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F^dl6#Fer>FdyFdy@$0F`s7#-Fg_m6#;FbpF_p>Fio-Fg^m6$/F^s-Fdcl6$f*Fcu6#F0FhnFhn-Fg^ m6$/Fbp7#-%$seqG6$&&F^tFap6#&Fju6#8$/Ffam;FbpT%F^tFhnFhn6&FBF`sF 8J-%7Involutive/checkIBginvG64F]pF_rF^qFeqF_pFdpFipF]vFdyFerFes&Fhr6#;Fbp%&_nva rG&Fhr6#;,&FdbmFbpFbpFbp,&FdbmFbpF_pFbpF\wF_wFawFcwFby>Feq&F]bmFfp>F_w&F]bmF[q> F\w&F]bmF]s>FfyFbp?(FhnFbpFbpFhnF^^m@%-Fhu6$Fc^m-Fdcl6$%&parseG-Fdcl6%Fjt7#-%&a liasGFhnF\uC%@$4-Fhu6$Fc^m-Fdcl6$Fgcm-Fdcl6%FjtF^qF\u>F^q7$Fg[m-Fgcm6#-Fjt6$Fc^ mF\u>F_wFf^m>F\wF[_m>FfyF[^m>F^q-F`u6$f*FcuFhnFduFhn-Fhu6$F^t-Fdcl6$%$rhsG&FjuF bsFhnFhn6$FRF]bmF^q>8K&F]bmFbs>FfyFbp?(FhnFbpFbpFhn2Ffy-F^dl6#F[fmC$>F[fm7$-F\[ l6#&F[fm6#;FbpFfy-F\[l6#-%%subsG6$/-Fgem6#&F[fmF^z-%$lhsGFagm&F[fm6#;F[^m!"">Ff yF[^m@$0&F]bmF`qFev>FdyF\hm>8I&F]bmFap>Fio-F[p6#7#F^t>8Q-F`u6$f*FcuFhnFduFhnFgu FhnFhn6$FGF^qF_q>Fjq5FjqF[r>FfyFbp?(FhnFbpFbpFhn1Ffy-F^dl6#FfhmC&@$0-F\[l6$Fev& FfhmF^zFc\m-Feo6#-Fft6$-Fjt6$FgimF\uFj\m?&Fajl-Fjbl6$-F\[l6$FbpFgimF`[mF^o@$4-F 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%Fb[o-F]gm6$Fe[o-Fg[o6$-%'normalG6#*&F`jnFbp-%'lcoeffGFh[oFhgmF`v-Fj[o6$F^\oF^v F`\oFhnFhnFhnFhn, Q8(-%*substringG6$-%(convertG6$-%+kerneloptsG6#%(versionG%'stringG;""""")@$ 5/FMQ)Maple~V,FJ/FMQ)Maple~6.FJ-%&ERRORG6#%]othis~procedure~is~only~available~f or~Maple~8.0~and~newer~versions.G@$0%7Involutive/initializedG.%%trueG-%0Involut ive/initGFJ@$4%4Involutive/ratcoeffG-F]o6#%fnnot~implemented~yet~for~involutive ~bases~over~the~integers.G@$0%2Involutive/characG""!-F]o6#%Ithe~modular~case~is ~not~implemented~yet.G>8).%'lambdaG>82F`p>83"#I>8*FZ>8-%%NULLG>84Faq>85Faq>86Fa q>87Faq>887">89%&falseG?(8%""'FZ9#Fdo@%-%%typeG6$&9"6#Far%)equationGC$@$4-Ffr6$ -%#opG6$FZFhrFX-F]o6#%\oexpecting~a~string~on~the~left~hand~side~of~an~optional ~equation.G@9/FasQ'paramsFJC$@$4-Ffr6$-Fbs6$""#FhrF,-F]o6#%Fexpecting~a~list~fo r~option~"params".G>FcqF_t/FasQ*firstevalFJC$@$34-Ffr6$F_t%'posintG0F_t%)infini tyG-F]o6#%Uexpecting~a~positive~integer~for~option~"firsteval".G>FeqF_t/FasQ*ev alpointFJC$@$F\t-F]o6#%Uexpecting~a~list~of~integers~for~option~"evalpoint".G>F gqF_t/FasQ)lessevalFJC$@$4-Ffr6$F_t%(booleanG-F]o6#%Sexpecting~"true"~or~"false "~for~option~"lesseval".G>F^rF_t/FasQ*paramdegsFJC$@$4-Ffr6$F_t-F,6#%*nonnegint G-F]o6#%\oexpecting~a~list~of~non-negative~integers~for~option~"paramdegs".G>Fi qF_t/FasQ&denomFJ>F^qF_t/FasQ3printfactordegreesFJC$@$4-Ffr6$F_t%%nameG-F]o6#%f nexpecting~an~indeterminate~for~option~"printfactordegrees".G>F[rF_t/FasQ*PolRe presFJC$@$45-Ffr6$F_t%'matrixG-Ffr6$F_t%'MatrixG-F]o6#%Kexpecting~a~matrix~for~ option~"PolRepres".G>F`q-FRF`y5/FasQ'degreeFJ/FasQ'maxdegFJC$@$F[u-F]o6#%Nexpec ting~a~positive~integer~as~degree~bound.G>F[qF_t/FasQ'mindegFJC$@$F[uF^z>FipF_t /-FO6$Fas;FZ""$Q$varFJC$@$F^x-F]o6#%\oexpecting~a~name~for~the~indeterminate~of ~the~minimal~polynomial.G>FepF_t-F]o6#%0invalid~option.GFc[l>8,-%6Involutive/pr oc_inputG6#9&>8+&-%5Involutive/proc_varsG6$9'&Fg[l6#FZFd\l@%/FcqFaq>Fcq-%'remov eG6%%2Involutive/hasvarG&Fg[l6#""(F]\l@$-FR6$-%$mapG6%%'memberGFcqF]\l%#orG-F]o 6#%Xthe~lists~of~variables~and~parameters~must~be~disjoint.G@$0FcqF\rC$@%/FgqFa qC$@%/FeqFaq>Fgq7#-%$maxG6$",+++++"*$-%4Involutive/maxcoeffG6#&Fg[l6#""%Fat>Fgq 7#Feq>Fgq7$-Fbs6#Fgq-%$seqG6$Far/Far;FZ,&-%%nopsG6#FcqFZ!""FZ@$0-F\`lFd_lF[`l-F ]o6#%Rexpecting~an~evaluation~point~for~each~parameter.G@$/FiqFaq>Fiq7#-%"$G6$F `uF[`l>8'-F\`l6#9(@$/F]alF`p-%'RETURNG6#Fep@$/F`qFaq>F`q-FR6$-%5Involutive/PolR epresG6&9%F[\lFb\lF`alFay@$0F^qFZ>F`q-%&evalaG6#*&F^qFZF`qFZ>8.-%:Involutive/mo nomcoefflistG6%-%8Involutive/PolInvReduceG6%9$F[\lFb\lF]\lF`al@%-&%'linalgG6#%' iszeroG6#FgblFcal>Fgbl-FR6$Fgbl%'VectorG>817#-Ficl6$F]alf*6#F4FJ6$%)operatorG%& arrowGFJ@%/F^clFZFZF`pFJFJFJ>8/-%&solveG6$<#-Ff_l6$,&*&&&F[dlFd\l6#8$FZ&80Fd\lF ZFZ&FgblFbelFZ/Fcel;FZF^al<#Fdel@$0FgdlFaq-Fdal6#-%%subsG6$Fgdl,&FepFZFdelFZ>Fa rFZ?(FJFZFZFJ1FarF[qC&-%)userinfoG6&F[[l%2PolMinPolyRatFuncG%+degree~~~~GFar>F[ dl7$-Fbs6#F[dl-&%.LinearAlgebraG6#%5MatrixVectorMultiplyG6$F`q&F[dl6#F^`l@$1Fip Far@%/F_pF`p@%/FcqF\rC&-Fgfl6%F^_lFifl%.solve~startedG>Fgdl-Fidl6$<#-Ff_l6$,&-% $addG6$*&&&F[dl6#,&8&FZFZFZFbelFZ&Feel6#F`ilFZ/F`il;F`pFarFZFfelFZFgel<#-Ff_l6$ FailFcil-Fgfl6%F^_lFifl%/solve~finishedG@$F[fl-Fdal6#-F_fl6$Fgdl,&)Fep,&FarFZFZ FZFZ-Fihl6$*&FailFZ)FepF`ilFZFcilFZC&-Fgfl6%F^_lFifl%6solveinterpol~startedG>Fg dl-%9Involutive/solveinterpolG6+FdhlFeilF`jlFcqFgqF[rF^rFiqF[`l-Fgfl6%F^_lFifl% 7solveinterpol~finishedG@$F[fl-Fdal6#Fgdl-F]o6#%5not~implemented~yet.G>FarFbjl- F]o6#%apstopped~calculation~of~minimal~polynomial~since~upper~bound~for~the~deg ree~is~reached.GFJFJFJFJ, Q=Involutive/DependsOnPowers.mFJ M7R0 I2Involutive/PolSumf*6%%#M1G%#M2G'%$varG%%listG6"6#%[oCopyright~(C)~2003-2005~b y~Mohamed~Barakat.~All~rights~reserved.GF*-%7Involutive/PolCokernelG6#9"F*F*F*F *, Q4Involutive/PolSum.mF* M7R0 I;Involutive/PolIntersectionf*6%%$_R1G%$_R2G'%$varG%%listG6(%"aG%"nG%#R1G%#R2G% #R0G%"ZG6#%^pCopyright~(C)~2003-2008~by~Mohamed~Barakat~and~Daniel~Robertz.~All ~rights~reserved.G6"C*>8&-%$mapG6$f*6#F+F36$%)operatorG%&arrowGF3&9$6#"""F3F3F3 &-%6Involutive/proc_inputG6#F@6#""%>8'-F86$f*F;F3F8%-%%no psG6#&F6FA>8(-F86$%#opG7$-F86$f*F;F3F8)-F8 6$f*F;F3FF`p7#7#- Feo6$FgoFS-F[p6%F`pF]p&9"6#;FH9#F3F3F3F3, Q=Involutive/PolIntersection.mF3 M7R0 IBInvolutive/findezugehoerigenpunktf*6$'%"nG%*nonnegintG'%#ALG-%%listG6#%'posin tG6$%"iG%"LG6#%[oCopyright~(C)~2007-2008~by~Moritz~Schroeer.~All~rights~reserve d.G6"C$@$1-%$mulG6$&9%6#8$/F=;"""-%%nopsG6#F;9$-%&ERRORG6#%4Index~out~of~range. G@%/F;7"FK7$-%%iquoG6$FD-F86$F:/F=;""#FA-%#opG6#-F"6$-%%iremGFO&F;6#;FT!""F3F3F 3F3, QDInvolutive/findezugehoerigenpunkt.mF3 M7R0 I@homalg/Involutive/PolInvoReducef*6%%"pG%#_MG%$varG6$%"MG%"vG6#%jnCopyright~(C )~2004-2008~by~Daniel~Robertz.~All~rights~reserved.G6"C%>8$-%6homalg/NormalizeI nputG6$9%%+InvolutiveG>8%-%5homalg/NormalizeRingG6$9&F5@%/&F76#""#7"-%8Involuti ve/PolInvReduceG6%9$F0&F76#"""-FC6&FEF0F>FFF-F-F-F-, QBhomalg/Involutive/PolInvoReduce.mF- M7R0 I8homalg/Involutive/mklstf*6#%"aG6"6#%[oCopyright~(C)~2004-2008~by~Mohamed~Bara kat.~All~rights~reserved.GF&@%-%%typeG6$9$%"=G/-F"6#-%$lhsG6#F--F"6#-%$rhsGF4@% -F+6$F-%%listGF-7#F-F&F&F&F&, Q:homalg/Involutive/mklst.mF& M7R0 I6Involutive/pdegrevlexf*6$%"aG%"bG6%%"iG%$tdaG%$tdbG6#%\pCopyright~(C)~2000-20 08~by~Carlos~F.~Cid~and~Daniel~Robertz.~All~rights~reserved.G6"C&>8%-%(convertG 6$&9$6#"""%"+G>8&-F26$&9%F6F8@'2F0F:-%'RETURNG6#%%trueG2F:F0-FB6#%&falseG?(8$-% %nopsG6#F4!""F7FD@&2&F=6#FJ&F4FRFA2FSFQFF@%2&F56#""#&F>FXFHFDF-F-F-F-, Q8Involutive/pdegrevlex.mF- M7R0 I8%-%(convertG6$&F26#"""%"+G>8&-FB6$&F6FEFG@'2F@FIF7 2FIF@F@&2&FL6#FQ&FDFXF72FYFWF<@%2-%$absG6#&F66#""$-Fhn6# &F2F[oF:F>F-F-F-F-, Q>Involutive/pnegdeglex_Z_POT.mF- M7R0 I5Involutive/block_ordf*6&%"aG%"bG%$sepG%+termordersG6#%"iG6#%jnCopyright~(C)~2 004-2008~by~Daniel~Robertz.~All~rights~reserved.G6"@'4-&9'6#"""6$7$&&9$F36#;F4& 9&F3&F96#""#7$&&9%F3F:&FDF?%&falseG/F7FBC$?(8$F@F4-%%nopsG6#F=%%trueG@&4-&F26#F J6$7$&F86#;,&&F=6#,&FJF4!""F4F4F4F4&F=FSF>7$&FCFWFE-%'RETURNG6#FF0FVFjn-F\o6#FN @%2F>FEFFFNFNF-F-F-F-, Q7Involutive/block_ord.mF- M7R0 I5Involutive/remove_lmf*6$%"LG%'lmprocG6'%"iG%"jG%"FG%#lmG%#LMG6#%jnCopyright~( C)~2006-2008~by~Daniel~Robertz.~All~rights~reserved.G6"C'>8&9$>8(7">8$"""?(F/F9 F9F/1F8-%%nopsG6#F2C$>8'-9%6#&&&F26#F86#F9FI@%-%'memberG6$&&FA6#""#FPF5>F2-%'su bsopG6$/F8%%NULLGF2C$>F57$-%#opG6#F5FN>F8,&F8F9F9F9F2F/F/F/F/, Q7Involutive/remove_lm.mF/ M7R0 I5Involutive/ginvBasisf*6='%"FG%%listG%$varG%)alg_elemG%(tr_elemG%'n_entrG%)rhs _entrG%'no_rhsG%"cG%&m_ordG%(var_ordG%)entr_posG%'vardegG%'tupdegG%(algextsG%-a lgextindetsG%/transextindetsG%%fextG%%algoG%+time_boundG%#trG%*quietmodeG%#GBG% *donotreadG%+tracedenomG%+movedboundG%-qlengthboundG%,degreeboundG6*%%fileG%&fn ameG%"iG%"rG%%nvarG%#mpG%+trans_elemG%"SG6#%jnCopyright~(C)~2006-2008~by~Daniel ~Robertz.