restart: with(LinearAlgebra): with(OreModules): march('open',"/Users/aquadrat/Documents/Travail/maple/Personnel/RankFactorizationProblem.mla"):

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShsaWJuYW1lR0YoNiVRUi9Vc2Vycy9hcXVhZHJhdC9Eb2N1bWVudHMvVHJhdmFpbC9tYXBsZS9QZXJzb25uZWxGKFFWL0xpYnJhcnkvRnJhbWV3b3Jrcy9NYXBsZS5mcmFtZXdvcmsvVmVyc2lvbnMvMjAyMy9saWJGKFFpby9Vc2Vycy9hcXVhZHJhdC9Eb2N1bWVudHMvVHJhdmFpbC9tYXBsZS9QZXJzb25uZWwvUmFua0ZhY3Rvcml6YXRpb25Qcm9ibGVtLm1sYUYoNyVGL0YwRjE=

with(RankFactorizationProblem);

NzZJLUFudGlEaWFnb25hbEc2IkkwQ2VudHJvSGVybWl0aWFuR0YkSS5GYWN0b3JpemF0aW9uR0YkSTVGaW5pdGVGcmVlUmVzb2x1dGlvbkdGJEktRml0dGluZ0lkZWFsR0YkSTJJc0NlbnRyb0hlcm1pdGlhbkdGJEktSXNJbnZlcnRpYmxlR0YkSSxJc05pbHBvdGVudEdGJEkrSXNTb2x1dGlvbkdGJEkqTGVlTWF0cml4R0YkSSlMZWZ0TGlmdEdGJEklTGlmdEdGJEkyTG9jYWxTeXp5Z3lNb2R1bGVHRiRJMlJhbmtGYWN0b3JpemF0aW9uR0YkSTBSZWR1Y2VkU3l6eWdpZXNHRiRJKlJpZ2h0TGlmdEdGJEkrU2F0dXJhdGlvbkdGJEkvU2ltcGxpZmljYXRpb25HRiRJKlNvbHV0aW9uc0dGJEkpU3l6eWdpZXNHRiQ=

R := DefineOreAlgebra(seq(diff=[x[i],t[i]],i=1..4),polynom=[seq(t[i],i=1..4)]): Example 1 of Inria Report 9438 M := Matrix([[1,0$2,1],[0$4],[0$4],[1,0$2,1]]);

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D1 := Matrix([[1,0$3],[0$4],[0$4],[0$3,-1]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMUdGKC1JJ1JUQUJMRUdGKDYlIjUhZTV4JT46KVskKm8kLUknTUFUUklYR0YoNiM3JjcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoRj5GPjcmRj5GPkY+Rj5GQTcmRj5GPkY+LUY4NiNRKyZ1bWludXMwOzFGKEknTWF0cml4R0YlNyMtRkY2Iy9JJCVpZEdGKEYx

D2 := Matrix([[0$4],[0,1,0$2],[0$2,-1,0],[0$4]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMkdGKC1JJ1JUQUJMRUdGKDYlIjU/UXJaPjopWyQqbyQtSSdNQVRSSVhHRig2IzcmNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjBGKEY3RjdGNzcmRjctRjg2I1EiMUYoRjdGNzcmRjdGNy1GODYjUSsmdW1pbnVzMDsxRihGN0Y2SSdNYXRyaXhHRiU3Iy1GRjYjL0kkJWlkR0YoRjE=

D3 := Matrix([[0$3,1],[0$4],[0$4],[-1,0$3]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEM0dGKC1JJ1JUQUJMRUdGKDYlIjUlKSkzeCU+OilbJCpvJC1JJ01BVFJJWEdGKDYjNyY3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMEYoRjdGNy1GODYjUSIxRig3JkY3RjdGN0Y3RkE3Ji1GODYjUSsmdW1pbnVzMDsxRihGN0Y3RjdJJ01hdHJpeEdGJTcjLUZGNiMvSSQlaWRHRihGMQ==

D4 := Matrix([[0$4],[0$2,1,0],[0,-1,0$2],[0$4]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNENEdGKC1JJ1JUQUJMRUdGKDYlIjVbUnFaPjopWyQqbyQtSSdNQVRSSVhHRig2IzcmNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjBGKEY3RjdGNzcmRjdGNy1GODYjUSIxRihGNzcmRjctRjg2I1ErJnVtaW51czA7MUYoRjdGN0Y2SSdNYXRyaXhHRiU3Iy1GRjYjL0kkJWlkR0YoRjE=

RF0 := RankFactorization(M,[D1,D2,D3,D4],0);

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

RF0bis := RankFactorization(M,[D1,D2,D3,D4],0,"reduced");

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

Sol0 := Solutions(M,[D1,D2,D3,D4],0);

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Solutions(M,[D1,D2,D3,D4],0,"reduced");

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

IsSolution(Sol0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyMvIiIiNyNJJXRydWVHRiZRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wiRjFGMg==

RF1 := RankFactorization(M,[D1,D2,D3,D4],1);

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

Sol1 := Solutions(M,[D1,D2,D3,D4],1);

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

IsSolution(Sol1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyQvIiIiNyNJJXRydWVHRiYvIiIjRjJRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wjRjFGMkY1RjI=

RF1bis := RankFactorization(M,[D1,D2,D3,D4],1,"reduced");

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

Sol1bis := Solutions(M,[D1,D2,D3,D4],1,"reduced");

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

IsSolution(Sol1bis);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyQvIiIiNyNJJXRydWVHRiYvIiIjRjJRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wjRjFGMkY1RjI=

RF2 := RankFactorization(M,[D1,D2,D3,D4],2);

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

Sol2 := Solutions(M,[D1,D2,D3,D4],2);

