Involutive.lib

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riate~polynomial~(possibly~with~rational~coefficients~in~previously~defined~alg
ebraic~elements)~for~option~"algext".G@$0-%*intersectG6$F^cl<#-F[\l6#Fbr<"-Ffo6
#%_qthe~univariate~polynomial~for~option~"algext"~may~not~contain~indeterminate
s~of~the~polynomial~ring.G@$4-F[v6$-F[\lFddlF`wC$>F]w7$-F[\l6#F]wF[cl>F`w7$Fhcl
F]flC&>F^cl-F`cl6$-Fccl6#Fh\lFecl@$5Fadl4-F_t6$Fh\lFhdlFjdl@$F^elFfel@$FjelC$>F
]w7$FaflFh\l>F`wFdfl/Fj[lQ)transextFin@'-F_t6$Fh\l-F(6#Fjal?&F[clFh\lF_o@$4-F[v
6$F[cl7$-F[\l6#FfqFfcl>Fbw7$FfclF[clFhal@$4-F[v6$Fh\lFbhl>Fbw7$FfclFh\l-Ffo6#%S
expecting~(list~of)~name(s)~for~option~"transext".G-Ffo6#%0invalid~option.G-F_t
6$F[[lF_u@%/F[[lFj_l>F\zF_oC$>83F[[l?(8(FcpFcp-%'lengthG6#FjilF_o@&/&Fjil6#F\jl
Q"LFin>FazF_o0FbjlQ"SFinF`ilF`il>%&_nvarG-FcdlFdel@$30FhrF^w4-F_t6$FczF(>Fcz7#-
%"$G6$Fcz-Fcdl6#Fhr@$0Fcs7#-Fd[m6#;FcpF`p>Fjo-%'subsopG6$/Fas-F]dl6$f*Ffu6#F0Fi
nFin-F`\m6$/Fcp7#-%$seqG6$&&FatFbp6#&F]v6#8$/Fc]m;FcpT%FatFinFin6&FBFcsF<F`p&Fj
oF`sFjo>8J-%7Involutive/checkIBginvG6/FjoFbrF`vFczFhrFhs&F[s6#;FcpFijl&F[s6#;,&
FijlFcpFcpFcp,&FijlFcpF`pFcpF]wF`wFbwFdwFaz>F_q&Fj]mFgp>8G&Fj]m6#"#5>Ffq&Fj]mF\
q>F`w&Fj]mF`s>F]w&Fj]mFes>FezFcp?(FinFcpFcpFin1Fez-FcdlFicl@%-F[v6$&F`wF][l-F]d
l6$%&parseG-F]dl6%F]u7#-%&aliasGFinF_uC%@$4-F[v6$Fj_m-F]dl6$F]`m-F]dl6%F]uF_qF_
u>F_q7$-F[\l6#F_q-F]`m6#-F]u6$Fj_mF_u>F`w-F`\m6$/FezFjyF`w>F]w-F`\m6$FgamF]w>Fe
z,&FezFcpFcpFcp>F_q-Fcu6$f*FfuFinFguFin-F[v6$Fat-F]dl6$%$rhsG&F]vFhqFinFin6$FRF
j]mF_q>8K&Fj]mFaq>8L&Fj]mFhq>FezFcp?(FinFcpFcpFin2Fez-Fcdl6#F\cmC$>F\cm7$-F[\l6
#&F\cm6#;FcpFez-F[\l6#-%%subsG6$/-Febm6#&F\cmF][l-%$lhsGFbdm&F\cm6#;F\bm!"">Fez
F\bm@$0&Fj]m6#"")Fhv>FczF]em>8I&Fj]mFbp>Fjo-F\p6#7#Fat>8R-Fcu6$f*FfuFinFguFinFj
uFinFin6$FGF_qF`q>Fiem-%>Involutive/algebraicextensionG6)Fh]mFiemF]wF`wFfqFibmF
i^m>Fh]m&FiemFbp>F]w&FiemF\q>F`w&FiemF`s>Fi^m&FiemFes>Fibm&FiemFaq>Ffq&FiemFhq>
Fbem3Fbem4&FiemF^em>Fiem&FiemFgp@$0Fi^mF^wC$>F]w-F^dm6$Fi^mF]w>Fh]m-F^dm6$Fi^mF
h]m@$0-F`cl6$<#-F[\l6#Fgq<$FchlFcelFeelC%>FbemF]z>F[cl7#-F[\l6#F_hm>Fbw7$Ffcl-F
[\lFdcl@$4FbemC$>F_q-%'selectG6$f*FfuFinFguFinFjuFinFin6$FenFdqF_q@%F\em-%?Invo
lutive/InvolutiveBasisGINVG6'&F\[l6#;FhpFidmF]emFiy/FfblF]w/FgglFbhl-Fiim6&F[jm
FiyF^jmF_jm@$4-%$hasG6$FatFbr@%0FgvFhv-%'RETURNG6#,&FgvFcpFatFidm-Fjjm6#,&FcvFc
pFatFidm@%/F`pFcp>8P-%7Involutive/ginvMinPolyG69&&Fh]mFbpFbpFbrF_qFfqF`pFepFjpF
`vFczFhr7#F`pF^^mFa^mF]wF`wFbwFdwF\zF_zFaxFcvFjv%)lowboundG-Ffo6#%Imodule~case~
not~implemented~yet~in~ginv.G@$F\z-Fjjm6#F^w@$/&Fc[nFbpFhv-Ffo6#%apstopped~calc
ulation~of~minimal~polynomial~since~upper~bound~for~the~degree~is~reached.G@$Fe
gm>Fc[n-F^dm6$-F]dl6$f*FfuFinFguFin/-Febm6#Fat-FedmF`]nFinFinFinFi^mFc[n?(Fez-F
cdl6#FibmFidmFcpF_o>Fc[n-F^dm6$&FibmF][lFc[n?(FezFacmFidmFcpF_o>Fc[n-F^dm6$Fcdm
Fc[n@%2Fhv,&-FcdlF_amFcpFf_mFcp@%Fhjm@%/FavFhv-F^dm6$/FcvFgv-%(collectG6$Fc\nFc
v-%$modG6$Fd^nFavFg^n@%Fhjm@%Fc^n-F^dm6$Ff^n-Fh^n6$-%'normalG6#*&Fc\nFcp-%'lcoe
ffGFi^nFidmFcv-F[_n6$F__nFavFa_nFin6#FijlFinFin
M7R0
I;Involutive/DependsOnPowersf*6''%"qG%(polynomG'%"pGF''%"JG%%listG'%%varsGF,'%#
FBGF,68%"aG%"iG%"jG%"nG%"vG%"xG%$denG%$varG%"FG%"MG%"QG%"SG%"UG%"VG%*low_boundG
%*upp_boundG%'paramsG%*firstevalG%*evalpointG%*paramdegsG%3printfactordegreesG%
)lessevalG6#%jnCopyright~(C)~2006-2010~by~Daniel~Robertz.~All~rights~reserved.G
6"CC>8(-%*substringG6$-%(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
M7R0
I2Involutive/PolSumf*6%%#M1G%#M2G'%$varG%%listG6"6#%[oCopyright~(C)~2003-2005~b
y~Mohamed~Barakat.~All~rights~reserved.GF*-%7Involutive/PolCokernelG6#9"F*F*F*F
*
M7R0
I;Involutive/PolIntersectionf*6%%$_R1G%$_R2G'%$varG%%listG6*%"aG%"nG%#R1G%#R2G%
#R0G%"ZG%*_inv_den2G%$resG6#%^pCopyright~(C)~2003-2010~by~Mohamed~Barakat~and~D
aniel~Robertz.~All~rights~reserved.G6"C.>8&-%$mapG6$f*6#F+F56$%)operatorG%&arro
wGF5&9$6#"""F5F5F5&-%6Involutive/proc_inputG6#FB6#""%>8'-F:6$f*F=F5F>F5FAF5F5F5
&-FG6#9%FI>8%-%%nopsG6#&F8FC>8(-F:6$%#opG7$-F:6$f*F=F5F>F5-F:6$Fhn7$FBFBF5F5F5F
8-F:6$f*F=F5F>F5-F:6$Fhn7$FB-%"$G6$""!T#F5F56$F,FUFL>8+-%;Involutive/Involutive
BasisG6%Fen9&""#>8*%)_inv_denG@$-%)assignedG6#%2PRINTelimfinishedG-%&printG6#Q5
elimination~finishedF5>8)-F:6$f*F=F5F>F5@$/&FB6#;FDFjo7#Ffo&FB6#;,&FjoFDFDFD!""
F5F5F[pF]p@$/F`q7">F`q7#7#-Fgo6$FioFU>F]p-F_p6%F`qFap&9"6#;FJ9#>Fep7#-Fhn6#-%&u
nionG6$<#-Fhn6#Fep<#-Fhn6#Fdp-%'RETURNG6#F]pF5FhsF5F5
M7R0
IBInvolutive/findezugehoerigenpunktf*6$'%"nG%*nonnegintG'%#ALG-%%listG6#%'posin
tG6$%"iG%"LG6#%[oCopyright~(C)~2007-2010~by~Moritz~Schroeer.~All~rights~reserve
d.G6"C$@$1-%$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$-%%iremGFO&F;6#;FT!""F3F3F
3F3
M7R0
I@homalg/Involutive/PolInvoReducef*6%%"pG%#_MG%$varG6$%"MG%"vG6#%jnCopyright~(C
)~2004-2010~by~Daniel~Robertz.~All~rights~reserved.G6"C%>8$-%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)~2004-2010~by~Mohamed~Bara
kat.~All~rights~reserved.GF&@%-%%typeG6$9$%"=G/-F"6#-%$lhsG6#F--F"6#-%$rhsGF4@%
-F+6$F-%%listGF-7#F-F&F&F&F&
M7R0
I;Involutive/LocalReduceGINVf*6%%#bbG%"MG%$varG6"6#%boCopyright~(C)~2007-2010~b
y~Markus~Lange-Hegermann.~All~rights~reserved.GF(C$@$5-%%typeG6$9$%)listlistG3-
F/6$F1-%%listG6#<$%"=GF7-F/6$-%$mapG6$%5Involutive/RemoveRHSGF1F2-%'RETURNG6#-F
>6$f*6#%"aGF(6$%)operatorG%&arrowGF(-%7Involutive/LocalReduceG6&F1T$T&Q%ginvF(F
(F(6&F&9%F'9&F1-FM6&F1FSFTFQF(F(F(F(
M7R0
I;Involutive/AugmentInvBasisf*6#%"pG6ho%"aG%"dG%"gG%"hG%"iG%"jG%"kG%"lG%#lmG%"m
G%"FG%"GG%#GBG%"HG%"RG%"QG%#Q2G%&ib_gbG%&m_ordG%&B_OrdG%&N_OrdG%&Q_OrdG%'lmproc
G%/default_lmprocG%'N_FormG%*N_Form_lmG%/N_Form_autoredG%'pseudoG%(seq_varG%%va
rsG%$varG%(var_ordG%'vt_degG%(deg_ordG%)tup_permG%-inv_tup_permG%.force_collect
G%,force_evalaG%'n_entrG%)rhs_entrG%*zero_listG%(allmultG%.rhs_zero_listG%'no_r
hsG%(do_normG%,no_transferG%%seqvG%(loc_varG%)critprocG%#ppG%#eqG%.last_was_zer
oG%.head_red_percG%+start_timeG%+time_boundG%+trans_elemG%)entr_posG%*pnumber_q
G%)strategyG%/tail_reductionG%'fbasisG%'Q2_valG%(newcritG%,newcrit_addG%+factor
timeG%/lastfactortimeG%,factorTsizeG%*printtimeG%.lastprinttimeG%,forceexpandG%
+savecharacG%-saveratcoeffG%*nowarningG%*denomlistG%,commondenomG%#hcG6#%jnCopy
right~(C)~2008-2010~by~Daniel~Robertz.~All~rights~reserved.G6"Cbq@$4-%)assigned
G6#%)P_T_ListG-%&ERRORG6#%Umissing~involutive~basis;~run~InvolutiveBasis~first.
G>8.-%6Involutive/proc_inputG6#7#9$>8J&F\q6#""">8K&F\q6#""#>8O&F\q6#""$>8I&F\q6
#""&>8en&F\q6#""(>F\q&F\q6#""%@%332F[r9#-%%typeG6$&9"F_r%%listG4-Fes6$Fgs-Fis6#
%(integerGC)>8BFgs>82-F^q6#&FhsFjq@$2Ffq&FdtFeq-Fhp6#%Xexpecting~list~of~relati
ons~for~the~residue~class~ring.G@$4&FdtF_r-Fhp6#%foright~hand~sides~for~relatio
ns~of~the~residue~class~ring~are~not~supported.G>Fdt&FdtF]s@%/&Fdt6$FfqFfq7#""!
