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6$f*F;F3FF`p7#7#- Feo6$FgoFS-F[p6%F`pF]p&9"6#;FH9#F3F3F3F3 M7R0 I@homalg/Involutive/PolInvoReducef*6%%"pG%#_MG%$varG6$%"MG%"vG6#%jnCopyright~(C )~2004-2007~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- M7R0 I8homalg/Involutive/mklstf*6#%"aG6"6#%[oCopyright~(C)~2004-2007~by~Mohamed~Bara kat.~All~rights~reserved.GF&@%-%%typeG6$9$%"=G/-F"6#-%$lhsG6#F--F"6#-%$rhsGF4@% -F+6$F-%%listGF-7#F-F&F&F&F& M7R0 I6Involutive/pdegrevlexf*6$%"aG%"bG6%%"iG%$tdaG%$tdbG6#%\pCopyright~(C)~2000-20 07~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$-% %nopsG6#F4!""F7FD@&2&F=6#FJ&F4FRFA2FSFQFF@%2&F56#""#&F>FXFHFDF-F-F-F- M7R0 I5Involutive/block_ordf*6&%"aG%"bG%$sepG%+termordersG6#%"iG6#%jnCopyright~(C)~2 004-2007~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$&FCFWFE-%'RETURNG6#FF0FVFjn-F\o6#FN @%2F>FEFFFNFNF-F-F-F- M7R0 I5Involutive/remove_lmf*6$%"LG%'lmprocG6'%"iG%"jG%"FG%#lmG%#LMG6#%jnCopyright~( C)~2006-2007~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$-%#opG6#F5FN>F8,&F8F9F9F9F2F/F/F/F/ M7R0 I5Involutive/ginvBasisf*69'%"FG%%listG%$varG%)alg_elemG%(tr_elemG%'n_entrG%)rhs _entrG%'no_rhsG%"cG%&m_ordG%(var_ordG%)entr_posG%'vardegG%'tupdegG%%fextG%%algo G%+time_boundG%#trG%*quietmodeG%*donotreadG%+tracedenomG%+movedboundG%-qlengthb oundG%,degreeboundG6*%%fileG%&fnameG%"iG%"rG%%nvarG%#mpG%+trans_elemG%"SG6#%jnC opyright~(C)~2006-2007~by~Daniel~Robertz.~All~rights~reserved.G6"Cgn@%9*@$2"&++ "9(-%&ERRORG6#%@length~of~tuples~exceeds~10000.G@$2FO,&FP"""-%%nopsG6#&&9$6#FX6 #""#FXFQ@$4%4Involutive/ratcoeffG-FR6#%Zup~to~now,~only~field~coefficients~are~ supported~by~ginv.G@$2"&Ob'9+-FR6#%?characteristic~must~be~<~2^16.G>8(-FZ6#9%>8 *-%%sortG6#7#-%#opG6#-%&minusG6$<#-Fep6#9'<#-FepF\p@$0907#-%"$G6$""!FP-FR6#%Yup ~to~now,~no~degrees~can~be~assigned~to~tuples~in~ginv.G@&2F[o-FZ6#9--FR6#%bpup~ to~now,~only~two~blocks~of~variables~for~elimination~ordering~are~supported~by~ ginv.G31FXF]r2FXFP-FR6#%^oup~to~now,~block~elimination~ordering~is~only~support ed~for~ideals.G@$2F[o-FZ6#9.