-_I,TypesettingG6$%*protectedGI(_syslibG6"I,mprintslashGF(6$7#>I%Sol2GF(7'7%,&*&&I"xGF(6#"""F5&F36#""$F5F5*&F6F5&F36#""%F5F5,&*$&F36#""#FAF5*$F6FA!"",&*&F2F5F?F5F5*&F?F5F:F5F57%,&F2F5F:FCF9FFX,%!GF(F([gl!"%!!!#1"%"%-I%msubG6$F&/I+modulenameGF(F$6$-I#miGFM6#Q"xF(-I#mnGFM6#Q"1F(-FV6#Q"0F(FY-I%mrowGFM6$-I#moGFM6#Q*&uminus0;F(-FL6$FQ-FV6#Q"4F(FY-FL6$FQ-FV6#Q"2F(-Fgn6$Fin-FL6$FQ-FV6#Q"3F(FYF]oFYFY-Fgn6$FinFKFYFio-Fgn6$FinFboFYKI&TABLEGF&6#7%/F5X,FJF(F([gl!"%!!!#1"%"%-Fgn6'-Fgn6%Fbo-Fjn6#Q1&InvisibleTimes;F(-FL6$-FR6#Q"yF(-Fgn6%Fdo-Fjn6#Q(&comma;F(FU-Fjn6#Q'&plus;F(-Fgn6%FioF\q-FL6$Faq-Fgn6%FUFfqFUFiq-FR6#Q#_yF(-Fgn6(Fin-Fgn6%FioF\q-FL6$Faq-Fgn6%F[pFfqFUFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%F_oFfqFUFiq-Fgn6%-I(mfencedGFM6#-Fgn6%FKFiqF]oF\q-FL6$Faq-Fgn6%-FV6#Q"5F(FfqFU-Fgn6,FinFjp-Fjn6#Q(&minus;F(F\rFctFbrFiq-Fgn6%FioF\q-Ffs6#-Fgn6--Fgn6%FdoF\qF^rFct-Fgn6%FioF\q-FL6$Faq-Fgn6%-FV6#Q"6F(FfqFUFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%-FV6#Q"7F(FfqFUFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%-FV6#Q"8F(FfqFUFiq-Fgn6%-Ffs6#-Fgn6%-Fgn6'FdoF\qFbrF\qF]oFiqFUF\q-FL6$Faq-Fgn6%-FV6#Q"9F(FfqFUFiq-Fgn6%-Ffs6#-Fgn6&FinF_wFctFUF\q-FL6$Faq-Fgn6%-FV6#Q#10F(FfqFUFiq-Fgn6%FboF\q-Ffs6#-Fgn6--Fgn6%FdoF\qF_qFiq-Fgn6%FboF\qF`uFct-Fgn6%FioF\qFiuFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%-FV6#Q#11F(FfqFUFiq-Fgn6%F[wF\q-FL6$Faq-Fgn6%-FV6#Q#12F(FfqFUFiq-Fgn6%FjwF\q-FL6$Faq-Fgn6%-FV6#Q#13F(FfqFU-Fgn6'-Fgn6%FboF\qFirFct-Fgn6%FioF\qF_sFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%-FV6#Q#14F(FfqFU-Fgn6%-Fgn6%FboF\q-FL6$Faq-Fgn6%FdoFfqFdoFiq-Fgn6%FioF\q-FL6$Faq-Fgn6%FUFfqFdo-Fgn6(Fin-Fgn6%FioF\q-FL6$Faq-Fgn6%F[pFfqFdoFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%F_oFfqFdoFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%F^tFfqFdo-Fgn6*FinF]\lFctFc\lFiq-Fgn6%FioF\q-Ffs6#-Fgn6--Fgn6%FdoF\qFe\lFct-Fgn6%FioF\q-FL6$Faq-Fgn6%FduFfqFdoFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%F]vFfqFdoFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%FfvFfqFdoFiq-Fgn6%F[wF\q-FL6$Faq-Fgn6%FewFfqFdoFiq-Fgn6%FjwF\q-FL6$Faq-Fgn6%FbxFfqFdoFiq-Fgn6%FboF\q-Ffs6#-Fgn6--Fgn6%FdoF\qF_\lFiq-Fgn6%FboF\qFi^lFct-Fgn6%FioF\qF__lFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%FgyFfqFdoFiq-Fgn6%F[wF\q-FL6$Faq-Fgn6%F`zFfqFdoFiq-Fgn6%FjwF\q-FL6$Faq-Fgn6%FizFfqFdo-Fgn6'-Fgn6%FboF\qF]]lFct-Fgn6%FioF\qFc]lFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%Fh[lFfqFdo-Fgn6%-Fgn6%FboF\q-FL6$Faq-Fgn6%FdoFfqF[pFiq-Fgn6%FioF\q-FL6$Faq-Fgn6%FUFfqF[p-Fgn6(Fin-Fgn6%FioF\q-FL6$Faq-Fgn6%F[pFfqF[pFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%F_oFfqF[pFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%F^tFfqF[p-Fgn6*FinFaclFctFgclFiq-Fgn6%FioF\q-Ffs6#-Fgn6--Fgn6%FdoF\qFiclFct-Fgn6%FioF\q-FL6$Faq-Fgn6%FduFfqF[pFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%F]vFfqF[pFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%FfvFfqF[pFiq-Fgn6%F[wF\q-FL6$Faq-Fgn6%FewFfqF[pFiq-Fgn6%FjwF\q-FL6$Faq-Fgn6%FbxFfqF[pFiq-Fgn6%FboF\q-Ffs6#-Fgn6--Fgn6%FdoF\qFcclFiq-Fgn6%FboF\qF]flFct-Fgn6%FioF\qFcflFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%FgyFfqF[pFiq-Fgn6%F[wF\q-FL6$Faq-Fgn6%F`zFfqF[pFiq-Fgn6%FjwF\q-FL6$Faq-Fgn6%FizFfqF[p-Fgn6'-Fgn6%FboF\qFadlFct-Fgn6%FioF\qFgdlFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%Fh[lFfqF[p-Fgn6'-Fgn6%FboF\q-FL6$Faq-Fgn6%FdoFfqF_oFiq-Fgn6%FioF\q-FL6$Faq-Fgn6%FUFfqF_oFiqFbr-Fgn6(Fin-Fgn6%FioF\q-FL6$Faq-Fgn6%F[pFfqF_oFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%F_oFfqF_oFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%F^tFfqF_o-Fgn6,FinFejlFctF[[mFctFbrFiq-Fgn6%FioF\q-Ffs6#-Fgn6--Fgn6%FdoF\qF][mFct-Fgn6%FioF\q-FL6$Faq-Fgn6%FduFfqF_oFiq-Fgn6%FboF\q-FL6$Faq-Fgn6%F]vFfqF_oFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%FfvFfqF_oFiq-Fgn6%F[wF\q-FL6$Faq-Fgn6%FewFfqF_oFiq-Fgn6%FjwF\q-FL6$Faq-Fgn6%FbxFfqF_oFiq-Fgn6%FboF\q-Ffs6#-Fgn6--Fgn6%FdoF\qFgjlFiq-Fgn6%FboF\qFa]mFct-Fgn6%FioF\qFg]mFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%FgyFfqF_oFiq-Fgn6%F[wF\q-FL6$Faq-Fgn6%F`zFfqF_oFiq-Fgn6%FjwF\q-FL6$Faq-Fgn6%FizFfqF_o-Fgn6'-Fgn6%FboF\qFe[mFct-Fgn6%FioF\qF[\mFiq-Fgn6%FesF\q-FL6$Faq-Fgn6%Fh[lFfqF_o/FAX,FJF(F([gl!"