>Fdt7"C$>Fdt7#-%$seqG6$-Fbv6$7$-%'subsopG6$/8(&Fdt6%8)FfqFfq7#-%"$G6$F[vFcq7#-F
aw6$F[vFhq/F[w;FfqFcq/F^w;Ffq-%%nopsG6#Fdt>F\q7$-%#opG6#F\q-F`xF\x>F[wF^sC&@$2F
csF[r-Fhp6#%Pexpecting~list~of~variables~as~second~argument.G>FbtFgt>FdtF]v>F[w
F`r>8A-%5Involutive/proc_varsG6$FbtFcq>8C&F^yFjq>8D&F^yF_r>8E&F^yF]s>8F&F^yFdr>
8fn&F^y6#""'>Fbt&F^yFeq>%&_nvarG-F[x6#Fbt@%0%2Involutive/characGF[v>F\q-%$modG6
$-%(collectG6%F\qFbt%,distributedGF[[l>F\qF`[l@$-%$hasG6$-%$mapG6$f*6#F'F_p6$%)
operatorG%&arrowGF_p3-Fes6$&FaqFeq-Fis6#-%(polynomG6$%)anythingGT#-Fes6$&FaqFjq
Fe\lF_pF_p6$FEFbtF\q%&falseG-Fhp6#-%$catG6%%Oexpecting~a~list~of~(lists~of)~pol
ynomials~in~G-%(convertG6$Fbt%'stringG%4~as~first~argument.G>8H-%&evalbG6#0-%&m
inusG6$<#-F`x6#Fgr<#-F`xFhz<">8R7#-Fbv6$-Fd]l6$%#_xGF^w/F^w;FfqFfz>8M7#-Faw6$%)
infinityGFfz>%(_nnformGF[v>%'_reducGF[v>%'_crit1GF[v>%'_crit2GF[v>%'_crit3GF[v>
%'_crit4GF[v>%,_inv_roundsGF[v>8QF[v>Fcy-%%subsG6$7#-Fbv6$/&Fbt6#F^w&F\_lFdalFc
_lFcy@$4%4Involutive/ratcoeffG@&0-Fc^l6$-%'indetsG6#-Fj[l6$f*F]\lF_pF^\lF_pFd\l
F_pF_pF_pF\qFh^lFj^l-Fhp6#%cono~parameters~allowed~in~involutive~basis~computat
ion~over~the~integers.GFbr-Fhp6#%apno~algebraic~extensions~are~allowed~in~invol
utive~basis~computation~over~the~integers.G>8;4Fbr>8P%%trueG@%/FcyF]v>86F^s>Fbc
l7#-Faw6$F^s-F[x6#Fcy>8ZF[v>8aoF[v>80F`]l>8inF^cl>8hnF[v>8X"$+">8jnF]v>8\oF`]l>
8]oF[v>8^oF[v>8`oF[v>8coF`]l>8foF`]l>8doF[[l>8eoFhal?(F^wF[wFfqFcsF^cl@)-Fes6$&
FhsFdalFj]l@%/F\flQ&denomF_pF_pC$>8/F\fl?(8*FfqFfq-%'lengthG6#FbflF^cl@(/&Fbfl6
#FdflQ"NF_p>F]clF`]l/FjflQ"SF_pC$>FbrF^cl>FjblF`]l0FjflQ!F_p-Fhp6#%aooptions~mu
st~be~given~by~a~string~consisting~of~letters~in~|fr"N",~"S"|hr.G5-Fes6$F\flF_t
-Fes6$F\flFis>FbclF\fl-Fes6$F\fl%)equationG@G/-F`x6$FfqF\flQ%charF_p@%3-Fes6$-F
`x6$F[rF\flF_t5/FjhlF[v-%(isprimeG6#FjhlC$>F[[lFjhl@$Fjz>FhalF^cl-Fhp6#%Texpect
ing~zero~or~a~prime~number~for~option~"char".G/FchlQ%timeF_pC$@$4-Fes6$Fjhl%*no
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CG@%9*@$2"'++59(-%&ERRORG6#%Alength~of~tuples~exceeds~100000.G@$2Fgn,&Fhn"""-%%
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two~blocks~of~variables~for~elimination~ordering~are~supported~by~ginv.G@$2Fio-
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mp.G>Faw-Fbx6#%Gecho~/tmp/$USER/Involutive-$PPID-$USERG@%2Fgq-Fdt6$Q"$FW&FawFho
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dt6$Q"|+FWFj_l?(FWF`oF`oFW2FgqF`xC&@%32F`oF`x/&Fj_l6#,&F`xF`o!""F`oQ"\FW-F^_l6%
F_^lQ#%aFW-Fbv6$Fj_l;F`o,&F`xF`o!"#F`o-F^_l6%F_^lFhbl-Fbv6$Fj_l;F`oFcbl-F^_l6$F
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@$2FgqFbalF\dl@$2Fb_lFc_l-F^_l6$F_^lQ$,\|+FW-F^_l6$F_^lQ#]|+FW@$F\t@%3Fh_lFZ-F^
_l6$F_^lQineqs~=~map(lambda~eq:~"("~+~eq.encode('latin1')~+~")*@~",~eqs)|+FW-F^
_l6$F_^l-Fa[l6%QReqs~=~map(lambda~eq:~(ginv.Poly(ip,~eq)).prolong(FW-Fev6$F[pF[
wQ)),~eqs)|+FW@$F\[lC(-F^_l6$F_^lQ<oldbasis~=~ginv.basisLoad("FW-F^_l6$F_^lF_[l
-F^_l6$F_^lQ.",~"TQ",~iD)|+FW-F^_l6$F_^lQ=for~i~in~oldbasis.iterIB():|+FW-F^_l6
$F_^lQ1~~eqs.append(i)|+FW-F^_l6$F_^lQ.del~oldbasis|+FW>Fj_lQ:basis~=~ginv.basi
sBuild("FW@%096Fhx>Fj_l-Fa[l6$Fj_lF^gl@%333/F_r7"5/Fi^lFio/Fi^l""%5/FgrFggl3/Fe
rF`o/&FgrFgoFhn/Fj^l7#-Feq6$F`oF[p>Fj_l-Fa[l6$Fj_lQ)TQDegreeFW>Fj_l-Fa[l6$Fj_lQ
#TQFW>Fj_l-Fa[l6$Fj_lQ(",~iD,~FW@%52Fgq9?2Fgq9@C1-F^_l6$F_^lQWeqs2~=~[]|+for~i~
in~eqs:|+~~~~eqs2.append(i)|+runden~=~0|+FW-F^_l6$F_^lQ-while~True:|+FW-F^_l6$F
_^lQX~~~~runden~=~runden+1|+~~~~print~"NEUE~RUNDE:~",~runden|+FW-F^_l6$F_^lQbo~
~~~print~"Eingabe:~",~len(eqs),~"~letzte~Basis:~",~len(eqs2)-len(eqs)|+FW@%Fdil
@%FfilC&-F^_l6$F_^l-Fa[l6%Q%~~~~FWFj_lQ2eqs2,~MovedBound=FW-F^_l6$F_^l-Fev6$Fei
lF[w-F^_l6$F_^lQ0,~QlengthBound=FW-F^_l6$F_^l-Fev6$FgilF[wC$FhjlF^[mC$-F^_l6$F_
^l-Fa[l6%F\[mFj_lQ4eqs2,~QlengthBound=FWFe[m@$2Fgq97C$-F^_l6$F_^lQ(,~time=FW-F^
_l6$F_^l-Fev6$Fb\mF[w@$2Fgq9AC$-F^_l6$F_^lQ/,~DegreeBound=FW-F^_l6$F_^l-Fev6$F]
]mF[w@$99-F^_l6$F_^lQ*,~quiet=1FW@$%2Involutive/absremG-F^_l6$F_^lQ@,~absolutel
ySmallestRemainder=1FW@$49;-F^_l6$F_^lQ,,~content=0FW-F^_l6$F_^lQ6,~skipHilbert
Poly=1)|+FW@%Fa\m-F^_l6$F_^lQio~~~~if~not~basis.computationInterrupted()~or~bas
is.outOfTime():|+~~~~~~~~break|+FW-F^_l6$F_^lQZ~~~~if~not~basis.computationInte
rrupted():|+~~~~~~~~break|+FW-F^_l6$F_^lQN~~~~del~eqs2|+~~~~eqs2~=~[]|+~~~~for~
i~in~eqs:|+FW-F^_l6$F_^lQU~~~~~~~~eqs2.append(i)|+~~~~for~i~in~basis.iterIB():|
+FW-F^_l6$F_^lQR~~~~~~~~eqs2.append(str(i)~+~'~')|+~~~~del~basis|+|+FWC*-F^_l6$
F_^l-Fa[l6$Fj_lQ$eqsFW@$Fa\mC$Fd\mFg\m@$F\]mC$F_]mFb]m@$F\^mF]^m@$Fa^mFc^m-F^_l
6$F_^lQ4,~skipHilbertPoly=1FW@$09GFgglC$-F^_l6$F_^lQ3,~hilbertFunction=FW-F^_l6
$F_^l-Fev6$Fj`mF[w-F^_l6$F_^lQ#)|+FW-F^_l6$F_^lQ1ginv.basisSave("FW-F^_l6$F_^l-
Fa[l6$FawFc[l-F^_l6$F_^lQ+",~basis)|+FW-%AInvolutive/writeGINV1MapleOutputG6,F_
^lFawQ&basisFWFhnFZ9:Fb\m9<9BF\_l@$Fe[lC&-F^_l6$F_^lQ+f~=~file("FW-F^_l6$F_^l-F
a[l6$FawQ'.readyFW-F^_l6$F_^lQ)",~"w")|+FW-F^_l6$F_^lQ+f.close()|+FW-%'fcloseG6
#F_^l@%Fe[lC&>F`x-Fbx6#-Fa[l6%Q'rm~-f~FWFawF`cm@$0&F`xFgoFgq-Fjn6#%>cannot~remo
ve~temporary~file.G>&%:Involutive/GINVlaunchdataG6#Fg]l73FawFhnFh^lFZFeuF^pFj^l
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F[w6#-Fdv6#-%&denomG6#FLFaq-%)userinfoG6%F[p%5NoetherNormalizationG-%$catG6$%-d
imension~=~G-%(convertG6$Fhu%'stringG>89Fbt>82Fcp?(FIFUFUFI2Fhu-F\q6#F]yC4>Ffz,
&FfzFUFUFU-Fjy6%F[pF\z-F^z6$%-step~~~~~~=~G-Fbz6$FfzFdz-Fjy6%F`pF\z-F^z6$%-roun
ds~~~~=~G-Fbz6$%,_inv_roundsGFdz-Fjy6%F[pF\z-F^z6$%-v~~~~~~~~~=~G-Fbz6$F]yFdz>8
-7#-Fip6#;FUF\t>Fg\l-%'removeG6$f*6#F*FIF\uFI-%$hasG6$&&%+PolTab_VarGFOFjo-%&mi
nusG6$<#-F[w6#T#<#-F[w6#T%FIFI6&F9F]oF.F]yFg\l@$/Fg\lFcp-Fhn6#%Rcannot~find~any
~good~leading~monomial~to~proceed.G>Fg\l-F_y6$Fg\lf*F[uFIFIFI@'2-F\q6#-Fi]l6$-F
av6$-Fdv6#Fe]lF[^l<#&Fb^l6#!""-F\q6#-Fi]l6$-Fav6$-Fdv6#&&Fg]lF[yFjoF[^lFg_lFcr2
F[`lF__lFjq-T'6$Fe]lFc`lFIFI6(F9F]oF.F]yF-Faq@%2"#I-F\q6#Fg\l-Fjy6%F[pF\z-F^z6$
%-lm~~~~~~~~=~G-Fbz6$7$-F[w6#-%$mapG6$f*Fa]lFIF\uFIFe]lFIFIFI&Fg\l6#;FUF\al%$..
