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"with(LinearAlgebra):\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 7 "rs:=7:\n" }{MPLTEXT 1 0 28 "list0:=seq(t[i],i=1..rs-1) ;\n" }{MPLTEXT 1 0 26 "MXs:=Matrix(rs-1,rs-1,0):\n" }{MPLTEXT 1 0 98 " for i from 1 to rs-1 do for j from 1 to rs-1 do if j<=i then MXs[i,j]: =t[rs-1-(i-j)]: fi: od: od:\n" }{MPLTEXT 1 0 5 "MXs;\n" }{MPLTEXT 1 0 28 "Diago:=Matrix(rs-1,rs-1,0):\n" }{MPLTEXT 1 0 46 "for i from 1 to r s-1 do Diago[i,i]:=rs-i: od:\n" }{MPLTEXT 1 0 7 "Diago;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "RHSMatrix:=Matrix(rs-1,rs-1,0):\n" } {MPLTEXT 1 0 116 "for i from 1 to rs-1 do for j from 1 to rs-1 do if j <=i then RHSMatrix[i,j]:=Q[rs-(i-j)](list0)/(rs-j): fi: od: od:\n" } {MPLTEXT 1 0 11 "RHSMatrix;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 35 " deltaQMatrix:=Matrix(rs-1,rs-1,0):\n" }{MPLTEXT 1 0 48 "for i from 1 t o rs-1 do for j from 1 to rs-1 do\n" }{MPLTEXT 1 0 60 "deltaQMatrix[i, j]:=1/(rs-i)*diff(Q[rs+1-i](list0),t[rs-j]):\n" }{MPLTEXT 1 0 8 "od: o d:\n" }{MPLTEXT 1 0 14 "deltaQMatrix:\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 20 "EquationSystem:=[]:\n" }{MPLTEXT 1 0 48 "for i from 1 to rs-1 do for j from 1 to rs-1 do\n" }{MPLTEXT 1 0 92 "EquationSyste m:=[op(EquationSystem),(Multiply(MXs,deltaQMatrix)-RHSMatrix)[i,j]=0]: od: od:\n" }{MPLTEXT 1 0 16 "EquationSystem:\n" }{MPLTEXT 1 0 30 "pds olve(\{op(EquationSystem)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&list 0G6\"6(&I\"tGF$6#\"\"\"&F'6#\"\"#&F'6#\"\"$&F'6#\"\"%&F'6#\"\"&&F'6#\" \"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,T ypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$6:-I$mtrGF$6+-I$mtdGF $6(-I%msubGF$6%-I#miGF$6&Q\"tF'/%'italicGQ%trueF'/%+foregroundGQ([0,0, 0]F'/%,mathvariantGQ'italicF'-F,6#-I#mnGF$6%Q\"6F'FA/FEQ'normalF'/%/su bscriptshiftGQ\"0F'/%)rowalignGQ!F'/%,columnalignGFT/%+groupalignGFT/% (rowspanGQ\"1F'/%+columnspanGFen-F56(-FJ6%FQFAFMFRFUFWFYFfnFhnFhnFhnFh nFRFUFW-F26+-F56(-F86%F:-F,6#-FJ6%Q\"5F'FAFMFOFRFUFWFYFfnF4FhnFhnFhnFh nFRFUFW-F26+-F56(-F86%F:-F,6#-FJ6%Q\"4F'FAFMFOFRFUFWFYFfnF^oF4FhnFhnFh nFRFUFW-F26+-F56(-F86%F:-F,6#-FJ6%Q\"3F'FAFMFOFRFUFWFYFfnFioF^oF4FhnFh nFRFUFW-F26+-F56(-F86%F:-F,6#-FJ6%Q\"2F'FAFMFOFRFUFWFYFfnFdpFioF^oF4Fh nFRFUFW-F26+-F56(-F86%F:-F,6#-FJ6%FenFAFMFOFRFUFWFYFfnF_qFdpFioF^oF4FR FUFW/%&alignGQ%axisF'/FSQ)baselineF'/FVQ'centerF'/FXQ'|frleft|hrF'/%/a lignmentscopeGF@/%,columnwidthGQ%autoF'/%&widthGF_s/%+rowspacingGQ&1.0 exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFjs/% &frameGFjs/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equa lcolumnsGFdt/%-displaystyleGFdt/%%sideGQ&rightF'/%0minlabelspacingGFgs FAFM/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I( mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I' mtableGF$6:-I$mtrGF$6+-I$mtdGF$6(-I#mnGF$6%Q\"6F'/%+foregroundGQ([0,0, 0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+group alignGFC/%(rowspanGQ\"1F'/%+columnspanGFJ-F56(-F86%Q\"0F'F;F>FAFDFFFHF KFMFMFMFMFAFDFF-F26+FM-F56(-F86%Q\"5F'F;F>FAFDFFFHFKFMFMFMFMFAFDFF-F26 +FMFM-F56(-F86%Q\"4F'F;F>FAFDFFFHFKFMFMFMFAFDFF-F26+FMFMFM-F56(-F86%Q \"3F'F;F>FAFDFFFHFKFMFMFAFDFF-F26+FMFMFMFM-F56(-F86%Q\"2F'F;F>FAFDFFFH FKFMFAFDFF-F26+FMFMFMFMFM-F56(-F86%FJF;F>FAFDFFFHFKFAFDFF/%&alignGQ%ax isF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%tr ueF'/%,columnwidthGQ%autoF'/%&widthGF\\q/%+rowspacingGQ&1.0exF'/%.colu mnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFgq/%&frameGFgq/ %-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFa r/%-displaystyleGFar/%%sideGFdp/%0minlabelspacingGFdqF;F>/%%openGQ\"[F '/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modu lenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$6:-I$mtr GF$6+-I$mtdGF$6(-F,6%-I&mfracGF$6)-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0 ,0]F'/%,mathvariantGQ'normalF'-F=6%Q\"6F'F@FC/%.linethicknessGF?/%+den omalignGQ'centerF'/%)numalignGFM/%)bevelledGQ&falseF'F@-I#moGF$6-Q1&In visibleTimes;F'FC/%&fenceGFR/%*separatorGFR/%)stretchyGFR/%*symmetricG FR/%(largeopGFR/%.movablelimitsGFR/%'accentGFR/%'lspaceGQ&0.0emF'/%'rs paceGFao-F,6#-F,6%-I%msubGF$6%-I#miGF$6&Q\"QF'/%'italicGQ%trueF'F@/FDQ 'italicF'-F,6#-F=6%Q\"7F'F@FC/%/subscriptshiftGQ\"0F'-FT6-Q0&ApplyFunc tion;F'FCFWFYFenFgnFinF[oF]oF_oFbo-F#6%-F,6--Fio6%-F\\p6&Q\"tF'F_pF@Fb p-F,6#FF2\"&+?\"*&,&*(FHF.F0F.F6F.!%+S*&FHF.F3F)! %v=F.F9#\"#NF;F.**FMF.F3F.F6F.F9#\"# " 0 "" {MPLTEXT 1 0 406 "Q[2] :=unapply( (6 0000*C6*t[6]^(43/6)+60000*C1*t[1]*t[6]^7+30000*C2*t[2]*t[6]^(41/6)+200 00*t[3]*C3*t[6]^(20/3)+15000*C4*t[4]*t[6]^(13/2)+12000*C5*t[5]*t[6]^(1 9/3)+(-4000*C2*t[3]*t[5]-1875*C2*t[4]^2)*t[6]^(35/6)-6000*C3*t[5]*t[4] *t[6]^(17/3)-3600*C4*t[5]^2*t[6]^(11/2)+2100*C2*t[5]^2*t[4]*t[6]^(29/6 )+1280*C3*t[5]^3*t[6]^(14/3)-364*C2*t[5]^4*t[6]^(23/6))/(60000*t[6]^7) ,t[1], t[2], t[3], t[4], t[5], t[6]);\n" }{MPLTEXT 1 0 235 " Q[3]:=una pply( C1*t[2]+2*C2*t[3]/(3*t[6]^(1/6))-t[4]*C2*t[5]/(10*t[6]^(7/6))+t[ 4]*C3/(2*t[6]^(1/3))+7*C2*t[5]^3/(375*t[6]^(13/6))-2*C3*t[5]^2/(25*t[6 ]^(4/3))+2*C4*t[5]/(5*sqrt(t[6]))+C5*t[6]^(1/3),t[1], t[2], t[3], t[4] , t[5], t[6]);\n" }{MPLTEXT 1 0 152 "Q[4]:=unapply( C1*t[3]+3*C2*t[4]/ (4*t[6]^(1/6))-3*C2*t[5]^2/(50*t[6]^(7/6))+3*C3*t[5]/(5*t[6]^(1/3))+C4 *sqrt(t[6]),t[1], t[2], t[3], t[4], t[5], t[6]);\n" }{MPLTEXT 1 0 99 " Q[5]:=unapply( C1*t[4]+4*C2*t[5]/(5*t[6]^(1/6))+C3*t[6]^(2/3),t[1], t[ 2], t[3], t[4], t[5], t[6]);\n" }{MPLTEXT 1 0 75 "Q[6]:= unapply( C1*t [5]+C2*t[6]^(5/6),t[1], t[2], t[3], t[4], t[5], t[6]);\n" }{MPLTEXT 1 0 62 "Q[7]:= unapply( C1*t[6], t[1], t[2], t[3], t[4], t[5], t[6]);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 16 "EquationSystem);" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"QG6\"6#\"\"#f*6 (I$t_1GF%I$t_2GF%I$t_3GF%I$t_4GF%I$t_5GF%I$t_6GF%F%6$I)operatorGF%I&ar rowGF%F%,$*&,:*&I#C6GF%\"\"\"9)#\"#V\"\"'\"&++'*(I#C1GF%F89$F8F9\"\"(F =*(I#C2GF%F89%F8F9#\"#TF<\"&++$*(9&F8I#C3GF%F8F9#\"#?