CoCalc -- OreModules.lib

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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Path: gap4r8 / pkg / RingsForHomalg-2018.01.07 / maple / OreModules.lib
Views: ⁴¹⁸³⁴⁶
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Ff[lFI0F`]l-Fa]l6#&Ff[l6#FRFirC$>82-Feu6$f*Fj[lF\\lF@F@F]\lF@F@6&F1F_uF-F[sFb[l
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M7R0
I?OreModules/ProjectiveDimensionf*6$%"RG'%$AlgG%%listG6)%"FG%"iG%"jG%"lG%"vG%%b
etaG%*is_MatrixG6#%\pCopyright~(C)~2004-2010~by~Alban~Quadrat~and~Daniel~Robert
z.~All~rights~reserved.G6"C&>8$-%:OreModules/FreeResolutionG6$9$9%>8'-%%nopsG6#
-%#opG6$""#-%%evalG6#F6?(F3"""FIF32FIF=C%>F=,&F=FI!""FI>8)-%8OreModules/RightIn
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ptsG6#%(versionG%'stringG;FI""(@%330FgnQ(Maple~VF30FgnQ(Maple~6F3-%%typeG6$FP%'
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FPF_p>Fip-%&evalmG6#7$F`q-Ffq6$7#-Ffq6$F[r-&%'linalgG6#%'coldimGFar-F_sFcr@%/F=
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M7R0
I6OreModules/PluralExtif*6%'%"RG%'matrixG'%$AlgG%%listG'%"iG%*nonnegintG6/%%fil
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%nopsG6#-%'removeG6%%$hasG&9%6#""#7$Q%diffF>Q&shiftF>-%&ERRORG6#%Rup~to~now,~on
ly~"diff"~and~"shift"~are~supported.G@$-FI6$-%&evalmG6#9$&FK6#""$-FR6#%doup~to~
now,~PluralExti~can~only~handle~systems~with~constant~coefficients.G>8%-%(ssyst
emG6#%Aecho~/tmp/OreModules-$PPID-$USERG>F]o&F]oFL>F]o-%*substringG6$F]o;""",&-
%'lengthG6#F]oFio!""Fio@$32Fio9#-%%typeG6$&9"FL%'stringG>F]o-%$catG6%F]oQ"-F>Ff
p>8$-%&fopenG6$F]o%&WRITEG>8(-FD6#FJ>8.7#-%$seqG6$-F[q6$%"xG8'/Far;FioFeq>8/7#-
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br>8)-FD6#&FK6#""'>8*7#-F\r6$-F[q6$FetFar/Far;FioF^t>8,7#-F\r6$/&FatFcs&FetFcsF
[u@%/F^tFB-%(fprintfG6$F_qQ,ring~r1=0,(F>C'-Fhu6$F_qQ,ring~r1=(0,F>>80Q!F>?(Far
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w-Fiv6$F\tFhp@$2FarFeq>F`vF^wFaw-Fhu6$F_qQ'),dp;|+F>-Fhu6&F_qQ2matrix~C[%d][%d]
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6$F_qQ"1F>-Fhu6$F_qQ";F>-Fhu6$F_qQ8|+system("PLURAL",C,D);|+F>-Fhu6$F_qQ*list~i
nv=F>>F`vFav?(FarFioFioFeqFcvC%>F`v-F[q6%F`vF\xF`w>F`v-F[q6$F`vFaz@$Fax>F`vF^wF
aw-Fhu6$F_qQ#;|+F>-Fhu6$F_qQBint~i;int~j;int~k;list~p;list~e;|+F>>F`v-Fiv6$-Fiv
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F_q&F`v6#;FM!"#-Fhu6%F_qQ>;|+resolution~L=nres(R,%d+1);|+F>9&-Fhu6%F_qQ4module~
L2=L[%d+1];|+F>F\^l-Fhu6%F_qQBmodule~L_adj=transpose(L[%d+1]);|+F>F\^l-Fhu6$F_q
Q^ofor~(i=1;~i<=size(inv);~i++)~|fr~L_adj=subst(L_adj,var(i),inv[i]);~|hr|+F>-F
hu6%F_qQBmodule~L_adj_i=transpose(L[%d]);|+F>F\^l-Fhu6$F_qQbofor~(i=1;~i<=size(
inv);~i++)~|fr~L_adj_i=subst(L_adj_i,var(i),inv[i]);~|hr|+F>-Fhu6$F_qQ6module~S
=syz(L_adj);|+F>@%Ffu-Fhu6$F_qQ,ring~r2=0,(F>C'-Fhu6$F_qQ,ring~r2=(0,F>>F`vFav?