.GFdz-Fjy6%F[pF\z-F^z6$Fcal-Fbz6$-Fjal6$f*Fa]lFIF\uFIFe]lFIFIFIFg\lFdz>8.-Fav6$
-Fdv6#&&Fg]l6#&Fg\lFTFjoFiv>8+7#-F[w6#-Fi]l6$F[cl<#&F]yFi_l@%/%2Involutive/char
acGFbtC(>8,-Fju6$F`clF[cl>8$7#-Fip6$FU-F\q6#Fecl@%-%%typeG6$&FaclFT%"+G>80-F^]l
6%Fc]l-%'selectG6$f*Fa]lFIF\uFI/-Fju6$FPF_^lF^^lFIFI6&F0FbdlF9F]oF`el-Fi]l6$Fiv
F[cl>FcelF`el>8(FU?(FIFUFUFI4-Fc]l6$-%(collectG6%-%%subsG6$7#-%$seqG6$/&FeclFhr
,&FbglFU*&&FfdlFhrFUF\dlFUFj_l/Far;FUFjdlFcelF]o%,distributedG)F\dlFbdlC$>Ffdl-
%'subsopG6$/Fbfl,&&Ffdl6#FbflFUFUFUFfdl>Fbfl,&-%$modG6$FbflFjdlFUFUFU>81F]glC(>
FfdlFgdl>FbflFU>Fihl7#-F_gl6$/Fbgl,&FbglFU)F\dlFeglFj_lFfgl>8=-Ffhl6$-Fhfl6%-F[
gl6$FihlF`elF]oFhglF_dl>Fbdl-Fju6$FeilFiv?(FIFUFUFI4-Fc]l6$FeilFiglC(-Fjy6%FZF\
z-F^z6$%.reject~su~=~~G-Fbz6$FihlFdz>FfdlF\hl>FbflFdhl>FihlF^il>FeilFfil>FbdlF]
jl-Fjy6%F[pF\z-F^z6$%-su~~~~~~~~=~GFijl>Fhz7$-F[w6#FhzFihl-Fjy6%F[pF\z-F^z6$%-n
ew~lm~~~~=~G-Fbz6$-%;Involutive/LeadingMonomialG6%FjilFaoFepFdz>Fes-Fgs6&-F[gl6
$FihlFesFaoFepF^r>FLFix>F]yF^y@$FiqC$>Fbfl-F^]l6$f*Fa]lFIF\uFI-%'memberG6$FP&F^
^l6#;,$Fb^lFj_lFj_lFIFI6&F9F]oF)FhuF]y@$2Fbt-F\qFbhlC&>Fecl-F^]l6$f*Fa]lFIF\uFI
-Fa]m6$FPF^^lFIFI6$F.F]y&F]o6#;,$FhuFj_lFj_l>Fihl7$-F[w6#-Fht6%f*F[uFIF\uFIF_uF
IFIFIFbflFecl-F[w6#-Fht6%f*F[uFIF\uFIF_uFIFIFIFeclFbfl>FhzFf[m>FesFd\m>83F]o?(F
arFUFU-F\qFh[mFcr>Ff_m-F[gl6$&FhzFhrFf_m7$Fes-Fht6%f*F[uFIF\uFIF_uFIFIFIF]oFf_m
FIFIFIFI
M7R0
I<Involutive/writeGINV1headerf*63%%fileG%$varG%)alg_elemG%+trans_elemG%'n_entrG
%)rhs_entrG%'no_rhsG%"cG%&m_ordG%(var_ordG%)entr_posG%'vardegG%'tupdegG%(algext
sG%-algextindetsG%/transextindetsG%+tracedenomG6&%"iG%"rG%%nvarG%#mpG6#%jnCopyr
ight~(C)~2006-2010~by~Daniel~Robertz.~All~rights~reserved.G6"C9>8&-%%nopsG6#9%-
%(fprintfG6$9$Q8#!~/usr/bin/env~python|+F=-FF6$FHQY#~temporary~file~created~by~
the~Maple~package~InvolutiveF=-FF6$FHQ+~(version~F=-FF6$FH-%(convertG6$%3Involu
tive/versionG%'stringG-FF6$FHQ#)|+F=-FF6$FHQ-import~ginv|+F=@%3/9("""9*-FF6$FHQ
Dst~=~ginv.SystemType("Polynomial")|+F=C%-FF6$FHQKst~=~ginv.SystemType("Polynom
ial",~module=F=@%F\o-FF6$FH-FS6$FjnFVC%-FF6$FH-FS6$,&FjnF[o9)F[oFV-FF6$FHQ-,~ri
ghtPart=F=FeoFW@'09-7"@%Fhn@%/9/7#-%"$G6$F[oF@-FF6$FHQGim~=~ginv.MonomInterface
("Elim",~st,~[F=-FF6$FHQJim~=~ginv.MonomInterface("ElimDeg",~st,~[F=@%/<#-%#opG
6#9,<#""#@%Fip-FF6$FHQJim~=~ginv.MonomInterface("PotElim",~st,~[F=-FF6$FHQMim~=
~ginv.MonomInterface("PotElimDeg",~st,~[F=@%Fip-FF6$FHQJim~=~ginv.MonomInterfac
e("TopElim",~st,~[F=-FF6$FHQMim~=~ginv.MonomInterface("TopElimDeg",~st,~[F=5/9.
Ffp3/-FB6#F^sF[o/&F^s6#F[oFjn@+/F[rF[o@%Fhn-FF6$FHQFim~=~ginv.MonomInterface("L
ex",~st,~[F=-FF6$FHQIim~=~ginv.MonomInterface("PotLex",~st,~[F=/F[rF]r@%Fhn@%Fi
p-FF6$FHQLim~=~ginv.MonomInterface("DegRevLex",~st,~[F=-FF6$FHQOim~=~ginv.Monom
Interface("DegRevLexDeg",~st,~[F=@%Fip-FF6$FHQOim~=~ginv.MonomInterface("PotDeg
RevLex",~st,~[F=-FF6$FHQRim~=~ginv.MonomInterface("PotDegRevLexDeg",~st,~[F=/F[
r""$@%FhnFis-FF6$FHQIim~=~ginv.MonomInterface("TopLex",~st,~[F=/F[r""%@%Fhn@%Fi
pFbtFet@%Fip-FF6$FHQOim~=~ginv.MonomInterface("TopDegRevLex",~st,~[F=-FF6$FHQRi
m~=~ginv.MonomInterface("TopDegRevLexDeg",~st,~[F=C$-%'fcloseG6#FH-%&ERRORG6#%\
oup~to~now,~the~chosen~monomial~ordering~is~not~supported~by~ginv.GC%@%Fdp@%Fip
-FF6$FHQTim~=~ginv.MonomInterface("PosElimElim",~st,~tupSep=F=-FF6$FHQWim~=~gin
v.MonomInterface("PosElimElimDeg",~st,~tupSep=F=@'F_u-FF6$FHQSim~=~ginv.MonomIn
terface("PosElimLex",~st,~tupSep=F=Feu@%Fip-FF6$FHQYim~=~ginv.MonomInterface("P
osElimDegRevLex",~st,~tupSep=F=-FF6$FHQfnim~=~ginv.MonomInterface("PosElimDegRe
vLexDeg",~st,~tupSep=F=C$FavFdv-FF6$FH-FS6$FdsFV-FF6$FHQ-,~independ=[F=?(8$F[oF
[oF@%%trueGC$-FF6$FH-%$catG6%Q"'F=-FS6$&FD6#FexFVF]y@$2FexF@-FF6$FHQ#,~F=@$4%4I
nvolutive/ratcoeffG-FF6$FHQ&,~'@'F=-FF6$FHQ"]F=@&FdpC$-FF6$FHQ*,~varSep=F=-FF6$
FH-FS6$-FB6#&FepFesFV3F`s0FdsFjnC$FbzF]x@$0FjpF[qC$-FF6$FHQ+,~degrees=F=@%Fiy-F
F6$FH-FS6$FjpFV-FF6$FH-FS6$7$-Fiq6#FjpF[oFVFW@%Fiy@%09+""!@+3/,&-FB6#9&F[o-FB6#
91F[oFe\l/,&-FB6#9'F[o-FB6#93F[oFe\lC$-FF6$FHQenic~=~ginv.CoeffInterface("Modul
arShort",~st,~modularShort=F=-FF6$FH-FS6$Fd\lFV32Fe\lFi\lF`]lC+-FF6$FHQjoic~=~g
inv.CoeffInterface("AlgebraicFieldExtensionModularShort",~st,~parameter=[F=>8'F
fp?(FexF[oF[oFj\lFfxC(@$0-Fiq6$Fe\l&F\]lFay%'RootOfGC$Fav-Fev6#-F[y6$-FS6$F^_lF
V%3~is~not~algebraic.G>Fg^l7$-Fiq6#Fg^l-%8Involutive/algext2aliasG6#-Fiq6$F[oF^
_l>8%-%&minusG6$-%'indetsG6#&Fg^l6#!""<$-Fiq6#-%$mapG6%FSF\]l%%nameG-Fiq6#92>Fg
^l-%'subsopG6$/F[al-F[y6$-%=Involutive/remove_backquotesG6#-FS6$-%%subsG6$/&Fb`
lFesF^_lFi`lFVQ"~F=Fg^l-FF6$FH-F[y6%Q""F=Fe_lF\cl@$2FexFj\lFdy?(FexF[oF[o-FBFda
lFfxC$@$52F[oFex2Fe\lFj\lFdy-FF6$FH-F[y6%F\cl-FS6$&FealFayFVF\cl-FF6$FHQ/],~ext
ension=[F=?(FexF[oF[oFj\lFfxC&-FF6$FHF\cl-FF6$FH&Fg^lFayFbdl@$F^clFdy?(FexF[oF[
oF]]lFfxC&@$FcclFdyFbdl-FF6$FH-F[y6$-FS6$&F_]lFayFVFgblFbdl-FF6$FHQ1],~modularS
hort=F=F\^l3Fh\l/Fa]lF[oC'-FF6$FHQaoic~=~ginv.CoeffInterface("OneParameterModul
arShort",~st,~modularShort=F=F\^l-FF6$FHQ.,~parameter=[F=@%/Fd]lFfp-FF6$FH-F[y6
%F\cl-FS6$&Fg]lFesFVF\cl-FF6$FH-F[y6%F\cl-FS6$&Fd]lFesFVF\clF]z3Fh\l/Fa]lF]rC(-
FF6$FHQaoic~=~ginv.CoeffInterface("TwoParameterModularShort",~st,~modularShort=
F=F\^lF[fl?(FexF[oF[oFb]lFfxC$-FF6$FH-F[y6%F\cl-FS6$&Fd]lFayFVF\cl@$2FexF]rFdy?
(FexF[oF[oFe]lFfxC$-FF6$FH-F[y6%F\cl-FS6$&Fg]lFayFVF\cl@$2FexFe]lFdyF]zC$Fav-Fe
v6#%5not~implemented~yet.G@-Fg\l-FF6$FHQDic~=~ginv.CoeffInterface("GmpZ",~stF=F
`^lC*-FF6$FHQboic~=~ginv.CoeffInterface("AlgebraicFieldExtensionGmpQ",~st,~para
meter=[F=>Fg^lFfp?(FexF[oF[oFj\lFfxC(@$F[_lC$Fav-Fev6#-F[y6$Fe_l%M~is~not~algeb
raic~over~the~rational~numbers.G>Fg^lFi_l>Fb`lFc`l>Fg^lFgalFhbl@$F^clFdy?(FexF[
oF[oF`clFfxC$@$FcclFdyFfclF]dl?(FexF[oF[oFj\lFfxC&FbdlFddlFbdl@$F^clFdy?(FexF[o
F[oF]]lFfxC&@$FcclFdyFbdlF[elFbdlF]zFeelC%-FF6$FHQgnic~=~ginv.CoeffInterface("O
neParameterGmpZ",~st,~parameter=[F=@%F_flF`flFgflF]zFh\lC&-FF6$FHQenic~=~ginv.C
oeffInterface("NParameterGmpZ",~st,~parameter=[F=?(FexF[oF[oFb]lFfxC$Ffgl@$2Fex
Fa]lFdy?(FexF[oF[oFe]lFfxC$Fahl@$FihlFdyF]z3Fa^l2Fe\lFa]lC--FF6$FHQ]pic~=~ginv.
CoeffInterface("AlgebraicFieldExtensionNParameter",~st,~fieldParameter=[F=?(Fex
F[oF[oFb]lFfxC$Ffgl@$Fi[mFdy?(FexF[oF[oFe]lFfxC$Fahl@$FihlFdy-FF6$FHQ/],~parame
ter=[F=>Fg^lFfp?(FexF[oF[oFj\lFfxC(@$F[_lC$FavF[jl>Fg^lFi_l>Fb`l-Fd`l6$Ff`l<&F]
alFcal-Fiq6#-F`al6%FSFd]lFbal-FiqFf]l>Fg^lFgalFhbl@$F^clFdy?(FexF[oF[oF`clFfxC$
@$FcclFdyFfclF]dl?(FexF[oF[oFj\lFfxC&FbdlFddlFbdl@$F^clFdy?(FexF[oF[oF]]lFfxC&@
$FcclFdyFbdlF[elFbdlF]zC$FavF[il-FF6$FHQEic~=~ginv.CoeffInterface("GmpZZ",~stF=
@$94-FF6$FHQ/,~traceDenom=1F=FW-FF6$FHQQip~=~ginv.PolyInterface("PolyList",~st,
~im,~ic)|+F=-FF6$FHQ:iw~=~ginv.WrapInterface("F=@+/%3Involutive/invcritGFfp-FF6
$FHQ(WithoutF=/Fg_m7$F[oF]r-FF6$FHQ.CritPartiallyF=/Fg_m7%F[oF]rF`u-FF6$FHQ'C1C
2C3F=/Fg_m7&F[oF]rF`uFfu-FF6$FHQ)C1C2C3C4F=C$Fav-Fev6#%Wundefined~involutive~cr
iteria;~see~?InvolutiveOptions.G-FF6$FHQ(",~ip)|+F=@%%5Involutive/janetlikeG-FF
6$FHQNiD~=~ginv.DivisionInterface("JanetLike",~iw)|+F=-FF6$FHQJiD~=~ginv.Divisi
onInterface("Janet",~iw)|+F=F=F=F=F=
M7R0
I<Involutive/writeGINV2headerf*63%%fileG%$varG%)alg_elemG%+trans_elemG%'n_entrG
%)rhs_entrG%'no_rhsG%"cG%&m_ordG%(var_ordG%)entr_posG%'vardegG%'tupdegG%(algext
sG%-algextindetsG%/transextindetsG%+tracedenomG6&%"iG%"rG%%nvarG%#mpG6#%jnCopyr
ight~(C)~2006-2010~by~Daniel~Robertz.~All~rights~reserved.G6"C8>8&-%%nopsG6#9%-
%(fprintfG6$9$Q8#!~/usr/bin/env~python|+F=-FF6$FHQY#~temporary~file~created~by~
the~Maple~package~InvolutiveF=-FF6$FHQ+~(version~F=-FF6$FH-%(convertG6$%3Involu
tive/versionG%'stringG-FF6$FHQ#)|+F=-FF6$FHQ-import~ginv|+F=@%3/9("""9*-FF6$FHQ
8st~=~ginv.Polynomial()|+F=C%-FF6$FHQ=st~=~ginv.Polynomial(module=F=@%F\o-FF6$F
H-FS6$FjnFVC%-FF6$FH-FS6$,&FjnF[o9)F[oFV-FF6$FHQ-,~rightPart=F=FeoFW@'09-7"@%Fh
n-FF6$FHQ5im~=~ginv.Elim(st,~[F=@%/<#-%#opG6#9,<#""#-FF6$FHQ8im~=~ginv.PotElim(
st,~[F=-FF6$FHQ8im~=~ginv.TopElim(st,~[F=5/9.Ffp3/-FB6#F\rF[o/&F\r6#F[oFjn@+/Fa
qF[o@%Fhn-FF6$FHQ4im~=~ginv.Lex(st,~[F=-FF6$FHQ7im~=~ginv.PotLex(st,~[F=/FaqFcq
@%Fhn@%/9/7#-%"$G6$F[oF@-FF6$FHQ:im~=~ginv.DegRevLex(st,~[F=-FF6$FHQ=im~=~ginv.