~All~rights~reserved.G6"Cjn@%9*@$2"&++"9(-%&ERRORG6#%@length~of~tuples ~exceeds~10000.G@$2FS,&FT"""-%%nopsG6#&&9$6#Ffn6#""#FfnFU@$2"&Ob'9+-FV6#%?chara cteristic~must~be~<~2^16.G>8(-Fhn6#9%>8*-%'removeG6$f*6#FEFM6$%)operatorG%&arro wGFM-%'memberG6$F\oT$FMFM6$F5929'@$0907#-%"$G6$""!FT-FV6#%Yup~to~now,~no~degree s~can~be~assigned~to~tuples~in~ginv.G@$309.7"43/-Fhn6#F[rFfn/&F[rF]oFT-FV6#%gnu p~to~now,~elimination~ordering~for~tuples~is~not~supported.G@$2F_o-Fhn6#9--FV6# %bpup~to~now,~only~two~blocks~of~variables~for~elimination~ordering~are~support ed~by~ginv.G@$2F_oF`r-FV6#%_pup~to~now,~only~two~blocks~of~tuples~for~eliminati on~ordering~are~supported~by~ginv.G@$32F_o,&-Fhn6#F]pFfn-Fhn6#93Ffn0%2Involutiv e/characGFdq-FV6#%_qup~to~now,~transcendental~extensions~of~degree~greater~than ~2~are~only~supported~over~the~rationals.G@'2Fdq-%+searchtextG6$Q&linuxFM-%+ker neloptsG6#%(versionGC&>8'-%(ssystemG6#%hnif~test~-d~/tmp/$USER~;~then~echo~true ~;~else~echo~false~;~fiG@$4-%&parseG6#&F^uF^oC$>F^u-F`u6#%1mkdir~/tmp/$USERG@$0 FhuQ!FM-FV6#%Ecannot~write~temporary~file~to~/tmp.G>8%-F`u6#%Gecho~/tmp/$USER/I nvolutive-$PPID-$USERG@%2Fdq-Fet6$Q"$FM&FevF^o>FevQ0/tmp/InvolutiveFM>Fev-%=Inv olutive/remove_whitespaceG6#F^w2Fdq-Fet6$Q&APPLEFMFht>Fev-%:Involutive/mac_gett mpnameGFM>FevQ1\TEMP\InvolutiveFM>Fev-%$catG6$Fev94>8$-%&fopenG6$Fev%&WRITEG-%( fprintfG6$FdxQ8#!~/usr/bin/env~python|+FM-Fjx6$FdxQY#~temporary~file~created~by ~the~Maple~package~InvolutiveFM-Fjx6$FdxQ+~(version~FM-Fjx6$Fdx-%(convertG6$%3I nvolutive/versionG%'stringG-Fjx6$FdxQ#)|+FM-Fjx6$FdxQ-import~ginv|+FM@%3/FTFfnF P-Fjx6$FdxQDst~=~ginv.SystemType("Polynomial")|+FMC%-Fjx6$FdxQKst~=~ginv.System Type("Polynomial",~module=FM@%FP-Fjx6$Fdx-Ffy6$FTFiyC%-Fjx6$Fdx-Ffy6$,&FTFfn9)F fnFiy-Fjx6$FdxQ-,~rightPart=FMF[[lFjy@'0F[sF\r@%Faz-Fjx6$FdxQGim~=~ginv.MonomIn terface("Elim",~st,~[FM@%/<#-%#opG6#9,<#F_o-Fjx6$FdxQJim~=~ginv.MonomInterface( "PotElim",~st,~[FM-Fjx6$FdxQJim~=~ginv.MonomInterface("TopElim",~st,~[FM5/F[rF\ rF^r@+/Fe\lFfn@%Faz-Fjx6$FdxQFim~=~ginv.MonomInterface("Lex",~st,~[FM-Fjx6$FdxQ Iim~=~ginv.MonomInterface("PotLex",~st,~[FM/Fe\lF_o@%Faz@%/9/7#-Fbq6$FfnFho-Fjx 6$FdxQLim~=~ginv.MonomInterface("DegRevLex",~st,~[FM-Fjx6$FdxQOim~=~ginv.MonomI nterface("DegRevLexDeg",~st,~[FM@%F[^l-Fjx6$FdxQOim~=~ginv.MonomInterface("PotD egRevLex",~st,~[FM-Fjx6$FdxQRim~=~ginv.MonomInterface("PotDegRevLexDeg",~st,~[F M/Fe\l""$@%FazFb]l-Fjx6$FdxQIim~=~ginv.MonomInterface("TopLex",~st,~[FM/Fe\l""% @%Faz@%F[^lF`^lFc^l@%F[^l-Fjx6$FdxQOim~=~ginv.MonomInterface("TopDegRevLex",~st ,~[FM-Fjx6$FdxQRim~=~ginv.MonomInterface("TopDegRevLexDeg",~st,~[FMC$-%'fcloseG 6#Fdx-FV6#%\oup~to~now,~the~chosen~monomial~ordering~is~not~supported~by~ginv.G C%@%Fj[l@%FP-Fjx6$FdxQTim~=~ginv.MonomInterface("PosElimElim",~st,~tupSep=FMC$F _`l-FV6#%dpup~to~now,~the~chosen~monomial~ordering~cannot~be~combined~with~righ t~hand~sides~in~ginv.G@'F]_l@%FP-Fjx6$FdxQSim~=~ginv.MonomInterface("PosElimLex ",~st,~tupSep=FMC$F_`lF\alFc_l@%FP@%F[^l-Fjx6$FdxQYim~=~ginv.MonomInterface("Po sElimDegRevLex",~st,~tupSep=FM-Fjx6$FdxQfnim~=~ginv.MonomInterface("PosElimDegR evLexDeg",~st,~tupSep=FMC$F_`lF\alC$F_`lFb`l-Fjx6$Fdx-Ffy6$FcrFiy-Fjx6$FdxQ$,~[ FM?(8&FfnFfnFho%%trueGC$-Fjx6$Fdx-F`x6%Q"'FM-Ffy6$&F[p6#FgblFiyF^cl@$2FgblFho-F jx6$FdxQ#,~FM@$4%4Involutive/ratcoeffG-Fjx6$FdxQ&,~'@'FM-Fjx6$FdxQ"]FM@&Fj[lC$- Fjx6$FdxQ*,~varSep=FM-Fjx6$Fdx-Ffy6$-Fhn6#&F[sF]oFiy3F_r0FcrFTC$FcdlF_bl@$0F\^l F]^lC$-Fjx6$FdxQ+,~degrees=FM@%Fjcl-Fjx6$Fdx-Ffy6$F\^lFiy-Fjx6$Fdx-Ffy6$7$-Fc\l 6#F\^lFfnFiyFjy@%Fjcl@%0FcoFdq@+3/,&-Fhn6#9&Ffn-Fhn6#91FfnFdq/FgsFdqC%-Fjx6$Fdx Qenic~=~ginv.CoeffInterface("ModularShort",~st,~modularShort=FM-Fjx6$Fdx-Ffy6$F coFiyFjy32FdqFhflF_glC,-Fjx6$FdxQjoic~=~ginv.CoeffInterface("AlgebraicFieldExte nsionModularShort",~st,~parameter=[FM>8)F\r?(FgblFfnFfnFiflFhblC(@$0-Fc\l6$Fdq& F[glFbcl%'RootOfGC$F_`l-FV6#-F`x6$-Ffy6$FfhlFiy%3~is~not~algebraic.G>F_hl7$-Fc\ l6#F_hl-%8Involutive/algext2aliasG6#-Fc\l6$FfnFfhl>F^u-%&minusG6$-%'indetsG6#&F _hl6#!""<$-Fc\l6#-%$mapG6%FfyF[gl%%nameG-Fc\l6#F[q>F_hl-%'subsopG6$/Fbjl-F`x6$- Ffy6$-%%subsG6$/&F^uF]oFfhlF`jlFiyQ"~FMF_hl-Fjx6$Fdx-F`x6%Q""FMF]ilF_\m@$2FgblF iflFecl?(FgblFfnFfn-FhnF[[mFhblC$@$52FfnFgbl2FdqFiflFecl-Fjx6$Fdx-F`x6%F_\m-Ffy 6$&F[qFbclFiyF_\m-Fjx6$FdxQ/],~extension=[FM?(FgblFfnFfnFiflFhblC&-Fjx6$FdxF_\m -Fjx6$Fdx&F_hlFbclFe]m@$Fa\mFecl?(FgblFfnFfnF\glFhblC&@$Ff\mFeclFe]m-Fjx6$Fdx-F `x6$-Ffy6$&F^glFbclFiyFj[mFe]m-Fjx6$FdxQ1],~modularShort=FMFdglFjy3Fgfl/FgsFfnC '-Fjx6$FdxQaoic~=~ginv.CoeffInterface("OneParameterModularShort",~st,~modularSh ort=FMFdgl-Fjx6$FdxQ.,~parameter=[FM@%/F]pF\r-Fjx6$Fdx-F`x6%F_\m-Ffy6$&F\tF]oFi yF_\m-Fjx6$Fdx-F`x6%F_\m-Ffy6$&F]pF]oFiyF_\m-Fjx6$FdxQ$])|+FM3Fgfl/FgsF_oC(-Fjx 6$FdxQaoic~=~ginv.CoeffInterface("TwoParameterModularShort",~st,~modularShort=F MFdglF^_m?(FgblFfnFfnFhsFhblC$-Fjx6$Fdx-F`x6%F_\m-Ffy6$&F]pFbclFiyF_\m@$2FgblF_ oFecl?(FgblFfnFfnFjsFhblC$-Fjx6$Fdx-F`x6%F_\m-Ffy6$&F\tFbclFiyF_\m@$2FgblFjsFec lFa`mC$F_`l-FV6#%5not~implemented~yet.G@-Fffl-Fjx6$FdxQFic~=~ginv.CoeffInterfac e("GmpZ",~st)|+FMFhglC*-Fjx6$FdxQboic~=~ginv.CoeffInterface("AlgebraicFieldExte nsionGmpQ",~st,~parameter=[FM>F_hlF\r?(FgblFfnFfnFiflFhblC(@$FchlC$F_`l-FV6#-F` x6$F]il%M~is~not~algebraic~over~the~rational~numbers.G>F_hlFail>F^uFjil>F_hlF][ mF[\m@$Fa\mFecl?(FgblFfnFfnFc\mFhblC$@$Ff\mFeclFi\mF`]m?(FgblFfnFfnFiflFhblC&Fe ]mFg]mFe]m@$Fa\mFecl?(FgblFfnFfnF\glFhblC&@$Ff\mFeclFe]mF^^mFe]mFa`mFh^mC%-Fjx6 $FdxQgnic~=~ginv.CoeffInterface("OneParameterGmpZ",~st,~parameter=[FM@%Fb_mFc_m Fj_mFa`mFgflC&-Fjx6$FdxQenic~=~ginv.CoeffInterface("NParameterGmpZ",~st,~parame ter=[FM?(FgblFfnFfnFhsFhblC$F\am@$2FgblFgsFecl?(FgblFfnFfnFjsFhblC$Fgam@$F_bmFe clFa`m3Figl2FdqFgsC--Fjx6$FdxQ]pic~=~ginv.CoeffInterface("AlgebraicFieldExtensi onNParameter",~st,~fieldParameter=[FM?(FgblFfnFfnFhsFhblC$F\am@$F_emFecl?(FgblF fnFfnFjsFhblC$Fgam@$F_bmFecl-Fjx6$FdxQ/],~parameter=[FM>F_hlF\r?(FgblFfnFfnFifl FhblC(@$FchlC$F_`lFacm>F_hlFail>F^u-F[jl6$F]jl<&-Fc\lF[tFdjlFjjl-Fc\l6#-Fgjl6%F fyF]pFijl>F_hlF][mF[\m@$Fa\mFecl?(FgblFfnFfnFc\mFhblC$@$Ff\mFeclFi\mF`]m?(FgblF fnFfnFiflFhblC&Fe]mFg]mFe]m@$Fa\mFecl?(FgblFfnFfnF\glFhblC&@$Ff\mFeclFe]mF^^mFe ]mFa`mC$F_`lFabm-Fjx6$FdxQGic~=~ginv.CoeffInterface("GmpZZ",~st)|+FM-Fjx6$FdxQQ ip~=~ginv.PolyInterface("PolyList",~st,~im,~ic)|+FM-Fjx6$FdxQ:iw~=~ginv.WrapInt erface("FM@+/%3Involutive/invcritGF\r-Fjx6$FdxQ(WithoutFM/Fhhm7$FfnF_o-Fjx6$Fdx Q.CritPartiallyFM/Fhhm7%FfnF_oF^_l-Fjx6$FdxQ'C1C2C3FM/Fhhm7&FfnF_oF^_lFd_l-Fjx6 $FdxQ)C1C2C3C4FMC$F_`l-FV6#%Wundefined~involutive~criteria;~see~?InvolutiveOpti ons.G-Fjx6$FdxQ(",~ip)|+FM@%%5Involutive/janetlikeG-Fjx6$FdxQNiD~=~ginv.Divisio nInterface("JanetLike",~iw)|+FM-Fjx6$FdxQJiD~=~ginv.DivisionInterface("Janet",~ iw)|+FM-Fjx6$FdxQ*eqs~=~[\|+FM?(FgblFfnFfn-Fhn6#F\oFhblC&@%FP@%Fbz>8+-F`x6$-Ffy 6$-Fc\l6#&F\o6$FgblFfnFiyFj[m>Fd[n-Ffy6$F[\nFiy>Fd[n-Ffy6$-Fgjl6$Fc\l&F\oFbclFi y?(FMFfnFfnFM2"'++5-%'lengthG6#Fd[nC&>F^u-Fet6$Q"|+FMFd[n?(FMFfnFfnFM2FdqF^uC&@ %32FfnF^u/&Fd[n6#,&F^uFfnFbjlFfnQ"\FM-Fjx6%FdxQ#%aFM-%*substringG6$Fd[n;Ffn,&F^ uFfn!"#Ffn-Fjx6%FdxF^^n-F`^n6$Fd[n;FfnFj]n-Fjx6$FdxQ#\|+FM>Fd[n-F`^n6$Fd[n;,&F^ uFfnFfnFfnFbjl>F^uF^]n-Fjx6%FdxF^^nFd[n>Fd[nF`v@$2FdqFi\nFc_n@$2FgblF^[n-Fjx6$F dxQ$,\|+FM-Fjx6$FdxQ#]|+FM@$Ficl@%Faz-Fjx6$FdxQineqs~=~map(lambda~eq:~"("~+~eq. encode('latin1')~+~")*@~",~eqs)|+FM-Fjx6$FdxQipeqs~=~map(lambda~eq:~eq.replace( '[',~'[(').replace(',~',~')*@,~(').replace(']',~')*@]'),~eqs)|+FM>Fd[nQ:basis~= ~ginv.basisBuild("FM@%095F`v>Fd[n-F`x6$Fd[nF\an@%333/F[sF\rFc_lF]]lF[^l>Fd[n-F` x6$Fd[nQ)TQDegreeFM>Fd[n-F`x6$Fd[nQ#TQFM>Fd[n-F`x6$Fd[nQ(",~iD,~FM@%52Fdq9<2Fdq 9=C/-Fjx6$FdxQWeqs2~=~[]|+for~i~in~eqs:|+~~~~eqs2.append(i)|+runden~=~0|+FM-Fjx 6$FdxQ-while~True:|+FM-Fjx6$FdxQX~~~~runden~=~runden+1|+~~~~print~"NEUE~RUNDE:~ ",~runden|+FM-Fjx6$FdxQbo~~~~print~"Eingabe:~",~len(eqs),~"~letzte~Basis:~",~le n(eqs2)-len(eqs)|+FM@%Fcbn@%FebnC&-Fjx6$Fdx-F`x6%Q%~~~~FMFd[nQ2eqs2,~MovedBound =FM-Fjx6$Fdx-Ffy6$FdbnFiy-Fjx6$FdxQ0,~QlengthBound=FM-Fjx6$Fdx-Ffy6$FfbnFiyC$Fg cnF]dnC$-Fjx6$Fdx-F`x6%F[dnFd[nQ4eqs2,~QlengthBound=FMFddn@$2Fdq96C$-Fjx6$FdxQ( ,~time=FM-Fjx6$Fdx-Ffy6$FaenFiy@$2Fdq9>C$-Fjx6$FdxQ/,~DegreeBound=FM-Fjx6$Fdx-F fy6$F\fnFiy@$98-Fjx6$FdxQ*,~quiet=1FMFjy@%F`en-Fjx6$FdxQio~~~~if~not~basis.comp utationInterrupted()~or~basis.outOfTime():|+~~~~~~~~break|+FM-Fjx6$FdxQZ~~~~if~ not~basis.computationInterrupted():|+~~~~~~~~break|+FM-Fjx6$FdxQN~~~~del~eqs2|+ ~~~~eqs2~=~[]|+~~~~for~i~in~eqs:|+FM-Fjx6$FdxQU~~~~~~~~eqs2.append(i)|+~~~~for~ i~in~basis.iterIB():|+FM-Fjx6$FdxQR~~~~~~~~eqs2.append(str(i)~+~'~')|+~~~~del~b asis|+|+FMC&-Fjx6$Fdx-F`x6$Fd[nQ$eqsFM@$F`enC$FcenFfen@$F[fnC$F^fnFafnFjy-Fjx6$ FdxQ1ginv.basisSave("FM-Fjx6$Fdx-F`x6$FevQ(.binaryFM-Fjx6$FdxQ+",~basis)|+FM-Fj x6$FdxQ+f~=~file("FM-Fjx6$Fdx-F`x6$FevQ'.janetFM-Fjx6$FdxQ)",~"w")|+FM@%9:C<-Fj x6$FdxQ6l~=~basis.lengthIB()|+FM-Fjx6$FdxQ'i~=~1|+FM-Fjx6$FdxQ:for~p~in~basis.i terIB():|+FM-Fjx6$FdxQ/~~~~if~i~<~l:|+FM@%Fjcl-Fjx6$FdxQB~~~~~~~~S~=~"\""+str(p )+"~\",\\"|+FM-Fjx6$FdxQ`o~~~~~~~~S~=~"\""+str(p).replace('*@',~'').replace('@' ,~'1')+"~\",\\"|+FM-Fjx6$FdxQ7~~~~~~~~print~>>~f,~S|+FM-Fjx6$FdxQ+~~~~else:|+FM @%Fjcl-Fjx6$FdxQ?