-FR6#%_pup~to~now,~only~two~blocks~of~tuples~for~el imination~ordering~are~supported~by~ginv.G@(309&7"0F_pFes-FR6#%`qup~to~now,~gin v~does~not~support~both~algebraic~and~transcendental~field~extensions~at~the~sa me~time.G2FX-FZ6#Fds-FR6#%`pup~to~now,~only~simple~algebraic~extensions~over~th e~rationals~are~supported~by~ginv.G32F[o-FZ6#F_p0%2Involutive/characGFgq-FR6#%_ qup~to~now,~transcendental~extensions~of~degree~greater~than~2~are~only~support ed~over~the~rationals.G@'2Fgq-%+searchtextG6$Q&linuxFI-%+kerneloptsG6#%(version GC&>8'-%(ssystemG6#%3test~-d~/tmp/$USERG@$0&FeuFinFgqC$>Feu-Fgu6#%1mkdir~/tmp/$ USERG@$F[v-FR6#%Ecannot~write~temporary~file~to~/tmp.G>8%-Fgu6#%Gecho~/tmp/$USE R/Involutive-$PPID-$USERG>Fgv-%=Involutive/remove_whitespaceG6#&FgvFjn2Fgq-F\u6 $Q&APPLEFIF_u>Fgv-%:Involutive/mac_gettmpnameGFI>FgvQ1\TEMP\InvolutiveFI>Fgv-%$ catG6$Fgv91>8$-%&fopenG6$Fgv%&WRITEG-%(fprintfG6$F_xQ8#!~/usr/bin/env~python|+F I-Fex6$F_xQY#~temporary~file~created~by~the~Maple~package~InvolutiveFI-Fex6$F_x Q+~(version~FI-Fex6$F_x-%(convertG6$%3Involutive/versionG%'stringG-Fex6$F_xQ#)| +FI-Fex6$F_xQ-import~ginv|+FI@%3/FPFXFL-Fex6$F_xQDst~=~ginv.SystemType("Polynom ial")|+FIC%-Fex6$F_xQKst~=~ginv.SystemType("Polynomial",~module=FI@%FL-Fex6$F_x -Fay6$FPFdyC%-Fex6$F_x-Fay6$,&FPFX9)FXFdy-Fex6$F_xQ-,~rightPart=FIFfzFey@'0F_rF es-Fex6$F_xQGim~=~ginv.MonomInterface("Elim",~st,~[FI3/F[sFX/&F]sFinFP@+/9,FX@% F\z-Fex6$F_xQFim~=~ginv.MonomInterface("Lex",~st,~[FI-Fex6$F_xQIim~=~ginv.Monom Interface("PotLex",~st,~[FI/F_\lF[o@%F\z@%/9/7#-Feq6$FXFjo-Fex6$F_xQLim~=~ginv. MonomInterface("DegRevLex",~st,~[FI-Fex6$F_xQOim~=~ginv.MonomInterface("DegRevL exDeg",~st,~[FI@%Fj\l-Fex6$F_xQOim~=~ginv.MonomInterface("PotDegRevLex",~st,~[F I-Fex6$F_xQRim~=~ginv.MonomInterface("PotDegRevLexDeg",~st,~[FI/F_\l""$@%F\zFa\ l-Fex6$F_xQIim~=~ginv.MonomInterface("TopLex",~st,~[FI/F_\l""%@%F\z@%Fj\lF_]lFb ]l@%Fj\l-Fex6$F_xQOim~=~ginv.MonomInterface("TopDegRevLex",~st,~[FI-Fex6$F_xQRi m~=~ginv.MonomInterface("TopDegRevLexDeg",~st,~[FIC$-%'fcloseG6#F_x-FR6#%\oup~t o~now,~the~chosen~monomial~ordering~is~not~supported~by~ginv.GC%-Fex6$F_xQPim~= ~ginv.MonomInterface("PosElim",~st,~varSep=FI-Fex6$F_x-Fay6$F\\lFdy-Fex6$F_xQ$, ~[FI?