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2 ":\n" }{MPLTEXT 1 0 4 "tdL;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Types ettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(- F,6%-I#miGF$6&Q&tdL11F'/%'italicGQ%trueF'/%+foregroundGQ([0,0,0]F'/%,m athvariantGQ'italicF'-I#moGF$6-Q0⁡F'/FDQ'normalF'/%&fenc eGQ&falseF'/%*separatorGFN/%)stretchyGFN/%*symmetricGFN/%(largeopGFN/% .movablelimitsGFN/%'accentGFN/%'lspaceGQ&0.0emF'/%'rspaceGFgn-F#6%-F,6 #-F:6&Q)λF'/F>FNF@FJF@FJ/%)rowalignGQ!F'/%,columnalignGFdo/%+gr oupalignGFdo/%(rowspanGQ\"1F'/%+columnspanGF[p-F56(-F,6%-F:6&Q&tdL12F' F=F@FCFFFjnFboFeoFgoFioF\\p-F56(-F,6%-F:6&Q&tdL13F'F=F@FCFFFjnFboFeoFg oFioF\\pFboFeoFgo-F26(-F56(-F,6%-F:6&Q&tdL21F'F=F@FCFFFjnFboFeoFgoFioF \\p-F56(-F,6%-F:6&Q&tdL22F'F=F@FCFFFjnFboFeoFgoFioF\\p-F56(-F,6%-F:6&Q &tdL23F'F=F@FCFFFjnFboFeoFgoFioF\\pFboFeoFgo-F26(-F56(-F,6%-F:6&Q&tdL3 1F'F=F@FCFFFjnFboFeoFgoFioF\\p-F56(-F,6%-F:6&Q&tdL32F'F=F@FCFFFjnFboFe oFgoFioF\\p-F56(-F,6%-F:6&Q&tdL33F'F=F@FCFFFjnFboFeoFgoFioF\\pFboFeoFg o/%&alignGQ%axisF'/FcoQ)baselineF'/FfoQ'centerF'/FhoQ'|frleft|hrF'/%/a lignmentscopeGF?/%,columnwidthGQ%autoF'/%&widthGFgt/%+rowspacingGQ&1.0 exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFbu/% &frameGFbu/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFN/%-equalcolumn sGFN/%-displaystyleGFN/%%sideGQ&rightF'/%0minlabelspacingGF_uF@FJ/%%op enGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "G:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 21 "G[1,1]:=G11(lambda):\n" } {MPLTEXT 1 0 8 "G[1,2]:=" }{MPLTEXT 1 0 3 "G12" }{MPLTEXT 1 0 8 "(lamb da)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 8 "G[1,3]:=" }{MPLTEXT 1 0 3 "G13" }{MPLTEXT 1 0 8 "(lambda)" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 8 "G[2,1]:=" }{MPLTEXT 1 0 3 "G21" }{MPLTEXT 1 0 8 " (lambda)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 8 "G[2,2]:=" }{MPLTEXT 1 0 3 "G22" }{MPLTEXT 1 0 8 "(lambda)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 9 "G[2,3]:=G" }{MPLTEXT 1 0 2 "23" }{MPLTEXT 1 0 8 "(lambda)" } {MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 8 "G[3,1]:=" }{MPLTEXT 1 0 3 "G31" }{MPLTEXT 1 0 8 "(lambda)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 8 "G[3, 2]:=" }{MPLTEXT 1 0 3 "G32" }{MPLTEXT 1 0 8 "(lambda)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 8 "G[3,3]:=" }{MPLTEXT 1 0 3 "G33" }{MPLTEXT 1 0 8 "(lambda)" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 3 "G;\n" }{MPLTEXT 1 0 26 "dGdlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 87 "for i from 1 to 3 do for j from 1 to 3 do dGdlambda[i,j]:=diff(G[i ,j],lambda): od: od:\n" }{MPLTEXT 1 0 10 "dGdlambda;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-F,6%-I#miGF$6&Q$G 11F'/%'italicGQ%trueF'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'italic F'-I#moGF$6-Q0⁡F'/FDQ'normalF'/%&fenceGQ&falseF'/%*separ atorGFN/%)stretchyGFN/%*symmetricGFN/%(largeopGFN/%.movablelimitsGFN/% 'accentGFN/%'lspaceGQ&0.0emF'/%'rspaceGFgn-F#6%-F,6#-F:6&Q)λF'/ F>FNF@FJF@FJ/%)rowalignGQ!F'/%,columnalignGFdo/%+groupalignGFdo/%(rows panGQ\"1F'/%+columnspanGF[p-F56(-F,6%-F:6&Q$G12F'F=F@FCFFFjnFboFeoFgoF ioF\\p-F56(-F,6%-F:6&Q$G13F'F=F@FCFFFjnFboFeoFgoFioF\\pFboFeoFgo-F26(- F56(-F,6%-F:6&Q$G21F'F=F@FCFFFjnFboFeoFgoFioF\\p-F56(-F,6%-F:6&Q$G22F' F=F@FCFFFjnFboFeoFgoFioF\\p-F56(-F,6%-F:6&Q$G23F'F=F@FCFFFjnFboFeoFgoF ioF\\pFboFeoFgo-F26(-F56(-F,6%-F:6&Q$G31F'F=F@FCFFFjnFboFeoFgoFioF\\p- F56(-F,6%-F:6&Q$G32F'F=F@FCFFFjnFboFeoFgoFioF\\p-F56(-F,6%-F:6&Q$G33F' F=F@FCFFFjnFboFeoFgoFioF\\pFboFeoFgo/%&alignGQ%axisF'/FcoQ)baselineF'/ FfoQ'centerF'/FhoQ'|frleft|hrF'/%/alignmentscopeGF?/%,columnwidthGQ%au toF'/%&widthGFgt/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)ro wlinesGQ%noneF'/%,columnlinesGFbu/%&frameGFbu/%-framespacingGQ,0.4em~0 .5exF'/%*equalrowsGFN/%-equalcolumnsGFN/%-displaystyleGFN/%%sideGQ&rig htF'/%0minlabelspacingGF_uF@FJ/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI( _syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-F,6%-I&mf racGF$6)-F,6#-I#moGF$6.Q0ⅆF'/%+foregroundGQ([0,0,0]F'/%, mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separatorGFJ/%)stretchyGFJ/ %*symmetricGFJ/%(largeopGFJ/%.movablelimitsGFJ/%'accentGFJ/%'lspaceGQ& 0.0emF'/%'rspaceGFY-F,6#-F,6$F>-I#miGF$6&Q)λF'/%'italicGFJFBFE/ %.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFeo/%)bevell edGFJFB-F?6-Q1⁢F'FEFHFKFMFOFQFSFUFWFZ-F,6%-F[o6&Q$G11F' /F_oQ%trueF'FB/FFQ'italicF'-F?6-Q0⁡F'FEFHFKFMFOFQFSFUFWF Z-F#6%-F,6#FjnFBFE/%)rowalignGQ!F'/%,columnalignGF_q/%+groupalignGF_q/ %(rowspanGFbo/%+columnspanGFbo-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G12F'FbpFBFd pFfpFipF]qF`qFbqFdqFfq-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G13F'FbpFBFdpFfpFipF ]qF`qFbqFdqFfqF]qF`qFbq-F26(-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G21F'FbpFBFdpF fpFipF]qF`qFbqFdqFfq-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G22F'FbpFBFdpFfpFipF]q F`qFbqFdqFfq-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G23F'FbpFBFdpFfpFipF]qF`qFbqFd qFfqF]qF`qFbq-F26(-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G31F'FbpFBFdpFfpFipF]qF` qFbqFdqFfq-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G32F'FbpFBFdpFfpFipF]qF`qFbqFdqF fq-F56(-F,6%F9Fjo-F,6%-F[o6&Q$G33F'FbpFBFdpFfpFipF]qF`qFbqFdqFfqF]qF`q Fbq/%&alignGQ%axisF'/F^qQ)baselineF'/FaqFeo/FcqQ'|frleft|hrF'/%/alignm entscopeGFcp/%,columnwidthGQ%autoF'/%&widthGF`w/%+rowspacingGQ&1.0exF' /%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF[x/%&fra meGF[x/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFJ/%-equalcolumnsGFJ /%-displaystyleGFJ/%%sideGQ&rightF'/%0minlabelspacingGFhwFBFE/%%openGQ \"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "ToC ancel:=simplify(L-Multiply(Multiply(G,tdL),G^(-1))-h*Multiply(dGdlambd a,G^(-1))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "G11:=unapply (1,lambda):\n" }{MPLTEXT 1 0 23 "G12:=unapply(0,lambda):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 24 "G13:=unapply(0,lambda):\n" }{MPLTEXT 1 0 36 "G23:=unapply(tdL13(lambda),lambda):\n" }{MPLTEXT 1 0 35 "G22:=unap ply(tdL12(lambda),lambda):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 35 "G21 :=unapply(tdL11(lambda),lambda):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 124 "G31:=unapply(tdL12(lambda)*tdL21(lambda)+tdL13(lambda)*tdL31(lamb da)+tdL11(lambda)^2+h*diff(tdL11(lambda), lambda),lambda):\n" } {MPLTEXT 1 0 136 "G32:=unapply(tdL12(lambda)*tdL22(lambda)+tdL11(lambd a)*tdL12(lambda)+tdL13(lambda)*tdL32(lambda)+h*diff(tdL12(lambda), lam bda),lambda):\n" }{MPLTEXT 1 0 136 "G33:=unapply(tdL12(lambda)*tdL23(l ambda)+tdL13(lambda)*tdL33(lambda)+tdL11(lambda)*tdL13(lambda)+h*diff( tdL13(lambda), lambda),lambda):\n" }{MPLTEXT 1 0 5207 "L32:=unapply((- 2*(diff(tdL11(lambda), lambda))*tdL13(lambda)*tdL33(lambda)*tdL12(lamb da)*h+2*(diff(tdL11(lambda), lambda))*tdL13(lambda)*tdL12(lambda)*tdL2 2(lambda)*h-tdL11(lambda)*(diff(tdL22(lambda), lambda))*tdL12(lambda)* tdL13(lambda)*h+tdL11(lambda)*(diff(tdL33(lambda), lambda))*tdL12(lamb da)*tdL13(lambda)*h-2*tdL11(lambda)*tdL22(lambda)*(diff(tdL12(lambda), lambda))*tdL13(lambda)*h+2*tdL11(lambda)*tdL12(lambda)*tdL33(lambda)* (diff(tdL13(lambda), lambda))*h-(diff(tdL22(lambda), lambda))*tdL12(la mbda)*tdL13(lambda)*tdL33(lambda)*h+(diff(tdL23(lambda), lambda))*tdL3 2(lambda)*tdL12(lambda)*tdL13(lambda)*h-(diff(tdL32(lambda), lambda))* tdL12(lambda)*tdL23(lambda)*tdL13(lambda)*h+(diff(tdL33(lambda), lambd a))*tdL22(lambda)*tdL12(lambda)*tdL13(lambda)*h+tdL22(lambda)*tdL32(la mbda)*tdL12(lambda)*tdL23(lambda)*tdL13(lambda)-tdL22(lambda)*tdL32(la mbda)*tdL13(lambda)*(diff(tdL13(lambda), lambda))*h+tdL22(lambda)*(dif f(tdL12(lambda), lambda))*tdL12(lambda)*tdL23(lambda)*h-2*tdL22(lambda )*(diff(tdL12(lambda), lambda))*tdL13(lambda)*tdL33(lambda)*h+2*tdL22( lambda)*tdL12(lambda)*tdL33(lambda)*(diff(tdL13(lambda), lambda))*h+3* tdL32(lambda)*(diff(tdL12(lambda), lambda))*tdL23(lambda)*tdL13(lambda )*h-tdL32(lambda)*tdL12(lambda)*tdL23(lambda)*tdL13(lambda)*tdL33(lamb da)-3*tdL32(lambda)*tdL12(lambda)*tdL23(lambda)*(diff(tdL13(lambda), l ambda))*h-tdL32(lambda)*tdL13(lambda)*tdL33(lambda)*(diff(tdL13(lambda ), lambda))*h+(diff(tdL12(lambda), lambda))*tdL12(lambda)*tdL23(lambda )*tdL33(lambda)*h+(diff(tdL13(lambda), lambda, lambda))*(diff(tdL12(la mbda), lambda))*h^3-(diff(tdL12(lambda), lambda, lambda))*(diff(tdL13( lambda), lambda))*h^3-tdL21(lambda)*tdL12(lambda)^3*tdL23(lambda)-tdL3 2(lambda)*tdL12(lambda)^2*tdL23(lambda)^2+tdL32(lambda)^2*tdL23(lambda )*tdL13(lambda)^2-2*tdL32(lambda)*(diff(tdL13(lambda), lambda))^2*h^2+ tdL31(lambda)*tdL32(lambda)*tdL13(lambda)^3+2*(diff(tdL12(lambda), lam bda))^2*tdL23(lambda)*h^2+(diff(tdL12(lambda), lambda))*tdL13(lambda)* tdL33(lambda)^2*h+2*(diff(tdL12(lambda), lambda))*tdL33(lambda)*(diff( tdL13(lambda), lambda))*h^2+2*(diff(tdL11(lambda), lambda))*(diff(tdL1 2(lambda), lambda))*tdL13(lambda)*h^2-2*(diff(tdL11(lambda), lambda))* tdL12(lambda)*(diff(tdL13(lambda), lambda))*h^2+tdL21(lambda)*tdL22(la mbda)*tdL12(lambda)^2*tdL13(lambda)+tdL21(lambda)*tdL32(lambda)*tdL12( lambda)*tdL13(lambda)^2-tdL21(lambda)*tdL12(lambda)^2*tdL13(lambda)*td L33(lambda)+tdL31(lambda)*tdL22(lambda)*tdL12(lambda)*tdL13(lambda)^2- tdL31(lambda)*tdL12(lambda)^2*tdL23(lambda)*tdL13(lambda)-tdL31(lambda )*tdL12(lambda)*tdL13(lambda)^2*tdL33(lambda)+tdL11(lambda)*(diff(tdL2 3(lambda), lambda))*tdL12(lambda)^2*h-tdL11(lambda)*(diff(tdL32(lambda ), lambda))*tdL13(lambda)^2*h-tdL11(lambda)*tdL22(lambda)^2*tdL12(lamb da)*tdL13(lambda)-tdL11(lambda)*tdL22(lambda)*tdL32(lambda)*tdL13(lamb da)^2+tdL11(lambda)*tdL22(lambda)*tdL12(lambda)^2*tdL23(lambda)-tdL11( lambda)*tdL32(lambda)*tdL13(lambda)^2*tdL33(lambda)+tdL11(lambda)*tdL1 2(lambda)^2*tdL23(lambda)*tdL33(lambda)+tdL11(lambda)*tdL12(lambda)*td L13(lambda)*tdL33(lambda)^2-(diff(tdL22(lambda), lambda))*tdL12(lambda )^2*tdL23(lambda)*h-(diff(tdL22(lambda), lambda))*tdL12(lambda)*(diff( tdL13(lambda), lambda))*h^2+(diff(tdL23(lambda), lambda))*tdL22(lambda )*tdL12(lambda)^2*h+(diff(tdL23(lambda), lambda))*(diff(tdL12(lambda), lambda))*tdL12(lambda)*h^2-(diff(tdL32(lambda), lambda))*tdL13(lambda )^2*tdL33(lambda)*h-(diff(tdL32(lambda), lambda))*tdL13(lambda)*(diff( tdL13(lambda), lambda))*h^2+(diff(tdL33(lambda), lambda))*tdL32(lambda )*tdL13(lambda)^2*h+(diff(tdL33(lambda), lambda))*(diff(tdL12(lambda), lambda))*tdL13(lambda)*h^2-tdL22(lambda)^2*tdL12(lambda)*tdL13(lambda )*tdL33(lambda)-tdL22(lambda)^2*tdL12(lambda)*(diff(tdL13(lambda), lam bda))*h-tdL22(lambda)*tdL32(lambda)*tdL13(lambda)^2*tdL33(lambda)-2*td L22(lambda)*(diff(tdL12(lambda), lambda))*(diff(tdL13(lambda), lambda) )*h^2+tdL22(lambda)*tdL12(lambda)^2*tdL23(lambda)*tdL33(lambda)+tdL22( lambda)*tdL12(lambda)*tdL13(lambda)*tdL33(lambda)^2+(diff(tdL12(lambda ), lambda))*tdL13(lambda)*tdL12(lambda)*tdL21(lambda)*h+2*(diff(tdL12( lambda), lambda))*tdL23(lambda)*tdL12(lambda)*tdL11(lambda)*h-(diff(td L13(lambda), lambda))*tdL13(lambda)*tdL12(lambda)*tdL31(lambda)*h-2*(d iff(tdL13(lambda), lambda))*tdL13(lambda)*tdL32(lambda)*tdL11(lambda)* h+(diff(tdL12(lambda), lambda))*tdL13(lambda)^2*tdL31(lambda)*h-(diff( tdL13(lambda), lambda))*tdL12(lambda)^2*tdL21(lambda)*h+2*(diff(tdL11( lambda), lambda))*tdL13(lambda)^2*tdL32(lambda)*h-2*(diff(tdL11(lambda ), lambda))*tdL23(lambda)*tdL12(lambda)^2*h+(diff(tdL13(lambda), lambd a, lambda))*tdL32(lambda)*tdL13(lambda)*h^2-(diff(tdL12(lambda), lambd a, lambda))*tdL11(lambda)*tdL13(lambda)*h^2-(diff(tdL12(lambda), lambd a, lambda))*tdL12(lambda)*tdL23(lambda)*h^2-(diff(tdL12(lambda), lambd a, lambda))*tdL13(lambda)*tdL33(lambda)*h^2+(diff(tdL13(lambda), lambd a, lambda))*tdL11(lambda)*tdL12(lambda)*h^2+(diff(tdL13(lambda), lambd a, lambda))*tdL22(lambda)*tdL12(lambda)*h^2)/(tdL13(lambda)*tdL12(lamb da)*tdL22(lambda)+tdL13(lambda)^2*tdL32(lambda)+h*tdL13(lambda)*(diff( tdL12(lambda), lambda))-tdL23(lambda)*tdL12(lambda)^2-tdL13(lambda)*td L33(lambda)*tdL12(lambda)-h*tdL12(lambda)*(diff(tdL13(lambda), lambda) )),lambda):\n" }{MPLTEXT 1 0 1422 "L33:=unapply(((diff(tdL12(lambda), \+ lambda, lambda))*tdL13(lambda)*h^2-(diff(tdL13(lambda), lambda, lambda ))*tdL12(lambda)*h^2+tdL13(lambda)*tdL12(lambda)*tdL22(lambda)*tdL11(l ambda)+tdL13(lambda)^2*tdL32(lambda)*tdL11(lambda)+(diff(tdL12(lambda) , lambda))*tdL13(lambda)*tdL11(lambda)*h-tdL23(lambda)*tdL12(lambda)^2 *tdL11(lambda)-tdL13(lambda)*tdL33(lambda)*tdL12(lambda)*tdL11(lambda) -(diff(tdL13(lambda), lambda))*tdL12(lambda)*tdL11(lambda)*h+(diff(tdL 22(lambda), lambda))*tdL13(lambda)*tdL12(lambda)*h-(diff(tdL23(lambda) , lambda))*tdL12(lambda)^2*h+(diff(tdL32(lambda), lambda))*tdL13(lambd a)^2*h-(diff(tdL33(lambda), lambda))*tdL13(lambda)*tdL12(lambda)*h+tdL 13(lambda)*tdL12(lambda)*tdL22(lambda)^2+tdL13(lambda)^2*tdL22(lambda) *tdL32(lambda)+2*(diff(tdL12(lambda), lambda))*tdL13(lambda)*tdL22(lam bda)*h-tdL23(lambda)*tdL12(lambda)^2*tdL22(lambda)+tdL13(lambda)^2*tdL 33(lambda)*tdL32(lambda)+2*(diff(tdL13(lambda), lambda))*tdL13(lambda) *tdL32(lambda)*h-2*(diff(tdL12(lambda), lambda))*tdL23(lambda)*tdL12(l ambda)*h-tdL23(lambda)*tdL33(lambda)*tdL12(lambda)^2-tdL13(lambda)*tdL 33(lambda)^2*tdL12(lambda)-2*(diff(tdL13(lambda), lambda))*tdL33(lambd a)*tdL12(lambda)*h)/(tdL13(lambda)*tdL12(lambda)*tdL22(lambda)+tdL13(l ambda)^2*tdL32(lambda)+h*tdL13(lambda)*(diff(tdL12(lambda), lambda))-t dL23(lambda)*tdL12(lambda)^2-tdL13(lambda)*tdL33(lambda)*tdL12(lambda) -h*tdL12(lambda)*(diff(tdL13(lambda), lambda))),lambda):\n" }{MPLTEXT 1 0 9432 "L31:=unapply(-(-(diff(tdL11(lambda), lambda))*(diff(tdL23(la mbda), lambda))*tdL12(lambda)^2*h^2+(diff(tdL11(lambda), lambda))*(dif f(tdL32(lambda), lambda))*tdL13(lambda)^2*h^2-tdL21(lambda)*(diff(tdL2 3(lambda), lambda))*tdL12(lambda)^3*h-2*tdL21(lambda)*(diff(tdL12(lamb da), lambda))^2*tdL13(lambda)*h^2-tdL21(lambda)*tdL12(lambda)^3*tdL23( lambda)*tdL33(lambda)-tdL21(lambda)*tdL12(lambda)^2*tdL13(lambda)*tdL3 3(lambda)^2+tdL31(lambda)*(diff(tdL32(lambda), lambda))*tdL13(lambda)^ 3*h+tdL31(lambda)*tdL22(lambda)^2*tdL12(lambda)*tdL13(lambda)^2+tdL31( lambda)*tdL22(lambda)*tdL32(lambda)*tdL13(lambda)^3+2*tdL31(lambda)*td L12(lambda)*(diff(tdL13(lambda), lambda))^2*h^2+tdL11(lambda)*tdL32(la mbda)^2*tdL23(lambda)*tdL13(lambda)^2-tdL11(lambda)*tdL32(lambda)*tdL1 2(lambda)^2*tdL23(lambda)^2-2*tdL11(lambda)*tdL32(lambda)*(diff(tdL13( lambda), lambda))^2*h^2+2*tdL11(lambda)*(diff(tdL12(lambda), lambda))^ 2*tdL23(lambda)*h^2+(diff(tdL21(lambda), lambda))*tdL12(lambda)^3*tdL2 3(lambda)*h+(diff(tdL21(lambda), lambda))*tdL12(lambda)^2*(diff(tdL13( lambda), lambda))*h^2-(diff(tdL31(lambda), lambda))*tdL32(lambda)*tdL1 3(lambda)^3*h-(diff(tdL31(lambda), lambda))*(diff(tdL12(lambda), lambd a))*tdL13(lambda)^2*h^2-(diff(tdL11(lambda), lambda, lambda))*tdL32(la mbda)*tdL13(lambda)^2*h^2+(diff(tdL13(lambda), lambda, lambda))*tdL11( lambda)*(diff(tdL12(lambda), lambda))*h^3+tdL31(lambda)*(diff(tdL12(la mbda), lambda, lambda))*tdL13(lambda)^2*h^2-(diff(tdL12(lambda), lambd a, lambda))*tdL11(lambda)*(diff(tdL13(lambda), lambda))*h^3-tdL21(lamb da)*(diff(tdL13(lambda), lambda, lambda))*tdL12(lambda)^2*h^2-(diff(td L11(lambda), lambda))*(diff(tdL13(lambda), lambda, lambda))*tdL12(lamb da)*h^3+(diff(tdL11(lambda), lambda))*(diff(tdL12(lambda), lambda, lam bda))*tdL13(lambda)*h^3+tdL21(lambda)*(diff(tdL12(lambda), lambda, lam bda))*tdL12(lambda)*tdL13(lambda)*h^2-tdL31(lambda)*(diff(tdL13(lambda ), lambda, lambda))*tdL12(lambda)*tdL13(lambda)*h^2+(diff(tdL11(lambda ), lambda, lambda))*tdL12(lambda)*(diff(tdL13(lambda), lambda))*h^3-(d iff(tdL11(lambda), lambda, lambda))*(diff(tdL12(lambda), lambda))*tdL1 3(lambda)*h^3+(diff(tdL11(lambda), lambda, lambda))*tdL12(lambda)^2*td L23(lambda)*h^2+tdL31(lambda)*tdL12(lambda)^3*tdL23(lambda)^2-tdL21(la mbda)*tdL32(lambda)^2*tdL13(lambda)^3-tdL21(lambda)*tdL22(lambda)*(dif f(tdL12(lambda), lambda))*tdL12(lambda)*tdL13(lambda)*h+3*tdL21(lambda )*tdL32(lambda)*tdL12(lambda)*tdL13(lambda)*(diff(tdL13(lambda), lambd a))*h+2*tdL21(lambda)*(diff(tdL12(lambda), lambda))*tdL12(lambda)*tdL1 3(lambda)*tdL33(lambda)*h-2*tdL31(lambda)*tdL22(lambda)*tdL12(lambda)* tdL13(lambda)*(diff(tdL13(lambda), lambda))*h-3*tdL31(lambda)*(diff(td L12(lambda), lambda))*tdL12(lambda)*tdL23(lambda)*tdL13(lambda)*h+tdL3 1(lambda)*tdL12(lambda)*tdL13(lambda)*tdL33(lambda)*(diff(tdL13(lambda ), lambda))*h-tdL11(lambda)*(diff(tdL22(lambda), lambda))*tdL12(lambda )*tdL13(lambda)*tdL33(lambda)*h+tdL11(lambda)*(diff(tdL23(lambda), lam bda))*tdL32(lambda)*tdL12(lambda)*tdL13(lambda)*h-tdL11(lambda)*(diff( tdL32(lambda), lambda))*tdL12(lambda)*tdL23(lambda)*tdL13(lambda)*h+td L11(lambda)*(diff(tdL33(lambda), lambda))*tdL22(lambda)*tdL12(lambda)* tdL13(lambda)*h+tdL11(lambda)*tdL22(lambda)*tdL32(lambda)*tdL12(lambda )*tdL23(lambda)*tdL13(lambda)-tdL11(lambda)*tdL22(lambda)*tdL32(lambda )*tdL13(lambda)*(diff(tdL13(lambda), lambda))*h+tdL11(lambda)*tdL22(la mbda)*(diff(tdL12(lambda), lambda))*tdL12(lambda)*tdL23(lambda)*h-2*td L11(lambda)*tdL22(lambda)*(diff(tdL12(lambda), lambda))*tdL13(lambda)* tdL33(lambda)*h+2*tdL11(lambda)*tdL22(lambda)*tdL12(lambda)*tdL33(lamb da)*(diff(tdL13(lambda), lambda))*h+3*tdL11(lambda)*tdL32(lambda)*(dif f(tdL12(lambda), lambda))*tdL23(lambda)*tdL13(lambda)*h-tdL11(lambda)* tdL32(lambda)*tdL12(lambda)*tdL23(lambda)*tdL13(lambda)*tdL33(lambda)- 3*tdL11(lambda)*tdL32(lambda)*tdL12(lambda)*tdL23(lambda)*(diff(tdL13( lambda), lambda))*h-tdL11(lambda)*tdL32(lambda)*tdL13(lambda)*tdL33(la mbda)*(diff(tdL13(lambda), lambda))*h+tdL11(lambda)*(diff(tdL12(lambda ), lambda))*tdL12(lambda)*tdL23(lambda)*tdL33(lambda)*h+(diff(tdL13(la mbda), lambda, lambda))*tdL11(lambda)*tdL32(lambda)*tdL13(lambda)*h^2- (diff(tdL11(lambda), lambda, lambda))*tdL22(lambda)*tdL12(lambda)*tdL1 3(lambda)*h^2+(diff(tdL11(lambda), lambda))*(diff(tdL22(lambda), lambd a))*tdL12(lambda)*tdL13(lambda)*h^2-(diff(tdL11(lambda), lambda))*(dif f(tdL33(lambda), lambda))*tdL12(lambda)*tdL13(lambda)*h^2+(diff(tdL11( lambda), lambda))*tdL22(lambda)^2*tdL12(lambda)*tdL13(lambda)*h+(diff( tdL11(lambda), lambda))*tdL22(lambda)*tdL32(lambda)*tdL13(lambda)^2*h+ 2*(diff(tdL11(lambda), lambda))*tdL22(lambda)*(diff(tdL12(lambda), lam bda))*tdL13(lambda)*h^2-(diff(tdL11(lambda), lambda))*tdL22(lambda)*td L12(lambda)^2*tdL23(lambda)*h+(diff(tdL11(lambda), lambda))*tdL32(lamb da)*tdL13(lambda)^2*tdL33(lambda)*h+2*(diff(tdL11(lambda), lambda))*td L32(lambda)*tdL13(lambda)*(diff(tdL13(lambda), lambda))*h^2-2*(diff(td L11(lambda), lambda))*(diff(tdL12(lambda), lambda))*tdL12(lambda)*tdL2 3(lambda)*h^2-(diff(tdL11(lambda), lambda))*tdL12(lambda)^2*tdL23(lamb da)*tdL33(lambda)*h-(diff(tdL11(lambda), lambda))*tdL12(lambda)*tdL13( lambda)*tdL33(lambda)^2*h-2*(diff(tdL11(lambda), lambda))*tdL12(lambda )*tdL33(lambda)*(diff(tdL13(lambda), lambda))*h^2+tdL21(lambda)*(diff( tdL22(lambda), lambda))*tdL12(lambda)^2*tdL13(lambda)*h+tdL21(lambda)* (diff(tdL32(lambda), lambda))*tdL12(lambda)*tdL13(lambda)^2*h-tdL21(la mbda)*(diff(tdL33(lambda), lambda))*tdL12(lambda)^2*tdL13(lambda)*h-td L21(lambda)*tdL22(lambda)*tdL32(lambda)*tdL12(lambda)*tdL13(lambda)^2+ tdL21(lambda)*tdL22(lambda)*tdL12(lambda)^2*tdL13(lambda)*tdL33(lambda )+tdL21(lambda)*tdL22(lambda)*tdL12(lambda)^2*(diff(tdL13(lambda), lam bda))*h-3*tdL21(lambda)*tdL32(lambda)*(diff(tdL12(lambda), lambda))*td L13(lambda)^2*h+tdL21(lambda)*tdL32(lambda)*tdL12(lambda)^2*tdL23(lamb da)*tdL13(lambda)+2*tdL21(lambda)*tdL32(lambda)*tdL12(lambda)*tdL13(la mbda)^2*tdL33(lambda)+2*tdL21(lambda)*(diff(tdL12(lambda), lambda))*td L12(lambda)*(diff(tdL13(lambda), lambda))*h^2-2*tdL21(lambda)*tdL12(la mbda)^2*tdL33(lambda)*(diff(tdL13(lambda), lambda))*h+tdL31(lambda)*(d iff(tdL22(lambda), lambda))*tdL12(lambda)*tdL13(lambda)^2*h-tdL31(lamb da)*(diff(tdL23(lambda), lambda))*tdL12(lambda)^2*tdL13(lambda)*h-tdL3 1(lambda)*(diff(tdL33(lambda), lambda))*tdL12(lambda)*tdL13(lambda)^2* h+2*tdL31(lambda)*tdL22(lambda)*(diff(tdL12(lambda), lambda))*tdL13(la mbda)^2*h-2*tdL31(lambda)*tdL22(lambda)*tdL12(lambda)^2*tdL23(lambda)* tdL13(lambda)-tdL31(lambda)*tdL22(lambda)*tdL12(lambda)*tdL13(lambda)^ 2*tdL33(lambda)-tdL31(lambda)*tdL32(lambda)*tdL12(lambda)*tdL23(lambda )*tdL13(lambda)^2-tdL31(lambda)*(diff(tdL12(lambda), lambda))*tdL13(la mbda)^2*tdL33(lambda)*h-2*tdL31(lambda)*(diff(tdL12(lambda), lambda))* tdL13(lambda)*(diff(tdL13(lambda), lambda))*h^2+tdL31(lambda)*tdL12(la mbda)^2*tdL23(lambda)*tdL13(lambda)*tdL33(lambda)+3*tdL31(lambda)*tdL1 2(lambda)^2*tdL23(lambda)*(diff(tdL13(lambda), lambda))*h-tdL11(lambda )*(diff(tdL22(lambda), lambda))*tdL12(lambda)^2*tdL23(lambda)*h-tdL11( lambda)*(diff(tdL22(lambda), lambda))*tdL12(lambda)*(diff(tdL13(lambda ), lambda))*h^2+tdL11(lambda)*(diff(tdL23(lambda), lambda))*tdL22(lamb