%!!!#1"%"%-Fgn6'FjpFiqF\rFiqFir-Fgn6(FinF`[lFiq-Fgn6%FboF\qFjsFiq-Fgn6%FesF\qF`u-Fgn6,FinFjpFctF\rFctFirFiq-Fgn6%FioF\q-Ffs6#-Fgn6+-Fgn6)FdoF\qFbrF\qF]oF\qFirFiq-Fgn6%FboF\qFbvFctF_yFiqFbrFiqF\uFiq-Fgn6%FboF\q-Ffs6#-Fgn6'FguFct-Fgn6%FioF\qFbvFiqF[y-Fgn6'F]sFct-Fgn6%FioF\qFjsFiq-Fgn6%FesF\qFaw-Fgn6'F]\lFiqFc\lFiqF]]l-Fgn6(FinFgblFiq-Fgn6%FboF\qFi]lFiq-Fgn6%FesF\qFi^l-Fgn6,FinF]\lFctFc\lFctF]]lFiq-Fgn6%FioF\q-Ffs6#-Fgn6)-Fgn6)FdoF\qFbrF\qF]oF\qF]]lFiq-Fgn6%FboF\qFe_lFctF_alFiqFe^lFiq-Fgn6%FboF\q-Ffs6#-Fgn6'F]_lFct-Fgn6%FioF\qFe_lFiqF[al-Fgn6'Fa]lFct-Fgn6%FioF\qFi]lFiq-Fgn6%FesF\qF[`l-Fgn6'FaclFiqFgclFiqFadl-Fgn6(FinF[jlFiq-Fgn6%FboF\qF]elFiq-Fgn6%FesF\qF]fl-Fgn6,FinFaclFctFgclFctFadlFiq-Fgn6%FioF\q-Ffs6#-Fgn6)-Fgn6)FdoF\qFbrF\qF]oF\qFadlFiq-Fgn6%FboF\qFiflFctFchlFiqFielFiq-Fgn6%FboF\q-Ffs6#-Fgn6'FaflFct-Fgn6%FioF\qFiflFiqF_hl-Fgn6'FedlFct-Fgn6%FioF\qF]elFiq-Fgn6%FesF\qF_gl-Fgn6'FejlFiqF[[mFiqFe[m-Fgn6(FinF_amFiq-Fgn6%FboF\qFa\mFiq-Fgn6%FesF\qFa]m-Fgn6,FinFejlFctF[[mFctFe[mFiq-Fgn6%FioF\q-Ffs6#-Fgn6+-Fgn6)FdoF\qFbrF\qF]oF\qFe[mFiq-Fgn6%FboF\qF]^mFctFg_mFiqFbrFiqF]]mFiq-Fgn6%FboF\q-Ffs6#-Fgn6'Fe]mFct-Fgn6%FioF\qF]^mFiqFc_m-Fgn6'Fi[mFct-Fgn6%FioF\qFa\mFiq-Fgn6%FesF\qFc^m/F8X,FJF(F([gl!"%!!!#1"%"%FiamF[bm-Fgn6,FinFjpFctF\rFctFirFiq-Fgn6%FioF\q-Ffs6#-Fgn6)-Fgn6)FbrF\qFioF\qF]oF\qFawFiqF[cmFctF_yFiqF\uFiq-Fgn6%FboF\q-Ffs6#-Fgn6-FibmFiqFguFctFccmFiqFbrFiqF[yFctFaw-Fgn6'F]sFctFgcmFiq-Fgn6%FesF\qF^xF[dmF]dm-Fgn6,FinF]\lFctFc\lFctF]]lFiq-Fgn6%FioF\q-Ffs6#-Fgn6)-Fgn6)FbrF\qFioF\qF]oF\qF[`lFiqF]emFctF_alFiqFe^lFiq-Fgn6%FboF\q-Ffs6#-Fgn6+F[emFiqF]_lFctFeemFiqF[alFctF[`l-Fgn6'Fa]lFctFiemFiq-Fgn6%FesF\qFa`lF]fmF_fm-Fgn6,FinFaclFctFgclFctFadlFiq-Fgn6%FioF\q-Ffs6#-Fgn6)-Fgn6)FbrF\qFioF\qF]oF\qF_glFiqF_gmFctFchlFiqFielFiq-Fgn6%FboF\q-Ffs6#-Fgn6+F]gmFiqFaflFctFggmFiqF_hlFctF_gl-Fgn6'FedlFctF[hmFiq-Fgn6%FesF\qFeglF_hmFahm-Fgn6,FinFejlFctF[[mFctFe[mFiq-Fgn6%FioF\q-Ffs6#-Fgn6)-Fgn6)FbrF\qFioF\qF]oF\qFc^mFiqFaimFctFg_mFiqF]]mFiq-Fgn6%FboF\q-Ffs6#-Fgn6-F_imFiqFe]mFctFiimFiqFbrFiqFc_mFctFc^m-Fgn6'Fi[mFctF]jmFiq-Fgn6%FesF\qFi^mQ(pprint0F(KFcp6#7%/F570I,Ore_algebraG6#/I'_localGF&I-_n4516853712GF(7'Q%diffF(F_`nF_`nF_`nF_`n7'&I"tGF(F4&Fb`nF@&Fb`nF7&Fb`nF;I#_tGF(7'F2F?F6F:I#_yGF%F``n7Z&I"yG6#/F\`nI-_n4662394464GF(6$F5F5&F[an6$F5FA&F[an6$F5F8&F[an6$F5F<&F[an6$FAF5&F[an6$FAFA&F[an6$FAF8&F[an6$FAF<&F[an6$F8F5&F[an6$F8FA&F[an6$F8F8&F[an6$F8F<&F[an6$F<F5&F[an6$F<FA&F[an6$F<F8&F[an6$F<F<&F[an6$""&F5&F[an6$F`cnFA&F[an6$F`cnF8&F[an6$F`cnF<&F[an6$""'F5&F[an6$FicnFA&F[an6$FicnF8&F[an6$FicnF<&F[an6$""(F5&F[an6$FbdnFA&F[an6$FbdnF8&F[an6$FbdnF<&F[an6$"")F5&F[an6$F[enFA&F[an6$F[enF8&F[an6$F[enF<&F[an6$""*F5&F[an6$FdenFA&F[an6$FdenF8&F[an6$FdenF<&F[an6$"#5F5&F[an6$F]fnFA&F[an6$F]fnF8&F[an6$F]fnF<&F[an6$"#6F5&F[an6$FffnFA&F[an6$FffnF8&F[an6$FffnF<&F[an6$"#7F5&F[an6$F_gnFA&F[an6$F_gnF8&F[an6$F_gnF<&F[an6$"#8F5&F[an6$FhgnFA&F[an6$FhgnF8&F[an6$FhgnF<&F[an6$"#9F5&F[an6$FahnFA&F[an6$FahnF8&F[an6$FahnF<""!7"FihnF``nFihnFihn7'/I%diffGF&7$F2Fa`n/F\in7$F?Fc`n/F\in7$F6Fd`n/F\in7$F:Fe`n/F\in7$Fh`nFf`n7'f*6#I#_aGF(F(6$I)operatorGF(I&arrowGF(F(,&*&9$F5F2F5F5-F\in6$F_jnFa`nFCF(F(F(f*FhinF(FjinF(,&*&F_jnF5F?F5F5-F\in6$F_jnFc`nFCF(F(F(f*FhinF(FjinF(,&*&F_jnF5F6F5F5-F\in6$F_jnFd`nFCF(F(F(f*FhinF(FjinF(,&*&F_jnF5F:F5F5-F\in6$F_jnFe`nFCF(F(F(f*FhinF(FjinF(,&*&F_jnF5Fh`nF5F5-F\in6$F_jnFf`nFCF(F(F(/FA70Fi_nF^`nF``nFg`nF``n7FFj`nF`anFbanFdanFfanFhanFjanF\bnF^bnF`bnFbbnFdbnFfbnFhbnFjbnF\cnF^cnFacnFccnFecnFgcnFjcnF\dnF^dnF`dnFcdnFednFgdnFidnF\enF^enF`enFbenFeenFgenFienFhhnFihnFihnF``nFihnFihnFjhnFfin/F870Fi_nF^`nF``nFg`nF``n7JFj`nF`anFbanFdanFfanFhanFjanF\bnF^bnF`bnFbbnFdbnFfbnFhbnFjbnF\cnF^cnFacnFccnFecnFgcnFjcnF\dnF^dnF`dnFcdnFednFgdnFidnF\enF^enF`enFbenFeenFgenFienF[fnF^fnF`fnFbfnFhhnFihnFihnF``nFihnFihnFjhnFfinQ(pprint1F(7#7'F/FG-I'MatrixGF%6#/I$%idGF("5oEsS?:)[$*o$-I&tableGF&6#/Fc\o"5!ejK%>:)[$*o$-Ff\o6#/Fc\o"5[:DV>:)[$*o$