(8&FXFXFjo%%trueGC$-Fex6$F_x-F[x6%Q"'FI-Fay6$&F]p6#F``lFdyFg`l@$2F``lFjo-F ex6$F_xQ#,~FI-Fex6$F_xQ"]FI@&Fe[lC$-Fex6$F_xQ*,~varSep=FI-Fex6$F_x-Fay6$-FZ6#&F _rFinFdy4Fi[lC$FfalFh_l@$0F[]lF\]lC$-Fex6$F_xQ+,~degrees=FI-Fex6$F_x-Fay6$F[]lF dyFey@%F^o@%0FeoFgq@+3/F[tFgq/FbtFgqC%-Fex6$F_xQenic~=~ginv.CoeffInterface("Mod ularShort",~st,~modularShort=FI-Fex6$F_x-Fay6$FeoFdyFey3/F[tFXFbclC,@$0-Fep6$Fg q&FdsFin%'RootOfGC$F^_l-FR6#-F[x6$-Fay6$FbdlFdy%M~is~not~algebraic~over~the~rat ional~numbers.G>8)-Fep6$FXFbdl>F]el-F[x6$-Fay6$-%%subsG6$/&-%'indetsG6#F]elFinF bdlF]elFdyQ"~FI-Fex6$F_xQioic~=~ginv.CoeffInterface("AlgebraicFieldExtensionMod ularShort",~st,~parametr=[FI-Fex6$F_x-F[x6%Q""FIFidlFefl-Fex6$F_xQ/],~extension ="FI-Fex6$F_xF]el-Fex6$F_xQ1",~modularShort=FIFgclFey3Facl/FbtFXC'-Fex6$F_xQ`oi c~=~ginv.CoeffInterface("OneParametrModularShort",~st,~modularShort=FIFgcl-Fex6 $F_xQ-,~parametr=[FI-Fex6$F_x-F[x6%Fefl-Fay6$&F_pFinFdyFefl-Fex6$F_xQ$])|+FI3Fa cl/FbtF[oC)-Fex6$F_xQ`oic~=~ginv.CoeffInterface("TwoParametrModularShort",~st,~ modularShort=FIFgclFdglFgglF^al-Fex6$F_x-F[x6%Fefl-Fay6$&F_pFjnFdyFeflF^hlC$F^_ l-FR6#%5not~implemented~yet.G@+F`cl-Fex6$F_xQFic~=~ginv.CoeffInterface("GmpZ",~ st)|+FIF[dlC*@$F_dlC$F^_lFedl>F]elF^el>F]elFael-Fex6$F_xQaoic~=~ginv.CoeffInter face("AlgebraicFieldExtensionGmpQ",~st,~parametr=[FIFaflFfflFifl-Fex6$F_xQ$")|+ FIF^glC%-Fex6$F_xQenic~=~ginv.CoeffInterface("OneParametrGmpZ",~st,~parametr=[F IFgglF^hlFaclC%-Fex6$F_xQZic~=~ginv.CoeffInterface("NParameterGmpZ",~st,~parame tr=[FI?