(FarFioFioF^tFcvC$>F`vFfv@$F\w>F`vF^wFawFcw>F`vFav?(FarFioFioFeqFcvC$>F`vFjw@$F
ax>F`vF^wFaw-Fhu6$F_qQ+),(c,lp);|+F>Ffx?(F[yFioFioF\yFcv?(FarF^yFioFixFcvF_yFby
?(FarFioFioFeqFcvC%Fgy@%F]zF_zFdzFgzFjz-Fhu6$F_qQ_omatrix~Sm=matrix(fetch(r1,S)
);~matrix~Rm=matrix(fetch(r1,L_adj_i));~F>-Fhu6$F_qQdpmatrix~Pm=transpose(matri
x(fetch(r1,L_adj)));~matrix~Lm=transpose(matrix(fetch(r1,L2)));|+F>-Fhu6$F_qQOm
atrix~M[nrows(Sm)+1][1+ncols(Rm)];matrix~MS;|+F>-Fhu6$F_qQ@for~(k=1;~k<=ncols(S
m);~k++)~|fr|+F>-Fhu6$F_qQRfor~(j=1;~j<=nrows(Sm);~j++)~|fr~M[j,1]=Sm[j,k];~|hr
|+F>-Fhu6$F_qQ5M[nrows(Sm)+1,1]=1;|+F>-Fhu6$F_qQ^pfor~(i=1;~i<=ncols(Rm);~i++)~
|fr~for~(j=1;~j<=nrows(Rm);~j++)~|fr~M[j,1+i]=Rm[j,i];~|hr|hr|+F>-Fhu6$F_qQ6MS=
std(M);~p=list();|+F>-Fhu6$F_qQiofor~(i=1;~i<=ncols(MS);~i++)~|fr~for~(j=1;~j<=
nrows(Sm)~and~MS[j,i]==0;~j++)~|fr|hr|+F>-Fhu6$F_qQLif~(j>nrows(Sm))~|fr~p=inse
rt(p,MS[j,i]);~|hr|hr|+F>-Fhu6$F_qQ1e=insert(e,p);|hr|+F>-Fhu6$F_qQ]pstring~s=s
printf("_RESULT_EXTI:=[linalg[blockmatrix](%%s,%%s,[",size(e),size(e));|+F>-Fhu
6$F_qQZfor~(k=size(e);~k>=1;~k--)~|fr~for~(j=size(e);~j>k;~j--)~|fr|+F>-Fhu6$F_
qQ\os=s+"[";~for~(i=1;~i<size(e[k]);~i++)~|fr~s=s+"0,";~|hr~s=s+"0],";~|hr|+F>-
Fhu6$F_qQaos=s+"[";for~(j=size(e[k]);~j>1;~j--)~|fr~s=s+sprintf("%%s,",e[k][j])
;~|hr|+F>-Fhu6$F_qQ>s=s+sprintf("%%s]",e[k][1]);|+F>-Fhu6$F_qQDfor~(j=k-1;~j>=1
;~j--)~|fr~s=s+",[";|+F>-Fhu6$F_qQXfor~(i=1;~i<size(e[k]);~i++)~|fr~s=s+"0,";~|
hr~s=s+"0]";~|hr|+F>-Fhu6$F_qQ8if~(k>1)~|fr~s=s+",";~|hr|hr|+F>-Fhu6$F_qQ+s=s+"
])";|+F>-Fhu6%F_qQ3write(":w~%s",s);|+F>-F[q6$F]oQ%.resF>-Fhu6$F_qQ3Sm=transpos
e(Sm);|+F>-Fhu6$F_qQUs=sprintf(",matrix(%%s,%%s,[",nrows(Sm),ncols(Sm));|+F>-Fh
u6%F_qQ6write(":a~%s",s,Sm);|+F>Fjdl-Fhu6$F_qQWs=sprintf("]),matrix(%%s,%%s,[",
nrows(Pm),ncols(Pm));|+F>-Fhu6%F_qQ6write(":a~%s",s,Pm);|+F>Fjdl-Fhu6$F_qQWs=sp
rintf("]),matrix(%%s,%%s,[",nrows(Lm),ncols(Lm));|+F>-Fhu6%F_qQCwrite(":a~%s",s
,Lm,"])]:");~quit;|+F>Fjdl-%'fcloseG6#F_q>8+-%'systemG6#-F[q6$Q(Plural~F>F]o@$0
FfflFB-FR6#%Uprogram~Plural~not~found,~please~check~installation.GAFjdl@$4-%)as
signedG6#%-_RESULT_EXTIG-FR6#%Cerror~in~computation~or~interface.G>F`vFhgl>F^u-
%$mapG6$f*6#%"aGF>6$%)operatorG%&arrowGF>/-%$rhsGFZ-%$lhsGFZF>F>F>F^u>F]s-F_hl6
$f*FbhlF>FdhlF>FghlF>F>F>F]s>F`v-F_hl6$f*FbhlF>FdhlF>-Fg\l6$7$-F[]l6#T#-F[]l6#T