\"\"$\"&++#*(I#C4 GF%F89'F8F9#\"#8F'\"&+]\"*(I#C5GF%F89(F8F9#\"#>FM\"&+?\"*&,&*(FCF8FIF8 FWF8!%+S*&FCF8FQF'!%v=F8F9#\"#NF&I\"QG6\"6#\"\"$f*6(I$t_1GF%I$t_2GF%I$t_3GF%I$t_4GF%I$t_ 5GF%I$t_6GF%F%6$I)operatorGF%I&arrowGF%F%,2*&I#C1GF%\"\"\"9%F6F6*(I#C2 GF%F69&F69)#!\"\"\"\"'#\"\"#F'**9'F6F9F69(F6F;#!\"(F>#F=\"#5*(FBF6I#C3 GF%F6F;#F=F'#F6F@*(F9F6FCF'F;#!#8F>#\"\"(\"$v$*(FIF6FCF@F;#!\"%F'#!\"# \"#D*(I#C4GF%F6FCF6F;#F=F@#F@\"\"&*&I#C5GF%F6F;#F6F'F6F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"QG6\"6#\"\"%f*6(I$t_1GF%I$t_2GF%I$t_3GF%I $t_4GF%I$t_5GF%I$t_6GF%F%6$I)operatorGF%I&arrowGF%F%,,*&I#C1GF%\"\"\"9 &F6F6*(I#C2GF%F69'F69)#!\"\"\"\"'#\"\"$F'*(F9F69(\"\"#F;#!\"(F>#!\"$\" #]*(I#C3GF%F6FBF6F;#F=F@#F@\"\"&*&I#C4GF%F6F;#F6FCF6F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"QG6\"6#\"\"&f*6(I$t_1GF%I$t_2GF%I$t_3GF%I$t _4GF%I$t_5GF%I$t_6GF%F%6$I)operatorGF%I&arrowGF%F%,(*&I#C1GF%\"\"\"9'F 6F6*(I#C2GF%F69(F69)#!\"\"\"\"'#\"\"%F'*&I#C3GF%F6F;#\"\"#\"\"$F6F%F%F %" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"QG6\"6#\"\"'f*6(I$t_1GF%I$t_2G F%I$t_3GF%I$t_4GF%I$t_5GF%I$t_6GF%F%6$I)operatorGF%I&arrowGF%F%,&*&I#C 1GF%\"\"\"9(F6F6*&I#C2GF%F69)#\"\"&F'F6F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"QG6\"6#\"\"(f*6(I$t_1GF%I$t_2GF%I$t_3GF%I$t_4GF%I$t_ 5GF%I$t_6GF%F%6$I)operatorGF%I&arrowGF%F%*&I#C1GF%\"\"\"9)F5F%F%F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "7F/\"\"!F$F#F#F#F#F#F#F#F#F#F#F#F#F#F#F# F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "FMatrix:=Matrix(rs-1,rs-1,0):\n" }{MPLTEXT 1 0 95 "fo r i from 1 to rs-1 do for j from 1 to rs-1 do if j<=i then FMatrix[i,j ]:=f[i,j]: fi: od: od:\n" }{MPLTEXT 1 0 9 "FMatrix;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "CMatrix:=Matrix(rs-1,1,0):\n" }{MPLTEXT 1 0 18 "CMatrix[1,1]:=C1:\n" }{MPLTEXT 1 0 18 "CMatrix[2,1]:=C2:\n" } {MPLTEXT 1 0 18 "CMatrix[3,1]:=C3:\n" }{MPLTEXT 1 0 18 "CMatrix[4,1]:= C4:\n" }{MPLTEXT 1 0 18 "CMatrix[5,1]:=C5:\n" }{MPLTEXT 1 0 17 "CMatri x[6,1]:=C6:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "CMatrix;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "QMatrix:=Matrix(rs- 1,1,0):\n" }{MPLTEXT 1 0 48 "for i from 1 to rs-1 do QMatrix[i,1]:=Q[r s+1-i](" }{MPLTEXT 1 0 35 "t[1], t[2], t[3], t[4], t[5], t[6])" } {MPLTEXT 1 0 6 ": od:\n" }{MPLTEXT 1 0 9 "QMatrix:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6 #/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$ 6:-I$mtrGF$6+-I$mtdGF$6(-I%msubGF$6%-I#miGF$6&Q\"fF'/%'italicGQ%trueF' /%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'italicF'-F,6%-I#mnGF$6%Q\"1F 'FA/FEQ'normalF'-I#moGF$6.Q\",F'FAFM/%&fenceGQ&falseF'/%*separatorGF@/ %)stretchyGFU/%*symmetricGFU/%(largeopGFU/%.movablelimitsGFU/%'accentG FU/%'lspaceGQ&0.0emF'/%'rspaceGQ,0.3333333emF'FI/%/subscriptshiftGQ\"0 F'/%)rowalignGQ!F'/%,columnalignGFgo/%+groupalignGFgo/%(rowspanGFL/%+c olumnspanGFL-F56(-FJ6%FdoFAFMFeoFhoFjoF\\pF^pF`pF`pF`pF`pFeoFhoFjo-F26 +-F56(-F86%F:-F,6%-FJ6%Q\"2F'FAFMFOFIFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F ,6%F\\qFOF\\qFboFeoFhoFjoF\\pF^pF`pF`pF`pF`pFeoFhoFjo-F26+-F56(-F86%F: -F,6%-FJ6%Q\"3F'FAFMFOFIFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%F]rFOF\\qF boFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%F]rFOF]rFboFeoFhoFjoF\\pF^pF`pF`pF` pFeoFhoFjo-F26+-F56(-F86%F:-F,6%-FJ6%Q\"4F'FAFMFOFIFboFeoFhoFjoF\\pF^p -F56(-F86%F:-F,6%FdsFOF\\qFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%FdsFOF]r FboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%FdsFOFdsFboFeoFhoFjoF\\pF^pF`pF`pF eoFhoFjo-F26+-F56(-F86%F:-F,6%-FJ6%Q\"5F'FAFMFOFIFboFeoFhoFjoF\\pF^p-F 56(-F86%F:-F,6%FauFOF\\qFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%FauFOF]rFb oFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%FauFOFdsFboFeoFhoFjoF\\pF^p-F56(-F86 %F:-F,6%FauFOFauFboFeoFhoFjoF\\pF^pF`pFeoFhoFjo-F26+-F56(-F86%F:-F,6%- FJ6%Q\"6F'FAFMFOFIFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%FdwFOF\\qFboFeoF hoFjoF\\pF^p-F56(-F86%F:-F,6%FdwFOF]rFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F ,6%FdwFOFdsFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%FdwFOFauFboFeoFhoFjoF \\pF^p-F56(-F86%F:-F,6%FdwFOFdwFboFeoFhoFjoF\\pF^pFeoFhoFjo/%&alignGQ% axisF'/FfoQ)baselineF'/FioQ'centerF'/F[pQ'|frleft|hrF'/%/alignmentscop eGF@/%,columnwidthGQ%autoF'/%&widthGFbz/%+rowspacingGQ&1.0exF'/%.colum nspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF][l/%&frameGF][l /%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFU/%-equalcolumnsGFU/%-dis playstyleGFU/%%sideGQ&rightF'/%0minlabelspacingGFjzFAFM/%%openGQ\"[F'/ %&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+module nameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$6:-I$mtrGF $6&-I$mtdGF$6(-I#miGF$6&Q#C1F'/%'italicGQ%trueF'/%+foregroundGQ([0,0,0 ]F'/%,mathvariantGQ'italicF'/%)rowalignGQ!F'/%,columnalignGFF/%+groupa lignGFF/%(rowspanGQ\"1F'/%+columnspanGFMFDFGFI-F26&-F56(-F86&Q#C2F'F;F >FAFDFGFIFKFNFDFGFI-F26&-F56(-F86&Q#C3F'F;F>FAFDFGFIFKFNFDFGFI-F26&-F5 6(-F86&Q#C4F'F;F>FAFDFGFIFKFNFDFGFI-F26&-F56(-F86&Q#C5F'F;F>FAFDFGFIFK FNFDFGFI-F26&-F56(-F86&Q#C6F'F;F>FAFDFGFIFKFNFDFGFI/%&alignGQ%axisF'/F EQ)baselineF'/FHQ'centerF'/FJQ'|frleft|hrF'/%/alignmentscopeGF=/%,colu mnwidthGQ%autoF'/%&widthGFjp/%+rowspacingGQ&1.0exF'/%.columnspacingGQ& 0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFeq/%&frameGFeq/%-framespaci ngGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGF_r/%-displays tyleGF_r/%%sideGQ&rightF'/%0minlabelspacingGFbqF>/FBQ'normalF'/%%openG Q\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "fo r i from 1 to rs-1 do f[i,1]:=t[rs-i]: od: \n" }{MPLTEXT 1 0 60 "for j from 1 to rs-1 do f[j,j]:=t[rs-1]^((rs-j)/(rs-1)): od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 24 "for j from 1 to rs-2 do " }{MPLTEXT 1 0 62 "f[j+1,j]:= (rs-j-1)/(rs-2)*t[rs-1]^((1-j)/(rs-1))*t[rs-2]: od:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 54 "f[4,2]:=(3*(25*t[4]*t[6]-2*t[5]^ 2))/(100*t[6]^(7/6));\n" }{MPLTEXT 1 0 49 "f[5,3]:=(25*t[4]*t[6]-4*t[5 ]^2)/(50*t[6]^(4/3));\n" }{MPLTEXT 1 0 50 "f[6,4]:=(25*t[4]*t[6]-6*t[5 ]^2)/(100*t[6]^(3/2));\n" }{MPLTEXT 1 0 73 "f[5,2]:=(500*t[3]*t[6]^2-7 5*t[4]*t[5]*t[6]+14*t[5]^3)/(750*t[6]^(13/6));\n" }{MPLTEXT 1 0 72 "f[ 6,3]:=(250*t[3]*t[6]^2-75*t[4]*t[5]*t[6]+16*t[5]^3)/(750*t[6]^(7/3)); \n" }{MPLTEXT 1 0 123 "f[6,2]:=(30000*t[2]*t[6]^3-4000*t[3]*t[5]*t[6]^ 2-1875*t[4]^2*t[6]^2+2100*t[4]*t[5]^2*t[6]-364*t[5]^4)/(60000*t[6]^(19 /6));\n" }{MPLTEXT 1 0 44 "simplify(Multiply(FMatrix,CMatrix)-QMatrix) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"fG6\"6$\"\"%\"\"#,$*&,&*&&I\"t GF%6#F'\"\"\"&F.6#\"\"'F0\"#D*$&F.6#\"\"&F(!\"#F0F1#!\"(F3#\"\"$\"$+\" " }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"fG6\"6$\"\"&\"\"$,$*&,&*&&I\"tG F%6#\"\"%\"\"\"&F.6#\"\"'F1\"#D*$&F.6#F'\"\"#!\"%F1F2#F:F(#F1\"#]" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I\"fG6\"6$\"\"'\"\"%,$*&,&*&&I\"tGF%6# F(\"\"\"&F.6#F'F0\"#D*$&F.6#\"\"&\"\"#!\"'F0F1#!\"$F8#F0\"$+\"" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I\"fG6\"6$\"\"&\"\"#,$*&,(*&&I\"tGF%6# \"\"$\"\"\"&F.6#\"\"'F(\"$+&*(&F.6#\"\"%F1&F.6#F'F1F2F1!#v*$F:F0\"#9F1 F2#!#8F4#F1\"$](" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"fG6\"6$\"\"'\" \"$,$*&,(*&&I\"tGF%6#F(\"\"\"&F.6#F'\"\"#\"$]#*(&F.6#\"\"%F0&F.6#\"\"& F0F1F0!#v*$F9F(\"#;F0F1#!\"(F(#F0\"$](" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"fG6\"6$\"\"'\"\"#,$*&,,*&&I\"tGF%6#F(\"\"\"&F.6#F'\"\"$\"&++$*( &F.6#F3F0&F.6#\"\"&F0F1F(!%+S*&&F.6#\"\"%F(F1F(!%v=*(F=F0F8F(F1F0\"%+@ *$F8F?!$k$F0F1#!#>F'#F0\"&++'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfen cedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtab leGF$6:-I$mtrGF$6&-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F' /%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalig nGFC/%(rowspanGQ\"1F'/%+columnspanGFJFAFDFFF1F1F1F1F1/%&alignGQ%axisF' /FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF' /%,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspa cingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-fra mespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-d isplaystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&cl oseGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart:\n" } {MPLTEXT 1 0 20 "with(LinearAlgebra):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "rinfty:=8:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 31 "list0:=seq(t[i],i=1..rinfty-3);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 37 "Minfty:=Matrix(rinfty-4,rinfty-4,0):\n" }{MPLTEXT 1 0 48 "for i from 1 to rinfty-4 do Minfty[i,i]:=1: od:\n" }{MPLTEXT 1 0 50 "for i from 1 to rinfty-5 do Minfty[i+1,i]:=0: od:\n" }{MPLTEXT 1 0 116 "for i from 1 to rinfty-4 do for j from 1 to rinfty-4 do if j <=i-2 then Minfty[i,j]:=t[rinfty-(i-j+1)]: fi: od: od:\n" }{MPLTEXT 1 0 7 "Minfty;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 41 "DiagoInfty:=Mat rix(rinfty-4,rinfty-4,0):\n" }{MPLTEXT 1 0 67 "for i from 1 to rinfty- 4 do DiagoInfty[i,i]:= 1/(rinfty-3-i): od: \n" }{MPLTEXT 1 0 12 "Diago Infty;\n" }{MPLTEXT 1 0 42 "DiagoInfty2:=Matrix(rinfty-4,rinfty-4,0): \n" }{MPLTEXT 1 0 68 "for i from 1 to rinfty-4 do DiagoInfty2[i,i]:= 1 /(rinfty-2-i): od: \n" }{MPLTEXT 1 0 12 "DiagoInfty2;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 40 "RHSMatrix:=Matrix(rinfty -4,rinfty-4,0):\n" }{MPLTEXT 1 0 28 "for i from 1 to rinfty-4 do " } {MPLTEXT 1 0 22 "RHSMatrix[i,i]:=1: od:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 128 "for i from 1 to rinfty-4 do for j from 1 to rinfty-4 do if j<=i-1 then RHSMatrix[i,j]:=Qinf[rinfty-3-(i-j)](list0): fi: od : od:\n" }{MPLTEXT 1 0 11 "RHSMatrix;\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 46 "deltaQinfMatrix:=Matrix(rinfty-4,rinfty-4,0):\n" } {MPLTEXT 1 0 56 "for i from 1 to rinfty-4 do for j from 1 to rinfty-4 \+ do\n" }{MPLTEXT 1 0 6 "deltaQ" }{MPLTEXT 1 0 3 "inf" }{MPLTEXT 1 0 58 "Matrix[i,j]:=diff(Qinf[rinfty-4-i](list0),t[rinfty-2-j]):\n" } {MPLTEXT 1 0 8 "od: od:\n" }{MPLTEXT 1 0 16 "deltaQinfMatrix;" } {MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&list0G6\"6'&I\" tGF$6#\"\"\"&F'6#\"\"#&F'6#\"\"$&F'6#\"\"%&F'6#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6'-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6)-I$mtdGF$6(-I#mnGF$6%Q\"1F'/% +foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,col umnalignGFC/%+groupalignGFC/%(rowspanGF:/%+columnspanGF:-F56(-F86%Q\"0 F'F;F>FAFDFFFHFJFLFLFAFDFF-F26)FLF4FLFLFAFDFF-F26)-F56(-I%msubGF$6%-I# miGF$6&Q\"tF'/%'italicGQ%trueF'F;/F?Q'italicF'-F,6#-F86%Q\"5F'F;F>/%/s ubscriptshiftGFPFAFDFFFHFJFLF4FLFAFDFF-F26)-F56(-FX6%FZ-F,6#-F86%Q\"4F 'F;F>FboFAFDFFFHFJFUFLF4FAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEQ'cen terF'/FGQ'|frleft|hrF'/%/alignmentscopeGFjn/%,columnwidthGQ%autoF'/%&w idthGF\\q/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesG Q%noneF'/%,columnlinesGFgq/%&frameGFgq/%-framespacingGQ,0.4em~0.5exF'/ %*equalrowsGQ&falseF'/%-equalcolumnsGFar/%-displaystyleGFar/%%sideGQ&r ightF'/%0minlabelspacingGFdqF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6)-I$mtdGF$6(-I&m fracGF$6)-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'nor malF'-F;6%Q\"4F'F>FA/%.linethicknessGF=/%+denomalignGQ'centerF'/%)numa lignGFK/%)bevelledGQ&falseF'F>/%)rowalignGQ!F'/%,columnalignGFS/%+grou palignGFS/%(rowspanGF=/%+columnspanGF=-F56(-F;6%Q\"0F'F>FAFQFTFVFXFZFf nFfnFQFTFV-F26)Ffn-F56(-F86)F:-F;6%Q\"3F'F>FAFGFIFLFNF>FQFTFVFXFZFfnFf nFQFTFV-F26)FfnFfn-F56(-F86)F:-F;6%Q\"2F'F>FAFGFIFLFNF>FQFTFVFXFZFfnFQ FTFV-F26)FfnFfnFfn-F56(F:FQFTFVFXFZFQFTFV/%&alignGQ%axisF'/FRQ)baselin eF'/FUFK/FWQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%au toF'/%&widthGF^q/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)ro wlinesGQ%noneF'/%,columnlinesGFiq/%&frameGFiq/%-framespacingGQ,0.4em~0 .5exF'/%*equalrowsGFP/%-equalcolumnsGFP/%-displaystyleGFP/%%sideGQ&rig htF'/%0minlabelspacingGFfqF>FA/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI( _syslibGF'6'-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6)-I$mtdGF$6(-I&mfracGF $6)-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'- F;6%Q\"5F'F>FA/%.linethicknessGF=/%+denomalignGQ'centerF'/%)numalignGF K/%)bevelledGQ&falseF'F>/%)rowalignGQ!F'/%,columnalignGFS/%+groupalign GFS/%(rowspanGF=/%+columnspanGF=-F56(-F;6%Q\"0F'F>FAFQFTFVFXFZFfnFfnFQ FTFV-F26)Ffn-F56(-F86)F:-F;6%Q\"4F'F>FAFGFIFLFNF>FQFTFVFXFZFfnFfnFQFTF V-F26)FfnFfn-F56(-F86)F:-F;6%Q\"3F'F>FAFGFIFLFNF>FQFTFVFXFZFfnFQFTFV-F 26)FfnFfnFfn-F56(-F86)F:-F;6%Q\"2F'F>FAFGFIFLFNF>FQFTFVFXFZFQFTFV/%&al ignGQ%axisF'/FRQ)baselineF'/FUFK/FWQ'|frleft|hrF'/%/alignmentscopeGQ%t rueF'/%,columnwidthGQ%autoF'/%&widthGFcq/%+rowspacingGQ&1.0exF'/%.colu mnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF^r/%&frameGF^r/ %-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFP/%-equalcolumnsGFP/%-disp laystyleGFP/%%sideGQ&rightF'/%0minlabelspacingGF[rF>FA/%%openGQ\"[F'/% &closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulen ameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$ 6)-I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ 'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGF :/%+columnspanGF:-F56(-F86%Q\"0F'F;F>FAFDFFFHFJFLFLFAFDFF-F26)-F56(-F, 6%-I%msubGF$6%-I#miGF$6&Q%QinfF'/%'italicGQ%trueF'F;/F?Q'italicF'-F,6# -F86%Q\"4F'F;F>/%/subscriptshiftGFP-I#moGF$6-Q0⁡F'F>/%&f enceGQ&falseF'/%*separatorGFjo/%)stretchyGFjo/%*symmetricGFjo/%(largeo pGFjo/%.movablelimitsGFjo/%'accentGFjo/%'lspaceGQ&0.0emF'/%'rspaceGFip -F#6%-F,6+-FX6%-Fen6&Q\"tF'FhnF;F[o-F,6#F7Fbo-Feo6.Q\",F'F;F>Fho/F\\pF jnF]pF_pFapFcpFepFgp/F[qQ,0.3333333emF'-FX6%Fbq-F,6#-F86%Q\"2F'F;F>Fbo Fgq-FX6%Fbq-F,6#-F86%Q\"3F'F;F>FboFgq-FX6%FbqF]oFboFgq-FX6%Fbq-F,6#-F8 6%Q\"5F'F;F>FboF;F>FAFDFFFHFJF4FLFLFAFDFF-F26)-F56(-F,6%-FX6%FZFfrFboF doF\\qFAFDFFFHFJFSF4FLFAFDFF-F26)-F56(-F,6%-FX6%FZF_rFboFdoF\\qFAFDFFF HFJFfsFSF4FAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEQ'centerF'/FGQ'|frl eft|hrF'/%/alignmentscopeGFjn/%,columnwidthGQ%autoF'/%&widthGFau/%+row spacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,colu mnlinesGF\\v/%&frameGF\\v/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGF jo/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sideGQ&rightF'/%0minlabelsp acingGFiuF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6)-I$mtdGF$6(-F,6%-I&mfracGF$6)-F, 6#-I#moGF$6.Q+∂F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'no rmalF'/%&fenceGQ&falseF'/%*separatorGFJ/%)stretchyGFJ/%*symmetricGFJ/% (largeopGFJ/%.movablelimitsGFJ/%'accentGFJ/%'lspaceGQ&0.0emF'/%'rspace GFY-F,6#-F,6$F>-I%msubGF$6%-I#miGF$6&Q\"tF'/%'italicGQ%trueF'FB/FFQ'it alicF'-F,6#-I#mnGF$6%Q\"5F'FBFE/%/subscriptshiftGQ\"0F'/%.linethicknes sGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFdp/%)bevelledGFJFB-F?6-Q1 ⁢F'FEFHFKFMFOFQFSFUFWFZ-F,6%-F[o6%-F^o6&Q%QinfF'FaoFBFd 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Fdt-F56(-F,6%FjtFipFfyF[tF^tF`tFbtFdt-F56(-F,6%FduFipFfyF[tF^tF`tFbtFd t-F56(-F,6%F^vFipFfyF[tF^tF`tFbtFdtF[tF^tF`t/%&alignGQ%axisF'/F\\tQ)ba selineF'/F_tFdp/FatQ'|frleft|hrF'/%/alignmentscopeGFco/%,columnwidthGQ %autoF'/%&widthGFf[l/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/ %)rowlinesGQ%noneF'/%,columnlinesGFa\\l/%&frameGFa\\l/%-framespacingGQ ,0.4em~0.5exF'/%*equalrowsGFJ/%-equalcolumnsGFJ/%-displaystyleGFJ/%%si deGQ&rightF'/%0minlabelspacingGF^\\lFBFE/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "SystemEquationInf:=[]:\n " }{MPLTEXT 1 0 56 "for i from 1 to rinfty-4 do for j from 1 to rinfty -4 do\n" }{MPLTEXT 1 0 61 "SystemEquationInf:=[op(SystemEquationInf),( Multiply(Multiply(" }{MPLTEXT 1 0 6 "Minfty" }{MPLTEXT 1 0 1 "," } {MPLTEXT 1 0 12 "DiagoInfty)," }{MPLTEXT 1 0 36 "deltaQinfMatrix)-Mult iply(RHSMatrix," }{MPLTEXT 1 0 12 "DiagoInfty2)" }{MPLTEXT 1 0 19 ")[i ,j]=0]: od: od:\n" }{MPLTEXT 1 0 19 "SystemEquationInf:\n" }{MPLTEXT 1 0 33 "pdsolve(\{op(SystemEquationInf)\});" }{MPLTEXT 1 0 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "<'/-&I%QinfG6\"6#\"\"!6'&I\"tGF'6#\"\"\" &F,6#\"\"#&F,6#\"\"$&F,6#\"\"%&F,6#\"\"&,.*&,&*$F8F1!#7F2\"$+\"F.-I$_F 2GF'6#F+F.#F.\"$!=*&F5F.F8F.#!\"\"\"#?*&F5F.-I$_F1GF'FCF.#F.F7*&-I$_F3 GF'FCF.F8F.#F.F:F/#F.F1-I$_F5GF'FCF./-&F&F-F*,,F2#F1F4*&FAF.F5F.#F:\" \"'F>#FH\"#D*&FKF.F8F.