(F``lFXFXFbtFa`lC$-Fex6$F_x-F[x6%Fefl-Fay6$&F_pF[alFdyFefl@$2F``lFbtF^al F^hlC$F^_lF_ilC$F^_lF_il-Fex6$F_xQQip~=~ginv.PolyInterface("PolyList",~st,~im,~ ic)|+FI-Fex6$F_xQ:iw~=~ginv.WrapInterface("FI@+/%3Involutive/invcritGFes-Fex6$F _xQ(WithoutFI/F^\m7$FXF[o-Fex6$F_xQ.CritPartiallyFI/F^\m7%FXF[oF]^l-Fex6$F_xQ'C 1C2C3FI/F^\m7&FXF[oF]^lFc^l-Fex6$F_xQ)C1C2C3C4FIC$F^_l-FR6#%Wundefined~involuti ve~criteria;~see~?InvolutiveOptions.G-Fex6$F_xQ(",~ip)|+FI@%%5Involutive/janetl ikeG-Fex6$F_xQNiD~=~ginv.DivisionInterface("JanetLike",~iw)|+FI-Fex6$F_xQJiD~=~ ginv.DivisionInterface("Janet",~iw)|+FI-Fex6$F_xQ*eqs~=~[\|+FI?(F``lFXFX-FZ6#Fh nFa`lC&@%FL@%F]z>8+-F[x6$-Fay6$-Fep6#&Fhn6$F``lFXFdyF]fl>Fj^m-Fay6$Fa_mFdy>Fj^m -Fay6$-%$mapG6$Fep&FhnF[alFdy?(FIFXFXFI2"'++5-%'lengthG6#Fj^mC&>Feu-F\u6$Q"|+FI Fj^m?(FIFXFXFI2FgqFeuC&@%32FXFeu/&Fj^m6#,&FeuFX!""FXQ"\FI-Fex6%F_xQ#%aFI-%*subs tringG6$Fj^m;FX,&FeuFX!"#FX-Fex6%F_xFfam-Fham6$Fj^m;FXFaam-Fex6$F_xQ#\|+FI>Fj^m -Fham6$Fj^m;,&FeuFXFXFXFbam>FeuFe`m-Fex6%F_xFfamFj^m>Fj^mQ!FI@$2FgqF``mF[cm@$2F ``lFd^m-Fex6$F_xQ$,\|+FI>Fj^mQ:basis~=~ginv.basisBuild("FI@%092F^cm>Fj^m-F[x6$F j^mFjcm@%3333/F_rFesFb^lFj[lF[\lFj\l>Fj^m-F[x6$Fj^mQ)TQDegreeFI>Fj^m-F[x6$Fj^mQ #TQFI>Fj^m-F[x6$Fj^mQ(",~iD,~FI@%52Fgq982Fgq99C/-Fex6$F_xQY]|+eqs2~=~[]|+for~i~ in~eqs:|+~~~~eqs2.append(i)|+runden~=~0|+FI-Fex6$F_xQ-while~True:|+FI-Fex6$F_xQ X~~~~runden~=~runden+1|+~~~~print~"NEUE~RUNDE:~",~runden|+FI-Fex6$F_xQbo~~~~pri nt~"Eingabe:~",~len(eqs),~"~letzte~Basis:~",~len(eqs2)-len(eqs)|+FI@%Fbem@%Fdem C&-Fex6$F_x-F[x6%Q%~~~~FIFj^mQ2eqs2,~MovedBound=FI-Fex6$F_x-Fay6$FcemFdy-Fex6$F _xQ0,~QlengthBound=FI-Fex6$F_x-Fay6$FeemFdyC$FffmF\gmC$-Fex6$F_x-F[x6%FjfmFj^mQ 4eqs2,~QlengthBound=FIFcgm@$2Fgq93C$-Fex6$F_xQ(,~time=FI-Fex6$F_x-Fay6$F`hmFdy@ $2Fgq9:C$-Fex6$F_xQ/,~DegreeBound=FI-Fex6$F_x-Fay6$F[imFdy@$95-Fex6$F_xQ*,~quie t=1FIFey@%F_hm-Fex6$F_xQio~~~~if~not~basis.computationInterrupted()~or~basis.ou tOfTime():|+~~~~~~~~break|+FI-Fex6$F_xQZ~~~~if~not~basis.computationInterrupted ():|+~~~~~~~~break|+FI-Fex6$F_xQN~~~~del~eqs2|+~~~~eqs2~=~[]|+~~~~for~i~in~eqs: |+FI-Fex6$F_xQU~~~~~~~~eqs2.append(i)|+~~~~for~i~in~basis.iterIB():|+FI-Fex6$F_ xQL~~~~~~~~eqs2.append(str(i))|+~~~~del~basis|+|+FIC&-Fex6$F_x-F[x6%Q#]|+FIFj^m Q$eqsFI@$F_hmC$FbhmFehm@$FjhmC$F]imF`imFey-Fex6$F_xQ1ginv.basisSave("FI-Fex6$F_ x-F[x6$FgvQ(.binaryFI-Fex6$F_xQ+",~basis)|+FI-Fex6$F_xQ+f~=~file("FI-Fex6$F_x-F [x6$FgvQ'.janetFI-Fex6$F_xQ)",~"w")|+FI@%96C:-Fex6$F_xQ6l~=~basis.lengthIB()|+F I-Fex6$F_xQ'i~=~1|+FI-Fex6$F_xQ:for~p~in~basis.iterIB():|+FI-Fex6$F_xQ/~~~~if~i ~<~l:|+FI-Fex6$F_xQB~~~~~~~~S~=~"\""+str(p)+"~\",\\"|+FI-Fex6$F_xQ7~~~~~~~~prin t~>>~f,~S|+FI-Fex6$F_xQ+~~~~else:|+FI-Fex6$F_xQ?~~~~~~~~S~=~"\""+str(p)+"~\""|+ FIF\^n-Fex6$F_xQ-~~~~i~=~i+1|+FI-Fex6$F_xQ+f.close()|+FIF_\n-Fex6$F_x-F[x6$FgvQ $.lmFIFg\n-Fex6$F_xQ>~f,~str(basis.outOfTime())|+FIC7@$F_hmC%-Fex6$F_x QIprint~>>~f,~"_IB_RESULTout_of_time~:=~"|+FIF[an-Fex6$F_xQ1print~>>~f,~":"|+FI -Fex6$F_xQ?print~>>~f,~"_IB_RESULT~:=~["|+FIF]]nF`]nFc]nFf]n-Fex6$F_xQ<~~~~~~~~ print~>>~f,~p,~","|+FIF_^n-Fex6$F_xQ7~~~~~~~~print~>>~f,~p|+FIFe^n-Fex6$F_xQ2pr int~>>~f,~"]:"|+FI-Fex6$F_xQAprint~>>~f,~"_IB_RESULTlm~:=~["|+FIF`]nF`_nFf]nFja nF_^nF]bnFe^nF`bn@$Fd_nC,-Fex6$F_xQ6l~=~ic.lengthDenom()|+FI-Fex6$F_xQDprint~>> ~f,~"_IB_RESULTdenom~:=~["|+FIF`]nF[`nFf]n-Fex6$F_xQ<~~~~~~~~print~>>~f,~c,~"," |+FIF_^n-Fex6$F_xQ7~~~~~~~~print~>>~f,~c|+FIFe^nF`bnFh^nF^_l@%FeimC$>Feu-Fgu6#- F[x6$Q)runginv~FIFgv>FeuF\v>Feu-%'systemGFhcn@$0FeuFgq-FR6#%Merror~during~call~ of~Python~or~interruption.G@$FjtC%>Feu-Fgu6#-F[x6'Q&if~[~FIFgvQ,.janet~-ot~FIFg vQ:~];~then~echo~-n~true;~fiFI@$2Fgq-Fa`m6#&FeuFjn-FR6#%dpoutput~file~of~ginv~i s~older~than~input~file~(probably,~program~ginv~stopped~abnormally).G@$4F[]nC$> Feu-Fgu6#-F[x6%Q*filesize~FIFgvFf\n@$/F\vFgqC$>F``l-%'sscanfG6$FcenQ#%dFI@$32Fg q-FZF[al2"'++I&F``lFin-%(WARNINGG6#Q\oresulting~involutive~basis~is~big;~readin g~it~may~take~a~while...FI@$F[]n-%'RETURNG6#FesAFd\n@$43-%)assignedG6#%+_IB_RES ULTG-F\hn6#%-_IB_RESULTlmG-FR6#%Cerror~in~computation~or~interface.G@$33F_hm-F\ hn6#%6_IB_RESULTout_of_timeG/Fjhn.%%TrueG-F`gn6#%[ocomputation~of~involutive~ba sis~stopped~due~to~time~restriction.G>%+_JB_factorG.Fbin>%3_JB_factor_multvarG. 