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C%>8'-F^^l6$FfvF`cl?(Fdcl,&F_\lFXFaelFXFXFeclFeq>Fav,&FavFX-Ficl6$,,FdclFXF_\lF
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F`gl6%Q,s~=~%d:~%a|+F$F]r-Fc`lFbr-F`gl6%Q-s~>=~%d:~%a~F$Fael-Ffz6$/8<.FP-%6Jane
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6&F:FdoF8FL>F\pf*F^pF>F_pF>FepF>F>F>>F[o&F[o6#FgnC$>F[o-%(unapplyG6%*&%#_aGFJ%#
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%%typeG6$Fep%'matrixG-Fbt6$Fep%)listlistG330FarQ)Maple~V,F>0FarQ)Maple~6.F>-Fbt
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6$F`s&Fep6$FU8)-F\p6#-F]x6$F`s&Feu6$Fhx8(/Fhx;FJFju/F_y;FJF_w/FU;FJF\w-Fcw6#-F`
u6%F\wF_w7#-FO6$7#FjwFdy3Fit-Fbt6$FeuF`uC'>FjuF[v@$0Fju-&%.LinearAlgebraG6#%-Ro
wDimensionGFfvFgv>F\wF]w>F_w-&Fgz6#%0ColumnDimensionGFfvFfy-Fbt6$Feu%'vectorGC'
>FjuF[v@$0Fju-&F]v6#%(vectdimGFfv-Fhv6#%cpnumber~of~columns~of~first~argument~d
oes~not~equal~number~of~entries~of~second~argument.G>F\wF]w>8%-F]x6$F`s-%&evalm
GFfv@%F`t-Fcw6#-Fb[l6$F\w7#-FO6$-F]x6$Fis-F`x6$-F[o6$Fdx-F\p6#&F`\l6#FhxF`yFdy-
Fcw6#-&%'VectorG6#%'columnGFi\l3Fit-Fbt6$FeuF[^lC'>FjuF[v@$Ff[lF[\l>F\wF]w>F`\l
Fa\lFg]l-Fbt6$FeuF)-Fhv6#%Rcannot~multiply~a~matrix~or~listlist~with~a~list.GC&
>F\wF]w>F_wF[v>F`\l-F\p6#-F]x6$F`sFeu@%F`t-Fcw6#-Fdt6%F\wF_w7#-FO6$7#-FO6$-F]x6
$Fis-F[o6$FdxF`\l/FhxFcyFdy-Fcw6#-F`uFg_l-Fbt6$FepFb[l@)5FbuF^zC'>FjuFbv@$0Fju-
Fh[lF]q-Fhv6#%`pnumber~of~entries~of~first~argument~does~not~equal~number~of~ro
ws~of~second~argument.G>F_wF`w>8$-F]x6$F`s-Fd\lF]q@%Fbu-Fcw6#-Fb[l6$F_w7#-FO6$-
F]x6$Fis-F`x6$-F[o6$&FdalFf]l-F\p6#-F]x6$F`s&Feu6$FhxFUF`y/FUFcy-Fcw6#-F[^lF\bl
5F`[lF^^lC%>FjuF^al@$Ff[l-Fhv6#%cpnumber~of~entries~of~first~argument~does~not~
equal~number~of~entries~of~second~argument.G-Fcw6#-F]x6$Fis-F`x6$-F[o6$-F]x6$F`
s&FepFf]l-F\p6#-F]x6$F`s&FeuFf]lF`yFf^l-Fhv6#%Fcannot~multiply~a~vector~with~a~
list.GC%>FjuF^al>F`\lF__l-Fcw6#-Fb[l6$Fju7#-FO6$-F]x6$Fis-F[o6$F`dlF`\lF`y3Fit-
Fbt6$FepF[^l@)Fi`lC'>FjuFbv@$F]alF_al>F_wF`w>FdalFealF^clFaclC%>FjuF^al@$Ff[lFe
clFhclFf^lFhdlC%>FjuF^al>F`\lF__l-Fcw6#-F[^lFael-Fbt6$FepF)@'5FcuF^z-Fhv6#%Fcan