da)*tdL12(lambda)^2*h+tdL11(lambda)*(diff(tdL23(lambda), lambda))*(dif f(tdL12(lambda), lambda))*tdL12(lambda)*h^2-tdL11(lambda)*(diff(tdL32( lambda), lambda))*tdL13(lambda)^2*tdL33(lambda)*h-tdL11(lambda)*(diff( tdL32(lambda), lambda))*tdL13(lambda)*(diff(tdL13(lambda), lambda))*h^ 2+tdL11(lambda)*(diff(tdL33(lambda), lambda))*tdL32(lambda)*tdL13(lamb da)^2*h+tdL11(lambda)*(diff(tdL33(lambda), lambda))*(diff(tdL12(lambda ), lambda))*tdL13(lambda)*h^2-tdL11(lambda)*tdL22(lambda)^2*tdL12(lamb da)*tdL13(lambda)*tdL33(lambda)-tdL11(lambda)*tdL22(lambda)^2*tdL12(la mbda)*(diff(tdL13(lambda), lambda))*h-tdL11(lambda)*tdL22(lambda)*tdL3 2(lambda)*tdL13(lambda)^2*tdL33(lambda)-2*tdL11(lambda)*tdL22(lambda)* (diff(tdL12(lambda), lambda))*(diff(tdL13(lambda), lambda))*h^2+tdL11( lambda)*tdL22(lambda)*tdL12(lambda)^2*tdL23(lambda)*tdL33(lambda)+tdL1 1(lambda)*tdL22(lambda)*tdL12(lambda)*tdL13(lambda)*tdL33(lambda)^2+td L11(lambda)*(diff(tdL12(lambda), lambda))*tdL13(lambda)*tdL33(lambda)^ 2*h+2*tdL11(lambda)*(diff(tdL12(lambda), lambda))*tdL33(lambda)*(diff( tdL13(lambda), lambda))*h^2-(diff(tdL21(lambda), lambda))*tdL22(lambda )*tdL12(lambda)^2*tdL13(lambda)*h-(diff(tdL21(lambda), lambda))*tdL32( lambda)*tdL12(lambda)*tdL13(lambda)^2*h-(diff(tdL21(lambda), lambda))* (diff(tdL12(lambda), lambda))*tdL12(lambda)*tdL13(lambda)*h^2+(diff(td L21(lambda), lambda))*tdL12(lambda)^2*tdL13(lambda)*tdL33(lambda)*h-(d iff(tdL31(lambda), lambda))*tdL22(lambda)*tdL12(lambda)*tdL13(lambda)^ 2*h+(diff(tdL31(lambda), lambda))*tdL12(lambda)^2*tdL23(lambda)*tdL13( lambda)*h+(diff(tdL31(lambda), lambda))*tdL12(lambda)*tdL13(lambda)^2* tdL33(lambda)*h+(diff(tdL31(lambda), lambda))*tdL12(lambda)*tdL13(lamb da)*(diff(tdL13(lambda), lambda))*h^2+(diff(tdL11(lambda), lambda, lam bda))*tdL12(lambda)*tdL13(lambda)*tdL33(lambda)*h^2-(diff(tdL12(lambda ), lambda, lambda))*tdL11(lambda)*tdL12(lambda)*tdL23(lambda)*h^2-(dif f(tdL12(lambda), lambda, lambda))*tdL11(lambda)*tdL13(lambda)*tdL33(la mbda)*h^2+(diff(tdL13(lambda), lambda, lambda))*tdL11(lambda)*tdL22(la mbda)*tdL12(lambda)*h^2)/(tdL13(lambda)*tdL12(lambda)*tdL22(lambda)+td L13(lambda)^2*tdL32(lambda)+h*tdL13(lambda)*(diff(tdL12(lambda), lambd a))-tdL23(lambda)*tdL12(lambda)^2-tdL13(lambda)*tdL33(lambda)*tdL12(la mbda)-h*tdL12(lambda)*(diff(tdL13(lambda), lambda))),lambda):\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "simplify(ToCancel);" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 13 "simplify(G);\n" }{MPLTEXT 1 0 23 "factor(Determinant(G));" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfence dG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtable GF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/% ,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignG FC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ )baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,c olumnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacing GQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-framesp acingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-displ aystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&closeG Q\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\" I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mt dGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normal F'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGF:/%+col umnspanGF:-F56(-F86%Q\"0F'F;F>FAFDFFFHFJFLFAFDFF-F26(-F56(-F,6%-I#miGF $6&Q&tdL11F'/%'italicGQ%trueF'F;/F?Q'italicF'-I#moGF$6-Q0&ApplyFunctio n;F'F>/%&fenceGQ&falseF'/%*separatorGF`o/%)stretchyGF`o/%*symmetricGF` o/%(largeopGF`o/%.movablelimitsGF`o/%'accentGF`o/%'lspaceGQ&0.0emF'/%' rspaceGF_p-F#6%-F,6#-FX6&Q)λF'/FfnF`oF;F>F;F>FAFDFFFHFJ-F56(-F, 6%-FX6&Q&tdL12F'FenF;FhnFjnFbpFAFDFFFHFJ-F56(-F,6%-FX6&Q&tdL13F'FenF;F hnFjnFbpFAFDFFFHFJFAFDFF-F26(-F56(-F,6)-F,6%F\\q-F[o6-Q1&InvisibleTime s;F'F>F^oFaoFcoFeoFgoFioF[pF]pF`p-F,6%-FX6&Q&tdL21F'FenF;FhnFjnFbp-F[o 6.Q\"+F'F;F>F^oFaoFcoFeoFgoFioF[p/F^pQ,0.2222222emF'/FapF\\s-F,6%FcqF` r-F,6%-FX6&Q&tdL31F'FenF;FhnFjnFbpFhr-F,6#-I%msupGF$6%FU-F86%Q\"2F'F;F >/%1superscriptshiftGFPFhr-F,6%-FX6&Q\"hF'FenF;FhnF`r-F#6%-F,6%-I&mfra cGF$6)-F,6#-F[o6.Q0ⅆF'F;F>F^oFaoFcoFeoFgoFioF[pF]pF`p-F, 6#-F,6$F]uFfp/%.linethicknessGF:/%+denomalignGQ'centerF'/%)numalignGFh u/%)bevelledGF`oF;F`rFUF;F>FAFDFFFHFJ-F56(-F,6'-F,6%FatF`r-F#6%-F,6%Fh tF`rF\\qF;F>Fhr-F,6%-F#6%-F,6%FUFhr-F,6%-FX6&Q&tdL22F'FenF;FhnFjnFbpF; F>F`rF\\qFhr-F,6%FcqF`r-F,6%-FX6&Q&tdL32F'FenF;FhnFjnFbpFAFDFFFHFJ-F56 (-F,6'-F,6%FatF`r-F#6%-F,6%FhtF`rFcqF;F>Fhr-F,6%-F#6%-F,6%FUFhr-F,6%-F X6&Q&tdL33F'FenF;FhnFjnFbpF;F>F`rFcqFhr-F,6%F\\qF`r-F,6%-FX6&Q&tdL23F' FenF;FhnFjnFbpFAFDFFFHFJFAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEFhu/F GQ'|frleft|hrF'/%/alignmentscopeGFgn/%,columnwidthGQ%autoF'/%&widthGFa z/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF' /%,columnlinesGF\\[l/%&frameGF\\[l/%-framespacingGQ,0.4em~0.5exF'/%*eq ualrowsGF`o/%-equalcolumnsGF`o/%-displaystyleGF`o/%%sideGQ&rightF'/%0m inlabelspacingGFizF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 " " {XPPMATH 20 ",.*(-I&tdL13G6\"6#I'lambdaGF&\"\"\"-I&tdL12GF&F'F)-I&td L22GF&F'F)!\"\"*&F$\"\"#-I&tdL32GF&F'F)F.*(I\"hGF&F)F$F)-I%diffG%*prot ectedG6$F*F(F)F.*&-I&tdL23GF&F'F)F*F0F)*(F$F)-I&tdL33GF&F'F)F*F)F)*(F4 F)F*F)-F66$F$F(F)F)" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 291 253 "Applica tion to the case of \\td\{L\}=L_1\\lambda+L_0. We take L_1=diag(t12,t2 2,t32) but L_0 remains free. In particular, we keep a_\{1,2\}, a_\{1,3 \} as free parameters that shall not be determined since they belongs \+ to the action by global conjugation of GL_3." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "tdL11:=unapply(t12*lambda+" }{MPLTEXT 1 0 13 "a11, lambda):\n" }{MPLTEXT 1 0 28 "tdL12:=unapply(a12,lambda):\n" }{MPLTEXT 1 0 28 "tdL13:=unapply(a13,lambda):\n" }{MPLTEXT 1 0 28 "tdL21:=unapp ly(a21,lambda):\n" }{MPLTEXT 1 0 39 "tdL22:=unapply(t22*lambda+a22,lam bda):\n" }{MPLTEXT 1 0 28 "tdL23:=unapply(a23,lambda):\n" }{MPLTEXT 1 0 27 "tdL31:=unapply(a31,lambda):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 28 "tdL32:=unapply(a32,lambda):\n" }{MPLTEXT 1 0 38 "tdL33:=unapply(t3 2*lambda+a33,lambda):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 15 "simplify (tdL);\n" }{MPLTEXT 1 0 51 "simplify(series(factor(Determinant(G)),lam bda=0));\n" }{MPLTEXT 1 0 13 "simplify(G);\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 26 "tdLinfty1:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 21 "tdLinf ty1[1,1]:=t12:\n" }{MPLTEXT 1 0 21 "tdLinfty1[2,2]:=t22:\n" }{MPLTEXT 1 0 20 "tdLinfty1[3,3]:=t32:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n " }{MPLTEXT 1 0 26 "tdLinfty0:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 21 "tdL infty0[1,1]:=a11:\n" }{MPLTEXT 1 0 20 "tdLinfty0[1,2]:=a12:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "tdLinfty0[1,3]:=a13:" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 21 "tdLinfty0[2,1]:=a21:\n" }{MPLTEXT 1 0 21 "tdLinf ty0[2,2]:=a22:\n" }{MPLTEXT 1 0 21 "tdLinfty0[2,3]:=a23:\n" }{MPLTEXT 1 0 21 "tdLinfty0[3,1]:=a31:\n" }{MPLTEXT 1 0 21 "tdLinfty0[3,2]:=a32: \n" }{MPLTEXT 1 0 20 "tdLinfty0[3,3]:=a33:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 15 "simplify(tdL);\n" }{MPLTEXT 1 0 12 "Trace(tdL);\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$ 6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-F,6%-F,6%-I#miGF$6&Q)λF' /%'italicGQ&falseF'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'- I#moGF$6-Q1⁢F'FE/%&fenceGFA/%*separatorGFA/%)stretchyGF A/%*symmetricGFA/%(largeopGFA/%.movablelimitsGFA/%'accentGFA/%'lspaceG Q&0.0emF'/%'rspaceGFfn-F<6&Q$t12F'/F@Q%trueF'FB/FFQ'italicF'-FI6.Q\"+F 'FBFEFLFNFPFRFTFVFX/FenQ,0.2222222emF'/FhnFdo-F<6&Q$a11F'F\\oFBF^o/%)r owalignGQ!F'/%,columnalignGF[p/%+groupalignGF[p/%(rowspanGQ\"1F'/%+col umnspanGFbp-F56(-F<6&Q$a12F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a13F' F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-F<6&Q$a21F'F\\oFBF^oFioF \\pF^pF`pFcp-F56(-F,6%-F,6%F;FH-F<6&Q$t22F'F\\oFBF^oF`o-F<6&Q$a22F'F \\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a23F'F\\oFBF^oFioF\\pF^pF`pFcpFioF \\pF^p-F26(-F56(-F<6&Q$a31F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a32F' F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FH-F<6&Q$t32F'F\\oFBF^oF`o-F <6&Q$a33F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p/%&alignGQ%axisF'/FjoQ)ba selineF'/F]pQ'centerF'/F_pQ'|frleft|hrF'/%/alignmentscopeGF]o/%,column widthGQ%autoF'/%&widthGF\\u/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0 .8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFgu/%&frameGFgu/%-framespacin gGQ,0.4em~0.5exF'/%*equalrowsGFA/%-equalcolumnsGFA/%-displaystyleGFA/% %sideGQ&rightF'/%0minlabelspacingGFduFBFE/%%openGQ\"[F'/%&closeGQ\"]F' " }}{PARA 11 "" 1 "" {XPPMATH 20 "+'I'lambdaG6\",(*&I$a12GF$\"\"#I$a23 GF$\"\"\"F**(I$a13GF$F*,&I$a22GF$F*I$a33GF$!