#F1F:-I$_F4GF'FCF./-&F&F0F*,(F5#F4F7*&FAF.F8F.F. FOF./-&F&F3F*,&F8#F7F:FKF./-&F&F6F*,$FA#F:F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "F2(t[1]):=3/5*U4;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 158 "Qinf[0](t[1], t[2], t[3], t[4], t[5]) := (1/180)*(-12*t[5]^2 +100*t[3])*F2(t[1])-(1/20)*t[4]*t[5]+(1/4)*t[4]*F1(t[1])+(1/5)*F3(t[1] )*t[5]+(1/2)*t[2]+F5(t[1]);\n" }{MPLTEXT 1 0 122 "Qinf[1](t[1], t[2], \+ t[3], t[4], t[5]) := 2*t[3]*(1/3)+5*F2(t[1])*t[4]*(1/6)-(1/25)*t[5]^2+ 2*F1(t[1])*t[5]*(1/5)+F4(t[1]);\n" }{MPLTEXT 1 0 79 "Qinf[2](t[1], t[2 ], t[3], t[4], t[5]) := 3*t[4]*(1/4)+F2(t[1])*t[5]+F3(t[1]); \n" } {MPLTEXT 1 0 64 "Qinf[3](t[1], t[2], t[3], t[4], t[5]) := 4*t[5]*(1/5) +F1(t[1]);\n" }{MPLTEXT 1 0 59 "Qinf[4](t[1], t[2], t[3], t[4], t[5]) \+ := 5*F2(t[1])*(1/3);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 19 " SystemEquationInf);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-I#F2G6\"6#&I\"t GF%6#\"\"\",$I#U4GF%#\"\"$\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-&I% QinfG6\"6#\"\"!6'&I\"tGF&6#\"\"\"&F+6#\"\"#&F+6#\"\"$&F+6#\"\"%&F+6#\" \"&,.*&,&*$F7F0!#7F1\"$+\"F-I#U4GF&F-#F-\"$+$*&F4F-F7F-#!\"\"\"#?*&F4F --I#F1GF&6#F*F-#F-F6*&-I#F3GF&FJF-F7F-#F-F9F.#F-F0-I#F5GF&FJF-" }} {PARA 11 "" 1 "" {XPPMATH 20 ">-&I%QinfG6\"6#\"\"\"6'&I\"tGF&F'&F+6#\" \"#&F+6#\"\"$&F+6#\"\"%&F+6#\"\"&,,F/#F.F1*&I#U4GF&F(F2F(#F(F.*$F5F.#! \"\"\"#D*&-I#F1GF&6#F*F(F5F(#F.F7-I#F4GF&FDF(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-&I%QinfG6\"6#\"\"#6'&I\"tGF&6#\"\"\"&F+F'&F+6#\"\"$&F+6 #\"\"%&F+6#\"\"&,(F2#F1F4*&I#U4GF&F-F5F-#F1F7-I#F3GF&6#F*F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-&I%QinfG6\"6#\"\"$6'&I\"tGF&6#\"\"\"&F+6#\" \"#&F+F'&F+6#\"\"%&F+6#\"\"&,&F5#F4F7-I#F1GF&6#F*F-" }}{PARA 11 "" 1 " " {XPPMATH 20 ">-&I%QinfG6\"6#\"\"%6'&I\"tGF&6#\"\"\"&F+6#\"\"#&F+6#\" \"$&F+F'&F+6#\"\"&I#U4GF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "72/\"\"!F$F #F#F#F#F#F#F#F#F#F#F#F#F#F#F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "GMatrix:=Matrix(rinfty-2," }{MPLTEXT 1 0 8 "rinfty-2" }{MPLTEXT 1 0 5 ",0):\n" }{MPLTEXT 1 0 16 "for i from 1 to " }{MPLTEXT 1 0 8 "ri nfty-2" }{MPLTEXT 1 0 20 " do for j from 1 to " }{MPLTEXT 1 0 8 "rinft y-2" }{MPLTEXT 1 0 51 " do if j<=i then GMatrix[i,j]:=g[i,j]: fi: od: \+ od:\n" }{MPLTEXT 1 0 9 "GMatrix;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "UMatrix:=Matrix(rinfty-2,1,0):\n" }{MPLTEXT 1 0 16 "UMatrix[1,1] :=1:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "UMatrix[2,1]:=U4:\n" } {MPLTEXT 1 0 18 "UMatrix[3,1]:=U3:\n" }{MPLTEXT 1 0 18 "UMatrix[4,1]:= U2:\n" }{MPLTEXT 1 0 17 "UMatrix[5,1]:=U1:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 17 "UMatrix[6,1]:=U0:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "UMatrix;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 34 "QinfMatrix:=Ma trix(rinfty-2,1,0):\n" }{MPLTEXT 1 0 19 "QinfMatrix[1,1]:=1:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 29 "for i from 2 to rinfty-2 do Q" } {MPLTEXT 1 0 3 "inf" }{MPLTEXT 1 0 36 "Matrix[i,1]:=Qinf[rinfty-2-i](l ist0)" }{MPLTEXT 1 0 6 ": od:\n" }{MPLTEXT 1 0 1 "Q" }{MPLTEXT 1 0 3 " inf" }{MPLTEXT 1 0 7 "Matrix;" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$6:-I$mtrGF$6+-I$mtdGF$6(-I%msubGF$6%-I#miGF$6 &Q\"gF'/%'italicGQ%trueF'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'ita licF'-F,6%-I#mnGF$6%Q\"1F'FA/FEQ'normalF'-I#moGF$6.Q\",F'FAFM/%&fenceG Q&falseF'/%*separatorGF@/%)stretchyGFU/%*symmetricGFU/%(largeopGFU/%.m ovablelimitsGFU/%'accentGFU/%'lspaceGQ&0.0emF'/%'rspaceGQ,0.3333333emF 'FI/%/subscriptshiftGQ\"0F'/%)rowalignGQ!F'/%,columnalignGFgo/%+groupa lignGFgo/%(rowspanGFL/%+columnspanGFL-F56(-FJ6%FdoFAFMFeoFhoFjoF\\pF^p F`pF`pF`pF`pFeoFhoFjo-F26+-F56(-F86%F:-F,6%-FJ6%Q\"2F'FAFMFOFIFboFeoFh oFjoF\\pF^p-F56(-F86%F:-F,6%F\\qFOF\\qFboFeoFhoFjoF\\pF^pF`pF`pF`pF`pF eoFhoFjo-F26+-F56(-F86%F:-F,6%-FJ6%Q\"3F'FAFMFOFIFboFeoFhoFjoF\\pF^p-F 56(-F86%F:-F,6%F]rFOF\\qFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%F]rFOF]rFb oFeoFhoFjoF\\pF^pF`pF`pF`pFeoFhoFjo-F26+-F56(-F86%F:-F,6%-FJ6%Q\"4F'FA FMFOFIFboFeoFhoFjoF\\pF^p-F56(-F86%F:-F,6%FdsFOF\\qFboFeoFhoFjoF\\pF^p 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GFjzFAFM/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6 #-I'mtableGF$6:-I$mtrGF$6&-I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([ 0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+g roupalignGFC/%(rowspanGF:/%+columnspanGF:FAFDFF-F26&-F56(-I#miGF$6&Q#U 4F'/%'italicGQ%trueF'F;/F?Q'italicF'FAFDFFFHFJFAFDFF-F26&-F56(-FQ6&Q#U 3F'FTF;FWFAFDFFFHFJFAFDFF-F26&-F56(-FQ6&Q#U2F'FTF;FWFAFDFFFHFJFAFDFF-F 26&-F56(-FQ6&Q#U1F'FTF;FWFAFDFFFHFJFAFDFF-F26&-F56(-FQ6&Q#U0F'FTF;FWFA FDFFFHFJFAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEQ'centerF'/FGQ'|frlef t|hrF'/%/alignmentscopeGFV/%,columnwidthGQ%autoF'/%&widthGF\\q/%+rowsp acingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,column linesGFgq/%&frameGFgq/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&fal seF'/%-equalcolumnsGFar/%-displaystyleGFar/%%sideGQ&rightF'/%0minlabel spacingGFdqF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$6:-I$mtrGF$6&-I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+fo regroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,column alignGFC/%+groupalignGFC/%(rowspanGF:/%+columnspanGF:FAFDFF-F26&-F56(- I#miGF$6&Q#U4F'/%'italicGQ%trueF'F;/F?Q'italicF'FAFDFFFHFJFAFDFF-F26&- F56(-F,6%-F,6%-I&mfracGF$6)-F86%Q\"4F'F;F>-F86%Q\"5F'F;F>/%.linethickn essGF:/%+denomalignGQ'centerF'/%)numalignGFho/%)bevelledGQ&falseF'F;-I #moGF$6-Q1⁢F'F>/%&fenceGF]p/%*separatorGF]p/%)stretchyG F]p/%*symmetricGF]p/%(largeopGF]p/%.movablelimitsGF]p/%'accentGF]p/%'l spaceGQ&0.0emF'/%'rspaceGFbq-F,6#-I%msubGF$6%-FQ6&Q\"tF'FTF;FW-F,6#Fao /%/subscriptshiftGQ\"0F'-F_p6.Q\"+F'F;F>FbpFdpFfpFhpFjpF\\qF^q/FaqQ,0. 