not~multiply~a~list~with~a~matrix.GFf^l-Fhv6#%Dcannot~multiply~a~list~with~a~li
st.GC$>F`\lF__l-Fcw6#-F]x6$Fis-Fgp6$f*6#F.F>F_pF>-T'6$-F]x6$F\qFepF_qF>F>6(F4F`
sF,F`\lF9F[oFep@/FcuC&>F\wFbv>F_wF`w>Fdal-F]x6$F`sFep-Fcw6#-Fdt6%F\wF_w7#-FO6$7
#-FO6$-F]x6$Fis-F[o6$Fdal-F\p6#-F]x6$F`s&FeuFgxFb`lFdyF^zC&>F\wFez>F_wF\[l>Fdal
Fjhl-Fcw6#-F`uF_ilF`[lC%>FjuFg[l>FdalFjhl-Fcw6#-Fb[l6$Fju7#-FO6$-F]x6$Fis-F[o6$
FdalFcdlF`yF^^lC%>FjuFg[l>FdalFjhl-Fcw6#-F[^lF\[mFfuC$>FdalFjhl-Fcw6#-F]x6$Fis-
Fgp6$f*F^hlF>F_pF>-Fgp6$f*FjpF>F_pF>-T)6$F\q-F`hl6#-F]x6$F_qFepF>F>6*F+F\qF4F_q
F;F`hlF9Fg\mFepF>F>6*F+FdalF4F`sF;F\pF9F[oFeuFf^lC$>FdalFjhl-Fcw6#-F]x6$Fis-Fgp
6$f*F^hlF>F_pF>Ff\mF>F>F^]mFeu-Fcw6#-F]x6$Fis-F[o6$FjhlF__lF>F>F>F>
M7R0
I9JanetOre/JanetOreOptionsf*6#%"aG6#%)oldvalueG6#%jnCopyright~(C)~2000-2010~by~
Daniel~Robertz.~All~rights~reserved.G6"C&@$0%5JanetOre/initializedG.%%trueG-%.J
anetOre/initGF*>8$%%NULLG@%-%%typeG6$9$%'stringG@A/F:Q$getF*-%'RETURNG6#-%&tabl
eG6#7,/Q/characteristicF*%0JanetOre/characG/Q)rationalF*%2JanetOre/ratcoeffG/Q'
matrixF*%4JanetOre/matrixtypeG/Q'absremF*%0JanetOre/absremG/Q*janetlikeF*%3Jane
tOre/janetlikeG/Q)criteriaF*%1JanetOre/invcritG/Q'JBasisF*%4JanetOre/JInvoBasis
G/Q+JInvReduceF*%2JanetOre/JIReduceG/Q/JGroebnerBasisF*%5JanetOre/JGroebBasisG/
Q.JSyzygyModuleF*%4JanetOre/JSyzygyModG/F:Q$setF*@%32"""9#-F86$&9"6#""#FCC,@%3-
F86$&Fgo6#FG%(integerG5/F`p""!-%(isprimeG6#F`p>FHF`p-%&ERRORG6#%Ginvalid~table~
entry:~"characteristic".G@%-F86$&Fgo6#FJ%(booleanG>FKFaq-F[q6#%Ainvalid~table~e
ntry:~"rational".G@%5/&Fgo6#FM%'matrixG/F[r%'MatrixG>FNF[r-F[q6#%?invalid~table
~entry:~"matrix".G@%-F86$&Fgo6#FPFcq>FQFgr-F[q6#%?invalid~table~entry:~"absrem"
.G@%-F86$&Fgo6#FSFcq>FTF`s-F[q6#%Binvalid~table~entry:~"janetlike".G@%54-F86$&F
go6#FV-%%listG6#%'posintG0-%'removeG6%%$hasGF[t7&FcoFjo""$""%7"-F[q6#%Ainvalid~
table~entry:~"criteria".G>FWF[t@%-F86$&Fgo6#FY%*procedureG>FZFau-F[q6#%?invalid
~table~entry:~"JBasis".G@%-F86$&Fgo6#FfnFcu>FgnF[v-F[q6#%Cinvalid~table~entry:~
"JInvReduce".G@%-F86$&Fgo6#FinFcu>FjnFdv-F[q6#%Ginvalid~table~entry:~"JGroebner
Basis".G@%-F86$&Fgo6#F\oFcu>F]oF]w-F[q6#%Finvalid~table~entry:~"JSyzygyModule".
