 . -102) T) ((-734 . -25) T) ((-734 . -72) T) ((-734 . -1118) T) ((-734 . -547) 113706) ((-734 . -1005) T) ((-734 . -23) T) ((-734 . -21) T) ((-734 . -961) 113690) ((-734 . -956) 113674) ((-734 . -80) 113653) ((-734 . -954) T) ((-734 . -962) T) ((-734 . -1015) T) ((-734 . -658) T) ((-734 . -38) 113623) ((-734 . -188) 113602) ((-734 . -184) 113575) ((-734 . -187) 113554) ((-732 . -329) 113538) ((-732 . -550) 113522) ((-732 . -943) 113506) ((-732 . -752) T) ((-732 . -749) T) ((-732 . -1015) T) ((-732 . -72) T) ((-732 . -1118) T) ((-732 . -547) 113488) ((-732 . -1005) T) ((-732 . -658) T) ((-732 . -747) T) ((-732 . -759) T) ((-731 . -225) 113472) ((-731 . -550) 113456) ((-731 . -943) 113440) ((-731 . -752) T) ((-731 . -72) T) ((-731 . -1005) T) ((-731 . -547) 113422) ((-731 . -749) T) ((-731 . -184) 113409) ((-731 . -1118) T) ((-731 . -187) T) ((-730 . -80) 113344) ((-730 . -956) 113295) ((-730 . -961) 113246) ((-730 . -21) T) ((-730 . -583) 113182) ((-730 . -23) T) ((-730 . -1005) T) ((-730 . -547) 113151) ((-730 . -1118) T) ((-730 . -72) T) ((-730 . -25) T) ((-730 . -102) T) ((-730 . -585) 113102) ((-730 . -188) T) ((-730 . -550) 113011) ((-730 . -658) T) ((-730 . -1015) T) ((-730 . -962) T) ((-730 . -954) T) ((-730 . -184) 112998) ((-730 . -187) T) ((-730 . -423) 112982) ((-730 . -308) 112961) ((-730 . -1123) 112940) ((-730 . -825) 112919) ((-730 . -489) 112898) ((-730 . -144) 112877) ((-730 . -649) 112814) ((-730 . -577) 112751) ((-730 . -38) 112688) ((-730 . -385) 112667) ((-730 . -254) 112646) ((-730 . -242) 112625) ((-730 . -198) 112604) ((-729 . -210) 112543) ((-729 . -550) 112287) ((-729 . -943) 112117) ((-729 . -548) NIL) ((-729 . -273) 112079) ((-729 . -348) 112063) ((-729 . -38) 111915) ((-729 . -80) 111740) ((-729 . -956) 111586) ((-729 . -961) 111432) ((-729 . -583) 111342) ((-729 . -585) 111231) ((-729 . -577) 111083) ((-729 . -649) 110935) ((-729 . -116) 110914) ((-729 . -118) 110893) ((-729 . -144) 110807) ((-729 . -489) 110741) ((-729 . -242) 110675) ((-729 . -47) 110637) ((-729 . -322) 110621) ((-729 . -575) 110569) ((-729 . -385) 110523) ((-729 . -447) 110388) ((-729 . -802) 110324) ((-729 . -799) 110223) ((-729 . -804) 110126) ((-729 . -789) NIL) ((-729 . -814) 110105) ((-729 . -1123) 110084) ((-729 . -854) 110031) ((-729 . -256) 110018) ((-729 . -188) 109997) ((-729 . -102) T) ((-729 . -25) T) ((-729 . -72) T) ((-729 . -547) 109979) ((-729 . -1005) T) ((-729 . -23) T) ((-729 . -21) T) ((-729 . -658) T) ((-729 . -1015) T) ((-729 . -962) T) ((-729 . -954) T) ((-729 . -184) 109927) ((-729 . -1118) T) ((-729 . -187) 109881) ((-729 . -222) 109865) ((-729 . -182) 109849) ((-728 . -193) 109828) ((-728 . -1176) 109798) ((-728 . -714) 109777) ((-728 . -711) 109756) ((-728 . -752) 109710) ((-728 . -749) 109664) ((-728 . -709) 109643) ((-728 . -710) 109622) ((-728 . -649) 109567) ((-728 . -577) 109492) ((-728 . -240) 109469) ((-728 . -238) 109446) ((-728 . -422) 109430) ((-728 . -447) 109363) ((-728 . -256) 109301) ((-728 . -34) T) ((-728 . -533) 109278) ((-728 . -943) 109107) ((-728 . -550) 108911) ((-728 . -348) 108880) ((-728 . -575) 108788) ((-728 . -585) 108627) ((-728 . -322) 108597) ((-728 . -313) 108576) ((-728 . -188) 108529) ((-728 . -583) 108317) ((-728 . -658) 108296) ((-728 . -1015) 108275) ((-728 . -962) 108254) ((-728 . -954) 108233) ((-728 . -184) 108129) ((-728 . -187) 108031) ((-728 . -222) 108001) ((-728 . -799) 107873) ((-728 . -804) 107747) ((-728 . -802) 107680) ((-728 . -182) 107650) ((-728 . -547) 107347) ((-728 . -961) 107272) ((-728 . -956) 107177) ((-728 . -80) 107097) ((-728 . -102) 106972) ((-728 . -25) 106809) ((-728 . -72) 106546) ((-728 . -1118) T) ((-728 . -1005) 106302) ((-728 . -23) 106158) ((-728 . -21) 106073) ((-715 . -713) 106057) ((-715 . -752) 106036) ((-715 . -749) 106015) ((-715 . -943) 105808) ((-715 . -550) 105661) ((-715 . -348) 105625) ((-715 . -238) 105583) ((-715 . -256) 105548) ((-715 . -447) 105460) ((-715 . -284) 105444) ((-715 . -313) 105423) ((-715 . -548) 105384) ((-715 . -118) 105363) ((-715 . -116) 105342) ((-715 . -649) 105326) ((-715 . -577) 105310) ((-715 . -585) 105284) ((-715 . -583) 105243) ((-715 . -102) T) ((-715 . -25) T) ((-715 . -72) T) ((-715 . -1118) T) ((-715 . -547) 105225) ((-715 . -1005) T) ((-715 . -23) T) ((-715 . -21) T) ((-715 . -961) 105209) ((-715 . -956) 105193) ((-715 . -80) 105172) ((-715 . -954) T) ((-715 . -962) T) ((-715 . -1015) T) ((-715 . -658) T) ((-715 . -38) 105156) ((-697 . -1144) 105140) ((-697 . -1055) 105118) ((-697 . -548) NIL) ((-697 . -256) 105105) ((-697 . -447) 105053) ((-697 . -273) 105030) ((-697 . -943) 104892) ((-697 . -348) 104876) ((-697 . -38) 104708) ((-697 . -80) 104513) ((-697 . -956) 104339) ((-697 . -961) 104165) ((-697 . -583) 104075) ((-697 . -585) 103964) 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-38) 101606) ((-696 . -550) 101379) ((-696 . -585) 101268) ((-696 . -583) 101178) ((-696 . -658) T) ((-696 . -1015) T) ((-696 . -962) T) ((-696 . -954) T) ((-696 . -80) 101003) ((-696 . -956) 100849) ((-696 . -961) 100695) ((-696 . -21) T) ((-696 . -23) T) ((-696 . -1005) T) ((-696 . -547) 100609) ((-696 . -1118) T) ((-696 . -72) T) ((-696 . -25) T) ((-696 . -102) T) ((-696 . -577) 100461) ((-696 . -649) 100313) ((-696 . -116) 100292) ((-696 . -118) 100271) ((-696 . -144) 100185) ((-696 . -489) 100119) ((-696 . -242) 100053) ((-696 . -47) 100025) ((-696 . -322) 100009) ((-696 . -575) 99957) ((-696 . -385) 99911) ((-696 . -802) 99895) ((-696 . -799) 99877) ((-696 . -804) 99861) ((-696 . -789) 99720) ((-696 . -814) 99699) ((-696 . -1123) 99678) ((-696 . -854) 99645) ((-689 . -1005) T) ((-689 . -547) 99627) ((-689 . -1118) T) ((-689 . -72) T) ((-687 . -710) T) ((-687 . -102) T) ((-687 . -25) T) ((-687 . -72) T) ((-687 . -1118) T) ((-687 . -547) 99609) ((-687 . -1005) T) ((-687 . -23) T) 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. -962) T) ((-647 . -1015) T) ((-647 . -658) T) ((-647 . -21) T) ((-647 . -583) 96495) ((-647 . -23) T) ((-647 . -1005) T) ((-647 . -547) 96477) ((-647 . -1118) T) ((-647 . -72) T) ((-647 . -25) T) ((-647 . -102) T) ((-647 . -585) 96464) ((-647 . -550) 96446) ((-646 . -954) T) ((-646 . -962) T) ((-646 . -1015) T) ((-646 . -658) T) ((-646 . -21) T) ((-646 . -583) 96391) ((-646 . -23) T) ((-646 . -1005) T) ((-646 . -547) 96373) ((-646 . -1118) T) ((-646 . -72) T) ((-646 . -25) T) ((-646 . -102) T) ((-646 . -585) 96333) ((-646 . -550) 96288) ((-646 . -943) 96258) ((-646 . -238) 96237) ((-646 . -118) 96216) ((-646 . -116) 96195) ((-646 . -38) 96165) ((-646 . -80) 96130) ((-646 . -956) 96100) ((-646 . -961) 96070) ((-646 . -577) 96040) ((-646 . -649) 96010) ((-645 . -749) T) ((-645 . -547) 95945) ((-645 . -1005) T) ((-645 . -72) T) ((-645 . -1118) T) ((-645 . -752) T) ((-645 . -423) 95895) ((-645 . -550) 95845) ((-644 . -1144) 95829) ((-644 . -1055) 95807) ((-644 . -548) NIL) ((-644 . -256) 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87139) ((-572 . -1118) T) ((-572 . -72) T) ((-572 . -313) T) ((-572 . -550) 87116) ((-567 . -676) 87100) ((-567 . -652) T) ((-567 . -678) T) ((-567 . -80) 87079) ((-567 . -956) 87063) ((-567 . -961) 87047) ((-567 . -21) T) ((-567 . -583) 87016) ((-567 . -23) T) ((-567 . -1005) T) ((-567 . -547) 86985) ((-567 . -1118) T) ((-567 . -72) T) ((-567 . -25) T) ((-567 . -102) T) ((-567 . -585) 86969) ((-567 . -577) 86953) ((-567 . -649) 86937) ((-567 . -354) 86902) ((-567 . -312) 86837) ((-567 . -238) 86795) ((-566 . -1096) 86770) ((-566 . -181) 86714) ((-566 . -76) 86658) ((-566 . -256) 86503) ((-566 . -447) 86303) ((-566 . -422) 86233) ((-566 . -122) 86177) ((-566 . -548) NIL) ((-566 . -190) 86121) ((-566 . -544) 86096) ((-566 . -240) 86071) ((-566 . -1118) T) ((-566 . -238) 86024) ((-566 . -1005) T) ((-566 . -547) 86006) ((-566 . -72) T) ((-566 . -34) T) ((-566 . -533) 85981) ((-561 . -406) T) ((-561 . -1015) T) ((-561 . -72) T) ((-561 . -1118) T) ((-561 . -547) 85963) ((-561 . -1005) T) 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. -550) 82173) ((-525 . -954) T) ((-525 . -962) T) ((-525 . -1015) T) ((-525 . -658) T) ((-525 . -21) T) ((-525 . -583) 82132) ((-525 . -23) T) ((-525 . -1005) T) ((-525 . -547) 82114) ((-525 . -1118) T) ((-525 . -72) T) ((-525 . -25) T) ((-525 . -102) T) ((-525 . -585) 82088) ((-525 . -550) 82046) ((-525 . -80) 81999) ((-525 . -956) 81959) ((-525 . -961) 81919) ((-525 . -489) 81898) ((-525 . -242) 81877) ((-525 . -144) 81856) ((-525 . -649) 81829) ((-525 . -577) 81802) ((-525 . -38) 81775) ((-524 . -1147) 81752) ((-524 . -47) 81729) ((-524 . -38) 81626) ((-524 . -577) 81523) ((-524 . -649) 81420) ((-524 . -550) 81302) ((-524 . -242) 81281) ((-524 . -489) 81260) ((-524 . -80) 81125) ((-524 . -956) 81011) ((-524 . -961) 80897) ((-524 . -144) 80851) ((-524 . -118) 80830) ((-524 . -116) 80809) ((-524 . -585) 80734) ((-524 . -583) 80644) ((-524 . -879) 80614) ((-524 . -804) 80527) ((-524 . -799) 80438) ((-524 . -802) 80351) ((-524 . -238) 80316) ((-524 . -187) 80275) ((-524 . -1118) T) 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. -72) T) ((-437 . -1005) T) ((-437 . -547) 74699) ((-437 . -1118) T) ((-437 . -72) T) ((-435 . -749) T) ((-435 . -547) 74681) ((-435 . -1005) T) ((-435 . -72) T) ((-435 . -1118) T) ((-435 . -752) T) ((-435 . -550) 74662) ((-433 . -94) T) ((-433 . -317) 74645) ((-433 . -752) T) ((-433 . -749) T) ((-433 . -122) 74628) ((-433 . -34) T) ((-433 . -72) T) ((-433 . -547) 74610) ((-433 . -256) NIL) ((-433 . -447) NIL) ((-433 . -1005) T) ((-433 . -422) 74593) ((-433 . -548) 74575) ((-433 . -238) 74526) ((-433 . -533) 74502) ((-433 . -240) 74478) ((-433 . -588) 74461) ((-433 . -19) 74444) ((-433 . -599) T) ((-433 . -1118) T) ((-433 . -82) T) ((-430 . -57) 74394) ((-430 . -34) T) ((-430 . -1118) T) ((-430 . -72) 74348) ((-430 . -547) 74283) ((-430 . -256) 74221) ((-430 . -447) 74154) ((-430 . -1005) 74132) ((-430 . -422) 74116) ((-429 . -19) 74100) ((-429 . -588) 74084) ((-429 . -240) 74061) ((-429 . -238) 74013) ((-429 . -533) 73990) ((-429 . -548) 73951) ((-429 . -422) 73935) ((-429 . -1005) 73888) ((-429 . -447) 73821) ((-429 . -256) 73759) ((-429 . -547) 73674) ((-429 . -72) 73608) ((-429 . -1118) T) ((-429 . -34) T) ((-429 . -122) 73592) ((-429 . -749) 73571) ((-429 . -752) 73550) ((-429 . -317) 73534) ((-428 . -250) T) ((-428 . -72) T) ((-428 . -1118) T) ((-428 . -547) 73516) ((-428 . -1005) T) ((-428 . -550) 73417) ((-428 . -943) 73360) ((-428 . -447) 73326) ((-428 . -256) 73313) ((-428 . -27) T) ((-428 . -908) T) ((-428 . -198) T) ((-428 . -80) 73262) ((-428 . -956) 73227) ((-428 . -961) 73192) ((-428 . -242) T) ((-428 . -649) 73157) ((-428 . -577) 73122) ((-428 . -585) 73072) ((-428 . -583) 73022) ((-428 . -102) T) ((-428 . -25) T) ((-428 . -23) T) ((-428 . -21) T) ((-428 . -954) T) ((-428 . -962) T) ((-428 . -1015) T) ((-428 . -658) T) ((-428 . -38) 72987) ((-428 . -254) T) ((-428 . -385) T) ((-428 . -144) T) ((-428 . -489) T) ((-428 . -825) T) ((-428 . -1123) T) ((-428 . -308) T) ((-428 . -575) 72947) ((-428 . -926) T) ((-428 . -548) 72892) ((-428 . -118) T) ((-428 . -188) T) ((-428 . -184) 72879) ((-428 . -187) T) ((-424 . -1005) T) ((-424 . -547) 72845) ((-424 . -1118) T) ((-424 . -72) T) ((-420 . -897) 72827) ((-420 . -1055) T) ((-420 . -550) 72777) ((-420 . -943) 72737) ((-420 . -548) 72667) ((-420 . -926) T) ((-420 . -814) NIL) ((-420 . -787) 72649) ((-420 . -748) T) ((-420 . -714) T) ((-420 . -711) T) ((-420 . -752) T) ((-420 . -749) T) ((-420 . -709) T) ((-420 . -707) T) ((-420 . -733) T) ((-420 . -789) 72631) ((-420 . -336) 72613) ((-420 . -575) 72595) ((-420 . -322) 72577) ((-420 . -238) NIL) ((-420 . -256) NIL) ((-420 . -447) NIL) ((-420 . -284) 72559) ((-420 . -198) T) ((-420 . -80) 72486) ((-420 . -956) 72436) ((-420 . -961) 72386) ((-420 . -242) T) ((-420 . -649) 72336) ((-420 . -577) 72286) ((-420 . -585) 72236) ((-420 . -583) 72186) ((-420 . -38) 72136) ((-420 . -254) T) ((-420 . -385) T) ((-420 . -144) T) ((-420 . -489) T) ((-420 . -825) T) ((-420 . -1123) T) ((-420 . -308) T) ((-420 . -188) T) ((-420 . -184) 72123) ((-420 . -187) T) ((-420 . -222) 72105) ((-420 . -799) NIL) ((-420 . -804) NIL) ((-420 . -802) NIL) ((-420 . -182) 72087) ((-420 . -118) T) ((-420 . -116) NIL) ((-420 . -102) T) ((-420 . -25) T) ((-420 . -72) T) ((-420 . -1118) T) ((-420 . -547) 72029) ((-420 . -1005) T) ((-420 . -23) T) ((-420 . -21) T) ((-420 . -954) T) ((-420 . -962) T) ((-420 . -1015) T) ((-420 . -658) T) ((-418 . -282) 71998) ((-418 . -102) T) ((-418 . -25) T) ((-418 . -72) T) ((-418 . -1118) T) ((-418 . -547) 71980) ((-418 . -1005) T) ((-418 . -23) T) ((-418 . -583) 71962) ((-418 . -21) T) ((-417 . -874) 71946) ((-417 . -422) 71930) ((-417 . -1005) 71908) ((-417 . -447) 71841) ((-417 . -256) 71779) ((-417 . -547) 71714) ((-417 . -72) 71668) ((-417 . -1118) T) ((-417 . -34) T) ((-417 . -76) 71652) ((-416 . -987) T) ((-416 . -423) 71633) ((-416 . -547) 71599) ((-416 . -550) 71580) ((-416 . -1005) T) ((-416 . -1118) T) ((-416 . -72) T) ((-416 . -64) T) ((-415 . -193) 71559) ((-415 . -1176) 71529) ((-415 . -714) 71508) 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64830) ((-412 . -122) 64778) ((-412 . -548) NIL) ((-412 . -190) 64726) ((-412 . -544) 64705) ((-412 . -240) 64684) ((-412 . -1118) T) ((-412 . -238) 64663) ((-412 . -1005) T) ((-412 . -547) 64645) ((-412 . -72) T) ((-412 . -34) T) ((-412 . -533) 64624) ((-411 . -987) T) ((-411 . -423) 64605) ((-411 . -547) 64571) ((-411 . -550) 64552) ((-411 . -1005) T) ((-411 . -1118) T) ((-411 . -72) T) ((-411 . -64) T) ((-410 . -308) T) ((-410 . -1123) T) ((-410 . -825) T) ((-410 . -489) T) ((-410 . -144) T) ((-410 . -550) 64502) ((-410 . -649) 64467) ((-410 . -577) 64432) ((-410 . -38) 64397) ((-410 . -385) T) ((-410 . -254) T) ((-410 . -585) 64362) ((-410 . -583) 64312) ((-410 . -658) T) ((-410 . -1015) T) ((-410 . -962) T) ((-410 . -954) T) ((-410 . -80) 64261) ((-410 . -956) 64226) ((-410 . -961) 64191) ((-410 . -21) T) ((-410 . -23) T) ((-410 . -1005) T) ((-410 . -547) 64143) ((-410 . -1118) T) ((-410 . -72) T) ((-410 . -25) T) ((-410 . -102) T) ((-410 . -242) T) ((-410 . -198) T) ((-410 . 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. -575) 55862) ((-343 . -585) 55778) ((-343 . -322) 55762) ((-343 . -238) 55720) ((-343 . -256) 55685) ((-343 . -447) 55597) ((-343 . -284) 55581) ((-343 . -198) T) ((-343 . -80) 55512) ((-343 . -956) 55464) ((-343 . -961) 55416) ((-343 . -242) T) ((-343 . -649) 55368) ((-343 . -577) 55320) ((-343 . -583) 55257) ((-343 . -38) 55209) ((-343 . -254) T) ((-343 . -385) T) ((-343 . -144) T) ((-343 . -489) T) ((-343 . -825) T) ((-343 . -1123) T) ((-343 . -308) T) ((-343 . -188) 55188) ((-343 . -184) 55136) ((-343 . -187) 55090) ((-343 . -222) 55074) ((-343 . -799) 54998) ((-343 . -804) 54924) ((-343 . -802) 54883) ((-343 . -182) 54867) ((-343 . -118) 54846) ((-343 . -116) 54825) ((-343 . -102) T) ((-343 . -25) T) ((-343 . -72) T) ((-343 . -1118) T) ((-343 . -547) 54807) ((-343 . -1005) T) ((-343 . -23) T) ((-343 . -21) T) ((-343 . -954) T) ((-343 . -962) T) ((-343 . -1015) T) ((-343 . -658) T) ((-341 . -489) T) ((-341 . -242) T) ((-341 . -144) T) ((-341 . -550) 54716) ((-341 . -649) 54690) 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53407) ((-333 . -961) 53391) ((-333 . -21) T) ((-333 . -583) 53360) ((-333 . -23) T) ((-333 . -1005) T) ((-333 . -547) 53342) ((-333 . -1118) T) ((-333 . -72) T) ((-333 . -25) T) ((-333 . -102) T) ((-333 . -585) 53326) ((-333 . -577) 53310) ((-333 . -649) 53294) ((-331 . -332) T) ((-331 . -72) T) ((-331 . -1118) T) ((-331 . -547) 53260) ((-331 . -1005) T) ((-331 . -550) 53241) ((-331 . -423) 53222) ((-330 . -329) 53206) ((-330 . -550) 53190) ((-330 . -943) 53174) ((-330 . -752) 53153) ((-330 . -749) 53132) ((-330 . -1015) T) ((-330 . -72) T) ((-330 . -1118) T) ((-330 . -547) 53114) ((-330 . -1005) T) ((-330 . -658) T) ((-327 . -328) 53093) ((-327 . -550) 53077) ((-327 . -943) 53061) ((-327 . -577) 53031) ((-327 . -649) 53001) ((-327 . -585) 52985) ((-327 . -583) 52954) ((-327 . -102) T) ((-327 . -25) T) ((-327 . -72) T) ((-327 . -1118) T) ((-327 . -547) 52936) ((-327 . -1005) T) ((-327 . -23) T) ((-327 . -21) T) ((-327 . -961) 52920) ((-327 . -956) 52904) ((-327 . -80) 52883) ((-326 . -80) 52862) ((-326 . -956) 52846) ((-326 . -961) 52830) ((-326 . -21) T) ((-326 . -583) 52799) ((-326 . -23) T) ((-326 . -1005) T) ((-326 . -547) 52781) ((-326 . -1118) T) ((-326 . -72) T) ((-326 . -25) T) ((-326 . -102) T) ((-326 . -585) 52765) ((-326 . -442) 52744) ((-326 . -649) 52714) ((-326 . -577) 52684) ((-323 . -340) T) ((-323 . -118) T) ((-323 . -550) 52634) ((-323 . -585) 52599) ((-323 . -583) 52549) ((-323 . -102) T) ((-323 . -25) T) ((-323 . -72) T) ((-323 . -1118) T) ((-323 . -547) 52516) ((-323 . -1005) T) ((-323 . -23) T) ((-323 . -21) T) ((-323 . -658) T) ((-323 . -1015) T) ((-323 . -962) T) ((-323 . -954) T) ((-323 . -548) 52430) ((-323 . -308) T) ((-323 . -1123) T) ((-323 . -825) T) ((-323 . -489) T) ((-323 . -144) T) ((-323 . -649) 52395) ((-323 . -577) 52360) ((-323 . -38) 52325) ((-323 . -385) T) ((-323 . -254) T) ((-323 . -80) 52274) ((-323 . -956) 52239) ((-323 . -961) 52204) ((-323 . -242) T) ((-323 . -198) T) ((-323 . -748) T) ((-323 . -714) T) ((-323 . -711) T) ((-323 . -752) T) ((-323 . -749) T) ((-323 . -709) T) ((-323 . -707) T) ((-323 . -789) 52186) ((-323 . -908) T) ((-323 . -926) T) ((-323 . -943) 52146) ((-323 . -965) T) ((-323 . -188) T) ((-323 . -184) 52133) ((-323 . -187) T) ((-323 . -1104) T) ((-323 . -1107) T) ((-323 . -426) T) ((-323 . -236) T) ((-323 . -66) T) ((-323 . -35) T) ((-323 . -552) 52115) ((-309 . -310) 52092) ((-309 . -72) T) ((-309 . -1118) T) ((-309 . -547) 52074) ((-309 . -1005) T) ((-306 . -406) T) ((-306 . -1015) T) ((-306 . -72) T) ((-306 . -1118) T) ((-306 . -547) 52056) ((-306 . -1005) T) ((-306 . -658) T) ((-306 . -943) 52040) ((-306 . -550) 52024) ((-304 . -276) 52008) ((-304 . -188) 51987) ((-304 . -184) 51960) ((-304 . -187) 51939) ((-304 . -313) 51918) ((-304 . -1055) 51897) ((-304 . -295) 51876) ((-304 . -118) 51855) ((-304 . -550) 51792) ((-304 . -585) 51744) ((-304 . -583) 51681) ((-304 . -102) T) ((-304 . -25) T) ((-304 . -72) T) ((-304 . -1118) T) ((-304 . -547) 51663) ((-304 . -1005) T) ((-304 . -23) T) ((-304 . -21) T) ((-304 . -658) T) ((-304 . -1015) T) ((-304 . -962) T) ((-304 . -954) T) ((-304 . -308) T) ((-304 . -1123) T) ((-304 . -825) T) ((-304 . -489) T) ((-304 . -144) T) ((-304 . -649) 51615) ((-304 . -577) 51567) ((-304 . -38) 51532) ((-304 . -385) T) ((-304 . -254) T) ((-304 . -80) 51463) ((-304 . -956) 51415) ((-304 . -961) 51367) ((-304 . -242) T) ((-304 . -198) T) ((-304 . -338) 51321) ((-304 . -116) 51275) ((-304 . -943) 51259) ((-304 . -1176) 51243) ((-304 . -1187) 51227) ((-300 . -276) 51211) ((-300 . -188) 51190) ((-300 . -184) 51163) ((-300 . -187) 51142) ((-300 . -313) 51121) ((-300 . -1055) 51100) ((-300 . -295) 51079) ((-300 . -118) 51058) ((-300 . -550) 50995) ((-300 . -585) 50947) ((-300 . -583) 50884) ((-300 . -102) T) ((-300 . -25) T) ((-300 . -72) T) ((-300 . -1118) T) ((-300 . -547) 50866) ((-300 . -1005) T) ((-300 . -23) T) ((-300 . -21) T) ((-300 . -658) T) ((-300 . -1015) T) ((-300 . -962) T) ((-300 . -954) T) ((-300 . -308) T) ((-300 . -1123) 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. -752) T) ((-84 . -740) 6971) ((-83 . -745) T) ((-83 . -752) T) ((-83 . -749) T) ((-83 . -1005) T) ((-83 . -547) 6953) ((-83 . -1118) T) ((-83 . -72) T) ((-83 . -313) T) ((-83 . -873) T) ((-83 . -599) T) ((-83 . -82) T) ((-83 . -548) 6935) ((-79 . -94) T) ((-79 . -317) 6918) ((-79 . -752) T) ((-79 . -749) T) ((-79 . -122) 6901) ((-79 . -34) T) ((-79 . -72) T) ((-79 . -547) 6883) ((-79 . -256) NIL) ((-79 . -447) NIL) ((-79 . -1005) T) ((-79 . -422) 6866) ((-79 . -548) 6848) ((-79 . -238) 6799) ((-79 . -533) 6775) ((-79 . -240) 6751) ((-79 . -588) 6734) ((-79 . -19) 6717) ((-79 . -599) T) ((-79 . -1118) T) ((-79 . -82) T) ((-78 . -547) 6699) ((-77 . -897) 6681) ((-77 . -1055) T) ((-77 . -550) 6631) ((-77 . -943) 6591) ((-77 . -548) 6521) ((-77 . -926) T) ((-77 . -814) NIL) ((-77 . -787) 6503) ((-77 . -748) T) ((-77 . -714) T) ((-77 . -711) T) ((-77 . -752) T) ((-77 . -749) T) ((-77 . -709) T) ((-77 . -707) T) ((-77 . -733) T) ((-77 . -789) 6485) ((-77 . -336) 6467) ((-77 . -575) 6449) 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. -90) 5558) ((-69 . -406) T) ((-69 . -1015) T) ((-69 . -72) T) ((-69 . -1118) T) ((-69 . -547) 5540) ((-69 . -1005) T) ((-69 . -658) T) ((-69 . -238) 5519) ((-67 . -987) T) ((-67 . -423) 5500) ((-67 . -547) 5466) ((-67 . -550) 5447) ((-67 . -1005) T) ((-67 . -1118) T) ((-67 . -72) T) ((-67 . -64) T) ((-62 . -1024) 5431) ((-62 . -422) 5415) ((-62 . -1005) 5393) ((-62 . -447) 5326) ((-62 . -256) 5264) ((-62 . -547) 5199) ((-62 . -72) 5153) ((-62 . -1118) T) ((-62 . -34) T) ((-62 . -76) 5137) ((-60 . -57) 5099) ((-60 . -34) T) ((-60 . -1118) T) ((-60 . -72) 5053) ((-60 . -547) 4988) ((-60 . -256) 4926) ((-60 . -447) 4859) ((-60 . -1005) 4837) ((-60 . -422) 4821) ((-58 . -19) 4805) ((-58 . -588) 4789) ((-58 . -240) 4766) ((-58 . -238) 4718) ((-58 . -533) 4695) ((-58 . -548) 4656) ((-58 . -422) 4640) ((-58 . -1005) 4593) ((-58 . -447) 4526) ((-58 . -256) 4464) ((-58 . -547) 4379) ((-58 . -72) 4313) ((-58 . -1118) T) ((-58 . -34) T) ((-58 . -122) 4297) ((-58 . -749) 4276) ((-58 . -752) 4255) ((-58 . -317) 4239) ((-55 . -1005) T) ((-55 . -547) 4221) ((-55 . -1118) T) ((-55 . -72) T) ((-55 . -943) 4203) ((-55 . -550) 4185) ((-51 . -1005) T) ((-51 . -547) 4167) ((-51 . -1118) T) ((-51 . -72) T) ((-50 . -555) 4151) ((-50 . -550) 4120) ((-50 . -585) 4094) ((-50 . -583) 4053) ((-50 . -658) T) ((-50 . -1015) T) ((-50 . -962) T) ((-50 . -954) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1005) T) ((-50 . -547) 4035) ((-50 . -1118) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -102) T) ((-50 . -943) 4019) ((-49 . -1005) T) ((-49 . -547) 4001) ((-49 . -1118) T) ((-49 . -72) T) ((-48 . -250) T) ((-48 . -72) T) ((-48 . -1118) T) ((-48 . -547) 3983) ((-48 . -1005) T) ((-48 . -550) 3884) ((-48 . -943) 3827) ((-48 . -447) 3793) ((-48 . -256) 3780) ((-48 . -27) T) ((-48 . -908) T) ((-48 . -198) T) ((-48 . -80) 3729) ((-48 . -956) 3694) ((-48 . -961) 3659) ((-48 . -242) T) ((-48 . -649) 3624) ((-48 . -577) 3589) ((-48 . -585) 3539) ((-48 . -583) 3489) ((-48 . -102) T) ((-48 . -25) T) 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1869) ((-44 . -956) 1853) ((-44 . -961) 1837) ((-44 . -21) T) ((-44 . -583) 1780) ((-44 . -23) T) ((-44 . -1005) T) ((-44 . -547) 1762) ((-44 . -72) T) ((-44 . -25) T) ((-44 . -102) T) ((-44 . -585) 1720) ((-44 . -577) 1704) ((-44 . -649) 1688) ((-44 . -312) 1672) ((-44 . -1118) T) ((-44 . -238) 1649) ((-40 . -287) 1623) ((-40 . -144) T) ((-40 . -550) 1553) ((-40 . -658) T) ((-40 . -1015) T) ((-40 . -962) T) ((-40 . -954) T) ((-40 . -585) 1455) ((-40 . -583) 1385) ((-40 . -102) T) ((-40 . -25) T) ((-40 . -72) T) ((-40 . -1118) T) ((-40 . -547) 1367) ((-40 . -1005) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -961) 1312) ((-40 . -956) 1257) ((-40 . -80) 1174) ((-40 . -548) 1158) ((-40 . -182) 1135) ((-40 . -802) 1087) ((-40 . -804) 999) ((-40 . -799) 909) ((-40 . -222) 886) ((-40 . -187) 826) ((-40 . -184) 760) ((-40 . -188) 732) ((-40 . -308) T) ((-40 . -1123) T) ((-40 . -825) T) ((-40 . -489) T) ((-40 . -649) 677) ((-40 . -577) 622) ((-40 . -38) 567) ((-40 . -385) T) ((-40 . -254) T) ((-40 . -242) T) ((-40 . -198) T) ((-40 . -313) NIL) ((-40 . -295) NIL) ((-40 . -1055) NIL) ((-40 . -116) 539) ((-40 . -338) NIL) ((-40 . -346) 511) ((-40 . -118) 483) ((-40 . -315) 455) ((-40 . -322) 432) ((-40 . -575) 366) ((-40 . -348) 343) ((-40 . -943) 220) ((-40 . -656) 192) ((-31 . -987) T) ((-31 . -423) 173) ((-31 . -547) 139) ((-31 . -550) 120) ((-31 . -1005) T) ((-31 . -1118) T) ((-31 . -72) T) ((-31 . -64) T) ((-30 . -859) T) ((-30 . -547) 102) ((0 . |EnumerationCategory|) T) ((0 . -547) 84) ((0 . -1005) T) ((0 . -72) T) ((0 . -1118) T) ((-2 . |RecordCategory|) T) ((-2 . -547) 66) ((-2 . -1005) T) ((-2 . -72) T) ((-2 . -1118) T) ((-3 . |UnionCategory|) T) ((-3 . -547) 48) ((-3 . -1005) T) ((-3 . -72) T) ((-3 . -1118) T) ((-1 . -1005) T) ((-1 . -547) 30) ((-1 . -1118) T) ((-1 . -72) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 1135c00d..52675c3a 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3525483390) -(4148 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3525500983) +(3982 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -18,22 +18,22 @@ |OneDimensionalArray| |OneDimensionalArrayFunctions2| |TwoDimensionalArray| |AssociatedEquations| |ArrayStack| |AbstractSyntaxCategory&| |AbstractSyntaxCategory| |ArcTrigonometricFunctionCategory&| - |ArcTrigonometricFunctionCategory| |AttributeAst| |AttributeButtons| - |AttributeRegistry| |Automorphism| |BalancedFactorisation| |BasicType&| - |BasicType| |BalancedBinaryTree| |BezoutMatrix| |BasicFunctions| - |BagAggregate&| |BagAggregate| |BinaryExpansion| |Binding| |Bits| |BiModule| - |BooleanLogic&| |BooleanLogic| |Boolean| |BasicOperator| - |BasicOperatorFunctions1| |BoundIntegerRoots| |BalancedPAdicInteger| - |BalancedPAdicRational| |BinaryRecursiveAggregate&| |BinaryRecursiveAggregate| - |BrillhartTests| |BinarySearchTree| |BitAggregate&| |BitAggregate| - |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| |BinaryTree| - |Byte| |ByteBuffer| |ByteOrder| |CancellationAbelianMonoid| |CachableSet| - |CapsuleAst| |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| - |CaseAst| |CategoryAst| |CategoryConstructor| |Category| |CharacterClass| - |CommonDenominator| |CombinatorialFunctionCategory| |Character| - |CharacteristicNonZero| |CharacteristicPolynomialPackage| |CharacteristicZero| - |ChangeOfVariable| |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| - |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| |CollectAst| + |ArcTrigonometricFunctionCategory| |AttributeAst| |AttributeRegistry| + |Automorphism| |BalancedFactorisation| |BasicType&| |BasicType| + |BalancedBinaryTree| |BezoutMatrix| |BagAggregate&| |BagAggregate| + |BinaryExpansion| |Binding| |Bits| |BiModule| |BooleanLogic&| |BooleanLogic| + |Boolean| |BasicOperator| |BasicOperatorFunctions1| |BoundIntegerRoots| + |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryRecursiveAggregate&| + |BinaryRecursiveAggregate| |BrillhartTests| |BinarySearchTree| |BitAggregate&| + |BitAggregate| |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| + |BinaryTree| |Byte| |ByteBuffer| |ByteOrder| |CancellationAbelianMonoid| + |CachableSet| |CapsuleAst| |CardinalNumber| |CartesianTensor| + |CartesianTensorFunctions2| |CaseAst| |CategoryAst| |CategoryConstructor| + |Category| |CharacterClass| |CommonDenominator| + |CombinatorialFunctionCategory| |Character| |CharacteristicNonZero| + |CharacteristicPolynomialPackage| |CharacteristicZero| |ChangeOfVariable| + |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| |Collection| + |CliffordAlgebra| |TwoDimensionalPlotClipping| |CollectAst| |ComplexRootPackage| |ColonAst| |Color| |CombinatorialFunction| |IntegerCombinatoricFunctions| |CombinatorialOpsCategory| |Commutator| |CommaAst| |CommonOperators| |CommuteUnivariatePolynomialCategory| @@ -76,22 +76,20 @@ |EltableAggregate| |EuclideanModularRing| |EntireRing| |Environment| |EigenPackage| |Equation| |EquationFunctions2| |EqTable| |ErrorFunctions| |ExpressionSpace&| |ExpressionSpace| |ExpressionSpaceFunctions1| - |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage| - |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| - |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |EuclideanDomain&| - |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| - |ExitAst| |ExponentialExpansion| |Expression| |ExpressionFunctions2| - |ExpressionToUnivariatePowerSeries| |ExpressionSpaceODESolver| - |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| - |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup| - |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| - |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| - |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| - |FortranCodePackage1| |FunctorData| |FiniteDivisor| |FiniteDivisorFunctions2| - |FiniteDivisorCategory&| |FiniteDivisorCategory| |FullyEvalableOver&| - |FullyEvalableOver| |FortranExpression| |FiniteField| |FunctionFieldCategory&| - |FunctionFieldCategory| |FunctionFieldCategoryFunctions2| - |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| + |ExpressionSpaceFunctions2| |EuclideanDomain&| |EuclideanDomain| |Evalable&| + |Evalable| |EvaluateCycleIndicators| |Exit| |ExitAst| |ExponentialExpansion| + |Expression| |ExpressionFunctions2| |ExpressionToUnivariatePowerSeries| + |ExpressionSpaceODESolver| |ExpressionTubePlot| + |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions| + |FactoringUtilities| |FreeAbelianGroup| |FreeAbelianMonoidCategory| + |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRing| + |FlexibleArray| |FiniteAlgebraicExtensionField&| + |FiniteAlgebraicExtensionField| |FourierComponent| |FunctorData| + |FiniteDivisor| |FiniteDivisorFunctions2| |FiniteDivisorCategory&| + |FiniteDivisorCategory| |FullyEvalableOver&| |FullyEvalableOver| |FiniteField| + |FunctionFieldCategory&| |FunctionFieldCategory| + |FunctionFieldCategoryFunctions2| |FiniteFieldCyclicGroup| + |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| @@ -105,17 +103,14 @@ |FiniteLinearAggregate| |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| |Float| |FloatingComplexPackage| - |FloatingRealPackage| |FreeModule| |FreeModule1| |FortranMatrixCategory| - |FreeModuleCat| |FortranMatrixFunctionCategory| |FreeMonoidCategory| - |FreeMonoid| |FortranMachineTypeCategory| |FileName| |FileNameCategory| - |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| - |FortranPackage| |FortranProgramCategory| |FortranFunctionCategory| - |FortranProgram| |FullPartialFractionExpansion| |FullyPatternMatchable| - |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| - |FloatingPointSystem&| |FloatingPointSystem| |Factored| |FactoredFunctions2| - |Fraction| |FractionFunctions2| |FramedAlgebra&| |FramedAlgebra| - |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdeal| - |FractionalIdealFunctions2| |FramedModule| + |FloatingRealPackage| |FreeModule| |FreeModule1| |FreeModuleCat| + |FreeMonoidCategory| |FreeMonoid| |FileName| |FileNameCategory| + |FreeNilpotentLie| |FindOrderFinite| |FullPartialFractionExpansion| + |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| + |FieldOfPrimeCharacteristic| |FloatingPointSystem&| |FloatingPointSystem| + |Factored| |FactoredFunctions2| |Fraction| |FractionFunctions2| + |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| + |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| |FunctionSpace&| |FunctionSpace| |FunctionSpaceFunctions2| @@ -124,9 +119,8 @@ |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FortranScalarType| - |FunctionSpaceUnivariatePolynomialFactor| |FortranType| |FortranTemplate| - |FunctionCalled| |FunctionDescriptor| |FortranVectorCategory| - |FortranVectorFunctionCategory| |GaloisGroupFactorizer| + |FunctionSpaceUnivariatePolynomialFactor| |FortranType| |FunctionCalled| + |FunctionDescriptor| |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |GroebnerPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| @@ -203,16 +197,15 @@ |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| |ListAggregate| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LieSquareMatrix| |ConstructAst| |LyndonWord| - |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| - |MacroAst| |Magma| |MappingPackageInternalHacks1| - |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingAst| - |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategory&| - |MatrixCategory| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| - |Matrix| |StorageEfficientMatrixOperations| |Maybe| - |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| + |LazyStreamAggregate&| |LazyStreamAggregate| |MacroAst| |Magma| + |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| + |MappingPackageInternalHacks3| |MappingAst| |MappingPackage1| + |MappingPackage2| |MappingPackage3| |MatrixCategory&| |MatrixCategory| + |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |Matrix| + |StorageEfficientMatrixOperations| |Maybe| |MatrixCommonDenominator| |MultiDictionary| |ModularDistinctDegreeFactorizer| - |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| - |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| + |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| + |ModularHermitianRowReduction| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| |MultipleMap| |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| @@ -228,53 +221,48 @@ |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| |NumericComplexEigenPackage| |NumericContinuedFraction| |NonCommutativeOperatorDivision| |NetworkClientSocket| - |NumberFieldIntegralBasis| |NumericalIntegrationProblem| - |NonLinearSolvePackage| |NonNegativeInteger| |NonLinearFirstOrderODESolver| - |None| |NoneFunctions1| |NormInMonogenicAlgebra| |NormalizationPackage| - |NormRetractPackage| |NPCoef| |NumericRealEigenPackage| - |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| - |NewSparseUnivariatePolynomialFunctions2| |NumberTheoreticPolynomialFunctions| - |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| - |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| + |NumberFieldIntegralBasis| |NonLinearSolvePackage| |NonNegativeInteger| + |NonLinearFirstOrderODESolver| |None| |NoneFunctions1| + |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| + |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| + |NewSparseUnivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| + |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| + |Numeric| |NumberFormats| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup&| |OrderedAbelianGroup| |OrderedAbelianMonoid&| |OrderedAbelianMonoid| |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OctonionCategory&| |OctonionCategory| |OrderedCancellationAbelianMonoid| |Octonion| - |OctonionCategoryFunctions2| |OrdinaryDifferentialEquationsSolverCategory| - |ConstantLODE| |ElementaryFunctionODESolver| |ODEIntegration| - |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| |PrimitiveRatRicDE| + |OctonionCategoryFunctions2| |ConstantLODE| |ElementaryFunctionODESolver| + |ODEIntegration| |PureAlgebraicLODE| |PrimitiveRatDE| |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| |OrderedIntegralDomain| |OppositeMonogenicLinearOperator| |OrderedMultisetAggregate| |OnePointCompletion| |OnePointCompletionFunctions2| |Operator| |OperatorCategory&| |OperatorCategory| |OperationsQuery| - |OperatorSignature| |NumericalOptimizationCategory| - |NumericalOptimizationProblem| |OrderedCompletion| - |OrderedCompletionFunctions2| |OrderedFinite| |OrderingFunctions| - |OrderedMonoid| |OrderedRing| |OrderedSet| |OrderedStructure| |OrderedType&| - |OrderedType| |UnivariateSkewPolynomialCategory&| - |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| - |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| - |OrthogonalPolynomialFunctions| |OrderedSemiGroup| |OrdSetInts| - |OutputPackage| |OutputByteConduit&| |OutputByteConduit| |OutputBinaryFile| - |OutputForm| |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials| - |PadeApproximants| |PadeApproximantPackage| |PAdicInteger| - |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Pair| - |Palette| |PolynomialAN2Expression| |ParameterAst| - |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| + |OperatorSignature| |OrderedCompletion| |OrderedCompletionFunctions2| + |OrderedFinite| |OrderingFunctions| |OrderedMonoid| |OrderedRing| |OrderedSet| + |OrderedStructure| |OrderedType&| |OrderedType| + |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| + |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| + |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrderedSemiGroup| + |OrdSetInts| |OutputPackage| |OutputByteConduit&| |OutputByteConduit| + |OutputBinaryFile| |OutputForm| |OrderedVariableList| |OverloadSet| + |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| + |PAdicInteger| |PAdicIntegerCategory| |PAdicRational| + |PAdicRationalConstructor| |Pair| |Palette| |PolynomialAN2Expression| + |ParameterAst| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |Parser| |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| |PatternMatchResult| |PatternMatchResultFunctions2| |Pattern| |PatternFunctions1| |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialDomain&| - |PartialDifferentialDomain| |PartialDifferentialEquationsSolverCategory| - |PolynomialDecomposition| |NumericalPDEProblem| |PartialDifferentialModule| - |PartialDifferentialRing| |PartialDifferentialSpace&| - |PartialDifferentialSpace| |PendantTree| |Permutation| |Permanent| - |PermutationCategory| |PermutationGroup| |PrimeField| - |PolynomialFactorizationByRecursion| + |PartialDifferentialDomain| |PolynomialDecomposition| + |PartialDifferentialModule| |PartialDifferentialRing| + |PartialDifferentialSpace&| |PartialDifferentialSpace| |PendantTree| + |Permutation| |Permanent| |PermutationCategory| |PermutationGroup| + |PrimeField| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| @@ -317,15 +305,15 @@ |RealZeroPackageQ| |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| |RegularTriangularSet| |RadicalEigenPackage| |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| - |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| - |ReturnAst| |RetractableTo&| |RetractableTo| |RetractSolvePackage| - |RationalFunction| |RandomFloatDistributions| |RationalFunctionFactor| + |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |ReturnAst| + |RetractableTo&| |RetractableTo| |RetractSolvePackage| |RationalFunction| + |RandomFloatDistributions| |RationalFunctionFactor| |RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| |RegularChain| |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| |RightLinearSet| |RectangularMatrixCategory&| |RectangularMatrixCategory| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RangeBinding| |RealNumberSystem&| |RealNumberSystem| - |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| + |RightOpenIntervalRootCharacterization| |RomanNumeral| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RepeatAst| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| @@ -339,8 +327,8 @@ |SegmentBinding| |SegmentBindingFunctions2| |SegmentCategory| |SegmentExpansionCategory| |SequenceAst| |Set| |SetAggregate&| |SetAggregate| |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |SExpression| - |SExpressionCategory| |SExpressionOf| |SimpleFortranProgram| - |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| + |SExpressionCategory| |SExpressionOf| |SquareFreeQuasiComponentPackage| + |SquareFreeRegularTriangularSetGcdPackage| |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| |Signature| |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| @@ -362,21 +350,20 @@ |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| |SparseUnivariatePuiseuxSeries| - |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| + |SparseUnivariateTaylorSeries| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| |SystemInteger| |SystemNonNegativeInteger| |SystemPointer| |SystemSolvePackage| |System| |TableauxBumpers| |Table| |Tableau| |TermAlgebraOperator| |TangentExpansions| - |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| - |TemplateUtilities| |TexFormat| |TexFormat1| |TextFile| |ToolsForSign| - |TopLevelThreeSpace| |TranscendentalFunctionCategory&| - |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| - |TrigonometricFunctionCategory| |TrigonometricManipulations| - |TriangularMatrixOperations| |TranscendentalManipulations| |TaylorSeries| - |TriangularSetCategory&| |TriangularSetCategory| |TubePlot| |TubePlotTools| - |Tuple| |TwoFactorize| |Type| |TypeAst| |UserDefinedPartialOrdering| - |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| - |UniqueFactorizationDomain| |UInt16| |UInt32| |UInt64| |UInt8| - |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| + |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| |TexFormat| + |TexFormat1| |TextFile| |ToolsForSign| |TopLevelThreeSpace| + |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| + |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| + |TrigonometricManipulations| |TriangularMatrixOperations| + |TranscendentalManipulations| |TaylorSeries| |TriangularSetCategory&| + |TriangularSetCategory| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| + |Type| |TypeAst| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| + |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UInt16| |UInt32| + |UInt64| |UInt8| |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| @@ -407,23 +394,22 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| - |Union| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot| |eq?| - |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom| |ratPoly| - |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank| |rightRank| - |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements| + |Union| |zerosOf| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot| + |eq?| |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom| + |ratPoly| |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank| + |rightRank| |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements| |basisOfLeftAnnihilator| |basisOfRightAnnihilator| |basisOfLeftNucleus| |basisOfRightNucleus| |basisOfMiddleNucleus| |basisOfNucleus| |basisOfCenter| |basisOfLeftNucloid| |basisOfRightNucloid| |basisOfCentroid| |radicalOfLeftTraceForm| |obj| |dom| |any| |applyRules| |localUnquote| |arbitrary| |setColumn!| |setRow!| |oneDimensionalArray| |associatedSystem| - |uncouplingMatrices| |associatedEquations| |arrayStack| |setButtonValue| - |setAttributeButtonStep| |resetAttributeButtons| |getButtonValue| |decrease| - |increase| |morphism| |balancedFactorisation| |before?| |mapDown!| |mapUp!| - |setleaves!| |balancedBinaryTree| |sylvesterMatrix| |bezoutMatrix| - |bezoutResultant| |bezoutDiscriminant| |bfEntry| |bfKeys| |inspect| |extract!| - |bag| |binding| |setProperties| |setProperty| |deleteProperty!| |has?| - |comparison| |equality| |nary?| |unary?| |nullary?| |properties| |derivative| - |constantOperator| |constantOpIfCan| |integerBound| |setright!| |setleft!| + |uncouplingMatrices| |associatedEquations| |arrayStack| |morphism| + |balancedFactorisation| |before?| |mapDown!| |mapUp!| |setleaves!| + |balancedBinaryTree| |sylvesterMatrix| |bezoutMatrix| |bezoutResultant| + |bezoutDiscriminant| |inspect| |extract!| |bag| |binding| |setProperties| + |setProperty| |deleteProperty!| |has?| |comparison| |equality| |nary?| + |unary?| |nullary?| |properties| |derivative| |constantOperator| + |constantOpIfCan| |integerBound| |setright!| |setleft!| |brillhartIrreducible?| |brillhartTrials| |noLinearFactor?| |insertRoot!| |binarySearchTree| |nor| |nand| |node| |binaryTournament| |binaryTree| |byte| |setLength!| |capacity| |byteBuffer| |unknownEndian| |bigEndian| @@ -480,74 +466,62 @@ |eigenvector| |generalizedEigenvector| |generalizedEigenvectors| |eigenvectors| |factorAndSplit| |rightOne| |leftOne| |rightZero| |leftZero| |swap| |error| |minPoly| |freeOf?| |operators| |tower| |kernels| |mainKernel| - |distribute| |subst| |functionIsFracPolynomial?| |problemPoints| |zerosOf| - |singularitiesOf| |polynomialZeros| |f2df| |ef2edf| |ocf2ocdf| |socf2socdf| - |df2fi| |edf2fi| |edf2df| |expenseOfEvaluation| |numberOfOperations| |edf2efi| - |dfRange| |dflist| |df2mf| |ldf2vmf| |edf2ef| |vedf2vef| |df2st| |f2st| - |ldf2lst| |sdf2lst| |getlo| |gethi| |outputMeasure| |measure2Result| - |att2Result| |iflist2Result| |pdf2ef| |pdf2df| |df2ef| |fi2df| |mat| |neglist| - |multiEuclidean| |extendedEuclidean| |euclideanSize| |sizeLess?| - |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| |tubePlot| - |exponentialOrder| |completeEval| |lowerPolynomial| |raisePolynomial| - |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| |binomThmExpt| - |pomopo!| |mapExponents| |linearAssociatedLog| |linearAssociatedOrder| - |linearAssociatedExp| |createNormalElement| |setLabelValue| |getCode| - |printCode| |code| |operation| |common| |printStatement| |save| |stop| |block| - |cond| |returns| |call| |comment| |continue| |goto| |repeatUntilLoop| - |whileLoop| |forLoop| |sin?| |zeroVector| |zeroSquareMatrix| - |identitySquareMatrix| |lookupFunction| |encodingDirectory| |attributeData| - |domainTemplate| |lSpaceBasis| |finiteBasis| |principal?| |divisor| - |useNagFunctions| |rationalPoints| |nonSingularModel| |algSplitSimple| - |hyperelliptic| |elliptic| |integralDerivationMatrix| |integralRepresents| - |integralCoordinates| |yCoordinates| |inverseIntegralMatrixAtInfinity| - |integralMatrixAtInfinity| |inverseIntegralMatrix| |integralMatrix| - |reduceBasisAtInfinity| |normalizeAtInfinity| |complementaryBasis| |integral?| - |integralAtInfinity?| |integralBasisAtInfinity| |ramified?| - |ramifiedAtInfinity?| |singular?| |singularAtInfinity?| |branchPoint?| - |branchPointAtInfinity?| |rationalPoint?| |absolutelyIrreducible?| |genus| - |getZechTable| |createZechTable| |createMultiplicationTable| - |createMultiplicationMatrix| |createLowComplexityTable| - |createLowComplexityNormalBasis| |representationType| |createPrimitiveElement| - |tableForDiscreteLogarithm| |factorsOfCyclicGroupSize| |sizeMultiplication| - |getMultiplicationMatrix| |getMultiplicationTable| |primitive?| - |numberOfIrreduciblePoly| |numberOfPrimitivePoly| |numberOfNormalPoly| - |createIrreduciblePoly| |createPrimitivePoly| |createNormalPoly| - |createNormalPrimitivePoly| |createPrimitiveNormalPoly| |nextIrreduciblePoly| - |nextPrimitivePoly| |nextNormalPoly| |nextNormalPrimitivePoly| - |nextPrimitiveNormalPoly| |leastAffineMultiple| |reducedQPowers| - |rootOfIrreduciblePoly| |write!| |read!| |iomode| |close!| |reopen!| |open| - |rightUnit| |leftUnit| |rightMinimalPolynomial| |leftMinimalPolynomial| - |associatorDependence| |lieAlgebra?| |jordanAlgebra?| - |noncommutativeJordanAlgebra?| |jordanAdmissible?| |lieAdmissible?| - |jacobiIdentity?| |powerAssociative?| |alternative?| |flexible?| - |rightAlternative?| |leftAlternative?| |antiAssociative?| |associative?| - |antiCommutative?| |commutative?| |rightCharacteristicPolynomial| - |leftCharacteristicPolynomial| |rightNorm| |leftNorm| |rightTrace| |leftTrace| - |someBasis| |sort!| |copyInto!| |sorted?| |LiePoly| |quickSort| |heapSort| - |shellSort| |outputSpacing| |outputGeneral| |outputFixed| |outputFloating| - |exp1| |log10| |log2| |rationalApproximation| |relerror| |complexSolve| - |complexRoots| |realRoots| |leadingTerm| |overlap| |hcrf| |hclf| |writable?| - |readable?| |exists?| |extension| |directory| |filename| |shallowExpand| - |deepExpand| |clearFortranOutputStack| |showFortranOutputStack| - |popFortranOutputStack| |pushFortranOutputStack| |topFortranOutputStack| - |linkToFortran| |setLegalFortranSourceExtensions| |fracPart| |polyPart| + |distribute| |subst| |multiEuclidean| |extendedEuclidean| |euclideanSize| + |sizeLess?| |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| + |tubePlot| |exponentialOrder| |completeEval| |lowerPolynomial| + |raisePolynomial| |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| + |binomThmExpt| |pomopo!| |mapExponents| |linearAssociatedLog| + |linearAssociatedOrder| |linearAssociatedExp| |createNormalElement| |sin?| + |lookupFunction| |encodingDirectory| |attributeData| |domainTemplate| + |lSpaceBasis| |finiteBasis| |principal?| |divisor| |rationalPoints| + |nonSingularModel| |algSplitSimple| |hyperelliptic| |elliptic| + |integralDerivationMatrix| |integralRepresents| |integralCoordinates| + |yCoordinates| |inverseIntegralMatrixAtInfinity| |integralMatrixAtInfinity| + |inverseIntegralMatrix| |integralMatrix| |reduceBasisAtInfinity| + |normalizeAtInfinity| |complementaryBasis| |integral?| |integralAtInfinity?| + |integralBasisAtInfinity| |ramified?| |ramifiedAtInfinity?| |singular?| + |singularAtInfinity?| |branchPoint?| |branchPointAtInfinity?| |rationalPoint?| + |absolutelyIrreducible?| |genus| |getZechTable| |createZechTable| + |createMultiplicationTable| |createMultiplicationMatrix| + |createLowComplexityTable| |createLowComplexityNormalBasis| + |representationType| |createPrimitiveElement| |tableForDiscreteLogarithm| + |factorsOfCyclicGroupSize| |sizeMultiplication| |getMultiplicationMatrix| + |getMultiplicationTable| |primitive?| |numberOfIrreduciblePoly| + |numberOfPrimitivePoly| |numberOfNormalPoly| |createIrreduciblePoly| + |createPrimitivePoly| |createNormalPoly| |createNormalPrimitivePoly| + |createPrimitiveNormalPoly| |nextIrreduciblePoly| |nextPrimitivePoly| + |nextNormalPoly| |nextNormalPrimitivePoly| |nextPrimitiveNormalPoly| + |leastAffineMultiple| |reducedQPowers| |rootOfIrreduciblePoly| |write!| + |read!| |iomode| |close!| |reopen!| |open| |rightUnit| |leftUnit| + |rightMinimalPolynomial| |leftMinimalPolynomial| |associatorDependence| + |lieAlgebra?| |jordanAlgebra?| |noncommutativeJordanAlgebra?| + |jordanAdmissible?| |lieAdmissible?| |jacobiIdentity?| |powerAssociative?| + |alternative?| |flexible?| |rightAlternative?| |leftAlternative?| + |antiAssociative?| |associative?| |antiCommutative?| |commutative?| + |rightCharacteristicPolynomial| |leftCharacteristicPolynomial| |rightNorm| + |leftNorm| |rightTrace| |leftTrace| |someBasis| |sort!| |copyInto!| |sorted?| + |LiePoly| |quickSort| |heapSort| |shellSort| |outputSpacing| |outputGeneral| + |outputFixed| |outputFloating| |exp1| |log10| |log2| |rationalApproximation| + |relerror| |complexSolve| |complexRoots| |realRoots| |leadingTerm| |overlap| + |hcrf| |hclf| |writable?| |readable?| |exists?| |extension| |directory| + |filename| |shallowExpand| |deepExpand| |fracPart| |polyPart| |fullPartialFraction| |primeFrobenius| |discreteLog| |decreasePrecision| - |increasePrecision| |bits| |unitNormalize| |unit| |flagFactor| |sqfrFactor| - |primeFactor| |nthFlag| |nthExponent| |irreducibleFactor| |factors| - |nilFactor| |regularRepresentation| |traceMatrix| |randomLC| |minimize| - |module| |rightRegularRepresentation| |leftRegularRepresentation| - |rightTraceMatrix| |leftTraceMatrix| |rightDiscriminant| |leftDiscriminant| - |represents| |mergeFactors| |isMult| |applyQuote| |ground| |ground?| - |exprToXXP| |exprToUPS| |exprToGenUPS| |localAbs| |universe| |complement| - |cardinality| |internalIntegrate0| |makeCos| |makeSin| |iiGamma| |iiabs| - |bringDown| |newReduc| |logical?| |character?| |doubleComplex?| |complex?| - |double?| |ffactor| |qfactor| |UP2ifCan| |anfactor| |fortranCharacter| - |fortranDoubleComplex| |fortranComplex| |fortranLogical| |fortranInteger| - |fortranDouble| |fortranReal| |external?| |dimensionsOf| |scalarTypeOf| - |fortranCarriageReturn| |fortranLiteral| |fortranLiteralLine| - |processTemplate| |makeFR| |musserTrials| |stopMusserTrials| |numberOfFactors| - |modularFactor| |useSingleFactorBound?| |useSingleFactorBound| - |useEisensteinCriterion?| |useEisensteinCriterion| |eisensteinIrreducible?| + |increasePrecision| |precision| |bits| |mantissa| |unitNormalize| |unit| + |flagFactor| |sqfrFactor| |primeFactor| |nthFlag| |nthExponent| + |irreducibleFactor| |factors| |nilFactor| |regularRepresentation| + |traceMatrix| |randomLC| |minimize| |module| |rightRegularRepresentation| + |leftRegularRepresentation| |rightTraceMatrix| |leftTraceMatrix| + |rightDiscriminant| |leftDiscriminant| |represents| |mergeFactors| |isMult| + |applyQuote| |ground| |ground?| |exprToXXP| |exprToUPS| |exprToGenUPS| + |localAbs| |universe| |complement| |cardinality| |internalIntegrate0| + |makeCos| |makeSin| |iiGamma| |iiabs| |bringDown| |newReduc| |logical?| + |character?| |doubleComplex?| |complex?| |double?| |ffactor| |qfactor| + |UP2ifCan| |anfactor| |fortranCharacter| |fortranDoubleComplex| + |fortranComplex| |fortranLogical| |fortranInteger| |fortranDouble| + |fortranReal| |external?| |dimensionsOf| |scalarTypeOf| |makeFR| + |musserTrials| |stopMusserTrials| |numberOfFactors| |modularFactor| + |useSingleFactorBound?| |useSingleFactorBound| |useEisensteinCriterion?| + |useEisensteinCriterion| |eisensteinIrreducible?| |tryFunctionalDecomposition?| |tryFunctionalDecomposition| |btwFact| |beauzamyBound| |bombieriNorm| |rootBound| |singleFactorBound| |quadraticNorm| |infinityNorm| |scaleRoots| |shiftRoots| |degreePartition| |factorOfDegree| @@ -631,26 +605,22 @@ |complexLimit| |limit| |linearlyDependent?| |linearDependence| |solveLinear| |linearElement| |reducedSystem| |leftReducedSystem| |linearForm| |setDifference| |setIntersection| |setUnion| |append| |null| |nil| - |substitute| |duplicates?| |mapGen| |mapExpon| |commutativeEquality| + |substitute| |duplicates?| |mapGen| |mapExpon| |commutativeEquality| |plus| |leftMult| |rightMult| |makeUnit| |reverse!| |reverse| |nthFactor| |nthExpon| |makeMulti| |makeTerm| |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| - |explicitlyEmpty?| |explicitEntries?| |matrixDimensions| |matrixConcat3D| - |setelt!| |plus| |identityMatrix| |zeroMatrix| |iter| |arg1| |arg2| |comp| - |mappingAst| |nullary| |fixedPoint| |id| |recur| |const| |curry| |diag| - |curryRight| |curryLeft| |constantRight| |constantLeft| |twist| - |setsubMatrix!| |subMatrix| |swapColumns!| |swapRows!| |vertConcat| - |horizConcat| |squareTop| |elRow1!| |elRow2!| |elColumn2!| - |fractionFreeGauss!| |invertIfCan| |copy!| |plus!| |minus!| |leftScalarTimes!| - |rightScalarTimes!| |times!| |power!| |nothing| |just| |gradient| |divergence| - |laplacian| |hessian| |bandedHessian| |jacobian| |bandedJacobian| |duplicates| - |removeDuplicates!| |linears| |ddFact| |separateFactors| |exptMod| - |meshPar2Var| |meshFun2Var| |meshPar1Var| |ptFunc| |minimumExponent| - |maximumExponent| |precision| |mantissa| |rowEch| |rowEchLocal| - |rowEchelonLocal| |normalizedDivide| |maxint| |binaryFunction| + |explicitlyEmpty?| |explicitEntries?| |iter| |arg1| |arg2| |comp| |mappingAst| + |nullary| |fixedPoint| |id| |recur| |const| |curry| |diag| |curryRight| + |curryLeft| |constantRight| |constantLeft| |twist| |setsubMatrix!| |subMatrix| + |swapColumns!| |swapRows!| |vertConcat| |horizConcat| |squareTop| |elRow1!| + |elRow2!| |elColumn2!| |fractionFreeGauss!| |invertIfCan| |copy!| |plus!| + |minus!| |leftScalarTimes!| |rightScalarTimes!| |times!| |power!| |nothing| + |just| |duplicates| |removeDuplicates!| |linears| |ddFact| |separateFactors| + |exptMod| |meshPar2Var| |meshFun2Var| |meshPar1Var| |ptFunc| |rowEch| + |rowEchLocal| |rowEchelonLocal| |normalizedDivide| |binaryFunction| |makeFloatFunction| |function| |makeRecord| |unaryFunction| |compiledFunction| |corrPoly| |lifting| |lifting1| |exprex| |coerceL| |coerceS| |frobenius| |computePowers| |pow| |An| |UnVectorise| |Vectorise| |setPoly| |index| @@ -668,45 +638,45 @@ |subResultantsChain| |lazyPseudoQuotient| |lazyPseudoRemainder| |bernoulliB| |eulerE| |numeric| |complexNumeric| |numericIfCan| |complexNumericIfCan| |FormatArabic| |ScanArabic| |FormatRoman| |ScanRoman| |ScanFloatIgnoreSpaces| - |ScanFloatIgnoreSpacesIfCan| |numericalIntegration| |rk4| |rk4a| |rk4qc| - |rk4f| |aromberg| |asimpson| |atrapezoidal| |romberg| |simpson| |trapezoidal| - |rombergo| |simpsono| |trapezoidalo| |sup| |inv| |imagE| |imagk| |imagj| - |imagi| |octon| |ODESolve| |constDsolve| |expint| |diff| |algDsolve| - |denomLODE| |indicialEquations| |indicialEquation| |denomRicDE| - |leadingCoefficientRicDE| |constantCoefficientRicDE| |changeVar| |ratDsolve| + |ScanFloatIgnoreSpacesIfCan| |rk4| |rk4a| |rk4qc| |rk4f| |aromberg| |asimpson| + |atrapezoidal| |romberg| |simpson| |trapezoidal| |rombergo| |simpsono| + |trapezoidalo| |sup| |inv| |imagE| |imagk| |imagj| |imagi| |octon| + |constDsolve| |expint| |diff| |algDsolve| |denomLODE| |indicialEquations| + |indicialEquation| |denomRicDE| |leadingCoefficientRicDE| + |constantCoefficientRicDE| |changeVar| |ratDsolve| |indicialEquationAtInfinity| |reduceLODE| |singRicDE| |polyRicDE| |ricDsolve| |triangulate| |solveInField| |wronskianMatrix| |variationOfParameters| |lexico| |po| |op| |infinity| |makeop| |opeval| |evaluateInverse| |evaluate| - |conjug| |adjoint| |arity| |getDatabase| |numericalOptimization| - |whatInfinity| |infinite?| |finite?| |minusInfinity| |plusInfinity| |pureLex| - |totalLex| |reverseLex| |min| |leftLcm| |rightExtendedGcd| |rightGcd| - |rightExactQuotient| |rightRemainder| |rightQuotient| |rightLcm| - |leftExtendedGcd| |leftGcd| |leftExactQuotient| |leftRemainder| |leftQuotient| - |times| |apply| |monicLeftDivide| |monicRightDivide| |leftDivide| - |rightDivide| |hermiteH| |laguerreL| |legendreP| |outputList| |writeBytes!| - |writeUInt8!| |writeInt8!| |writeByte!| |isOpen?| |outputBinaryFile| |not| - |or| |and| |quo| |rem| |div| >= > ~= |blankSeparate| |semicolonSeparate| - |commaSeparate| |pile| |paren| |bracket| |prod| |overlabel| |overbar| |prime| - |quote| |supersub| |presuper| |presub| |super| |sub| |rarrow| |assign| |slash| - |over| |zag| |box| |label| |infix?| |postfix| |infix| |prefix| |vconcat| - |hconcat| |rspace| |vspace| |hspace| |superHeight| |subHeight| |height| - |width| |doubleFloatFormat| |messagePrint| |message| |members| |padecf| |pade| - |root| |quotientByP| |moduloP| |modulus| |digits| |continuedFraction| |pair| - |light| |pastel| |bright| |dim| |dark| |getSyntaxFormsFromFile| |surface| - |coordinate| |conjugates| |shuffle| |shufflein| |sequences| |permutations| - |lists| |makeResult| |is?| |Is| |addMatchRestricted| |insertMatch| |addMatch| - |getMatch| |failed| |failed?| |optpair| |getBadValues| |resetBadValues| - |hasTopPredicate?| |topPredicate| |setTopPredicate| |patternVariable| - |withPredicates| |setPredicates| |predicates| |hasPredicate?| |optional?| - |multiple?| |generic?| |quoted?| |inR?| |isList| |isQuotient| |isOp| |Zero| - |satisfy?| |addBadValue| |badValues| |retractable?| |ListOfTerms| |One| - |PDESolve| |measure| |leftFactor| |rightFactorCandidate| D |ptree| - |coerceImages| |fixedPoints| |odd?| |even?| |numberOfCycles| |cyclePartition| - |coerceListOfPairs| |coercePreimagesImages| |listRepresentation| |permanent| - |cycles| |cycle| |initializeGroupForWordProblem| <= < |support| - |wordInGenerators| |wordInStrongGenerators| |orbits| |orbit| - |permutationGroup| |wordsForStrongGenerators| |strongGenerators| |base| - |generators| |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion| + |conjug| |adjoint| |arity| |getDatabase| |whatInfinity| |infinite?| |finite?| + |minusInfinity| |plusInfinity| |pureLex| |totalLex| |reverseLex| |min| + |leftLcm| |rightExtendedGcd| |rightGcd| |rightExactQuotient| |rightRemainder| + |rightQuotient| |rightLcm| |leftExtendedGcd| |leftGcd| |leftExactQuotient| + |leftRemainder| |leftQuotient| |times| |apply| |monicLeftDivide| + |monicRightDivide| |leftDivide| |rightDivide| |hermiteH| |laguerreL| + |legendreP| |outputList| |writeBytes!| |writeUInt8!| |writeInt8!| |writeByte!| + |isOpen?| |outputBinaryFile| |not| |or| |and| |quo| |rem| |div| >= > ~= + |blankSeparate| |semicolonSeparate| |commaSeparate| |pile| |paren| |bracket| + |prod| |overlabel| |overbar| |prime| |quote| |supersub| |presuper| |presub| + |super| |sub| |rarrow| |assign| |slash| |over| |zag| |box| |label| |infix?| + |postfix| |infix| |prefix| |vconcat| |hconcat| |rspace| |vspace| |hspace| + |superHeight| |subHeight| |height| |width| |doubleFloatFormat| |messagePrint| + |message| |members| |padecf| |pade| |root| |quotientByP| |moduloP| |modulus| + |digits| |continuedFraction| |pair| |light| |pastel| |bright| |dim| |dark| + |getSyntaxFormsFromFile| |surface| |coordinate| |conjugates| |shuffle| + |shufflein| |sequences| |permutations| |lists| |makeResult| |is?| |Is| + |addMatchRestricted| |insertMatch| |addMatch| |getMatch| |failed| |failed?| + |optpair| |getBadValues| |resetBadValues| |hasTopPredicate?| |topPredicate| + |setTopPredicate| |patternVariable| |withPredicates| |setPredicates| + |predicates| |hasPredicate?| |optional?| |multiple?| |generic?| |quoted?| + |inR?| |isList| |isQuotient| |isOp| |Zero| |satisfy?| |addBadValue| + |badValues| |retractable?| |ListOfTerms| |One| |leftFactor| + |rightFactorCandidate| D |ptree| |coerceImages| |fixedPoints| |odd?| |even?| + |numberOfCycles| |cyclePartition| |coerceListOfPairs| |coercePreimagesImages| + |listRepresentation| |permanent| |cycles| |cycle| + |initializeGroupForWordProblem| <= < |support| |wordInGenerators| + |wordInStrongGenerators| |orbits| |orbit| |permutationGroup| + |wordsForStrongGenerators| |strongGenerators| |base| |generators| + |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion| |factorByRecursion| |factorSquareFreeByRecursion| |randomR| |factorSFBRlcUnit| |charthRoot| |conditionP| |solveLinearPolynomialEquation| |factorSquareFreePolynomial| |factorPolynomial| |squareFreePolynomial| @@ -789,22 +759,16 @@ |tensorProduct| |permutationRepresentation| |completeEchelonBasis| |createRandomElement| |cyclicSubmodule| |standardBasisOfCyclicSubmodule| |areEquivalent?| |isAbsolutelyIrreducible?| |meatAxe| |scanOneDimSubspaces| - |double| |expt| |lift| |showArrayValues| |showScalarValues| |solveRetract| - |variables| |mainVariable| |univariate| |multivariate| |uniform01| |normal01| - |exponential1| |chiSquare1| |normal| |exponential| |chiSquare| F |t| - |factorFraction| |componentUpperBound| |blue| |green| |red| |whitePoint| - |uniform| |binomial| |poisson| |geometric| |ridHack1| |interpolate| - |nullSpace| |nullity| |rank| |rowEchelon| |column| |row| |qelt| |ncols| - |nrows| |maxColIndex| |minColIndex| |maxRowIndex| |minRowIndex| - |antisymmetric?| |symmetric?| |diagonal?| |square?| |matrix| + |double| |expt| |lift| |solveRetract| |variables| |mainVariable| |univariate| + |multivariate| |uniform01| |normal01| |exponential1| |chiSquare1| |normal| + |exponential| |chiSquare| F |t| |factorFraction| |componentUpperBound| |blue| + |green| |red| |whitePoint| |uniform| |binomial| |poisson| |geometric| + |ridHack1| |interpolate| |nullSpace| |nullity| |rank| |rowEchelon| |column| + |row| |qelt| |ncols| |nrows| |maxColIndex| |minColIndex| |maxRowIndex| + |minRowIndex| |antisymmetric?| |symmetric?| |diagonal?| |square?| |matrix| |rectangularMatrix| |characteristic| |round| |fractionPart| |wholePart| |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size| |right| - |left| |roman| |recoverAfterFail| |showTheRoutinesTable| |deleteRoutine!| - |getExplanations| |getMeasure| |changeMeasure| |changeThreshhold| - |selectMultiDimensionalRoutines| |selectNonFiniteRoutines| - |selectSumOfSquaresRoutines| |selectFiniteRoutines| |selectODEIVPRoutines| - |selectPDERoutines| |selectOptimizationRoutines| |selectIntegrationRoutines| - |routines| |mainSquareFreePart| |mainPrimitivePart| |mainContent| + |left| |roman| |mainSquareFreePart| |mainPrimitivePart| |mainContent| |primitivePart!| |gcd| |nextsubResultant2| |LazardQuotient2| |LazardQuotient| |subResultantChain| |halfExtendedSubResultantGcd2| |halfExtendedSubResultantGcd1| |extendedSubResultantGcd| |exactQuotient!| @@ -829,7 +793,7 @@ |hash| |delta| |member?| |enumerate| |setOfMinN| |elements| |replaceKthElement| |incrementKthElement| |cdr| |car| |expr| |float| |integer| |symbol| |destruct| |float?| |integer?| |symbol?| |string?| |list?| |pair?| - |atom?| |null?| |eq| |fortran| |startTable!| |stopTable!| |supDimElseRittWu?| + |atom?| |null?| |eq| |startTable!| |stopTable!| |supDimElseRittWu?| |algebraicSort| |moreAlgebraic?| |subTriSet?| |subPolSet?| |internalSubPolSet?| |internalInfRittWu?| |internalSubQuasiComponent?| |subQuasiComponent?| |removeSuperfluousQuasiComponents| |subCase?| @@ -879,79 +843,78 @@ |defineProperty| |closeComponent| |modifyPoint| |addPointLast| |addPoint2| |addPoint| |merge| |deepCopy| |shallowCopy| |numberOfChildren| |children| |child| |birth| |internal?| |root?| |leaf?| |rhs| |lhs| |construct| - |predicate| |sum| |outputForm| NOT AND EQ OR GE LE GT LT |list| |string| - |argscript| |superscript| |subscript| |script| |scripts| |scripted?| |name| - |resetNew| |symFunc| |symbolTableOf| |argumentListOf| |returnTypeOf| - |printHeader| |returnType!| |argumentList!| |endSubProgram| - |currentSubProgram| |newSubProgram| |clearTheSymbolTable| |showTheSymbolTable| - |symbolTable| |printTypes| |newTypeLists| |typeLists| |externalList| - |typeList| |parametersOf| |fortranTypeOf| |declare!| |empty| |case| - |compound?| |getOperands| |getOperator| |nil?