DegRevLexDeg(st,~[F=@%F`s-FF6$FHQ=im~=~ginv.PotDegRevLex(st,~[F=-FF6$FHQ@im~=~g
inv.PotDegRevLexDeg(st,~[F=/Faq""$@%FhnFgr-FF6$FHQ7im~=~ginv.TopLex(st,~[F=/Faq
""%@%Fhn@%F`sFfsFis@%F`s-FF6$FHQ=im~=~ginv.TopDegRevLex(st,~[F=-FF6$FHQ@im~=~gi
nv.TopDegRevLexDeg(st,~[F=C$-%'fcloseG6#FH-%&ERRORG6#%\oup~to~now,~the~chosen~m
onomial~ordering~is~not~supported~by~ginv.GC%@%Fdp-FF6$FHQBim~=~ginv.PosElimEli
m(st,~tupSep=F=@'Fct-FF6$FHQAim~=~ginv.PosElimLex(st,~tupSep=F=Fit@%F`s-FF6$FHQ
Gim~=~ginv.PosElimDegRevLex(st,~tupSep=F=-FF6$FHQJim~=~ginv.PosElimDegRevLexDeg
(st,~tupSep=F=C$FeuFhu-FF6$FH-FS6$FbrFV-FF6$FHQ-,~independ=[F=?(8$F[oF[oF@%%tru
eGC$-FF6$FH-%$catG6%Q"'F=-FS6$&FD6#FewFVF]x@$2FewF@-FF6$FHQ#,~F=@$4%4Involutive
/ratcoeffG-FF6$FHQ&,~'@'F=-FF6$FHQ"]F=@&FdpC$-FF6$FHQ*,~varSep=F=-FF6$FH-FS6$-F
B6#&FepFcrFV3F^r0FbrFjnC$FbyF]w@$0FasFbsC$-FF6$FHQ+,~degrees=F=@%Fix-FF6$FH-FS6
$FasFV-FF6$FH-FS6$7$-F_q6#FasF[oFVFW@%Fix@%09+""!@+3/,&-FB6#9&F[o-FB6#91F[oFe[l
/,&-FB6#9'F[o-FB6#93F[oFe[lC$-FF6$FHQIic~=~ginv.ModularShort(st,~modularShort=F
=-FF6$FH-FS6$Fd[lFV32Fe[lFi[lF`\lC+-FF6$FHQhnic~=~ginv.AlgebraicFieldExtensionM
odularShort(st,~parameter=[F=>8'Ffp?(FewF[oF[oFj[lFfwC(@$0-F_q6$Fe[l&F\\lFax%'R
ootOfGC$Feu-Fiu6#-F[x6$-FS6$F^^lFV%3~is~not~algebraic.G>Fg]l7$-F_q6#Fg]l-%8Invo
lutive/algext2aliasG6#-F_q6$F[oF^^l>8%-%&minusG6$-%'indetsG6#&Fg]l6#!""<$-F_q6#
-%$mapG6%FSF\\l%%nameG-F_q6#92>Fg]l-%'subsopG6$/F[`l-F[x6$-%=Involutive/remove_
backquotesG6#-FS6$-%%subsG6$/&Fb_lFcrF^^lFi_lFVQ"~F=Fg]l-FF6$FH-F[x6%Q""F=Fe^lF
\bl@$2FewFj[lFdx?(FewF[oF[o-FBFd`lFfwC$@$52F[oFew2Fe[lFj[lFdx-FF6$FH-F[x6%F\bl-
FS6$&Fe`lFaxFVF\bl-FF6$FHQ/],~extension=[F=?(FewF[oF[oFj[lFfwC&-FF6$FHF\bl-FF6$
FH&Fg]lFaxFbcl@$F^blFdx?(FewF[oF[oF]\lFfwC&@$FcblFdxFbcl-FF6$FH-F[x6$-FS6$&F_\l
FaxFVFgalFbcl-FF6$FHQ1],~modularShort=F=F\]l3Fh[l/Fa\lF[oC'-FF6$FHQUic~=~ginv.O
neParameterModularShort(st,~modularShort=F=F\]l-FF6$FHQ.,~parameter=[F=@%/Fd\lF
fp-FF6$FH-F[x6%F\bl-FS6$&Fg\lFcrFVF\bl-FF6$FH-F[x6%F\bl-FS6$&Fd\lFcrFVF\blF]y3F
h[l/Fa\lFcqC(-FF6$FHQUic~=~ginv.TwoParameterModularShort(st,~modularShort=F=F\]
lF[el?(FewF[oF[oFb\lFfwC$-FF6$FH-F[x6%F\bl-FS6$&Fd\lFaxFVF\bl@$2FewFcqFdx?(FewF
[oF[oFe\lFfwC$-FF6$FH-F[x6%F\bl-FS6$&Fg\lFaxFVF\bl@$2FewFe\lFdxF]yC$Feu-Fiu6#%5
not~implemented~yet.G@-Fg[l-FF6$FHQ2ic~=~ginv.GmpZ(stF=F`]lC*-FF6$FHQVic~=~ginv
.AlgebraicFieldExtensionGmpQ(st,~parameter=[F=>Fg]lFfp?(FewF[oF[oFj[lFfwC(@$F[^
lC$Feu-Fiu6#-F[x6$Fe^l%M~is~not~algebraic~over~the~rational~numbers.G>Fg]lFi^l>
Fb_lFc_l>Fg]lFg`lFhal@$F^blFdx?(FewF[oF[oF`blFfwC$@$FcblFdxFfblF]cl?(FewF[oF[oF
j[lFfwC&FbclFdclFbcl@$F^blFdx?(FewF[oF[oF]\lFfwC&@$FcblFdxFbclF[dlFbclF]yFedlC%
-FF6$FHQKic~=~ginv.OneParameterGmpZ(st,~parameter=[F=@%F_elF`elFgelF]yFh[lC&-FF
6$FHQIic~=~ginv.NParameterGmpZ(st,~parameter=[F=?(FewF[oF[oFb\lFfwC$Fffl@$2FewF
a\lFdx?(FewF[oF[oFe\lFfwC$Fagl@$FiglFdxF]y3Fa]l2Fe[lFa\lC--FF6$FHQ[oic~=~ginv.A
lgebraicFieldExtensionNParameter(st,~fieldParameter=[F=?(FewF[oF[oFb\lFfwC$Fffl
@$FijlFdx?(FewF[oF[oFe\lFfwC$Fagl@$FiglFdx-FF6$FHQ/],~parameter=[F=>Fg]lFfp?(Fe
wF[oF[oFj[lFfwC(@$F[^lC$FeuF[il>Fg]lFi^l>Fb_l-Fd_l6$Ff_l<&F]`lFc`l-F_q6#-F``l6%
FSFd\lFb`l-F_qFf\l>Fg]lFg`lFhal@$F^blFdx?(FewF[oF[oF`blFfwC$@$FcblFdxFfblF]cl?(
FewF[oF[oFj[lFfwC&FbclFdclFbcl@$F^blFdx?(FewF[oF[oF]\lFfwC&@$FcblFdxFbclF[dlFbc
lF]yC$FeuF[hl-FF6$FHQ3ic~=~ginv.GmpZZ(stF=FW-FF6$FHQ@ip~=~ginv.PolyList(st,~im,
~ic)|+F=-FF6$FHQ+iw~=~ginv.F=@+/%3Involutive/invcritGFfp-FF6$FHQ)Without(F=/Fb^
m7$F[oFcq-FF6$FHQ/CritPartially(F=/Fb^m7%F[oFcqFdt-FF6$FHQ(C1C2C3(F=/Fb^m7&F[oF
cqFdtFjt-FF6$FHQ*C1C2C3C4(F=C$Feu-Fiu6#%Wundefined~involutive~criteria;~see~?In
volutiveOptions.G-FF6$FHQ(",~ip)|+F=@%%5Involutive/janetlikeG-FF6$FHQ9iD~=~ginv
.JanetLike(iw)|+F=-FF6$FHQ5iD~=~ginv.Janet(iw)|+F=F=F=F=F=
M7R0
I<Involutive/ginvBasisHomogenf*6F%"FG%$varG%)alg_elemG%(tr_elemG%'n_entrG%)rhs_
entrG%'no_rhsG%"cG%&m_ordG%(var_ordG%)entr_posG%'vardegG%'tupdegG%(algextsG%-al
gextindetsG%/transextindetsG%%fextG%1extendbasis_fextG%%algoG%+time_boundG%#trG
%*quietmodeG%#GBG%%contG%*donotreadG%*nowarningG%+tracedenomG%+movedboundG%-qle
ngthboundG%,degreeboundG%,whichoutputG%)tup_permG%(do_normG%(rootofsG%)radicals
G%#hfG6,%%fileG%&fnameG%-extend_fnameG%"iG%"rG%"tG%%nvarG%+trans_elemG%'std_wsG
%"SG6#%enCopyright~(C)~2010~by~Daniel~Robertz.~All~rights~reserved.G6"Cao@$4%4I
nvolutive/ratcoeffG-%&ERRORG6#%[qinvolutive~basis~computation~via~homogenizatio
n~not~implemented~yet~for~integers~as~ground~ring.G@%9*@$2"'++59(-Ffn6#%Alength
~of~tuples~exceeds~100000.G@$2F]o,&F^o"""-%%nopsG6#&&9$6#Feo6#""#FeoF_o>8*-Fgo6
#9%>8+-%'removeG6$f*6#FMFV6$%)operatorG%&arrowGFV-%'memberG6$F[pT$FVFV6$F3929'@
$0907#-%"$G6$""!F^o-Ffn6#%Yup~to~now,~no~degrees~can~be~assigned~to~tuples~in~g
inv.G@$2F^p-Fgo6#9--Ffn6#%bpup~to~now,~only~two~blocks~of~variables~for~elimina
tion~ordering~are~supported~by~ginv.G@$2F^p-Fgo6#9.-Ffn6#%_pup~to~now,~only~two
~blocks~of~tuples~for~elimination~ordering~are~supported~by~ginv.G@$32F^p,&-Fgo
6#FepFeo-Fgo6#93Feo0%2Involutive/characGF\r-Ffn6#%_qup~to~now,~transcendental~e
xtensions~of~degree~greater~than~2~are~only~supported~over~the~rationals.G@$32F
\rFcsFY-Ffn6#%doup~to~now,~transcendental~extensions~are~not~supported~over~the
~integers.G@'2F\r-%+searchtextG6$Q&linuxFV-%+kerneloptsG6#%(versionGC$@%/-F[u6#
%)wordsizeG"#k@$2"+[O[Z@9+-Ffn6#%?characteristic~must~be~<~2^31.G@$2"&oF$Fhu-Ff
n6#%?characteristic~must~be~<~2^15.G@%/-%*substringG6$-%(convertG6$-%*interface
G6#.F]u%'stringG;Feo"#GQ=Standard~Worksheet~InterfaceFVC$>8%-%CInvolutive/stdin
terface_gettmpnameGFV>8,%%trueGC&@$4-%;Involutive/ssystem_booleanG6#%3test~-d~/
tmp/$USERGC$>8(-%(ssystemG6#%1mkdir~/tmp/$USERG@$0&FcxF]pQ!FV-Ffn6#%Ecannot~wri
te~temporary~file~to~/tmp.G>Fdw-Fex6#%Gecho~/tmp/$USER/Involutive-$PPID-$USERG@
%2F\r-Fgt6$Q"$FV&FdwF]p>FdwQ0/tmp/InvolutiveFV>Fdw-%=Involutive/remove_whitespa
ceG6#Fhy>Fhw%&falseG2F\r-Fgt6$Q&APPLEFVFjtC%@$F]vF_v>FdwFew>FhwFiwC%@$F]vF_v>Fd
wQ1\TEMP\InvolutiveFV>FhwF`z@$095F[y>8&-%$catG6%FdwF`[lQ(.binaryFV>Fdw-Fd[l6$Fd
w94>8$-%&fopenG6$Fdw%&WRITEG-%<Involutive/writeGINV1headerG63F\\lFcp9&FepF^o9)F
jnFhu""%7"Fg\l9/Fgq91FcqFhs9>-%(fprintfG6$F\\lQ*eqs~=~[\|+FV?(8'FeoFeo-Fgo6#F[p
FiwC&@%Fjn@%/F^oFeo>8--Fd[l6$-Fhv6$-%#opG6#&F[p6$F`]lFeoF^wQ"~FV>Fh]l-Fhv6$F`^l
F^w>Fh]l-Fhv6$-%$mapG6$F^^l&F[p6#F`]lF^w?(FVFeoFeoFV2F]o-%'lengthG6#Fh]lC&>Fcx-
Fgt6$Q"|+FVFh]l?(FVFeoFeoFV2F\rFcxC&@%32FeoFcx/&Fh]l6#,&FcxFeo!""FeoQ"\FV-F\]l6
%F\\lQ#%aFV-Fev6$Fh]l;Feo,&FcxFeo!"#Feo-F\]l6%F\\lFf`l-Fev6$Fh]l;FeoFa`l-F\]l6$