2222222emF'/FdqFfr-F,6%-FQ6&Q#F1F'FTF;FW-F_p6-Q0⁡F'F>Fbp FdpFfpFhpFjpF\\qF^qF`qFcq-F#6%-F,6#-Fhq6%Fjq-F,6#F7F_rF;F>FAFDFFFHFJFA FDFF-F26&-F56(-F,6'-F,6%-F\\o6)-F86%Q\"3F'F;F>F^oFdoFfoFioF[pF;F^p-F,6 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'/FEFho/FGQ'|frleft|hrF'/%/alignmentscopeGFV/%,columnwidthGQ%autoF'/%& widthGFi]l/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlines GQ%noneF'/%,columnlinesGFd^l/%&frameGFd^l/%-framespacingGQ,0.4em~0.5ex F'/%*equalrowsGF]p/%-equalcolumnsGF]p/%-displaystyleGF]p/%%sideGQ&righ tF'/%0minlabelspacingGFa^lF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "F1(t[1]):=U3;\n" }{MPLTEXT 1 0 13 "F2(t[1]):=0;\n" }{MPLTEXT 1 0 13 "F3(t[1]):=U2;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 13 "F4(t[1]):=U1;" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 13 "F5(t[1]):=U0;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 43 "for i from 1 to rinfty-2 do g[i,i]:=1: od:\n" }{MPLTEXT 1 0 45 "for i from 1 to rinfty-3 do g[i+1,i]:=0: od:\n" }{MPLTEXT 1 0 18 "g[3,1]:=4 /5*t[5];\n" }{MPLTEXT 1 0 18 "g[4,2]:=3/5*t[5];\n" }{MPLTEXT 1 0 18 "g [5,3]:=2/5*t[5];\n" }{MPLTEXT 1 0 17 "g[6,4]:=1/5*t[5];" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "g[4,1]:=3/4*t[4];\n" } {MPLTEXT 1 0 20 "g[5,2]:=(1/2)*t[4];\n" }{MPLTEXT 1 0 20 "g[6,3]:=(1/4 )*t[4];\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 36 "g[5,1]:=2*t[3]*(1/3) -(1/25)*t[5]^2;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 35 "g[6,2]:=-(1/ 25)*t[5]^2+(1/3)*t[3];\n" }{MPLTEXT 1 0 38 "g[6,1]:=-(1/20)*t[4]*t[5]+ (1/2)*t[2];\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 47 "simplify(Multipl y(GMatrix,UMatrix)-QinfMatrix);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-I#F1G6\"6#&I\"tGF%6#\"\"\"I#U3GF%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-I#F2G6\"6#&I\"tGF%6#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-I#F3G6\"6#&I\"tGF%6#\"\"\"I#U2GF%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-I#F4G6\"6#&I\"tGF%6#\"\"\"I#U1GF%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-I#F5G6\"6#&I\"tGF%6#\"\"\"I#U0GF%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"$\"\"\",$&I\"tGF%6#\"\"&#\"\"%F-" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"%\"\"#,$&I\"tGF%6#\"\"&# \"\"$F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"&\"\"$,$&I\"t GF%6#F'#\"\"#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"'\"\" %,$&I\"tGF%6#\"\"&#\"\"\"F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6 \"6$\"\"%\"\"\",$&I\"tGF%6#F'#\"\"$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"&\"\"#,$&I\"tGF%6#\"\"%#\"\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"'\"\"$,$&I\"tGF%6#\"\"%#\"\"\"F-" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"&\"\"\",&&I\"tGF%6#\"\"$ #\"\"#F-*$&F+6#F'F/#!\"\"\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG 6\"6$\"\"'\"\"#,&*$&I\"tGF%6#\"\"&F(#!\"\"\"#D&F,6#\"\"$#\"\"\"F4" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"'\"\"\",&*&&I\"tGF%6#\" \"%F(&F,6#\"\"&F(#!\"\"\"#?&F,6#\"\"##F(F7" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$6:-I$mtrGF$6&-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+fo regroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,column alignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJFAFDFFF1F1F1F 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od:\n" }{MPLTEXT 1 0 116 "for i from 1 to rinfty-3 do for j fr om 1 to rinfty-3 do if j<=i-2 then Minfty[i,j]:=t[rinfty-(i-j+1)]: fi : od: od:\n" }{MPLTEXT 1 0 8 "Minfty;\n" }{MPLTEXT 1 0 41 "DiagoInfty: =Matrix(rinfty-3,rinfty-3,0):\n" }{MPLTEXT 1 0 67 "for i from 1 to rin fty-3 do DiagoInfty[i,i]:= 1/(rinfty-2-i): od: \n" }{MPLTEXT 1 0 12 "D iagoInfty;\n" }{MPLTEXT 1 0 42 "DiagoInfty2:=Matrix(rinfty-3,rinfty-3, 0):\n" }{MPLTEXT 1 0 68 "for i from 1 to rinfty-3 do DiagoInfty2[i,i]: = 1/(rinfty-2-i): od: \n" }{MPLTEXT 1 0 13 "DiagoInfty2;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 40 "RHSMatrix:=Matrix(rinfty-3,rinfty-3,0):\n " }{MPLTEXT 1 0 52 "for i from 1 to rinfty-3 do RHSMatrix[i,i]:=-1: od :\n" }{MPLTEXT 1 0 125 "for i from 1 to rinfty-3 do for j from 1 to ri nfty-3 do if j<=i-2 then RHSMatrix[i,j]:=R[rinfty-2-(i-j)](list0): fi: od: od:\n" }{MPLTEXT 1 0 11 "RHSMatrix;\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 46 "deltaRinfMatrix:=Matrix(rinfty-3,rinfty-3,0):\n" } {MPLTEXT 1 0 56 "for i from 1 to rinfty-3 do for j from 1 to rinfty-3 \+ do\n" }{MPLTEXT 1 0 64 "deltaRinfMatrix[i,j]:=diff(R[rinfty-3-i](list0 ),t[rinfty-2-j]):\n" }{MPLTEXT 1 0 8 "od: od:\n" }{MPLTEXT 1 0 16 "del taRinfMatrix;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&list0G6\"6)&I\"tGF$6#\"\"\"&F'6#\"\"#&F'6#\"\"$& F'6#\"\"%&F'6#\"\"&&F'6#\"\"'&F'6#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowG F$6#-I'mtableGF$6;-I$mtrGF$6,-I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundG Q([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/ %+groupalignGFC/%(rowspanGF:/%+columnspanGF:-F56(-F86%Q\"0F'F;F>FAFDFF FHFJFLFLFLFLFLFAFDFF-F26,FLF4FLFLFLFLFLFAFDFF-F26,-F56(-I%msubGF$6%-I# miGF$6&Q\"tF'/%'italicGQ%trueF'F;/F?Q'italicF'-F,6#-F86%Q\"7F'F;F>/%/s ubscriptshiftGFPFAFDFFFHFJFLF4FLFLFLFLFAFDFF-F26,-F56(-FX6%FZ-F,6#-F86 %Q\"6F'F;F>FboFAFDFFFHFJFUFLF4FLFLFLFAFDFF-F26,-F56(-FX6%FZ-F,6#-F86%Q 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TFVFXFZFfnFfnFfnFfnFfnFQFTFV-F26,Ffn-F56(-F86)F:-F;6%Q\"6F'F>FAFGFIFLF NF>FQFTFVFXFZFfnFfnFfnFfnFfnFQFTFV-F26,FfnFfn-F56(-F86)F:-F;6%Q\"5F'F> FAFGFIFLFNF>FQFTFVFXFZFfnFfnFfnFfnFQFTFV-F26,FfnFfnFfn-F56(-F86)F:-F;6 %Q\"4F'F>FAFGFIFLFNF>FQFTFVFXFZFfnFfnFfnFQFTFV-F26,FfnFfnFfnFfn-F56(-F 86)F:-F;6%Q\"3F'F>FAFGFIFLFNF>FQFTFVFXFZFfnFfnFQFTFV-F26,FfnFfnFfnFfnF fn-F56(-F86)F:-F;6%Q\"2F'F>FAFGFIFLFNF>FQFTFVFXFZFfnFQFTFV-F26,FfnFfnF