| |buildSyntax| |autoCoerce| - |solve| |triangularSystems| |loadNativeModule| |nativeModuleExtension| - |hostByteOrder| |hostPlatform| |rootDirectory| |bumprow| |bumptab| |bumptab1| - |untab| |bat1| |bat| |tab1| |tab| |lex| |slex| |inverse| |maxrow| |mr| - |tableau| |listOfLists| |operator| |tanSum| |tanAn| |tanNa| |table| - |initTable!| |printInfo!| |startStats!| |printStats!| |clearTable!| - |usingTable?| |printingInfo?| |makingStats?| |extractIfCan| |insert!| - |interpretString| |stripCommentsAndBlanks| |setPrologue!| |setTex!| - |setEpilogue!| |prologue| |new| |tex| |epilogue| |display| |endOfFile?| - |readIfCan!| |readLineIfCan!| |readLine!| |writeLine!| |sign| |nonQsign| - |direction| |createThreeSpace| |pi| |cyclicParents| |cyclicEqual?| - |cyclicEntries| |cyclicCopy| |tree| |cyclic?| |cos| |cot| |csc| |sec| |sin| - |tan| |complexNormalize| |complexElementary| |trigs| |real| |imag| |real?| - |complexForm| |UpTriBddDenomInv| |LowTriBddDenomInv| |simplify| |htrigs| - |simplifyExp| |simplifyLog| |expandPower| |expandLog| |cos2sec| |cosh2sech| - |cot2trig| |coth2trigh| |csc2sin| |csch2sinh| |sec2cos| |sech2cosh| |sin2csc| - |sinh2csch| |tan2trig| |tanh2trigh| |tan2cot| |tanh2coth| |cot2tan| - |coth2tanh| |removeCosSq| |removeSinSq| |removeCoshSq| |removeSinhSq| - |expandTrigProducts| |fintegrate| |coefficient| |coHeight| |extendIfCan| - |algebraicVariables| |zeroSetSplitIntoTriangularSystems| |zeroSetSplit| - |reduceByQuasiMonic| |collectQuasiMonic| |removeZero| |initiallyReduce| - |headReduce| |stronglyReduce| |rewriteSetWithReduction| |autoReduced?| - |initiallyReduced?| |headReduced?| |stronglyReduced?| |reduced?| |normalized?| - |quasiComponent| |initials| |basicSet| |infRittWu?| |getCurve| |listLoops| - |closed?| |open?| |setClosed| |tube| |point| |unitVector| |cosSinInfo| - |loopPoints| |select| |generalTwoFactor| |generalSqFr| |twoFactor| |setOrder| - |getOrder| |less?| |userOrdered?| |largest| |more?| |setVariableOrder| - |getVariableOrder| |resetVariableOrder| |prime?| |sample| |bitior| |bitand| - |rationalFunction| |taylorIfCan| |taylor| |removeZeroes| |taylorRep| |factor| - |factorSquareFree| |henselFact| |hasHi| |segment| SEGMENT |fmecg| - |commonDenominator| |clearDenominator| |splitDenominator| - |monicRightFactorIfCan| |rightFactorIfCan| |leftFactorIfCan| - |monicDecomposeIfCan| |monicCompleteDecompose| |divideIfCan| |noKaratsuba| - |karatsubaOnce| |karatsuba| |separate| |pseudoDivide| |pseudoQuotient| - |composite| |subResultantGcd| |resultant| |discriminant| |differentiate| - |pseudoRemainder| |shiftLeft| |shiftRight| |karatsubaDivide| |monicDivide| - |divideExponents| |unmakeSUP| |makeSUP| |vectorise| |eval| |extend| - |approximate| |truncate| |order| |center| |terms| |squareFreePart| - |BumInSepFFE| |multiplyExponents| |laurentIfCan| |laurent| |laurentRep| - |rationalPower| |puiseux| |dominantTerm| |limitPlus| |split!| |setlast!| - |setrest!| |setelt| |setfirst!| |cycleSplit!| |concat!| |cycleTail| - |cycleLength| |cycleEntry| |third| |second| |tail| |last| |rest| |elt| |first| - |concat| |invmultisect| |multisect| |revert| |generalLambert| |evenlambert| - |oddlambert| |lambert| |lagrange| |univariatePolynomial| |integrate| ** - |polynomial| |multiplyCoefficients| |quoByVar| |coefficients| |series| - |stFunc1| |stFunc2| |stFuncN| |fixedPointExquo| |ode1| |ode2| |ode| |mpsode| - UP2UTS UTS2UP LODO2FUN RF2UTS |variable| |magnitude| |length| |cross| - |outerProduct| |dot| - |zero| + |vector| |scan| |reduce| |graphCurves| - |drawCurves| |update| |show| |scale| |connect| |region| |points| |units| - |getGraph| |putGraph| |graphs| |graphStates| |graphState| |makeViewport2D| - |viewport2D| |getPickedPoints| |key| |close| |write| |colorDef| |reset| - |intensity| |lighting| |clipSurface| |showClipRegion| |showRegion| - |hitherPlane| |eyeDistance| |perspective| |translate| |zoom| |rotate| - |drawStyle| |outlineRender| |diagonals| |axes| |controlPanel| |viewpoint| - |dimensions| |title| |resize| |move| |options| |modifyPointData| |subspace| - |makeViewport3D| |viewport3D| |viewDeltaYDefault| |viewDeltaXDefault| - |viewZoomDefault| |viewPhiDefault| |viewThetaDefault| |pointColorDefault| - |lineColorDefault| |axesColorDefault| |unitsColorDefault| |pointSizeDefault| - |viewPosDefault| |viewSizeDefault| |viewDefaults| |viewWriteDefault| - |viewWriteAvailable| |var1StepsDefault| |var2StepsDefault| |tubePointsDefault| - |tubeRadiusDefault| |void| |dimension| |crest| |cfirst| |sts2stst| |clikeUniv| - |weierstrass| |qqq| |integralBasis| |localIntegralBasis| |qualifier| - |mainExpression| |condition| |changeWeightLevel| |characteristicSerie| - |characteristicSet| |medialSet| |Hausdorff| |Frobenius| |transcendenceDegree| - |extensionDegree| |inGroundField?| |transcendent?| |algebraic?| |varList| |sh| - |mirror| |monomial?| |monom| |rquo| |lquo| |mindegTerm| |log| |exp| |product| + |predicate| |sum| |outputForm| |list| |string| |argscript| |superscript| + |subscript| |script| |scripts| |scripted?| |name| |resetNew| |symFunc| + |symbolTableOf| |argumentListOf| |returnTypeOf| |printHeader| |returnType!| + |argumentList!| |endSubProgram| |currentSubProgram| |newSubProgram| + |clearTheSymbolTable| |showTheSymbolTable| |symbolTable| |printTypes| + |newTypeLists| |typeLists| |externalList| |typeList| |parametersOf| + |fortranTypeOf| |declare!| |empty| |case| |compound?| |getOperands| + |getOperator| |nil?| |buildSyntax| |autoCoerce| |solve| |triangularSystems| + |loadNativeModule| |nativeModuleExtension| |hostByteOrder| |hostPlatform| + |rootDirectory| |bumprow| |bumptab| |bumptab1| |untab| |bat1| |bat| |tab1| + |tab| |lex| |slex| |inverse| |maxrow| |mr| |tableau| |listOfLists| |operator| + |tanSum| |tanAn| |tanNa| |table| |initTable!| |printInfo!| |startStats!| + |printStats!| |clearTable!| |usingTable?| |printingInfo?| |makingStats?| + |extractIfCan| |insert!| |setPrologue!| |setTex!| |setEpilogue!| |prologue| + |new| |tex| |epilogue| |display| |endOfFile?| |readIfCan!| |readLineIfCan!| + |readLine!| |writeLine!| |sign| |nonQsign| |direction| |createThreeSpace| |pi| + |cyclicParents| |cyclicEqual?| |cyclicEntries| |cyclicCopy| |tree| |cyclic?| + |cos| |cot| |csc| |sec| |sin| |tan| |complexNormalize| |complexElementary| + |trigs| |real| |imag| |real?| |complexForm| |UpTriBddDenomInv| + |LowTriBddDenomInv| |simplify| |htrigs| |simplifyExp| |simplifyLog| + |expandPower| |expandLog| |cos2sec| |cosh2sech| |cot2trig| |coth2trigh| + |csc2sin| |csch2sinh| |sec2cos| |sech2cosh| |sin2csc| |sinh2csch| |tan2trig| + |tanh2trigh| |tan2cot| |tanh2coth| |cot2tan| |coth2tanh| |removeCosSq| + |removeSinSq| |removeCoshSq| |removeSinhSq| |expandTrigProducts| |fintegrate| + |coefficient| |coHeight| |extendIfCan| |algebraicVariables| + |zeroSetSplitIntoTriangularSystems| |zeroSetSplit| |reduceByQuasiMonic| + |collectQuasiMonic| |removeZero| |initiallyReduce| |headReduce| + |stronglyReduce| |rewriteSetWithReduction| |autoReduced?| |initiallyReduced?| + |headReduced?| |stronglyReduced?| |reduced?| |normalized?| |quasiComponent| + |initials| |basicSet| |infRittWu?| |getCurve| |listLoops| |closed?| |open?| + |setClosed| |tube| |point| |unitVector| |cosSinInfo| |loopPoints| |select| + |generalTwoFactor| |generalSqFr| |twoFactor| |setOrder| |getOrder| |less?| + |userOrdered?| |largest| |more?| |setVariableOrder| |getVariableOrder| + |resetVariableOrder| |prime?| |sample| |bitior| |bitand| |rationalFunction| + |taylorIfCan| |taylor| |removeZeroes| |taylorRep| |factor| |factorSquareFree| + |henselFact| |hasHi| |segment| SEGMENT |fmecg| |commonDenominator| + |clearDenominator| |splitDenominator| |monicRightFactorIfCan| + |rightFactorIfCan| |leftFactorIfCan| |monicDecomposeIfCan| + |monicCompleteDecompose| |divideIfCan| |noKaratsuba| |karatsubaOnce| + |karatsuba| |separate| |pseudoDivide| |pseudoQuotient| |composite| + |subResultantGcd| |resultant| |discriminant| |differentiate| |pseudoRemainder| + |shiftLeft| |shiftRight| |karatsubaDivide| |monicDivide| |divideExponents| + |unmakeSUP| |makeSUP| |vectorise| |eval| |extend| |approximate| |truncate| + |order| |center| |terms| |squareFreePart| |BumInSepFFE| |multiplyExponents| + |laurentIfCan| |laurent| |laurentRep| |rationalPower| |puiseux| |dominantTerm| + |limitPlus| |split!| |setlast!| |setrest!| |setelt| |setfirst!| |cycleSplit!| + |concat!| |cycleTail| |cycleLength| |cycleEntry| |third| |second| |tail| + |last| |rest| |elt| |first| |concat| |invmultisect| |multisect| |revert| + |generalLambert| |evenlambert| |oddlambert| |lambert| |lagrange| + |univariatePolynomial| |integrate| ** |polynomial| |multiplyCoefficients| + |quoByVar| |coefficients| |series| |stFunc1| |stFunc2| |stFuncN| + |fixedPointExquo| |ode1| |ode2| |ode| |mpsode| UP2UTS UTS2UP LODO2FUN RF2UTS + |variable| |magnitude| |length| |cross| |outerProduct| |dot| - |zero| + + |vector| |scan| |reduce| |graphCurves| |drawCurves| |update| |show| |scale| + |connect| |region| |points| |units| |getGraph| |putGraph| |graphs| + |graphStates| |graphState| |makeViewport2D| |viewport2D| |getPickedPoints| + |key| |close| |write| |colorDef| |reset| |intensity| |lighting| |clipSurface| + |showClipRegion| |showRegion| |hitherPlane| |eyeDistance| |perspective| + |translate| |zoom| |rotate| |drawStyle| |outlineRender| |diagonals| |axes| + |controlPanel| |viewpoint| |dimensions| |title| |resize| |move| |options| + |modifyPointData| |subspace| |makeViewport3D| |viewport3D| |viewDeltaYDefault| + |viewDeltaXDefault| |viewZoomDefault| |viewPhiDefault| |viewThetaDefault| + |pointColorDefault| |lineColorDefault| |axesColorDefault| |unitsColorDefault| + |pointSizeDefault| |viewPosDefault| |viewSizeDefault| |viewDefaults| + |viewWriteDefault| |viewWriteAvailable| |var1StepsDefault| |var2StepsDefault| + |tubePointsDefault| |tubeRadiusDefault| |void| |dimension| |crest| |cfirst| + |sts2stst| |clikeUniv| |weierstrass| |qqq| |integralBasis| + |localIntegralBasis| |qualifier| |mainExpression| |condition| + |changeWeightLevel| |characteristicSerie| |characteristicSet| |medialSet| + |Hausdorff| |Frobenius| |transcendenceDegree| |extensionDegree| + |inGroundField?| |transcendent?| |algebraic?| |varList| |sh| |mirror| + |monomial?| |monom| |rquo| |lquo| |mindegTerm| |log| |exp| |product| |LiePolyIfCan| |coerce| |trunc| |degree| / |quasiRegular| |quasiRegular?| |constant| |constant?| |coef| |mindeg| |maxdeg| |#| |map| |reductum| * |RemainderList| |unexpand| |expand| |shape| |youngDiagram| Y |triangSolve| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 4c2e1365..adcb6b6a 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4140 +1,4001 @@ -(2928076 . 3525483402) -((-1825 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1823 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3938 ((|#2| $ (-499) |#2|) NIL T ELT) ((|#2| $ (-1174 (-499)) |#2|) 44 T ELT)) (-2397 (($ $) 80 T ELT)) (-3992 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3559 (((-499) (-1 (-85) |#2|) $) 27 T ELT) (((-499) |#2| $) NIL T ELT) (((-499) |#2| $ (-499)) 96 T ELT)) (-3010 (((-599 |#2|) $) 13 T ELT)) (-3658 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2051 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-4108 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2404 (($ |#2| $ (-499)) NIL T ELT) (($ $ $ (-499)) 67 T ELT)) (-1387 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-2049 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3950 ((|#2| $ (-499) |#2|) NIL T ELT) ((|#2| $ (-499)) NIL T ELT) (($ $ (-1174 (-499))) 66 T ELT)) (-2405 (($ $ (-499)) 76 T ELT) (($ $ (-1174 (-499))) 75 T ELT)) (-2048 (((-714) (-1 (-85) |#2|) $) 34 T ELT) (((-714) |#2| $) NIL T ELT)) (-1824 (($ $ $ (-499)) 69 T ELT)) (-3540 (($ $) 68 T ELT)) (-3670 (($ (-599 |#2|)) 73 T ELT)) (-3952 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-599 $)) 85 T ELT)) (-4096 (((-797) $) 92 T ELT)) (-2050 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3174 (((-85) $ $) 95 T ELT)) (-2806 (((-85) $ $) 99 T ELT))) -(((-18 |#1| |#2|) (-10 -7 (-15 -3174 ((-85) |#1| |#1|)) (-15 -4096 ((-797) |#1|)) (-15 -2806 ((-85) |#1| |#1|)) (-15 -1823 (|#1| |#1|)) (-15 -1823 (|#1| (-1 (-85) |#2| |#2|) |#1|)) (-15 -2397 (|#1| |#1|)) (-15 -1824 (|#1| |#1| |#1| (-499))) (-15 -1825 ((-85) |#1|)) (-15 -3658 (|#1| |#1| |#1|)) (-15 -3559 ((-499) |#2| |#1| (-499))) (-15 -3559 ((-499) |#2| |#1|)) (-15 -3559 ((-499) (-1 (-85) |#2|) |#1|)) (-15 -1825 ((-85) (-1 (-85) |#2| |#2|) |#1|)) (-15 -3658 (|#1| (-1 (-85) |#2| |#2|) |#1| |#1|)) (-15 -3938 (|#2| |#1| (-1174 (-499)) |#2|)) (-15 -2404 (|#1| |#1| |#1| (-499))) (-15 -2404 (|#1| |#2| |#1| (-499))) (-15 -2405 (|#1| |#1| (-1174 (-499)))) (-15 -2405 (|#1| |#1| (-499))) (-15 -4108 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3952 (|#1| (-599 |#1|))) (-15 -3952 (|#1| |#1| |#1|)) (-15 -3952 (|#1| |#2| |#1|)) (-15 -3952 (|#1| |#1| |#2|)) 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T) ((-23) . T) ((-25) . T) ((-38 (-361 (-499))) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-38 |#1|) . T) ((-38 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-305)) (|has| |#1| (-318)) (|has| |#1| (-261))) ((-35) |has| |#1| (-1143)) ((-66) |has| |#1| (-1143)) ((-73) . T) ((-82 (-361 (-499)) (-361 (-499))) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-82 |#1| |#1|) . T) ((-82 $ $) . T) ((-104) . T) ((-118) -3677 (|has| |#1| (-305)) (|has| |#1| (-118))) ((-120) |has| |#1| (-120)) ((-571 (-361 (-499))) -3677 (|has| |#1| (-978 (-361 (-499)))) (|has| |#1| (-305)) (|has| |#1| (-318))) ((-571 (-499)) . T) ((-571 |#1|) . T) ((-571 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-305)) (|has| |#1| (-318)) (|has| |#1| (-261))) ((-568 (-797)) . T) ((-146) . T) ((-569 (-142 (-179))) |has| |#1| (-960)) ((-569 (-142 (-333))) |has| |#1| (-960)) ((-569 (-488)) |has| |#1| (-569 (-488))) ((-569 (-825 (-333))) |has| |#1| (-569 (-825 (-333)))) ((-569 (-825 (-499))) |has| |#1| (-569 (-825 (-499)))) ((-569 (-1111 |#1|)) . T) ((-186 $) -3677 (|has| |#1| (-305)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-184 |#1|) . T) ((-190) -3677 (|has| |#1| (-305)) (|has| |#1| (-190))) ((-189) -3677 (|has| |#1| (-305)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-224 |#1|) . T) ((-200) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-238) |has| |#1| (-1143)) ((-240 |#1| $) |has| |#1| (-240 |#1| |#1|)) ((-244) -3677 (|has| |#1| (-510)) (|has| |#1| (-305)) (|has| |#1| (-318)) (|has| |#1| (-261))) ((-261) -3677 (|has| |#1| (-305)) (|has| |#1| (-318)) (|has| |#1| (-261))) ((-263 |#1|) |has| |#1| (-263 |#1|)) ((-318) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-356) |has| |#1| (-305)) ((-323) -3677 (|has| |#1| (-305)) (|has| |#1| (-323))) ((-305) |has| |#1| (-305)) ((-325 |#1| (-1111 |#1|)) . T) ((-364 |#1| (-1111 |#1|)) . T) ((-293 |#1|) . T) ((-332 |#1|) . T) ((-354 |#1|) . T) ((-366 |#1|) . T) ((-406) -3677 (|has| |#1| (-305)) (|has| |#1| (-318)) (|has| |#1| (-261))) ((-447) |has| |#1| (-1143)) ((-468 (-1117) |#1|) |has| |#1| (-468 (-1117) |#1|)) ((-468 |#1| |#1|) |has| |#1| (-263 |#1|)) ((-510) -3677 (|has| |#1| (-510)) (|has| |#1| (-305)) (|has| |#1| (-318)) (|has| |#1| (-261))) ((-604 (-361 (-499))) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-604 (-499)) . T) ((-604 |#1|) . T) ((-604 $) . T) ((-606 (-361 (-499))) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-606 (-499)) |has| |#1| (-596 (-499))) ((-606 |#1|) . T) ((-606 $) . T) ((-598 (-361 (-499))) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-598 |#1|) . T) ((-598 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-305)) (|has| |#1| (-318)) (|has| |#1| (-261))) ((-596 (-499)) |has| |#1| (-596 (-499))) ((-596 |#1|) . T) ((-675 (-361 (-499))) -3677 (|has| |#1| (-305)) (|has| |#1| (-318))) ((-675 |#1|) . 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T) ((-73) -3677 (|has| |#2| (-1041)) (|has| |#2| (-989)) (|has| |#2| (-781)) (|has| |#2| (-738)) (|has| |#2| (-684)) (|has| |#2| (-323)) (|has| |#2| (-318)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-73)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-82 |#2| |#2|) -3677 (|has| |#2| (-989)) (|has| |#2| (-318)) (|has| |#2| (-146))) ((-104) -3677 (|has| |#2| (-989)) (|has| |#2| (-738)) (|has| |#2| (-318)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-21))) ((-571 (-361 (-499))) -12 (|has| |#2| (-978 (-361 (-499)))) (|has| |#2| (-1041))) ((-571 (-499)) -3677 (|has| |#2| (-989)) (-12 (|has| |#2| (-978 (-499))) (|has| |#2| (-1041)))) ((-571 |#2|) |has| |#2| (-1041)) ((-568 (-797)) -3677 (|has| |#2| (-1041)) (|has| |#2| (-989)) (|has| |#2| (-781)) (|has| |#2| (-738)) (|has| |#2| (-684)) (|has| |#2| (-323)) (|has| |#2| (-318)) (|has| |#2| (-146)) (|has| |#2| (-568 (-797))) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-568 (-1207 |#2|)) . T) ((-186 $) -3677 (-12 (|has| |#2| (-189)) (|has| |#2| (-989))) (-12 (|has| |#2| (-190)) (|has| |#2| (-989)))) ((-184 |#2|) |has| |#2| (-989)) ((-190) -12 (|has| |#2| (-190)) (|has| |#2| (-989))) ((-189) -3677 (-12 (|has| |#2| (-189)) (|has| |#2| (-989))) (-12 (|has| |#2| (-190)) (|has| |#2| (-989)))) ((-224 |#2|) |has| |#2| (-989)) ((-240 (-499) |#2|) . T) ((-242 (-499) |#2|) . T) ((-263 |#2|) -12 (|has| |#2| (-263 |#2|)) (|has| |#2| (-1041))) ((-323) |has| |#2| (-323)) ((-332 |#2|) |has| |#2| (-989)) ((-366 |#2|) |has| |#2| (-1041)) ((-443 |#2|) . T) ((-554 (-499) |#2|) . T) ((-468 |#2| |#2|) -12 (|has| |#2| (-263 |#2|)) (|has| |#2| (-1041))) ((-604 (-499)) -3677 (|has| |#2| (-989)) (|has| |#2| (-318)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-604 |#2|) -3677 (|has| |#2| (-989)) (|has| |#2| (-684)) (|has| |#2| (-318)) (|has| |#2| (-146))) ((-604 $) |has| |#2| (-989)) ((-606 (-499)) -12 (|has| |#2| (-596 (-499))) (|has| |#2| (-989))) ((-606 |#2|) -3677 (|has| |#2| (-989)) (|has| |#2| (-318)) (|has| |#2| (-146))) ((-606 $) |has| |#2| (-989)) ((-598 |#2|) -3677 (|has| |#2| (-684)) (|has| |#2| (-318)) (|has| |#2| (-146))) ((-596 (-499)) -12 (|has| |#2| (-596 (-499))) (|has| |#2| (-989))) ((-596 |#2|) |has| |#2| (-989)) ((-675 |#2|) -3677 (|has| |#2| (-318)) (|has| |#2| (-146))) ((-684) |has| |#2| (-989)) ((-737) |has| |#2| (-738)) ((-738) |has| |#2| (-738)) ((-739) |has| |#2| (-738)) ((-742) |has| |#2| (-738)) ((-781) -3677 (|has| |#2| (-781)) (|has| |#2| (-738))) ((-784) -3677 (|has| |#2| (-781)) (|has| |#2| (-738))) ((-831 $ (-1117)) -3677 (-12 (|has| |#2| (-838 (-1117))) (|has| |#2| (-989))) (-12 (|has| |#2| (-836 (-1117))) (|has| |#2| (-989)))) ((-836 (-1117)) -12 (|has| |#2| (-836 (-1117))) (|has| |#2| (-989))) ((-838 (-1117)) -3677 (-12 (|has| |#2| (-838 (-1117))) (|has| |#2| (-989))) (-12 (|has| |#2| (-836 (-1117))) (|has| |#2| (-989)))) ((-978 (-361 (-499))) -12 (|has| |#2| (-978 (-361 (-499)))) (|has| |#2| (-1041))) ((-978 (-499)) -12 (|has| |#2| (-978 (-499))) (|has| |#2| (-1041))) ((-978 |#2|) |has| |#2| (-1041)) ((-991 |#2|) -3677 (|has| |#2| (-989)) (|has| |#2| (-684)) (|has| |#2| (-318)) (|has| |#2| (-146))) ((-996 |#2|) -3677 (|has| |#2| (-989)) (|has| |#2| (-318)) (|has| |#2| (-146))) ((-989) |has| |#2| (-989)) ((-997) |has| |#2| (-989)) ((-1052) |has| |#2| (-989)) ((-1041) -3677 (|has| |#2| (-1041)) (|has| |#2| (-989)) (|has| |#2| (-781)) (|has| |#2| (-738)) (|has| |#2| (-684)) (|has| |#2| (-323)) (|has| |#2| (-318)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1157) . T) ((-1215 |#2|) |has| |#2| (-318))) -((-2687 (((-85) $ $) NIL (|has| |#2| (-73)) ELT)) (-3326 (((-85) $) NIL (|has| |#2| (-23)) ELT)) (-3857 (($ (-857)) 63 (|has| |#2| (-989)) ELT)) (-2299 (((-1213) $ (-499) (-499)) NIL (|has| $ (-6 -4146)) ELT)) (-2600 (($ $ $) 69 (|has| |#2| (-738)) ELT)) (-1345 (((-3 $ #1="failed") $ $) 54 (|has| |#2| (-104)) ELT)) (-3258 (((-714)) NIL (|has| |#2| (-323)) ELT)) (-3938 ((|#2| $ (-499) |#2|) NIL (|has| $ (-6 -4146)) ELT)) (-3874 (($) NIL T CONST)) (-3295 (((-3 (-499) #1#) $) NIL (-12 (|has| |#2| (-978 (-499))) (|has| |#2| (-1041))) ELT) (((-3 (-361 (-499)) #1#) $) NIL (-12 (|has| |#2| (-978 (-361 (-499)))) (|has| |#2| (-1041))) ELT) (((-3 |#2| #1#) $) 31 (|has| |#2| (-1041)) ELT)) (-3294 (((-499) $) NIL (-12 (|has| |#2| (-978 (-499))) (|has| |#2| (-1041))) ELT) (((-361 (-499)) $) NIL (-12 (|has| |#2| (-978 (-361 (-499)))) (|has| |#2| (-1041))) ELT) ((|#2| $) 29 (|has| |#2| (-1041)) ELT)) (-2380 (((-647 (-499)) (-647 $)) NIL (-12 (|has| |#2| (-596 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T) ((-23) . T) ((-25) . T) ((-38 (-343 (-478))) OR (|has| |#1| (-295)) (|has| |#1| (-308))) ((-38 |#1|) . T) ((-38 $) OR (|has| |#1| (-489)) (|has| |#1| (-295)) (|has| |#1| (-308)) (|has| |#1| (-254))) ((-35) |has| |#1| (-1104)) ((-66) |has| |#1| (-1104)) ((-72) . T) ((-80 (-343 (-478)) (-343 (-478))) OR (|has| |#1| (-295)) (|has| |#1| (-308))) ((-80 |#1| |#1|) . T) ((-80 $ $) . T) ((-102) . T) ((-116) OR (|has| |#1| (-295)) (|has| |#1| (-116))) ((-118) |has| |#1| (-118)) ((-550 (-343 (-478))) OR (|has| |#1| (-943 (-343 (-478)))) (|has| |#1| (-295)) (|has| |#1| (-308))) ((-550 (-478)) . T) ((-550 |#1|) . T) ((-550 $) OR (|has| |#1| (-489)) (|has| |#1| (-295)) (|has| |#1| (-308)) (|has| |#1| (-254))) ((-547 (-765)) . T) ((-144) . T) ((-548 (-140 (-177))) |has| |#1| (-926)) ((-548 (-140 (-323))) |has| |#1| (-926)) ((-548 (-467)) |has| |#1| (-548 (-467))) ((-548 (-793 (-323))) |has| |#1| (-548 (-793 (-323)))) ((-548 (-793 (-478))) |has| |#1| (-548 (-793 (-478)))) ((-548 (-1074 |#1|)) . 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(-710)) (-6 (-710)) |%noBranch|) (IF (|has| |t#2| (-308)) (-6 (-1176 |t#2|)) |%noBranch|))) +(((-21) OR (|has| |#2| (-954)) (|has| |#2| (-308)) (|has| |#2| (-144)) (|has| |#2| (-21))) ((-23) OR (|has| |#2| (-954)) (|has| |#2| (-710)) (|has| |#2| (-308)) (|has| |#2| (-144)) (|has| |#2| (-102)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) OR (|has| |#2| (-954)) (|has| |#2| (-710)) (|has| |#2| (-308)) (|has| |#2| (-144)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-72) OR (|has| |#2| (-1005)) (|has| |#2| (-954)) (|has| |#2| (-749)) (|has| |#2| (-710)) (|has| |#2| (-658)) (|has| |#2| (-313)) (|has| |#2| (-308)) (|has| |#2| (-144)) (|has| |#2| (-102)) (|has| |#2| (-72)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-80 |#2| |#2|) OR (|has| |#2| (-954)) (|has| |#2| (-308)) (|has| |#2| (-144))) ((-102) OR (|has| |#2| (-954)) (|has| |#2| (-710)) (|has| |#2| (-308)) (|has| |#2| (-144)) (|has| |#2| (-102)) (|has| |#2| (-21))) ((-550 (-343 (-478))) -12 (|has| |#2| (-943 (-343 (-478)))) (|has| |#2| (-1005))) ((-550 (-478)) OR (|has| |#2| (-954)) (-12 (|has| |#2| (-943 (-478))) (|has| |#2| (-1005)))) ((-550 |#2|) |has| |#2| (-1005)) ((-547 (-765)) OR (|has| |#2| (-1005)) (|has| |#2| (-954)) (|has| |#2| (-749)) (|has| |#2| (-710)) (|has| |#2| (-658)) (|has| |#2| (-313)) (|has| |#2| (-308)) (|has| |#2| (-144)) (|has| |#2| (-547 (-765))) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-547 (-1168 |#2|)) . T) ((-184 $) OR (-12 (|has| |#2| (-187)) (|has| |#2| (-954))) (-12 (|has| |#2| (-188)) (|has| |#2| (-954)))) ((-182 |#2|) |has| |#2| (-954)) ((-188) -12 (|has| |#2| (-188)) (|has| |#2| (-954))) ((-187) OR (-12 (|has| |#2| (-187)) (|has| |#2| (-954))) (-12 (|has| |#2| (-188)) (|has| |#2| (-954)))) ((-222 |#2|) |has| |#2| (-954)) ((-238 (-478) |#2|) . T) ((-240 (-478) |#2|) . T) ((-256 |#2|) -12 (|has| |#2| (-256 |#2|)) (|has| |#2| (-1005))) ((-313) |has| |#2| (-313)) ((-322 |#2|) |has| |#2| (-954)) ((-348 |#2|) |has| |#2| (-1005)) ((-422 |#2|) . T) ((-533 (-478) |#2|) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 (-343 (-478))) |has| |#1| (-38 (-343 (-478)))) ((-38 |#1|) |has| |#1| (-144)) ((-38 $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385))) ((-72) . T) ((-80 (-343 (-478)) (-343 (-478))) |has| |#1| (-38 (-343 (-478)))) ((-80 |#1| |#1|) . T) ((-80 $ $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385)) (|has| |#1| (-144))) ((-102) . T) ((-116) |has| |#1| (-116)) ((-118) |has| |#1| (-118)) ((-550 (-343 (-478))) OR (|has| |#1| (-943 (-343 (-478)))) (|has| |#1| (-38 (-343 (-478))))) ((-550 (-478)) . T) ((-550 |#1|) . T) ((-550 |#2|) . T) ((-550 |#3|) . T) ((-550 $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385))) ((-547 (-765)) . T) ((-144) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385)) (|has| |#1| (-144))) ((-548 (-467)) -12 (|has| |#1| (-548 (-467))) (|has| |#3| (-548 (-467)))) ((-548 (-793 (-323))) -12 (|has| |#1| (-548 (-793 (-323)))) (|has| |#3| (-548 (-793 (-323))))) ((-548 (-793 (-478))) -12 (|has| |#1| (-548 (-793 (-478)))) (|has| |#3| (-548 (-793 (-478))))) ((-184 $) OR (|has| |#1| (-187)) (|has| |#1| (-188))) ((-182 |#1|) . T) ((-188) |has| |#1| (-188)) ((-187) OR (|has| |#1| (-187)) (|has| |#1| (-188))) ((-222 |#1|) . T) ((-242) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385))) ((-256 $) . T) ((-273 |#1| |#4|) . T) ((-322 |#1|) . T) ((-348 |#1|) . T) ((-385) OR (|has| |#1| (-814)) (|has| |#1| (-385))) ((-447 |#2| |#1|) |has| |#1| (-188)) ((-447 |#2| $) |has| |#1| (-188)) ((-447 |#3| |#1|) . T) ((-447 |#3| $) . T) ((-447 $ $) . T) ((-489) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385))) ((-583 (-343 (-478))) |has| |#1| (-38 (-343 (-478)))) ((-583 (-478)) . 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T) ((-814) |has| |#1| (-814)) ((-943 (-343 (-478))) |has| |#1| (-943 (-343 (-478)))) ((-943 (-478)) |has| |#1| (-943 (-478))) ((-943 |#1|) . T) ((-943 |#2|) . T) ((-943 |#3|) . T) ((-956 (-343 (-478))) |has| |#1| (-38 (-343 (-478)))) ((-956 |#1|) . T) ((-956 $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385)) (|has| |#1| (-144))) ((-961 (-343 (-478))) |has| |#1| (-38 (-343 (-478)))) ((-961 |#1|) . T) ((-961 $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385)) (|has| |#1| (-144))) ((-954) . T) ((-962) . T) ((-1015) . T) ((-1005) . T) ((-1118) . 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T) ((-23) . T) ((-47 |#1| (-499)) . T) ((-25) . T) ((-38 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-318)) ((-38 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-318))) ((-35) |has| |#1| (-38 (-361 (-499)))) ((-66) |has| |#1| (-38 (-361 (-499)))) ((-73) . T) ((-82 (-361 (-499)) (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-318)) ((-82 $ $) -3677 (|has| |#1| (-510)) (|has| |#1| (-318)) (|has| |#1| (-146))) ((-104) . T) ((-118) -3677 (-12 (|has| |#1| (-318)) (|has| |#2| (-118))) (|has| |#1| (-118))) ((-120) -3677 (-12 (|has| |#1| (-318)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-571 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-571 (-499)) . T) ((-571 (-1117)) -12 (|has| |#1| (-318)) (|has| |#2| (-978 (-1117)))) ((-571 |#1|) |has| |#1| (-146)) ((-571 |#2|) . T) ((-571 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-318))) ((-568 (-797)) . T) ((-146) -3677 (|has| |#1| (-510)) (|has| |#1| (-318)) (|has| |#1| (-146))) ((-569 (-179)) -12 (|has| |#1| (-318)) (|has| |#2| (-960))) ((-569 (-333)) -12 (|has| |#1| (-318)) (|has| |#2| (-960))) ((-569 (-488)) -12 (|has| |#1| (-318)) (|has| |#2| (-569 (-488)))) ((-569 (-825 (-333))) -12 (|has| |#1| (-318)) (|has| |#2| (-569 (-825 (-333))))) ((-569 (-825 (-499))) -12 (|has| |#1| (-318)) (|has| |#2| (-569 (-825 (-499))))) ((-186 $) -3677 (|has| |#1| (-15 * (|#1| (-499) |#1|))) (-12 (|has| |#1| (-318)) (|has| |#2| (-189))) (-12 (|has| |#1| (-318)) (|has| |#2| (-190)))) ((-184 |#2|) |has| |#1| (-318)) ((-190) -3677 (|has| |#1| (-15 * (|#1| (-499) |#1|))) (-12 (|has| |#1| (-318)) (|has| |#2| (-190)))) ((-189) -3677 (|has| |#1| (-15 * (|#1| (-499) |#1|))) (-12 (|has| |#1| (-318)) (|has| |#2| (-189))) (-12 (|has| |#1| (-318)) (|has| |#2| (-190)))) ((-224 |#2|) |has| |#1| (-318)) ((-200) |has| |#1| (-318)) ((-238) |has| |#1| (-38 (-361 (-499)))) ((-240 (-499) |#1|) . T) ((-240 |#2| $) -12 (|has| |#1| (-318)) (|has| |#2| (-240 |#2| |#2|))) ((-240 $ $) |has| (-499) (-1052)) ((-244) -3677 (|has| |#1| (-510)) (|has| |#1| (-318))) ((-261) |has| |#1| (-318)) ((-263 |#2|) -12 (|has| |#1| (-318)) (|has| |#2| (-263 |#2|))) ((-318) |has| |#1| (-318)) ((-293 |#2|) |has| |#1| (-318)) ((-332 |#2|) |has| |#1| (-318)) ((-354 |#2|) |has| |#1| (-318)) ((-406) |has| |#1| (-318)) ((-447) |has| |#1| (-38 (-361 (-499)))) ((-468 (-1117) |#2|) -12 (|has| |#1| (-318)) (|has| |#2| (-468 (-1117) |#2|))) ((-468 |#2| |#2|) -12 (|has| |#1| (-318)) (|has| |#2| (-263 |#2|))) ((-510) -3677 (|has| |#1| (-510)) (|has| |#1| (-318))) ((-604 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-604 (-499)) . T) ((-604 |#1|) . T) ((-604 |#2|) |has| |#1| (-318)) ((-604 $) . T) ((-606 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-606 (-499)) -12 (|has| |#1| (-318)) (|has| |#2| (-596 (-499)))) ((-606 |#1|) . T) ((-606 |#2|) |has| |#1| (-318)) ((-606 $) . T) ((-598 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-598 |#1|) |has| |#1| (-146)) ((-598 |#2|) |has| |#1| (-318)) ((-598 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-318))) ((-596 (-499)) -12 (|has| |#1| (-318)) (|has| |#2| (-596 (-499)))) ((-596 |#2|) |has| |#1| (-318)) ((-675 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-675 |#1|) |has| |#1| (-146)) ((-675 |#2|) |has| |#1| (-318)) ((-675 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-318))) ((-684) . T) ((-735) -12 (|has| |#1| (-318)) (|has| |#2| (-763))) ((-737) -12 (|has| |#1| (-318)) (|has| |#2| (-763))) ((-739) -12 (|has| |#1| (-318)) (|has| |#2| (-763))) ((-742) -12 (|has| |#1| (-318)) (|has| |#2| (-763))) ((-763) -12 (|has| |#1| (-318)) (|has| |#2| (-763))) ((-780) -12 (|has| |#1| (-318)) (|has| |#2| (-763))) ((-781) -3677 (-12 (|has| |#1| (-318)) (|has| |#2| (-781))) (-12 (|has| |#1| (-318)) (|has| |#2| (-763)))) ((-784) -3677 (-12 (|has| |#1| (-318)) (|has| |#2| (-781))) (-12 (|has| |#1| (-318)) (|has| |#2| (-763)))) ((-831 $ (-1117)) -3677 (-12 (|has| |#1| (-836 (-1117))) (|has| |#1| (-15 * (|#1| (-499) |#1|)))) (-12 (|has| |#1| (-318)) (|has| |#2| (-838 (-1117)))) (-12 (|has| |#1| (-318)) (|has| |#2| (-836 (-1117))))) ((-836 (-1117)) -3677 (-12 (|has| |#1| (-836 (-1117))) (|has| |#1| (-15 * (|#1| (-499) |#1|)))) (-12 (|has| |#1| (-318)) (|has| |#2| (-836 (-1117))))) ((-838 (-1117)) -3677 (-12 (|has| |#1| (-836 (-1117))) (|has| |#1| (-15 * (|#1| (-499) |#1|)))) (-12 (|has| |#1| (-318)) (|has| |#2| (-838 (-1117)))) (-12 (|has| |#1| (-318)) (|has| |#2| (-836 (-1117))))) ((-821 (-333)) -12 (|has| |#1| (-318)) (|has| |#2| (-821 (-333)))) ((-821 (-499)) -12 (|has| |#1| (-318)) (|has| |#2| (-821 (-499)))) ((-819 |#2|) |has| |#1| (-318)) ((-848) -12 (|has| |#1| (-318)) (|has| |#2| (-848))) ((-913 |#1| (-499) (-1022)) . T) ((-859) |has| |#1| (-318)) ((-931 |#2|) |has| |#1| (-318)) ((-942) |has| |#1| (-38 (-361 (-499)))) ((-960) -12 (|has| |#1| (-318)) (|has| |#2| (-960))) ((-978 (-361 (-499))) -12 (|has| |#1| (-318)) (|has| |#2| (-978 (-499)))) ((-978 (-499)) -12 (|has| |#1| (-318)) (|has| |#2| (-978 (-499)))) ((-978 (-1117)) -12 (|has| |#1| (-318)) (|has| |#2| (-978 (-1117)))) ((-978 |#2|) . T) ((-991 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-991 |#1|) . T) ((-991 |#2|) |has| |#1| (-318)) ((-991 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-318)) (|has| |#1| (-146))) ((-996 (-361 (-499))) -3677 (|has| |#1| (-318)) (|has| |#1| (-38 (-361 (-499))))) ((-996 |#1|) . T) ((-996 |#2|) |has| |#1| (-318)) ((-996 $) -3677 (|has| |#1| (-510)) (|has| |#1| (-318)) (|has| |#1| (-146))) ((-989) . T) ((-997) . T) ((-1052) . T) ((-1041) . 