F\\lQ#\|+FV>Fh]l-Fev6$Fh]l;,&FcxFeoFeoFeoFb`l>FcxFe_l-F\]l6%F\\lFf`lFh]l>Fh]lF[
y@$2F\rF`_lFjal@$2F`]lFa]l-F\]l6$F\\lQ$,\|+FV-F\]l6$F\\lQ#]|+FV-F\]l6$F\\lQNeqs
~=~map(lambda~eq:~ginv.Poly(ip,~eq),~eqs)|+FV-F\]l6$F\\lQ/for~p~in~eqs:|+FV-F\]
l6$F\\l-Fd[l6%Q2~~~~p.homogenize(FV-Fhv6$,&F`pFeoFb`lFeoF^wQ#)|+FV@$F_[lC(-F\]l
6$F\\lQ<oldbasis~=~ginv.basisLoad("FV-F\]l6$F\\lFb[l-F\]l6$F\\lQ.",~"TQ",~iD)|+
FV-F\]l6$F\\lQ=for~i~in~oldbasis.iterIB():|+FV-F\]l6$F\\lQ1~~eqs.append(i)|+FV-
F\]l6$F\\lQ.del~oldbasis|+FV>Fh]lQJbasis1~=~ginv.basisBuild("TQDegree",~iD,~FV@
%52F\r9?2F\r9@C1-F\]l6$F\\lQWeqs2~=~[]|+for~i~in~eqs:|+~~~~eqs2.append(i)|+rund
en~=~0|+FV-F\]l6$F\\lQ-while~True:|+FV-F\]l6$F\\lQX~~~~runden~=~runden+1|+~~~~p
rint~"NEUE~RUNDE:~",~runden|+FV-F\]l6$F\\lQbo~~~~print~"Eingabe:~",~len(eqs),~"
~letzte~Basis:~",~len(eqs2)-len(eqs)|+FV@%F]el@%F_elC&-F\]l6$F\\l-Fd[l6%Q%~~~~F
VFh]lQ2eqs2,~MovedBound=FV-F\]l6$F\\l-Fhv6$F^elF^w-F\]l6$F\\lQ0,~QlengthBound=F
V-F\]l6$F\\l-Fhv6$F`elF^wC$FaflFgflC$-F\]l6$F\\l-Fd[l6%FeflFh]lQ4eqs2,~QlengthB
ound=FVF^gl@$2F\r97C$-F\]l6$F\\lQ(,~time=FV-F\]l6$F\\l-Fhv6$F[hlF^w@$2F\r9AC$-F
\]l6$F\\lQ/,~DegreeBound=FV-F\]l6$F\\l-Fhv6$FfhlF^w@$99-F\]l6$F\\lQ*,~quiet=1FV
@$%2Involutive/absremG-F\]l6$F\\lQ@,~absolutelySmallestRemainder=1FV@$49;-F\]l6
$F\\lQ,,~content=0FV-F\]l6$F\\lQ6,~skipHilbertPoly=1)|+FV@%Fjgl-F\]l6$F\\lQio~~
~~if~not~basis.computationInterrupted()~or~basis.outOfTime():|+~~~~~~~~break|+F
V-F\]l6$F\\lQZ~~~~if~not~basis.computationInterrupted():|+~~~~~~~~break|+FV-F\]
l6$F\\lQN~~~~del~eqs2|+~~~~eqs2~=~[]|+~~~~for~i~in~eqs:|+FV-F\]l6$F\\lQU~~~~~~~
~eqs2.append(i)|+~~~~for~i~in~basis.iterIB():|+FV-F\]l6$F\\lQR~~~~~~~~eqs2.appe
nd(str(i)~+~'~')|+~~~~del~basis|+|+FVC*-F\]l6$F\\l-Fd[l6$Fh]lQ$eqsFV@$FjglC$F]h
lF`hl@$FehlC$FhhlF[il@$FeilFfil@$FjilF\jl-F\]l6$F\\lQ4,~skipHilbertPoly=1FV@$09
GFg\lC$-F\]l6$F\\lQ3,~hilbertFunction=FV-F\]l6$F\\l-Fhv6$Fc\mF^w-F\]l6$F\\lFecl
-F\]l6$F\\lQ1ginv.basisSave("FV-F\]l6$F\\l-Fd[l6$FdwQ..step1.binaryFV-F\]l6$F\\
lQ,",~basis1)|+FV-%AInvolutive/writeGINV1MapleOutputG6,F\\l-Fd[l6$FdwQ'.step1FV
Q'basis1FVF^oFjn9:F[hl9<Q)invbasisFVFj\l@'0FdrFg\l@%3Ff]lFjn@%/Fh\l7#-Fjq6$FeoF
`p-F\]l6$F\\lQHim2~=~ginv.MonomInterface("Elim",~st,~[FV-F\]l6$F\\lQKim2~=~ginv
.MonomInterface("ElimDeg",~st,~[FV@%/<#-F^^l6#9,<#F^p@%Fh^m-F\]l6$F\\lQKim2~=~g
inv.MonomInterface("PotElim",~st,~[FV-F\]l6$F\\lQNim2~=~ginv.MonomInterface("Po
tElimDeg",~st,~[FV@%Fh^m-F\]l6$F\\lQKim2~=~ginv.MonomInterface("TopElim",~st,~[
FV-F\]l6$F\\lQNim2~=~ginv.MonomInterface("TopElimDeg",~st,~[FV5/F\sFg\l3/FjrFeo
/&F\sF\pF^o@+/Fg_mFeo@%Ff^m-F\]l6$F\\lQGim2~=~ginv.MonomInterface("Lex",~st,~[F
V-F\]l6$F\\lQJim2~=~ginv.MonomInterface("PotLex",~st,~[FV/Fg_mF^p@%Ff^m@%Fh^m-F
\]l6$F\\lQMim2~=~ginv.MonomInterface("DegRevLex",~st,~[FV-F\]l6$F\\lQPim2~=~gin
v.MonomInterface("DegRevLexDeg",~st,~[FV@%Fh^m-F\]l6$F\\lQPim2~=~ginv.MonomInte
rface("PotDegRevLex",~st,~[FV-F\]l6$F\\lQSim2~=~ginv.MonomInterface("PotDegRevL
exDeg",~st,~[FV/Fg_m""$@%Ff^mF`am-F\]l6$F\\lQJim2~=~ginv.MonomInterface("TopLex
",~st,~[FV/Fg_mFf\l@%Ff^m@%Fh^mFiamF\bm@%Fh^m-F\]l6$F\\lQPim2~=~ginv.MonomInter
face("TopDegRevLex",~st,~[FV-F\]l6$F\\lQSim2~=~ginv.MonomInterface("TopDegRevLe
xDeg",~st,~[FVC$-%'fcloseG6#F\\l-Ffn6#%\oup~to~now,~the~chosen~monomial~orderin
g~is~not~supported~by~ginv.GC%@%Fd^m@%Fh^m-F\]l6$F\\lQUim2~=~ginv.MonomInterfac
e("PosElimElim",~st,~tupSep=FV-F\]l6$F\\lQXim2~=~ginv.MonomInterface("PosElimEl
imDeg",~st,~tupSep=FV@'Ffbm-F\]l6$F\\lQTim2~=~ginv.MonomInterface("PosElimLex",
~st,~tupSep=FVF\cm@%Fh^m-F\]l6$F\\lQZim2~=~ginv.MonomInterface("PosElimDegRevLe
x",~st,~tupSep=FV-F\]l6$F\\lQgnim2~=~ginv.MonomInterface("PosElimDegRevLexDeg",
~st,~tupSep=FVC$FgcmFjcm-F\]l6$F\\l-Fhv6$F\amF^w-F\]l6$F\\lQ-,~independ=[FV?(F`
]lFeoFeoF`pFiwC$-F\]l6$F\\l-Fd[l6%Q"'FV-Fhv6$&FcpF]_lF^wF_fm@$2F`]lF`p-F\]l6$F\
\lQ#,~FV@$FY-F\]l6$F\\lQ&,~'@'FV-F\]l6$F\\lQ"]FV@&Fd^mC$-F\]l6$F\\lQ*,~varSep=F
V-F\]l6$F\\l-Fhv6$-Fgo6#&FdrF\pF^w3Fj`m0F\amF^oC$FagmFbem@$0Fh\lFi^mC$-F\]l6$F\
\lQ+,~degrees=FV@%FZ-F\]l6$F\\l-Fhv6$Fh\lF^w-F\]l6$F\\l-Fhv6$7$-F^^l6#Fh\lFeoF^
wF\]m-F\]l6$F\\lQSip2~=~ginv.PolyInterface("PolyList",~st,~im2,~ic)|+FV-F\]l6$F
\\lQ;iw2~=~ginv.WrapInterface("FV@+/%3Involutive/invcritGFg\l-F\]l6$F\\lQ(Witho
utFV/Fhim7$FeoF^p-F\]l6$F\\lQ.CritPartiallyFV/Fhim7%FeoF^pFgbm-F\]l6$F\\lQ'C1C2
C3FV/Fhim7&FeoF^pFgbmFf\l-F\]l6$F\\lQ)C1C2C3C4FVC$Fgcm-Ffn6#%Wundefined~involut
ive~criteria;~see~?InvolutiveOptions.G-F\]l6$F\\lQ)",~ip2)|+FV@%%5Involutive/ja
netlikeG-F\]l6$F\\lQPiD2~=~ginv.DivisionInterface("JanetLike",~iw2)|+FV-F\]l6$F
\\lQLiD2~=~ginv.DivisionInterface("Janet",~iw2)|+FV-F\]l6$F\\lQ+eqs2~=~[]|+FV-F
\]l6$F\\lQ;for~p~in~basis1.iterIB():|+FV-F\]l6$F\\lQM~~~~eqs2.append(p.changePo
lyInterface(ip2))|+FV-F\]l6$F\\lQhnbasis2~=~ginv.basisBuild("TQ",~iD2,~eqs2,~sk
ipHilbertPoly=1)|+FVF^]m-F\]l6$F\\l-Fd[l6$FdwQ..step2.binaryFV-F\]l6$F\\lQ,",~b
asis2)|+FV-Fj]m6,F\\l-Fd[l6$FdwQ'.step2FVQ'basis2FVF^oFjnF`^mF[hlFa^mFb^mFj\l-F
\]l6$F\\lQ+eqs3~=~[]|+FV-F\]l6$F\\lQ;for~p~in~basis2.iterIB():|+FV-F\]l6$F\\l-F
d[l6%Q4~~~~p.dehomogenize(FVFbclFecl-F\]l6$F\\lQ4~~~~eqs3.append(p)|+FV>Fh]lQ;b
asis3~=~ginv.basisBuild("FV@%096F[y>Fh]l-Fd[l6$Fh]lFf^n@%333/FdrFg\l5FfamF\cmFg
`mFh^m>Fh]l-Fd[l6$Fh]lQ)TQDegreeFV>Fh]l-Fd[l6$Fh]lQ#TQFV>Fh]l-Fd[l6$Fh]lQB",~iD
2,~eqs3,~skipHilbertPoly=1)|+FV-F\]l6$F\\lFh]lF^]m-F\]l6$F\\l-Fd[l6$FdwFf[l-F\]
l6$F\\lQ,",~basis3)|+FV-Fj]m6,F\\lFdwQ'basis3FVF^oFjnF`^mF[hlFa^m9BFj\lFgcm@%F`
il@%FhwC%>Fcx-Fex6#-Fd[l6$Q)runginv~FVFdw@$/Fcx%%NULLG-Ffn6#%Acould~not~run~pro
gram~'runginv'.G>Fcx&FcxF\pC$>Fcx-Fex6#-Fd[l6%FaanFdwQ-~>~/dev/nullFV@%3/FianF\
r/FjxF[y>FcxF\r>FcxFeoC$>Fcx-%'systemGF^an@$FcanFean@$0FcxF\r-Ffn6#%Merror~duri
ng~call~of~Python~or~interruption.G@$FetC%>Fcx-Fex6#-Fd[l6'Q&if~[~FVFdwQ,.janet
~-ot~FVFdwQ:~];~then~echo~-n~true;~fiFV@$2F\r-Fa_l6#Fjx-Ffn6#%dpoutput~file~of~
ginv~is~older~than~input~file~(probably,~program~ginv~stopped~abnormally).G@$4F
a^mC$>Fcx-Fex6#-Fd[l6%Q*filesize~FVFdwQ'.janetFV@$30FcxFdanFcbnC$>F`]l-%'sscanf
G6$FjxQ#%dFV@$3349=2F\r-FgoF]_l2"'++I&F`]lF\p-%(WARNINGG6#Q\oresulting~involuti
ve~basis~is~big;~reading~it~may~take~a~while...FV@$Fa^m-%'RETURNG6#Fg\lA-Fd[l6$
FdwF[en@$333FhenFjgl-%)assignedG6#%6_IB_RESULTout_of_timeG/Fagn.%%TrueG-F`fn6#%
[ocomputation~of~involutive~basis~stopped~due~to~time~restriction.G>%*_JB_compa
G.Fign@$Fj\l>%._GINV_inv_denG%0_IB_RESULTdenomG@+5/Fh`nFg\l/-Fev6$Fh`n;Feo"#dQZ