~~~~~~~~S~=~"\""+str(p)+"~\""|+FM-Fjx6$FdxQ]o~~~~~~~~S~=~"\""+ str(p).replace('*@',~'').replace('@',~'1')+"~\""|+FMF`[o-Fjx6$FdxQ-~~~~i~=~i+1| +FM-Fjx6$FdxQ+f.close()|+FMF_in-Fjx6$Fdx-F`x6$FevQ$.lmFMFginF`jn-Fjx6$FdxQ>~f,~"_IB_RESULTGB~:=~["|+FM-Fjx6$FdxQ6l~=~basis.lengthGB()| +FMF`jn-Fjx6$FdxQ:for~p~in~basis.iterGB():|+FMFfjn@%FjclFjjnF][oF`[oFc[o@%FjclF g[oFj[oF`[oF]\o-Fjx6$FdxQ2print~>>~f,~"]:"|+FM@$F`enC'F`\oF_in-Fjx6$Fdx-F`x6$Fe vQ+.outoftimeFMFgin-Fjx6$FdxQDprint~>>~f,~str(basis.outOfTime())|+FMCK@$F`enC%- Fjx6$FdxQIprint~>>~f,~"_IB_RESULTout_of_time~:=~"|+FMF[`o-Fjx6$FdxQ1print~>>~f, ~":"|+FM-Fjx6$FdxQ?print~>>~f,~"_IB_RESULT~:=~["|+FMF]jnF`jnFcjnFfjn@%Fjcl-Fjx6 $FdxQ<~~~~~~~~print~>>~f,~p,~","|+FM-Fjx6$FdxQ_o~~~~~~~~print~>>~f,~str(p).repl ace('*@',~'').replace('@',~'1'),~","|+FMFc[o@%Fjcl-Fjx6$FdxQ7~~~~~~~~print~>>~f ,~p|+FM-Fjx6$FdxQjn~~~~~~~~print~>>~f,~str(p).replace('*@',~'').replace('@',~'1 ')|+FMF]\oFa_o-Fjx6$FdxQAprint~>>~f,~"_IB_RESULTlm~:=~["|+FMF`jn-Fjx6$FdxQ6c~=~ basis.iterLcIB()|+FMFh\oFfjn@%Fjcl-Fjx6$FdxQao~~~~~~~~print~>>~f,~"[[",~c.next( ),~",",~p,~"],",~p.dependVar(),~"],"|+FM-Fjx6$FdxQjq~~~~~~~~print~>>~f,~"[[",~c .next(),~",",~str(p).replace('*@',~'').replace('@',~'1'),~"],",~p.dependVar(),~ "],"|+FMFc[o@%Fjcl-Fjx6$FdxQ`o~~~~~~~~print~>>~f,~"[[",~c.next(),~",",~p,~"],", ~p.dependVar(),~"]"|+FM-Fjx6$FdxQiq~~~~~~~~print~>>~f,~"[[",~c.next(),~",",~str (p).replace('*@',~'').replace('@',~'1'),~"],",~p.dependVar(),~"]"|+FMF]\oFa_o-F jx6$FdxQBprint~>>~f,~"_IB_RESULTanc~:=~["|+FMF`jn-Fjx6$FdxQ=for~p~in~basis.iter AncIB():|+FMFfjn@%Fjcl-Fjx6$FdxQV~~~~~~~~print~>>~f,~"[",~p,~",",~p.dependVar() ,~"],"|+FM-Fjx6$FdxQip~~~~~~~~print~>>~f,~"[",~str(p).replace('*@',~'').replace ('@',~'1'),~",",~p.dependVar(),~"],"|+FMFc[o@%Fjcl-Fjx6$FdxQU~~~~~~~~print~>>~f ,~"[",~p,~",",~p.dependVar(),~"]"|+FM-Fjx6$FdxQhp~~~~~~~~print~>>~f,~"[",~str(p ).replace('*@',~'').replace('@',~'1'),~",",~p.dependVar(),~"]"|+FMF]\oFa_o-Fjx6 $FdxQFprint~>>~f,~"_IB_RESULTmultvar~:=~["|+FMF`jn-Fjx6$FdxQAfor~j~in~basis.ite rMultVarIB():|+FMFfjn-Fjx6$FdxQI~~~~~~~~print~>>~f,~[k~for~k~in~j],~","|+FMFc[o -Fjx6$FdxQD~~~~~~~~print~>>~f,~[k~for~k~in~j]|+FMF]\oFa_o@$F^]oC,-Fjx6$FdxQ6l~= ~ic.lengthDenom()|+FM-Fjx6$FdxQDprint~>>~f,~"_IB_RESULTdenom~:=~["|+FMF`jnFe]oF fjn-Fjx6$FdxQ<~~~~~~~~print~>>~f,~c,~","|+FMFc[o-Fjx6$FdxQ7~~~~~~~~print~>>~f,~ c|+FMF]\oFa_o@$F_^oC,Ff^oFi^oF`jnF\_oFfjn@%FjclF[aoF^aoFc[o@%FjclFbaoFeaoF]\oFa _oF`\oF_`l@%Fffn@%FewC%>F^u-F`u6#-F`x6$Q)runginv~FMFev@$/F^u%%NULLG-FV6#%Acould ~not~run~program~'runginv'.G>F^uFi[mC$>F^u-F`u6#-F`x6%FffoFevQ-~>~/dev/nullFM@% 3/Fi[mFdq/FhuF`v>F^uFdq>F^uFfnC$>F^u-%'systemGFcfo@$FhfoFjfo@$0F^uFdq-FV6#%Merr or~during~call~of~Python~or~interruption.G@$FctC%>F^u-F`u6#-F`x6'Q&if~[~FMFevQ, .janet~-ot~FMFevQ:~];~then~echo~-n~true;~fiFM@$2Fdq-Fj\nFgu-FV6#%dpoutput~file~ of~ginv~is~older~than~input~file~(probably,~program~ginv~stopped~abnormally).G@ 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"F7FD@&2&F=6#FJ&F4FRFA2FSFQFFFDF-F-F-F-, Q>Involutive/pdegrevlex_block.mF- M7R0 I6Involutive/gb_leadmonf*6"6#%"sG6#%jnCopyright~(C)~2006-2008~by~Daniel~Robertz .~All~rights~reserved.GF$C$>8$-%(convertG6$-%+kerneloptsG6#%(versionG%'stringG@ '5555/-%*substringG6$F+;"""""(Q(Maple~VF$/F:Q(Maple~6F$/F:Q(Maple~7F$/F:Q(Maple ~8F$/-F;6$F+;F>""*Q*Maple~9.5F$&%)GroebnerG6#%(leadmonG/FHQ*Maple~9.0F$C$FN,$FP !""&FN6#%,LeadingTermGF$F$F$F$, Q8Involutive/gb_leadmon.mF$ M7R0 I5Involutive/proc_varsf*6$'%%varsG%%listG%'n_entrG60%"aG%"iG%"jG%"lG%"vG%$varG% (var_ordG%(deg_ordG%(var_degG%(tup_degG%)tup_permG%(tup_numG%'blocksG%)entr_pos G6#%jnCopyright~(C)~2002-2008~by~Daniel~Robertz.~All~rights~reserved.G6"C9>8)%% NULLG>8*F>>8,F>>8+F>>8-7#-%"$G6$""!9%>8.F>>817">8/7#-FI6#;"""FL>8'FX@$/9$FQ-%&E RRORG6#%Gexpecting~non-empty~list~of~variables.G?(8%FXFX-%%nopsG6#Fgn%%trueG@%- %%typeG6$&Fgn6#F]oF'C%@$/FfoFQ-Fin6#%Punexpected~empty~list~in~the~list~of~vari ables.G@%-Fdo6$&Ffo6#FX%)equationG>8&-%#opG6$FXFap>FepFap@)-Fdo6$Fep%*nonposint G-Fin6$%Zi-th~standard~basis~vector~does~not~exist~in~given~moduleG/.F]oFep-Fdo 6$Fep%'posintGC)@&/FZFX>80Fao4Fjq-Fin6#%`pexpecting~either~a~sequence~of~entry~ numbers~or~a~sequence~of~lists~of~entry~numbers.G>8(-%$mapG6$f*6#F*F:6$%)operat orG%&arrowGF:@%-Fdo6$FgnFcp7$-Fgp6$FXFgn-Fgp6$""#Fgn7$FgnFKF:F:F:Ffo>Fep-%'sele ctG6$f*FerF:FfrF:-%&evalbG6#52&FgnFbpFX2T$F]tF:F:6$F(FLF`r@$0FepFQ-Fin6$F`q/Fbq &&FepFbpFbp?(FepFXFX-F_o6#F`rFao@%/&FS6#&&F`r6#FepFbpFK-Fin6#%joentry~numbers~a re~not~allowed~to~occur~more~than~once~in~the~list~of~variables.GC%>FN6$FNF_u>F S-%'subsopG6$/F_uFKFS>FF-Fju6$/F_u&F`u6#FasFF@%/FPFQ>FP7#Fit>FP7$-Fgp6#FP,&&FP6 #!""FXFitFX>FZ,&FZFXFitFX-Fdo6$Fep%%nameGC*@$2FXFZ-Fin6#%`pin~the~variable~list ~the~numbers~of~standard~basis~vectors~must~follow~the~variables.G@&/F=F>>FjqFa oF[r-Fin6#%hoexpecting~either~a~sequence~of~variables~or~a~sequence~of~lists~of ~variables.G>F`r-Fbr6$f*FerF:FfrF:@%FjrF\s7$FgnFXF:F:F:Ffo@$0-F_o6#-Fes6%%(hast ypeG-Fbr6$f*FerF:FfrF:F]tF:F:F:F`rFcwFit-Fin6#%@variables~must~be~of~type~name. G>F=6$F=-Fgp6#-Fbr6$f*FerF:FfrF:F]tF:F:F:F`r>FB6$FB-Fgp6#-Fbr6$f*FerF:FfrF:&Fgn FbvF:F:F:F`r>F@6$F@-Fbr6$f*FerF:FfrF:F]tF:F:F:F`r>FD6$FD-Fbr6$f*FerF:FfrF:FazF: F:F:F`rF`yC$@%-Fdo6$FfoFcp>Fep-Fgp6$FXFfo>FepFfo@)F[qF^qFcq@$2FKFLC&@&Fhq>Fjq%& falseGFjqF\r@$2FLFepF^q@%/&FSFauFKFbuC%>FN6$FNFep>FS-Fju6$/FepFKFS@$F^[l>FF-Fju 6$/Fep-Fgp6$FasFfoFF>FZ,&FZFXFXFXFawC'@$FfwFgw@$0F@F>-Fin6#%^pthe~variable~list ~must~contain~names~for~variables~or~lists~of~names~for~variables.G@&F[x>FjqFj[ lFjq-Fin6#%\oexpecting~either~list~of~variables~or~list~of~lists~of~variables.G >F=6$F=Fep@%F^[l>FB6$FBF\]l>FB6$FBFXF`y?(F]oFXFXFLFao@$0&FSFgoFK>FN6$FNF]o>FB7# FB@$4-Fdo6$FB-F'6#Feq-Fin6#%Qexpecting~natural~number~as~degree~for~variable.G@ $4-Fdo6$FF-F'6#%(integerG-Fin6#%Wexpecting~integer~as~degree~for~standard~basis ~vector.G@$Fdv>FP7#FL>%,_entrblocksGFQ>F]oFX?(F:FXFXF:1F]oFLC&>FepFX?(F:FXFXF:3 1Fep-F_oFjv2&FPFauF]o>Fep,&FepFXFXFX@%Fj`l>Fb`l7$-Fgp6#Fb`lFep[>F]o,&F]oFXFXFX> Fb`l7$Fcal-FI6#;F]oFL>%(_vardegGFB>%(_tupdegGFF7(7#F=7#F@7$-Fgp6#FB-Fgp6#FF7#FD 7#FNFPF:6%F^blF`blFb`lF:F:, Q7Involutive/proc_vars.mF: M7R0 I:Involutive/proc_termorderf*6(%&m_ordG%%seqvG%(var_degG%(tup_degG%)entr_posG%/ default_lmprocG62%#_aG%#_bG%#_cG%$cmpG%'lmprocG%&B_OrdG%,B_Ord_blockG%&N_OrdG%, N_Ord_blockG%$POTG%"sG%,str_testordG%.str_testorderG%-str_leadtermG%)str_seqvG% 1str_negtestorderG6#%jnCopyright~(C)~2002-2008~by~Daniel~Robertz.~All~rights~re served.G6"C)>82-%$catG6$-%#opG6#-%$mapG6$f*6#F6F>6$%)operatorG%&arrowGF>-FC6$-% (convertG6$9$%'stringGQ",F>F>F>F>&9%6#;"""!"#-FS6$&FY6#!""FV>8.-FS6$-%+kernelop tsG6#%(versionGFV@'5555/-%*substringG6$F^o;Ffn""(Q(Maple~VF>/F[pQ(Maple~6F>/F[p Q(Maple~7F>/F[pQ(Maple~8F>/-F\p6$F^o;Ffn""*Q*Maple~9.5F>C$>8/Q4Groebner[testord er]F>>81Q:_a->Groebner[leadmon](_a,F>/FhpQ*Maple~9.0F>C$>F_qQ4Groebner:-testord erF>>FbqQ:_a->Groebner:-leadmon(_a,F>C$>F_qQ4Groebner[TestOrder]F>>FbqQ>_a->Gro 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>F]vF\yC%@%F\uC$>F_u%:Involutive/pdegrevlex_POTG>Fbu%6Involutive/pdegrevlexGC$> F_u%Fbu%8Involutive/pdegrevlex_ZG>Fju%F]vF`\l/FU""$C(>F_s%&falseG>FbsFcs@%F[t>F]tF^t>F]tFct@%3/-Fj v6#9(Ffn/&F`]l6#FfnFgz@%F\uC$>F_uFcu>FbuFcuC$>F_uFhu>FbuFhu@%F\uC$>F_u%FbuFcuC$>F_u%>Involutive/pplex_Z_entr_blockG>FbuFhu>FjuF[ v>F]vF[v/FU""%C$>F_sFf\l@%FcvC'>FbsF^w@%F[t>F]tFgw>F]tF\x@%F\]l@%F\uC$>F_uFex>F buFexC$>F_uFjx>FbuFjx@%F\uC$>F_u%EInvolutive/pdegrevlex_deg_entr_blockG>FbuFexC $>F_u%GInvolutive/pdegrevlex_deg_Z_entr_blockG>FbuFjx>FjuF\y>F]vF\yC%>FbsF`y@%F [t>F]tFgy>F]tF\z@%FazC%@%F\]l@%F\uC$>F_uFex>FbuFexC$>F_uFjx>FbuFjx@%F\uC$>F_uF[ `l>FbuFexC$>F_uF_`l>FbuFjx>FjuF\y>F]vF\yC%@%F\]l@%F\uC$>F_uFi[l>FbuFi[lC$>F_uF^ \l>FbuF^\l@%F\uC$>F_u%AInvolutive/pdegrevlex_entr_blockG>FbuFi[lC$>F_u%CInvolut ive/pdegrevlex_Z_entr_blockG>FbuF^\l>FjuF`\l>F]vF`\l/FU""&C$>F_sF`s@%Fcv-%&ERRO RG6#%5not~implemented~yet.GC%>Fbs-Fds6#-FC6+QIproc(_a,_b)~local~d1,d2;~d1:=degr ee(_a,|frF>FAQ4|hr);~d2:=degree(_b,|frF>FAQ<|hr);~if~d1F_qQ -(_a,_b,plex(F>FAQC)))~then~true;~else~false;~fi;~endF>>F]t-Fds6#-FC6-QQproc(_c )~local~d1,d2,i,j,n,C,L;~C~:=~[coeffs(_c,F>FhtQ[q,~'L')];~n~:=~nops(C);~if~n~=~ 1~then~RETURN(C[1],~L);~fi;~L~:=~[L];~j~:=~1;~d1~:=~degree(L[j],~|frF>FAQN|hr); ~for~i~from~2~to~n~do~d2~:=~degree(L[i],~|frF>FAQ@|hr);~if~d1~<~d2~or~(d1~=~d2~ and~F>F_qQ3(L[j],~L[i],~plex(F>FAQen)))~then~j~:=~i;~d1~:=~d2;~fi;~od;~RETURN(C [j],~L[j]);~endF>@%FazFdclC%@%F\uC$>F_u%7Involutive/pdeglex_POTG>Fbu%3Involutiv e/pdeglexGC$>F_u%9Involutive/pdeglex_Z_POTG>Fbu%5Involutive/pdeglex_ZG>Fju%9Inv olutive/pdeglex_blockG>F]vF\fl/FU""'C$>F_sFf\l@%FcvFdclC%>FbsFjcl>F]tFddl@%FazF dclC%@%F\]l@%F\uC$>F_uFeel>FbuFeelC$>F_uFjel>FbuFjel@%F\uC$>F_u%>Involutive/pde glex_entr_blockG>FbuFeelC$>F_u%@Involutive/pdeglex_Z_entr_blockG>FbuFjel>FjuF\f l>F]vF\fl/FUF\oC(>F_sF`s>Fbs-Fds6#-FC6&FgrFhsFAFis>F]t-Fds6#-FC6)QKproc(_c)~loc al~i,j,n,C,L;~C~:=~[coeffs(_c,F>FhtQcq,~'L')];~n~:=~nops(C);~if~n~=~1~then~RETU RN(C[1],~L);~fi;~L~:=~[L];~j~:=~1;~for~i~from~2~to~n~do~if~not~F>F_qF\elFAQP))~ then~j~:=~i;~fi;~od;~RETURN(C[j],~L[j]);~endF>@%F\uC$>F_u%8Involutive/pnegplex_ POTG>FbuFcuC%-Fecl6#%Tlocal~orders~not~supported~yet~in~the~integer~case.G>F_u% :Involutive/pnegplex_Z_POTG>FbuFhu>Fju%:Involutive/pnegplex_blockG>F]vF[v/FUFgn C)@$5FcvFaz-Fecl6#%apUp~to~now,~only~default~degrees~for~variables~and~tuples~a re~allowed~for~local~orders.G>F_sF`s>Fbs-Fds6#-FC6+F^dlFAF_dlFAQ<|hr);~if~d1>d2 ~or~(d1=d2~and~F>F_qQ-(_a,_b,tdeg(F>FAFbdl>F]t-Fds6#-FC6-FhdlFhtFidlFAFjdlFAQ@| hr);~if~d1~>~d2~or~(d1~=~d2~and~F>F_qQ3(L[j],~L[i],~tdeg(F>FAF]el@%F\uC$>F_u%=I nvolutive/pnegdegrevlex_POTG>FbuFi[lC%Fail>F_u%?Involutive/pnegdegrevlex_Z_POTG >FbuF^\l>Fju%?Involutive/pnegdegrevlex_blockG>F]vF`\l/FU!"$C(>F_sFf\l>FbsF_hl>F ]tFdhl@%F\]l@%F\uC$>F_u%4Involutive/pnegplexG>FbuFcuC%Fail>F_uFf\m>FbuFhu@%F\uC 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rootofsG6#%jnCopyright~(C)~2000-2008~by~Daniel~Robertz.~All~rights~reserved.G6" Cco>80-%6Involutive/proc_inputG6#9$>8-&FV6#""">8.&FV6#""#>8/&FV6#""$>8?&FV6#""' >8@&FV6#""(>8A&FV6#"")>FV&FV6#""%@%332F^o9#-%%typeG6$&9"Fbo%%listG4-F]q6$F_q-Fa q6#%(integerGC)>82F_q>81-FX6#&F`qF]o@$2Fin&F\rFhn-%&ERRORG6#%Xexpecting~list~of ~relations~for~the~residue~class~ring.G@$4&F\rFbo-Fdr6#%foright~hand~sides~for~ relations~of~the~residue~class~ring~are~not~supported.G>F\r&F\rFep@%/&F\r6$FinF in7#""!>F\r7"C$>F\r7#-%$seqG6$-F[t6$7$-%'subsopG6$/8&&F\r6%8'FinFin7#-%"$G6$Fds Ffn7#-Fjt6$FdsF[o/Fdt;FinFfn/Fgt;Fin-%%nopsG6#F\r>FV7$-%#opG6#FV-FiuFeu>8*FfpC& @$2F[qF^o-Fdr6#%Pexpecting~list~of~variables~as~second~argument.G>FjqF_r>F\rFfs >F]vFco>Fjq-%5Involutive/proc_varsG6$FjqFfn>83&FjqF]o>84&FjqFbo>85&FjqFep>87&Fj q6#""&>8B&FjqFgo>Fjq&FjqFhn>%&_nvarG-Fdu6#Fjq@%0%2Involutive/characGFds>FV-%$mo dG6$-%(collectG6%FVFjq%,distributedGFdx>FVFix>Fjo-%'removeG6$f*6#F)FS6$%)operat 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G-F]q6$F\_l%)equationG@=/-Fiu6$FinF\_lQ%NameFSC$@$4-F]q6$-Fiu6$F^oF\_lFc[l-Fdr6 #%Fexpecting~a~string~for~option~"Name".G>Fj\lF`bl/FhalQ%charFSC$@$4-F]q6$F`bl% *nonnegintG-Fdr6#%Qexpecting~0~or~a~prime~number~for~option~"char".G>Fe[lF`bl/F halQ%timeFSC$@$Fjbl-Fdr6#%Sexpecting~time~bound~in~seconds~for~option~"time".G> F_]lF`bl/FhalQ)GroebnerFSFS/FhalQ'algextFS@%-F]q6$F`blFaq?&8(F`blFh\lC&>8,-%&mi nusG6$-%'indetsG6#Fbdl<&-Fiu6#Fc\l-Fiu6#Fe\l-Fiu6#-%$mapG6%F][lFeo%%nameG-Fiu6# -Fdel6%F][lFjoFfel@$50-Fdu6#FedlFin4-F]q6$Fbdl-%(polynomG6$%)anythingGFedl-Fdr6 #%`sexpecting~a~univariate~polynomial~(possibly~with~rational~coefficients~in~p reviously~defined~algebraic~elements)~for~option~"algext".G@$0-%*intersectG6$Fe dl<#-FiuFax<"-Fdr6#%_qthe~univariate~polynomial~for~option~"algext"~may~not~con tain~indeterminates~of~the~polynomial~ring.G@$4-Fhy6$-FiuF_flFc\lC%>Fa\l7$-Fiu6 #Fa\lFbdl>Fc\l7$F]elFigl@$-%(hastypeG6$Fbdl%(nonrealG>F_pFh\lC&>Fedl-Fgdl6$-Fjd l6#F`blF\el@$5F]fl4-F]q6$F`blFcflFgfl@$F[glFbgl@$FfglC%>Fa\l7$F]hlF`bl>Fc\lF`hl @$-Fchl6$F`blFehl>F_pFh\l/FhalQ)transextFS@'-F]q6$F`bl-Faq6#Ffel?&FbdlF`blFh\l@ $4-Fhy6$Fbdl7$-Fiu6#FjoF_el>Fe\l7$F_elFbdl-F]q6$F`blFfel@$4-Fhy6$F`blFhjl>Fe\l7 $F_elF`bl-Fdr6#%Sexpecting~(list~of)~name(s)~for~option~"transext".G/FhalQ*algo rithmFSC$>F]]lF`bl@$54-F]q6$F]]lFc[l33330F]]lQ#TQFS0F]]lQ)TQDegreeFS0F]]lQ*TQGr adingFS0F]]lQ,TQBlockHighFS0F]]lQ+TQBlockLowFS-Fdr6#%gqexpecting~strings~"TQ"~o r~"TQDegree"~or~"TQBlockHigh"~or~"TQBlockLow"~or~"TQGrading"~for~option~"algori thm".G/FhalQ&quietFSC$@$4-F]q6$F`bl%(booleanG-Fdr6#%Lexpecting~boolean~value~fo r~option~"quiet".G>Fd]lF`bl/FhalF``lC$@$Ff]m-Fdr6#%Lexpecting~boolean~value~for ~option~"denom".G>F`^lF`bl/FhalF]`lC$@$Ff]m-Fdr6#%Pexpecting~boolean~value~for~ option~"donotread".G>F^^lF`bl/FhalQ+MovedBoundFSC$@$Fjbl-Fdr6#%Zexpecting~a~non -negative~integer~for~option~"MovedBound".G>Fb^lF`bl/FhalQ-QlengthBoundFSC$@$Fj bl-Fdr6#%fnexpecting~a~non-negative~integer~for~option~"QlengthBound".G>Fd^lF`b l/FhalQ,DegreeBoundFSC$@$Fjbl-Fdr6#%enexpecting~a~non-negative~integer~for~opti on~"DegreeBound".G>Ff^lF`blF`alF`al>Fd`l-%4Involutive/proc_ordG6*Fi[lFjqF\wF_wF bwFjqFjwFh\l>86&Fd`lFep@$Fi`m>FjwFfs@$0Few7#-Fjt6#F`u>FV-Fdel6$f*Fcy6#F*FSFS-Fa t6$/Fin7#-F[t6$&&FZFhn6#&Fjy6#Fj\l/Fj\l;FinT%FZFSFS6&F:FewF0FfnFV>%)_inv_denG.F gbm?&Fdt-Fjdl6$Fa\l%'algextGFh\l@$4-Fhy6$FdtFeo>Feo7$-Fiu6#FeoFdt>FdtFin?(FSFin FinFS1Fdt-FduFdcmC&@$0-Fiu6$Fds&FeoF]_l%'RootOfG-Fdr6#-%$catG6$-F][l6$F^dmFc[l% 3~is~not~algebraic.G?&Fgt-Fjdl6$-Fiu6$FinF^dmF\cmFh\l@$4-Fhy6$FgtFeo>Feo7$FccmF gt@$-Fchl6$F[emFehl>F_pFh\l>Fdt,&FdtFinFinFin>FdtFin?(FSFinFinFS2FdtFhcm@%-%$ha sG6$F[em&Feo6#;Fhem!"">Feo7$-Fiu6#-Fat6$/Fdt%%NULLGFeoF^dm>FdtFhem>FdtFin>FgtFd s>8MFfs?(FSFinFinFSFgcm@%2Fds-Fj]l6$Q'RootOfFSFedm@%-Fhy6%F^dm7#-F[t6$-F_dm6$&F a\lF[el&Fc\lF[el/Fbdl;Fin-FduF^hl.F]vC&>F`gm7$-Fiu6#F`gm/&Fc\l6#F]vF^dm>FV-%%su bsG6$/F^dmF[imFV>Fa\l-F_im6$FaimFa\l>Feo-Fat6$Fjfm-F_im6$FaimFeoC+>F`gm7$Fhhm/- Fcdm6$.%%_algGFgtF^dm>Fedl-Fgdl6$-Fjdl6#F[em<#F]el>F]vFin?(FSFinFinFS31F]vFchm4 -F^fm6$&Fa\lF\imF^dm>F]v,&F]vFinFinFin@%F[[nC$>Fa\l-Fat6$/F]v6$-%CInvolutive/su bsindetunivariatepolyG6%F[em&FedlFhnF^jmF_[nFa\l>Fc\l-Fat6$/F]v6$F^jmF[imFc\lC$ >Fa\l7$F]hlFi[n>Fc\l7$F]elF^jm>FV-F_im6$/F^dmF^jmFV>Fa\l-F_im6$Fj\nFa\l>Feo-Fat 6$Fjfm-F_im6$Fj\nFeo>Fgt,&FgtFinFinFin>FdtFhem>FdtFin?(FSFinFinFS1Fdt-FduF^el@% -Fhy6$&Fc\lF]_lFeoC$>Fc\l-Fat6$FjfmFc\l>Fa\l-Fat6$FjfmFa\l>FdtFhem@$3330-%*subs tringG6$F[[l;FinF]pQ(Maple~VFS0F[_nQ(Maple~6FS0F[_nQ(Maple~7FSF_pC%>Fc\l7$%#_IG F]el>Fa\l7$,&*$Fg_nF^oFinFinFin-Fiu6#-F_im6$/^#FinFg_nFa\l>FV-F_im6$F``nFV>88-% 5Involutive/ginvBasisG6=FVFjqFeoFjoFfnF[oF`oFe[lFi[lF\wFjw&F_w6#;FinF_x&F_w6#;, &F_xFinFinFin,&F_xFinFfnFinFa\lFc\lFe\lFj\lF]]lF_]lFa]lFd]lFh\lF^^lF`^lFb^lFd^l Ff^l@$F^^l-%'RETURNGFS@$3F`^l-%)assignedG6#%._GINV_inv_denG>FgbmFjan>Ff`n&Ff`nF hn>89%-_IB_RESULTGBG?(Fdt-FduFihmFcfmFinFh\lC%>Ff`n-F_im6$&F`gmF]_lFf`n>F_bn-F_ im6$FgbnF_bn>Fgbm-F_im6$FgbnFgbm@$Fg^nC%>Ff`n-F_im6$/Fg_nFa`nFf`n>F_bn-F_im6$Fc cnF_bn>Fgbm-F_im6$FccnFgbm@$F^amC%>Few-Fdel6$f*FcyFfamFSFSC$-Fhy6%FZFjy.Fj\lFj\ lFSFS6$F:FewF_am>Ff`n-Fdel6$f*FcyFfamFSFS7$-F[t6$&FZF_bmFbbm-F[t6$&FZFabm/Fj\l; ,&FdbmFinFinFin-FduFYFSFSFebmFf`n>F_bn-Fdel6$f*FcyFfamFSFSFidnFSFSFebmF_bn@%F`o @$/Ff`nFfs@%/FfnFin>F_bnFcs>F_bn7#Fht@%F\fn@%/F[oFinC%>Fiz-Fdel6$f*FcyFSFdyFS@$ 3/F^bmFds0&FZ6#,&FjyFinFinFinFdsF\gnFSFS6$F0FfnFf`n>F_bn-Fdel6$f*FcyFSFdyFS@$0F ^bmFds/F^bmF\gnFSFSF_gnF_bn@$/F_bnFfs>F_bn7#/FdsFdsC%>Fiz-Fdel6$f*FcyFSFdyFS@$3 Fjfn0&FZ6#;F^gn,&FjyFinFdbmFin7#-Fjt6$FdsFdbmFdhnFSFS6&F0FfnF1F[oFf`n>F_bn-Fdel 6$f*FcyFSFdyFS@$Fegn/F^bmFdhnFSFSF[inF_bn@$Fhgn>F_bn7#/FdsF\u@%FbfnC%>Fiz-Fdel6 $f*FcyFSFdyFS@$3/&FZ6#;FinFjy7#-Fjt6$FdsFjyF[gnF\gnFSFSF_gnFf`n>F_bn-Fdel6$f*Fc yFSFdyFS@$0F_jnFbjn/F_jnF\gnFSFSF_gnF_bn@$Fhgn>F_bn7#/FhtFdsC%>Fiz-Fdel6$f*FcyF SFdyFS@$3F^jnFchnFdhnFSFSF[inFf`n>F_bn-Fdel6$f*FcyFSFdyFS@$Fjjn/F_jnFdhnFSFSF[i nF_bn@$Fhgn>F_bn7#/FhtF\u7#-F[t6$&F_bn6#,$FdtFcfm/Fdt;Fin-Fdu6#F_bnFS6+F_xF_zF] zFazFczFezFgzFizFgbmFSFS, Q?Involutive/GroebnerBasisGINV.mFS M7R0 I=Involutive/InvolutiveOptionsf*6#%"aG6#%)oldvalueG6#%jnCopyright~(C)~2000-2008 ~by~Daniel~Robertz.~All~rights~reserved.G6"C%>8$%%NULLG@%-%%typeG6$9$%'stringG@ ?