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2458008 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1090 2445319 2449902 2449945 "STAGG" 2450372 STAGG (NIL T) -9 NIL 2450546 NIL) (-1089 2443698 2444446 2445314 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1088 2441855 2443525 2443617 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1087 2441178 2441686 2441716 "SRING" 2441721 SRING (NIL) -9 NIL 2441741 NIL) (-1086 2433793 2439710 2440150 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1085 2427553 2428992 2430497 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1084 2419981 2424892 2424922 "SRAGG" 2426221 SRAGG (NIL) -9 NIL 2426825 NIL) (-1083 2419278 2419598 2419976 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1082 2413397 2418600 2419023 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1081 2407610 2410779 2411501 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1080 2404039 2404858 2405495 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1079 2403014 2403319 2403349 "SPFCAT" 2403793 SPFCAT (NIL) -9 NIL NIL NIL) (-1078 2401951 2402203 2402467 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1077 2392707 2394985 2395015 "SPADXPT" 2399656 SPADXPT (NIL) -9 NIL 2401785 NIL) (-1076 2392509 2392555 2392624 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1075 2390161 2392473 2392504 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1074 2381847 2383936 2383978 "SPACEC" 2388293 SPACEC (NIL T) -9 NIL 2390098 NIL) (-1073 2379676 2381794 2381842 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1072 2378609 2378798 2379087 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1071 2377013 2377346 2377757 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1070 2376278 2376512 2376773 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1069 2372458 2373418 2374413 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1068 2368816 2369515 2370244 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1067 2362612 2368166 2368263 "SNTSCAT" 2368268 SNTSCAT (NIL T T T T) -9 NIL 2368338 NIL) (-1066 2356497 2361253 2361643 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1065 2350327 2356416 2356492 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1064 2348759 2349090 2349488 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1063 2340437 2345351 2345453 "SMATCAT" 2346796 SMATCAT (NIL NIL T T T) -9 NIL 2347344 NIL) (-1062 2338278 2339262 2340432 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1061 2335876 2337490 2337533 "SKAGG" 2337794 SKAGG (NIL T) -9 NIL 2337928 NIL) (-1060 2331738 2335527 2335696 "SINT" NIL SINT (NIL) -8 NIL NIL 2335848) (-1059 2331548 2331592 2331658 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1058 2330623 2330855 2331123 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1057 2329627 2329789 2330065 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1056 2328972 2329312 2329436 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1055 2328318 2328625 2328765 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1054 2326429 2326921 2327427 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1053 2319965 2326348 2326424 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1052 2319480 2319717 2319747 "SGROUP" 2319840 SGROUP (NIL) -9 NIL 2319902 NIL) (-1051 2319370 2319402 2319475 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1050 2316793 2317562 2318284 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1049 2310687 2316241 2316338 "SFRTCAT" 2316343 SFRTCAT (NIL T T T T) -9 NIL 2316382 NIL) (-1048 2305043 2306156 2307285 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1047 2299181 2300342 2301508 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1046 2298842 2298949 2299060 "SFORT" NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1045 2297814 2298716 2298837 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1044 2293434 2294329 2294424 "SEXCAT" 2297037 SEXCAT (NIL T T T T T) -9 NIL 2297588 NIL) (-1043 2292407 2293361 2293429 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1042 2290798 2291383 2291685 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1041 2290333 2290518 2290548 "SETCAT" 2290665 SETCAT (NIL) -9 NIL 2290749 NIL) (-1040 2290165 2290229 2290328 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1039 2286400 2288631 2288674 "SETAGG" 2289542 SETAGG (NIL T) -9 NIL 2289880 NIL) (-1038 2286006 2286158 2286395 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1037 2282960 2285953 2286001 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1036 2282425 2282735 2282836 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1035 2281552 2281918 2281979 "SEGXCAT" 2282265 SEGXCAT (NIL T T) -9 NIL 2282385 NIL) (-1034 2280477 2280745 2280788 "SEGCAT" 2281310 SEGCAT (NIL T) -9 NIL 2281531 NIL) (-1033 2280157 2280222 2280335 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1032 2279223 2279693 2279901 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1031 2278800 2279079 2279156 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1030 2278165 2278301 2278505 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1029 2277231 2277978 2278160 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1028 2276484 2277179 2277226 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1027 2268027 2276351 2276479 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1026 2266881 2267171 2267490 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1025 2266179 2266391 2266581 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-1024 2265523 2265680 2265858 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1023 2265106 2265337 2265367 "SASTCAT" 2265372 SASTCAT (NIL) -9 NIL 2265385 NIL) (-1022 2264570 2264995 2265071 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-1021 2264170 2264211 2264384 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1020 2263798 2263839 2263998 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1019 2256926 2263713 2263793 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1018 2255571 2255900 2256298 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1017 2254321 2254684 2254988 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1016 2253942 2254163 2254246 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1015 2251392 2252026 2252481 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1014 2251228 2251261 2251331 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-1013 2250714 2251017 2251111 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-1012 2246299 2247167 2248082 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1011 2235073 2240627 2240724 "RSETCAT" 2244834 RSETCAT (NIL T T T T) -9 NIL 2245922 NIL) (-1010 2233607 2234249 2235068 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1009 2227338 2228783 2230294 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1008 2225220 2225777 2225851 "RRCC" 2226934 RRCC (NIL T T) -9 NIL 2227275 NIL) (-1007 2224742 2224941 2225215 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-1006 2224207 2224517 2224618 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-1005 2196695 2207364 2207430 "RPOLCAT" 2218000 RPOLCAT (NIL T T T) -9 NIL 2221145 NIL) (-1004 2190791 2193614 2196690 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-1003 2181719 2189462 2189944 "ROUTINE" NIL ROUTINE (NIL) -8 NIL NIL NIL) (-1002 2177946 2181463 2181603 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-1001 2176264 2177003 2177262 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1000 2171986 2174736 2174766 "RNS" 2175035 RNS (NIL) -9 NIL 2175287 NIL) (-999 2170895 2171380 2171912 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-998 2170013 2170414 2170614 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-997 2169313 2169813 2169841 "RNG" 2169846 RNG (NIL) -9 NIL 2169867 NIL) (-996 2168618 2169092 2169132 "RMODULE" 2169137 RMODULE (NIL T) -9 NIL 2169163 NIL) (-995 2167557 2167663 2167993 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-994 2164435 2167147 2167440 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-993 2157127 2159588 2159700 "RMATCAT" 2163005 RMATCAT (NIL NIL NIL T T T) -9 NIL 2163982 NIL) (-992 2156644 2156823 2157122 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-991 2156224 2156435 2156476 "RLINSET" 2156537 RLINSET (NIL T) -9 NIL 2156581 NIL) (-990 2155869 2155950 2156076 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-989 2154804 2155473 2155501 "RING" 2155556 RING (NIL) -9 NIL 2155647 NIL) (-988 2154649 2154705 2154799 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-987 2153703 2153970 2154226 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-986 2144689 2153330 2153532 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-985 2143957 2144437 2144476 "RGBCSPC" 2144533 RGBCSPC (NIL T) -9 NIL 2144584 NIL) (-984 2143034 2143489 2143528 "RGBCMDL" 2143756 RGBCMDL (NIL T) -9 NIL 2143870 NIL) (-983 2142746 2142815 2142916 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-982 2142509 2142550 2142645 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-981 2140933 2141363 2141743 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-980 2138520 2139188 2139856 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-979 2138070 2138168 2138328 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-978 2137692 2137790 2137831 "RETRACT" 2137962 RETRACT (NIL T) -9 NIL 2138049 NIL) (-977 2137572 2137603 2137687 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-976 2137174 2137445 2137513 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-975 2129653 2136942 2137063 "RESULT" NIL RESULT (NIL) -8 NIL NIL NIL) (-974 2128197 2129024 2129221 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-973 2127888 2127949 2128045 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-972 2127631 2127672 2127777 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-971 2127366 2127407 2127516 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-970 2122436 2123888 2125103 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-969 2119535 2120293 2121101 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-968 2117504 2118126 2118726 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-967 2110131 2116048 2116486 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-966 2109068 2109504 2109751 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-965 2108553 2108668 2108833 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-964 2104198 2107952 2108175 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-963 2103430 2103629 2103842 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-962 2100720 2101558 2102440 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-961 2097302 2098338 2099397 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-960 2097138 2097191 2097219 "REAL" 2097224 REAL (NIL) -9 NIL 2097259 NIL) (-959 2096628 2096931 2097023 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-958 2096108 2096186 2096391 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-957 2095341 2095533 2095744 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-956 2094229 2094526 2094893 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-955 2092496 2092966 2093499 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-954 2091418 2091695 2092082 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-953 2090245 2090554 2090973 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-952 2083684 2087131 2087159 "RCFIELD" 2088436 RCFIELD (NIL) -9 NIL 2089166 NIL) (-951 2082310 2082920 2083611 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-950 2078516 2080408 2080449 "RCAGG" 2081516 RCAGG (NIL T) -9 NIL 2081977 NIL) (-949 2078243 2078353 2078511 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-948 2077688 2077817 2077978 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-947 2077305 2077384 2077503 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-946 2076720 2076870 2077020 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-945 2076502 2076552 2076623 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-944 2069005 2075620 2075928 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-943 2058732 2068872 2069000 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-942 2058366 2058459 2058487 "RADCAT" 2058644 RADCAT (NIL) -9 NIL NIL NIL) (-941 2058204 2058264 2058361 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-940 2056304 2058035 2058124 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-939 2055985 2056034 2056161 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-938 2048330 2052353 2052393 "QUATCAT" 2053172 QUATCAT (NIL T) -9 NIL 2053937 NIL) (-937 2045588 2046866 2048236 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-936 2041488 2045538 2045583 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-935 2038881 2040548 2040589 "QUAGG" 2040964 QUAGG (NIL T) -9 NIL 2041138 NIL) (-934 2038483 2038754 2038822 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-933 2037521 2038119 2038282 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-932 2037202 2037251 2037378 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-931 2026894 2033004 2033044 "QFCAT" 2033702 QFCAT (NIL T) -9 NIL 2034695 NIL) (-930 2023794 2025229 2026800 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-929 2023340 2023474 2023604 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-928 2017498 2018659 2019823 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-927 2016917 2017097 2017329 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-926 2014739 2015267 2015690 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-925 2013638 2013880 2014197 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-924 2011999 2012197 2012550 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-923 2007755 2008971 2009012 "PTRANFN" 2010896 PTRANFN (NIL T) -9 NIL NIL NIL) (-922 2006402 2006747 2007068 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-921 2006095 2006158 2006265 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-920 2000171 2004894 2004934 "PTCAT" 2005226 PTCAT (NIL T) -9 NIL 2005379 NIL) (-919 1999864 1999905 2000029 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-918 1998743 1999059 1999393 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-917 1987584 1990145 1992455 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-916 1980482 1983378 1983473 "PSETCAT" 1986467 PSETCAT (NIL T T T T) -9 NIL 1987274 NIL) (-915 1978931 1979665 1980477 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-914 1978250 1978445 1978473 "PSCURVE" 1978741 PSCURVE (NIL) -9 NIL 1978908 NIL) (-913 1973928 1975686 1975750 "PSCAT" 1976585 PSCAT (NIL T T T) -9 NIL 1976824 NIL) (-912 1973242 1973524 1973923 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-911 1971672 1972554 1972817 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-910 1971162 1971465 1971557 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-909 1962182 1964604 1966792 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-908 1959931 1961508 1961548 "PRQAGG" 1961731 PRQAGG (NIL T) -9 NIL 1961832 NIL) (-907 1959116 1959562 1959590 "PROPLOG" 1959729 PROPLOG (NIL) -9 NIL 1959843 NIL) (-906 1958791 1958854 1958977 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-905 1958227 1958366 1958538 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-904 1956475 1957238 1957535 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-903 1956028 1956159 1956287 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-902 1950627 1954968 1955788 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-901 1950456 1950494 1950553 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-900 1949895 1950035 1950186 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-899 1948363 1948782 1949248 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-898 1948080 1948141 1948169 "PRIMCAT" 1948293 PRIMCAT (NIL) -9 NIL NIL NIL) (-897 1947251 1947447 1947675 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-896 1943129 1947201 1947246 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-895 1942828 1942890 1943001 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-894 1940025 1942477 1942710 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-893 1939476 1939633 1939661 "PPCURVE" 1939866 PPCURVE (NIL) -9 NIL 1940002 NIL) (-892 1939089 1939334 1939417 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-891 1936845 1937266 1937858 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-890 1936288 1936352 1936585 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-889 1933008 1933494 1934105 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-888 1918648 1924718 1924782 "POLYCAT" 1928267 POLYCAT (NIL T T T) -9 NIL 1930144 NIL) (-887 1914158 1916305 1918643 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-886 1913815 1913889 1914008 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-885 1913508 1913571 1913678 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-884 1906929 1913241 1913400 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-883 1905816 1906079 1906355 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-882 1904420 1904733 1905063 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-881 1899582 1904370 1904415 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-880 1898070 1898481 1898856 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-879 1896827 1897136 1897532 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-878 1896498 1896582 1896699 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-877 1896077 1896152 1896326 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-876 1895563 1895659 1895819 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-875 1895035 1895155 1895309 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-874 1893930 1894148 1894525 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-873 1893541 1893626 1893778 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-872 1893092 1893174 1893355 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-871 1892784 1892865 1892978 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-870 1892297 1892372 1892580 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-869 1891645 1891773 1891975 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-868 1891007 1891141 1891304 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-867 1890311 1890493 1890674 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-866 1890034 1890108 1890202 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-865 1886602 1887791 1888707 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-864 1885686 1885887 1886122 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-863 1881251 1882635 1883777 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-862 1861172 1866059 1870906 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-861 1860912 1860965 1861068 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-860 1860353 1860487 1860667 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-859 1858450 1859609 1859637 "PID" 1859834 PID (NIL) -9 NIL 1859961 NIL) (-858 1858238 1858281 1858356 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-857 1857425 1858085 1858172 "PI" NIL PI (NIL) -8 NIL NIL 1858212) (-856 1856877 1857028 1857204 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-855 1853205 1854163 1855068 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-854 1851569 1851858 1852224 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-853 1851011 1851126 1851287 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-852 1847616 1849880 1850233 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-851 1846222 1846502 1846827 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-850 1844987 1845241 1845589 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-849 1843697 1843924 1844276 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-848 1840795 1842293 1842321 "PFECAT" 1842914 PFECAT (NIL) -9 NIL 1843291 NIL) (-847 1840418 1840583 1840790 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-846 1839242 1839524 1839825 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-845 1837424 1837811 1838241 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-844 1833458 1837350 1837419 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-843 1829361 1830508 1831375 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-842 1827284 1828388 1828429 "PERMCAT" 1828828 PERMCAT (NIL T) -9 NIL 1829125 NIL) (-841 1826980 1827027 1827150 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-840 1823414 1825110 1825755 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-839 1820879 1823169 1823290 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-838 1819760 1820023 1820064 "PDSPC" 1820597 PDSPC (NIL T) -9 NIL 1820842 NIL) (-837 1819127 1819393 1819755 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-836 1817850 1818781 1818822 "PDRING" 1818827 PDRING (NIL T) -9 NIL 1818854 NIL) (-835 1816603 1817361 1817414 "PDMOD" 1817419 PDMOD (NIL T T) -9 NIL 1817522 NIL) (-834 1814421 1815244 1815912 "PDEPROB" NIL PDEPROB (NIL) -8 NIL NIL NIL) (-833 1813514 1813726 1813975 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-832 1811038 1811925 1811953 "PDECAT" 1812739 PDECAT (NIL) -9 NIL 1813451 NIL) (-831 1810655 1810722 1810776 "PDDOM" 1810941 PDDOM (NIL T T) -9 NIL 1811021 NIL) (-830 1810507 1810543 1810650 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-829 1810293 1810332 1810421 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-828 1808615 1809368 1809663 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-827 1808304 1808367 1808476 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-826 1806442 1806872 1807323 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-825 1800070 1801899 1803183 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-824 1799701 1799774 1799906 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-823 1797403 1798083 1798564 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-822 1795607 1796035 1796438 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-821 1795065 1795313 1795354 "PATMAB" 1795461 PATMAB (NIL T) -9 NIL 1795544 NIL) (-820 1793712 1794116 1794373 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-819 1793250 1793381 1793422 "PATAB" 1793427 PATAB (NIL T) -9 NIL 1793599 NIL) (-818 1791793 1792230 1792653 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-817 1791471 1791546 1791648 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-816 1791160 1791223 1791332 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-815 1790965 1791011 1791078 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-814 1790643 1790718 1790820 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-813 1790332 1790395 1790504 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-812 1790023 1790093 1790190 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-811 1789712 1789775 1789884 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-810 1788872 1789251 1789431 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-809 1788479 1788577 1788696 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-808 1787447 1787872 1788091 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-807 1786109 1786766 1787126 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-806 1779260 1785513 1785707 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-805 1771742 1778758 1778942 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-804 1768555 1770408 1770448 "PADICCT" 1771029 PADICCT (NIL NIL) -9 NIL 1771311 NIL) (-803 1766609 1768505 1768550 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-802 1765771 1765981 1766247 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-801 1765113 1765256 1765460 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-800 1763558 1764521 1764799 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-799 1763083 1763341 1763438 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-798 1762142 1762820 1762992 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-797 1752564 1755433 1757632 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-796 1751956 1752270 1752396 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-795 1751233 1751428 1751456 "OUTBCON" 1751774 OUTBCON (NIL) -9 NIL 1751940 NIL) (-794 1750941 1751071 1751228 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-793 1750322 1750467 1750628 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-792 1749694 1750120 1750209 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-791 1749121 1749536 1749564 "OSGROUP" 1749569 OSGROUP (NIL) -9 NIL 1749591 NIL) (-790 1748085 1748346 1748631 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-789 1745418 1747960 1748080 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-788 1742623 1745169 1745295 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-787 1740641 1741169 1741729 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-786 1734071 1736549 1736589 "OREPCAT" 1738910 OREPCAT (NIL T) -9 NIL 1740012 NIL) (-785 1732097 1733031 1734066 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-784 1731306 1731577 1731605 "ORDTYPE" 1731910 ORDTYPE (NIL) -9 NIL 1732068 NIL) (-783 1730840 1731051 1731301 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-782 1730302 1730678 1730835 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-781 1729808 1730171 1730199 "ORDSET" 1730204 ORDSET (NIL) -9 NIL 1730226 NIL) (-780 1728474 1729434 1729462 "ORDRING" 1729467 ORDRING (NIL) -9 NIL 1729495 NIL) (-779 1727734 1728291 1728319 "ORDMON" 1728324 ORDMON (NIL) -9 NIL 1728345 NIL) (-778 1727038 1727200 1727392 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-777 1726261 1726769 1726797 "ORDFIN" 1726862 ORDFIN (NIL) -9 NIL 1726936 NIL) (-776 1725655 1725794 1725980 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-775 1722426 1724623 1725029 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-774 1719744 1720711 1721525 "OPTPROB" NIL OPTPROB (NIL) -8 NIL NIL NIL) (-773 1717367 1718188 1718216 "OPTCAT" 1719033 OPTCAT (NIL) -9 NIL 1719681 NIL) (-772 1716774 1717129 1717234 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-771 1716582 1716627 1716693 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-770 1715895 1716171 1716212 "OPERCAT" 1716423 OPERCAT (NIL T) -9 NIL 1716519 NIL) (-769 1715707 1715774 1715890 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-768 1713137 1714509 1715005 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-767 1712558 1712685 1712859 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-766 1709555 1711697 1712063 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-765 1706198 1708997 1709037 "OMSAGG" 1709098 OMSAGG (NIL T) -9 NIL 1709162 NIL) (-764 1704674 1705869 1706037 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-763 1702971 1704150 1704178 "OINTDOM" 1704183 OINTDOM (NIL) -9 NIL 1704204 NIL) (-762 1700401 1701973 1702302 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-761 1699655 1700351 1700396 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-760 1696921 1699496 1699650 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-759 1688516 1696792 1696916 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-758 1682023 1688407 1688511 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-757 1680995 1681232 1681505 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-756 1678629 1679299 1680003 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-755 1674406 1675366 1676389 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-754 1673914 1674002 1674196 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-753 1671363 1671945 1672618 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-752 1668758 1669266 1669862 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-751 1667122 1667763 1668249 "ODEPROB" NIL ODEPROB (NIL) -8 NIL NIL NIL) (-750 1664119 1664658 1665304 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-749 1663474 1663582 1663840 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-748 1662632 1662757 1662978 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-747 1658916 1659712 1660625 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-746 1658356 1658451 1658673 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-745 1656426 1657131 1657159 "ODECAT" 1657763 ODECAT (NIL) -9 NIL 1658293 NIL) (-744 1656107 1656156 1656283 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-743 1652758 1655906 1656025 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-742 1651961 1652552 1652580 "OCAMON" 1652585 OCAMON (NIL) -9 NIL 1652606 NIL) (-741 1646261 1649011 1649051 "OC" 1650147 OC (NIL T) -9 NIL 1651004 NIL) (-740 1644269 1645193 1646167 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-739 1643697 1644115 1644143 "OASGP" 1644148 OASGP (NIL) -9 NIL 1644168 NIL) (-738 1642803 1643421 1643449 "OAMONS" 1643489 OAMONS (NIL) -9 NIL 1643532 NIL) (-737 1641991 1642541 1642569 "OAMON" 1642626 OAMON (NIL) -9 NIL 1642677 NIL) (-736 1641887 1641919 1641986 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-735 1640681 1641424 1641452 "OAGROUP" 1641598 OAGROUP (NIL) -9 NIL 1641690 NIL) (-734 1640472 1640559 1640676 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-733 1640212 1640268 1640356 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-732 1635274 1636837 1638364 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-731 1631969 1633003 1634038 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-730 1629270 1630201 1630229 "NUMINT" 1631148 NUMINT (NIL) -9 NIL 1631906 NIL) (-729 1628380 1628613 1628831 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-728 1617238 1620269 1622717 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-727 1611134 1616688 1616783 "NTSCAT" 1616788 NTSCAT (NIL T T T T) -9 NIL 1616827 NIL) (-726 1610475 1610654 1610847 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-725 1610168 1610231 1610338 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-724 1597853 1607788 1608598 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-723 1586904 1597717 1597848 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-722 1585624 1585949 1586306 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-721 1584460 1584724 1585082 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-720 1583627 1583760 1583976 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-719 1581933 1582252 1582660 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-718 1581646 1581680 1581804 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-717 1581465 1581500 1581569 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-716 1581241 1581431 1581460 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-715 1580805 1580872 1581049 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-714 1579123 1580168 1580423 "NNI" NIL NNI (NIL) -8 NIL NIL 1580770) (-713 1577851 1578188 1578552 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-712 1574914 1575966 1576865 "NIPROB" NIL NIPROB (NIL) -8 NIL NIL NIL) (-711 1573891 1574143 1574445 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-710 1572978 1573543 1573584 "NETCLT" 1573755 NETCLT (NIL T) -9 NIL 1573836 NIL) (-709 1571882 1572149 1572430 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-708 1571681 1571724 1571799 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-707 1570212 1570600 1571020 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-706 1568888 1569823 1569851 "NASRING" 1569961 NASRING (NIL) -9 NIL 1570041 NIL) (-705 1568733 1568789 1568883 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-704 1567705 1568352 1568380 "NARNG" 1568497 NARNG (NIL) -9 NIL 1568588 NIL) (-703 1567481 1567566 1567700 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-702 1566290 1567013 1567053 "NAALG" 1567132 NAALG (NIL T) -9 NIL 1567193 NIL) (-701 1566160 1566195 1566285 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-700 1561139 1562324 1563510 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-699 1560534 1560621 1560805 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-698 1552623 1557052 1557104 "MTSCAT" 1558164 MTSCAT (NIL T T) -9 NIL 1558678 NIL) (-697 1552389 1552449 1552541 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-696 1552215 1552254 1552314 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-695 1549089 1551778 1551819 "MSETAGG" 1551824 MSETAGG (NIL T) -9 NIL 1551858 NIL) (-694 1545226 1548135 1548453 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-693 1541564 1543323 1544063 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-692 1541201 1541274 1541403 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-691 1540854 1540895 1541039 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-690 1538719 1539056 1539487 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-689 1532175 1538618 1538714 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-688 1531700 1531741 1531949 