invbasis,invbasislm,invbasisanc,multvar,factormodulebasisFVC%@$54333-F_gn6#%+_I
B_RESULTG-F_gn6#%-_IB_RESULTlmG-F_gn6#%._IB_RESULTancG-F_gn6#%2_IB_RESULTmultva
rG3FZ43-F_gn6#%1_IB_RESULTfactorG-F_gn6#%8_IB_RESULTfactormultvarG-Ffn6#%Cerror
~in~computation~or~interface.G@$FZC%>8)&-%4Involutive/proc_ordG6*Ff\lFcpFg\l7$F
^im-F^^l6#FgqFg\lFcp7#F^oFiw6#""&@%2FeoF^oC%>%+_JB_factorG-%%sortG6$-%$zipG6%f*
6$FM%"jGFVF[qFV7$F[pFcpFVFVFVF`jnFcjnf*Fa\oFVFVFV@'2&&FcpF\pF]pFioFiw2FioFg\oF`
z-T#6$&FjoF\p&Fh\oF\pFVFV6$FOFjjn>%3_JB_factor_multvarG-Fj^l6$f*FjpFVF[qFV&F[pF
]pFVFVFVFi[o>Fi[o-Fj^l6$f*FjpFVF[qFV-%'subsopG6$/,&FioFeoFeoFeoF]]o7#-Fjq6$F\rF
aqFVFV6$F)F^oFi[oC%>Fi[o-F[\o6$-F^\o6%f*Fa\oFVF[qFVFc\oFVFVFVF`jnFcjnf*Fa\oFVF[
qFV-F[]o6$FjoFh\oFVFVF_]o>Fa]o-Fj^l6$f*FjpFVF[qFVFe]oFVFVFVFi[o>Fi[o-Fj^l6$f*Fj
pFVF[qFVFjoFVFVFVFi[o>%(_JB_varGFcp-Fefn6#7&FainFginFdinFjin/-Fev6$Fh`n;Feo"#RQ
Hinvbasis,invbasislm,invbasisanc,multvarFVC$@$F[inFdjnFg_o/Fh`nFb^mC$@$4F_inFdj
n-Fefn6#7&FainFg\lFg\lFg\l/Fh`nQ2factormodulebasisFVC&@$F\jnFdjn>FjjnF[[o@%Ff[o
C%>Fi[o-F[\o6$-F^\o6%f*Fa\oFVF[qFVFc\oFVFVFVF`jnFcjnf*Fa\oFVFVFV@'Ff\oFiwFi\oF`
zFj\oFVFVF_]o>Fa]o-Fj^l6$f*FjpFVF[qFVFe]oFVFVFVFi[o>Fi[o-Fj^l6$f*FjpFVF[qFVFj]o
FVFVFb^oFi[oC%>Fi[o-F[\o6$-F^\o6%f*Fa\oFVF[qFVFc\oFVFVFVF`jnFcjnf*Fa\oFVF[qFVF[
_oFVFVF_]o>Fa]o-Fj^l6$f*FjpFVF[qFVFe]oFVFVFVFi[o>Fi[o-Fj^l6$f*FjpFVF[qFVFjoFVFV
FVFi[o>Ff_oFcp-Ffn6#%4error~in~interface.GFV6'Fi[oFa]oFf_oFignF]hnFVFV
M7R0
I1Involutive/pplexf*6$%"aG%"bG6#%"iG6#%\pCopyright~(C)~2000-2010~by~Carlos~F.~C
id~and~Daniel~Robertz.~All~rights~reserved.G6"C$?(8$"""F/-%%nopsG6#&9$6#F/%%tru
eG@&2&F36#F.&&9%F5F:-%'RETURNG6#F62F;F9-F?6#%&falseG@%2&F46#""#&F=FHFDF6F+F+F+F
+
M7R0
IAInvolutive/pnegplex_Z_entr_blockf*6$%"aG%"bG6"6#%jnCopyright~(C)~2006-2010~by
~Daniel~Robertz.~All~rights~reserved.GF'@'2&%,_entrblocksG6#&9$6#""#&F-6#&9%F1%
&falseG2F3F,%%trueG4-%3Involutive/pplex_ZG6$F0F6F'F'F'F'
M7R0
IAInvolutive/pnormal_form_Z_lm_oldf*6(%"fG%"FG%%seqvG%'lmprocG%'ppprocG%(loc_va
rG6+%"aG%"hG%"iG%"lG%#lmG%$divG%'n_entrG%*zero_listG%.rhs_zero_listG6#%jnCopyri
ght~(C)~2004-2010~by~Daniel~Robertz.~All~rights~reserved.G6"C+>%(_nnformG,&F:""
"F<F<>8%9$>8*-%%nopsG6#&F>6#F<>8+7#-%"$G6$""!FA>8,7#-FK6$FM-FC6#&F>6#""#>8)%%tr
ueG>8(-9'FD?(F7F<F<F73FY0&Ffn6$FWF<FMC%>8&F<>FY%&falseG?(F7F<F<F731F`o-FC6#9%4F
YC$@$30FEFH-%7Involutive/pinv_divideG6%&Fho6$F`o""$&Fho6$F`o""&&FfnFFC%>%'_redu
cG,&FjpF<F<F<>8'-%%iquoG6$F\o&Fho6%F`o""'F<@$0F]qFMC%>F>7$-%'normalG6#,&FEF<-%$
mapG6$f*6#F,F76$%)operatorG%&arrowGF7**T#F<&T%6$FWFWF<&T(6%T)FcqFW!""F?F<F7F76*
F/F]qF0FfnF&FhoF.F`o&Fho6%F`oF<F<F^s-Fjq6#,&FUF<-F^r6$f*FarF7FbrF7FerF7F7F_s&Fh
o6%F`oF<FWF^s>FYFZ>FfnFgn>F`o,&F`oF<F<F<@'3/FEFH0FUFOC$@$4-%7Involutive/member_
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RG6#%5not~implemented~yet.GC%>Fbs-Fds6#-FC6+QIproc(_a,_b)~local~d1,d2;~d1:=degr
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-(_a,_b,plex(F>FAQC)))~then~true;~else~false;~fi;~endF>>F]t-Fds6#-FC6-QQproc(_c
)~local~d1,d2,i,j,n,C,L;~C~:=~[coeffs(_c,F>FhtQ[q,~'L')];~n~:=~nops(C);~if~n~=~
1~then~RETURN(C[1],~L);~fi;~L~:=~[L];~j~:=~1;~d1~:=~degree(L[j],~|frF>FAQN|hr);
~for~i~from~2~to~n~do~d2~:=~degree(L[i],~|frF>FAQ@|hr);~if~d1~<~d2~or~(d1~=~d2~
and~F>F_qQ3(L[j],~L[i],~plex(F>FAQen)))~then~j~:=~i;~d1~:=~d2;~fi;~od;~RETURN(C
[j],~L[j]);~endF>@%FazFdclC%@%F\uC$>F_u%7Involutive/pdeglex_POTG>Fbu%3Involutiv
e/pdeglexGC$>F_u%9Involutive/pdeglex_Z_POTG>Fbu%5Involutive/pdeglex_ZG>Fju%9Inv
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al~i,j,n,C,L;~C~:=~[coeffs(_c,F>FhtQcq,~'L')];~n~:=~nops(C);~if~n~=~1~then~RETU
RN(C[1],~L);~fi;~L~:=~[L];~j~:=~1;~for~i~from~2~to~n~do~if~not~F>F_qF\elFAQP))~
then~j~:=~i;~fi;~od;~RETURN(C[j],~L[j]);~endF>@%F\uC$>F_u%8Involutive/pnegplex_
POTG>FbuFcuC%-Fecl6#%Tlocal~orders~not~supported~yet~in~the~integer~case.G>F_u%
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nvolutive/pnegdegrevlex_POTG>FbuFi[lC%Fail>F_u%?Involutive/pnegdegrevlex_Z_POTG
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$>F_u%?Involutive/pnegplex_entr_blockG>FbuFcuC%Fail>F_u%AInvolutive/pnegplex_Z_
entr_blockG>FbuFhu>FjuFhil>F]vF[v/FU!"%C)@$F]jl-Fecl6#%apup~to~now,~only~defaul
t~degrees~for~variables~and~tuples~are~allowed~for~local~orders.G>F_sFf\l>FbsFc
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FAF^[mF_qF\elFAF]el@%F\uC$>F_u%:Involutive/pnegdeglex_POTG>FbuFeelC%Fail>F_u%<I
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U!"'C)@$F]jlFj]m>F_sFf\l>FbsFj_m>F]tF_`m@%F\]l@%F\uC$>F_u%6Involutive/pnegdegle
xG>FbuFeelC%Fail>F_u%8Involutive/pnegdeglex_ZG>FbuFjel@%F\uC$>F_u%AInvolutive/p
negdeglex_entr_blockG>FbuFeelC%Fail>F_u%CInvolutive/pnegdeglex_Z_entr_blockG>Fb
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C)~2000-2010~by~Daniel~Robertz.~All~rights~reserved.G6"C%>8*%%trueG@%543-%)assi
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GFgs7&F_oFfo""$""%7"-Fgp6#%Ainvalid~table~entry:~"criteria".G>FPFgs@%-F16$&Fco6
#FR%*procedureG>FSF]u-Fgp6#%Hinvalid~table~entry:~"InvolutiveBasis".G@%-F16$&Fc
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YF`v-Fgp6#%Finvalid~table~entry:~"GroebnerBasis".G@%-F16$&Fco6#FenF_u>FfnFiv-Fg
p6#%Einvalid~table~entry:~"SyzygyModule".G@%-F16$&Fco6#FhnF\t>FinFbw-Fgp6#%Linv
alid~table~entry:~"ResolutionAutoTrunc".G-Fgp6#%Gexpecting~a~table~as~second~pa
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ting~either~"Maple",~"C++",~or~"GINV"~as~second~parameter.GFe\l/F3Q)InvBasisF*C
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F3;F_o""'Q'MatrixF*/F[clFFC$>F-FG@$F^o@%5/FcoFiq/FcoF[r>FGFco-Fgp6#%Texpecting~
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M7R0
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sG6#%jnCopyright~(C)~2006-2010~by~Daniel~Robertz.~All~rights~reserved.G6"CC@$0%
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tG6#9$@$4&Fgn6#""$-%&ERRORG6#%Fexpecting~L~without~right~hand~sides.G>8=&Fgn6#"
""@$&Fgn6#""&-Fbo6#%jnPolResolutionFast~cannot~compute~in~algebraic~field~exten
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nd(p)|+F/-F46$F6-F;6$FJQ0List.reverse()|+F/-F46$F6Q?print~>>~f,~"_IB_RESULT~:=~
["|+F/FL-F46$F6-F;6%FSFJQ'List:|+F/FU@%FY-F46$F6Q<~~~~~~~~print~>>~f,~p,~","|+F
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6-F;6%Q%c~=~F/FJQ-.iterLcIB()|+F/-F46$F6Q-lmList~=~[]|+F/-F46$F6-F;6%Q*for~m~in
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f,~m|+F/FgoF`]l-F46$F6Q.ancList~=~[]|+F/-F46$F6-F;6%Q*for~a~in~F/FJQ/.iterAncIB