G-F[q6#%Gexpecting~a~table~as~second~parameter.G/F:Q&MapleF*C&>FZ%1JanetOre/JIB
asisG>Fgn%6JanetOre/JInvolReduceG>Fjn%6JanetOre/JGroebnerBasG>F]o%4JanetOre/JSy
zModuleG/F:Q$C++F*C&>FZ%:JanetOre/JBasisFastAssertG>Fgn%8JanetOre/JInvReduceFas
tG>Fjn%<JanetOre/JGroebnerBasisFastG>F]o%;JanetOre/JSyzygyModuleFastG5/F:Q,Comp
utationF*/F:Q,computationF*C$@%5/FZFex/FZ%4JanetOre/JBasisFastG>F4Fbx>F4Fgw@$Fb
o@%-F86$FgoF;@'/FgoFgwC&>FZFjw>FgnF\x>FjnF^x>F]oF`x/FgoFbxC&>FZFex>FgnFgx>FjnFi
x>F]oF[y-F[q6#%Wexpecting~either~"Maple"~or~"C++"~as~second~parameter.GFjz/F:Q)
InvBasisF*C$>F4FZ@$Fbo@%-F86$FgoFcu>FZFgo-F[q6#%Kexpecting~a~procedure~as~secon
d~parameter.G/F:Q*InvReduceF*C$>F4Fgn@$Fbo@%Fc[l>FgnFgoFf[l/F:Q-SyzygyModuleF*C
$>F4F]o@$Fbo@%Fc[l>F]oFgoFf[l5/-%*substringG6$F:;FcoFhtQ%CharF*/Fi\lQ%charF*C$>
F4FH@$Fbo@%3-F86$FgoFbp5/FgoFep-Fgp6#FgoC%>FHFgo@$0FHFep>FKF0@$0FHF4C$>%)J_T_Li
stG.Fd^l>%*_JOStatssG.Fg^l-F[q6#%Lexpecting~prime~number~as~second~parameter.G5
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^l>Fg^lFh^l-F[q6#%Mexpecting~boolean~value~as~second~parameter.G5/-Fj\l6$F:;Fco
""'Q'MatrixF*/Fd`lFMC$>F4FN@$Fbo@%5/FgoF]r/FgoF_r>FNFgo-F[q6#%Texpecting~'matri
x'~or~'Matrix'~as~second~parameter.G/F:Q'GBasisF*C$>F4Fjn@$Fbo@%Fc[l>FjnFgoFf[l
/F:Q*JanetLikeF*C$>F4FT@$Fbo@%Fd_l>FTFgoF_`l5/F:Q)CriteriaF*/F:FVC$>F4FW@$Fbo@%
54-F86$FgoF]t0-Fct6%FetFgoFftFit-F[q6#%jnexpecting~list~of~integers~between~1~a
nd~4~as~second~parameter.G>FW-%%sortGFj]l/F:Q<AbsolutelySmallestRemainderF*C%@$
FK-F[q6#%`poption~'AbsolutelySmallestRemainder'~only~applies~for~computations~o
ver~the~integers.G>F4FQ@$Fbo@%Fd_l>FQFgoF_`l-F[q6#%Finvalid~option;~see~?JanetO
reOptions.G-F[q6#%fnexpecting~a~string~as~first~argument;~see~?JanetOreOptions.
GF4F*6.Fd^lFg^lFHFKFNFTFQFZFgnFjnF]oFWF*F*
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I:JanetOre/JHilbertFunctionf*6"6,%"iG%"jG%"qG%"rG%"sG%+n_exteriorG%,given_basis
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los~F.~Cid,~Arne~Lorenz~and~Daniel~Robertz.~All~rights~reserved.GF$C)@$/9#""!-%
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quationG/-%#opG6$FBFNQ$varF$>F;-FT6$""#FN>F;FNC$>FE%%trueG?(8$FBFBF5Fhn@%3-FL6$
&FO6#FjnFQ/-FT6$FBF_oFV>F;-FT6$FZF_o>F>6$F>F_o@%FE>6$8-8,-%5JanetOre/setup_basi
sG6#F>@$4-%)assignedG6#%)J_T_ListG-%&ERRORG6#%Lmissing~involutive~basis;~run~JB
asis~first.G@%-Fdp6#%/_jvar_exteriorG@%-FL6$F^q%%listG>8)-%%nopsGF]q-Fhp6$QSwro
ng~format~of~the~global~variable~_jvar_exteriorF$F^q>FdqF6@)-FL6$F;%'stringGC(>
8&-%2JanetOre/pmax_degGFep@$2F6Fdq>Far-%$maxG6$,&FdqFBFBFBFar?(FjnF6FB,&FarFB!"