\"\"F*F'F*F0*&F,F(I$a32GF$ F*F0\"\"!,$*(F'F*F,F*,&I$t22GF$F*I$t32GF$F0F*F0F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$67-I$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:-F56(-F86%Q\"0F'F ;F>FAFDFFFHFJFLFAFDFF-F26(-F56(-F,6%-F,6%-I#miGF$6&Q)λF'/%'ital icGQ&falseF'F;F>-I#moGF$6-Q1⁢F'F>/%&fenceGFin/%*separat orGFin/%)stretchyGFin/%*symmetricGFin/%(largeopGFin/%.movablelimitsGFi n/%'accentGFin/%'lspaceGQ&0.0emF'/%'rspaceGF^p-FZ6&Q$t12F'/FhnQ%trueF' F;/F?Q'italicF'-F[o6.Q\"+F'F;F>F^oF`oFboFdoFfoFhoFjo/F]pQ,0.2222222emF '/F`pF\\q-FZ6&Q$a11F'FdpF;FfpFAFDFFFHFJ-F56(-FZ6&Q$a12F'FdpF;FfpFAFDFF FHFJ-F56(-FZ6&Q$a13F'FdpF;FfpFAFDFFFHFJFAFDFF-F26(-F56(-F,6+-F,6%-I%ms upGF$6%FY-F86%Q\"2F'F;F>/%1superscriptshiftGFPFjn-Fdr6%FapFfrFirFhp-F, 6%-F#6%-F,6%-F,6'FfrFjnF^qFjnFYFhp-FZ6&Q\"hF'FdpF;FfpF;F>FjnFapFhp-F,6 #-Fdr6%F^qFfrFirFhp-F,6%FcqFjn-FZ6&Q$a21F'FdpF;FfpFhp-F,6%FhqFjn-FZ6&Q $a31F'FdpF;FfpFAFDFFFHFJ-F56(-F,6%-F,6%-F#6%-F,6'-F,6%-F#6%-F,6%FapFhp -FZ6&Q$t22F'FdpF;FfpF;F>FjnFYFhpF^qFhp-FZ6&Q$a22F'FdpF;FfpF;F>FjnFcqFh p-F,6%FhqFjn-FZ6&Q$a32F'FdpF;FfpFAFDFFFHFJ-F56(-F,6%-F,6%-F#6%-F,6'-F, 6%-F#6%-F,6%FapFhp-FZ6&Q$t32F'FdpF;FfpF;F>FjnFYFhpF^qFhp-FZ6&Q$a33F'Fd pF;FfpF;F>FjnFhqFhp-F,6%FcqFjn-FZ6&Q$a23F'FdpF;FfpFAFDFFFHFJFAFDFF/%&a lignGQ%axisF'/FBQ)baselineF'/FEQ'centerF'/FGQ'|frleft|hrF'/%/alignment scopeGFep/%,columnwidthGQ%autoF'/%&widthGFix/%+rowspacingGQ&1.0exF'/%. columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFdy/%&frameG Fdy/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFin/%-equalcolumnsGFin/ %-displaystyleGFin/%%sideGQ&rightF'/%0minlabelspacingGFayF;F>/%%openGQ \"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+ modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I $mtrGF$6(-I$mtdGF$6(-F,6%-F,6%-I#miGF$6&Q)λF'/%'italicGQ&falseF '/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'-I#moGF$6-Q1&Invisi bleTimes;F'FE/%&fenceGFA/%*separatorGFA/%)stretchyGFA/%*symmetricGFA/% (largeopGFA/%.movablelimitsGFA/%'accentGFA/%'lspaceGQ&0.0emF'/%'rspace GFfn-F<6&Q$t12F'/F@Q%trueF'FB/FFQ'italicF'-FI6.Q\"+F'FBFEFLFNFPFRFTFVF X/FenQ,0.2222222emF'/FhnFdo-F<6&Q$a11F'F\\oFBF^o/%)rowalignGQ!F'/%,col umnalignGF[p/%+groupalignGF[p/%(rowspanGQ\"1F'/%+columnspanGFbp-F56(-F <6&Q$a12F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a13F'F\\oFBF^oFioF\\pF^ pF`pFcpFioF\\pF^p-F26(-F56(-F<6&Q$a21F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(- F,6%-F,6%F;FH-F<6&Q$t22F'F\\oFBF^oF`o-F<6&Q$a22F'F\\oFBF^oFioF\\pF^pF` pFcp-F56(-F<6&Q$a23F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-F<6 &Q$a31F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a32F'F\\oFBF^oFioF\\pF^pF `pFcp-F56(-F,6%-F,6%F;FH-F<6&Q$t32F'F\\oFBF^oF`o-F<6&Q$a33F'F\\oFBF^oF ioF\\pF^pF`pFcpFioF\\pF^p/%&alignGQ%axisF'/FjoQ)baselineF'/F]pQ'center F'/F_pQ'|frleft|hrF'/%/alignmentscopeGF]o/%,columnwidthGQ%autoF'/%&wid thGF\\u/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ% noneF'/%,columnlinesGFgu/%&frameGFgu/%-framespacingGQ,0.4em~0.5exF'/%* equalrowsGFA/%-equalcolumnsGFA/%-displaystyleGFA/%%sideGQ&rightF'/%0mi nlabelspacingGFduFBFE/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.*&I'lambdaG6\"\"\"\"I$t12GF%F&F&*&F$F&I$t22GF%F&F&*&F$ F&I$t32GF%F&F&I$a11GF%F&I$a22GF%F&I$a33GF%F&" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 276 40 "Definition of the apparent singularity q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "Qsing:=(a12^2*a23-a12*a13*a22+a12*a 13*a33-a13^2*a32)/(a12*a13*(t22-t32));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&QsingG6\"**,**&I$a12GF$\"\"#I$a23GF$\"\"\"F+*(F(F+I$a13GF$F+I$a22 GF$F+!\"\"*(F(F+F-F+I$a33GF$F+F+*&F-F)I$a32GF$F+F/F+F(F/F-F/,&I$t22GF$ F+I$t32GF$F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "R31:=fact or(residue(L31(lambda),lambda=" }{MPLTEXT 1 0 5 "Qsing" }{MPLTEXT 1 0 4 ")):\n" }{MPLTEXT 1 0 39 "R32:=factor(residue(L32(lambda),lambda=" } {MPLTEXT 1 0 5 "Qsing" }{MPLTEXT 1 0 4 ")):\n" }{MPLTEXT 1 0 39 "R33:= factor(residue(L33(lambda),lambda=" }{MPLTEXT 1 0 5 "Qsing" }{MPLTEXT 1 0 3 "));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$R33G6\"I\"hGF$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 567 "L31bis:=(a11*a12*a13*a22*a3 3*t22-a11*a12*a13*a22*a33*t32-a11*a12*a13*a23*a32*t22+a11*a12*a13*a23* a32*t32-a12^2*a13*a21*a33*t22+a12^2*a13*a21*a33*t32+a12^2*a13*a23*a31* t22-a12^2*a13*a23*a31*t32+a12*a13^2*a21*a32*t22-a12*a13^2*a21*a32*t32- a12*a13^2*a22*a31*t22+a12*a13^2*a22*a31*t32+h*a12^2*a23*t12*t22-h*a12* a13*a22*t12*t22+h*a12*a13*a33*t12*t32-h*a13^2*a32*t12*t32)/(a12*a13*(t 22-t32))+(a11*a22*t32+a11*a33*t22-a12*a21*t32-a13*a31*t22+a22*a33*t12- a23*a32*t12-h*t12*t22-h*t12*t32)*lambda+(a11*t22*t32+a22*t12*t32+a33*t 12*t22)*lambda^2+t12*t22*t32*lambda^3+R31/(lambda-" }{MPLTEXT 1 0 5 "Q sing" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 56 "L32bis:=-a11*a22-a11*a3 3+a12*a21+a13*a31-a22*a33+a23*a32" }{MPLTEXT 1 0 113 "+h*t12+(-a11*t22 -a11*t32-a22*t12-a22*t32-a33*t12-a33*t22)*lambda+(-t12*t22-t12*t32-t22 *t32)*lambda^2+R32/(lambda-" }{MPLTEXT 1 0 5 "Qsing" }{MPLTEXT 1 0 1 " )" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 52 "L33bis:= (t12+t22+t32)*lambda+a11+a22+a33+ h/(lambda-" }{MPLTEXT 1 0 5 "Qsing" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 30 "simplify (L31(lambda)-L31bis);\n" }{MPLTEXT 1 0 30 "simplify(L32(lambda)-L32bis );\n" }{MPLTEXT 1 0 30 "simplify(L33(lambda)-L33bis);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 16 "L:=simplify(L):\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 29 "L31:=unapply(L31bis,lambda):\n" }{MPLTEXT 1 0 29 "L32 :=unapply(L32bis,lambda):\n" }{MPLTEXT 1 0 28 "L33:=unapply(L33bis,lam bda):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'L31bisG6\",,**,B*.I$a11GF$\" \"\"I$a12GF$F*I$a13GF$F*I$a22GF$F*I$a33GF$F*I$t22GF$F*F**.F)F*F+F*F,F* F-F*F.F*I$t32GF$F*!\"\"*.F)F*F+F*F,F*I$a23GF$F*I$a32GF$F*F/F*F2*.F)F*F +F*F,F*F4F*F5F*F1F*F**,F+\"\"#F,F*I$a21GF$F*F.F*F/F*F2*,F+F8F,F*F9F*F. F*F1F*F**,F+F8F,F*F4F*I$a31GF$F*F/F*F**,F+F8F,F*F4F*FI'L32bisG 6\",6*&I$a11GF$\"\"\"I$a22GF$F(!\"\"*&F'F(I$a33GF$F(F**&I$a12GF$F(I$a2 1GF$F(F(*&I$a13GF$F(I$a31GF$F(F(*&F)F(F,F(F**&I$a23GF$F(I$a32GF$F(F(*& I\"hGF$F(I$t12GF$F(F(*&,.*&F'F(I$t22GF$F(F**&F'F(I$t32GF$F(F**&F)F(F9F (F**&F)F(F?F(F**&F,F(F9F(F**&F,F(F=F(F*F(I'lambdaGF$F(F(*&,(*&F9F(F=F( F**&F9F(F?F(F**&F=F(F?F(F*F(FD\"\"#F(*.,6**F'F(F.F(F1F(F=F(F(**F'F(F.F (F1F(F?F(F**(F.FJF5F(F9F(F(*(F.FJF5F(F=F(F(**F.F(F1F(F)F(F9F(F***F.F(F 1F(F)F(F?F(F***F.F(F1F(F,F(F9F(F(**F.F(F1F(F,F(F=F(F(*(F1FJF6F(F9F(F** (F1FJF6F(F?F(F*F(F.F*F1F*F8F(,&F=F(F?F*F*,&FDF(**,**&F.FJF5F(F(*(F.F(F 1F(F)F(F**(F.F(F1F(F,F(F(*&F1FJF6F(F*F(F.F*F1F*FWF*F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'L33bisG6\",,*&,(I$t12GF$\"\"\"I$t22GF$F)I$t32G F$F)F)I'lambdaGF$F)F)I$a11GF$F)I$a22GF$F)I$a33GF$F)*&I\"hGF$F),&F,F)** ,**&I$a12GF$\"\"#I$a23GF$F)F)*(F6F)I$a13GF$F)F.F)!\"\"*(F6F)F:F)F/F)F) *&F:F7I$a32GF$F)F;F)F6F;F:F;,&F*F)F+F;F;F;F;F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 290 51 "Verification of the gauge formula with the formula " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "J33:=unapply(j33/(lambda-" }{MPLTEXT 1 0 5 "Qsing" }{MPLTEXT 1 0 11 "),lambda):\n" }{MPLTEXT 1 0 25 "J32:=unapp ly(j32/(lambda-" }{MPLTEXT 1 0 5 "Qsing" }{MPLTEXT 1 0 11 "),lambda): \n" }{MPLTEXT 1 0 25 "J31:=unapply(j31/(lambda-" }{MPLTEXT 1 0 5 "Qsin g" }{MPLTEXT 1 0 11 "),lambda):\n" }{MPLTEXT 1 0 8 "j33:=1:\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "J:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 11 "J[1,1]:=1:\n" }{MPLTEXT 1 0 11 "J[2,2]:=1:\n" }{MPLTEXT 1 0 21 "J[3,1]:=J31(lambda):\n" }{MPLTEXT 1 0 21 "J[3,2]:=J32(lambda):\n" }{MPLTEXT 1 0 21 "J[3,3]:=J33(lambda):\n" }{MPLTEXT 1 0 3 "J:\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "Jprime:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 84 "for i from 1 to 3 do for j from 1 to 3 do Jprime[i,j] :=diff(J[i,j],lambda): od: od:\n" }{MPLTEXT 1 0 8 "Jprime:\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 75 "checkL:=simplify(Multiply(Multip ly(J,L),J^(-1))+h*Multiply(Jprime,J^(-1))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 755 "j31 :=factor( (a11*a12^3*a13*a23*t22^2-a11*a12^3* a13*a23*t22*t32-a11*a12^2*a13^2*a22*t22*t32+a11*a12^2*a13^2*a22*t32^2+ a11*a12^2*a13^2*a33*t22^2-a11*a12^2*a13^2*a33*t22*t32-a11*a12*a13^3*a3 2*t22*t32+a11*a12*a13^3*a32*t32^2+a12^4*a23^2*t12*t22-a12^3*a13^2*a21* t22^2+2*a12^3*a13^2*a21*t22*t32-a12^3*a13^2*a21*t32^2-a12^3*a13*a22*a2 3*t12*t22-a12^3*a13*a22*a23*t12*t32+2*a12^3*a13*a23*a33*t12*t22-a12^2* a13^3*a31*t22^2+2*a12^2*a13^3*a31*t22*t32-a12^2*a13^3*a31*t32^2+a12^2* a13^2*a22^2*t12*t32-a12^2*a13^2*a22*a33*t12*t22-a12^2*a13^2*a22*a33*t1 2*t32-a12^2*a13^2*a23*a32*t12*t22-a12^2*a13^2*a23*a32*t12*t32+a12^2*a1 3^2*a33^2*t12*t22+2*a12*a13^3*a22*a32*t12*t32-a12*a13^3*a32*a33*t12*t2 2-a12*a13^3*a32*a33*t12*t32+a13^4*a32^2*t12*t32)/(a12^2*a13^2*(t22-t32 )^2))-" }{MPLTEXT 1 0 7 "h*t12;\n" }{MPLTEXT 1 0 191 "j32 :=factor( -( a11*a12*a13*t22-a11*a12*a13*t32+a12^2*a23*t12+a12^2*a23*t22-a12*a13*a2 2*t12-a12*a13*a22*t32+a12*a13*a33*t12+a12*a13*a33*t22-a13^2*a32*t12-a1 3^2*a32*t32)/(a12*a13*(t22-t32)));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 49 "factor(simplify(residue(checkL[3,1],lambda=Q)));\n" }{MPLTEXT 1 0 49 "factor(simplify(residue(checkL[3,2],lambda=Q)));\n" }{MPLTEXT 1 0 49 "factor(simplify(residue(checkL[3,3],lambda=Q)));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 16 "J:=simplify(J):\n" }{MPLTEXT 1 0 25 "chec kL:=simplify(checkL):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$j31G6\",&**, Z*,I$a11GF$\"\"\"I$a12GF$\"\"$I$a13GF$F*I$a23GF$F*I$t22GF$\"\"#F**.F)F *F+F,F-F*F.F*F/F*I$t32GF$F*!\"\"*.F)F*F+F0F-F0I$a22GF$F*F/F*F2F*F3*,F) F*F+F0F-F0F5F*F2F0F**,F)F*F+F0F-F0I$a33GF$F*F/F0F**.F)F*F+F0F-F0F8F*F/ F*F2F*F3*.F)F*F+F*F-F,I$a32GF$F*F/F*F2F*F3*,F)F*F+F*F-F,F;F*F2F0F***F+ \"\"%F.F0I$t12GF$F*F/F*F***F+F,F-F0I$a21GF$F*F/F0F3*,F+F,F-F0FAF*F/F*F 2F*F0**F+F,F-F0FAF*F2F0F3*.F+F,F-F*F5F*F.F*F?F*F/F*F3*.F+F,F-F*F5F*F.F *F?F*F2F*F3*.F+F,F-F*F.F*F8F*F?F*F/F*F0**F+F0F-F,I$a31GF$F*F/F0F3*,F+F 0F-F,FHF*F/F*F2F*F0**F+F0F-F,FHF*F2F0F3*,F+F0F-F0F5F0F?F*F2F*F**.F+F0F -F0F5F*F8F*F?F*F/F*F3*.F+F0F-F0F5F*F8F*F?F*F2F*F3*.F+F0F-F0F.F*F;F*F?F *F/F*F3*.F+F0F-F0F.F*F;F*F?F*F2F*F3*,F+F0F-F0F8F0F?F*F/F*F**.F+F*F-F,F 5F*F;F*F?F*F2F*F0*.F+F*F-F,F;F*F8F*F?F*F/F*F3*.F+F*F-F,F;F*F8F*F?F*F2F *F3**F-F>F;F0F?F*F2F*F*F*F+!\"#F-FU,&F/F*F2F3FUF**&I\"hGF$F*F?F*F3" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I$j32G6\",$**,6**I$a11GF$\"\"\"I$a12GF$ F*I$a13GF$F*I$t22GF$F*F***F)F*F+F*F,F*I$t32GF$F*!\"\"*(F+\"\"#I$a23GF$ F*I$t12GF$F*F**(F+F2F3F*F-F*F***F+F*F,F*I$a22GF$F*F4F*F0**F+F*F,F*F7F* F/F*F0**F+F*F,F*I$a33GF$F*F4F*F***F+F*F,F*F:F*F-F*F**(F,F2I$a32GF$F*F4 F*F0*(F,F2F=F*F/F*F0F*F+F0F,F0,&F-F*F/F0F0F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "series(simplify(series(" }{MPLTEXT 1 0 26 "factor(series(checkL[2, 1]-" }{MPLTEXT 1 0 23 "h*t12,lambda=infinity))" }{MPLTEXT 1 0 35 ",lam bda=infinity)),lambda=infinity)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 7 "series(" } {MPLTEXT 1 0 7 "factor(" }{MPLTEXT 1 0 35 "series(checkL[2,2],lambda=i nfinity)" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 18 ",lambda=infinity))" } {MPLTEXT 1 0 17 ",lambda=infinity)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 7 "series(" } {MPLTEXT 1 0 7 "factor(" }{MPLTEXT 1 0 35 "series(checkL[2,3],lambda=i nfinity)" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 18 ",lambda=infinity))" } {MPLTEXT 1 0 17 ",lambda=infinity)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 9 "simplify(" } {MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 7 "factor(" }{MPLTEXT 1 0 43 "s eries(checkL[3,1]-h*t12^2,lambda=infinity)" }{MPLTEXT 1 0 1 ")" } {MPLTEXT 1 0 18 ",lambda=infinity))" }{MPLTEXT 1 0 17 ",lambda=infinit y)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 9 "s implify(" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 7 "factor(" } {MPLTEXT 1 0 35 "series(checkL[3,2],lambda=infinity)" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 18 ",lambda=infinity))" }{MPLTEXT 1 0 17 ",lambda=in finity)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 7 "factor(" } {MPLTEXT 1 0 35 "series(checkL[3,3],lambda=infinity)" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 18 ",lambda=infinity))" }{MPLTEXT 1 0 17 ",lambda=in finity)" }{MPLTEXT 1 0 1 ";" }}{PARA 11 "" 1 "" {XPPMATH 20 "**,,**I$a 12G6\"\"\"%I$a23GF&\"\"#I$t12GF&\"\"\"I$t22GF&F+!