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-687 1531259 1531308 1531491 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-686 1530533 1530626 1530845 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-685 1529150 1529511 1529901 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-684 1528302 1528681 1528709 "MONOID" 1528927 MONOID (NIL) -9 NIL 1529073 NIL) (-683 1527969 1528117 1528297 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-682 1516896 1523719 1523778 "MONOGEN" 1524452 MONOGEN (NIL T T) -9 NIL 1524908 NIL) (-681 1514908 1515794 1516777 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-680 1513632 1514176 1514204 "MONADWU" 1514595 MONADWU (NIL) -9 NIL 1514832 NIL) (-679 1513180 1513380 1513627 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-678 1512469 1512770 1512798 "MONAD" 1513005 MONAD (NIL) -9 NIL 1513117 NIL) (-677 1512236 1512332 1512464 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-676 1510626 1511396 1511675 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-675 1509803 1510299 1510339 "MODULE" 1510344 MODULE (NIL T) -9 NIL 1510382 NIL) (-674 1509482 1509608 1509798 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-673 1507257 1508079 1508393 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-672 1504500 1505853 1506366 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-671 1503134 1503708 1503984 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-670 1492371 1501799 1502212 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-669 1489391 1491371 1491640 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-668 1488475 1488842 1489032 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-667 1488044 1488093 1488272 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-666 1485957 1486891 1486931 "MLO" 1487348 MLO (NIL T) -9 NIL 1487588 NIL) (-665 1483838 1484365 1484960 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-664 1483306 1483402 1483556 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-663 1482976 1483052 1483175 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-662 1482188 1482374 1482602 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-661 1481681 1481797 1481953 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-660 1481053 1481167 1481352 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-659 1477212 1480723 1480859 "MINT" NIL MINT (NIL) -8 NIL NIL NIL) (-658 1476239 1476512 1476789 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-657 1471424 1475161 1475564 "MFLOAT" NIL MFLOAT (NIL) -8 NIL NIL NIL) (-656 1470857 1470945 1471116 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-655 1468015 1468894 1469773 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-654 1466682 1467030 1467383 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-653 1463345 1465812 1465853 "MDAGG" 1466110 MDAGG (NIL T) -9 NIL 1466255 NIL) (-652 1451340 1462825 1463032 "MCMPLX" NIL MCMPLX (NIL) -8 NIL NIL NIL) (-651 1450614 1450778 1450978 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-650 1448732 1449044 1449424 "MCALCFN" NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-649 1447810 1448096 1448326 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-648 1445907 1446484 1447045 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-647 1441677 1445497 1445744 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-646 1438024 1438795 1439529 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-645 1436777 1436946 1437275 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-644 1426296 1429885 1429961 "MATCAT" 1434949 MATCAT (NIL T T T) -9 NIL 1436417 NIL) (-643 1423577 1424883 1426291 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-642 1421978 1422338 1422722 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-641 1421111 1421308 1421530 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-640 1419862 1420188 1420515 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-639 1419023 1419425 1419602 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-638 1418692 1418756 1418879 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-637 1418340 1418413 1418527 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-636 1417875 1417990 1418132 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-635 1416084 1416852 1417153 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-634 1415577 1415879 1415970 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-633 1412383 1414248 1414708 "M3D" NIL M3D (NIL T) -8 NIL NIL NIL) (-632 1405898 1410704 1410745 "LZSTAGG" 1411522 LZSTAGG (NIL T) -9 NIL 1411812 NIL) (-631 1403017 1404451 1405893 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-630 1400404 1401370 1401853 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-629 1399984 1400263 1400338 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-628 1392212 1399845 1399979 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-627 1391575 1391720 1391948 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-626 1389059 1389757 1390469 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-625 1387171 1387494 1387942 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-624 1380343 1386261 1386302 "LSAGG" 1386364 LSAGG (NIL T) -9 NIL 1386442 NIL) (-623 1378037 1379136 1380338 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-622 1375549 1377386 1377635 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-621 1375216 1375307 1375430 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-620 1374899 1374978 1375006 "LOGIC" 1375117 LOGIC (NIL) -9 NIL 1375199 NIL) (-619 1374794 1374823 1374894 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-618 1374113 1374271 1374464 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-617 1372898 1373147 1373498 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-616 1368810 1371545 1371585 "LODOCAT" 1372017 LODOCAT (NIL T) -9 NIL 1372228 NIL) (-615 1368603 1368679 1368805 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-614 1365667 1368480 1368598 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-613 1362829 1365617 1365662 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-612 1359980 1362759 1362824 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-611 1359033 1359208 1359510 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-610 1357197 1358295 1358548 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-609 1352298 1355362 1355403 "LNAGG" 1356265 LNAGG (NIL T) -9 NIL 1356700 NIL) (-608 1351685 1351952 1352293 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-607 1348257 1349198 1349835 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-606 1347562 1348036 1348076 "LMODULE" 1348081 LMODULE (NIL T) -9 NIL 1348107 NIL) (-605 1344741 1347299 1347421 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-604 1344321 1344532 1344573 "LLINSET" 1344634 LLINSET (NIL T) -9 NIL 1344678 NIL) (-603 1343996 1344256 1344316 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-602 1343595 1343675 1343814 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-601 1342046 1342394 1342793 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-600 1341217 1341413 1341641 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-599 1334264 1340473 1340727 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-598 1333853 1334086 1334127 "LINSET" 1334132 LINSET (NIL T) -9 NIL 1334165 NIL) (-597 1332786 1333476 1333643 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-596 1331095 1331819 1331859 "LINEXP" 1332345 LINEXP (NIL T) -9 NIL 1332618 NIL) (-595 1329804 1330704 1330885 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-594 1328631 1328903 1329205 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-593 1327844 1328433 1328543 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-592 1325394 1326116 1326866 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-591 1324024 1324321 1324712 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-590 1322860 1323431 1323471 "LIECAT" 1323611 LIECAT (NIL T) -9 NIL 1323762 NIL) (-589 1322734 1322767 1322855 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-588 1316989 1322424 1322652 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-587 1309320 1316665 1316821 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-586 1305772 1306721 1307656 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-585 1304396 1305304 1305332 "LFCAT" 1305539 LFCAT (NIL) -9 NIL 1305678 NIL) (-584 1302635 1302965 1303310 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-583 1300152 1300817 1301498 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-582 1297164 1298142 1298645 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-581 1296655 1296957 1297049 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-580 1295362 1295686 1296086 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-579 1294622 1294707 1294935 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-578 1289689 1293190 1293726 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-577 1289314 1289364 1289524 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-576 1288173 1288884 1288924 "LALG" 1288985 LALG (NIL T) -9 NIL 1289043 NIL) (-575 1287956 1288033 1288168 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-574 1285873 1287224 1287475 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-573 1285702 1285732 1285773 "KVTFROM" 1285835 KVTFROM (NIL T) -9 NIL NIL NIL) (-572 1284636 1285240 1285422 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-571 1284465 1284495 1284536 "KRCFROM" 1284598 KRCFROM (NIL T) -9 NIL NIL NIL) (-570 1283567 1283764 1284059 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-569 1283396 1283426 1283467 "KONVERT" 1283529 KONVERT (NIL T) -9 NIL NIL NIL) (-568 1283225 1283255 1283296 "KOERCE" 1283358 KOERCE (NIL T) -9 NIL NIL NIL) (-567 1282795 1282888 1283020 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-566 1280848 1281742 1282114 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-565 1274031 1279046 1279100 "KDAGG" 1279476 KDAGG (NIL T T) -9 NIL 1279683 NIL) (-564 1273679 1273821 1274026 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-563 1266509 1273460 1273617 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-562 1266159 1266441 1266504 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-561 1265127 1265628 1265877 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-560 1264251 1264702 1264907 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-559 1263115 1263607 1263907 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-558 1262395 1262796 1262957 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-557 1262105 1262341 1262390 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-556 1256359 1261795 1262023 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-555 1255776 1256109 1256230 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-554 1251944 1253959 1254013 "IXAGG" 1254940 IXAGG (NIL T T) -9 NIL 1255397 NIL) (-553 1251150 1251521 1251939 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-552 1246404 1251086 1251145 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-551 1245371 1245646 1245909 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-550 1244033 1244240 1244533 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-549 1242984 1243206 1243489 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-548 1242659 1242722 1242845 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-547 1241921 1242293 1242467 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-546 1239961 1241197 1241471 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-545 1229570 1235278 1236435 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-544 1228815 1228967 1229203 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-543 1228306 1228608 1228700 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-542 1227596 1227687 1227901 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-541 1226728 1226953 1227193 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-540 1225141 1225522 1225950 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-539 1224926 1224970 1225046 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-538 1223776 1224073 1224368 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-537 1223049 1223400 1223551 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-536 1222252 1222383 1222596 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-535 1220407 1220904 1221448 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-534 1217520 1218756 1219445 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-533 1217345 1217385 1217445 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-532 1213407 1217271 1217340 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-531 1211474 1213346 1213402 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-530 1210845 1211144 1211274 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-529 1210298 1210586 1210718 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-528 1209379 1210004 1210130 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-527 1208789 1209283 1209311 "IOBCON" 1209316 IOBCON (NIL) -9 NIL 1209337 NIL) (-526 1208360 1208424 1208606 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-525 1200404 1202775 1205100 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-524 1197515 1198298 1199162 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-523 1197192 1197289 1197406 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-522 1194698 1197128 1197187 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-521 1192810 1193339 1193906 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-520 1192312 1192426 1192566 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-519 1190696 1191102 1191564 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-518 1188475 1189069 1189680 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-517 1185848 1186458 1187178 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-516 1185252 1185410 1185618 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-515 1184771 1184857 1185045 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-514 1182976 1183497 1183954 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-513 1176058 1177711 1179440 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-512 1175424 1175586 1175759 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-511 1173297 1173761 1174305 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-510 1171511 1172399 1172427 "INTDOM" 1172726 INTDOM (NIL) -9 NIL 1172931 NIL) (-509 1171064 1171266 1171506 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-508 1166962 1169369 1169423 "INTCAT" 1170219 INTCAT (NIL T) -9 NIL 1170535 NIL) (-507 1166527 1166647 1166774 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-506 1165367 1165539 1165845 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-505 1164940 1165036 1165193 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-504 1157962 1164795 1164935 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-503 1157260 1157815 1157880 "INT8" NIL INT8 (NIL) -8 NIL NIL 1157914) (-502 1156557 1157112 1157177 "INT64" NIL INT64 (NIL) -8 NIL NIL 1157211) (-501 1155854 1156409 1156474 "INT32" NIL INT32 (NIL) -8 NIL NIL 1156508) (-500 1155151 1155706 1155771 "INT16" NIL INT16 (NIL) -8 NIL NIL 1155805) (-499 1151676 1155070 1155146 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-498 1145824 1149242 1149270 "INS" 1150200 INS (NIL) -9 NIL 1150859 NIL) (-497 1143902 1144816 1145751 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-496 1142961 1143184 1143459 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-495 1142175 1142316 1142513 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-494 1141165 1141306 1141543 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-493 1140317 1140481 1140741 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-492 1139597 1139712 1139900 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-491 1138336 1138605 1138929 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-490 1137616 1137757 1137940 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-489 1137279 1137351 1137449 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-488 1134365 1135851 1136366 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-487 1133964 1134071 1134185 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-486 1133120 1133765 1133866 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-485 1131970 1132238 1132559 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-484 1131042 1131900 1131965 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-483 1130667 1130747 1130864 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-482 1129581 1130126 1130330 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-481 1125676 1126731 1127674 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-480 1124530 1124853 1124881 "INBCON" 1125394 INBCON (NIL) -9 NIL 1125660 NIL) (-479 1123984 1124249 1124525 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-478 1123477 1123779 1123870 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-477 1122933 1123242 1123348 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-476 1119033 1122825 1122928 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1117873 1118012 1118327 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-474 1116297 1116564 1116901 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-473 1114113 1116179 1116292 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-472 1109005 1114044 1114108 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-471 1108385 1108718 1108834 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-470 1103192 1107823 1108009 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-469 1102254 1103114 1103187 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-468 1101826 1101903 1101957 "IEVALAB" 1102164 IEVALAB (NIL T T) -9 NIL NIL NIL) (-467 1101581 1101661 1101821 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-466 1100654 1101501 1101576 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-465 1099796 1100574 1100649 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-464 1099199 1099730 1099791 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-463 1097691 1098215 1098266 "IDPC" 1098772 IDPC (NIL T T) -9 NIL 1099052 NIL) (-462 1097057 1097613 1097686 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-461 1096306 1096979 1097052 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-460 1095999 1096212 1096272 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-459 1093070 1093951 1094843 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-458 1086696 1087973 1089012 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-457 1085958 1086088 1086287 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-456 1085132 1085630 1085768 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-455 1083521 1083852 1084243 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-454 1078954 1083223 1083335 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-453 1076212 1076836 1077531 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-452 1074438 1074918 1075451 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-451 1072202 1074330 1074433 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-450 1068071 1072140 1072197 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-449 1061714 1067035 1067503 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-448 1061282 1061345 1061518 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-447 1060774 1060923 1060951 "HYPCAT" 1061158 HYPCAT (NIL) -9 NIL NIL NIL) (-446 1060430 1060583 1060769 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-445 1060043 1060288 1060371 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-444 1059876 1059925 1059966 "HOMOTOP" 1059971 HOMOTOP (NIL T) -9 NIL 1060004 NIL) (-443 1056450 1057824 1057865 "HOAGG" 1058840 HOAGG (NIL T) -9 NIL 1059561 NIL) (-442 1055456 1055926 1056445 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-441 1048717 1055181 1055329 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-440 1047652 1047910 1048173 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-439 1046619 1047517 1047647 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-438 1044813 1046452 1046540 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-437 1044127 1044479 1044613 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-436 1037677 1044060 1044122 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-435 1030874 1037413 1037564 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-434 1030327 1030484 1030647 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-433 1023392 1030218 1030322 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-432 1022883 1023185 1023277 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-431 1020497 1022670 1022849 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-430 1015889 1020379 1020492 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-429 1008957 1015786 1015884 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-428 1000952 1008326 1008581 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-427 999988 1000497 1000525 "GROUP" 1000728 GROUP (NIL) -9 NIL 1000862 NIL) (-426 999531 999732 999983 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-425 998203 998542 998929 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-424 997035 997392 997443 "GRMOD" 997972 GRMOD (NIL T T) -9 NIL 998140 NIL) (-423 996854 996902 997030 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-422 992977 994188 995188 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-421 991699 992023 992338 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-420 991252 991380 991521 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-419 990335 990834 990885 "GRALG" 991038 GRALG (NIL T T) -9 NIL 991130 NIL) (-418 990070 990167 990330 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-417 986785 989750 989927 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-416 986198 986261 986518 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-415 982084 982948 983473 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-414 981259 981461 981699 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-413 976262 977189 978208 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-412 976010 976067 976156 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-411 975492 975581 975746 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-410 975001 975042 975255 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-409 973802 974085 974389 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-408 967136 973492 973653 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-407 956949 961926 963030 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-406 955089 956130 956158 "GCDDOM" 956413 GCDDOM (NIL) -9 NIL 956570 NIL) (-405 954712 954869 955084 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-404 945505 947975 950363 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-403 943640 943965 944383 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-402 942581 942770 943037 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-401 941452 941659 941963 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-400 940915 941057 941205 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-399 939527 939875 940188 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-398 938072 938393 938715 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-397 935698 936054 936459 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-396 928950 930611 932189 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-395 926236 926996 927024 "FVFUN" 928180 FVFUN (NIL) -9 NIL 928900 NIL) (-394 925466 925684 925712 "FVC" 926003 FVC (NIL) -9 NIL 926186 NIL) (-393 925118 925339 925407 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-392 924742 924963 925044 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-391 923605 924226 924429 "FTEM" NIL FTEM (NIL) -8 NIL NIL NIL) (-390 921702 922385 922845 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-389 920295 920602 920994 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-388 918950 919309 919633 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-387 918253 918377 918564 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-386 917227 917493 917840 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-385 914885 915415 915897 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-384 914468 914528 914697 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-383 912832 913682 913985 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-382 911980 912114 912337 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-381 911151 911312 911539 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-380 907146 910097 910138 "FSAGG" 910508 FSAGG (NIL T) -9 NIL 910767 NIL) (-379 905500 906259 907051 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-378 903456 903752 904296 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-377 902503 902685 902985 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-376 902184 902233 902360 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-375 882492 891918 891959 "FS" 895829 FS (NIL T) -9 NIL 898107 NIL) (-374 874731 878222 882195 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-373 874265 874392 874544 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-372 868831 871958 871998 "FRNAALG" 873318 FRNAALG (NIL T) -9 NIL 873916 NIL) (-371 865572 866823 868081 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-370 865253 865302 865429 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-369 863740 864297 864591 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-368 863026 863119 863406 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-367 860860 861626 861942 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-366 859969 860412 860453 "FRETRCT" 860458 FRETRCT (NIL T) -9 NIL 860629 NIL) (-365 859342 859620 859964 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-364 856174 857632 857691 "FRAMALG" 858573 FRAMALG (NIL T T) -9 NIL 858865 NIL) (-363 854770 855321 855951 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-362 854463 854526 854633 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-361 848165 854268 854458 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-360 847858 847921 848028 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-359 840229 844737 846065 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-358 834093 837534 837562 "FPS" 838681 FPS (NIL) -9 NIL 839238 NIL) (-357 833650 833783 833947 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-356 830549 832529 832557 "FPC" 832782 FPC (NIL) -9 NIL 832924 NIL) (-355 830395 830447 830544 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-354 829157 829884 829925 "FPATMAB" 829930 FPATMAB (NIL T) -9 NIL 830082 NIL) (-353 827587 828183 828530 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-352 823486 824086 824768 "FORTRAN" NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-351 821060 821724 821752 "FORTFN" 822812 FORTFN (NIL) -9 NIL 823436 NIL) (-350 820812 820874 820902 "FORTCAT" 820961 FORTCAT (NIL) -9 NIL 821023 NIL) (-349 819017 819547 820086 "FORT" NIL FORT (NIL) -7 NIL NIL NIL) (-348 818592 818650 818823 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-347 817825 818025 818218 "FOP" NIL FOP (NIL) -7 NIL NIL NIL) (-346 816360 817223 817397 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-345 814987 815492 815520 "FNCAT" 815977 FNCAT (NIL) -9 NIL 816234 NIL) (-344 814444 814954 814982 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-343 812789 813951 813979 "FMTC" 813984 FMTC (NIL) -9 NIL 814019 NIL) (-342 811376 812738 812784 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-341 807976 809334 809375 "FMONCAT" 810592 FMONCAT (NIL T) -9 NIL 811196 NIL) (-340 805298 806046 806074 "FMFUN" 807218 FMFUN (NIL) -9 NIL 807926 NIL) (-339 802199 803246 803299 "FMCAT" 804480 FMCAT (NIL T T) -9 NIL 804972 NIL) (-338 801432 801649 801677 "FMC" 801967 FMC (NIL) -9 NIL 802149 NIL) (-337 800164 801255 801354 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-336 799292 800012 800159 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-335 797479 797931 798425 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-334 795414 795950 796528 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-333 788864 793751 794365 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-332 787388 788458 788498 "FLINEXP" 788503 FLINEXP (NIL T) -9 NIL 788596 NIL) (-331 786797 787056 787383 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-330 786012 786171 786392 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-329 782938 783986 784038 "FLALG" 785265 FLALG (NIL T T) -9 NIL 785732 NIL) (-328 782109 782270 782497 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-327 775521 779531 779572 "FLAGG" 780827 FLAGG (NIL T) -9 NIL 781472 NIL) (-326 774629 775033 775516 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-325 771278 772480 772539 "FINRALG" 773667 FINRALG (NIL T T) -9 NIL 774175 NIL) (-324 770669 770934 771273 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-323 769979 770275 770303 "FINITE" 770499 FINITE (NIL) -9 NIL 770606 NIL) (-322 761983 764543 764583 "FINAALG" 768235 FINAALG (NIL T) -9 NIL 769673 NIL) (-321 758250 759495 760618 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-320 756814 757233 757287 "FILECAT" 757971 FILECAT (NIL T T) -9 NIL 758187 NIL) (-319 756165 756639 756742 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-318 753501 755317 755345 "FIELD" 755385 FIELD (NIL) -9 NIL 755465 NIL) (-317 752526 752987 753496 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-316 750530 751476 751822 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-315 749773 749954 750173 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-314 745092 749711 749768 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-313 744754 744821 744956 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-312 744294 744336 744545 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-311 740974 741851 742628 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-310 736307 740906 740969 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-309 731035 735796 735986 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-308 725565 730316 730574 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-307 719821 725016 725227 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-306 718844 719054 719369 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-305 714373 717015 717043 "FFIELDC" 717662 FFIELDC (NIL) -9 NIL 718037 NIL) (-304 713450 713888 714368 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-303 713065 713123 713247 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-302 711209 711732 712249 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-301 706352 711008 711109 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-300 701499 706141 706248 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-299 696214 701290 701398 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-298 695668 695717 695952 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-297 674208 685219 685305 "FFCAT" 690455 FFCAT (NIL T T T) -9 NIL 691891 NIL) (-296 670448 671674 672980 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-295 665340 670379 670443 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-294 655297 659512 660694 "FEXPR" NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-293 654225 654694 654735 "FEVALAB" 654819 FEVALAB (NIL T) -9 NIL 655080 NIL) (-292 653630 653882 654220 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-291 650500 651380 651495 "FDIVCAT" 653062 FDIVCAT (NIL T T T T) -9 NIL 653498 NIL) (-290 650294 650326 650495 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-289 649601 649694 649971 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-288 648119 649085 649288 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-287 