/F3Q&MapleF*C&>%5Involutive/InvoBasisG%4Involutive/InvBasisG>%6Involutive/PolI ReduceG%:Involutive/PolInvolReduceG>%6Involutive/GroebBasisG%7Involutive/Groebn erBasG>%5Involutive/SyzygyModG%5Involutive/SyzModuleG/F3Q$C++F*C&>F:%>Involutiv e/InvBasisFastAssertG>F=%F@%=Involutive/GroebnerB asisFastG>FC%F:%>Involutive/InvBasis GINVAssertG>F=%F@%=Involutive/GroebnerBasisGINVG> FC%F-FF5/F:FT/F:%?Involutive/InvolutiveBasisG INVG>F-FQ>F-F7@$2"""9#@%-F16$&9"6#""#F4@)/F^pF7C&>F:F;>F=F>>F@FA>FCFD/F^pFFC&>F :FI>F=FK>F@FM>FCFO/F^pFQC&>F:FT>F=FV>F@FX>FCFZ-%&ERRORG6#%jnexpecting~either~"M aple",~"C++",~or~"GINV"~as~second~parameter.GFeq/F3Q)InvBasisF*C$>F-F:@$Fho@%-F 16$F^p%*procedureG>F:F^p-Ffq6#%Kexpecting~a~procedure~as~second~parameter.G/F3Q *InvReduceF*C$>F-F=@$Fho@%F_r>F=F^pFcr/F3Q4ResolutionAutoTruncF*C$>F-%?Involuti ve/ResolutionAutoTruncG@$Fho@%-F16$F^p%'posintG>FasF^p-Ffq6#%Rexpecting~a~posit ive~integer~as~second~parameter.G/F3Q-SyzygyModuleF*C$>F-FC@$Fho@%F_r>FCF^pFcr5 /-%*substringG6$F3;Fio""%Q%CharF*/FdtQ%charF*C$>F-%2Involutive/characG@$Fho@%3- F16$F^p%(integerG5/F^p""!-%(isprimeG6#F^pC%>F^uF^p@$0F^uFgu>%4Involutive/ratcoe ffG%%trueG@$0F^uF-C$>%)P_T_ListG.Ffv>%(_StatssG.Fiv-Ffq6#%Vexpecting~zero~or~a~ prime~number~as~second~parameter.G5/F3Q)RationalF*/F3Q)rationalF*C$>F-F`v@$Fho@ %-F16$F^p%(booleanGC%>F`vF^p@$4F`v>F^uFgu@$0F`vF-C$>FfvFgv>FivFjv-Ffq6#%Mexpect ing~boolean~value~as~second~parameter.G5/-Fet6$F3;Fio""'Q'MatrixF*/FixQ'matrixF *C$>F-%6Involutive/matrixtypeG@$Fho@%5/F^p%'matrixG/F^p%'MatrixG>FbyF^p-Ffq6#%T expecting~'matrix'~or~'Matrix'~as~second~parameter.G/F3Q'GBasisF*C$>F-F@@$Fho@% F_r>F@F^pFcr/F3Q*JanetLikeF*C$>F-%5Involutive/janetlikeG@$Fho@%Fgw>FizF^pFdx5/F 3Q)CriteriaF*/F3Q)criteriaF*C$>F-%3Involutive/invcritG@$Fho@%54-F16$F^p-%%listG 6#Ffs0-%'removeG6%%$hasGF^p7&FioFap""$Fht7"-Ffq6#%jnexpecting~list~of~integers~ between~1~and~4~as~second~parameter.G>Fd[l-%%sortGFju-Ffq6#%Hinvalid~option;~se e~?InvolutiveOptions.G-Ffq6#%hnexpecting~a~string~as~first~argument;~see~?Invol utiveOptions.GF-F*6.FfvFivF:F=F^uF`vFbyFizF@FCFd[lFasF*F*, Q?Involutive/InvolutiveOptions.mF* M7R0 I8Involutive/SyzygyModulef*6#%"LG6$%"aG%"SG6#%jnCopyright~(C)~2002-2008~by~Dani el~Robertz.~All~rights~reserved.G6"C&@$0%7Involutive/initializedG.%%trueG-%0Inv olutive/initGF+>8%-%5Involutive/SyzygyModG6#9"@$30F57"/F7%8&""!@%%5Involutive/ja netlikeG?&8%9$%%trueGC$>8$,&-%(convertG6$&F46$""$"""%"+GFA-F<6$-%%subsG6$/%)inf inityGF0&F46#""&FBFA@$2F/F9>F/F9?&F4F5F6C$>F9F;@$FN>F/F9-%'RETURNG6#F/F,F,F,F,, Q6Involutive/pmax_deg.mF, M7R0 I>Involutive/PolHilbertFunctionf*6"6+%"iG%"jG%"qG%"rG%"sG%,given_basisG%/args_w ithout_sG%$varG%2tmp_P_T_List_dataG6#%\pCopyright~(C)~2000-2008~by~Carlos~F.~Ci d~and~Daniel~Robertz.~All~rights~reserved.GF$C(@$/9#""!-%'RETURNG6#F">8(.F:>8*% %NULLG@%1F4"""C$>8)%&falseG@$/F4FA@%3-%%typeG6$&9"6#FA%)equationG/-%#opG6$FAFMQ $varF$>F:-FS6$""#FM>F:FMC$>FD%%trueG?(8$FAFAF4Fgn@%3-FK6$&FN6#FinFP/-FS6$FAF^oF U>F:-FS6$FYF^o>F=6$F=F^o@%FD>6$8,8+-%7Involutive/setup_basisG6#F=@$4-%)assigned G6#%)P_T_ListG-%&ERRORG6#%Umissing~involutive~basis;~run~InvolutiveBasis~first. G@)-FK6$F:%'stringGC'>8&-%4Involutive/pmax_degGFdp?(FinF5FA,&F`qFA!""FAFgn-%'pr intfG6%Q0Dim(M.%d)~=~%a|+F$Fin-F"F_o-Fgq6%Q;Dim(M.s)~=~%a,~for~s~>=~%dF$-%@Invo lutive/PolHilbertPolynomialG6#F;F`q@$FD-%;Involutive/restoreP_T_ListG6#F[p-F76# F>3-FK6$F:%(numericG/F:F5C%>8'-%1Involutive/PolHFG6#F:@$FDFbrF^sFhrC%>F^s-%)sim plifyG6#,&F_sFA-F`s6#,&F:FAFeqFAFeq@$FDFbrF^sC$@$FDFbrf*6#F&F$6$%)operatorG%&ar rowGF$-F"6$FN/FU9$F$F$F$F$F$F$F$, Q@Involutive/PolHilbertFunction.mF$ M7R0 I6Involutive/jetsmklistf*6#%"LG6"6#%[oCopyright~(C)~2000-2002~by~Mohamed~Baraka t.~All~rights~reserved.GF&@)-%%typeG6$9$%%listGF--F+6$F-%$setG-%(convertGF,-F+6 $F-%&arrayG-F36$F-%)listlistG7#F-F&F&F&F&, Q8Involutive/jetsmklist.mF& M7R0 I=Involutive/PolResolutionFastf*6#%"LG6L%"aG%"eG%"iG%"jG%"kG%"lG%#lmG%"pG%"tG%" vG%"BG%#BBG%"FG%#L2G%"MG%#MsG%#MVG%$MV2G%"RG%#RRG%"SG%"TG%#IBG%'lmprocG%$lmpG%' n_entrG%$varG%%varsG%)new_varsG%(var_ordG%'vt_degG%(deg_ordG%+deg_or_matG%)tup_ permG%¶mG%%seqvG%&m_ordG%*m_ord_POTG%#trG%*cmp_basisG%+trans_elemG%)entr_po sG6#%jnCopyright~(C)~2006-2008~by~Daniel~Robertz.~All~rights~reserved.G6"CC@$0% 7Involutive/initializedG.%%trueG-%0Involutive/initGFS>80-%6Involutive/proc_inpu tG6#9$@$4&Fgn6#""$-%&ERRORG6#%Fexpecting~L~without~right~hand~sides.G>8=&Fgn6#" ""@$&Fgn6#""&-Fbo6#%jnPolResolutionFast~cannot~compute~in~algebraic~field~exten sions.G>8L&Fgn6#""(@%32""#9#-%%typeG6$&9"F_o%%listGC(>8?F^q>86-Fin6#&F_q6#Fip@$ 2Fio&FeqFho-Fbo6#%Xexpecting~list~of~relations~for~the~residue~class~ring.G@$4& FeqF_o-Fbo6#%foright~hand~sides~for~relations~of~the~residue~class~ring~are~not ~supported.G@%/&Feq6%""%FioFio7#""!>Feq7">FeqFhq>8(FjrC&@$2FjpFip-Fbo6#%Pexpect ing~list~of~variables~as~second~argument.G>FcqFhq>FeqF^s>FasF`o>8>-%5Involutive /proc_varsG6$FcqFfo>8A&F\tFiq>8B&F\tF_o>8C&F\t6#Fjr>8E&F\tF\p>8M&F\t6#""'>F\t&F \tFho>%&_nvarG-%%nopsG6#F\t>8G7#-%$seqG6$-%$catG6$%#_xG8'/Fcv;FioFeu@$0-%&minus G6$<#-%#opG6#Fbp<#-F]wFhu<"-Fbo6#%Lno~parameters~allowed~in~PolResolutionFast.G >8DFio>8+F\s>8JF\s>8:%%NULLG>8HFip>8K%&falseG?(FcvFasFioFjpFYC$>88&F_q6#Fcv@)-F \q6$Ffx%'stringG?(8&FioFio-%'lengthG6#FfxFY@2/&Ffx6#F^yQ"CFS>FaxFY/FdyQ"DFS>Ffw F\s/FdyQ"GFSC$>FhwFip>8F-F`v6$-%*substringG6$Ffx;Fio,&F^yFio!""Fio-Fdz6$Ffx;,&F ^yFioFioFioF_y/FdyQ"MFS>FfwFio/FdyQ"OFS>FhwFio/FdyQ"SFSFS/FdyQ"TFS>F_xFjr0FdyQ! 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ember_multG6%FV%&P_HOMGF\t>Fiv7$-%#opG6#FivFV7$F`uFPFav7$FIFV7$F`uFVF86%FivF;Fi pF8F8, QAInvolutive/simp_pnormal_form_Z.mF8 M7R0 I6Involutive/ginvReducef*66'%"gG%%listG%$varG%)alg_elemG%(tr_elemG%'n_entrG%)rh s_entrG%'no_rhsG%"cG%&m_ordG%(var_ordG%)entr_posG%'vardegG%'tupdegG%(algextsG%- algextindetsG%/transextindetsG%%fextG%*donotreadG%+tracedenomG%*quietmodeG6)%%f ileG%&fnameG%%nvarG%+trans_elemG%#mpG%"iG%"rG6#%jnCopyright~(C)~2000-2008~by~Da niel~Robertz.~All~rights~reserved.G6"CS@%9*@$2"&++"9(-%&ERRORG6#%@length~of~tup les~exceeds~10000.G@$2FK,&FL"""-%%nopsG6#&&%"FG6#FT6#""#FTFM@$2"&Ob'9+-FN6#%?ch aracteristic~must~be~<~2^16.G>8&-FV6#9%>8'-%'removeG6$f*6#FAFE6$%)operatorG%&ar rowGFE-%'memberG6$9$T$FEFE6$F5929'@$0907#-%"$G6$""!FL-FN6#%Yup~to~now,~no~degre es~can~be~assigned~to~tuples~in~ginv.G@$2Fgn-FV6#9--FN6#%bpup~to~now,~only~two~ blocks~of~variables~for~elimination~ordering~are~supported~by~ginv.G@$2Fgn-FV6# 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/versionG%'stringG-Fjw6$FawQ#)|+FE-Fjw6$FawQ-import~ginv|+FE@%3/FLFTFH-Fjw6$Faw QDst~=~ginv.SystemType("Polynomial")|+FEC%-Fjw6$FawQKst~=~ginv.SystemType("Poly nomial",~module=FE@%FH-Fjw6$Faw-Ffx6$FLFixC%-Fjw6$Faw-Ffx6$,&FLFT9)FTFix-Fjw6$F awQ-,~rightPart=FEF[zFjx@'0Feq7"@%Fay-Fjw6$FawQGim~=~ginv.MonomInterface("Elim" ,~st,~[FE@%/<#-%#opG6#9,<#Fgn-Fjw6$FawQJim~=~ginv.MonomInterface("PotElim",~st, ~[FE-Fjw6$FawQJim~=~ginv.MonomInterface("TopElim",~st,~[FE3/F[rFT/&F]rFenFL@+/F f[lFT@%Fay-Fjw6$FawQFim~=~ginv.MonomInterface("Lex",~st,~[FE-Fjw6$FawQIim~=~gin v.MonomInterface("PotLex",~st,~[FE/Ff[lFgn@%Fay@%/9/7#-F[q6$FTF`o-Fjw6$FawQLim~ =~ginv.MonomInterface("DegRevLex",~st,~[FE-Fjw6$FawQOim~=~ginv.MonomInterface(" DegRevLexDeg",~st,~[FE@%F^]l-Fjw6$FawQOim~=~ginv.MonomInterface("PotDegRevLex", ~st,~[FE-Fjw6$FawQRim~=~ginv.MonomInterface("PotDegRevLexDeg",~st,~[FE/Ff[l""$@ %FayFe\l-Fjw6$FawQIim~=~ginv.MonomInterface("TopLex",~st,~[FE/Ff[l""%@%Fay@%F^] lFc]lFf]l@%F^]l-Fjw6$FawQOim~=~ginv.MonomInterface("TopDegRevLex",~st,~[FE-Fjw6 $FawQRim~=~ginv.MonomInterface("TopDegRevLexDeg",~st,~[FEC$-%'fcloseG6#Faw-FN6# %\oup~to~now,~the~chosen~monomial~ordering~is~not~supported~by~ginv.GC%@%Fjz@%F H-Fjw6$FawQTim~=~ginv.MonomInterface("PosElimElim",~st,~tupSep=FEC$Fb_l-FN6#%dp up~to~now,~the~chosen~monomial~ordering~cannot~be~combined~with~right~hand~side s~in~ginv.G@'F`^l@%FH-Fjw6$FawQSim~=~ginv.MonomInterface("PosElimLex",~st,~tupS ep=FEC$Fb_lF_`lFf^l@%FH@%F^]l-Fjw6$FawQYim~=~ginv.MonomInterface("PosElimDegRev Lex",~st,~tupSep=FE-Fjw6$FawQfnim~=~ginv.MonomInterface("PosElimDegRevLexDeg",~ st,~tupSep=FEC$Fb_lF_`lC$Fb_lFe_l-Fjw6$Faw-Ffx6$Fa\lFix-Fjw6$FawQ$,~[FE?(8)FTFT F`o%%trueGC$-Fjw6$Faw-F]w6%Q"'FE-Ffx6$&Fco6#FjalFixFabl@$2FjalF`o-Fjw6$FawQ#,~F E@$4%4Involutive/ratcoeffG-Fjw6$FawQ&,~'@'FE-Fjw6$FawQ"]FE@&FjzC$-Fjw6$FawQ*,~v arSep=FE-Fjw6$Faw-Ffx6$-FV6#&FeqFenFix4F^\lC$FfclFbal@$0F_]lF`]lC$-Fjw6$FawQ+,~ degrees=FE@%F]cl-Fjw6$Faw-Ffx6$F_]lFix-Fjw6$Faw-Ffx6$7$-Fd[l6#F_]lFTFixFjx@%F]c l@%0F[oF]q@+3/,&-FV6#9&FT-FV6#91FTF]q/FdrF]qC%-Fjw6$FawQenic~=~ginv.CoeffInterf ace("ModularShort",~st,~modularShort=FE-Fjw6$Faw-Ffx6$F[oFixFjx32F]qFjelFaflC,- Fjw6$FawQjoic~=~ginv.CoeffInterface("AlgebraicFieldExtensionModularShort",~st,~ parameter=[FE>8(F[[l?