\"\"*(,&*(I$a21GF&F+, &F,F+I$t32GF&F-F)I$a13GF&F+F-*&F(F+,(*&F,F)I$a11GF&F+F+*&,&*&F3F+F8F+F -*&F*F+,&I$a33GF&!\"#I$a22GF&F+F+F-F+F,F+F+*(F*F+F3F+F@F+F-F+F+F+F4F+F %\"\"$F-*(,**(I$a31GF&F+F2F)F4F+F-*(F8F+F,F)F>F+F+*&,&*(F8F+,&F>F+F@F+ F+F3F+F-*&F*F+,(*&F@F+F>F+F+*&F(F+I$a32GF&F+F+*$F>F)F-F+F-F+F,F+F+*&,& *(F3F+F8F+F@F+F+*&F*F+,(*$F@F)F+FNF-FOF-F+F+F+F3F+F+F+F4F)F%F)F-**FPF+ F4FB,&*&,&*&F8F+F3F+F+*&F>F+F*F+F+F+F,F+F+*&,&F;F+*&,&F@F+F>#F-F)F+F*F +F)F+F3F+F-F+F%F+F+**F4F'FPF)F*F+F3F+F-F+F%F?F4F?F2F?" }}{PARA 11 "" 1 "" {XPPMATH 20 "**,(*(I$a23G6\"\"\"\",&I$t12GF&F'I$t22GF&F'F'I$a12GF& \"\"#!\"\"*(,(*&F)F',&I$a22GF&F'I$a33GF&F-F'F'*&,&I$a11GF&F-F3F-F'F*F' F'*&I$t32GF&F',&F6F'F2F'F'F'F'I$a13GF&F'F+F'F'*(F:F,I$a32GF&F',&F)F'F8 F'F'F'F'F+F-F:F-,&F*F-F8F'F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I'lamb daG6\"\"\"\"**,(*&I$a12GF$\"\"#I$a23GF$F%!\"\"*(I$a13GF$F%,&I$a22GF$F% I$a33GF$F,F%F)F%F%*&F.F*I$a32GF$F%F%F%F)F,F.F,,&I$t22GF$F%I$t32GF$F,F, F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(**,(*&I$t22G6\"\"\"$I$t32GF'\"\" \"!\"\"*&F&\"\"#F)F-F-*&F&F*F)F(F+F*I$t12GF'F*,&F&F*F)F+!\"#I'lambdaGF 'F-F+*,,(*.I$a13GF'F*,&*&F&F*F)F*F+*$F)F-F*F*F&F*F/F*I$a23GF'F*I$a12GF 'F(F+*(,&*&,**(I$a22GF'F*F&F*F)F-F**&FAF*F)F(F+*&I$a33GF'F*F&F(F+*(FDF *F&F-F)F*F*F*F/F*F***F&F*F)F*I$a11GF'F*F0F-F+F*F6F-F;F-F+*.I$a32GF'F*F 6F(F)F*,&*$F&F-F+F8F*F*F/F*F;F*F*F*F;F1F6F1F0F1F2F*F***,,*,F/F*F&F*F:F -,&F/F*F&F*F*F;\"\"%F+*(,&**I$a21GF'F*F0F-FOF*F6F*F+*&F:F*,(*&,&*&,&FA F+FDF-F*F&F*F**&FAF*F)F*F+F*F/F-F**(F&F*,&*&,(FGF*FAF+FDF*F*F&F*F**&F) F*,(FGF*FAF*FDF+F*F+F*F/F*F**(F&F-FGF*F0F*F*F*F*F*F6F*F;F(F+*(,***I$a3 1GF'F*F0F-,&F/F*F)F*F*F6F*F+*&,&*&,(*&FAF*FDF*F+*&F:F*FIF*F+*$FDF-F*F* F&F*F**&F)F*,(*$FAF-F*FfoF+FgoF+F*F*F*F/F-F**&,(*(FDF*,&FGF*FAF+F*F&F- F**(,**&FGF*,&FDF*FAF*F*F*F[pF+FgoF-FhoF+F*F)F*F&F*F+*(FAF*F)F-,&FGF*F DF+F*F*F*F/F*F**,F&F*F)F*FGF*F0F*,&FAF*FDF+F*F+F*F6F-F;F-F+**FIF*,(*&, &*&FDF*F&F*F**&,&FAF*FD#F+F-F*F)F*F1F*F/F-F**(FgnF*F)F*F/F*F**(F)F-FGF *F0F*F*F*F6F(F;F*F**,F/F*F)F*F6FPFIF-FaoF*F+F*F;F1F6F1F0F1F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(,&*&,&*$I$t22G6\"\"\"#\"\"\"*$I$t32GF)F*! \"\"F+I$t12GF)F+F+*(F-F+F(F+,&F(F.F-F+F+F.F+F1F.I'lambdaGF)F+F+**,(*(I $a23GF)F+,(*$F/F*F+*&F/F+F(F+F+F'F+F+I$a12GF)F*F.*(,(*&,&I$a22GF)F+I$a 33GF)F.F+F/F*F+*&,&*&,&I$a11GF)F.F?F+F+F(F+F+*&F-F+,&FEF+F@F.F+F+F+F/F +F+*(F-F+,&F@F+F?F.F+F(F+F.F+I$a13GF)F+F:F+F+*(FJF*I$a32GF)F+,(F8F+*&F /F+F-F+F+F,F+F+F+F+F:F.FJF.F1F.F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&* (,(*&,&I$t22G6\"\"\"\"I$t32GF(!\"\"F)I$t12GF(F)F)*$F'\"\"#F)*$F*F.F+F) F&F+I'lambdaGF(F)F)**,(*(I$a23GF(F),&F,F)F'F)F)I$a12GF(F.F+*(I$a13GF(F ),(*&F,F),&I$a22GF(F)I$a33GF(F+F)F)*&F " 0 "" {MPLTEXT 1 0 22 " Gnorm:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 37 "Gnorm[1,1]:=Gnorm111*lambda +Gnorm11:\n" }{MPLTEXT 1 0 37 "Gnorm[1,2]:=Gnorm112*lambda+Gnorm12:\n" }{MPLTEXT 1 0 37 "Gnorm[1,3]:=Gnorm113*lambda+Gnorm13:\n" }{MPLTEXT 1 0 37 "Gnorm[2,1]:=Gnorm121*lambda+Gnorm21:\n" }{MPLTEXT 1 0 37 "Gnor m[2,2]:=Gnorm122*lambda+Gnorm22:\n" }{MPLTEXT 1 0 37 "Gnorm[2,3]:=Gnor m123*lambda+Gnorm23:\n" }{MPLTEXT 1 0 37 "Gnorm[3,1]:=Gnorm131*lambda+ Gnorm31:\n" }{MPLTEXT 1 0 37 "Gnorm[3,2]:=Gnorm132*lambda+Gnorm32:\n" }{MPLTEXT 1 0 37 "Gnorm[3,3]:=Gnorm133*lambda+Gnorm33:\n" }{MPLTEXT 1 0 6 "Gnorm;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 5 "Gnorm" }{MPLTEXT 1 0 22 "prime:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do " }{MPLTEXT 1 0 5 "Gnorm" } {MPLTEXT 1 0 17 "prime[i,j]:=diff(" }{MPLTEXT 1 0 5 "Gnorm" }{MPLTEXT 1 0 23 "[i,j],lambda): od: od:\n" }{MPLTEXT 1 0 5 "Gnorm" }{MPLTEXT 1 0 6 "prime;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenam eG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6( -I$mtdGF$6(-F,6%-F,6%-I#miGF$6&Q)λF'/%'italicGQ&falseF'/%+foreg roundGQ([0,0,0]F'/%,mathvariantGQ'normalF'-I#moGF$6-Q1⁢ F'FE/%&fenceGFA/%*separatorGFA/%)stretchyGFA/%*symmetricGFA/%(largeopG FA/%.movablelimitsGFA/%'accentGFA/%'lspaceGQ&0.0emF'/%'rspaceGFfn-F<6& Q)Gnorm111F'/F@Q%trueF'FB/FFQ'italicF'-FI6.Q\"+F'FBFEFLFNFPFRFTFVFX/Fe nQ,0.2222222emF'/FhnFdo-F<6&Q(Gnorm11F'F\\oFBF^o/%)rowalignGQ!F'/%,col umnalignGF[p/%+groupalignGF[p/%(rowspanGQ\"1F'/%+columnspanGFbp-F56(-F ,6%-F,6%F;FH-F<6&Q)Gnorm112F'F\\oFBF^oF`o-F<6&Q(Gnorm12F'F\\oFBF^oFioF \\pF^pF`pFcp-F56(-F,6%-F,6%F;FH-F<6&Q)Gnorm113F'F\\oFBF^oF`o-F<6&Q(Gno rm13F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-F,6%-F,6%F;FH-F<6& Q)Gnorm121F'F\\oFBF^oF`o-F<6&Q(Gnorm21F'F\\oFBF^oFioF\\pF^pF`pFcp-F56( -F,6%-F,6%F;FH-F<6&Q)Gnorm122F'F\\oFBF^oF`o-F<6&Q(Gnorm22F'F\\oFBF^oFi oF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FH-F<6&Q)Gnorm123F'F\\oFBF^oF`o-F<6&Q(G norm23F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-F,6%-F,6%F;FH-F< 6&Q)Gnorm131F'F\\oFBF^oF`o-F<6&Q(Gnorm31F'F\\oFBF^oFioF\\pF^pF`pFcp-F5 6(-F,6%-F,6%F;FH-F<6&Q)Gnorm132F'F\\oFBF^oF`o-F<6&Q(Gnorm32F'F\\oFBF^o FioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FH-F<6&Q)Gnorm133F'F\\oFBF^oF`o-F<6&Q (Gnorm33F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p/%&alignGQ%axisF'/FjoQ)ba selineF'/F]pQ'centerF'/F_pQ'|frleft|hrF'/%/alignmentscopeGF]o/%,column widthGQ%autoF'/%&widthGFfw/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0. 8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFax/%&frameGFax/%-framespacing GQ,0.4em~0.5exF'/%*equalrowsGFA/%-equalcolumnsGFA/%-displaystyleGFA/%% sideGQ&rightF'/%0minlabelspacingGF^xFBFE/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Types ettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(- I#miGF$6&Q)Gnorm111F'/%'italicGQ%trueF'/%+foregroundGQ([0,0,0]F'/%,mat hvariantGQ'italicF'/%)rowalignGQ!F'/%,columnalignGFF/%+groupalignGFF/% (rowspanGQ\"1F'/%+columnspanGFM-F56(-F86&Q)Gnorm112F'F;F>FAFDFGFIFKFN- F56(-F86&Q)Gnorm113F'F;F>FAFDFGFIFKFNFDFGFI-F26(-F56(-F86&Q)Gnorm121F' F;F>FAFDFGFIFKFN-F56(-F86&Q)Gnorm122F'F;F>FAFDFGFIFKFN-F56(-F86&Q)Gnor m123F'F;F>FAFDFGFIFKFNFDFGFI-F26(-F56(-F86&Q)Gnorm131F'F;F>FAFDFGFIFKF N-F56(-F86&Q)Gnorm132F'F;F>FAFDFGFIFKFN-F56(-F86&Q)Gnorm133F'F;F>FAFDF GFIFKFNFDFGFI/%&alignGQ%axisF'/FEQ)baselineF'/FHQ'centerF'/FJQ'|frleft |hrF'/%/alignmentscopeGF=/%,columnwidthGQ%autoF'/%&widthGFcq/%+rowspac ingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnli nesGF^r/%&frameGF^r/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&false F'/%-equalcolumnsGFhr/%-displaystyleGFhr/%%sideGQ&rightF'/%0minlabelsp acingGF[rF>/FBQ'normalF'/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "TdLtheo:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 30 "TdLtheo[1,1]:=t12*lambda+a11:\n" }{MPLTEXT 1 0 18 "Td Ltheo[1,2]:=a12:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "TdLtheo[1,3]: =a13:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 14 "TdLtheo[2,1]:=" } {MPLTEXT 1 0 5 "a21:\n" }{MPLTEXT 1 0 14 "TdLtheo[2,2]:=" }{MPLTEXT 1 0 14 "t22*lambda+a22" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 14 "TdLtheo[ 2,3]:=" }{MPLTEXT 1 0 3 "a23" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "TdLtheo[3,1]:=a31:\n" }{MPLTEXT 1 0 19 "TdLtheo[3,2 ]:=a32:\n" }{MPLTEXT 1 0 14 "TdLtheo[3,3]:=" }{MPLTEXT 1 0 11 "t32*lam bda+" }{MPLTEXT 1 0 4 "a33:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "TdL theo;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 88 "Equ ationToCancel:=simplify(Multiply(TdLtheo,Gnorm)-Multiply(Gnorm,checkL) -h*Gnormprime):" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modul enameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrG F$6(-I$mtdGF$6(-F,6%-F,6%-I#miGF$6&Q)λF'/%'italicGQ&falseF'/%+f oregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'-I#moGF$6-Q1&InvisibleTi mes;F'FE/%&fenceGFA/%*separatorGFA/%)stretchyGFA/%*symmetricGFA/%(larg eopGFA/%.movablelimitsGFA/%'accentGFA/%'lspaceGQ&0.0emF'/%'rspaceGFfn- F<6&Q$t12F'/F@Q%trueF'FB/FFQ'italicF'-FI6.Q\"+F'FBFEFLFNFPFRFTFVFX/Fen Q,0.2222222emF'/FhnFdo-F<6&Q$a11F'F\\oFBF^o/%)rowalignGQ!F'/%,columnal ignGF[p/%+groupalignGF[p/%(rowspanGQ\"1F'/%+columnspanGFbp-F56(-F<6&Q$ a12F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a13F'F\\oFBF^oFioF\\pF^pF`pF cpFioF\\pF^p-F26(-F56(-F<6&Q$a21F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F,6%- F,6%F;FH-F<6&Q$t22F'F\\oFBF^oF`o-F<6&Q$a22F'F\\oFBF^oFioF\\pF^pF`pFcp- F56(-F<6&Q$a23F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-F<6&Q$a3 1F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a32F'F\\oFBF^oFioF\\pF^pF`pFcp -F56(-F,6%-F,6%F;FH-F<6&Q$t32F'F\\oFBF^oF`o-F<6&Q$a33F'F\\oFBF^oFioF \\pF^pF`pFcpFioF\\pF^p/%&alignGQ%axisF'/FjoQ)baselineF'/F]pQ'centerF'/ F_pQ'|frleft|hrF'/%/alignmentscopeGF]o/%,columnwidthGQ%autoF'/%&widthG F\\u/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%non eF'/%,columnlinesGFgu/%&frameGFgu/%-framespacingGQ,0.4em~0.5exF'/%*equ alrowsGFA/%-equalcolumnsGFA/%-displaystyleGFA/%%sideGQ&rightF'/%0minla belspacingGFduFBFE/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Gnorm113:=0:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[1,1]/lambda^4,lambda=infinity ));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[1,2]/lambda^ 4,lambda=infinity));\n" }{MPLTEXT 1 0 65 "factor(-residue(EquationToCa ncel[1,3]/lambda^4,lambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 12 "Gnorm123:=0:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-r esidue(EquationToCancel[2,1]/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[2,2]/lambda^4,lambda=infinity ));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[2,3]/lambda^ 4,lambda=infinity));\n" }{MPLTEXT 1 0 12 "Gnorm133:=0:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[3,1]/lambda^ 4,lambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCa ncel[3,2]/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 65 "factor(-res idue(EquationToCancel[3,3]/lambda^4,lambda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Gnorm112:=0:\n" }{MPLTEXT 