IsSolution(Sol2);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyUvIiIiNyNJJXRydWVHRiYvIiIjRjIvIiIkRjJRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wkRjFGMkY1RjJGN0Yy

RF2bis := RankFactorization(M,[D1,D2,D3,D4],2,"reduced");

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

Sol2bis := Solutions(M,[D1,D2,D3,D4],2,"reduced");

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

IsSolution(Sol2bis);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyUvIiIiNyNJJXRydWVHRiYvIiIjRjIvIiIkRjJRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wkRjFGMkY1RjJGN0Yy

RF3 := RankFactorization(M,[D1,D2,D3,D4],3);

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

RankFactorization(M,[D1,D2,D3,D4],3,"reduced");

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Sol3 := Solutions(M,[D1,D2,D3,D4],3);

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IsSolution(Sol3);

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Sol3bis := Solutions(M,[D1,D2,D3,D4],3,"reduced");

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IsSolution(Sol3bis);

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Example 2 of Inria Report 9438 M := Matrix([[1,0],[0,1]]);

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D1 := Matrix([[-1,-2],[1,2]]);

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D2 := Matrix([[-3,-4],[3,4]]);

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Sol0 := Solutions(M,[D1,D2],0);

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Sol1 := Solutions(M,[D1,D2],1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVTb2wxR0YoUS1Ob35zb2x1dGlvbnNGKDcjRi4=

Example 3 of Inria Report 9438 M := Matrix([[15,14,13],[24,20,16]]);

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D1 := Matrix([[1,-1],[1,1]]);

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D2 := Matrix([[1,2],[-1,2]]);

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D3 := Matrix([[1,3],[4,3]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEM0dGKC1JJ1JUQUJMRUdGKDYlIjU/KSplcD86KVskKm8kLUknTUFUUklYR0YoNiM3JDckLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiM0YoNyQtRjg2I1EiNEYoRj5JJ01hdHJpeEdGJTcjLUZFNiMvSSQlaWRHRihGMQ==

RF0 := RankFactorization(M,[D1,D2,D3],0);

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

Sol0 := Solutions(M,[D1,D2,D3],0);

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

IsSolution(Sol0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyUvIiIiNyNJJXRydWVHRiYvIiIjRjIvIiIkRjJRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wkRjFGMkY1RjJGN0Yy

RF0bis := RankFactorization(M,[D1,D2,D3],0,"reduced");

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

Sol0bis := Solutions(M,[D1,D2,D3],0,"reduced");

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

IsSolution(Sol0bis);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyUvIiIiNyNJJXRydWVHRiYvIiIjRjIvIiIkRjJRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wkRjFGMkY1RjJGN0Yy

Sol1 := Solutions(M,[D1,D2,D3],1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVTb2wxR0YoUS1Ob35zb2x1dGlvbnNGKDcjRi4=

Example 4 of Inria Report 9438 D1 := Matrix([[0$3,2],[3,0$2,1],[0$4],[0$3,2]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMUdGKC1JJ1JUQUJMRUdGKDYlIjVnV2JgPzopWyQqbyQtSSdNQVRSSVhHRig2IzcmNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjBGKEY3RjctRjg2I1EiMkYoNyYtRjg2I1EiM0YoRjdGNy1GODYjUSIxRig3JkY3RjdGN0Y3RjZJJ01hdHJpeEdGJTcjLUZJNiMvSSQlaWRHRihGMQ==

D2 := Matrix([[5,3,0$2],[0$4],[0,5,2,0],[0,3,2,0]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMkdGKC1JJ1JUQUJMRUdGKDYlIjUhKUglUjBfIilbJCpvJC1JJ01BVFJJWEdGKDYjNyY3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiNUYoLUY4NiNRIjNGKC1GODYjUSIwRihGQTcmRkFGQUZBRkE3JkZBRjctRjg2I1EiMkYoRkE3JkZBRj5GRkZBSSdNYXRyaXhHRiU3Iy1GSjYjL0kkJWlkR0YoRjE=

M := Matrix([[30,0$2],[0$3],[12,0$2],[12,0$2]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNTtuJVIwXyIpWyQqbyQtSSdNQVRSSVhHRig2IzcmNyUtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIzMwRigtRjg2I1EiMEYoRj43JUY+Rj5GPjclLUY4NiNRIzEyRihGPkY+RkJJJ01hdHJpeEdGJTcjLUZGNiMvSSQlaWRHRihGMQ==

Sol1 := Solutions(M,[D1,D2],1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVTb2wxR0YoUS1Ob35zb2x1dGlvbnNGKDcjRi4=

RF0 := RankFactorization(M,[D1,D2],0);