(FjalFTFTF[flF[blC(@$0-Fd[l6$F]q&F]flFebl%'RootOfGC$Fb_l-F N6#-F]w6$-Ffx6$FhglFix%3~is~not~algebraic.G>Fagl7$-Fd[l6#Fagl-%8Involutive/alge xt2aliasG6#-Fd[l6$FTFhgl>F[t-%&minusG6$-%'indetsG6#&Fagl6#!""<$-Fd[l6#-%$mapG6% FfxF]fl%%nameG-Fd[l6#Fdp>Fagl-%'subsopG6$/Fdil-F]w6$-Ffx6$-%%subsG6$/&F[tFenFhg lFbilFixQ"~FEFagl-Fjw6$Faw-F]w6%Q""FEF_hlFa[m@$2FjalF[flFhbl?(FjalFTFT-FVF]jlF[ blC$@$52FTFjal2F]qF[flFhbl-Fjw6$Faw-F]w6%Fa[m-Ffx6$&FdpFeblFixFa[m-Fjw6$FawQ/], ~extension=[FE?(FjalFTFTF[flF[blC&-Fjw6$FawFa[m-Fjw6$Faw&FaglFeblFg\m@$Fc[mFhbl ?(FjalFTFTF^flF[blC&@$Fh[mFhblFg\m-Fjw6$Faw-F]w6$-Ffx6$&F`flFeblFixF\[mFg\m-Fjw 6$FawQ1],~modularShort=FEFfflFjx3Fiel/FdrFTC'-Fjw6$FawQaoic~=~ginv.CoeffInterfa ce("OneParameterModularShort",~st,~modularShort=FEFffl-Fjw6$FawQ.,~parameter=[F E@%/FeoF[[l-Fjw6$Faw-F]w6%Fa[m-Ffx6$&FirFenFixFa[m-Fjw6$Faw-F]w6%Fa[m-Ffx6$&Feo FenFixFa[m-Fjw6$FawQ$])|+FE3Fiel/FdrFgnC(-Fjw6$FawQaoic~=~ginv.CoeffInterface(" TwoParameterModularShort",~st,~modularShort=FEFfflF`^m?(FjalFTFTFerF[blC$-Fjw6$ Faw-F]w6%Fa[m-Ffx6$&FeoFeblFixFa[m@$2FjalFgnFhbl?(FjalFTFTFgrF[blC$-Fjw6$Faw-F] w6%Fa[m-Ffx6$&FirFeblFixFa[m@$2FjalFgrFhblFc_mC$Fb_l-FN6#%5not~implemented~yet. G@-Fhel-Fjw6$FawQFic~=~ginv.CoeffInterface("GmpZ",~st)|+FEFjflC*-Fjw6$FawQboic~ =~ginv.CoeffInterface("AlgebraicFieldExtensionGmpQ",~st,~parameter=[FE>FaglF[[l ?(FjalFTFTF[flF[blC(@$FeglC$Fb_l-FN6#-F]w6$F_hl%M~is~not~algebraic~over~the~rat ional~numbers.G>FaglFchl>F[tF\il>FaglF_jlF][m@$Fc[mFhbl?(FjalFTFTFe[mF[blC$@$Fh [mFhblF[\mFb\m?(FjalFTFTF[flF[blC&Fg\mFi\mFg\m@$Fc[mFhbl?(FjalFTFTF^flF[blC&@$F h[mFhblFg\mF`]mFg\mFc_mFj]mC%-Fjw6$FawQgnic~=~ginv.CoeffInterface("OneParameter GmpZ",~st,~parameter=[FE@%Fd^mFe^mF\_mFc_mFielC&-Fjw6$FawQenic~=~ginv.CoeffInte rface("NParameterGmpZ",~st,~parameter=[FE?(FjalFTFTFerF[blC$F^`m@$2FjalFdrFhbl? (FjalFTFTFgrF[blC$Fi`m@$FaamFhblFc_m3F[gl2F]qFdrC--Fjw6$FawQ]pic~=~ginv.CoeffIn terface("AlgebraicFieldExtensionNParameter",~st,~fieldParameter=[FE?(FjalFTFTFe rF[blC$F^`m@$FadmFhbl?(FjalFTFTFgrF[blC$Fi`m@$FaamFhbl-Fjw6$FawQ/],~parameter=[ FE>FaglF[[l?(FjalFTFTF[flF[blC(@$FeglC$Fb_lFcbm>FaglFchl>F[t-F]il6$F_il<&-Fd[lF hrFfilF\jl-Fd[l6#-Fiil6%FfxFeoF[jl>FaglF_jlF][m@$Fc[mFhbl?(FjalFTFTFe[mF[blC$@$ Fh[mFhblF[\mFb\m?(FjalFTFTF[flF[blC&Fg\mFi\mFg\m@$Fc[mFhbl?(FjalFTFTF^flF[blC&@ $Fh[mFhblFg\mF`]mFg\mFc_mC$Fb_lFcam-Fjw6$FawQGic~=~ginv.CoeffInterface("GmpZZ", ~st)|+FE-Fjw6$FawQQip~=~ginv.PolyInterface("PolyList",~st,~im,~ic)|+FE-Fjw6$Faw Q:iw~=~ginv.WrapInterface("FE@+/%3Involutive/invcritGF[[l-Fjw6$FawQ(WithoutFE/F jgm7$FTFgn-Fjw6$FawQ.CritPartiallyFE/Fjgm7%FTFgnFa^l-Fjw6$FawQ'C1C2C3FE/Fjgm7&F TFgnFa^lFg^l-Fjw6$FawQ)C1C2C3C4FEC$Fb_l-FN6#%Wundefined~involutive~criteria;~se e~?InvolutiveOptions.G-Fjw6$FawQ(",~ip)|+FE@%%5Involutive/janetlikeG-Fjw6$FawQN iD~=~ginv.DivisionInterface("JanetLike",~iw)|+FE-Fjw6$FawQJiD~=~ginv.DivisionIn terface("Janet",~iw)|+FE-Fjw6$FawQ9basis~=~ginv.basisLoad("FE-Fjw6$Faw-F]w6$Fbu Q(.binaryFE-Fjw6$FawQ.",~"TQ",~iD)|+FE-Fjw6$FawQ+f~=~file("FE-Fjw6$Faw-F]w6$Fbu Q%.resFE-Fjw6$FawQ)",~"w")|+FE-Fjw6$FawQCprint~>>~f,~"_RESULT_REDUCE~:=~["|+FE? (FjalFTFT-FV6#FapF[blC$@%F]clC&-Fjw6$FawQ4r~=~ginv.Poly(ip,~"FE-Fjw6$Faw-Ffx6$& FapFeblFix-Fjw6$FawQ%~")|+FE-Fjw6$FawQ9print~>>~f,~basis.nf(r)|+FEC$@%FayC%F[\n -Fjw6$Faw-F]w6%Q"(FEF`\nQ%)*@~FEFc\nC%-Fjw6$Faw-F]w6%Q&s~=~"FEF`\nQ$~"|+FE-Fjw6 $FawQaos~=~s.replace('[',~'[(').replace(',~',~')*@,~(').replace(']',~')*@]')|+F E-Fjw6$FawQ6r~=~ginv.Poly(ip,~s)|+FE-Fjw6$FawQ\oprint~>>~f,~str(basis.nf(r)).re place('*@',~'').replace('@',~'1')|+FE@$2FjalFf[n-Fjw6$FawQ1print~>>~f,~","|+FE- Fjw6$FawQ2print~>>~f,~"]:"|+FE-Fjw6$FawQ+f.close()|+FEFb_l@%97@%FbvC%>F[t-F]t6# -F]w6%Q)runginv~FEFbuFgw@$/F[t%%NULLG-FN6#%Acould~not~run~program~'runginv'.G>F [tF[[mC$>F[t-F]t6#-F]w6%Ff_nFbuQ1.red~>~/dev/nullFE@%3/F[[mF]q/FetF]u>F[tF]q>F[ tFTC$>F[t-%'systemGFc_n@$Fh_nFj_n@$0F[tF]q-FN6#%Merror~during~call~of~Python~or ~interruption.G@$F`sC%>F[t-F]t6#-F]w6'Q&if~[~FEFbuQ*.res~-ot~FEFbuQ>.red~];~the n~echo~-n~true;~fiFE@$2F]q-%'lengthGFdt-FN6#%dpoutput~file~of~ginv~is~older~tha n~input~file~(probably,~program~ginv~stopped~abnormally).G@$495C$>F[t-F]t6#-F]w 6%Q*filesize~FEFbuF^[n@$30F[tFi_nFg`nC$>F[t-%'sscanfG6$FetQ#%dFE@$32F]q-FV6#F[t 2"'++IF[[m-%(WARNINGG6#Qgnresulting~normal~form~is~big;~reading~it~may~take~a~w hile...FE@$Fhbn-%'RETURNG6#F[[lAF\[n@$4-%)assignedG6#%/_RESULT_REDUCEG-FN6#%Cer ror~in~computation~or~interface.G-FfdnF]enFEFEFEFE, Q8Involutive/ginvReduce.mFE M7R0 I0Involutive/pLCMf*6$%"aG%"bG6$%"iG%"LG6#%inCopyright~(C)~2000-2002~by~Carlos~F .~Cid.~All~rights~reserved.G6"C%@$0&9$6#""#&9%F2-%&ERRORG6#%Oinput~for~pLCM~mus t~be~in~the~same~list~entry.G>8%7#-%$seqG6$-%$maxG6$&F16$"""8$&F5FD/FF;FE%&_nva rG-%'RETURNG6#7$F;F0F,F,F,F,, Q2Involutive/pLCM.mF, M7R0 I;Involutive/pjanet_div_onlyf*6#%"LG6+%"aG%"iG%"jG%"lG%"FG%"kG%"nG%#suG%(allmul tG6#%jnCopyright~(C)~2006-2008~by~Daniel~Robertz.~All~rights~reserved.G6"C)>8*- %%nopsG6#9$@$/F5""!-%'RETURNGF8>8,7#-%"$G6$%)infinityG%&_nvarG>8(F9>FH-%'subsop 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I7Involutive/ginvMinPolyf*69'%"gG%%listG%$varG%)alg_elemG%(tr_elemG%'n_entrG%)r hs_entrG%'no_rhsG%"cG%&m_ordG%(var_ordG%)entr_posG%'vardegG%'tupdegG%(algextsG% -algextindetsG%/transextindetsG%%fextG%*donotreadG%+tracedenomG%*quietmodeG%-mi npolyindetG%)uppboundG%)lowboundG6)%%fileG%&fnameG%%nvarG%+trans_elemG%#mpG%"iG %"rG6#%jnCopyright~(C)~2000-2008~by~Daniel~Robertz.~All~rights~reserved.G6"CS@% 9*@$2"&++"9(-%&ERRORG6#%@length~of~tuples~exceeds~10000.G@$2FN,&FO"""-%%nopsG6# &&%"FG6#FW6#""#FWFP@$2"&Ob'9+-FQ6#%?characteristic~must~be~<~2^16.G>8&-FY6#9%>8 '-%'removeG6$f*6#FDFH6$%)operatorG%&arrowGFH-%'memberG6$9$T$FHFH6$F5929'@$0907# -%"$G6$""!FO-FQ6#%Yup~to~now,~no~degrees~can~be~assigned~to~tuples~in~ginv.G@$2 Fjn-FY6#9--FQ6#%bpup~to~now,~only~two~blocks~of~variables~for~elimination~order ing~are~supported~by~ginv.G@$2Fjn-FY6#9.-FQ6#%_pup~to~now,~only~two~blocks~of~t uples~for~elimination~ordering~are~supported~by~ginv.G@$32Fjn,&-FY6#FhoFW-FY6#9 3FW0%2Involutive/characGF`q-FQ6#%_qup~to~now,~transcendental~extensions~of~degr ee~greater~than~2~are~only~supported~over~the~rationals.G@'2F`q-%+searchtextG6$ Q&linuxFH-%+kerneloptsG6#%(versionGC&>8*-%(ssystemG6#%hnif~test~-d~/tmp/$USER~; ~then~echo~true~;~else~echo~false~;~fiG@$4-%&parseG6#&F^tFinC$>F^t-F`t6#%1mkdir ~/tmp/$USERG@$0FhtQ!FH-FQ6#%Ecannot~write~temporary~file~to~/tmp.G>8%-F`t6#%Gec ho~/tmp/$USER/Involutive-$PPID-$USERG@%2F`q-Fes6$Q"$FH&FeuFin>FeuQ0/tmp/Involut iveFH>Feu-%=Involutive/remove_whitespaceG6#F^v2F`q-Fes6$Q&APPLEFHFhs>Feu-%:Invo lutive/mac_gettmpnameGFH>FeuQ1\TEMP\InvolutiveFH>Feu-%$catG6$Feu94>8$-%&fopenG6 $-F`w6$FeuQ%.minFH%&WRITEG-%(fprintfG6$FdwQ8#!~/usr/bin/env~python|+FH-F]x6$Fdw QY#~temporary~file~created~by~the~Maple~package~InvolutiveFH-F]x6$FdwQ+~(versio n~FH-F]x6$Fdw-%(convertG6$%3Involutive/versionG%'stringG-F]x6$FdwQ#)|+FH-F]x6$F dwQ-import~ginv|+FH@%3/FOFWFK-F]x6$FdwQDst~=~ginv.SystemType("Polynomial")|+FHC %-F]x6$FdwQKst~=~ginv.SystemType("Polynomial",~module=FH@%FK-F]x6$Fdw-Fix6$FOF\ yC%-F]x6$Fdw-Fix6$,&FOFW9)FWF\y-F]x6$FdwQ-,~rightPart=FHF^zF]y@'0Fhq7"@%Fdy-F]x 6$FdwQGim~=~ginv.MonomInterface("Elim",~st,~[FH@%/<#-%#opG6#9,<#Fjn-F]x6$FdwQJi m~=~ginv.MonomInterface("PotElim",~st,~[FH-F]x6$FdwQJim~=~ginv.MonomInterface(" TopElim",~st,~[FH3/F^rFW/&F`rFhnFO@+/Fi[lFW@%Fdy-F]x6$FdwQFim~=~ginv.MonomInter face("Lex",~st,~[FH-F]x6$FdwQIim~=~ginv.MonomInterface("PotLex",~st,~[FH/Fi[lFj n@%Fdy@%/9/7#-F^q6$FWFco-F]x6$FdwQLim~=~ginv.MonomInterface("DegRevLex",~st,~[F H-F]x6$FdwQOim~=~ginv.MonomInterface("DegRevLexDeg",~st,~[FH@%Fa]l-F]x6$FdwQOim ~=~ginv.MonomInterface("PotDegRevLex",~st,~[FH-F]x6$FdwQRim~=~ginv.MonomInterfa ce("PotDegRevLexDeg",~st,~[FH/Fi[l""$@%FdyFh\l-F]x6$FdwQIim~=~ginv.MonomInterfa ce("TopLex",~st,~[FH/Fi[l""%@%Fdy@%Fa]lFf]lFi]l@%Fa]l-F]x6$FdwQOim~=~ginv.Monom Interface("TopDegRevLex",~st,~[FH-F]x6$FdwQRim~=~ginv.MonomInterface("TopDegRev LexDeg",~st,~[FHC$-%'fcloseG6#Fdw-FQ6#%\oup~to~now,~the~chosen~monomial~orderin g~is~not~supported~by~ginv.GC%@%F][l@%FK-F]x6$FdwQTim~=~ginv.MonomInterface("Po sElimElim",~st,~tupSep=FHC$Fe_l-FQ6#%dpup~to~now,~the~chosen~monomial~ordering~ cannot~be~combined~with~right~hand~sides~in~ginv.G@'Fc^l@%FK-F]x6$FdwQSim~=~gin v.MonomInterface("PosElimLex",~st,~tupSep=FHC$Fe_lFb`lFi^l@%FK@%Fa]l-F]x6$FdwQY im~=~ginv.MonomInterface("PosElimDegRevLex",~st,~tupSep=FH-F]x6$FdwQfnim~=~ginv .MonomInterface("PosElimDegRevLexDeg",~st,~tupSep=FHC$Fe_lFb`lC$Fe_lFh_l-F]x6$F dw-Fix6$Fd\lF\y-F]x6$FdwQ$,~[FH?