1 0 26 "Gnorm111:=Gnorm13*t32*t22;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[1,1]/lambda^3,lambda=infinity)); \n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[1,2]/lambda^3,l ambda=infinity));\n" }{MPLTEXT 1 0 65 "factor(-residue(EquationToCance l[1,3]/lambda^3,lambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 13 "Gnorm122:=0:\n" }{MPLTEXT 1 0 26 "Gnorm121:=Gnorm23*t32*t12;" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel [2,1]/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residue (EquationToCancel[2,2]/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[2,3]/lambda^3,lambda=infinity)); \n" }{MPLTEXT 1 0 13 "Gnorm132:=0:\n" }{MPLTEXT 1 0 26 "Gnorm131:=Gnor m33*t22*t12;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-residue(E quationToCancel[3,1]/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 66 " factor(-residue(EquationToCancel[3,2]/lambda^3,lambda=infinity));\n" } {MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[3,3]/lambda^3,lambda =infinity));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "Gnorm:=simplify (Gnorm);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Gnorm111G6\"*(I(Gnorm13GF $\"\"\"I$t32GF$F'I$t22GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Gnorm121G6\"*(I(Gnorm23GF$\" \"\"I$t12GF$F'I$t32GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Gnorm131G6\"*(I(Gnorm33GF$\" \"\"I$t12GF$F'I$t22GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I ,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtd GF$6(-F,6%-F,6)-I#miGF$6&Q(Gnorm13F'/%'italicGQ%trueF'/%+foregroundGQ( [0,0,0]F'/%,mathvariantGQ'italicF'-I#moGF$6-Q1⁢F'/FFQ'n ormalF'/%&fenceGQ&falseF'/%*separatorGFP/%)stretchyGFP/%*symmetricGFP/ %(largeopGFP/%.movablelimitsGFP/%'accentGFP/%'lspaceGQ&0.0emF'/%'rspac eGFin-F<6&Q)λF'/F@FPFBFLFH-F<6&Q$t22F'F?FBFEFH-F<6&Q$t32F'F?FBF E-FI6.Q\"+F'FBFLFNFQFSFUFWFYFen/FhnQ,0.2222222emF'/F[oFjo-F<6&Q(Gnorm1 1F'F?FBFE/%)rowalignGQ!F'/%,columnalignGFap/%+groupalignGFap/%(rowspan GQ\"1F'/%+columnspanGFhp-F56(-F<6&Q(Gnorm12F'F?FBFEF_pFbpFdpFfpFip-F56 (F;F_pFbpFdpFfpFipF_pFbpFdp-F26(-F56(-F,6%-F,6)-F<6&Q(Gnorm23F'F?FBFEF HF\\oFH-F<6&Q$t12F'F?FBFEFHFcoFfo-F<6&Q(Gnorm21F'F?FBFEF_pFbpFdpFfpFip -F56(-F<6&Q(Gnorm22F'F?FBFEF_pFbpFdpFfpFip-F56(FjqF_pFbpFdpFfpFipF_pFb pFdp-F26(-F56(-F,6%-F,6)-F<6&Q(Gnorm33F'F?FBFEFHF\\oFHF]rFHF`oFfo-F<6& Q(Gnorm31F'F?FBFEF_pFbpFdpFfpFip-F56(-F<6&Q(Gnorm32F'F?FBFEF_pFbpFdpFf pFip-F56(FbsF_pFbpFdpFfpFipF_pFbpFdp/%&alignGQ%axisF'/F`pQ)baselineF'/ FcpQ'centerF'/FepQ'|frleft|hrF'/%/alignmentscopeGFA/%,columnwidthGQ%au toF'/%&widthGF\\u/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)r owlinesGQ%noneF'/%,columnlinesGFgu/%&frameGFgu/%-framespacingGQ,0.4em~ 0.5exF'/%*equalrowsGFP/%-equalcolumnsGFP/%-displaystyleGFP/%%sideGQ&ri ghtF'/%0minlabelspacingGFduFBFL/%%openGQ\"[F'/%&closeGQ\"]F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Gnorm12:=-Gnorm13*(t22+t32); \n" }{MPLTEXT 1 0 143 "Gnorm13:=(Gnorm23*a12*t32+Gnorm33*a13*t22+Gnorm 11)*a13*a12*(t22-t32)/(a12^2*a23*t22*t32-a12*a13*a22*t32^2+a12*a13*a33 *t22^2-a13^2*a32*t22*t32);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "fac tor(-residue(EquationToCancel[1,1]/lambda^2,lambda=infinity));\n" } {MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[1,2]/lambda^2,lambda =infinity));\n" }{MPLTEXT 1 0 65 "factor(-residue(EquationToCancel[1,3 ]/lambda^2,lambda=infinity));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm12G6\",$*&I(Gnorm13GF$\"\"\",&I$t22GF$F(I$t32GF$F (F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm13G6\"*,,(*(I(Gnorm2 3GF$\"\"\"I$a12GF$F)I$t32GF$F)F)*(I(Gnorm33GF$F)I$a13GF$F)I$t22GF$F)F) I(Gnorm11GF$F)F)F.F)F*F),&F/F)F+!\"\"F),***F*\"\"#I$a23GF$F)F/F)F+F)F) **F*F)F.F)I$a22GF$F)F+F5F2**F*F)F.F)I$a33GF$F)F/F5F)**F.F5I$a32GF$F)F/ F)F+F)F2F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Gnorm22:=-Gnorm23*(t12+t32);\n" } {MPLTEXT 1 0 1099 "Gnorm23:=(Gnorm33*a12^2*a23^2*t12*t22*t32+Gnorm33*a 12*a13^2*a21*t22^2*t32-Gnorm33*a12*a13^2*a21*t22*t32^2-Gnorm33*a12*a13 *a22*a23*t12*t32^2+Gnorm33*a12*a13*a23*a33*t12*t22^2-Gnorm33*a13^2*a23 *a32*t12*t22*t32+Gnorm11*a12*a13*a21*t22*t32-Gnorm11*a12*a13*a21*t32^2 +Gnorm21*a12^2*a23*t22*t32-Gnorm21*a12*a13*a22*t32^2+Gnorm21*a12*a13*a 33*t22^2-Gnorm21*a13^2*a32*t22*t32)*a12*a13*(t22-t32)/(a11*a12^3*a13*a 23*t22^2*t32^2-a11*a12^3*a13*a23*t22*t32^3-a11*a12^2*a13^2*a22*t22*t32 ^3+a11*a12^2*a13^2*a22*t32^4+a11*a12^2*a13^2*a33*t22^3*t32-a11*a12^2*a 13^2*a33*t22^2*t32^2-a11*a12*a13^3*a32*t22^2*t32^2+a11*a12*a13^3*a32*t 22*t32^3+a12^4*a23^2*t12*t22*t32^2-a12^3*a13^2*a21*t22^2*t32^2+2*a12^3 *a13^2*a21*t22*t32^3-a12^3*a13^2*a21*t32^4-a12^3*a13*a22*a23*t12*t22*t 32^2-a12^3*a13*a22*a23*t12*t32^3+2*a12^3*a13*a23*a33*t12*t22^2*t32+a12 ^2*a13^2*a22^2*t12*t32^3-a12^2*a13^2*a22*a33*t12*t22^2*t32-a12^2*a13^2 *a22*a33*t12*t22*t32^2-2*a12^2*a13^2*a23*a32*t12*t22*t32^2+a12^2*a13^2 *a33^2*t12*t22^3+a12*a13^3*a22*a32*t12*t22*t32^2+a12*a13^3*a22*a32*t12 *t32^3-2*a12*a13^3*a32*a33*t12*t22^2*t32+a13^4*a32^2*t12*t22*t32^2);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCance l[2,1]/lambda^2,lambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residu e(EquationToCancel[2,2]/lambda^2,lambda=infinity));\n" }{MPLTEXT 1 0 65 "factor(-residue(EquationToCancel[2,3]/lambda^2,lambda=infinity));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm22G6\",$*& I(Gnorm23GF$\"\"\",&I$t12GF$F(I$t32GF$F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm23G6\"*,,:*.I(Gnorm33GF$\"\"\"I$a12GF$\"\"#I$a23G F$F+I$t12GF$F)I$t22GF$F)I$t32GF$F)F)*.F(F)F*F)I$a13GF$F+I$a21GF$F)F.F+ F/F)F)*.F(F)F*F)F1F+F2F)F.F)F/F+!\"\"*0F(F)F*F)F1F)I$a22GF$F)F,F)F-F)F /F+F4*0F(F)F*F)F1F)F,F)I$a33GF$F)F-F)F.F+F)*0F(F)F1F+F,F)I$a32GF$F)F-F )F.F)F/F)F4*.I(Gnorm11GF$F)F*F)F1F)F2F)F.F)F/F)F)*,F " 0 "" {MPLTEXT 1 0 28 "Gnorm32:=-Gnorm33*(t12+t22);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 97 "Gnorm33:=factor(solve(factor(-residue(EquationToCancel[3,1]/lambda ^2,lambda=infinity)),Gnorm33)):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[3,1]/lambda^2,lambda=infinity)); \n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[3,2]/lambda^2,l ambda=infinity));\n" }{MPLTEXT 1 0 65 "factor(-residue(EquationToCance l[3,3]/lambda^2,lambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "Gnorm:=simplify(Gnorm):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnor m32G6\",$*&I(Gnorm33GF$\"\"\",&I$t12GF$F(I$t22GF$F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "Gnorm31:=factor(solve(factor(-residue(EquationToCance l[3,3]/lambda^1,lambda=infinity)),Gnorm31)):\n" }{MPLTEXT 1 0 66 "fact or(-residue(EquationToCancel[3,3]/lambda^1,lambda=infinity));\n" } {MPLTEXT 1 0 1 "f" }{MPLTEXT 1 0 64 "actor(-residue(EquationToCancel[3 ,2]/lambda^1,lambda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"! " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "Gnorm11:=Gnorm21*a12^2*a13*(t22-t32)^2/(a11*a12*a13* t22*t32-a11*a12*a13*t32^2+a12^2*a23*t12*t22-a12*a13*a22*t12*t32+a12*a1 3*a33*t12*t22-a13^2*a32*t12*t32);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I(Gnorm11G6\"*,I(Gnorm21GF$\"\"\"I$a12GF$\"\"#I$a13GF$F',&I$t22GF$F'I$ t32GF$!\"\"F),.*,I$a11GF$F'F(F'F*F'F,F'F-F'F'**F1F'F(F'F*F'F-F)F.**F(F )I$a23GF$F'I$t12GF$F'F,F'F'*,F(F'F*F'I$a22GF$F'F5F'F-F'F.*,F(F'F*F'I$a 33GF$F'F5F'F,F'F'**F*F)I$a32GF$F'F5F'F-F'F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[3,1]/lambda^1,l ambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCance l[2,1]/lambda^1,lambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residu e(EquationToCancel[2,2]/lambda^1,lambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[2,3]/lambda^1,lambda=infinity)); \n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCancel[1,1]/lambda^1,l ambda=infinity));\n" }{MPLTEXT 1 0 66 "factor(-residue(EquationToCance l[1,2]/lambda^1,lambda=infinity));\n" }{MPLTEXT 1 0 65 "factor(-residu e(EquationToCancel[1,3]/lambda^1,lambda=infinity));" }}{PARA 11 "" 1 " " {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Gnorm11:=factor(Gnorm11);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "Gnorm12:=factor(Gnorm12);\n" }{MPLTEXT 1 0 9 "Gnorm1 3:=" }{MPLTEXT 1 0 17 "factor(Gnorm13);\n" }{MPLTEXT 1 0 25 "Gnorm21:= factor(Gnorm21);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "Gnorm22:=" } {MPLTEXT 1 0 17 "factor(Gnorm22);\n" }{MPLTEXT 1 0 9 "Gnorm23:=" } {MPLTEXT 1 0 17 "factor(Gnorm23);\n" }{MPLTEXT 1 0 9 "Gnorm31:=" } {MPLTEXT 1 0 17 "factor(Gnorm31);\n" }{MPLTEXT 1 0 26 "Gnorm32:=factor (Gnorm32);\n" }{MPLTEXT 1 0 26 "Gnorm33:=factor(Gnorm33);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 150 "Gnorm21:=(a11*a12*a13*t22*t32-a11*a12*a 13*t32^2+a12^2*a23*t12*t22-a12*a13*a22*t12*t32+a12*a13*a33*t12*t22-a13 ^2*a32*t12*t32)/(a12^2*(t22-t32)^2*a13):\n" }{MPLTEXT 1 0 23 "Gnorm:=s implify(Gnorm);" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I(Gnorm11G6\"*,I(Gnorm21GF$\"\"\"I$a12GF$\"\"#I$a13GF$F',&I$t22GF$F'I $t32GF$!\"\"F),.*,I$a11GF$F'F(F'F*F'F,F'F-F'F'**F1F'F(F'F*F'F-F)F.**F( F)I$a23GF$F'I$t12GF$F'F,F'F'*,F(F'F*F'I$a22GF$F'F5F'F-F'F.*,F(F'F*F'I$ a33GF$F'F5F'F,F'F'**F*F)I$a32GF$F'F5F'F-F'F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm12G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(G norm13G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm21G6\"F#" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm22G6\",$*.,&I$t12GF$\"\"\"I$t32G F$F)F),&I$t22GF$F)F*!\"\"F)I$a12GF$F)I$a13GF$F)I(Gnorm21GF$F),.*,I$a11 GF$F)F.F)F/F)F,F)F*F)F)**F3F)F.F)F/F)F*\"\"#F-**F.F5I$a23GF$F)F(F)F,F) F)*,F.F)F/F)I$a22GF$F)F(F)F*F)F-*,F.F)F/F)I$a33GF$F)F(F)F,F)F)**F/F5I$ a32GF$F)F(F)F*F)F-F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm23G6\" *,,&I$t22GF$\"\"\"I$t32GF$!\"\"F(I$a12GF$F(I$a13GF$F(I(Gnorm21GF$F(,.* ,I$a11GF$F(F+F(F,F(F'F(F)F(F(**F0F(F+F(F,F(F)\"\"#F***F+F2I$a23GF$F(I$ t12GF$F(F'F(F(*,F+F(F,F(I$a22GF$F(F5F(F)F(F**,F+F(F,F(I$a33GF$F(F5F(F' F(F(**F,F2I$a32GF$F(F5F(F)F(F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(G norm31G6\",$*,,.**I$a11GF$\"\"\"I$a12GF$F*I$a13GF$F*I$t22GF$\"\"#F**,F )F*F+F*F,F*F-F*I$t32GF$F*!\"\"**F+F.I$a23GF$F*I$t12GF$F*F-F*F**,F+F*F, F*I$a22GF$F*F4F*F0F*F1*,F+F*F,F*I$a33GF$F*F4F*F-F*F***F,F.I$a32GF$F*F4 F*F0F*F1F*I(Gnorm21GF$F*F+F*,.F/F***F)F*F+F*F,F*F0F.F1F2F*F5F1F7F*F9F1 F1F,F1F1" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm32G6\"*,,&I$t12GF$\" \"\"I$t22GF$F(F(,&F)F(I$t32GF$!