%FenF>F>6&F8F]sF7F^uF`v-%'RETURNG6#F`vF>F>F>F>
M7R0
I9OreModules/dual_fractionf*6(%"fG'%#vlG%%listG'%#vrGF(%,dualmulprocG'%$AlgG-%$
AndG6$%&tableG-%$NotG6#%'matrixG'%&involGF(6&%"dG%"gG%"hG%"iG6#%jnCopyright~(C)
~2006-2010~by~Daniel~Robertz.~All~rights~reserved.G6"C$>8%9$@)-%%typeG6$FB%"+GC
&>8&FB>FB""!?(F?"""FOF?-FF6$FKFHC$>FB,&FBFO-F"6(-%#opG6$FOFK9%9&9'9(9)FO>FK,&FK
FOFW!"",&FBFO-F"6(FKFZFenFfnFgnFhnFO-FF6$FB%"*GC)>8$FO?(8'FOFO-%%nopsG6#FB%%tru
eG@$3-FF6$-FX6$FfoFB%"^G2-FX6$""#F_pFM>Fdo*&FdoFOF_pFO>Fdo*$FdoF[o>FB-%%subsG6$
Fhn-%;OreModules/dual_polynomialG6&*&FBFOFdoFOFZFenFfn>Fdo-F\q6$Fhn-F_q6&FdoFZF
enFfn>FK&&&Fgn6#Q,commutationF?6#Q5non_inv_right_indetsF?6#FO@%/-Fho6#&Fjq6#Q,l
eft_indetsF?FO-&Fjq6&Q(productF?FKQ.rational_caseF?Q,terminationF?6%FBFip&Fgn6$
Q&extraF?FK-&Fjq6&FjrFKF[sQ(generalF?F]s-FF6$FBFap-%'subsopG6$/FO-F"6(-FX6$FOFB
FZFenFfnFgnFhnFB-F\q6$Fhn-F_q6&FBFZFenFfnF?F?F?F?
M7R0
I6OreModules/Involutionf*6$%"MG'%$AlgG%%listG6*%%Alg2G%"aG%"iG%"sG%"vG%#vlG%#vr
G%*dual_fracG6#%`qCopyright~(C)~2003-2010~by~Frederic~Chyzak~and~Alban~Quadrat~
and~Daniel~Robertz.~All~rights~reserved.G6"C$>8+f*6%%"fG'%&involGF('F'-%$AndG6$
%&tableG-%$NotG6#%'matrixG6&%"dG%"gG%"hGF,F4F4C$>8%9$@)-%%typeG6$FL%"+GC&>8&FL>
FL""!?(F4"""FYF4-FP6$FUFRC$>FL,&FLFY-T#6%-%#opG6$FYFU9%9&FY>FU,&FUFYF\o!"",&FLF
Y-Fjn6%FUF_oF`oFY-FP6$FL%"*GC)>8$FY?(8'FYFY-%%nopsG6#FL%%trueG@$3-FP6$-F]o6$F^p
FL%"^G2-F]o6$""#FgpFW>F\p*&F\pFYFgpFY>F\p*$F\pFco>FL-%%subsG6$F_o-&%,Ore_algebr
aG6#%0dual_polynomialG6%*&FLFYF\pFYF`oQ&fullyF4>F\p-Fdq6$F_o-Fgq6%F\pF`oF]r>FU&
&&F`o6#Q,commutationF46#Q5non_inv_right_indetsF46#FY@%/-F`p6#&Ffr6#Q-right_inde
tsF4FY-&Ffr6&Q(productF4FUQ.rational_caseF4Q,terminationF46%FLFaq&F`o6$Q&extraF
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FL-Fdq6$F_o-Fgq6%FLF`oF]rF4F46$F1F7@)/FM%%ZEROGFbu/FM7"Fdu-FP6$FM.%)functionG-F
dq6$7$/%$INJG%%SURJG/F^vF]vFMC$>8(-%*substringG6$-%(convertG6$-%+kerneloptsG6#%
(versionG%'stringG;FY""(@)-%$hasG6$&F_o6#F]qQ1shift+dual_shiftF4C'>F\p&F_oF[s>8
*7#-F]o6#&&FiwFgrFir?(FUFYFY,&-F`p6#F[xFYFcoFYFbp>&F\p6$F\t&F[x6#FU-F]o6#-Fdt6$
/""&Fgs7#Ffx>8)-%$mapG6$f*6#F+F46$%)operatorG%&arrowGF4/FM,$FMFcoF4F4F4&F_o6#""
$@%330FbvQ(Maple~VF40FbvQ(Maple~6F4-FP6$FM%'MatrixG-&%.LinearAlgebraG6#%*Transp
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#FM&T$F^z&F]\l6#""%&F]\l6#"#9T%T'F4F46(F'F_oF*F\pF/FbyFM-&%'linalgG6#%*transpos