"FBFhn-%'printfG6%Q0Dim(M.%d)~=~%a|+F$Fjn-F"F`o-F_s6%Q;Dim(M.s)~=~%a,~for~s~>=~
%dF$-%<JanetOre/JHilbertPolynomialGF$Far@$FE-%9JanetOre/restoreJ_T_ListG6#F\p-F
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M7R0
I0JanetOre/JSyzOpf*6$%#_AG'%$varG%%listG6%%"AG%$resG%$opsG6#%[oCopyright~(C)~20
03-2010~by~Mohamed~Barakat.~All~rights~reserved.G6"C&>8$-%4JanetOre/jets_mkmatG
6#-%$mapG6$f*6#%"aGF/6$%)operatorG%&arrowGF/&9$6#"""F/F/F/&-%3JanetOre/procinpu
tG6#F@6#""%@%2""#9#>8&&9"6#""$>FN%%NULLG>8%-%5JanetOre/JResolutionG6'F29%FNQ$CG
TF/FB@%2FB-%%nopsG6#FV-%%copyG6#&FV6#!"#@%/%4JanetOre/matrixtypeG%'MatrixG-F\o6
#-Fdo6#7#7#-%"$G6$""!-&%'linalgG6#%'rowdimG6#&FV6#!""-F\o6#-%'matrixGFhoF/F/F/F
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M7R0
I5JanetOre/JInvolutionf*6%%"aG'%%varsG%%listG%$opsG6+%"jG%"pG%"sG%"vG%$varG%#vl
G%#vrG%,dualmulprocG%*only_diffG6#%jnCopyright~(C)~2006-2010~by~Daniel~Robertz.
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M7R0
I8JanetOre/JGroebnerBasisf*6#%"LG6&%"GG%*tmp_J_HOMG%-tmp_jinv_denG%0tmp_JBOre_c
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$0%5JanetOre/initializedG.%%trueG-%.JanetOre/initGF->8$-%5JanetOre/JGroebBasisG
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M7R0
I-JanetOre/JHPf*6"62%"aG%"bG%"dG%"iG%"kG%"nG%"mG%"pG%"sG%%termG%&n_mulG%+n_exte
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#FjnFQ/-FT6$FBF_oFV>F:-FT6$FZF_o>F=6$F=F_o@%FE>6$8382-%5JanetOre/setup_basisG6#
F=@$4-%)assignedG6#%)J_T_ListG-%&ERRORG6#%Lmissing~involutive~basis;~run~JBasis
~first.G>8*-%%nopsG6#&Ffp6%FBFBFB>8)-F^q6#&Ffp6%FB""$FB@%-Fdp6#%/_jvar_exterior
G@%-FL6$F\r%%listG>8/-F^qF[r-Fhp6$QSwrong~format~of~the~global~variable~_jvar_e
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F$
M7R0
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8&-%%nopsGF2-%&ERRORG6$QSwrong~format~of~the~global~variable~_jvar_exteriorF$F3
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pmax_degGFV@$2FBF:>Fhn-%$maxG6$,&F:"""FboFboFhn?(8$FBFboFhnFI@$/-%-JanetOre/JHP
G6#Fdo-%-JanetOre/JHFGFioC$@$FH-%9JanetOre/restoreJ_T_ListG6#FL-%'RETURNGFioF$F
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M7R0
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F-%&arrayG-F36$F-%)listlistG7#F-F&F&F&F&
M7R0
I6JanetOre/jets_zerocolf*6#%"MG6#%#ZLG6#%inCopyright~(C)~2000-2002~by~Gehrt~Har
tjen.~All~rights~reserved.G6"C$>8$7#-%"$G6$""!-&%'linalgG6#%'rowdimG6#9$-%$mapG
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M7R0
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I<JanetOre/copyright_JanetOref*6"F$6#%jnCopyright~(C)~2003-2010~by~Daniel~Rober
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I1JanetOre/pplex_Zf*6$%"aG%"bG6#%"iG6#%jnCopyright~(C)~2004-2010~by~Daniel~Robe
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I6JanetOre/pnegplex_POTf*6$%"aG%"bG6"6#%jnCopyright~(C)~2002-2010~by~Daniel~Rob
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I3JanetOre/block_ordf*6&%"aG%"bG%$sepG%+termordersG6#%"iG6#%jnCopyright~(C)~200
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