\"\"F(I$a12GF$\"\"#I(Gnorm21GF$F(,.*,I$ a11GF$F(F-F(I$a13GF$F(F)F(F+F(F(**F2F(F-F(F3F(F+F.F,**F-F.I$a23GF$F(F' F(F)F(F(*,F-F(F3F(I$a22GF$F(F'F(F+F(F,*,F-F(F3F(I$a33GF$F(F'F(F)F(F(** F3F.I$a32GF$F(F'F(F+F(F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Gnorm33 G6\",$**,&I$t22GF$\"\"\"I$t32GF$!\"\"F)I$a12GF$\"\"#I(Gnorm21GF$F),.*, I$a11GF$F)F,F)I$a13GF$F)F(F)F*F)F)**F1F)F,F)F2F)F*F-F+**F,F-I$a23GF$F) I$t12GF$F)F(F)F)*,F,F)F2F)I$a22GF$F)F6F)F*F)F+*,F,F)F2F)I$a33GF$F)F6F) F(F)F)**F2F-I$a32GF$F)F6F)F*F)F+F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 " -I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6# -I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([0 ,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+gr oupalignGFC/%(rowspanGF:/%+columnspanGF:-F56(-F86%Q\"0F'F;F>FAFDFFFHFJ FLFAFDFF-F26(-F56(-I&mfracGF$6)-F,6#-F,6'-F,6)-I%msupGF$6%-I#miGF$6&Q$ a12F'/%'italicGQ%trueF'F;/F?Q'italicF'-F86%Q\"2F'F;F>/%1superscriptshi ftGFP-I#moGF$6-Q1⁢F'F>/%&fenceGQ&falseF'/%*separatorGF_ p/%)stretchyGF_p/%*symmetricGF_p/%(largeopGF_p/%.movablelimitsGF_p/%'a ccentGF_p/%'lspaceGQ&0.0emF'/%'rspaceGF^q-F\\o6&Q$a23F'F_oF;FboFio-F \\o6&Q$t12F'F_oF;FboFio-F\\o6&Q$t22F'F_oF;Fbo-Fjo6.Q(−F'F;F>F]pF `pFbpFdpFfpFhpFjp/F]qQ,0.2222222emF'/F`qF^r-F,6'-F#6%-F,6'-F,6%-F#6%-F ,6%-F,6%-F\\o6&Q)λF'/F`oF_pF;F>FioFdq-Fjo6.Q\"+F'F;F>F]pF`pFbpF dpFfpFhpFjpF]rF_r-F\\o6&Q$a11F'F_oF;FboF;F>Fio-Fin6%-F\\o6&Q$t32F'F_oF ;FboFdoFgoFbs-F,6%-F#6%-F,6%-F,6%-F#6%-F,6&-Fjo6.Q*&uminus0;F'F;F>F]pF `pFbpFdpFfpFhpFjpF]rF_r-F,6%F^sFioFgqFbs-F\\o6&Q$a22F'F_oF;FboF;F>FioF dqFjq-F,6%FesFioFgqF;F>FioFjsFjq-F,6'-F\\o6&Q$a33F'F_oF;FboFioFdqFioFg qF;F>Fio-F\\o6&Q$a13F'F_oF;FboFioF[oFjq-F,6)-Fin6%FhuFdoFgoFio-F\\o6&Q $a32F'F_oF;FboFioFdqFioFjs-F,6'FhuFioFhnFio-Fin6%-F#6%-F,6&FitFgqFbsFj sF;F>FdoFgo/%.linethicknessGF:/%+denomalignGQ'centerF'/%)numalignGF^w/ %)bevelledGF_pF;FAFDFFFHFJ-F56(-FV6)-F,6#-F,6&FitFdqFjqFjs-F,6%F[oFio- F#6%-F,6%FgqFjqFjsF;F>FjvF\\wF_wFawF;FAFDFFFHFJ-F56(-FV6)F7F[xFjvF\\wF _wFawF;FAFDFFFHFJFAFDFF-F26(-F56(-FV6)-F,6#-F,6(FitFfnFbs-F,6'FhuFio-F #6%-F,6'-F,6%-F#6%-F,6&FitF\\sFjqFesF;F>Fio-Fin6%FgqFdoFgoFbs-F,6%-F#6 %-F,6%-F,6%-F#6%-F,6%-F,6%F^sFioFjsFjqFeuF;F>FioFdqFbs-F,6%FjsFioFesF; F>FioFgqFbs-F,6'FdqFioFjsFioF^uF;F>FioF[oFbsF[v-F,6'F[oFioFdvFioF]vFjv F\\wF_wFawF;FAFDFFFHFJ-F56(-FV6)-F,6#-F,6%FdqFbsFgq-F,6%FhuFioF]xFjvF \\wF_wFawF;FAFDFFFHFJ-F56(-F,6$Fit-FV6)F7Fi[lFjvF\\wF_wFawF;FAFDFFFHFJ FAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEF^w/FGQ'|frleft|hrF'/%/alignm entscopeGFao/%,columnwidthGQ%autoF'/%&widthGF]]l/%+rowspacingGQ&1.0exF '/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFh]l/%&f rameGFh]l/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGF_p/%-equalcolumn sGF_p/%-displaystyleGF_p/%%sideGQ&rightF'/%0minlabelspacingGFe]lF;F>/% %openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 277 82 "W e verify that G is indeed equal to G^\{-1\} J^\{-1\} and give the expr ession of Gnorm" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "Gnormali sationinfini:=simplify(Multiply(G^(-1),J^(-1))):\n" }{MPLTEXT 1 0 1 "d " }{MPLTEXT 1 0 44 "Gnormalisationinfinidlambda:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 125 "for i from 1 to 3 do for j from 1 to 3 do dGnormalis ationinfinidlambda[i,j]:=diff(Gnormalisationinfini[i,j],lambda): od: o d:\n" }{MPLTEXT 1 0 15 "simplify(Gnorm-" }{MPLTEXT 1 0 22 "Gnormalisat ioninfini);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "factor(-(residue(G norm[1,1]/lambda^2,lambda=infinity) ));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 55 "factor(-(residue(Gnorm[1,1]/lambda,lambda=infinity) ) );" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "factor (-(residue(Gnorm[2,1]/lambda^2,lambda=infinity) ));" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 56 "factor(-(residue(Gnorm[2,1]/lambda,lambda=infini ty) ));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "factor(-(residue(Gno rm[2,2]/lambda^2,lambda=infinity) ));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 55 "factor(-(residue(Gnorm[2,2]/lambda,lambda=infinity) ));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "factor(-(re sidue(Gnorm[2,3]/lambda^2,lambda=infinity) ));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 55 "factor(-(residue(Gnorm[2,3]/lambda,lambda=infinity) ) );" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "factor (-(residue(Gnorm[3,1]/lambda^2,lambda=infinity) ));" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 55 "factor(-(residue(Gnorm[3,1]/lambda,lambda=infini ty) ));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 58 "f actor(-(residue(Gnorm[3,2]/lambda^2,lambda=infinity) ));\n" }{MPLTEXT 1 0 55 "factor(-(residue(Gnorm[3,2]/lambda,lambda=infinity) ));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 58 "factor(-(re sidue(Gnorm[3,3]/lambda^2,lambda=infinity) ));\n" }{MPLTEXT 1 0 55 "fa ctor(-(residue(Gnorm[3,3]/lambda,lambda=infinity) ));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "factor(Determinant(Gnorm ));" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6 #/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$ 67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%,ma thvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/ %(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ)ba selineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,colu mnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacingGQ& 0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-framespaci ngGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-displays tyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\" ]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "**I$t12G6\"\"\"\" I$t32GF$F%I$a12GF$!\"\",&I$t22GF$F%F&F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "**,.*,I$a11G6\"\"\"\"I$a12GF&F'I$a13GF&F'I$t22GF&F'I$t32G F&F'F'**F%F'F(F'F)F'F+\"\"#!\"\"**F(F-I$a23GF&F'I$t12GF&F'F*F'F'*,F(F' F)F'I$a22GF&F'F1F'F+F'F.*,F(F'F)F'I$a33GF&F'F1F'F*F'F'**F)F-I$a32GF&F' F1F'F+F'F.F'F(!\"#,&F*F'F+F.F8F)F." }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(I$a12G6\"!\"\",&I$t12GF%\"\" \"I$t32GF%F)F),&I$t22GF%F)F*F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&I$a12G6\"!\"\",&I$t22GF$\"\"\"I $t32GF$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I$t12G6\"\"\"\"I$t22G F%F&I$a13GF%!\"\",&F'F&I$t32GF%F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**,.**I$a11G6\"\"\"\"I$a12GF'F(I$a13GF'F(I$t22GF'\"\"#F(*,F&F(F)F(F *F(F+F(I$t32GF'F(!\"\"**F)F,I$a23GF'F(I$t12GF'F(F+F(F(*,F)F(F*F(I$a22G F'F(F2F(F.F(F/*,F)F(F*F(I$a33GF'F(F2F(F+F(F(**F*F,I$a32GF'F(F2F(F.F(F/ F(F)F/,&F+F(F.F/!\"#F*F:F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "*(I$a13G6\"!\"\",&I$t12GF$\"\"\"I$t22GF$ F(F(,&F)F(I$t32GF$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ",$*&I$a13G6\"!\"\",&I$t22GF%\"\"\"I$t32G F%F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(I$a12G6\"!\"\"I$a13GF%F& ,&I$t22GF%\"\"\"I$t32GF%F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 278 71 "Verification that TdLtheo is really the normalized version of \\ch eck\{L\}" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "simplify(TdLthe o-Multiply(Multiply(Gnorm,checkL),Gnorm^(-1))-h*Multiply(Gnormprime" } {MPLTEXT 1 0 12 ",Gnorm^(-1))" }{MPLTEXT 1 0 2 ");" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF' 6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+f oregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,colum nalignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1 F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alig nmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ& 1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF` o/%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-e qualcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F> /%%openGQ\"[F'/%&closeGQ\"]F'" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 290 157 "Expression of the Lax matrices \\td\{L\}, L and gauge matrices us ing irregular times after computing the local diagonalization of the s ingular part at infinity." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Ginfinity:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 70 "Ginfinity[1,1]:=1+g111 *lambda^(-1)+ g112*lambda^(-2)+E11*lambda^(-3):\n" }{MPLTEXT 1 0 70 "G infinity[1,2]:= g121*lambda^(-1)+ g122*lambda^(-2)+E12*lambda^(-3):\n " }{MPLTEXT 1 0 70 "Ginfinity[1,3]:= g131*lambda^(-1)+ g132*lambda^(- 2)+E13*lambda^(-3):\n" }{MPLTEXT 1 0 70 "Ginfinity[2,1]:= g211*lambda ^(-1)+ g212*lambda^(-2)+E21*lambda^(-3):\n" }{MPLTEXT 1 0 70 "Ginfinit y[2,2]:=1+g221*lambda^(-1)+ g222*lambda^(-2)+E22*lambda^(-3):\n" } {MPLTEXT 1 0 70 "Ginfinity[2,3]:= g231*lambda^(-1)+ g231*lambda^(-2)+ E23*lambda^(-3):\n" }{MPLTEXT 1 0 70 "Ginfinity[3,1]:= g311*lambda^(- 1)+ g312*lambda^(-2)+E31*lambda^(-3):\n" }{MPLTEXT 1 0 70 "Ginfinity[3 ,2]:= g321*lambda^(-1)+ g322*lambda^(-2)+E32*lambda^(-3):\n" } {MPLTEXT 1 0 70 "Ginfinity[3,3]:=1+g331*lambda^(-1)+ g332*lambda^(-2)+ E33*lambda^(-3):\n" }{MPLTEXT 1 0 10 "Ginfinity;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "Ginfinityprime:=Matrix(3,3,0): \n" }{MPLTEXT 1 0 100 "for i from 1 to 3 do for j from 1 to 3 do Ginfi nityprime[i,j]:=diff(Ginfinity[i,j],lambda): od: od:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "Linfinity:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 16 "Linfinity[1,1]:=" }{MPLTEXT 1 0 15 "t12*lambda+t11+" }{MPLTEXT 1 0 25 "t10/lambda+u11/lambda^2+v" }{MPLTEXT 1 0 11 "11/lambda^3" } {MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 28 "Linfinity[1,2]:=u12/lambda^2" } {MPLTEXT 1 0 2 "+v" }{MPLTEXT 1 0 11 "12/lambda^3" }{MPLTEXT 1 0 2 ": \n" }{MPLTEXT 1 0 28 "Linfinity[1,3]:=u13/lambda^2" }{MPLTEXT 1 0 2 "+ v" }{MPLTEXT 1 0 11 "13/lambda^3" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 28 "Linfinity[2,1]:=u21/lambda^2" }{MPLTEXT 1 0 3 "+v2" }{MPLTEXT 1 0 10 "1/lambda^3" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 54 "Linfinity[2,2] :=t22*lambda+t21+t20/lambda+u22/lambda^2" }{MPLTEXT 1 0 4 "+v22" } {MPLTEXT 1 0 9 "/lambda^3" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 43 "Lin finity[2,3]:=u23/lambda^2+v23/lambda^3:\n" }{MPLTEXT 1 0 29 "Linfinity [3,1]:=u31/lambda^2+" }{MPLTEXT 1 0 3 "v31" }{MPLTEXT 1 0 9 "/lambda^3 " }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 29 "Linfinity [3,2]:=u32/lambda^2+" }{MPLTEXT 