eG6#-Fdy6$f*FgyF4FhyF4Fc[lF4F4Ff\lFM5-Fbw6$<#-F]o6#FdwQ&shiftF4-Fbw6$Fc]lQ+dual
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F4-Fd[l6#-Fe\l6%Fi[lFjnFd\lF4F46(F/FbyF*F\pF1F7FM-Fh\l6#-Fdy6$f*FgyF4FhyF4Ff^lF
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fxFjx>F[x-Fdy6$f*FgyF4FhyF4F[zF4F4F4&F_oF_\l@%Faz-F[[l6#-Fdy6$f*FgyF4FhyF4Fh^lF
4F46(F0F[xF*F\pF1F7FM-Fh\l6#-Fdy6$f*FgyF4FhyF4Fh^lF4F4Fg`lFMC$-%(WARNINGG6#%_on
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[\l-Fh\l6#-%&evalmGF[\lF4F4F4F4
M7R0
I9OreModules/IntTorsionRatf*6$%"RG'%$AlgG%%listG66%"cG%"iG%"jG%"kG%"mG%"nG%"rG%
"sG%$extG%#lrG%#vlG%"CG%"LG%"SG%"TG%$solG%$sysG%,torsionfreeG%$verG%*is_MatrixG
6#%\pCopyright~(C)~2004-2010~by~Alban~Quadrat~and~Daniel~Robertz.~All~rights~re
served.G6"C)@$31""$9#0&9"6#FEQ-presentationF@-%&ERRORG6#%Uinvalid~optional~argu
ment;~expecting~"presentation".G>8,-%3OreModules/ExtiRatG6%-%6OreModules/Involu
tionG6$9$9%FY""">8.&FYFJ>86-%*substringG6$-%(convertG6$-%+kerneloptsG6#%(versio
nG%'stringG;FZ""(@%330FinQ(Maple~VF@0FinQ(Maple~6F@-%%typeG6$FX%'MatrixGC$>87%%
trueG>85-%&evalbG6#/-%'removeG6$f*6#F,F@6$%)operatorG%&arrowGF@/FX""!F@F@F@-%$m
apG6$%#opG-F^o6$,&&FQ6#FZFZ!""FZ%)listlistG7"C$>Fdp%&falseG>Fgp-&%'linalgG6#%'i
szeroG6#F\r@%Fgp>827%FarFar-%%copyG6#&FQ6#""#C+>F^sF`s@%FdpC&>81-%8OreModules/S
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p@$-%'memberG6%Fgw&FY6#""%.8+@$30&&FYFds6#FeblQ%diffF@0FiblQ&eulerF@-FM6#%bpup~
to~now~integration~of~torsion~elements~is~only~supported~for~differential~equat
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I8OreModules/RightInversef*6$%"RG'%$AlgG%%listG6"6#%`qCopyright~(C)~2003-2010~b
y~Frederic~Chyzak~and~Alban~Quadrat~and~Daniel~Robertz.~All~rights~reserved.GF)
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M7R0
I9OreModules/Integrabilityf*6$%"RG'%$AlgG%%listG64%"aG%"iG%"jG%"pG%"qG%"vG%'lam
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I;homalg/OreModules/Multiplyf*6"F$6#%\pCopyright~(C)~2005-2010~by~Alban~Quadrat
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%5homalg/NormalizeRingG6$&F+6#!""%+OreModulesG6#F.F$F$F$F$
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I9OreModules/BoundaryTermsf*6&%"zG%"PG%"yG'%$AlgG%%listG6,%#btG%"iG%"jG%"kG%"sG
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