fnFfnFfnFfn-F56(F:FQFTFVFXFZFQFTFV/%&alignGQ%axisF'/FRQ)baselineF'/FUF K/FWQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%& widthGFir/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesG Q%noneF'/%,columnlinesGFds/%&frameGFds/%-framespacingGQ,0.4em~0.5exF'/ %*equalrowsGFP/%-equalcolumnsGFP/%-displaystyleGFP/%%sideGQ&rightF'/%0 minlabelspacingGFasF>FA/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6'-I%mrowGF$6#-I'mtableGF$6;-I$mtrGF$6,-I$mtdGF$6(-I&mfracGF$6)-I#mn 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olumnsGFP/%-displaystyleGFP/%%sideGQ&rightF'/%0minlabelspacingGFasF>FA /%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfen cedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtab leGF$6;-I$mtrGF$6,-I$mtdGF$6(-F,6$-I#moGF$6.Q*&uminus0;F'/%+foreground GQ([0,0,0]F'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separatorGFE /%)stretchyGFE/%*symmetricGFE/%(largeopGFE/%.movablelimitsGFE/%'accent GFE/%'lspaceGQ,0.2222222emF'/%'rspaceGFT-I#mnGF$6%Q\"1F'F=F@/%)rowalig nGQ!F'/%,columnalignGFgn/%+groupalignGFgn/%(rowspanGFZ/%+columnspanGFZ -F56(-FX6%Q\"0F'F=F@FenFhnFjnF\\oF^oF`oF`oF`oF`oF`oFenFhnFjn-F26,F`oF4 F`oF`oF`oF`oF`oFenFhnFjn-F26,-F56(-F,6%-I%msubGF$6%-I#miGF$6&Q\"RF'/%' italicGQ%trueF'F=/FAQ'italicF'-F,6#-FX6%Q\"6F'F=F@/%/subscriptshiftGFd o-F:6-Q0⁡F'F@FCFFFHFJFLFNFP/FSQ&0.0emF'/FVFdq-F#6%-F,6/- F^p6%-Fap6&Q\"tF'FdpF=Fgp-F,6#FWF^q-F:6.Q\",F'F=F@FC/FGFfpFHFJFLFNFPFc q/FVQ,0.3333333emF'-F^p6%F\\r-F,6#-FX6%Q\"2F'F=F@F^qFar-F^p6%F\\r-F,6# 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#-I'mtableGF$6;-I$mtrGF$6,-I$mtdGF$6(-F,6%-I&mfracGF$6)-F,6#-I#moGF$6. Q+∂F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%&fen ceGQ&falseF'/%*separatorGFJ/%)stretchyGFJ/%*symmetricGFJ/%(largeopGFJ/ %.movablelimitsGFJ/%'accentGFJ/%'lspaceGQ&0.0emF'/%'rspaceGFY-F,6#-F,6 $F>-I%msubGF$6%-I#miGF$6&Q\"tF'/%'italicGQ%trueF'FB/FFQ'italicF'-F,6#- I#mnGF$6%Q\"7F'FBFE/%/subscriptshiftGQ\"0F'/%.linethicknessGQ\"1F'/%+d enomalignGQ'centerF'/%)numalignGFdp/%)bevelledGFJFB-F?6-Q1&InvisibleTi mes;F'FEFHFKFMFOFQFSFUFWFZ-F,6%-F[o6%-F^o6&Q\"RF'FaoFBFdo-F,6#-Fio6%Q \"6F'FBFEF\\p-F?6-Q0⁡F'FEFHFKFMFOFQFSFUFWFZ-F#6%-F,6/-F[ o6%F]o-F,6#-Fio6%FapFBFEF\\p-F?6.Q\",F'FBFEFH/FLFcoFMFOFQFSFUFW/FenQ,0 .3333333emF'-F[o6%F]o-F,6#-Fio6%Q\"2F'FBFEF\\pFer-F[o6%F]o-F,6#-Fio6%Q \"3F'FBFEF\\pFer-F[o6%F]o-F,6#-Fio6%Q\"4F'FBFEF\\pFer-F[o6%F]o-F,6#-Fi o6%Q\"5F'FBFEF\\pFer-F[o6%F]oFcqF\\pFerFjnFBFE/%)rowalignGQ!F'/%,colum nalignGF[u/%+groupalignGF[u/%(rowspanGFap/%+columnspanGFap-F56(-F,6%-F :6)F<-F,6#-F,6$F>FgtF_pFbpFepFgpFBFipF\\qFitF\\uF^uF`uFbu-F56(-F,6%-F: 6)F<-F,6#-F,6$F>F`tF_pFbpFepFgpFBFipF\\qFitF\\uF^uF`uFbu-F56(-F,6%-F:6 )F<-F,6#-F,6$F>FisF_pFbpFepFgpFBFipF\\qFitF\\uF^uF`uFbu-F56(-F,6%-F:6) F<-F,6#-F,6$F>FbsF_pFbpFepFgpFBFipF\\qFitF\\uF^uF`uFbu-F56(-F,6%-F:6)F <-F,6#-F,6$F>F[sF_pFbpFepFgpFBFipF\\qFitF\\uF^uF`uFbu-F56(-F,6%-F:6)F< -F,6#-F,6$F>F_rF_pFbpFepFgpFBFipF\\qFitF\\uF^uF`uFbuFitF\\uF^u-F26,-F5 6(-F,6%F9Fip-F,6%-F[o6%F`qFbtF\\pFhqF[rFitF\\uF^uF`uFbu-F56(-F,6%FhuFi pFfyFitF\\uF^uF`uFbu-F56(-F,6%FbvFipFfyFitF\\uF^uF`uFbu-F56(-F,6%F\\wF ipFfyFitF\\uF^uF`uFbu-F56(-F,6%FfwFipFfyFitF\\uF^uF`uFbu-F56(-F,6%F`xF ipFfyFitF\\uF^uF`uFbu-F56(-F,6%FjxFipFfyFitF\\uF^uF`uFbuFitF\\uF^u-F26 ,-F56(-F,6%F9Fip-F,6%-F[o6%F`qF[tF\\pFhqF[rFitF\\uF^uF`uFbu-F56(-F,6%F huFipFh[lFitF\\uF^uF`uFbu-F56(-F,6%FbvFipFh[lFitF\\uF^uF`uFbu-F56(-F,6 %F\\wFipFh[lFitF\\uF^uF`uFbu-F56(-F,6%FfwFipFh[lFitF\\uF^uF`uFbu-F56(- F,6%F`xFipFh[lFitF\\uF^uF`uFbu-F56(-F,6%FjxFipFh[lFitF\\uF^uF`uFbuFitF \\uF^u-F26,-F56(-F,6%F9Fip-F,6%-F[o6%F`qFdsF\\pFhqF[rFitF\\uF^uF`uFbu- F56(-F,6%FhuFipFj]lFitF\\uF^uF`uFbu-F56(-F,6%FbvFipFj]lFitF\\uF^uF`uFb u-F56(-F,6%F\\wFipFj]lFitF\\uF^uF`uFbu-F56(-F,6%FfwFipFj]lFitF\\uF^uF` uFbu-F56(-F,6%F`xFipFj]lFitF\\uF^uF`uFbu-F56(-F,6%FjxFipFj]lFitF\\uF^u F`uFbuFitF\\uF^u-F26,-F56(-F,6%F9Fip-F,6%-F[o6%F`qF]sF\\pFhqF[rFitF\\u F^uF`uFbu-F56(-F,6%FhuFipF\\`lFitF\\uF^uF`uFbu-F56(-F,6%FbvFipF\\`lFit F\\uF^uF`uFbu-F56(-F,6%F\\wFipF\\`lFitF\\uF^uF`uFbu-F56(-F,6%FfwFipF \\`lFitF\\uF^uF`uFbu-F56(-F,6%F`xFipF\\`lFitF\\uF^uF`uFbu-F56(-F,6%Fjx FipF\\`lFitF\\uF^uF`uFbuFitF\\uF^u-F26,-F56(-F,6%F9Fip-F,6%-F[o6%F`qFa rF\\pFhqF[rFitF\\uF^uF`uFbu-F56(-F,6%FhuFipF^blFitF\\uF^uF`uFbu-F56(-F ,6%FbvFipF^blFitF\\uF^uF`uFbu-F56(-F,6%F\\wFipF^blFitF\\uF^uF`uFbu-F56 (-F,6%FfwFipF^blFitF\\uF^uF`uFbu-F56(-F,6%F`xFipF^blFitF\\uF^uF`uFbu-F 56(-F,6%FjxFipF^blFitF\\uF^uF`uFbuFitF\\uF^u-F26,-F56(-F,6%F9Fip-F,6%- F[o6%F`q-F,6#-Fio6%F^pFBFEF\\pFhqF[rFitF\\uF^uF`uFbu-F56(-F,6%FhuFipF` dlFitF\\uF^uF`uFbu-F56(-F,6%FbvFipF`dlFitF\\uF^uF`uFbu-F56(-F,6%F\\wFi pF`dlFitF\\uF^uF`uFbu-F56(-F,6%FfwFipF`dlFitF\\uF^uF`uFbu-F56(-F,6%F`x FipF`dlFitF\\uF^uF`uFbu-F56(-F,6%FjxFipF`dlFitF\\uF^uF`uFbuFitF\\uF^u/ %&alignGQ%axisF'/FjtQ)baselineF'/F]uFdp/F_uQ'|frleft|hrF'/%/alignments copeGFco/%,columnwidthGQ%autoF'/%&widthGF\\gl/%+rowspacingGQ&1.0exF'/% .columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFggl/%&fram eGFggl/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFJ/%-equalcolumnsGFJ /%-displaystyleGFJ/%%sideGQ&rightF'/%0minlabelspacingGFdglFBFE/%%openG Q\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Sy stemEquationR:=[]:\n" }{MPLTEXT 1 0 56 "for i from 1 to rinfty-3 do fo r j from 1 to rinfty-3 do\n" }{MPLTEXT 1 0 143 "SystemEquationR:=[op(S ystemEquationR),(Multiply(Multiply(Minfty,DiagoInfty),deltaRinfMatrix) -Multiply(RHSMatrix,DiagoInfty2))[i,j]=0]: od: od:\n" }{MPLTEXT 1 0 17 "SystemEquationR:\n" }{MPLTEXT 1 0 31 "pdsolve(\{op(SystemEquationR )\});" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "<)/-&I\"RG6 \"6#\"\"!6)&I\"tGF'6#\"\"\"&F,6#\"\"#&F,6#\"\"$&F,6#\"\"%&F,6#\"\"&&F, 6#\"\"'&F,6#\"\"(,4*&I$_C2GF'F.F>F4#\"#6\"%H5*&I$_C4GF'F.F>F1#!