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List.append([str(a).replace('*@',~'').replace('@',~'1'),~a.dependVar()])|+F/-F4
6$F6Q3ancList.reverse()|+F/-F46$F6QBprint~>>~f,~"_IB_RESULTanc~:=~["|+F/FL-F46$
F6Q3for~a~in~ancList:|+F/FU-F46$F6Q<~~~~~~~~print~>>~f,~a,~","|+F/F]o-F46$F6Q7~
~~~~~~~print~>>~f,~a|+F/FgoF`]l-F46$F6Q2multVarList~=~[]|+F/-F46$F6-F;6%Q*for~j
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k~in~j],~","|+F/C(-F46$F6Q5j~=~F.iterMultVar()|+F/FauFav-F46$F6QR~~~~~~~~print~
>>~f,~[1-k~for~k~in~j.next()],~","|+F/F]o-F46$F6Q2~~~~~~~~j.next()|+F/FbwFixF\y
FayFdyFgyFayF\zF_zFayFjoF/F/F/F/
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ICInvolutive/simp_pnormal_form_Z_absf*6(%"fG%"FG%%seqvG%'lmprocG%'ppprocG%(loc_
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F<>8%9$>8+7#-%"$G6$""!-%%nopsG6#&F>6#F<>8,7#-FD6$FF-FH6#&F>6#""#>8(7$FAFM>8)-9'
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iquoG6$Fin&Ffo6%F]o""'F<@&0FipFFC$>F>-%(collectG6%7$-%'normalG6#,&FJF<-%$mapG6$
f*6#F,F76$%)operatorG%&arrowGF7**T#F<&T%6$FUFUF<&T(6%T)F_qFU!""F?F<F7F76*F/FipF
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M7R0
I6Involutive/linear_varf*6$%"pG%$varG6$%"iG%"jG6#%jnCopyright~(C)~2005-2010~by~
Daniel~Robertz.~All~rights~reserved.G6"C%@%2""#9#>8%&9"6#""$>F3"""?(8$F3F9-%%no
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I7Involutive/ginvMinPolyf*69'%"gG%%listG%$varG%)alg_elemG%(tr_elemG%'n_entrG%)r
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degrees~can~be~assigned~to~tuples~in~ginv.G@$2F\o-Fen6#9--FS6#%bpup~to~now,~onl
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M7R0
I=Involutive/PolMinPolyRatFuncf*6&'%"pG%(polynomG'%"JG%%listG'%%varsGF*'%#FBGF*
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I5Involutive/polresdimf*6#'%$resG-%%listG6#%'matrixG6"6#%[oCopyright~(C)~2003-2
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I9Involutive/PolKernelGINVf*6&%"MG%"AG%"NG'%%varsG%%listG6-%"aG%"iG%"jG%"nG%"RG
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d.G6"C(>8*&-%6Involutive/proc_inputG6#9&6#""">8+&-%5Involutive/proc_varsG6$9'F<
FB>8-%&falseG>8,FM?(8%""&FC9#%%trueG@'-%%typeG6$&9"6#FQ%'stringG@%/FYQ"NF9>FLFT
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FIF4F4F4F`oF8>FP7$F;-FW6$-FW6$7%-Fgn6$FinF[oF\o-Fgn6$FinFhoF]pFap>FP7$F;-FU6#-F
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0F3F-F-F-F-
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G%"SG6#%jnCopyright~(C)~2006-2010~by~Daniel~Robertz.~All~rights~reserved.G6"CJ@
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le~10FW/F]\lQ)Maple~11FW/F]\lQ)Maple~12FW-Fjn6#%Ucan~only~'launch'~GINV~in~Mapl
e~version~13~or~newer.G>Fiv-Fiz6%FivQ(-launchFW-F]v6$%;Involutive/launchGINVcou
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g]lQ*eqs~=~[\|+FW?(8'F`oF`o-Fbo6#FfoF^wC&@%FZ@%/FhnF`o>8--Fiz6$-F]v6$-%#opG6#&F
fo6$Fj^lF`oFcvQ"~FW>Fb_l-F]v6$Fj_lFcv>Fb_l-F]v6$-%$mapG6$Fh_l&Ffo6#Fj^lFcv?(FWF
`oF`oFW2Fgn-%'lengthG6#Fb_lC&>Fhw-F\t6$Q"|+FWFb_l?(FWF`oF`oFW2FgqFhwC&@%32F`oFh
w/&Fb_l6#,&FhwF`o!""F`oQ"\FW-Ff^l6%Fg]lQ#%aFW-Fju6$Fb_l;F`o,&FhwF`o!"#F`o-Ff^l6
%Fg]lF`bl-Fju6$Fb_l;F`oF[bl-Ff^l6$Fg]lQ#\|+FW>Fb_l-Fju6$Fb_l;,&FhwF`oF`oF`oF\bl
>FhwF_al-Ff^l6%Fg]lF`blFb_l>Fb_lF`x@$2FgqFj`lFdcl@$2Fj^lF[_l-Ff^l6$Fg]lQ$,\|+FW
-Ff^l6$Fg]lQ#]|+FW@$4%4Involutive/ratcoeffG@%3F`_lFZ-Ff^l6$Fg]lQineqs~=~map(lam
bda~eq:~"("~+~eq.encode('latin1')~+~")*@~",~eqs)|+FW-Ff^l6$Fg]l-Fiz6%QReqs~=~ma
p(lambda~eq:~(ginv.Poly(ip,~eq)).prolong(FW-F]v6$F[pFcvQ)),~eqs)|+FW@$FdzC(-Ff^
l6$Fg]lQ<oldbasis~=~ginv.basisLoad("FW-Ff^l6$Fg]lFgz-Ff^l6$Fg]lQ.",~"TQ",~iD)|+
FW-Ff^l6$Fg]lQ=for~i~in~oldbasis.iterIB():|+FW-Ff^l6$Fg]lQ1~~eqs.append(i)|+FW-
Ff^l6$Fg]lQ.del~oldbasis|+FW>Fb_lQ:basis~=~ginv.basisBuild("FW@%096F`x>Fb_l-Fiz
6$Fb_lFhfl@%333/F_r7"5/Fa^lFio/Fa^l""%5/FgrFagl3/FerF`o/&FgrFgoFhn/Fb^l7#-Feq6$
F`oF[p>Fb_l-Fiz6$Fb_lQ)TQDegreeFW>Fb_l-Fiz6$Fb_lQ#TQFW>Fb_l-Fiz6$Fb_lQ(",~iD,~F
W@%52Fgq9>2Fgq9?C0-Ff^l6$Fg]lQWeqs2~=~[]|+for~i~in~eqs:|+~~~~eqs2.append(i)|+ru
nden~=~0|+FW-Ff^l6$Fg]lQ-while~True:|+FW-Ff^l6$Fg]lQX~~~~runden~=~runden+1|+~~~
~print~"NEUE~RUNDE:~",~runden|+FW-Ff^l6$Fg]lQbo~~~~print~"Eingabe:~",~len(eqs),
~"~letzte~Basis:~",~len(eqs2)-len(eqs)|+FW@%F^il@%F`ilC&-Ff^l6$Fg]l-Fiz6%Q%~~~~
FWFb_lQ2eqs2,~MovedBound=FW-Ff^l6$Fg]l-F]v6$F_ilFcv-Ff^l6$Fg]lQ0,~QlengthBound=
FW-Ff^l6$Fg]l-F]v6$FailFcvC$FbjlFhjlC$-Ff^l6$Fg]l-Fiz6%FfjlFb_lQ4eqs2,~QlengthB
ound=FWF_[m@$2Fgq97C$-Ff^l6$Fg]lQ(,~time=FW-Ff^l6$Fg]l-F]v6$F\\mFcv@$2Fgq9@C$-F
f^l6$Fg]lQ/,~DegreeBound=FW-Ff^l6$Fg]l-F]v6$Fg\mFcv@$99-Ff^l6$Fg]lQ*,~quiet=1FW
@$%2Involutive/absremG-Ff^l6$Fg]lQ@,~absolutelySmallestRemainder=1FW-Ff^l6$Fg]l
Q6,~skipHilbertPoly=1)|+FW@%F[\m-Ff^l6$Fg]lQio~~~~if~not~basis.computationInter
rupted()~or~basis.outOfTime():|+~~~~~~~~break|+FW-Ff^l6$Fg]lQZ~~~~if~not~basis.
computationInterrupted():|+~~~~~~~~break|+FW-Ff^l6$Fg]lQN~~~~del~eqs2|+~~~~eqs2
~=~[]|+~~~~for~i~in~eqs:|+FW-Ff^l6$Fg]lQU~~~~~~~~eqs2.append(i)|+~~~~for~i~in~b
asis.iterIB():|+FW-Ff^l6$Fg]lQR~~~~~~~~eqs2.append(str(i)~+~'~')|+~~~~del~basis
|+|+FWC'-Ff^l6$Fg]l-Fiz6$Fb_lQ$eqsFW@$F[\mC$F^\mFa\m@$Ff\mC$Fi\mF\]m@$Ff]mFg]mF
j]m-Ff^l6$Fg]lQ1ginv.basisSave("FW-Ff^l6$Fg]l-Fiz6$FivF[[l-Ff^l6$Fg]lQ+",~basis
)|+FW-Ff^l6$Fg]lQ+f~=~file("FW-Ff^l6$Fg]l-Fiz6$FivQ'.janetFW-Ff^l6$Fg]lQ)",~"w"
)|+FW@%9;CJ-Ff^l6$Fg]lQ6l~=~basis.lengthIB()|+FW-Ff^l6$Fg]lQ'i~=~1|+FW-Ff^l6$Fg
]lQ1for~p~in~basis:|+FW-Ff^l6$Fg]lQ/~~~~if~i~<~l:|+FW@%Fcdl-Ff^l6$Fg]lQB~~~~~~~
~S~=~"\""+str(p)+"~\",\\"|+FW-Ff^l6$Fg]lQ`o~~~~~~~~S~=~"\""+str(p).replace('*@'
,~'').replace('@',~'1')+"~\",\\"|+FW-Ff^l6$Fg]lQ7~~~~~~~~print~>>~f,~S|+FW-Ff^l
6$Fg]lQ+~~~~else:|+FW@%Fcdl-Ff^l6$Fg]lQ?~~~~~~~~S~=~"\""+str(p)+"~\""|+FW-Ff^l6
$Fg]lQ]o~~~~~~~~S~=~"\""+str(p).replace('*@',~'').replace('@',~'1')+"~\""|+FWFc
bm-Ff^l6$Fg]lQ-~~~~i~=~i+1|+FW-Ff^l6$Fg]lQ+f.close()|+FWFb`m-Ff^l6$Fg]l-Fiz6$Fi
vQ$.lmFWFj`mFcam-Ff^l6$Fg]lQ:for~p~in~basis.iterLm():|+FWFiam@%FcdlF]bmF`bmFcbm
Ffbm@%FcdlFjbmF]cmFcbmF`cm@$Fd^lC/FccmFb`m-Ff^l6$Fg]l-Fiz6$FivQ'.denomFWFj`mFca
m-Ff^l6$Fg]lQ:for~c~in~ic.iterDenom():|+FWFiam-Ff^l6$Fg]lQB~~~~~~~~S~=~"\""+str
(c)+"~\",\\"|+FWFcbmFfbm-Ff^l6$Fg]lQ?~~~~~~~~S~=~"\""+str(c)+"~\""|+FWFcbmF`cm@
$9:C0FccmFb`m-Ff^l6$Fg]l-Fiz6$FivQ$.GBFWFj`m-Ff^l6$Fg]lQ6l~=~basis.lengthGB()|+
FWFcam-Ff^l6$Fg]lQ:for~p~in~basis.iterGB():|+FWFiam@%FcdlF]bmF`bmFcbmFfbm@%Fcdl
FjbmF]cmFcbmF`cm@$3Fcdl5/9AFagl2Fgq-F\t6$Q2factormodulebasisFWFdfmC+-Ff^l6$Fg]l
QTiF~=~ginv.DivisionComplementInterface("Janet",~iw)|+FW-Ff^l6$Fg]lQAF~=~basis.