-_I,TypesettingG6$%*protectedGI(_syslibG6"I,mprintslashGF(6$7#>I$RF0GF(7*7&,(*&&I"xGF(6#"""F5&F36#""%F5""#*&&F36#F9F5F6F5!"$*&&F36#""$F5F6F5!"#,&*&F2F5F;F5FAF:F5,(*$F2F9F9*&F2F5F?F5FBF:F5,(*&F;F9F6F5""**(F;F5F?F5F6F5""'*&F;F5F6F9F9X,%!GF(F([gl!"%!!!#)"#"%-I%msubG6$F&/I+modulenameGF(F$6$-I#miGFR6#Q"xF(-I#mnGFR6#Q"2F(-FQ6$FV-Fen6#Q"4F(-I%mrowGFR6%-F^o6%FZ-I#moGFR6#Q1&InvisibleTimes;F(-FQ6$FV-Fen6#Q"1F(-Fco6#Q(&minus;F(-F^o6%FZFbo-FQ6$FV-Fen6#Q"3F(-F^o6%FbpFboFhn-Fen6#Q"0F(-F^o6%-F^o6%FbpFboFfo-Fco6#Q'&plus;F(FhnFgp-F^o6'-F^o6'-Fen6#Q"9F(FboFPFboFhnF^q-F^o6'-Fen6#Q"6F(FboF`pFboFhnF^q-F^o6%FZFbo-I(msubsupGFR6%FVFjnFZ-I'RTABLEGF(6%"5_GlD@:)[$*o$-I'MATRIXGF(6#7#7%FjqFgpFgpI'MatrixGF%7%,&F:""&F>F9,&FGFAF>F5,&*&F?F9F6F5FL*&F?F5F6F9F^sKI&TABLEGF&6#7%/F5X,FOF(F([gl!"%!!!#%"%""Fgp-I&mfracGFR6$-F^o6%FZFbo-FW6#Q#_yF(FbpFgpFgp/F9X,FOF(F([gl!"%!!!#%"%""FgpFgpF^tFgp/FAX,FOF(F([gl!"%!!!#%"%""Fgp-F^o6$-Fco6#Q*&uminus0;F(-F^o6'FbpFboF^tFboF`pFgp-Fjs6$-F^o6%-Fen6#Q"5F(FboF^tFZQ(pprint0F(KFds6#7%/F5-I*mverbatimGFR6$Q^]p-%'RTABLEG6&"5g3dr>:)[$*o$-I'mtableG6$%*protectedG/%+modulenameGI,TypesettingG6$F)%(_syslibG6$-I$mtrG6$F)/F+F,6#-I$mtdG6$F)/F+F,6#-I(mfencedG6$F)/F+F,6%-F'6&-F16--F66#-I#mnG6$F)/F+F,6#Q"36"-F66#-FF6#Q"0FKFLFLFLFLFLFLFLFL-F66#-I#moG6$F)/F+F,6#Q)&hellip;FK-F16--F66#-FF6#Q+&uminus0;1FK-F66#-I%mrowG6$F)/F+F,6'-F]o6%-FF6#Q#18FK-FT6#Q1&InvisibleTimes;FK-I%msubG6$F)/F+F,6$-I#miG6$F)/F+F,6#Q"xFK-FF6#Q"2FK-FT6#Q'&plus;FK-F]o6%-FF6#Q#12FKFfo-Fjo6$F^pFEFgp-F]o6%-FF6#Q"4FKFfo-Fjo6$F^pFcq-F66#-F]o6'-F]o6%-FF6#Q"9FKFfoFioFgp-F]o6%-FF6#Q"6FKFfoF_qFgp-F]o6%FdpFfoFfq-F66#-F]o6'-F]o6)-FF6#Q#24FKFfo-F_p6#Q#_yFKFfoF_qFfoFfqFgp-F]o6'-FF6#Q#20FKFfoFasFfo-I(msubsupG6$F)/F+F,6%F^pFcqFdpFgpFcoFLFLFLFLFLFLFQ-F16-FLFL-F66#-F]o6$-FT6#Q*&uminus0;FK-F]o6%FcrFfoFfqFL-F66#-F]o6$FdtFfr-F66#Fio-F66#-F]o6%F\r-FT6#Q(&minus;FKFfr-F66#-F]o6%-F]o6'FcrFfoF_qFfoFfqFgp-F]o6%FdpFfoFis-F66#Fdp-F66#-F]o6'FcqFfoFasFfoFisFQ-F16-FL-F66#-FF6#Q+&uminus0;6FKFL-F66#-F]o6$Fdt-F]o6'-FF6#Q#30FKFfoFasFfoFfq-F66#-FF6#Q"1FKFLFdw-F66#-F]o6(Fdt-I&mfracG6$F)/F+F,6$F\rFdpFcu-F]o6%FEFfoF_qFcuFfq-F66#-F]o6&Fdt-F]o6'FEFfoFasFfoFioFcu-F]o6'FdpFfoFasFfoF_q-F66#-F]o6$Fdt-F]o6'FdpFfoFasFfoFfqFQ/I%openG6$F)F.Q'&lsqb;FK/I&closeG6$F)F.Q'&rsqb;FK-F16#-F66$-I&mtextG6$F)/F+F,6$Q44|ir&times;|ir16|irMatrixFK/%)mathsizeGQ&smallFK/%,columnalignGQ&rightFKI'MatrixG6$F)F.%'HandleGF(-Fcr6&"5g3dr>:)[$*o$-I'mtableGFR6$-I$mtrGFR6#-I$mtdGFR6#-I(mfencedGFR6%-F`v6&-Fcv6--Ffv6#Fbp-Ffv6#FgpFawFawFawFawFawFawFawFaw-Ffv6#-Fco6#Q)&hellip;F(-Fcv6--Ffv6#-Fen6#Q+&uminus0;1F(-Ffv6#-F^o6'-F^o6%-Fen6#Q#18F(FboFPF^q-F^o6%-Fen6#Q#12F(FboF`pF^q-F^o6%FjnFboFhn-Ffv6#-F^o6'-F^o6%FeqFboFPF^q-F^o6%FjqFboF`pF^q-F^o6%FZFboFhn-Ffv6#-F^o6'-F^o6)-Fen6#Q#24F(FboF^tFboF`pFboFhnF^q-F^o6'-Fen6#Q#20F(FboF^tFboF_rF^qFexFawFawFawFawFawFawFcw-Fcv6-FawFaw-Ffv6#-F^o6$Fgt-F^o6%FjqFboFhnFaw-Ffv6#-F^o6$FgtFgy-Ffv6#FP-Ffv6#-F^o6%FcyF[pFgy-Ffv6#-F^o6%FhqF^qF]r-Ffv6#FZ-Ffv6#-F^o6'FjnFboF^tFboF_rFcw-Fcv6-Faw-Ffv6#-Fen6#Q+&uminus0;6F(Faw-Ffv6#-F^o6$Fgt-F^o6'-Fen6#Q#30F(FboF^tFboFhn-Ffv6#FhoFawFc]l-Ffv6#-F^o6(Fgt-Fjs6$FcyFZF[p-F^o6%FbpFboF`pF[pFhn-Ffv6#-F^o6&Fgt-F^o6'FbpFboF^tFboFPF[p-F^o6'FZFboF^tFboF`p-Ffv6#-F^o6$Fgt-F^o6'FZFboF^tFboFhnFcw/I%openGF%Q'&lsqb;F(/I&closeGF%Q'&rsqb;F(-Fcv6#-Ffv6$-I&mtextGFR6$Q44~&times;~16~MatrixF(/I)mathsizeGF(Q&smallF(/I,columnalignGF(Q&rightF(F[sI'HandleGF(/F9-Fiu6$Q\[p-%'RTABLEG6&"5+,<C@:)[$*o$-I'mtableG6$%*protectedG/%+modulenameGI,TypesettingG6$F)%(_syslibG6$-I$mtrG6$F)/F+F,6#-I$mtdG6$F)/F+F,6#-I(mfencedG6$F)/F+F,6%-F'6&-F16--F66#-I#mnG6$F)/F+F,6#Q"36"-F66#-FF6#Q"0FKFLFLFLFLFLFLFLFL-F66#-I#moG6$F)/F+F,6#Q)&hellip;FK-F16--F66#-FF6#Q+&uminus0;1FK-F66#-I%mrowG6$F)/F+F,6%-F]o6%-FF6#Q#12FK-FT6#Q1&InvisibleTimes;FK-I%msubG6$F)/F+F,6$-I#miG6$F)/F+F,6#Q"xFKFE-FT6#Q'&plus;FK-F]o6%-FF6#Q"4FKFfo-Fjo6$F^pFip-F66#-F]o6%-F]o6%-FF6#Q"6FKFfoFioFdp-F]o6%-FF6#Q"2FKFfoF\q-F66#-FF6#Q+&uminus0;6FK-F66#-FF6#Q+&uminus0;2FKF\r-F66#Fip-F66#FdqFLFLFQ-F16-FLFL-F66#-F]o6$-FT6#Q*&uminus0;FK-F]o6%FdqFfoF\q-F66#-F]o6$F`s-F]o6'FiqFfo-F_p6#Q#_yFKFfo-I(msubsupG6$F)/F+F,6%F^pFipFiqFes-F66#-F]o6&F`s-F]o6)FdqFfoF[tFfoFioFfoF\q-FT6#Q(&minus;FK-F]o6'-FF6#Q#10FKFfoF[tFfoF^t-F66#-F]o6'FipFfoF[tFfoF^t-F66#Fis-F66#-F]o6$F`sFgqFguFQ-F16-FLF\rFL-F66#-F]o6%-F]o6'-FF6#Q"9FKFfoF[tFfoFioFdp-F]o6%F[tFfoF\q-F66#-F]o6%-F]o6'FEFfoF[tFfoFioFdpFfv-F66#-F]o6%-F]o6'FcoFfoF[tFfoFioFdp-F]o6'-FF6#Q"5FKFfoF[tFfoF\q-F66#-F]o6&F`s-F]o6'FdqFfoF[tFfoFioFit-F]o6'FiqFfoF[tFfoF\q-F66#-F]o6&F`sFavFitFfv-F66#-FF6#Q"1FKFexFQ/I%openG6$F)F.Q'&lsqb;FK/I&closeG6$F)F.Q'&rsqb;FK-F16#-F66$-I&mtextG6$F)/F+F,6$Q44|ir&times;|ir12|irMatrixFK/%)mathsizeGQ&smallFK/%,columnalignGQ&rightFKI'MatrixG6$F)F.