647212 647596 647798 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-286 646137 646426 646715 "FCPAK1" NIL FCPAK1 (NIL) -7 NIL NIL NIL) (-285 645259 645748 645888 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-284 632106 635935 639469 "FC" NIL FC (NIL) -8 NIL NIL NIL) (-283 623760 628356 628396 "FAXF" 630197 FAXF (NIL T) -9 NIL 630887 NIL) (-282 621676 622480 623295 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-281 616540 621198 621372 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-280 611071 613432 613484 "FAMR" 614495 FAMR (NIL T T) -9 NIL 614954 NIL) (-279 610270 610635 611066 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-278 609323 610212 610265 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-277 606960 607808 607861 "FAMONC" 608802 FAMONC (NIL T T) -9 NIL 609187 NIL) (-276 605548 606818 606955 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-275 603628 603989 604391 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-274 602905 603102 603324 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-273 594823 602352 602551 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-272 592842 593412 593998 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-271 589744 590386 591106 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-270 584901 585608 586413 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-269 584590 584653 584762 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-268 569489 583639 584065 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-267 560077 568809 569097 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-266 559571 559872 559963 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-265 559347 559537 559566 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-264 559036 559104 559217 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-263 558553 558695 558736 "EVALAB" 558906 EVALAB (NIL T) -9 NIL 559010 NIL) (-262 558181 558327 558548 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-261 555312 556845 556873 "EUCDOM" 557427 EUCDOM (NIL) -9 NIL 557776 NIL) (-260 554239 554732 555307 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-259 553932 553995 554102 "ESTOOLS2" NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-258 553725 553773 553853 "ESTOOLS1" NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-257 543803 546773 549512 "ESTOOLS" NIL ESTOOLS (NIL) -7 NIL NIL NIL) (-256 543583 543620 543701 "ESCONT1" NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-255 540654 541480 542259 "ESCONT" NIL ESCONT (NIL) -7 NIL NIL NIL) (-254 540379 540435 540535 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-253 540067 540131 540240 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-252 533850 535750 535778 "ES" 538520 ES (NIL) -9 NIL 539904 NIL) (-251 530365 531897 533689 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-250 529713 529866 530042 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-249 522784 529617 529708 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-248 522473 522536 522645 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-247 516184 519219 520652 "EQ" NIL -3676 (NIL T) -8 NIL NIL NIL) (-246 512487 513583 514676 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-245 511313 511664 511970 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-244 510286 510955 510983 "ENTIRER" 510988 ENTIRER (NIL) -9 NIL 511032 NIL) (-243 506983 508716 509065 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-242 506087 506298 506352 "ELTAGG" 506732 ELTAGG (NIL T T) -9 NIL 506943 NIL) (-241 505867 505941 506082 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-240 505625 505660 505714 "ELTAB" 505798 ELTAB (NIL T T) -9 NIL 505850 NIL) (-239 504876 505046 505245 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-238 504600 504674 504702 "ELEMFUN" 504807 ELEMFUN (NIL) -9 NIL NIL NIL) (-237 504500 504527 504595 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-236 499052 502547 502588 "ELAGG" 503525 ELAGG (NIL T) -9 NIL 503985 NIL) (-235 497850 498388 499047 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-234 497268 497435 497591 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-233 496181 496500 496779 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-232 489574 491572 492399 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-231 483553 485549 486359 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-230 481367 481773 482244 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-229 472367 474280 475821 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-228 471481 471981 472130 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-227 470191 470865 470905 "DVARCAT" 471188 DVARCAT (NIL T) -9 NIL 471328 NIL) (-226 469610 469874 470186 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-225 461735 469478 469605 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-224 460085 460876 460917 "DSEXT" 461280 DSEXT (NIL T) -9 NIL 461574 NIL) (-223 458890 459414 460080 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-222 458614 458679 458777 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-221 454765 455981 457112 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-220 450411 451766 452830 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-219 449086 449447 449833 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-218 448772 448831 448949 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-217 447747 448045 448335 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-216 447332 447407 447557 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-215 439745 441857 443972 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-214 435262 436281 437360 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-213 431863 433932 433973 "DQAGG" 434602 DQAGG (NIL T) -9 NIL 434875 NIL) (-212 418443 426024 426106 "DPOLCAT" 427943 DPOLCAT (NIL T T T T) -9 NIL 428486 NIL) (-211 414851 416499 418438 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-210 407899 414749 414846 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-209 400856 407728 407894 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-208 400450 400709 400798 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-207 399864 400312 400392 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-206 399150 399475 399626 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-205 392347 398886 399037 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-204 390133 391419 391459 "DMEXT" 391464 DMEXT (NIL T) -9 NIL 391639 NIL) (-203 389789 389851 389995 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-202 383114 389274 389464 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-201 379786 381943 381984 "DLAGG" 382534 DLAGG (NIL T) -9 NIL 382763 NIL) (-200 378225 379034 379062 "DIVRING" 379154 DIVRING (NIL) -9 NIL 379237 NIL) (-199 377676 377920 378220 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-198 376104 376521 376927 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-197 375141 375362 375627 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-196 368711 375073 375136 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-195 357101 363465 363518 "DIRPCAT" 363774 DIRPCAT (NIL NIL T) -9 NIL 364647 NIL) (-194 355115 355883 356764 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-193 354562 354728 354914 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-192 351114 353454 353495 "DIOPS" 353927 DIOPS (NIL T) -9 NIL 354153 NIL) (-191 350774 350918 351109 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-190 349690 350457 350485 "DIFRING" 350490 DIFRING (NIL) -9 NIL 350511 NIL) (-189 349338 349436 349464 "DIFFSPC" 349583 DIFFSPC (NIL) -9 NIL 349658 NIL) (-188 349079 349181 349333 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348025 348619 348659 "DIFFMOD" 348664 DIFFMOD (NIL T) -9 NIL 348761 NIL) (-186 347721 347778 347819 "DIFFDOM" 347940 DIFFDOM (NIL T) -9 NIL 348008 NIL) (-185 347602 347632 347716 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345351 346810 346850 "DIFEXT" 346855 DIFEXT (NIL T) -9 NIL 347007 NIL) (-183 342518 344858 344899 "DIAGG" 344904 DIAGG (NIL T) -9 NIL 344924 NIL) (-182 342074 342264 342513 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337286 341264 341541 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 333744 334797 335807 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328357 332898 333225 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 326923 327215 327590 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324107 325295 325691 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 321827 323938 324027 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321210 321355 321537 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 318528 319252 320052 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 316637 317095 317657 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 316019 316352 316467 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309280 315744 315892 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307200 307710 308214 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 306839 306888 307039 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 306098 306660 306751 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304122 304564 304924 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303414 303703 303849 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 302865 303011 303163 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300227 301020 301747 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 299666 299812 299983 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 297738 298049 298416 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297295 297550 297651 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 296508 296891 296919 "CTORCAT" 297100 CTORCAT (NIL) -9 NIL 297212 NIL) (-159 296211 296345 296503 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 295704 295961 296069 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295120 295551 295624 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 294579 294696 294849 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 290973 291729 292484 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 290463 290766 290858 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 289682 289891 290119 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289186 289291 289495 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 288939 288973 289079 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 285878 286640 287358 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 285397 285539 285678 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 281354 283860 284352 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281228 281255 281283 "CONDUIT" 281320 CONDUIT (NIL) -9 NIL NIL NIL) (-146 280195 280864 280892 "COMRING" 280897 COMRING (NIL) -9 NIL 280947 NIL) (-145 279360 279727 279905 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 279056 279097 279225 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 278749 278812 278919 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267578 278699 278744 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 267039 267178 267338 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 266792 266833 266931 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 248131 260411 260451 "COMPCAT" 261454 COMPCAT (NIL T) -9 NIL 262798 NIL) (-138 240677 244188 247775 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240436 240470 240572 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240266 240305 240363 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239846 240125 240200 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239423 239664 239751 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 238618 238866 238894 "COMBOPC" 239232 COMBOPC (NIL) -9 NIL 239407 NIL) (-132 237682 237934 238176 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 234614 235298 235921 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233494 233945 234180 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232985 233287 233379 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 232672 232725 232850 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 232142 232451 232550 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 228662 229732 230812 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 227021 227942 228180 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 223139 225147 225188 "CLAGG" 226114 CLAGG (NIL T) -9 NIL 226647 NIL) (-123 222032 222559 223134 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 221661 221752 221892 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 219598 220105 220653 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218647 219316 219344 "CHARZ" 219349 CHARZ (NIL) -9 NIL 219363 NIL) (-119 218441 218487 218565 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 217368 218069 218097 "CHARNZ" 218158 CHARNZ (NIL) -9 NIL 218206 NIL) (-117 214846 215943 216466 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214554 214633 214661 "CFCAT" 214772 CFCAT (NIL) -9 NIL NIL NIL) (-115 213897 214026 214208 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 209886 213310 213590 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 209264 209451 209628 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 208792 209211 209259 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 208264 208573 208671 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 207755 208057 208149 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 207004 207164 207385 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 203104 204361 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T) ((-23) . T) ((-47 |#1| (-687)) . T) ((-25) . T) ((-38 (-343 (-478))) |has| |#1| (-38 (-343 (-478)))) ((-38 |#1|) |has| |#1| (-144)) ((-38 $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385)) (|has| |#1| (-308))) ((-72) . T) ((-80 (-343 (-478)) (-343 (-478))) |has| |#1| (-38 (-343 (-478)))) ((-80 |#1| |#1|) . T) ((-80 $ $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385)) (|has| |#1| (-308)) (|has| |#1| (-144))) ((-102) . T) ((-116) |has| |#1| (-116)) ((-118) |has| |#1| (-118)) ((-550 (-343 (-478))) OR (|has| |#1| (-943 (-343 (-478)))) (|has| |#1| (-38 (-343 (-478))))) ((-550 (-478)) . T) ((-550 (-986)) . T) ((-550 |#1|) . T) ((-550 $) OR (|has| |#1| (-814)) (|has| |#1| (-489)) (|has| |#1| (-385)) (|has| |#1| (-308))) ((-547 (-765)) . 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2425781 2426074 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1077 2411358 2419199 2419461 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1076 2410637 2410776 2410993 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1075 2410321 2410386 2410497 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1074 2401108 2410033 2410158 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1073 2399844 2400140 2400493 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1072 2399252 2399329 2399519 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1071 2381468 2398751 2398992 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1070 2381068 2381339 2381408 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1069 2380404 2380685 2380825 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1068 2375006 2376265 2377218 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1067 2374538 2374638 2374802 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1066 2369649 2370931 2372078 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1065 2364107 2365578 2366889 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1064 2357022 2359086 2360877 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1063 2349852 2356934 2357017 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1062 2344546 2349566 2349681 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1061 2344133 2344216 2344360 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1060 2343284 2343485 2343720 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1059 2343024 2343082 2343175 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1058 2335762 2341229 2341835 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1057 2334938 2335143 2335374 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1056 2334183 2334554 2334701 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1055 2333683 2333925 2333955 "STEP" 2334049 STEP (NIL) -9 NIL 2334120 NIL) (-1054 2326786 2333601 2333678 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1053 2321013 2325596 2325639 "STAGG" 2326066 STAGG (NIL T) -9 NIL 2326240 NIL) (-1052 2319392 2320140 2321008 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1051 2317549 2319219 2319311 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1050 2316872 2317380 2317410 "SRING" 2317415 SRING (NIL) -9 NIL 2317435 NIL) (-1049 2309493 2315410 2315849 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1048 2303267 2304706 2306210 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1047 2295704 2300615 2300645 "SRAGG" 2301944 SRAGG (NIL) -9 NIL 2302548 NIL) (-1046 2295001 2295321 2295699 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1045 2289120 2294323 2294746 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1044 2283333 2286502 2287224 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1043 2279762 2280581 2281218 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1042 2278737 2279042 2279072 "SPFCAT" 2279516 SPFCAT (NIL) -9 NIL NIL NIL) (-1041 2277674 2277926 2278190 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1040 2268450 2270722 2270752 "SPADXPT" 2275387 SPADXPT (NIL) -9 NIL 2277509 NIL) (-1039 2268252 2268298 2268367 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1038 2265910 2268216 2268247 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1037 2257596 2259685 2259727 "SPACEC" 2264042 SPACEC (NIL T) -9 NIL 2265847 NIL) (-1036 2255425 2257543 2257591 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1035 2254358 2254547 2254836 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1034 2252762 2253095 2253506 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1033 2252027 2252261 2252522 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1032 2248207 2249167 2250162 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1031 2244565 2245264 2245993 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1030 2238363 2243917 2244013 "SNTSCAT" 2244018 SNTSCAT (NIL T T T T) -9 NIL 2244088 NIL) (-1029 2232248 2237004 2237394 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1028 2226084 2232167 2232243 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1027 2224516 2224847 2225245 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1026 2216212 2221126 2221228 "SMATCAT" 2222571 SMATCAT (NIL NIL T T T) -9 NIL 2223119 NIL) (-1025 2214053 2215037 2216207 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1024 2211657 2213271 2213314 "SKAGG" 2213575 SKAGG (NIL T) -9 NIL 2213709 NIL) (-1023 2207519 2211308 2211477 "SINT" NIL SINT (NIL) -8 NIL NIL 2211629) (-1022 2207329 2207373 2207439 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1021 2206404 2206636 2206904 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1020 2205408 2205570 2205846 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1019 2204754 2205094 2205217 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1018 2204100 2204407 2204547 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1017 2202211 2202703 2203209 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1016 2195750 2202130 2202206 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1015 2195265 2195502 2195532 "SGROUP" 2195625 SGROUP (NIL) -9 NIL 2195687 NIL) (-1014 2195155 2195187 2195260 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1013 2192578 2193347 2194069 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1012 2186475 2192029 2192125 "SFRTCAT" 2192130 SFRTCAT (NIL T T T T) -9 NIL 2192168 NIL) (-1011 2180867 2181980 2183107 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1010 2175043 2176204 2177368 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1009 2174015 2174917 2175038 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1008 2169635 2170530 2170625 "SEXCAT" 2173238 SEXCAT (NIL T T T T T) -9 NIL 2173789 NIL) (-1007 2168608 2169562 2169630 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1006 2166999 2167584 2167886 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1005 2166534 2166719 2166749 "SETCAT" 2166866 SETCAT (NIL) -9 NIL 2166950 NIL) (-1004 2166366 2166430 2166529 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1003 2162601 2164832 2164875 "SETAGG" 2165743 SETAGG (NIL T) -9 NIL 2166081 NIL) (-1002 2162207 2162359 2162596 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1001 2159161 2162154 2162202 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1000 2158627 2158937 2159037 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-999 2157761 2158127 2158186 "SEGXCAT" 2158469 SEGXCAT (NIL T T) -9 NIL 2158588 NIL) (-998 2156696 2156964 2157005 "SEGCAT" 2157519 SEGCAT (NIL T) -9 NIL 2157740 NIL) (-997 2156385 2156448 2156557 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-996 2155469 2155931 2156134 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-995 2155050 2155329 2155403 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-994 2154428 2154561 2154760 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-993 2153498 2154245 2154423 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-992 2152753 2153448 2153493 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-991 2144354 2152624 2152748 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-990 2143214 2143504 2143821 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-989 2142520 2142732 2142920 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-988 2141870 2142027 2142203 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-987 2141455 2141686 2141714 "SASTCAT" 2141719 SASTCAT (NIL) -9 NIL 2141732 NIL) (-986 2140922 2141347 2141421 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-985 2140525 2140566 2140737 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-984 2140156 2140197 2140354 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-983 2133301 2140073 2140151 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-982 2131951 2132280 2132676 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-981 2130712 2131073 2131373 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-980 2130336 2130557 2130638 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-979 2127796 2128430 2128883 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-978 2127635 2127668 2127736 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-977 2127126 2127429 2127520 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-976 2122754 2123622 2124533 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-975 2111585 2117139 2117233 "RSETCAT" 2121289 RSETCAT (NIL T T T T) -9 NIL 2122377 NIL) (-974 2110123 2110765 2111580 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-973 2103897 2105342 2106849 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-972 2101791 2102348 2102420 "RRCC" 2103493 RRCC (NIL T T) -9 NIL 2103834 NIL) (-971 2101316 2101515 2101786 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-970 2100786 2101096 2101194 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-969 2073429 2084077 2084141 "RPOLCAT" 2094615 RPOLCAT (NIL T T T) -9 NIL 2097760 NIL) (-968 2067528 2070351 2073424 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-967 2063759 2067276 2067414 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-966 2062087 2062826 2063082 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-965 2057818 2060568 2060596 "RNS" 2060858 RNS (NIL) -9 NIL 2061110 NIL) (-964 2056729 2057214 2057745 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-963 2055851 2056252 2056451 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-962 2055151 2055651 2055679 "RNG" 2055684 RNG (NIL) -9 NIL 2055705 NIL) (-961 2054456 2054930 2054970 "RMODULE" 2054975 RMODULE (NIL T) -9 NIL 2055001 NIL) (-960 2053395 2053501 2053831 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-959 2050273 2052985 2053278 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-958 2042965 2045426 2045538 "RMATCAT" 2048843 RMATCAT (NIL NIL NIL T T T) -9 NIL 2049820 NIL) (-957 2042482 2042661 2042960 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-956 2042062 2042273 2042314 "RLINSET" 2042375 RLINSET (NIL T) -9 NIL 2042419 NIL) (-955 2041707 2041788 2041914 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-954 2040642 2041311 2041339 "RING" 2041394 RING (NIL) -9 NIL 2041485 NIL) (-953 2040487 2040543 2040637 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-952 2039544 2039810 2040065 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-951 2030531 2039172 2039373 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-950 2029799 2030279 2030318 "RGBCSPC" 2030375 RGBCSPC (NIL T) -9 NIL 2030426 NIL) (-949 2028876 2029331 2029370 "RGBCMDL" 2029598 RGBCMDL (NIL T) -9 NIL 2029712 NIL) (-948 2028588 2028657 2028758 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-947 2028351 2028392 2028487 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-946 2026775 2027205 2027585 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-945 2024362 2025030 2025698 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-944 2023912 2024010 2024170 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-943 2023534 2023632 2023673 "RETRACT" 2023804 RETRACT (NIL T) -9 NIL 2023891 NIL) (-942 2023414 2023445 2023529 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-941 2023017 2023288 2023355 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-940 2021561 2022388 2022585 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-939 2021252 2021313 2021409 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-938 2020995 2021036 2021141 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-937 2020730 2020771 2020880 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-936 2015800 2017252 2018467 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-935 2012899 2013657 2014465 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-934 2010868 2011490 2012090 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-933 2003502 2009419 2009855 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-932 2002439 2002875 2003122 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-931 2001924 2002039 2002204 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-930 1997581 2001327 2001548 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-929 1996813 1997012 1997225 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-928 1994103 1994941 1995823 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-927 1990685 1991721 1992780 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-926 1990521 1990574 1990602 "REAL" 1990607 REAL (NIL) -9 NIL 1990642 NIL) (-925 1990012 1990315 1990406 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-924 1989492 1989570 1989775 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-923 1988725 1988917 1989128 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-922 1987613 1987910 1988277 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-921 1985880 1986350 1986883 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-920 1984802 1985079 1985466 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-919 1983629 1983938 1984357 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-918 1977068 1980515 1980543 "RCFIELD" 1981820 RCFIELD (NIL) -9 NIL 1982550 NIL) (-917 1975694 1976304 1976995 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-916 1971906 1973798 1973839 "RCAGG" 1974906 RCAGG (NIL T) -9 NIL 1975367 NIL) (-915 1971633 1971743 1971901 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-914 1971078 1971207 1971368 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-913 1970695 1970774 1970893 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-912 1970110 1970260 1970410 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-911 1969892 1969942 1970013 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-910 1962398 1969010 1969318 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-909 1952164 1962265 1962393 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-908 1951798 1951891 1951919 "RADCAT" 1952076 RADCAT (NIL) -9 NIL NIL NIL) (-907 1951636 1951696 1951793 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-906 1949736 1951467 1951556 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-905 1949417 1949466 1949593 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-904 1941795 1945814 1945854 "QUATCAT" 1946632 QUATCAT (NIL T) -9 NIL 1947396 NIL) (-903 1939053 1940331 1941701 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-902 1934957 1939003 1939048 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-901 1932356 1934023 1934064 "QUAGG" 1934439 QUAGG (NIL T) -9 NIL 1934613 NIL) (-900 1931959 1932230 1932297 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-899 1930997 1931595 1931758 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-898 1930678 1930727 1930854 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-897 1920391 1926498 1926538 "QFCAT" 1927196 QFCAT (NIL T) -9 NIL 1928189 NIL) (-896 1917291 1918726 1920297 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-895 1916837 1916971 1917101 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-894 1911033 1912194 1913356 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-893 1910452 1910632 1910864 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-892 1908274 1908802 1909225 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-891 1907173 1907415 1907732 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-890 1905534 1905732 1906085 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-889 1901290 1902506 1902547 "PTRANFN" 1904431 PTRANFN (NIL T) -9 NIL NIL NIL) (-888 1899937 1900282 1900603 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-887 1899630 1899693 1899800 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-886 1893715 1898438 1898478 "PTCAT" 1898770 PTCAT (NIL T) -9 NIL 1898923 NIL) (-885 1893408 1893449 1893573 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-884 1892287 1892603 1892937 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-883 1881166 1883727 1886036 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-882 1874085 1876981 1877075 "PSETCAT" 1880049 PSETCAT (NIL T T T T) -9 NIL 1880856 NIL) (-881 1872535 1873269 1874080 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-880 1871863 1872055 1872083 "PSCURVE" 1872348 PSCURVE (NIL) -9 NIL 1872512 NIL) (-879 1867553 1869311 1869375 "PSCAT" 1870210 PSCAT (NIL T T T) -9 NIL 1870449 NIL) (-878 1866867 1867149 1867548 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-877 1865297 1866179 1866442 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-876 1864788 1865091 1865182 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-875 1855808 1858230 1860418 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-874 1853563 1855140 1855180 "PRQAGG" 1855363 PRQAGG (NIL T) -9 NIL 1855464 NIL) (-873 1852748 1853194 1853222 "PROPLOG" 1853361 PROPLOG (NIL) -9 NIL 1853475 NIL) (-872 1852423 1852486 1852609 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-871 1851859 1851998 1852170 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-870 1850107 1850870 1851167 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-869 1849660 1849791 1849919 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-868 1844316 1848600 1849420 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-867 1844145 1844183 1844242 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-866 1843584 1843724 1843875 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-865 1842052 1842471 1842937 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-864 