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RG6#%_oexpecting~an~indeterminate~for~the~Hilbert~series~as~first~argument.GC$> FI%%trueG?(8$FFFFFEFfo@%3-FQ6$&FT6#FhoFV/-FY6$FFF]pFenC$>F>-FY6$FinF]p@$F\o-Fao 6#%Sexpecting~an~indeterminate~for~the~Hilbert~series.G>FA6$FAF]p@%FI>6$8786-%7 Involutive/setup_basisG6#FAC$@$333/%5Involutive/InvoBasisG%>Involutive/InvBasis FastAssertG-%)assignedG6#%+_JB_factorG-F]r6#%3_JB_factor_multvarG-F]r6#%(_JB_va rGC%>8(-%$seqG6$/&FerF^pF>/Fho;FF-%%nopsGFdr>8.-%'expandG6#-%$addG6$*&-%%subsG6 $Fhr&F_rF^pFF),&FFFFF>!""-%*numboccurG6$&FbrF^pFFFat/Fho;FF-FasF^r@%-FQ6$Fcs%%l istG-%'RETURNG6#-%(convertG6$Fcs%"+G-F^u6#Fcs@$4-F]r6#%)P_T_ListG-Fao6#%Umissin g~involutive~basis;~run~InvolutiveBasis~first.G>8'-Fas6#&Fju6%FF""$FF>Fhr-%4Inv olutive/pmax_degGFiu>Fcs-%1Involutive/PolHPG6#F>>80-%1Involutive/PolHFG6#,&FhrF FFatFF>8*-%'matrixG6#-%$mapG6$f*6#%"aGF$6$%)operatorG%&arrowGF$-Fhw6$f*6#%"bGF$ F]xF$-%)binomialG6$,(T$FF9$FFT%FatFjxF$F$6&F\xFjxF*F[y7#-%"$G6#;FFT#F$F$6&F)F_v 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SystemType("Polynomial")|+FBC%-Fax6$FhwQKst~=~ginv.SystemType("Polynomial",~mod ule=FB@%FE-Fax6$Fhw-F]y6$FIF`yC%-Fax6$Fhw-F]y6$,&FIFQ9)FQF`y-Fax6$FhwQ-,~rightP art=FBFbzFay@'0FhqF^s-Fax6$FhwQGim~=~ginv.MonomInterface("Elim",~st,~[FB3/FdrFQ /&FfrFXFI@+/9,FQ@%Fhy-Fax6$FhwQFim~=~ginv.MonomInterface("Lex",~st,~[FB-Fax6$Fh wQIim~=~ginv.MonomInterface("PotLex",~st,~[FB/F[\lFZ@%Fhy@%/9/7#-F^q6$FQFco-Fax 6$FhwQLim~=~ginv.MonomInterface("DegRevLex",~st,~[FB-Fax6$FhwQOim~=~ginv.MonomI nterface("DegRevLexDeg",~st,~[FB@%Ff\l-Fax6$FhwQOim~=~ginv.MonomInterface("PotD egRevLex",~st,~[FB-Fax6$FhwQRim~=~ginv.MonomInterface("PotDegRevLexDeg",~st,~[F B/F[\l""$@%FhyF]\l-Fax6$FhwQIim~=~ginv.MonomInterface("TopLex",~st,~[FB/F[\l""% @%Fhy@%Ff\lF[]lF^]l@%Ff\l-Fax6$FhwQOim~=~ginv.MonomInterface("TopDegRevLex",~st ,~[FB-Fax6$FhwQRim~=~ginv.MonomInterface("TopDegRevLexDeg",~st,~[FBC$-%'fcloseG 6#Fhw-FK6#%\oup~to~now,~the~chosen~monomial~ordering~is~not~supported~by~ginv.G C%-Fax6$FhwQPim~=~ginv.MonomInterface("PosElim",~st,~varSep=FB-Fax6$Fhw-F]y6$Fh [lF`y-Fax6$FhwQ$,~[FB?