%'HandleGF(-Fcr6&"5+,<C@:)[$*o$-F`v6$-Fcv6#-Ffv6#-Fiv6%-F`v6&F]w-Fcv6-Fjw-Ffv6#-F^o6%FhxF^qF]y-Ffv6#-F^o6%FeyF^qFgyFe\l-Ffv6#-Fen6#Q+&uminus0;2F(Fe\l-Ffv6#Fjn-Ffv6#FjqFawFawFcw-Fcv6-FawFawFiz-Ffv6#-F^o6$Fgt-F^o6'FZFboF^tFboF_rFfbl-Ffv6#-F^o6&Fgt-F^o6)FjqFboF^tFboF`pFboFhnF[p-F^o6'-Fen6#Q#10F(FboF^tFboF_rF_\l-Ffv6#FjblF_[lF_[lFcw-Fcv6-FawFe\lFaw-Ffv6#-F^o6%-F^o6'FeqFboF^tFboF`pF^q-F^o6%F^tFboFhn-Ffv6#-F^o6%FjtF^qFadl-Ffv6#-F^o6%-F^o6'FjxFboF^tFboF`pF^q-F^o6'F`uFboF^tFboFhn-Ffv6#-F^o6&Fgt-F^o6'FjqFboF^tFboF`pF[pFi^l-Ffv6#-F^o6&FgtF_dlF[pFadlFc]lFc]lFcwF[_lF^_l-Fcv6#-Ffv6$-Ff_l6$Q44~&times;~12~MatrixF(Fi_lF\`lF[sF_`l/FA-Fiu6$Qefp-%'RTABLEG6&"5K2sS?:)[$*o$-I'mtableG6$%*protectedG/%+modulenameGI,TypesettingG6$F)%(_syslibG6$-I$mtrG6$F)/F+F,6#-I$mtdG6$F)/F+F,6#-I(mfencedG6$F)/F+F,6%-F'6&-F16--F66#-I#mnG6$F)/F+F,6#Q"36"-F66#-FF6#Q"0FKFLFLFLFLFLFLFLFL-F66#-I#moG6$F)/F+F,6#Q)&hellip;FK-F16--F66#-FF6#Q+&uminus0;1FK-F66#-I%mrowG6$F)/F+F,6'-F]o6%-FF6#Q#18FK-FT6#Q1&InvisibleTimes;FK-I%msubG6$F)/F+F,6$-I#miG6$F)/F+F,6#Q"xFK-FF6#Q"2FK-FT6#Q'&plus;FK-F]o6%-FF6#Q#12FKFfo-Fjo6$F^pFEFgp-F]o6%-FF6#Q"4FKFfo-Fjo6$F^pFcq-F66#-F]o6'-F]o6%-FF6#Q"9FKFfoFioFgp-F]o6%-FF6#Q"6FKFfoF_qFgp-F]o6%FdpFfoFfqFLFLFLFLFLFLFLFQ-F16-FLFL-F66#-F]o6$-FT6#Q*&uminus0;FK-F]o6%FcrFfoFfq-F66#-F]o6$F^sFfr-F66#Fio-F66#-F]o6%F\r-FT6#Q(&minus;FKFfr-F66#-F]o6%-F]o6'FcrFfoF_qFfoFfqFgp-F]o6%FdpFfo-I(msubsupG6$F)/F+F,6%F^pFcqFdp-F66#-FF6#Q+&uminus0;2FK-F66#-F]o6$F^s-F]o6'FdpFfo-F_p6#Q#_yFKFfo-Fit6%F^pFcqFE-F66#-F]o6'-FF6#Q#10FKFfoFhuFfoF[vFQ-F16-FL-F66#-FF6#Q+&uminus0;6FKFL-F66#-FF6#Q"1FKFLF[w-F66#-F]o6(F^s-I&mfracG6$F)/F+F,6$F\rFdpF]t-F]o6%FEFfoF_qF]tFfq-F66#-F]o6)-F]o6%F^rFfo-F]o6'FhuFfoFioFfoF_qFgp-F]o6%-Few6$-FF6#Q#15FKFdpFfo-F]o6'FhuFfoFioFfoFfqFgp-F]o6%FcrFfo-F]o6%FhuFfo-Fit6%F^pFEFdpFgp-F]o6%-FF6#Q"5FKFfo-F]o6'FhuFfoF_qFfoFfq-F66#-F]o6&F^s-F]o6)FEFfoFhuFfoFioFfoFfqFgp-F]o6%FhuFfoFht-F66#-F]o6%-F]o6)FgxFfoFhuFfoFioFfoFfqF]t-F]o6'FdyFfoFhuFfoFhtFQ/I%openG6$F)F.Q'&lsqb;FK/I&closeG6$F)F.Q'&rsqb;FK-F16#-F66$-I&mtextG6$F)/F+F,6$Q44|ir&times;|ir13|irMatrixFK/%)mathsizeGQ&smallFK/%,columnalignGQ&rightFKI'MatrixG6$F)F.%'HandleGF(-Fcr6&"5K2sS?:)[$*o$-F`v6$-Fcv6#-Ffv6#-Fiv6%-F`v6&F]w-Fcv6-FjwF_xF_yFawFawFawFawFawFawFawFcw-Fcv6-FawFawFizF_[lFc[lFe[lFi[lF[bl-Ffv6#-F^o6$Fgt-F^o6'FZFboF^tFbo-F`r6%FVFjnFbp-Ffv6#-F^o6'FdclFboF^tFboF[hlFcw-Fcv6-FawFe\lFawFc]lFawFc]lFe]l-Ffv6#-F^o6)-F^o6%FeqFbo-F^o6'F^tFboFPFboF`pF^q-F^o6%-Fjs6$-Fen6#Q#15F(FZFbo-F^o6'F^tFboFPFboFhnF^q-F^o6%FjqFbo-F^o6%F^tFbo-F`r6%FVFbpFZF^q-F^o6%F`uFbo-F^o6'F^tFboF`pFboFhn-Ffv6#-F^o6&Fgt-F^o6)FbpFboF^tFboFPFboFhnF^q-F^o6%F^tFboF_r-Ffv6#-F^o6%-F^o6)F_ilFboF^tFboFPFboFhnF[p-F^o6'F`uFboF^tFboF_rFcwF[_lF^_l-Fcv6#-Ffv6$-Ff_l6$Q44~&times;~13~MatrixF(Fi_lF\`lF[sF_`lQ(pprint1F(70I,Ore_algebraG6#/I'_localGF&I-_n4573023760GF(7'Q%diffF(F]\mF]\mF]\mF]\m7'&I"tGF(F4&F`\mF<&F`\mF@&F`\mF7I#_tGF(7'F2F;F?F6I#_yGF%F^\m7"""!Fg\mFg\mF^\mFg\mFg\m7'/I%diffGF&7$F2F_\m/F[]m7$F;Fa\m/F[]m7$F?Fb\m/F[]m7$F6Fc\m/F[]m7$Ff\mFd\m7'f*6#I#_aGF(F(6$I)operatorGF(I&arrowGF(F(,&*&9$F5F2F5F5-F[]m6$F^^mF_\m!""F(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5F;F5F5-F[]m6$F^^mFa\mFa^mF(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5F?F5F5-F[]m6$F^^mFb\mFa^mF(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5F6F5F5-F[]m6$F^^mFc\mFa^mF(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5Ff\mF5F5-F[]m6$F^^mFd\mFa^mF(F(F(X,FOF(F([gl!"%!!!#)"%"#FgyFjpFgpFgy-F^o6%-F^o6%F`uFboFfoF^q-F^o6%FbpFboFPFgp-F^o6%-F^o6%F`uFboFPF^qF^p-F^o6%F[`mF^qF^p7#7*F/-F[s6#/I$%idGF("5wOIF?:)[$*o$-F[s6#/Fh`mFerF\s-I&tableGF&6#/Fh`m"5s(fK._")[$*o$-F^am6#/Fh`m"5O5N$*>:)[$*o$Ff[m-F[s6#/Fh`m"57!\c7_")[$*o$