(8)FWFWFco%%trueGC$-F]x6$Fdw-F`w6%Q"'FH-Fix6$&F fo6#F]blF\yFdbl@$2F]blFco-F]x6$FdwQ#,~FH@$4%4Involutive/ratcoeffG-F]x6$FdwQ&,~' @'FH-F]x6$FdwQ"]FH@&F][lC$-F]x6$FdwQ*,~varSep=FH-F]x6$Fdw-Fix6$-FY6#&FhqFhnF\y4 Fa\lC$FiclFeal@$0Fb]lFc]lC$-F]x6$FdwQ+,~degrees=FH@%F`cl-F]x6$Fdw-Fix6$Fb]lF\y- F]x6$Fdw-Fix6$7$-Fg[l6#Fb]lFWF\yF]y@%F`cl@%0F^oF`q@+3/,&-FY6#9&FW-FY6#91FWF`q/F grF`qC%-F]x6$FdwQenic~=~ginv.CoeffInterface("ModularShort",~st,~modularShort=FH -F]x6$Fdw-Fix6$F^oF\yF]y32F`qF]flFdflC,-F]x6$FdwQjoic~=~ginv.CoeffInterface("Al gebraicFieldExtensionModularShort",~st,~parameter=[FH>8(F^[l?(F]blFWFWF^flF^blC (@$0-Fg[l6$F`q&F`flFhbl%'RootOfGC$Fe_l-FQ6#-F`w6$-Fix6$F[hlF\y%3~is~not~algebra ic.G>Fdgl7$-Fg[l6#Fdgl-%8Involutive/algext2aliasG6#-Fg[l6$FWF[hl>F^t-%&minusG6$ -%'indetsG6#&Fdgl6#!""<$-Fg[l6#-%$mapG6%FixF`fl%%nameG-Fg[l6#Fgp>Fdgl-%'subsopG 6$/Fgil-F`w6$-Fix6$-%%subsG6$/&F^tFhnF[hlFeilF\yQ"~FHFdgl-F]x6$Fdw-F`w6%Q""FHFb hlFd[m@$2F]blF^flF[cl?(F]blFWFW-FYF`jlF^blC$@$52FWF]bl2F`qF^flF[cl-F]x6$Fdw-F`w 6%Fd[m-Fix6$&FgpFhblF\yFd[m-F]x6$FdwQ/],~extension=[FH?(F]blFWFWF^flF^blC&-F]x6 $FdwFd[m-F]x6$Fdw&FdglFhblFj\m@$Ff[mF[cl?(F]blFWFWFaflF^blC&@$F[\mF[clFj\m-F]x6 $Fdw-F`w6$-Fix6$&FcflFhblF\yF_[mFj\m-F]x6$FdwQ1],~modularShort=FHFiflF]y3F\fl/F grFWC'-F]x6$FdwQaoic~=~ginv.CoeffInterface("OneParameterModularShort",~st,~modu larShort=FHFifl-F]x6$FdwQ.,~parameter=[FH@%/FhoF^[l-F]x6$Fdw-F`w6%Fd[m-Fix6$&F\ sFhnF\yFd[m-F]x6$Fdw-F`w6%Fd[m-Fix6$&FhoFhnF\yFd[m-F]x6$FdwQ$])|+FH3F\fl/FgrFjn C(-F]x6$FdwQaoic~=~ginv.CoeffInterface("TwoParameterModularShort",~st,~modularS hort=FHFiflFc^m?(F]blFWFWFhrF^blC$-F]x6$Fdw-F`w6%Fd[m-Fix6$&FhoFhblF\yFd[m@$2F] blFjnF[cl?(F]blFWFWFjrF^blC$-F]x6$Fdw-F`w6%Fd[m-Fix6$&F\sFhblF\yFd[m@$2F]blFjrF [clFf_mC$Fe_l-FQ6#%5not~implemented~yet.G@-F[fl-F]x6$FdwQFic~=~ginv.CoeffInterf ace("GmpZ",~st)|+FHF]glC*-F]x6$FdwQboic~=~ginv.CoeffInterface("AlgebraicFieldEx tensionGmpQ",~st,~parameter=[FH>FdglF^[l?(F]blFWFWF^flF^blC(@$FhglC$Fe_l-FQ6#-F `w6$Fbhl%M~is~not~algebraic~over~the~rational~numbers.G>FdglFfhl>F^tF_il>FdglFb jlF`[m@$Ff[mF[cl?(F]blFWFWFh[mF^blC$@$F[\mF[clF^\mFe\m?(F]blFWFWF^flF^blC&Fj\mF \]mFj\m@$Ff[mF[cl?(F]blFWFWFaflF^blC&@$F[\mF[clFj\mFc]mFj\mFf_mF]^mC%-F]x6$FdwQ gnic~=~ginv.CoeffInterface("OneParameterGmpZ",~st,~parameter=[FH@%Fg^mFh^mF__mF f_mF\flC&-F]x6$FdwQenic~=~ginv.CoeffInterface("NParameterGmpZ",~st,~parameter=[ FH?(F]blFWFWFhrF^blC$Fa`m@$2F]blFgrF[cl?(F]blFWFWFjrF^blC$F\am@$FdamF[clFf_m3F^ gl2F`qFgrC--F]x6$FdwQ]pic~=~ginv.CoeffInterface("AlgebraicFieldExtensionNParame ter",~st,~fieldParameter=[FH?(F]blFWFWFhrF^blC$Fa`m@$FddmF[cl?(F]blFWFWFjrF^blC $F\am@$FdamF[cl-F]x6$FdwQ/],~parameter=[FH>FdglF^[l?(F]blFWFWF^flF^blC(@$FhglC$ Fe_lFfbm>FdglFfhl>F^t-F`il6$Fbil<&-Fg[lF[sFiilF_jl-Fg[l6#-F\jl6%FixFhoF^jl>Fdgl FbjlF`[m@$Ff[mF[cl?(F]blFWFWFh[mF^blC$@$F[\mF[clF^\mFe\m?(F]blFWFWF^flF^blC&Fj\ mF\]mFj\m@$Ff[mF[cl?(F]blFWFWFaflF^blC&@$F[\mF[clFj\mFc]mFj\mFf_mC$Fe_lFfam-F]x 6$FdwQGic~=~ginv.CoeffInterface("GmpZZ",~st)|+FH-F]x6$FdwQQip~=~ginv.PolyInterf ace("PolyList",~st,~im,~ic)|+FH-F]x6$FdwQ:iw~=~ginv.WrapInterface("FH@+/%3Invol utive/invcritGF^[l-F]x6$FdwQ(WithoutFH/F]hm7$FWFjn-F]x6$FdwQ.CritPartiallyFH/F] hm7%FWFjnFd^l-F]x6$FdwQ'C1C2C3FH/F]hm7&FWFjnFd^lFj^l-F]x6$FdwQ)C1C2C3C4FHC$Fe_l -FQ6#%Wundefined~involutive~criteria;~see~?InvolutiveOptions.G-F]x6$FdwQ(",~ip) |+FH@%%5Involutive/janetlikeG@%F`cl-F]x6$FdwQNiD~=~ginv.DivisionInterface("Jane tLike",~iw)|+FHC$Fe_l-FQ6#%\oJanet-like~division~not~implemented~yet~for~intege r~coefficients.G@%F`cl-F]x6$FdwQJiD~=~ginv.DivisionInterface("Janet",~iw)|+FH-F ]x6$FdwQLiD~=~ginv.DivisionInterface("JanetZZ",~iw)|+FH-F]x6$FdwQ9basis~=~ginv. basisLoad("FH-F]x6$Fdw-F`w6$FeuQ(.binaryFH-F]x6$FdwQ.",~"TQ",~iD)|+FH-F]x6$FdwQ +f~=~file("FH-F]x6$Fdw-F`w6$FeuQ%.resFH-F]x6$FdwQ)",~"w")|+FH-F]x6$FdwQDprint~> >~f,~"_RESULT_MINPOLY~:=~["|+FH?(F]blFWFW-FY6#FdpF^blC(-F]x6$FdwQ>~f,~b asis.minPoly("FH-F]x6$Fdw-Fix6$&FdpFhblF\y-F]x6$FdwQ*~",~var="FH-F]x6$Fdw-Fix6$ 98F\y-F]x6$FdwQ$")|+FH@$2F]blFb\n-F]x6$FdwQ1print~>>~f,~","|+FH-F]x6$FdwQ2print ~>>~f,~"]:"|+FH-F]x6$FdwQ+f.close()|+FHFe_l@%97@%FevC%>F^t-F`t6#-F`w6%Q)runginv ~FHFeuFjw@$/F^t%%NULLG-FQ6#%Acould~not~run~program~'runginv'.G>F^tF^[mC$>F^t-F` t6#-F`w6%F\_nFeuQ1.min~>~/dev/nullFH@%3/F^[mF`q/FhtF`u>F^tF`q>F^tFWC$>F^t-%'sys temGFi^n@$F^_nF`_n@$0F^tF`q-FQ6#%Merror~during~call~of~Python~or~interruption.G @$FcsC'>F^t-F`t6#-F`w6%%,if~test~-r~GFeu%I~;~then~echo~true~;~else~echo~false~; ~fiG@$Fdt-FQ6#-F`w6%%8cannot~find~input~file~GFeu%+~for~ginv.G>F^t-F`t6#-F`w6'Q &if~[~FHFeuQ&~-ot~FHFeuQ>.min~];~then~echo~-n~true;~fiFH@$2F`q-%'lengthGFgt-FQ6 #%dpoutput~file~of~ginv~is~older~than~input~file~(probably,~program~ginv~stoppe d~abnormally).G@$495C$>F^t-F`t6#-F`w6%Q*filesize~FHFeuFj[n@$30F^tF__nF]`nC$>F^t -%'sscanfG6$FhtQ#%dFH@$32F`q-FY6#F^t2"'++IF^[m-%(WARNINGG6#Q^oresulting~minimal ~polynomial~is~big;~reading~it~may~take~a~while...FH@$F\cn-%'RETURNG6#F^[lAFh[n @$4-%)assignedG6#%0_RESULT_MINPOLYG-FQ6#%Cerror~in~computation~or~interface.G-F jdnFaenFHFHFHFH, Q9Involutive/ginvMinPoly.mFH M7R0 I=Involutive/PolMinPolyRatFuncf*6&'%"pG%(polynomG'%"JG%%listG'%%varsGF*'%#FBGF* 6,%"aG%"iG%"jG%"nG%"vG%"xG%#suG%$varG%"FG%"MG6#%jnCopyright~(C)~2006-2008~by~Da niel~Robertz.~All~rights~reserved.G6"C1>8(-%*substringG6$-%(convertG6$-%+kernel optsG6#%(versionG%'stringG;""""")@$5/F?Q)Maple~V,F8).%'lambdaG>8*""! >8-%%NULLG?(8%""&FL9#Ffn@%-%%typeG6$&9"6#Fjo%)equationGC$@$4-F_p6$-%#opG6$FLFap FJ-FU6#%\oexpecting~a~string~on~the~left~hand~side~of~an~optional~equation.G@-/ FjpQ*PolRepresFFgo-FDF^r5/FjpQ'degreeFF`oFiq/-FA6$Fjp;FL""%Q%su bsF<>FdoFiq-FU6#%0invalid~option.GF\u>8,-%6Involutive/proc_inputG6#9%>8+&-%5Inv olutive/proc_varsG6$9&&F`u6#FLF]v>8'-%%nopsG6#9'@$/F_vFeo@%0FdoFeo-%'RETURNG6#F do-Fiv6#F`o@$4-%$hasG6$9$Ffu@%Fgv-Fiv6#,&FdoFLFbw!""-Fiv6#,&F`oFLFbwFgw@$/FgoFh o>Fgo-FD6$-%5Involutive/PolRepresG6&FbwFduF[vFcvF_r@%Fgv-%%subsG6$/F`oFdo-%:Inv olutive/MinPolyRatFuncG6$FgoF`oFhxF8(&9"6#""$>F9""!>8'-%%nopsG6#-%;Involutive/InvolutiveBasisG6%9$9%F6>8&7$FA -FC6#&%)P_T_ListG6%"""FRFR@$5/F9F?2FRF9C%>8)-%$mapG6$f*6#%"aGF26$%)operatorG%&a 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F+F+F+F+, Q7Involutive/polresdim.mF+ M7R0 I:InvolutiveZeroSets/homalg=6"%&falseGE\[l)%.BasisOfModuleG%Ahomalg/InvolutiveZ eroSets/IBasisG%'ReduceG%@homalg/Involutive/PolInvoReduceG%.SimplifyBasisG%8Inv olutive/jetsdepcheckG%1PresentationInfoG%Chomalg/Involutive/PolHilbertCartanG%' IsUnitG%9homalg/Involutive/IsUnitG%3SyzygiesGeneratorsG%Fhomalg/InvolutiveZeroS ets/PolSyzygiesG%,ZeroSetsVarGQ-_InvZeroSetsF$%1CollectsZeroSetsG%%trueGF$, QInvolutive/pplex_Z_entr_blockf*6$%"aG%"bG6#%"iG6#%jnCopyright~(C)~2006-2008~b y~Daniel~Robertz.~All~rights~reserved.G6"C'@&2&%,_entrblocksG6#&9$6#""#&F06#&9% F4-%'RETURNG6#%&falseG2F6F/-F;6#%%trueG?(8$"""FD-%%nopsG6#&F36#FDFA@&2&FH6#FC&& F9FIFMF?2FNFLF:@&2-%$absG6#&F96#""$-FT6#&F3FWF:2FYFSF?@$2F2F8F:FAF+F+F+F+, Q@Involutive/pplex_Z_entr_block.mF+ M7R0 I4Involutive/pnegplexf*6$%"aG%"bG6"6#%jnCopyright~(C)~2002-2008~by~Daniel~Rober tz.~All~rights~reserved.GF'@%/&9$6#"""&9%F.@%2&F-6#""#&F1F5%&falseG%%trueG4-%1I nvolutive/pplexG6$F-F1F'F'F'F', Q6Involutive/pnegplex.mF' M7R0 IFInvolutive/pnegdegrevlex_Z_entr_blockf*6$%"aG%"bG6%%"iG%$tdaG%$tdbG6#%jnCopyr ight~(C)~2006-2008~by~Daniel~Robertz.~All~rights~reserved.G6"C)@&2&%,_entrblock sG6#&9$6#""#&F26#&9%F6-%'RETURNG6#%&falseG2F8F1-F=6#%%trueG>8%-%(convertG6$&F56 #"""%"+G>8&-FG6$&F;FJFL@'2FEFNF<2FNFEFA?(8$-%%nopsG6#FI!""FKFC@&2&FQ6#FV&FIFhnF A2FinFgnF<@&2-%$absG6#&F;6#""$-F^o6#&F5FaoF<2FcoF]oFA@$2F4F:F8%-%%nopsG6#&9$6#""">8&, &-%$addG6$*&&F56#8$F8&%(_vardegGFAF8/FB;F8F1F8&%(_tupdegG6#&F66#""#F8>8',&-F=6$ *&&&9%F7FAF8FCF8FEF8&FH6#&FUFKF8@'2F:FN-%'RETURNG6#%%trueG2FNF:-Ffn6#%&falseGC% >F:F<>FNFP@'FZFenFinFjn?(FBF8F8F1Fhn@&2FSF@Fjn2F@FSFen@&2-%$absG6#&FU6#""$-Fho6 #&F6F[pFjn2F]pFgoFen@%2FJFXF\oFhnF.F.F.F., Q;Involutive/pdeglex_deg_Z.mF. M7R0 I=Involutive/pdeglex_deg_Z_POTf*6$%"aG%"bG6&%"iG%"nG%$tdaG%$tdbG6#%jnCopyright~ (C)~2004-2008~by~Daniel~Robertz.