(8)FQFQFco%%trueGC$-Fax6$Fhw-Fdw6%Q"'FB-F]y6$&Ffo6#F\`lF` yFc`l@$2F\`lFco-Fax6$FhwQ#,~FB-Fax6$FhwQ"]FB@&Fa[lC$-Fax6$FhwQ*,~varSep=FB-Fax6 $Fhw-F]y6$-FS6#&FhqFXF`y4Fe[lC$FbalFd_l@$0Fg\lFh\lC$-Fax6$FhwQ+,~degrees=FB-Fax 6$Fhw-F]y6$Fg\lF`yFay@%Fgn@%0F^oF`q@+3/FdsF`q/F[tF`qC%-Fax6$FhwQenic~=~ginv.Coe ffInterface("ModularShort",~st,~modularShort=FB-Fax6$Fhw-F]y6$F^oF`yFay3/FdsFQF ^clC,@$0-F^p6$F`q&F]sFX%'RootOfGC$Fj^l-FK6#-Fdw6$-F]y6$F^dlF`y%M~is~not~algebra ic~over~the~rational~numbers.G>8(-F^p6$FQF^dl>Fidl-Fdw6$-F]y6$-%%subsG6$/&-%'in detsG6#FidlFXF^dlFidlF`yQ"~FB-Fax6$FhwQioic~=~ginv.CoeffInterface("AlgebraicFie ldExtensionModularShort",~st,~parametr=[FB-Fax6$Fhw-Fdw6%Q""FBFedlFafl-Fax6$Fhw Q/],~extension="FB-Fax6$FhwFidl-Fax6$FhwQ1",~modularShort=FBFcclFay3F]cl/F[tFQC '-Fax6$FhwQ`oic~=~ginv.CoeffInterface("OneParametrModularShort",~st,~modularSho rt=FBFccl-Fax6$FhwQ-,~parametr=[FB-Fax6$Fhw-Fdw6%Fafl-F]y6$&FhoFXF`yFafl-Fax6$F hwQ$])|+FB3F]cl/F[tFZC)-Fax6$FhwQ`oic~=~ginv.CoeffInterface("TwoParametrModular Short",~st,~modularShort=FBFcclF`glFcglFj`l-Fax6$Fhw-Fdw6%Fafl-F]y6$&FhoFYF`yFa flFjglC$Fj^l-FK6#%5not~implemented~yet.G@+F\cl-Fax6$FhwQFic~=~ginv.CoeffInterfa ce("GmpZ",~st)|+FBFgclC*@$F[dlC$Fj^lFadl>FidlFjdl>FidlF]el-Fax6$FhwQaoic~=~ginv .CoeffInterface("AlgebraicFieldExtensionGmpQ",~st,~parametr=[FBF]flFbflFefl-Fax 6$FhwQ$")|+FBFjflC%-Fax6$FhwQenic~=~ginv.CoeffInterface("OneParametrGmpZ",~st,~ parametr=[FBFcglFjglF]clC%-Fax6$FhwQZic~=~ginv.CoeffInterface("NParameterGmpZ", ~st,~parametr=[FB?(F\`lFQFQF[tF]`lC$-Fax6$Fhw-Fdw6%Fafl-F]y6$&FhoFg`lF`yFafl@$2 F\`lF[tFj`lFjglC$Fj^lF[ilC$Fj^lF[il-Fax6$FhwQQip~=~ginv.PolyInterface("PolyList ",~st,~im,~ic)|+FB-Fax6$FhwQ:iw~=~ginv.WrapInterface("FB@+/%3Involutive/invcrit GF^s-Fax6$FhwQ(WithoutFB/Fj[m7$FQFZ-Fax6$FhwQ.CritPartiallyFB/Fj[m7%FQFZFi]l-Fa 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