RF0 := RankFactorization(M,[D1,D2],0,"reduced");

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

Sol0 := Solutions(M,[D1,D2],0,"reduced");

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

Example 7 of Inria Report 9438 M := Matrix([[0$3],[0$3]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVN2Y3A/OilbJCpvJC1JJ01BVFJJWEdGKDYjNyQ3JS1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMEYoRjdGN0Y2SSdNYXRyaXhHRiU3Iy1GPjYjL0kkJWlkR0YoRjE=

D1 := DiagonalMatrix([1$2]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMUdGKC1JJ1JUQUJMRUdGKDYlIjU/KXAmcD86KVskKm8kLUknTUFUUklYR0YoNiM3JDckLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoNyRGPkY3SSdNYXRyaXhHRiU3Iy1GQjYjL0kkJWlkR0YoRjE=

D2 := Matrix([[0,1],[1,0]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMkdGKC1JJ1JUQUJMRUdGKDYlIjVrVGNwPzopWyQqbyQtSSdNQVRSSVhHRig2IzckNyQtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjBGKC1GODYjUSIxRig3JEY+RjdJJ01hdHJpeEdGJTcjLUZCNiMvSSQlaWRHRihGMQ==

D3 := Matrix([[2,1],[1,2]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEM0dGKC1JJ1JUQUJMRUdGKDYlIjUvaWNwPzopWyQqbyQtSSdNQVRSSVhHRig2IzckNyQtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjJGKC1GODYjUSIxRig3JEY+RjdJJ01hdHJpeEdGJTcjLUZCNiMvSSQlaWRHRihGMQ==

RF0 := RankFactorization(M,[D1,D2,D3],0);

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

RF1 := RankFactorization(M,[D1,D2,D3],1);

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

RF2 := RankFactorization(M,[D1,D2,D3],2);

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

Sol0 := Solutions(M,[D1,D2,D3],0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVTb2wwR0YoNyc3IyIiIUYvWCwlIUdGKEYoW2dsISIlISEhIyciIyIkLUklbXN1Ykc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiQtSSNtaUdGNTYjUSJ4RigtSSNtbkdGNTYjUSIxRigtRjQ2JEY5LUY+NiNRIjJGKEZBRjMtSSVtcm93R0Y1NiUtRkc2JUZDLUkjbW9HRjU2I1ExJkludmlzaWJsZVRpbWVzO0YoRjMtRkw2I1EnJnBsdXM7RihGQS1GRzYlRjNGTy1GRzYlRkNGS0ZBS0kmVEFCTEVHRiY2IzcjLyIiIlgsRjJGKEYoW2dsISIlISEhIyoiJCIkLUZHNiVGQ0ZLLUY0NiQtRjo2I1EieUYoLUZHNiVGPS1GTDYjUSgmY29tbWE7RihGPUZpbi1GRzYkLUZMNiNRKiZ1bWludXMwO0YoRmluLUZHNiVGQ0ZLLUY0NiRGW28tRkc2JUY9RmBvRkNGam8tRkc2JEZlb0Zqby1GRzYlRkNGSy1GNDYkRltvLUZHNiVGPUZgby1GPjYjUSIzRihGYnAtRkc2JEZlb0ZicFEocHByaW50MEYoS0ZXNiM3Iy9GZW43MEksT3JlX2FsZ2VicmFHNiMvSSdfbG9jYWxHRiZJLV9uNDcyMjAzMjg0MEdGKDckUSVkaWZmRihGZ3E3JCZJInRHRig2I0ZlbiZGanE2IyIiIzckJkkieEdGKEZbciZGYXJGXXJGaHE3JSZJInlHNiMvRmRxSS1fbjQ2MDUyMTUyNjRHRig2JEZlbkZlbiZGZXI2JEZlbkZeciZGZXI2JEZlbiIiJEYwNyJGX3NGaHFGX3NGX3M3JC9JJWRpZmZHRiY3JEZgckZpcS9GYnM3JEZickZccjckZio2I0kjX2FHRihGKDYkSSlvcGVyYXRvckdGKEkmYXJyb3dHRihGKCwmKiY5JEZlbkZgckZlbkZlbi1GYnM2JEZfdEZpcSEiIkYoRihGKGYqRmhzRihGanNGKCwmKiZGX3RGZW5GYnJGZW5GZW4tRmJzNiRGX3RGXHJGYnRGKEYoRihRKHBwcmludDFGKDcjNydGL0YvLUknTWF0cml4R0YlNiMvSSQlaWRHRigiNVdFS3E/OilbJCpvJC1JJnRhYmxlR0YmNiMvRl91IjVHUz1RPzopWyQqbyQtRmJ1NiMvRl91IjVnc2dXQDopWyQqbyQ=

IsSolution(Sol0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyMvIiIiNyNJJXRydWVHRiZRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wiRjFGMg==

Sol1 := Solutions(M,[D1,D2,D3],1);

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

IsSolution(Sol1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyMvIiIiNyNJJXRydWVHRiZRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wiRjFGMg==

Sol2 := Solutions(M,[D1,D2,D3],2);

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

IsSolution(Sol2);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyNLSSZUQUJMRUdGJjYjNyMvIiIiNyNJJXRydWVHRiZRKHBwcmludDBGKDcjPUYoSSZmYWxzZUdGJkVcW2wiRjFGMg==

M := Matrix([[30,0$2],[0$3],[12,0$2],[12,0$2]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNU8nKlEpKT46KVskKm8kLUknTUFUUklYR0YoNiM3JjclLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSMzMEYoLUY4NiNRIjBGKEY+NyVGPkY+Rj43JS1GODYjUSMxMkYoRj5GPkZCSSdNYXRyaXhHRiU3Iy1GRjYjL0kkJWlkR0YoRjE=

D1 := Matrix([[0$3,2],[3,0$2,1],[0$4],[0$3,2]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMUdGKC1JJ1JUQUJMRUdGKDYlIjVTXFEpKT46KVskKm8kLUknTUFUUklYR0YoNiM3JjcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIwRihGN0Y3LUY4NiNRIjJGKDcmLUY4NiNRIjNGKEY3RjctRjg2I1EiMUYoNyZGN0Y3RjdGN0Y2SSdNYXRyaXhHRiU3Iy1GSTYjL0kkJWlkR0YoRjE=

D2 := Matrix([[5,3,0$2],[0$4],[0,5,2,0],[0,3,2,0]]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNEMkdGKC1JJ1JUQUJMRUdGKDYlIjUlMyJRKSk+OilbJCpvJC1JJ01BVFJJWEdGKDYjNyY3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiNUYoLUY4NiNRIjNGKC1GODYjUSIwRihGQTcmRkFGQUZBRkE3JkZBRjctRjg2I1EiMkYoRkE3JkZBRj5GRkZBSSdNYXRyaXhHRiU3Iy1GSjYjL0kkJWlkR0YoRjE=