1841772 1841832 1841860 "PRIMCAT" 1841983 PRIMCAT (NIL) -9 NIL NIL NIL) (-863 1840943 1841139 1841367 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-862 1836821 1840893 1840938 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-861 1836520 1836582 1836693 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-860 1833720 1836169 1836402 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-859 1833177 1833332 1833360 "PPCURVE" 1833563 PPCURVE (NIL) -9 NIL 1833697 NIL) (-858 1832790 1833035 1833118 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-857 1830546 1830967 1831559 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-856 1829989 1830053 1830286 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-855 1826709 1827195 1827806 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-854 1812391 1818455 1818519 "POLYCAT" 1822004 POLYCAT (NIL T T T) -9 NIL 1823881 NIL) (-853 1807901 1810048 1812386 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-852 1807558 1807632 1807751 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-851 1807251 1807314 1807421 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-850 1800678 1806984 1807143 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-849 1799565 1799828 1800104 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-848 1798169 1798482 1798812 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-847 1793331 1798119 1798164 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-846 1791819 1792230 1792605 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-845 1790576 1790885 1791281 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-844 1790247 1790331 1790448 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-843 1789826 1789901 1790075 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-842 1789312 1789408 1789568 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-841 1788784 1788904 1789058 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-840 1787679 1787897 1788274 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-839 1787290 1787375 1787527 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-838 1786841 1786923 1787104 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-837 1786533 1786614 1786727 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-836 1786046 1786121 1786329 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-835 1785394 1785522 1785724 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-834 1784756 1784890 1785053 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-833 1784060 1784242 1784423 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-832 1783786 1783859 1783952 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-831 1780397 1781567 1782467 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-830 1779490 1779688 1779920 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-829 1775113 1776474 1777595 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-828 1755034 1759921 1764768 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-827 1754774 1754827 1754930 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-826 1754215 1754349 1754529 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-825 1752312 1753471 1753499 "PID" 1753696 PID (NIL) -9 NIL 1753823 NIL) (-824 1752100 1752143 1752218 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-823 1751287 1751947 1752034 "PI" NIL PI (NIL) -8 NIL NIL 1752074) (-822 1750739 1750890 1751066 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-821 1747067 1748025 1748930 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-820 1745431 1745720 1746086 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-819 1744873 1744988 1745149 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-818 1741478 1743742 1744095 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-817 1740084 1740364 1740689 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-816 1738849 1739103 1739451 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-815 1737559 1737786 1738138 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-814 1734657 1736155 1736183 "PFECAT" 1736776 PFECAT (NIL) -9 NIL 1737153 NIL) (-813 1734280 1734445 1734652 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-812 1733104 1733386 1733687 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-811 1731286 1731673 1732103 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-810 1727320 1731212 1731281 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-809 1723223 1724370 1725237 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-808 1721167 1722256 1722297 "PERMCAT" 1722696 PERMCAT (NIL T) -9 NIL 1722993 NIL) (-807 1720863 1720910 1721033 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-806 1717312 1718993 1719638 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-805 1714777 1717067 1717188 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-804 1713658 1713921 1713962 "PDSPC" 1714495 PDSPC (NIL T) -9 NIL 1714740 NIL) (-803 1713025 1713291 1713653 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-802 1711748 1712679 1712720 "PDRING" 1712725 PDRING (NIL T) -9 NIL 1712752 NIL) (-801 1710501 1711259 1711312 "PDMOD" 1711317 PDMOD (NIL T T) -9 NIL 1711420 NIL) (-800 1709594 1709806 1710055 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-799 1709211 1709278 1709332 "PDDOM" 1709497 PDDOM (NIL T T) -9 NIL 1709577 NIL) (-798 1709063 1709099 1709206 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-797 1708849 1708888 1708977 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-796 1707171 1707924 1708219 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-795 1706860 1706923 1707032 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-794 1704998 1705428 1705879 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-793 1698626 1700455 1701739 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-792 1698257 1698330 1698462 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-791 1695959 1696639 1697120 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-790 1694163 1694591 1694994 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-789 1693621 1693869 1693910 "PATMAB" 1694017 PATMAB (NIL T) -9 NIL 1694100 NIL) (-788 1692268 1692672 1692929 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-787 1691806 1691937 1691978 "PATAB" 1691983 PATAB (NIL T) -9 NIL 1692155 NIL) (-786 1690349 1690786 1691209 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-785 1690027 1690102 1690204 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-784 1689716 1689779 1689888 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-783 1689521 1689567 1689634 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-782 1689199 1689274 1689376 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-781 1688888 1688951 1689060 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-780 1688579 1688649 1688746 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-779 1688268 1688331 1688440 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-778 1687429 1687808 1687987 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-777 1687036 1687134 1687253 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-776 1686004 1686429 1686648 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-775 1684669 1685323 1685683 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-774 1677823 1684073 1684267 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-773 1670308 1677321 1677505 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-772 1667121 1668974 1669014 "PADICCT" 1669595 PADICCT (NIL NIL) -9 NIL 1669877 NIL) (-771 1665175 1667071 1667116 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-770 1664337 1664547 1664813 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-769 1663679 1663822 1664026 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-768 1662124 1663087 1663365 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-767 1661649 1661907 1662004 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-766 1660708 1661386 1661558 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-765 1651130 1653999 1656198 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-764 1650524 1650836 1650962 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-763 1649807 1650000 1650028 "OUTBCON" 1650344 OUTBCON (NIL) -9 NIL 1650508 NIL) (-762 1649515 1649645 1649802 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-761 1648896 1649041 1649202 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-760 1648268 1648694 1648783 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-759 1647695 1648110 1648138 "OSGROUP" 1648143 OSGROUP (NIL) -9 NIL 1648165 NIL) (-758 1646659 1646920 1647205 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-757 1643992 1646534 1646654 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-756 1641197 1643743 1643869 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-755 1639215 1639743 1640303 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-754 1632645 1635123 1635163 "OREPCAT" 1637484 OREPCAT (NIL T) -9 NIL 1638586 NIL) (-753 1630671 1631605 1632640 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-752 1629880 1630151 1630179 "ORDTYPE" 1630484 ORDTYPE (NIL) -9 NIL 1630642 NIL) (-751 1629414 1629625 1629875 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-750 1628876 1629252 1629409 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-749 1628382 1628745 1628773 "ORDSET" 1628778 ORDSET (NIL) -9 NIL 1628800 NIL) (-748 1627048 1628008 1628036 "ORDRING" 1628041 ORDRING (NIL) -9 NIL 1628069 NIL) (-747 1626308 1626865 1626893 "ORDMON" 1626898 ORDMON (NIL) -9 NIL 1626919 NIL) (-746 1625612 1625774 1625966 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-745 1624835 1625343 1625371 "ORDFIN" 1625436 ORDFIN (NIL) -9 NIL 1625510 NIL) (-744 1624229 1624368 1624554 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-743 1621003 1623197 1623603 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-742 1620410 1620765 1620870 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-741 1620218 1620263 1620329 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-740 1619531 1619807 1619848 "OPERCAT" 1620059 OPERCAT (NIL T) -9 NIL 1620155 NIL) (-739 1619343 1619410 1619526 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-738 1616773 1618145 1618641 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-737 1616194 1616321 1616495 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-736 1613194 1615333 1615699 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-735 1609837 1612636 1612676 "OMSAGG" 1612737 OMSAGG (NIL T) -9 NIL 1612801 NIL) (-734 1608313 1609508 1609676 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-733 1606610 1607789 1607817 "OINTDOM" 1607822 OINTDOM (NIL) -9 NIL 1607843 NIL) (-732 1604040 1605612 1605941 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-731 1603294 1603990 1604035 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-730 1600560 1603135 1603289 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-729 1592161 1600431 1600555 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-728 1585671 1592052 1592156 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-727 1584643 1584880 1585153 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-726 1582277 1582947 1583651 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-725 1578054 1579014 1580037 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-724 1577562 1577650 1577844 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-723 1575011 1575593 1576266 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-722 1572406 1572914 1573510 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-721 1569403 1569942 1570588 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-720 1568758 1568866 1569124 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-719 1567916 1568041 1568262 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-718 1564200 1564996 1565909 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-717 1563640 1563735 1563957 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-716 1563321 1563370 1563497 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-715 1559988 1563120 1563239 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-714 1559191 1559782 1559810 "OCAMON" 1559815 OCAMON (NIL) -9 NIL 1559836 NIL) (-713 1553494 1556243 1556283 "OC" 1557378 OC (NIL T) -9 NIL 1558234 NIL) (-712 1551502 1552426 1553400 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-711 1550930 1551348 1551376 "OASGP" 1551381 OASGP (NIL) -9 NIL 1551401 NIL) (-710 1550036 1550654 1550682 "OAMONS" 1550722 OAMONS (NIL) -9 NIL 1550765 NIL) (-709 1549224 1549774 1549802 "OAMON" 1549859 OAMON (NIL) -9 NIL 1549910 NIL) (-708 1549120 1549152 1549219 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-707 1547914 1548657 1548685 "OAGROUP" 1548831 OAGROUP (NIL) -9 NIL 1548923 NIL) (-706 1547705 1547792 1547909 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-705 1547445 1547501 1547589 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-704 1542507 1544070 1545597 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-703 1539202 1540236 1541271 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-702 1538312 1538545 1538763 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-701 1527170 1530201 1532649 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-700 1521069 1526623 1526717 "NTSCAT" 1526722 NTSCAT (NIL T T T T) -9 NIL 1526760 NIL) (-699 1520410 1520589 1520782 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-698 1520103 1520166 1520273 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-697 1507834 1517723 1518533 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-696 1496907 1507699 1507829 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-695 1495627 1495952 1496309 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-694 1494463 1494727 1495085 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-693 1493630 1493763 1493979 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-692 1491948 1492267 1492673 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-691 1491661 1491695 1491819 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-690 1491480 1491515 1491584 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-689 1491256 1491446 1491475 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-688 1490820 1490887 1491064 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-687 1489138 1490183 1490438 "NNI" NIL NNI (NIL) -8 NIL NIL 1490785) (-686 1487866 1488203 1488567 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-685 1486843 1487095 1487397 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-684 1485933 1486495 1486536 "NETCLT" 1486707 NETCLT (NIL T) -9 NIL 1486788 NIL) (-683 1484837 1485104 1485385 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-682 1484636 1484679 1484754 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-681 1483167 1483555 1483975 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-680 1481843 1482778 1482806 "NASRING" 1482916 NASRING (NIL) -9 NIL 1482996 NIL) (-679 1481688 1481744 1481838 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-678 1480660 1481307 1481335 "NARNG" 1481452 NARNG (NIL) -9 NIL 1481543 NIL) (-677 1480436 1480521 1480655 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-676 1479245 1479968 1480008 "NAALG" 1480087 NAALG (NIL T) -9 NIL 1480148 NIL) (-675 1479115 1479150 1479240 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-674 1474094 1475279 1476465 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-673 1473489 1473576 1473760 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-672 1465590 1470019 1470071 "MTSCAT" 1471131 MTSCAT (NIL T T) -9 NIL 1471645 NIL) (-671 1465356 1465416 1465508 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-670 1465182 1465221 1465281 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-669 1462056 1464745 1464786 "MSETAGG" 1464791 MSETAGG (NIL T) -9 NIL 1464825 NIL) (-668 1458193 1461102 1461420 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-667 1454531 1456290 1457030 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-666 1454168 1454241 1454370 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-665 1453821 1453862 1454006 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-664 1451686 1452023 1452454 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-663 1445148 1451585 1451681 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-662 1444673 1444714 1444922 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-661 1444232 1444281 1444464 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-660 1443506 1443599 1443818 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-659 1442123 1442484 1442874 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-658 1441275 1441654 1441682 "MONOID" 1441900 MONOID (NIL) -9 NIL 1442046 NIL) (-657 1440942 1441090 1441270 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-656 1429968 1436776 1436835 "MONOGEN" 1437509 MONOGEN (NIL T T) -9 NIL 1437965 NIL) (-655 1427980 1428866 1429849 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-654 1426704 1427248 1427276 "MONADWU" 1427667 MONADWU (NIL) -9 NIL 1427904 NIL) (-653 1426252 1426452 1426699 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-652 1425541 1425842 1425870 "MONAD" 1426077 MONAD (NIL) -9 NIL 1426189 NIL) (-651 1425308 1425404 1425536 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-650 1423698 1424468 1424747 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-649 1422875 1423371 1423411 "MODULE" 1423416 MODULE (NIL T) -9 NIL 1423454 NIL) (-648 1422554 1422680 1422870 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-647 1420329 1421151 1421465 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-646 1417572 1418925 1419438 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-645 1416206 1416780 1417056 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-644 1405489 1414871 1415284 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-643 1402509 1404489 1404758 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-642 1401593 1401960 1402150 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-641 1401162 1401211 1401390 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-640 1399075 1400009 1400049 "MLO" 1400466 MLO (NIL T) -9 NIL 1400706 NIL) (-639 1396956 1397483 1398078 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-638 1396424 1396520 1396674 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-637 1396094 1396170 1396293 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-636 1395306 1395492 1395720 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-635 1394799 1394915 1395071 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-634 1394171 1394285 1394470 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-633 1393198 1393471 1393748 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-632 1392631 1392719 1392890 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-631 1389812 1390682 1391552 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-630 1388479 1388827 1389180 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-629 1385148 1387615 1387656 "MDAGG" 1387913 MDAGG (NIL T) -9 NIL 1388058 NIL) (-628 1384422 1384586 1384786 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-627 1383500 1383786 1384016 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-626 1381597 1382174 1382735 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-625 1377367 1381187 1381434 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-624 1373714 1374485 1375219 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-623 1372467 1372636 1372965 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-622 1361992 1365581 1365657 "MATCAT" 1370645 MATCAT (NIL T T T) -9 NIL 1372113 NIL) (-621 1359273 1360579 1361987 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-620 1357674 1358034 1358418 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-619 1356807 1357004 1357226 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-618 1355558 1355884 1356211 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-617 1354720 1355122 1355298 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-616 1354389 1354453 1354576 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-615 1354037 1354110 1354224 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-614 1353572 1353687 1353829 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-613 1351781 1352549 1352850 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-612 1351275 1351577 1351667 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-611 1344796 1349602 1349643 "LZSTAGG" 1350420 LZSTAGG (NIL T) -9 NIL 1350710 NIL) (-610 1341915 1343349 1344791 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-609 1339302 1340268 1340751 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-608 1338883 1339162 1339236 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-607 1331111 1338744 1338878 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-606 1330474 1330619 1330847 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-605 1327958 1328656 1329368 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-604 1326070 1326393 1326841 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-603 1319251 1325169 1325210 "LSAGG" 1325272 LSAGG (NIL T) -9 NIL 1325350 NIL) (-602 1316945 1318044 1319246 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-601 1314457 1316294 1316543 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-600 1314124 1314215 1314338 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-599 1313807 1313886 1313914 "LOGIC" 1314025 LOGIC (NIL) -9 NIL 1314107 NIL) (-598 1313702 1313731 1313802 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-597 1313021 1313179 1313372 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-596 1311806 1312055 1312406 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-595 1307718 1310453 1310493 "LODOCAT" 1310925 LODOCAT (NIL T) -9 NIL 1311136 NIL) (-594 1307511 1307587 1307713 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-593 1304575 1307388 1307506 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-592 1301737 1304525 1304570 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-591 1298888 1301667 1301732 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-590 1297941 1298116 1298418 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-589 1296105 1297203 1297456 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-588 1291212 1294276 1294317 "LNAGG" 1295179 LNAGG (NIL T) -9 NIL 1295614 NIL) (-587 1290599 1290866 1291207 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-586 1287171 1288112 1288749 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-585 1286476 1286950 1286990 "LMODULE" 1286995 LMODULE (NIL T) -9 NIL 1287021 NIL) (-584 1283655 1286213 1286335 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-583 1283235 1283446 1283487 "LLINSET" 1283548 LLINSET (NIL T) -9 NIL 1283592 NIL) (-582 1282911 1283171 1283230 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-581 1282510 1282590 1282729 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-580 1280961 1281309 1281708 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-579 1280132 1280328 1280556 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-578 1273179 1279388 1279642 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-577 1272768 1273001 1273042 "LINSET" 1273047 LINSET (NIL T) -9 NIL 1273080 NIL) (-576 1271701 1272391 1272558 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-575 1270010 1270734 1270774 "LINEXP" 1271260 LINEXP (NIL T) -9 NIL 1271533 NIL) (-574 1268719 1269619 1269800 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-573 1267546 1267818 1268120 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-572 1266759 1267348 1267458 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-571 1264309 1265031 1265781 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-570 1262939 1263236 1263627 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-569 1261775 1262346 1262386 "LIECAT" 1262526 LIECAT (NIL T) -9 NIL 1262677 NIL) (-568 1261649 1261682 1261770 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-567 1255937 1261339 1261567 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-566 1248286 1255613 1255769 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-565 1244738 1245687 1246622 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-564 1243363 1244270 1244298 "LFCAT" 1244505 LFCAT (NIL) -9 NIL 1244644 NIL) (-563 1241605 1241934 1242278 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-562 1239122 1239787 1240468 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-561 1236134 1237112 1237615 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-560 1235626 1235928 1236019 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-559 1234333 1234657 1235057 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-558 1233599 1233684 1233910 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-557 1228666 1232167 1232703 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-556 1228291 1228341 1228501 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-555 1227150 1227861 1227901 "LALG" 1227962 LALG (NIL T) -9 NIL 1228020 NIL) (-554 1226933 1227010 1227145 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-553 1224850 1226201 1226452 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-552 1224679 1224709 1224750 "KVTFROM" 1224812 KVTFROM (NIL T) -9 NIL NIL NIL) (-551 1223613 1224217 1224399 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-550 1223442 1223472 1223513 "KRCFROM" 1223575 KRCFROM (NIL T) -9 NIL NIL NIL) (-549 1222544 1222741 1223036 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-548 1222373 1222403 1222444 "KONVERT" 1222506 KONVERT (NIL T) -9 NIL NIL NIL) (-547 1222202 1222232 1222273 "KOERCE" 1222335 KOERCE (NIL T) -9 NIL NIL NIL) (-546 1221772 1221865 1221997 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-545 1219825 1220719 1221091 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-544 1213014 1218029 1218083 "KDAGG" 1218459 KDAGG (NIL T T) -9 NIL 1218666 NIL) (-543 1212662 1212804 1213009 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-542 1205492 1212443 1212600 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-541 1205145 1205425 1205487 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-540 1204113 1204614 1204863 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-539 1203237 1203688 1203893 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-538 1202103 1202594 1202893 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-537 1201383 1201784 1201945 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-536 1201096 1201330 1201378 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-535 1195383 1200786 1201014 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-534 1194801 1195134 1195254 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-533 1190975 1192990 1193044 "IXAGG" 1193971 IXAGG (NIL T T) -9 NIL 1194428 NIL) (-532 1190181 1190552 1190970 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-531 1185435 1190117 1190176 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-530 1184402 1184677 1184940 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-529 1183064 1183271 1183564 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-528 1182015 1182237 1182520 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-527 1181690 1181753 1181876 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-526 1180952 1181324 1181498 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-525 1178992 1180228 1180502 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-524 1168604 1174309 1175466 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-523 1167852 1168003 1168238 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-522 1167344 1167646 1167737 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-521 1166637 1166728 1166941 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-520 1165769 1165994 1166234 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-519 1164182 1164563 1164991 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-518 1163967 1164011 1164087 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-517 1162817 1163114 1163409 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-516 1162090 1162441 1162592 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-515 1161293 1161424 1161637 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-514 1159448 1159945 1160489 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-513 1156561 1157797 1158486 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-512 1156386 1156426 1156486 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-511 1152448 1156312 1156381 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-510 1150515 1152387 1152443 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-509 1149889 1150187 1150316 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-508 1149342 1149630 1149762 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-507 1148426 1149048 1149174 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-506 1147839 1148330 1148358 "IOBCON" 1148363 IOBCON (NIL) -9 NIL 1148384 NIL) (-505 1147410 1147474 1147656 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-504 1139454 1141825 1144150 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-503 1136565 1137348 1138212 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-502 1136242 1136339 1136456 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-501 1133748 1136178 1136237 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-500 1131860 1132389 1132956 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-499 1131362 1131476 1131616 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-498 1129746 1130152 1130614 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-497 1127525 1128119 1128730 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-496 1124898 1125508 1126228 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-495 1124302 1124460 1124668 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-494 1123821 1123907 1124095 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-493 1122026 1122547 1123004 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-492 1115108 1116761 1118490 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-491 1114474 1114636 1114809 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-490 1112347 1112811 1113355 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-489 1110561 1111449 1111477 "INTDOM" 1111776 INTDOM (NIL) -9 NIL 1111981 NIL) (-488 1110114 1110316 1110556 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-487 1106012 1108419 1108473 "INTCAT" 1109269 INTCAT (NIL T) -9 NIL 1109585 NIL) (-486 1105577 1105697 1105824 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-485 1104417 1104589 1104895 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-484 1103990 1104086 1104243 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-483 1097030 1103845 1103985 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-482 1096328 1096883 1096948 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096982) (-481 1095625 1096180 1096245 "INT64" NIL INT64 (NIL) -8 NIL NIL 1096279) (-480 1094922 1095477 1095542 "INT32" NIL INT32 (NIL) -8 NIL NIL 1095576) (-479 1094219 1094774 1094839 "INT16" NIL INT16 (NIL) -8 NIL NIL 1094873) (-478 1090744 1094138 1094214 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-477 1084892 1088310 1088338 "INS" 1089268 INS (NIL) -9 NIL 1089927 NIL) (-476 1082970 1083884 1084819 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-475 1082029 1082252 1082527 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-474 1081243 1081384 1081581 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-473 1080233 1080374 1080611 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-472 1079385 1079549 1079809 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-471 1078665 1078780 1078968 