factorModuleBasis(iF)|+FW-Ff^l6$Fg]lQEprint~>>~f,~"_IB_RESULTfactor~:=~["|+FW-F
f^l6$Fg]lQ4for~m~in~F.iter():|+FW@%FZ@%F`_l-Ff^l6$Fg]lQ8~~~~print~>>~f,~m,~","|
+FW-Ff^l6$Fg]lQR~~~~print~>>~f,~"[",~m,~",",~m.dependVar(),~"],"|+FWC$-Ff^l6$Fg
]l-Fiz6%Q8~~~~if~m.dependVar()~<~FW-F]v6$FhnFcvQ#:|+FW@%F`_l-Ff^l6$Fg]lQ<~~~~~~
~~print~>>~f,~m,~","|+FW-Ff^l6$Fg]lQV~~~~~~~~print~>>~f,~"[",~m,~",",~m.dependV
ar(),~"],"|+FW-Ff^l6$Fg]lQ6print~>>~f,~"NULL]:"|+FW-Ff^l6$Fg]lQLprint~>>~f,~"_I
B_RESULTfactormultvar~:=~["|+FW@%FZC$-Ff^l6$Fg]lQ;for~j~in~F.iterMultVar():|+FW
-Ff^l6$Fg]lQG~~~~print~>>~f,~[1-k~for~k~in~j],~","|+FWC(-Ff^l6$Fg]lQ5j~=~F.iter
MultVar()|+FWFcgmF_hm-Ff^l6$Fg]lQR~~~~~~~~print~>>~f,~[1-k~for~k~in~j.next()],~
","|+FWFfbm-Ff^l6$Fg]lQ2~~~~~~~~j.next()|+FWF^im@$F[\mC'FccmFb`m-Ff^l6$Fg]l-Fiz
6$FivQ+.outoftimeFWFj`m-Ff^l6$Fg]lQDprint~>>~f,~str(basis.outOfTime())|+FWFccmF
b`m-Ff^l6$Fg]l-Fiz6$FivQ&.timeFWFj`m-Ff^l6$Fg]lQFprint~>>~f,~"_IB_RESULTuserTim
e~:=~"|+FW-Ff^l6$Fg]lQCprint~>>~f,~str(basis.userTime())|+FW-Ff^l6$Fg]lQ1print~
>>~f,~":"|+FW-Ff^l6$Fg]lQEprint~>>~f,~"_IB_RESULTsysTime~:=~"|+FW-Ff^l6$Fg]lQBp
rint~>>~f,~str(basis.sysTime())|+FWF[\n-Ff^l6$Fg]lQFprint~>>~f,~"_IB_RESULTreal
Time~:=~"|+FW-Ff^l6$Fg]lQCprint~>>~f,~str(basis.realTime())|+FWF[\nCU@$F[\mC%-F
f^l6$Fg]lQIprint~>>~f,~"_IB_RESULTout_of_time~:=~"|+FWF][nF[\n-Ff^l6$Fg]lQ?prin
t~>>~f,~"_IB_RESULT~:=~["|+FWF`amFcamFfamFiam@%Fcdl-Ff^l6$Fg]lQ<~~~~~~~~print~>
>~f,~p,~","|+FW-Ff^l6$Fg]lQ_o~~~~~~~~print~>>~f,~str(p).replace('*@',~'').repla
ce('@',~'1'),~","|+FWFfbm@%Fcdl-Ff^l6$Fg]lQ7~~~~~~~~print~>>~f,~p|+FW-Ff^l6$Fg]
lQjn~~~~~~~~print~>>~f,~str(p).replace('*@',~'').replace('@',~'1')|+FWF`cm-Ff^l
6$Fg]lQ2print~>>~f,~"]:"|+FW-Ff^l6$Fg]lQAprint~>>~f,~"_IB_RESULTlm~:=~["|+FWFca
m-Ff^l6$Fg]lQ4c~=~basis.iterLc()|+FWF[dmFiam@%Fcdl@%F`_l-Ff^l6$Fg]lQfn~~~~~~~~p
rint~>>~f,~"[[",~c.next(),~",",~p,~"],",~-1,~"],"|+FW-Ff^l6$Fg]lQao~~~~~~~~prin
t~>>~f,~"[[",~c.next(),~",",~p,~"],",~p.dependVar(),~"],"|+FW@%F`_l-Ff^l6$Fg]lQ
_q~~~~~~~~print~>>~f,~"[[",~c.next(),~",",~str(p).replace('*@',~'').replace('@'
,~'1'),~"],",~-1,~"],"|+FW-Ff^l6$Fg]lQjq~~~~~~~~print~>>~f,~"[[",~c.next(),~","
,~str(p).replace('*@',~'').replace('@',~'1'),~"],",~p.dependVar(),~"],"|+FWFfbm
@%Fcdl@%F`_l-Ff^l6$Fg]lQen~~~~~~~~print~>>~f,~"[[",~c.next(),~",",~p,~"],",~-1,
~"]"|+FW-Ff^l6$Fg]lQ`o~~~~~~~~print~>>~f,~"[[",~c.next(),~",",~p,~"],",~p.depen
dVar(),~"]"|+FW@%F`_l-Ff^l6$Fg]lQ^q~~~~~~~~print~>>~f,~"[[",~c.next(),~",",~str
(p).replace('*@',~'').replace('@',~'1'),~"],",~-1,~"]"|+FW-Ff^l6$Fg]lQiq~~~~~~~
~print~>>~f,~"[[",~c.next(),~",",~str(p).replace('*@',~'').replace('@',~'1'),~"
],",~p.dependVar(),~"]"|+FWF`cmFa^n-Ff^l6$Fg]lQBprint~>>~f,~"_IB_RESULTanc~:=~[
"|+FWFcam-Ff^l6$Fg]lQ;for~p~in~basis.iterAnc():|+FWFiam@%Fcdl@%F`_l-Ff^l6$Fg]lQ
K~~~~~~~~print~>>~f,~"[",~p,~",",~-1,~"],"|+FW-Ff^l6$Fg]lQV~~~~~~~~print~>>~f,~
"[",~p,~",",~p.dependVar(),~"],"|+FW@%F`_l-Ff^l6$Fg]lQ^p~~~~~~~~print~>>~f,~"["
,~str(p).replace('*@',~'').replace('@',~'1'),~",",~-1,~"],"|+FW-Ff^l6$Fg]lQip~~
~~~~~~print~>>~f,~"[",~str(p).replace('*@',~'').replace('@',~'1'),~",",~p.depen
dVar(),~"],"|+FWFfbm@%Fcdl@%F`_l-Ff^l6$Fg]lQJ~~~~~~~~print~>>~f,~"[",~p,~",",~-
1,~"]"|+FW-Ff^l6$Fg]lQU~~~~~~~~print~>>~f,~"[",~p,~",",~p.dependVar(),~"]"|+FW@
%F`_l-Ff^l6$Fg]lQ]p~~~~~~~~print~>>~f,~"[",~str(p).replace('*@',~'').replace('@
',~'1'),~",",~-1,~"]"|+FW-Ff^l6$Fg]lQhp~~~~~~~~print~>>~f,~"[",~str(p).replace(
'*@',~'').replace('@',~'1'),~",",~p.dependVar(),~"]"|+FWF`cmFa^n-Ff^l6$Fg]lQFpr
int~>>~f,~"_IB_RESULTmultvar~:=~["|+FWFcam-Ff^l6$Fg]lQ?for~j~in~basis.iterMultV
ar():|+FWFiam-Ff^l6$Fg]lQI~~~~~~~~print~>>~f,~[k~for~k~in~j],~","|+FWFfbm-Ff^l6
$Fg]lQD~~~~~~~~print~>>~f,~[k~for~k~in~j]|+FWF`cmFa^n@$Fd^lC,-Ff^l6$Fg]lQ6l~=~i
c.lengthDenom()|+FW-Ff^l6$Fg]lQDprint~>>~f,~"_IB_RESULTdenom~:=~["|+FWFcamFgdmF
iam-Ff^l6$Fg]lQ<~~~~~~~~print~>>~f,~c,~","|+FWFfbm-Ff^l6$Fg]lQ7~~~~~~~~print~>>
~f,~c|+FWF`cmFa^n@$FaemC,-Ff^l6$Fg]lQAprint~>>~f,~"_IB_RESULTGB~:=~["|+FWFhemFc
amF[fmFiam@%FcdlFd]nFg]nFfbm@%FcdlF[^nF^^nF`cmFa^n@$FafmC+FjfmF]gmF`gmFcgm@%FZ@
%F`_lFhgmF[hmC$F_hm@%F`_lFhhmF[imF^imFaim@%FZC$FfimFiimC(F]jmFcgmF_hmF`jmFfbmFc
jmF^imFe[nFh[nF[\nF^\nFa\nF[\nFd\nFg\nF[\nFccm@$F][lC&Fb`m-Ff^l6$Fg]l-Fiz6$FivQ
'.readyFWFj`mFccm-%'fcloseG6#Fg]l@%F][lC&>Fhw-Fjw6#-Fiz6%Q'rm~-f~FWFivF\fn@$0&F
hwFgoFgq-Fjn6#%>cannot~remove~temporary~file.G>&%:Involutive/GINVlaunchdataG6#F
_]l73FivFhnF`^lFZF]uF^pFb^lFbq9B9D9E9CFaem9<F\\mFd^lFdfm-%'RETURNG6#7$,&F_]lF`o
F\blF`o-&%'systemG6#%'launchG6$Q)runginv2FWFivC$@%Fa]m@%F]wC%>Fhw-Fjw6#-Fiz6$Q*
runginv2~FWFiv@$/Fhw%%NULLG-Fjn6#%Acould~not~run~program~'runginv'.G>FhwFjfnC$>
Fhw-Fjw6#-Fiz6%F]inFivQ-~>~/dev/nullFW@%3/FjfnFgq/F_xF`x>FhwFgq>FhwF`oC$>Fhw-F_
hnFjhn@$F_inFain@$0FhwFgq-Fjn6#%Merror~during~call~of~Python~or~interruption.G@
$FjsC%>Fhw-Fjw6#-Fiz6'Q&if~[~FWFivQ,.janet~-ot~FWFivQ:~];~then~echo~-n~true;~fi
FW@$2Fgq-F[al6#F_x-Fjn6#%dpoutput~file~of~ginv~is~older~than~input~file~(probab
ly,~program~ginv~stopped~abnormally).G@$4F^amC$>Fhw-Fjw6#-Fiz6%Q*filesize~FWFiv
Fi`m@$30FhwF`inF^jnC$>Fj^l-%'sscanfG6$F_xQ#%dFW@$334Fggn2Fgq-FboFg`l2"'++I&Fj^l
Fgo-%(WARNINGG6#Q\oresulting~involutive~basis~is~big;~reading~it~may~take~a~whi
le...FW@$F^am-Fign6#FaglAFg`m@$333Fa]oF[\m-%)assignedG6#%6_IB_RESULTout_of_time
G/Ff^o.%%TrueG-Fh]o6#%[ocomputation~of~involutive~basis~stopped~due~to~time~res
triction.G>%*_JB_compaG.F^_o@$Fd^l>%._GINV_inv_denG%0_IB_RESULTdenomG@+5Fcfm/-F
ju6$Fdfm;F`o"#dQZinvbasis,invbasislm,invbasisanc,multvar,factormodulebasisFWC%@
$54333-Fd^o6#%+_IB_RESULTG-Fd^o6#%-_IB_RESULTlmG-Fd^o6#%._IB_RESULTancG-Fd^o6#%
2_IB_RESULTmultvarG3Fcdl43-Fd^o6#%1_IB_RESULTfactorG-Fd^o6#%8_IB_RESULTfactormu
ltvarG-Fjn6#%Cerror~in~computation~or~interface.G@$FcdlC%>8)&-%4Involutive/proc
_ordG6*FeglF^pFagl7$-Fh_l6#Fb^l-Fh_l6#FbqFaglF^p7#FhnF^w6#""&@%2F`oFhnC%>%+_JB_
factorG-%%sortG6$-%$zipG6%f*6$FN%"jGFWFfpFW7$FfoF^pFWFWFWFdaoFgaof*FgcoFWFWFW@'
2&&F^pFgoFhoFdoF^w2FdoF]doFey-T#6$&FeoFgo&F^doFgoFWFW6$FPF^bo>%3_JB_factor_mult
varG-Fd`l6$f*FepFWFfpFW&FfoFhoFWFWFWF_co>F_co-Fd`l6$f*FepFWFfpFW-%'subsopG6$/,&
FdoF`oF`oF`oFcdo7#-Feq6$FgqF\qFWFW6$F+FhnF_coC%>F_co-Faco6$-Fdco6%f*FgcoFWFfpFW
FicoFWFWFWFdaoFgaof*FgcoFWFfpFW-Fado6$FeoF^doFWFWFedo>Fgdo-Fd`l6$f*FepFWFfpFWF[
eoFWFWFWF_co>F_co-Fd`l6$f*FepFWFfpFWFeoFWFWFWF_co>%(_JB_varGF^p-Fign6#7&7#-%$se
qG6$&Fe`o6#,&-FboFd`oF`oFj^lF\bl/Fj^l;Fgq,&FggoF`oF\blF`o7#-Fbgo6$&F[ao6#,&-Fbo
Fj`oF`oFj^lF\bl/Fj^l;Fgq,&FahoF`oF\blF`o7#-Fbgo6$&Fh`o6#,&-FboFg`oF`oFj^lF\bl/F
j^l;Fgq,&F[ioF`oF\blF`o7#-Fbgo6$&F^ao6#,&-FboF]aoF`oFj^lF\bl/Fj^l;Fgq,&FeioF`oF
\blF`o/-Fju6$Fdfm;F`o"#RQHinvbasis,invbasislm,invbasisanc,multvarFWC$@$F_`oFhao
F]go/FdfmQ)invbasisFWC$@$4Fc`oFhao-Fign6#7&F`goFaglFaglFagl/FdfmFhfmC&@$F`aoFha
o>F^boF_bo@%F\coC%>F_co-Faco6$-Fdco6%f*FgcoFWFfpFWFicoFWFWFWFdaoFgaof*FgcoFWFWF
W@'F\doF^wF_doFeyF`doFWFWFedo>Fgdo-Fd`l6$f*FepFWFfpFWF[eoFWFWFWF_co>F_co-Fd`l6$
f*FepFWFfpFWF`eoFWFWFheoF_coC%>F_co-Faco6$-Fdco6%f*FgcoFWFfpFWFicoFWFWFWFdaoFga
of*FgcoFWFfpFWFafoFWFWFedo>Fgdo-Fd`l6$f*FepFWFfpFWF[eoFWFWFWF_co>F_co-Fd`l6$f*F
epFWFfpFWFeoFWFWFWF_co>F\goF^p-Fjn6#%4error~in~interface.GFW6)F_coFgdoF\goF^_oF
b_oF_]lF`gnFWFW
M7R0
I6Involutive/Homogenizef*6%%"pG'%$varG%%listG%"hG6%%"dG%"iG%"vG6#%enCopyright~(
C)~2010~by~Daniel~Robertz.~All~rights~reserved.G6"@%-%%typeG6$9$F(-%$mapG6&F"F5
9%9&C%>8&<#-%#opG6#F9>8$-%'degreeG6$F5F=-F76$f*6#F,F06$%)operatorG%&arrowGF0*&)
T$,&T%"""-FE6$F5T'!""FSF5FSF0F06(F)F:F+FCF-F=-%(collectG6%F5F9%,distributedGF0F
0F0F0
M7R0
I7Involutive/pplex_Z_POTf*6$%"aG%"bG6#%"iG6#%jnCopyright~(C)~2004-2010~by~Danie
l~Robertz.~All~rights~reserved.G6"C%@&2&9$6#""#&9%F1-%'RETURNG6#%&falseG2F3F/-F
66#%%trueG?(8$"""F?-%%nopsG6#&F06#F?F<@&2&FC6#F>&&F4FDFHF:2FIFGF5@%2-%$absG6#&F
46#""$-FO6#&F0FRF8F<F+F+F+F+
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I7Involutive/pplex_blockf*6$%"aG%"bG6#%"iG6#%jnCopyright~(C)~2004-2010~by~Danie
l~Robertz.~All~rights~reserved.G6"C$?(8$"""F/-%%nopsG6#&9$6#F/%%trueG@&2&F36#F.
&&9%F5F:-%'RETURNG6#F62F;F9-F?6#%&falseGF6F+F+F+F+
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I2Involutive/pplex3f*6$%"aG%"bG6"6#%\pCopyright~(C)~2000-2010~by~Carlos~F.~Cid~
and~Daniel~Robertz.~All~rights~reserved.GF'-%1Involutive/pplexG6$&9$6#""$&9%F/F
'F'F'F'
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I?Involutive/pnegdegrevlex_Z_POTf*6$%"aG%"bG6%%"iG%$tdaG%$tdbG6#%jnCopyright~(C
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I?Involutive/pnegdegrevlex_blockf*6$%"aG%"bG6%%"iG%$tdaG%$tdbG6#%jnCopyright~(C
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I3Involutive/pdeglexf*6$%"aG%"bG6%%"iG%$tdaG%$tdbG6#%\pCopyright~(C)~2000-2010~
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