\"#\"# \\*&,(*&I$_C1GF'F.F;F.!%5W*&FCF.F8F.!%GNI$_C6GF'\"%?))F.F>F.#F.\"&S<'* &,&*$F;F1!%:F1#!\"$FK*&,&*&FCF.F;F.! $S\"F[o\"$?%F.F>F.#F.\"%q9*&FOF.F8F.#F1F:*&FCF.F5F.#F.F1*&F;F.FHF.#F.F 4I$_C5GF'F.F/F^o/-&F&F0F*,,*&,&*$F>F1!#IF8\"$%HF.FCF.#F.\"$!\\FNF`p*&F HF.F>F.#F4F@FSF.F2F^o/-&F&F3F*,*F5F^oFho#F1F4*&FOF.F>F.#F7F@F[oF./-&F& F6F*,(F8F^o*&FCF.F>F.#F:F@FHF./-&F&F9F*,&F;F^oFOF./-&F&FF^oFCF. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 233 "R[0](t[1], t[2], t[3], t[4], t[5], t[6], t[7]) := 11*V6*t[7]^3*(1/1029)-2*V4*t[7]^2*(1/49)+( 1/61740)*(-4410*V5*t[6]-3528*V6*t[5]+8820*V2)*t[7]+(1/61740)*(-1715*t[ 6]^2+20580*t[3])*V6+(1/4)*V5*t[4]+(1/5)*t[5]*V4+(1/6)*t[6]*V3+V0-t[1]; \n" }{MPLTEXT 1 0 159 "R[1](t[1], t[2], t[3], t[4], t[5], t[6], t[7]) \+ := -3*V5*t[7]^2*(1/49)+(1/1470)*(-140*V6*t[6]+420*V3)*t[7]+2*V5*t[5]*( 1/5)+(1/2)*V6*t[4]+(1/3)*t[6]*V4+V1-t[2];\n" }{MPLTEXT 1 0 122 "R[2](t [1], t[2], t[3], t[4], t[5], t[6], t[7]) := (1/490)*(-30*t[7]^2+294*t[ 5])*V6+(1/2)*V5*t[6]+3*V4*t[7]*(1/7)+V2-t[3];\n" }{MPLTEXT 1 0 92 "R[3 ](t[1], t[2], t[3], t[4], t[5], t[6], t[7]) := -t[4]+2*V6*t[6]*(1/3)+4 *V5*t[7]*(1/7)+V3;\n" }{MPLTEXT 1 0 76 "R[4](t[1], t[2], t[3], t[4], t [5], t[6], t[7]) := -t[5]+5*V6*t[7]*(1/7)+V4;\n" }{MPLTEXT 1 0 60 "R[5 ](t[1], t[2], t[3], t[4], t[5], t[6], t[7]) := -t[6]+V5;\n" }{MPLTEXT 1 0 60 "R[6](t[1], t[2], t[3], t[4], t[5], t[6], t[7]) := -t[7]+V6;\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 17 "SystemEquationR);" }} {PARA 11 "" 1 "" {XPPMATH 20 ">-&I\"RG6\"6#\"\"!6)&I\"tGF&6#\"\"\"&F+6 #\"\"#&F+6#\"\"$&F+6#\"\"%&F+6#\"\"&&F+6#\"\"'&F+6#\"\"(,4*&I#V6GF&F-F =F3#\"#6\"%H5*&I#V4GF&F-F=F0#!\"#\"#\\*&,(*&I#V5GF&F-F:F-!%5W*&FBF-F7F -!%GNI#V2GF&\"%?))F-F=F-#F-\"&S<'*&,&*$F:F0!%:-&I\"RG6\"6#\"\"\"6)&I\"tGF&F'&F+6#\"\"#&F+6# \"\"$&F+6#\"\"%&F+6#\"\"&&F+6#\"\"'&F+6#\"\"(,0*&I#V5GF&F(F;F.#!\"$\"# \\*&,&*&I#V6GF&F(F8F(!$S\"I#V3GF&\"$?%F(F;F(#F(\"%q9*&F@F(F5F(#F.F7*&F GF(F2F(#F(F.*&F8F(I#V4GF&F(#F(F1I#V1GF&F(F,!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-&I\"RG6\"6#\"\"#6)&I\"tGF&6#\"\"\"&F+F'&F+6#\"\"$&F+6# \"\"%&F+6#\"\"&&F+6#\"\"'&F+6#\"\"(,,*&,&*$F;F(!#IF5\"$%HF-I#V6GF&F-#F -\"$!\\*&I#V5GF&F-F8F-#F-F(*&I#V4GF&F-F;F-#F1F=I#V2GF&F-F/!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 ">-&I\"RG6\"6#\"\"$6)&I\"tGF&6#\"\"\"&F+6 #\"\"#&F+F'&F+6#\"\"%&F+6#\"\"&&F+6#\"\"'&F+6#\"\"(,*F2!\"\"*&I#V6GF&F -F8F-#F0F(*&I#V5GF&F-F;F-#F4F=I#V3GF&F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-&I\"RG6\"6#\"\"%6)&I\"tGF&6#\"\"\"&F+6#\"\"#&F+6#\"\"$&F+F'&F+6# \"\"&&F+6#\"\"'&F+6#\"\"(,(F5!\"\"*&I#V6GF&F-F;F-#F7F=I#V4GF&F-" }} {PARA 11 "" 1 "" {XPPMATH 20 ">-&I\"RG6\"6#\"\"&6)&I\"tGF&6#\"\"\"&F+6 #\"\"#&F+6#\"\"$&F+6#\"\"%&F+F'&F+6#\"\"'&F+6#\"\"(,&F8!\"\"I#V5GF&F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">-&I\"RG6\"6#\"\"'6)&I\"tGF&6#\"\"\"& F+6#\"\"#&F+6#\"\"$&F+6#\"\"%&F+6#\"\"&&F+F'&F+6#\"\"(,&F;!\"\"I#V6GF& F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "7S/\"\"!F$F#F#F#F#F#F#F#F#F#F#F#F# F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F#F# F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "GMatrix:=Matrix(rinft y-3,rinfty-3,0):\n" }{MPLTEXT 1 0 103 "for i from 1 to rinfty-3 do for j from 1 to rinfty-3 do if j<=i then GMatrix[i,j]:=g[i,j]: fi: od: od :\n" }{MPLTEXT 1 0 9 "GMatrix;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "VMatrix:=Matrix(rinfty-3,1,0):\n" }{MPLTEXT 1 0 18 "VMatrix[1,1]:= V6:\n" }{MPLTEXT 1 0 18 "VMatrix[2,1]:=V5:\n" }{MPLTEXT 1 0 18 "VMatri x[3,1]:=V4:\n" }{MPLTEXT 1 0 18 "VMatrix[4,1]:=V3:\n" }{MPLTEXT 1 0 18 "VMatrix[5,1]:=V2:\n" }{MPLTEXT 1 0 18 "VMatrix[6,1]:=V1:\n" } {MPLTEXT 1 0 17 "VMatrix[7,1]:=V0:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "VMatrix;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "RMatrix:=Matri x(rinfty-3,1,0):\n" }{MPLTEXT 1 0 68 "for i from 1 to rinfty-3 do RMat rix[i,1]:=R[rinfty-3-i](list0): od:\n" }{MPLTEXT 1 0 8 "RMatrix:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "TMatrix:=Ma trix(rinfty-3,1,0):\n" }{MPLTEXT 1 0 60 "for k from 1 to rinfty-3 do T Matrix[k]:=t[rinfty-2-k]: od: \n" }{MPLTEXT 1 0 8 "TMatrix;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI( _syslibGF'6'-I%mrowGF$6#-I'mtableGF$6;-I$mtrGF$6,-I$mtdGF$6(-I%msubGF$ 6%-I#miGF$6&Q\"gF'/%'italicGQ%trueF'/%+foregroundGQ([0,0,0]F'/%,mathva riantGQ'italicF'-F,6%-I#mnGF$6%Q\"1F'FA/FEQ'normalF'-I#moGF$6.Q\",F'FA FM/%&fenceGQ&falseF'/%*separatorGF@/%)stretchyGFU/%*symmetricGFU/%(lar 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ly(GMatrix,VMatrix)-" }{MPLTEXT 1 0 7 "TMatrix" }{MPLTEXT 1 0 10 "-RMa trix);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6 $\"\"&\"\"\",&*$&I\"tGF%6#\"\"(\"\"##!\"$\"#\\&F,6#F'#\"\"$F'" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"'\"\"#,&*$&I\"tGF%6#\"\" (F(#!\"$\"#\\&F,6#\"\"&#F(F4" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6 \"6$\"\"'\"\"\",&*&&I\"tGF%6#F'F(&F,6#\"\"(F(#!\"#\"#@&F,6#\"\"%#F(\" \"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"(\"\"$,&*$&I\"tGF %6#F'\"\"##!\"#\"#\\&F,6#\"\"&#\"\"\"F4" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"(\"\"#,&&I\"tGF%6#\"\"%#\"\"\"F-*&&F+6#\"\"'F/&F+6 #F'F/#!\"\"\"#9" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"gG6\"6$\"\"(\"\" \",**$&I\"tGF%6#F'\"\"$#\"#6\"%H5*&&F,6#\"\"&F(F+F(#!\"#\"#N*$&F,6#\" \"'\"\"##!\"\"\"#O&F,6#F.#F(F." }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfe ncedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mta bleGF$6;-I$mtrGF$6&-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F 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