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-470 1077404 1077673 1077997 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-469 1076684 1076825 1077008 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-468 1076347 1076419 1076517 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-467 1073433 1074919 1075434 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-466 1073032 1073139 1073253 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-465 1072191 1072833 1072934 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-464 1071041 1071309 1071630 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-463 1070113 1070971 1071036 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-462 1069738 1069818 1069935 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-461 1068653 1069197 1069401 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-460 1064748 1065803 1066746 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-459 1063605 1063927 1063955 "INBCON" 1064467 INBCON (NIL) -9 NIL 1064732 NIL) (-458 1063059 1063324 1063600 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-457 1062553 1062855 1062945 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-456 1062010 1062319 1062424 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-455 1058110 1061902 1062005 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-454 1056950 1057089 1057404 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-453 1055374 1055641 1055978 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-452 1053190 1055256 1055369 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-451 1048097 1053121 1053185 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-450 1047478 1047811 1047926 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-449 1042285 1046916 1047102 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-448 1041347 1042207 1042280 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-447 1040919 1040996 1041050 "IEVALAB" 1041257 IEVALAB (NIL T T) -9 NIL NIL NIL) (-446 1040674 1040754 1040914 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-445 1039747 1040594 1040669 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-444 1038889 1039667 1039742 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-443 1038292 1038823 1038884 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-442 1036784 1037308 1037359 "IDPC" 1037865 IDPC (NIL T T) -9 NIL 1038145 NIL) (-441 1036150 1036706 1036779 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-440 1035399 1036072 1036145 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-439 1035092 1035305 1035365 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-438 1032163 1033044 1033936 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-437 1025789 1027066 1028105 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-436 1025051 1025181 1025380 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-435 1024225 1024723 1024861 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-434 1022614 1022945 1023336 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-433 1018047 1022316 1022428 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-432 1015305 1015929 1016624 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-431 1013531 1014011 1014544 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-430 1011295 1013423 1013526 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-429 1007164 1011233 1011290 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-428 1000807 1006128 1006596 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-427 1000375 1000438 1000611 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-426 999867 1000016 1000044 "HYPCAT" 1000251 HYPCAT (NIL) -9 NIL NIL NIL) (-425 999523 999676 999862 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-424 999136 999381 999464 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-423 998969 999018 999059 "HOMOTOP" 999064 HOMOTOP (NIL T) -9 NIL 999097 NIL) (-422 995549 996923 996964 "HOAGG" 997939 HOAGG (NIL T) -9 NIL 998660 NIL) (-421 994555 995025 995544 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-420 987819 994280 994428 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-419 986754 987012 987275 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-418 985721 986619 986749 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-417 983915 985554 985642 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-416 983230 983582 983715 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-415 976783 983163 983225 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-414 969986 976519 976670 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-413 969439 969596 969759 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-412 962522 969330 969434 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-411 962014 962316 962407 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-410 959628 961801 961980 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-409 955021 959511 959623 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-408 948107 954918 955016 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-407 940108 947476 947731 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-406 939144 939653 939681 "GROUP" 939884 GROUP (NIL) -9 NIL 940018 NIL) (-405 938687 938888 939139 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-404 937359 937698 938085 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-403 936191 936548 936599 "GRMOD" 937128 GRMOD (NIL T T) -9 NIL 937296 NIL) (-402 936010 936058 936186 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-401 932141 933349 934346 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-400 930863 931187 931502 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-399 930416 930544 930685 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-398 929499 929998 930049 "GRALG" 930202 GRALG (NIL T T) -9 NIL 930294 NIL) (-397 929234 929331 929494 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-396 925951 928916 929092 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-395 925364 925427 925684 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-394 921250 922114 922639 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-393 920425 920627 920865 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-392 915428 916355 917374 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-391 915176 915233 915322 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-390 914658 914747 914912 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-389 914167 914208 914421 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-388 912968 913251 913555 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-387 906308 912658 912819 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-386 896121 901098 902202 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-385 894261 895302 895330 "GCDDOM" 895585 GCDDOM (NIL) -9 NIL 895742 NIL) (-384 893884 894041 894256 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-383 884677 887147 889535 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-382 882812 883137 883555 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-381 881753 881942 882209 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-380 880624 880831 881135 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-379 880087 880229 880377 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-378 878699 879047 879360 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-377 877244 877565 877887 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-376 874870 875226 875631 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-375 868122 869783 871361 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-374 867774 867995 868063 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-373 867398 867619 867700 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-372 865495 866178 866638 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-371 864088 864395 864787 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-370 862743 863102 863426 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-369 862046 862170 862357 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-368 861020 861286 861633 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-367 858678 859208 859690 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-366 858261 858321 858490 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-365 856625 857475 857778 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-364 855773 855907 856130 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-363 854944 855105 855332 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-362 850939 853890 853931 "FSAGG" 854301 FSAGG (NIL T) -9 NIL 854560 NIL) (-361 849293 850052 850844 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-360 847249 847545 848089 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-359 846296 846478 846778 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-358 845977 846026 846153 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-357 826357 835759 835800 "FS" 839670 FS (NIL T) -9 NIL 841948 NIL) (-356 818596 822087 826060 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-355 818130 818257 818409 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-354 812696 815823 815863 "FRNAALG" 817183 FRNAALG (NIL T) -9 NIL 817781 NIL) (-353 809437 810688 811946 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-352 809118 809167 809294 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-351 807605 808162 808456 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-350 806891 806984 807271 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-349 804725 805491 805807 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-348 803834 804277 804318 "FRETRCT" 804323 FRETRCT (NIL T) -9 NIL 804494 NIL) (-347 803207 803485 803829 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-346 800039 801497 801556 "FRAMALG" 802438 FRAMALG (NIL T T) -9 NIL 802730 NIL) (-345 798635 799186 799816 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-344 798328 798391 798498 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-343 792033 798133 798323 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-342 791726 791789 791896 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-341 784097 788605 789933 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-340 777963 781404 781432 "FPS" 782551 FPS (NIL) -9 NIL 783107 NIL) (-339 777520 777653 777817 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-338 774419 776399 776427 "FPC" 776652 FPC (NIL) -9 NIL 776794 NIL) (-337 774265 774317 774414 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-336 773054 773763 773804 "FPATMAB" 773809 FPATMAB (NIL T) -9 NIL 773961 NIL) (-335 771484 772080 772427 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-334 771059 771117 771290 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-333 769594 770457 770631 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-332 768221 768726 768754 "FNCAT" 769211 FNCAT (NIL) -9 NIL 769468 NIL) (-331 767678 768188 768216 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-330 766265 767627 767673 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-329 762865 764223 764264 "FMONCAT" 765481 FMONCAT (NIL T) -9 NIL 766085 NIL) (-328 759766 760813 760866 "FMCAT" 762047 FMCAT (NIL T T) -9 NIL 762539 NIL) (-327 758498 759589 759688 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-326 757626 758346 758493 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-325 755813 756265 756759 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-324 753748 754284 754862 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-323 747198 752085 752699 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-322 745722 746792 746832 "FLINEXP" 746837 FLINEXP (NIL T) -9 NIL 746930 NIL) (-321 745131 745390 745717 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-320 744346 744505 744726 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-319 741272 742320 742372 "FLALG" 743599 FLALG (NIL T T) -9 NIL 744066 NIL) (-318 740443 740604 740831 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-317 733864 737874 737915 "FLAGG" 739170 FLAGG (NIL T) -9 NIL 739815 NIL) (-316 732972 733376 733859 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-315 729621 730823 730882 "FINRALG" 732010 FINRALG (NIL T T) -9 NIL 732518 NIL) (-314 729012 729277 729616 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-313 728322 728618 728646 "FINITE" 728842 FINITE (NIL) -9 NIL 728949 NIL) (-312 720326 722886 722926 "FINAALG" 726578 FINAALG (NIL T) -9 NIL 728016 NIL) (-311 716593 717838 718961 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-310 715157 715576 715630 "FILECAT" 716314 FILECAT (NIL T T) -9 NIL 716530 NIL) (-309 714508 714982 715085 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-308 711844 713660 713688 "FIELD" 713728 FIELD (NIL) -9 NIL 713808 NIL) (-307 710869 711330 711839 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-306 708873 709819 710165 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-305 708116 708297 708516 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-304 703450 708054 708111 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-303 703112 703179 703314 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-302 702652 702694 702903 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-301 699332 700209 700986 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-300 694680 699264 699327 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-299 689423 694169 694359 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-298 683968 688704 688962 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-297 678239 683419 683630 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-296 677262 677472 677787 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-295 672791 675433 675461 "FFIELDC" 676080 FFIELDC (NIL) -9 NIL 676455 NIL) (-294 671868 672306 672786 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-293 671483 671541 671665 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-292 669627 670150 670667 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-291 664785 669426 669527 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-290 659947 664574 664681 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-289 654677 659738 659846 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-288 654131 654180 654415 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-287 632794 643766 643852 "FFCAT" 649002 FFCAT (NIL T T T) -9 NIL 650438 NIL) (-286 629034 630260 631566 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-285 623941 628965 629029 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-284 622869 623338 623379 "FEVALAB" 623463 FEVALAB (NIL T) -9 NIL 623724 NIL) (-283 622274 622526 622864 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-282 619144 620024 620139 "FDIVCAT" 621706 FDIVCAT (NIL T T T T) -9 NIL 622142 NIL) (-281 618938 618970 619139 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-280 618245 618338 618615 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-279 616763 617729 617932 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-278 615856 616240 616442 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-277 614978 615467 615607 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-276 606653 611234 611274 "FAXF" 613075 FAXF (NIL T) -9 NIL 613765 NIL) (-275 604569 605373 606188 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-274 599433 604091 604265 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-273 593982 596340 596392 "FAMR" 597403 FAMR (NIL T T) -9 NIL 597862 NIL) (-272 593181 593546 593977 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-271 592234 593123 593176 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-270 589871 590719 590772 "FAMONC" 591713 FAMONC (NIL T T) -9 NIL 592098 NIL) (-269 588459 589729 589866 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-268 586539 586900 587302 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-267 585816 586013 586235 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-266 577740 585263 585462 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-265 575771 576337 576919 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-264 572673 573315 574035 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-263 567830 568537 569342 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-262 567519 567582 567691 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-261 552472 566568 566994 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-260 543063 551792 552080 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-259 542558 542859 542949 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-258 542334 542524 542553 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-257 542023 542091 542204 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-256 541540 541682 541723 "EVALAB" 541893 EVALAB (NIL T) -9 NIL 541997 NIL) (-255 541168 541314 541535 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-254 538299 539832 539860 "EUCDOM" 540414 EUCDOM (NIL) -9 NIL 540763 NIL) (-253 537226 537719 538294 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-252 536951 537007 537107 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-251 536639 536703 536812 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-250 530422 532322 532350 "ES" 535092 ES (NIL) -9 NIL 536476 NIL) (-249 526937 528469 530261 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-248 526285 526438 526614 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-247 519374 526189 526280 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-246 519063 519126 519235 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-245 512789 515815 517248 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-244 509092 510188 511281 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-243 507921 508271 508576 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-242 506894 507563 507591 "ENTIRER" 507596 ENTIRER (NIL) -9 NIL 507640 NIL) (-241 503591 505324 505673 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-240 502695 502906 502960 "ELTAGG" 503340 ELTAGG (NIL T T) -9 NIL 503551 NIL) (-239 502475 502549 502690 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-238 502233 502268 502322 "ELTAB" 502406 ELTAB (NIL T T) -9 NIL 502458 NIL) (-237 501484 501654 501853 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-236 501208 501282 501310 "ELEMFUN" 501415 ELEMFUN (NIL) -9 NIL NIL NIL) (-235 501108 501135 501203 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-234 495666 499161 499202 "ELAGG" 500139 ELAGG (NIL T) -9 NIL 500599 NIL) (-233 494464 495002 495661 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-232 493882 494049 494205 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-231 492795 493114 493393 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-230 486188 488186 489013 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-229 480167 482163 482973 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-228 477981 478387 478858 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-227 468981 470894 472435 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-226 468095 468595 468744 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-225 466805 467479 467519 "DVARCAT" 467802 DVARCAT (NIL T) -9 NIL 467942 NIL) (-224 466224 466488 466800 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-223 458355 466092 466219 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-222 456705 457496 457537 "DSEXT" 457900 DSEXT (NIL T) -9 NIL 458194 NIL) (-221 455510 456034 456700 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-220 455234 455299 455397 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-219 451390 452604 453733 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-218 447048 448399 449459 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-217 445723 446084 446470 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-216 445415 445472 445588 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-215 444400 444694 444980 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-214 443985 444060 444210 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-213 436494 438570 440649 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-212 432075 433070 434125 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-211 428682 430751 430792 "DQAGG" 431421 DQAGG (NIL T) -9 NIL 431694 NIL) (-210 415316 422891 422973 "DPOLCAT" 424810 DPOLCAT (NIL T T T T) -9 NIL 425353 NIL) (-209 411724 413372 415311 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-208 404811 411622 411719 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-207 397807 404640 404806 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-206 397401 397660 397749 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-205 396815 397263 397343 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-204 396101 396426 396577 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-203 389304 395837 395988 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-202 387096 388382 388422 "DMEXT" 388427 DMEXT (NIL T) -9 NIL 388602 NIL) (-201 386752 386814 386958 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-200 380077 386237 386427 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-199 376755 378912 378953 "DLAGG" 379503 DLAGG (NIL T) -9 NIL 379732 NIL) (-198 375194 376003 376031 "DIVRING" 376123 DIVRING (NIL) -9 NIL 376206 NIL) (-197 374645 374889 375189 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-196 373073 373490 373896 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-195 372110 372331 372596 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-194 365683 372042 372105 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-193 354142 360503 360556 "DIRPCAT" 360812 DIRPCAT (NIL NIL T) -9 NIL 361685 NIL) (-192 352156 352924 353805 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-191 351603 351769 351955 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-190 348161 350501 350542 "DIOPS" 350974 DIOPS (NIL T) -9 NIL 351200 NIL) (-189 347821 347965 348156 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-188 346737 347504 347532 "DIFRING" 347537 DIFRING (NIL) -9 NIL 347558 NIL) (-187 346385 346483 346511 "DIFFSPC" 346630 DIFFSPC (NIL) -9 NIL 346705 NIL) (-186 346126 346228 346380 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-185 345072 345666 345706 "DIFFMOD" 345711 DIFFMOD (NIL T) -9 NIL 345808 NIL) (-184 344768 344825 344866 "DIFFDOM" 344987 DIFFDOM (NIL T) -9 NIL 345055 NIL) (-183 344649 344679 344763 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-182 342410 343869 343909 "DIFEXT" 343914 DIFEXT (NIL T) -9 NIL 344066 NIL) (-181 339583 341923 341964 "DIAGG" 341969 DIAGG (NIL T) -9 NIL 341989 NIL) (-180 339139 339329 339578 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-179 334351 338329 338606 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-178 330809 331862 332872 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-177 325422 329963 330290 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-176 323988 324280 324655 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-175 321172 322360 322756 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-174 318892 321003 321092 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-173 318275 318420 318602 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-172 315605 316325 317121 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-171 313720 314176 314736 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-170 313103 313436 313550 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-169 306367 312828 312976 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-168 304287 304797 305301 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-167 303926 303975 304126 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-166 303185 303747 303838 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-165 301209 301651 302011 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-164 300501 300790 300936 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-163 299952 300098 300250 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-162 297314 298107 298834 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-161 296753 296899 297070 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-160 294825 295136 295503 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-159 294382 294637 294738 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-158 293595 293978 294006 "CTORCAT" 294187 CTORCAT (NIL) -9 NIL 294299 NIL) (-157 293298 293432 293590 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-156 292791 293048 293156 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-155 292207 292638 292711 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-154 291666 291783 291936 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-153 288060 288816 289571 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-152 287551 287854 287945 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-151 286770 286979 287207 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-150 286274 286379 286583 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-149 286027 286061 286167 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-148 282966 283728 284446 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-147 282485 282627 282766 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-146 278442 280948 281440 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-145 278316 278343 278371 "CONDUIT" 278408 CONDUIT (NIL) -9 NIL NIL NIL) (-144 277283 277952 277980 "COMRING" 277985 COMRING (NIL) -9 NIL 278035 NIL) (-143 276448 276815 276993 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-142 276144 276185 276313 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-141 275837 275900 276007 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-140 264743 275787 275832 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-139 264204 264343 264503 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-138 263957 263998 264096 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-137 245476 257664 257704 "COMPCAT" 258705 COMPCAT (NIL T) -9 NIL 260047 NIL) (-136 238022 241533 245120 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-135 237781 237815 237917 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-134 237611 237650 237708 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-133 237192 237471 237545 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-132 236769 237010 237097 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-131 235970 236216 236244 "COMBOPC" 236580 COMBOPC (NIL) -9 NIL 236753 NIL) (-130 235034 235286 235528 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-129 231972 232654 233275 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-128 230852 231303 231538 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-127 230344 230646 230737 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-126 230031 230084 230209 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-125 229502 229811 229909 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-124 226064 227120 228186 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-123 224423 225344 225582 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-122 220547 222555 222596 "CLAGG" 223522 CLAGG (NIL T) -9 NIL 224055 NIL) (-121 219440 219967 220542 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-120 219069 219160 219300 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-119 217006 217513 218061 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-118 216055 216724 216752 "CHARZ" 216757 CHARZ (NIL) -9 NIL 216771 NIL) (-117 215849 215895 215973 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-116 214776 215477 215505 "CHARNZ" 215566 CHARNZ (NIL) -9 NIL 215614 NIL) (-115 212254 213351 213874 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-114 211962 212041 212069 "CFCAT" 212180 CFCAT (NIL) -9 NIL NIL NIL) (-113 211305 211434 211616 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-112 207294 210718 210998 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-111 206672 206859 207036 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-110 206200 206619 206667 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-109 205673 205982 206079 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-108 205165 205467 205558 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-107 204414 204574 204795 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-106 200514 201771 202479 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-105 198912 199911 200162 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-104 198493 198772 198846 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-103 197939 198192 198220 "CACHSET" 198352 CACHSET (NIL) -9 NIL 198430 NIL) (-102 197334 197718 197746 "CABMON" 197796 CABMON (NIL) -9 NIL 197852 NIL) (-101 196864 197128 197238 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-100 192197 196523 196693 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-99 191172 191877 192010 "BYTE" NIL BYTE (NIL) -8 NIL NIL 192169) (-98 188647 190943 191047 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-97 186078 188390 188509 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-96 183330 185534 185573 "BTCAT" 185640 BTCAT (NIL T) -9 NIL 185716 NIL) (-95 183081 183179 183325 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-94 178203 182324 182350 "BTAGG" 182461 BTAGG (NIL) -9 NIL 182569 NIL) (-93 177834 177995 178198 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-92 174896 177304 177516 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-91 174166 174318 174496 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-90 170711 172884 172923 "BRAGG" 173564 BRAGG (NIL T) -9 NIL 173821 NIL) (-89 169666 170161 170706 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-88 162264 169171 169352 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-87 160320 162216 162259 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-86 160053 160089 160200 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-85 158292 158725 159173 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-84 154258 155674 156564 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-83 153134 154025 154147 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-82 152732 152889 152915 "BOOLE" 153023 BOOLE (NIL) -9 NIL 153104 NIL) (-81 152637 152664 152727 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-80 151818 152314 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(-3879 . 58694) (-3880 . 58593) + (-3881 . 58492) (-3882 . 58391) (-3883 . 58290) (-3884 . 58189) + (-3885 . 58074) (-3886 . 57959) (-3887 . 57908) (-3888 . 57791) + (-3889 . 57733) (-3890 . 57632) (-3891 . 57531) (-3892 . 57430) + (-3893 . 57314) (-3894 . 57285) (-3895 . 56554) (-3896 . 56429) + (-3897 . 56304) (-3898 . 56164) (-3899 . 56046) (-3900 . 55921) + (-3901 . 55766) (-3902 . 54783) (-3903 . 53924) (-3904 . 53870) + (-3905 . 53816) (-3906 . 53608) (-3907 . 53236) (-3908 . 52825) + (-3909 . 52467) (-3910 . 52109) (-3911 . 51957) (-3912 . 51655) + (-3913 . 51499) (-3914 . 51173) (-3915 . 51103) (-3916 . 51033) + (-3917 . 50824) (-3918 . 50215) (-3919 . 50011) (-3920 . 49638) + (-3921 . 49129) (-3922 . 48864) (-3923 . 48383) (-3924 . 47902) + (-3925 . 47777) (-3926 . 46677) (-3927 . 45601) (-3928 . 45030) + (-3929 . 44812) (-3930 . 36489) (-3931 . 36304) (-3932 . 34221) + (-3933 . 32053) (-3934 . 31907) (-3935 . 31729) (-3936 . 31322) + (-3937 . 31027) (-3938 . 30679) (-3939 . 30513) (-3940 . 30347) + (-3941 . 29934) (-3942 . 16069) (-3943 . 14962) (* . 10915) (-3945 . 10661) + (-3946 . 10477) (-3947 . 9522) (-3948 . 9469) (-3949 . 9409) (-3950 . 9140) + (-3951 . 8513) (-3952 . 7240) (-3953 . 5996) (-3954 . 5127) (-3955 . 3864) + (-3956 . 420) (-3957 . 306) (-3958 . 173) (-3959 . 30))
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