~All~rights~reserved.G6"C(@&2&9$6#""#&9%F4-%'RE TURNG6#%&falseG2F6F2-F96#%%trueG>8%-%%nopsG6#&F36#""">8&-%$addG6$*&&FE6#8$FG&%( _vardegGFOFG/FP;FGFA>8'-FK6$*&&&F7FFFOFGFQFGFS@'2FIFVF=2FVFIF8?(FPFGFGFAF?@&2FZ FNF82FNFZF=@%2-%$absG6#&F76#""$-F`o6#&F3FcoF;F?F.F.F.F., Q?Involutive/pdeglex_deg_Z_POT.mF. M7R0 IAInvolutive/pnegdeglex_entr_blockf*6$%"aG%"bG6%%"iG%$tdaG%$tdbG6#%jnCopyright~ (C)~2006-2008~by~Daniel~Robertz.~All~rights~reserved.G6"C(@&2&%,_entrblocksG6#& 9$6#""#&F26#&9%F6-%'RETURNG6#%&falseG2F8F1-F=6#%%trueG>8%-%(convertG6$&F56#"""% "+G>8&-FG6$&F;FJFL@'2FEFNF<2FNFEFA?(8$FKFK-%%nopsG6#FIFC@&2&FQ6#FV&FIFgnF<2FhnF fnFA@$2F4F:F8&-%%iquoG6$,(F@FAFCF AFAFA""#@%-FF6$F<&FI6#F[o@%-FMFcoFI-F"6)F81-%%nopsG6#&9$6#" "">837#-%"$G6$""!FH>8(FL@$49&>8)&FM6#""#@$09*7"C'>84<#-%$seqG6$&9(6#&F]o6#8*/F[ p;FO-FJ6#F]o>85-FJ6#Fao>86F^o>FX-%9Involutive/cancel_locvarG6%FXFgoF]o@$FZ>Fgn- Fhp6%FgnFgoF]o>8--FJ6#9%>8/FQ>8%7#-FT6$FVF_q>8.FO>8,-9)6#FX?(FEFOFOFE0&F]r6$Fjn FOFVC)>F[pFO>80%&falseG>82*&FcrFO&F]r6$FjnFjnFO@$F\o>87,&-%$maxG6#-Fdo6$-%'degr eeG6$&FX6#8+Fao/F]t;FOFHFO-%$addG6$&&F]r6$FOFO6#&F]oF\t/F]t;FOFap!""?(FEFOFOFE3 1F[pF_q4Fhr@%-%7Involutive/pinv_divideG6%&Fbq6$F[p""$&Fbq6$F[p""&&F]rFNC$@%F\oC ,>88,&-Fds6#-Fdo6$-Fis6$&&Fbq6%F[pFOFOF\tFaoF^tFO-Fat6$&&Fbq6%F[pFeuFOFftFhtFjt 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GF$C/>89%&falseG>8:FM>87FM>88FM>8?FM>8=""%>8DFM@'5/9#"""32FinFhn-%%typeG6$&9"6# ""#%'stringGC$>8AFM>8&Fbo2""!FhnC$>Ffo%%trueG>Fho""$-%&ERRORG6#%goexpecting~eit her~an~involutive~basis~or~list~of~variables~as~first~argument.G?(8%FhoFinFhnF] p@'5-F]o6$&F`o6#Fep%(integerG-F]o6$Fjp%%listG>FWFjp-F]o6$FjpFcoC$>8-Fjp?(8'FinF in-%'lengthG6#FeqF]p@./&Feq6#FgqQ"CF$>FLF]p/F]rQ"GF$>FQF]p/F]rQ"LF$>FSF]p/F]rQ" MF$>FOF]p/F]rQ"SF$>FUF]p0F]rQ!F$-Fap6#%[poptions~must~be~given~by~a~string~cons isting~of~letters~in~|fr"C",~"G",~"L",~"M"|hr.G-Fap6#%0invalid~option.G@%FfoC3> 8,-%6Involutive/proc_inputG6#&F`o6#Fin>8<&FhsF]t>FU5FU&Fhs6#""&>8E73%)P_T_ListG %*pnumber_tG%+PolTab_VarG%&_nvarG%&_pvarG%(_vardegG%(_tupdegG%,_entrblocksG%&P_ HOMG%)_pno_rhsG%0_pforce_collectG%._pforce_evalaG%)_inv_denG%+_JB_factorG%3_JB_ factor_multvarG%(_JB_varG%*_JB_compaG>8/-%5Involutive/proc_varsG6$F_oF_t>8@&F[v Fao>8>&F[v6#F_p>8B&F[v6#""'>80&F[vF]t>827#-%$seqG6$-%$catG6$%#_xGFep/Fep;Fin-%% 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Feq6$Feq-Fbw6$7$*&FhoFinF`anFinF_bn/Fho;Fin,&FcfnFinFdblFin@$/&Fit6%FepFetFidlF egl?(FhoFinFinFeanF]pC$>F`anFjan>Feq6$Feq7$F`anF_bn@$F]elC&>FgqFibn>FeelF_gl>Fe elF]cn?(F$FinFinF$F`cnC&>F`anFccn@$Fbfn>FeqFffn@$F_gn?(FhoFinFinFeanF]pC$>F`anF jan>FeqFfgn>FeelF]cn/F[anF_glC$>F`an-F^bl6$)Fhbm&FitFfhlF[cm>Feq6$Feq-Fbw6$Fifn /Fho;FboF]gn@$FbfnC$>F`anF[in>FeqFffn>Fd\mf*Ff\mF$F$F$@)Fj\mFMF^]mF]p/*&Fa]mFin -%'coeffsG6#Fa]mFdbl*&Fb]mFin-F_jn6#Fb]mFdbl-%&evalbG6#1-%$absG6#F^jn-Fijn6#Fbj nF_]mF$F$Fc]m>Feq-Fgel6$7#FeqFd\m@$FfoF^\m@%2FinF_t-F[_l6$f*F^_lF$Fg_lF$-Fgil6$ /F[]mFa]mF]enF$F$6$F>F_tFeq-F[_l6$f*F^_lF$Fg_lF$Fa]mF$F$F$FeqF$F$F$F$, Q?Involutive/FactorModuleBasis.mF$ M7R0 I:Involutive/isMinimalBasisf*6#%#lmG6$%"iG%"rG6#%jnCopyright~(C)~2002-2008~by~D aniel~Robertz.~All~rights~reserved.G6"C$@%/%4Involutive/ratcoeffG%&falseGC$>8$" ""?(F+F4F4F+1F3%*pnumber_tGC$@$33/&&9$6#F46#""#&&&%)P_T_ListG6#F36#""$FA-%:Invo lutive/conv_divisibleG6$F>FD2-%$absG6#&&F?FAF@-FO6#&&FE6#""'F@-%'RETURNG6#F0>F3 ,&F3F4F4F4C$>F3F4?(F+F4F4F+F6C$@$F;FY>F3Fgn-FZ6#%%trueGF+F+F+F+, Q8.-%6Involutive /proc_inputG6#9$>8?&Fen6#""">8A&Fen6#""#>8B&Fen6#""$>8F&Fen6#""&>8G&Fen6#""(@%3 32Fco9#-%%typeG6$&9"FgoF'4-Fip6$F[q-F'6#%(integerGC'>83F[q>81-Fgn6#&F\qFbo@$2F^ o&FgqF]o-%&ERRORG6#%Xexpecting~list~of~relations~for~the~residue~class~ring.G@$ 4&FgqFgo-F_r6#%foright~hand~sides~for~relations~of~the~residue~class~ring~are~n ot~supported.G>8,""%C%@$2FgpFco-F_r6#%Pexpecting~list~of~variables~as~second~ar gument.G>FeqFjq>FirFho>82-%5Involutive/proc_varsG6$FeqF[o>8;&FdsFbo>8<&FdsFgo>8 =&Fds6#Fjr>8>&FdsF\p>8@&Fds6#""'>Feq&FdsF]o>%&_nvarG-%%nopsG6#Feq>8C7#-%$seqG6$ -%$catG6$%#_xG8'/F[v;F^oF]u>Fis-%%subsG6$7#-Feu6$/&Feq6#F[vFguF\vFis@%0%2Involu tive/characG""!>Fen-%$modG6$-%(collectG6%&FenFatFeq%,distributedGFjv>FenF`w>8E- %&evalbG6#0-%&minusG6$<#-%#opG6#F_p<#-FaxF`u<">864Fjo@%/Fis7">88Fjr>F]y7#-%"$G6 $Fjr-F_u6#Fis>8IF[y?(F[vFirF^oFgpFW@)-Fip6$&F\qFgv%)equationG@%/-Fax6$F^oF[zQ(e 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stG6*FenF[oF`oFi_lFh^lFctFeqFeo@$0FfyF[yC&>%)P_T_ListG-%$mapG6$f*6#F,FQF]\lFQ&F dclFhnFQFQFQFfy>%+PolTab_VarG-Ffcl6$f*FiclFQF]\lFQ&F\dlFhnFQFQFQFfy>F\cl-Ffcl6$ f*FiclFQF]\lFQ&Fe\lFhnFQFQ6$F4F\clFfy>%*pnumber_tG-F_u6#Ffy>8D-%F\el7#-%'coeffsG6#F\el>F[vF^o?(FQF^oF^ oFQ31F[v-F_uFhel1F[w&F\elFgv>F[v,&F[vF^oF^oF^o@$F\fl-F_r6#%hqthe~given~list~L~i s~not~an~involutive~basis~w.r.t.~the~variables~var.~You~have~to~call~Involutive Basis~again.G>8HF^o>F[vF^o?(FQF^oF^oFQ3/FgflF^o1F[v-F_u6#FdclC%>8(F^o?(FQF^oF^o FQ3F[gl1FaglF]uC$@$2&Fdcl6%F[vF]pFagl%)infinityGC&>FirFafl>8-7%F[wF[w-%'subsopG 6$/F^o-Fahl6$/Fagl,(&Fdcl6&F[vFhoF^oFaglF^oFhglF^oF^oF^o&Fdcl6%F[vFhoF^o&Fdcl6$ F[vFho?(FQF^oF^oFQ31FirF]gl-Fe^l6$&Fdcl6#FirF^hl>Fir,&FirF^oF^oF^o@$/&F^hlFgo&F dcl6$,&FirF^o!""F^oFho>FgflF[w>Fagl,&FaglF^oF^oF^o>F[vFafl>%&_pvarGFds>%)_pno_r hsGFeo>%0_pforce_collectGFgw>%._pforce_evalaGFjo>%(_StatssG7*FaalFcalFealFgalFi alF[blFgflF[w-%'RETURNG6#F\clFQ66F]uFcjlFejlFgjlFijlFaalFcalFealFgalFialF[blF[[ mF`blFcblFfblFiblF]blFhdlFdclF\dlFQFQ, Q8/-%6Involutive/proc_inputG6#9$>8-&F fn6#"""@$4&Ffn6#""$-%&ERRORG6#%Fexpecting~L~without~right~hand~sides.G>8>&Ffn6# ""'>8?&Ffn6#""(>8D&Ffn6#"")>Ffn&Ffn6#""%>8.-%%nopsG6#Ffn>8*7#-%"$G6$""!F]q>Ffn7 #-%$seqG6$-%'subsopG6$/F_o7$-%#opG6#&Ffn6$8&F_o-Fcr6#-F^r6$/FgrF_oFbq&Ffn6#Fgr/ Fgr;F_oF^q@%332""#9#-%%typeG6$&9"Fco%%listG4-Fhs6$Fjs-F\t6#%(integerGC)>84Fjs>8 1-Fhn6#&F[t6#Fes@$2F_o&FgtF^o-Ffo6#%Xexpecting~list~of~relations~for~the~residu e~class~ring.G@$4&FgtFco-Ffo6#%foright~hand~sides~for~relations~of~the~residue~ class~ring~are~not~supported.G>Fgt-%'expandG6#&FgtFjp@%/&Fgt6$F_oF_o7#Fgq>Fgt7" C$>Fgt7#-F[r6$-F[r6$7$7$-Fcr6#-F^r6$/Fgr&Fgt6%8'F_oF_o7#-Feq6$FgqF\oFdqFav/Fgr; F_oF\o/Fdw;F_o-F_q6#Fgt>Ffn7$-FcrF`q-FcrF]x>FbqF[qC&@$2FfsFes-Ffo6#%Pexpecting~ list~of~variables~as~second~argument.G>FetFjt>FgtFcv>FbqFdo>Fet-%5Involutive/pr oc_varsG6$FetF\o>87&FetF[u>88&FetFco>89&FetFjp>8:&Fet6#""&>8F&FetF\p>Fet&FetF^o >85-F_q6#Fet@%0%2Involutive/characGFgq>Ffn-%$modG6$-%(collectG6%FfnFet%,distrib utedGFiz>FfnF^[l>8%Fiz>8AFcv>8BFcv>8CFcv>83Q!FR>8@FX@%/FayFcv>82F[q>Fc\l7#-Feq6 $F[q-F_q6#Fay>8EFgq>8;%&falseG>8+-%(convertG6$-%+kerneloptsG6#%(versionG%'strin gG>8H-%&evalbG6#2Fgq-%+searchtextG6$Q&APPLEFRF`]l>8GF]\l>8IFgq>8JFgq>8KFgq?(Fgr FbqF_oFfsFX@)5-Fhs6$&F[tF^sFbt-Fhs6$F`_lF\t>Fc\lF`_l-Fhs6$F`_lFh]lC$>8)F`_l?(Fd wF_oF_o-%'lengthG6#Fh_lFX@&/&Fh_l6#FdwQ"NFR>F_\lF^]l0F_`lF]\l-Ffo6#%0invalid~op tion.G-Fhs6$F`_l%)equationG@;/-Fcr6$F_oF`_lQ%NameFRC$@$4-Fhs6$-Fcr6$FesF`_lFh]l -Ffo6#%Fexpecting~a~string~for~option~"Name".G>F\\lFdal/F\alQ$modFRC%>F`]l-%*su bstringG6$F`]l;F_oFgp>80Fdal@%55-Fhs6$FcblF\t-Fhs6$Fcbl%'matrixG330F`]lQ)Maple~ V,FR0F`]lQ)Maple~6.FR-Fhs6$Fcbl%'MatrixG@$0FcblFcvC)>Fcbl-Fhn6#Fcbl@$4&FcblFco- Ffo6#%gnexpecting~argument~to~option~"mod"~without~right~hand~sides.G@$0&FcblF^ oF\o-Ffo6#%bplength~of~tuples~in~option~"mod"~does~not~match~length~of~tuples~i n~the~generating~set.G?&Fdw&FcblF\pFX@$4-%'memberG6$FdwFjo>Fjo7$-Fcr6#FjoFdw?&F dw&FcblFapFX@$4-F\el6$FdwF_p>F_p7$-Fcr6#F_pFdw>Fcbl-%$mapG6$f*6#F'FR6$%)operato rG%&arrowGFR-F^r6$/F_o7$-Fcr6#&FjnF^o-Feq6$FgqT#FjnFRFR6$F1F]q&FcblFjp>Ffn7$F`x -FcrFjcl-Ffo6#%Wexpecting~list~or~matrix~as~argument~for~option~"mod".G/F\alQ%c harFRC$@$4-Fhs6$Fdal%*nonnegintG-Ffo6#%Qexpecting~0~or~a~prime~number~for~optio n~"char".G>Fd[lFdal/F\alQ%timeFRC$@$F[hl-Ffo6#%Sexpecting~time~bound~in~seconds ~for~option~"time".G>F[]lFdal/F\alQ)GroebnerFRC$@$4-Fhs6$Fdal%(booleanG-Ffo6#%O expecting~boolean~value~for~option~"Groebner".G>F]]lFdal/F\alQ'algextFR@%-Fhs6$ FdalF\t?&8(FdalFXC&>8,-%&minusG6$-%'indetsG6#F]jl<&-Fcr6#Fj[l-Fcr6#Fh[l-Fcr6#-F ^fl6%Fb]lF_p%%nameG-Fcr6#-F^fl6%Fb]lFjoF`[m@$50-F_q6#F`jlF_o4-Fhs6$F]jl-%(polyn omG6$%)anythingGF`jl-Ffo6#%`sexpecting~a~univariate~polynomial~(possibly~with~r ational~coefficients~in~previously~defined~algebraic~elements)~for~option~"alge 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