RF0 := RankFactorization(M,[D1,D2],0);

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FboFhn-Ffv6#-F^o6%FjtF^qFadl-Ffv6#-F^o6%-F^o6'FjxFboF^tFboF`pF^q-F^o6'F`uFboF^tFboFhn-Ffv6#-F^o6&Fgt-F^o6'FjqFboF^tFboF`pF[pFi^l-Ffv6#-F^o6&FgtF_dlF[pFadlFc]lFc]lFcwF[_lF^_l-Fcv6#-Ffv6$-Ff_l6$Q44~&times;~12~MatrixF(Fi_lF\`lF[sF_`l/FA-Fiu6$Qefp-%'RTABLEG6&"53Dfz>:)[$*o$-I'mtableG6$%*protectedG/%+modulenameGI,TypesettingG6$F)%(_syslibG6$-I$mtrG6$F)/F+F,6#-I$mtdG6$F)/F+F,6#-I(mfencedG6$F)/F+F,6%-F'6&-F16--F66#-I#mnG6$F)/F+F,6#Q"36"-F66#-FF6#Q"0FKFLFLFLFLFLFLFLFL-F66#-I#moG6$F)/F+F,6#Q)&hellip;FK-F16--F66#-FF6#Q+&uminus0;1FK-F66#-I%mrowG6$F)/F+F,6'-F]o6%-FF6#Q#18FK-FT6#Q1&InvisibleTimes;FK-I%msubG6$F)/F+F,6$-I#miG6$F)/F+F,6#Q"xFK-FF6#Q"2FK-FT6#Q'&plus;FK-F]o6%-FF6#Q#12FKFfo-Fjo6$F^pFEFgp-F]o6%-FF6#Q"4FKFfo-Fjo6$F^pFcq-F66#-F]o6'-F]o6%-FF6#Q"9FKFfoFioFgp-F]o6%-FF6#Q"6FKFfoF_qFgp-F]o6%FdpFfoFfqFLFLFLFLFLFLFLFQ-F16-FLFL-F66#-F]o6$-FT6#Q*&uminus0;FK-F]o6%FcrFfoFfq-F66#-F]o6$F^sFfr-F66#Fio-F66#-F]o6%F\r-FT6#Q(&minus;FKFfr-F66#-F]o6%-F]o6'FcrFfoF_qFfoFfqFgp-F]o6%FdpFfo-I(msubsupG6$F)/F+F,6%F^pFcqFdp-F66#-FF6#Q+&uminus0;2FK-F66#-F]o6$F^s-F]o6'FdpFfo-F_p6#Q#_yFKFfo-Fit6%F^pFcqFE-F66#-F]o6'-FF6#Q#10FKFfoFhuFfoF[vFQ-F16-FL-F66#-FF6#Q+&uminus0;6FKFL-F66#-FF6#Q"1FKFLF[w-F66#-F]o6(F^s-I&mfracG6$F)/F+F,6$F\rFdpF]t-F]o6%FEFfoF_qF]tFfq-F66#-F]o6)-F]o6%F^rFfo-F]o6'FhuFfoFioFfoF_qFgp-F]o6%-Few6$-FF6#Q#15FKFdpFfo-F]o6'FhuFfoFioFfoFfqFgp-F]o6%FcrFfo-F]o6%FhuFfo-Fit6%F^pFEFdpFgp-F]o6%-FF6#Q"5FKFfo-F]o6'FhuFfoF_qFfoFfq-F66#-F]o6&F^s-F]o6)FEFfoFhuFfoFioFfoFfqFgp-F]o6%FhuFfoFht-F66#-F]o6%-F]o6)FgxFfoFhuFfoFioFfoFfqF]t-F]o6'FdyFfoFhuFfoFhtFQ/I%openG6$F)F.Q'&lsqb;FK/I&closeG6$F)F.Q'&rsqb;FK-F16#-F66$-I&mtextG6$F)/F+F,6$Q44|ir&times;|ir13|irMatrixFK/%)mathsizeGQ&smallFK/%,columnalignGQ&rightFKI'MatrixG6$F)F.%'HandleGF(-Fcr6&"53Dfz>:)[$*o$-F`v6$-Fcv6#-Ffv6#-Fiv6%-F`v6&F]w-Fcv6-FjwF_xF_yFawFawFawFawFawFawFawFcw-Fcv6-FawFawFizF_[lFc[lFe[lFi[lF[bl-Ffv6#-F^o6$Fgt-F^o6'FZFboF^tFbo-F`r6%FVFjnFbp-Ffv6#-F^o6'FdclFboF^tFboF[hlFcw-Fcv6-FawFe\lFawFc]lFawFc]lFe]l-Ffv6#-F^o6)-F^o6%FeqFbo-F^o6'F^tFboFPFboF`pF^q-F^o6%-Fjs6$-Fen6#Q#15F(FZFbo-F^o6'F^tFboFPFboFhnF^q-F^o6%FjqFbo-F^o6%F^tFbo-F`r6%FVFbpFZF^q-F^o6%F`uFbo-F^o6'F^tFboF`pFboFhn-Ffv6#-F^o6&Fgt-F^o6)FbpFboF^tFboFPFboFhnF^q-F^o6%F^tFboF_r-Ffv6#-F^o6%-F^o6)F_ilFboF^tFboFPFboFhnF[p-F^o6'F`uFboF^tFboF_rFcwF[_lF^_l-Fcv6#-Ffv6$-Ff_l6$Q44~&times;~13~MatrixF(Fi_lF\`lF[sF_`lQ(pprint1F(70I,Ore_algebraG6#/I'_localGF&I-_n4573023760GF(7'Q%diffF(F]\mF]\mF]\mF]\m7'&I"tGF(F4&F`\mF<&F`\mF@&F`\mF7I#_tGF(7'F2F;F?F6I#_yGF%F^\m7"""!Fg\mFg\mF^\mFg\mFg\m7'/I%diffGF&7$F2F_\m/F[]m7$F;Fa\m/F[]m7$F?Fb\m/F[]m7$F6Fc\m/F[]m7$Ff\mFd\m7'f*6#I#_aGF(F(6$I)operatorGF(I&arrowGF(F(,&*&9$F5F2F5F5-F[]m6$F^^mF_\m!""F(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5F;F5F5-F[]m6$F^^mFa\mFa^mF(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5F?F5F5-F[]m6$F^^mFb\mFa^mF(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5F6F5F5-F[]m6$F^^mFc\mFa^mF(F(F(f*Fg]mF(Fi]mF(,&*&F^^mF5Ff\mF5F5-F[]m6$F^^mFd\mFa^mF(F(F(X,FOF(F([gl!"%!!!#)"%"#FgyFjpFgpFgy-F^o6%-F^o6%F`uFboFfoF^q-F^o6%FbpFboFPFgp-F^o6%-F^o6%F`uFboFPF^qF^p-F^o6%F[`mF^qF^p7#7*F/-F[s6#/I$%idGF("5s$fW-_")[$*o$-F[s6#/Fh`mFerF\s-I&tableGF&6#/Fh`m"5K">69_")[$*o$-F^am6#/Fh`m"5+&4:7_")[$*o$Ff[m-F[s6#/Fh`m"53xP))>:)[$*o$

RF0bis := RankFactorization(M,[D1,D2],0,"reduced");

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv 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