1 0 3 "v32" }{MPLTEXT 1 0 9 "/lambda^3 " }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 55 "Linfinity [3,3]:=t32*lambda+t31+t30/lambda+u33/lambda^2+" }{MPLTEXT 1 0 3 "v33" }{MPLTEXT 1 0 9 "/lambda^3" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 10 "Li nfinity;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6 \"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$ mtdGF$6(-F,6)-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ 'normalF'-I#moGF$6.Q\"+F'F=F@/%&fenceGQ&falseF'/%*separatorGFI/%)stret chyGFI/%*symmetricGFI/%(largeopGFI/%.movablelimitsGFI/%'accentGFI/%'ls paceGQ,0.2222222emF'/%'rspaceGFX-I&mfracGF$6)-F,6#-I#miGF$6&Q%g111F'/% 'italicGQ%trueF'F=/FAQ'italicF'-F,6#-F[o6&Q)λF'/F_oFIF=F@/%.lin ethicknessGF " 0 "" {MPLTEXT 1 0 20 " tdL:=simplify(tdL):\n" }{MPLTEXT 1 0 134 "ToCancel2:=simplify(simplify (tdL)-(Multiply(Multiply(Ginfinity,Linfinity),Ginfinity^(-1))+h*Multip ly(Ginfinityprime,Ginfinity^(-1)))):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g121:=-a12/(t12-t22);\n" }{MPLTEXT 1 0 50 "residue(ToCancel2[1,2]/lambda^2,lambda=infinity);\n" }{MPLTEXT 1 0 47 "residue(ToCancel2[1,2]/lambda,lambda=infinity);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "g131:=-a13/(t12-t32);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 50 "residue(ToCancel2[1,3]/lambda^2,lambda=infinity);\n " }{MPLTEXT 1 0 48 "residue(ToCancel2[1,3]/lambda,lambda=infinity);\n" }{MPLTEXT 1 0 22 "g211:=-a21/(t22-t12);\n" }{MPLTEXT 1 0 50 "residue( ToCancel2[2,1]/lambda^2,lambda=infinity);\n" }{MPLTEXT 1 0 48 "residue (ToCancel2[2,1]/lambda,lambda=infinity);\n" }{MPLTEXT 1 0 10 "a22:=t21 ;\n" }{MPLTEXT 1 0 50 "residue(ToCancel2[2,2]/lambda^2,lambda=infinity );\n" }{MPLTEXT 1 0 48 "residue(ToCancel2[2,2]/lambda,lambda=infinity) ;\n" }{MPLTEXT 1 0 22 "g231:=-a23/(t22-t32);\n" }{MPLTEXT 1 0 50 "resi due(ToCancel2[2,3]/lambda^2,lambda=infinity);\n" }{MPLTEXT 1 0 48 "res idue(ToCancel2[2,3]/lambda,lambda=infinity);\n" }{MPLTEXT 1 0 22 "g311 :=-a31/(t32-t12);\n" }{MPLTEXT 1 0 50 "residue(ToCancel2[3,1]/lambda^2 ,lambda=infinity);\n" }{MPLTEXT 1 0 48 "residue(ToCancel2[3,1]/lambda, lambda=infinity);\n" }{MPLTEXT 1 0 21 "g321:=a32/(t22-t32);\n" } {MPLTEXT 1 0 50 "residue(ToCancel2[3,2]/lambda^2,lambda=infinity);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 49 "residue(ToCancel2[3,2]/l ambda,lambda=infinity));\n" }{MPLTEXT 1 0 10 "a33:=t31;\n" }{MPLTEXT 1 0 50 "residue(ToCancel2[3,3]/lambda^2,lambda=infinity);\n" }{MPLTEXT 1 0 58 "simplify(residue(ToCancel2[3,3]/lambda,lambda=infinity));\n" }{MPLTEXT 1 0 10 "a11:=t11;\n" }{MPLTEXT 1 0 47 "residue(ToCancel2[1,1 ]/lambda,lambda=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g121G6 \",$*&I$a12GF$\"\"\",&I$t12GF$F(I$t22GF$!\"\"F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g131G6\",$*&I$a13GF$\"\"\",&I$t12GF$F(I$t32GF$ !\"\"F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g211G6\",$*&I$a 21GF$\"\"\",&I$t12GF$!\"\"I$t22GF$F(F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$a22G6\"I$t21GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"! " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g231G6\",$*&I$a23GF$\"\"\",&I$t22GF$F(I$t32GF$!\"\"F,F," }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g311G6\",$*&I$a31GF$\"\"\",& I$t12GF$!\"\"I$t32GF$F(F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I%g321G6\"*&I$a32GF$\"\"\",&I$t22GF$F'I$t32GF$!\"\"F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I$a33G6\"I$t31GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$a11G6\"I$t11GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "NonTrivialRela tion:=residue(ToCancel2[1,1],lambda=infinity);\n" }{MPLTEXT 1 0 19 "td L:=simplify(tdL);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 169 "g212:=(a21*t12^2*g111-a21*t12*t22*g111-a21*t12*t32*g111+a21* t22*t32*g111-a21*t12*t11+a21*t12*t21+a21*t32*t11-a21*t32*t21+a23*a31*t 12-a23*a31*t22)/(t12-t22)^2/(t12-t32);\n" }{MPLTEXT 1 0 50 "simplify(r esidue(ToCancel2[2,1],lambda=infinity));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "NonTrivialRelation2:=" }{MPLTEXT 1 0 50 "simplify(residue(ToCancel2[2,2],lambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 153 "g331:=(a13*a21*t22 -a13*a21*t32+a23*t12*t22-a23*t12*t32+a23*t12*t21-a23*t12*t31-a23*t22*t 32+a23*t32^2-a23*t32*t21+a23*t32*t31)/((t12-t32)*(t22-t32)*a23);\n" } {MPLTEXT 1 0 50 "simplify(residue(ToCancel2[2,3],lambda=infinity));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 169 "g312:=(a31 *t12^2*g111-a31*t12*t22*g111-a31*t12*t32*g111+a31*t22*t32*g111+a21*a32 *t12-a21*a32*t32-a31*t12*t11+a31*t12*t31+a31*t22*t11-a31*t22*t31)/(t12 -t32)^2/(t12-t22);\n" }{MPLTEXT 1 0 50 "simplify(residue(ToCancel2[2,3 ],lambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 171 "g322:=-(-a32*t12*t22*g221+a32*t12*t32*g221+a32*t22^2 *g221-a32*t22*t32*g221+a12*a31*t22-a12*a31*t32+a32*t12*t21-a32*t12*t31 -a32*t22*t21+a32*t22*t31)/(t22-t32)^2/(t12-t22);\n" }{MPLTEXT 1 0 51 " simplify(residue(ToCancel2[3,2],lambda=infinity));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 71 "NonTrivialRelation3:=simplify(residue(ToCancel2 [3,3],lambda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3NonTrivia lRelationG6\",(*(I$a21GF$\"\"\",&I$t12GF$!\"\"I$t22GF$F(F+I$a12GF$F(F( *(I$a31GF$F(,&F*F+I$t32GF$F(F+I$a13GF$F(F(I$t10GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-F,6%-F,6%-I#miGF$ 6&Q)λF'/%'italicGQ&falseF'/%+foregroundGQ([0,0,0]F'/%,mathvaria ntGQ'normalF'-I#moGF$6-Q1⁢F'FE/%&fenceGFA/%*separatorGF A/%)stretchyGFA/%*symmetricGFA/%(largeopGFA/%.movablelimitsGFA/%'accen tGFA/%'lspaceGQ&0.0emF'/%'rspaceGFfn-F<6&Q$t12F'/F@Q%trueF'FB/FFQ'ital icF'-FI6.Q\"+F'FBFEFLFNFPFRFTFVFX/FenQ,0.2222222emF'/FhnFdo-F<6&Q$t11F 'F\\oFBF^o/%)rowalignGQ!F'/%,columnalignGF[p/%+groupalignGF[p/%(rowspa nGQ\"1F'/%+columnspanGFbp-F56(-F<6&Q$a12F'F\\oFBF^oFioF\\pF^pF`pFcp-F5 6(-F<6&Q$a13F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-F<6&Q$a21F 'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FH-F<6&Q$t22F'F\\oFBF^oF`o- F<6&Q$t21F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a23F'F\\oFBF^oFioF\\pF ^pF`pFcpFioF\\pF^p-F26(-F56(-F<6&Q$a31F'F\\oFBF^oFioF\\pF^pF`pFcp-F56( -F<6&Q$a32F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FH-F<6&Q$t32F'F \\oFBF^oF`o-F<6&Q$t31F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p/%&alignGQ%a xisF'/FjoQ)baselineF'/F]pQ'centerF'/F_pQ'|frleft|hrF'/%/alignmentscope GF]o/%,columnwidthGQ%autoF'/%&widthGF\\u/%+rowspacingGQ&1.0exF'/%.colu mnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFgu/%&frameGFgu/ %-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFA/%-equalcolumnsGFA/%-disp laystyleGFA/%%sideGQ&rightF'/%0minlabelspacingGFduFBFE/%%openGQ\"[F'/% &closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g212G6\"*(,6*(I$a21G F$\"\"\"I%g111GF$F)I$t12GF$\"\"#F)**F(F)F*F)F+F)I$t22GF$F)!\"\"**F(F)F *F)F+F)I$t32GF$F)F/**F(F)F*F)F.F)F1F)F)*(F(F)I$t11GF$F)F+F)F/*(F(F)F4F )F1F)F)*(F(F)F+F)I$t21GF$F)F)*(F(F)F7F)F1F)F/*(I$a23GF$F)I$a31GF$F)F+F )F)*(F:F)F;F)F.F)F/F),&F+F)F.F/!\"#,&F+F)F1F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I4NonTrivialRelat ion2G6\"*(,**&I$t20GF$\"\"\"I$t22GF$\"\"#!\"\"*&,**&I$a12GF$F)I$a21GF$ F)F)*&I$a23GF$F)I$a32GF$F)F)*&I$t12GF$F)F(F)F)*&F(F)I$t32GF$F)F)F)F*F) F)*&,&F2F,F7F,F)F6F)F)*(F0F)F1F)F8F)F,F),&F6F)F*F,F,,&F*F)F8F,F," }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%g331G6\"**,6*(I$a13GF$\"\"\"I$a21GF$F )I$t22GF$F)F)*(F(F)F*F)I$t32GF$F)!\"\"*(I$a23GF$F)I$t12GF$F)I$t21GF$F) F)*(F0F)F1F)F+F)F)*(F0F)F1F)I$t31GF$F)F.*(F0F)F1F)F-F)F.*(F0F)F2F)F-F) F.*(F0F)F+F)F-F)F.*(F0F)F5F)F-F)F)*&F0F)F-\"\"#F)F),&F1F)F-F.F.,&F+F)F -F.F.F0F." }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g312G6\"*(,6*(I$a31GF$\"\"\"I%g111GF$F)I$t12GF$\"\"#F) **F(F)F*F)F+F)I$t22GF$F)!\"\"**F(F)F*F)F+F)I$t32GF$F)F/**F(F)F*F)F.F)F 1F)F)*(I$a21GF$F)I$a32GF$F)F+F)F)*(F4F)F5F)F1F)F/*(F(F)I$t11GF$F)F+F)F /*(F(F)F8F)F.F)F)*(F(F)F+F)I$t31GF$F)F)*(F(F)F.F)F;F)F/F),&F+F)F1F/!\" #,&F+F)F.F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g322G6\",$*(,6**I$a32GF$\"\"\"I%g221GF$F*I$t12GF$F* I$t22GF$F*!\"\"**F)F*F+F*F,F*I$t32GF$F*F**(F)F*F+F*F-\"\"#F***F)F*F+F* F-F*F0F*F.*(I$a12GF$F*I$a31GF$F*F-F*F**(F5F*F6F*F0F*F.*(F)F*F,F*I$t21G F$F*F**(F)F*F,F*I$t31GF$F*F.*(F)F*F9F*F-F*F.*(F)F*F-F*F;F*F*F*,&F-F*F0 F.!\"#,&F,F*F-F.F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I4NonTrivialRelation3G6\"*(,**&I$t30GF$\"\"\" I$t32GF$\"\"#F)*&,**&I$a13GF$F)I$a31GF$F)!\"\"*&I$a23GF$F)I$a32GF$F)F1 *&I$t12GF$F)F(F)F1*&I$t22GF$F)F(F)F1F)F*F)F)*&,&F2F)F7F)F)F6F)F)*(F/F) F0F)F8F)F)F),&F6F)F*F1F1,&F8F)F*F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "NonTrivialRelation:=simplify(NonTrivialRelation);\n" }{MPLTEXT 1 0 21 "NonTrivialRelation2;\n" }{MPLTEXT 1 0 20 "NonTrivial Relation3;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 14 "t10:=-t20-t30;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 96 "a21 := (a23 *a32*t12-a23*a32*t22-t12*t22*t20+t12*t32*t20+t22^2*t20-t22*t32*t20)/(a 12*(t22-t32));\n" }{MPLTEXT 1 0 97 "a31 := -(a23*a32*t12-a23*a32*t32+t 12*t22*t30-t12*t32*t30-t22*t32*t30+t32^2*t30)/(a13*(t22-t32));\n" } {MPLTEXT 1 0 30 "simplify(NonTrivialRelation);\n" }{MPLTEXT 1 0 31 "si mplify(NonTrivialRelation2);\n" }{MPLTEXT 1 0 31 "simplify(NonTrivialR elation3);\n" }{MPLTEXT 1 0 19 "tdL:=simplify(tdL);" }}{PARA 11 "" 1 " " {XPPMATH 20 ">I3NonTrivialRelationG6\"*(,,*&I$t10GF$\"\"\"I$t12GF$\" \"#F)*&,(*&,&I$t22GF$!\"\"I$t32GF$F1F)F(F)F)*&I$a12GF$F)I$a21GF$F)F1*& I$a13GF$F)I$a31GF$F)F1F)F*F)F)*(F4F)F5F)F2F)F)*(F7F)F8F)F0F)F)*(F(F)F0 F)F2F)F)F),&F*F)F0F1F1,&F*F)F2F1F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "*( ,**&I$t20G6\"\"\"\"I$t22GF&\"\"#!\"\"*&,**&I$a12GF&F'I$a21GF&F'F'*&I$a 23GF&F'I$a32GF&F'F'*&I$t12GF&F'F%F'F'*&F%F'I$t32GF&F'F'F'F(F'F'*&,&F0F *F5F*F'F4F'F'*(F.F'F/F'F6F'F*F',&F4F'F(F*F*,&F(F'F6F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,**&I$t30G6\"\"\"\"I$t32GF&\"\"#F'*&,**&I$a13GF&F 'I$a31GF&F'!\"\"*&I$a23GF&F'I$a32GF&F'F/*&I$t12GF&F'F%F'F/*&I$t22GF&F' F%F'F/F'F(F'F'*&,&F0F'F5F'F'F4F'F'*(F-F'F.F'F6F'F'F',&F4F'F(F/F/,&F6F' F(F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$t10G6\",&I$t20GF$!\"\"I$t30 GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$a21G6\"*(,.*(I$a23GF$\"\"\"I $a32GF$F)I$t12GF$F)F)*(F(F)F*F)I$t22GF$F)!\"\"*(F+F)I$t20GF$F)F-F)F.*( F+F)F0F)I$t32GF$F)F)*&F0F)F-\"\"#F)*(F0F)F-F)F2F)F.F)I$a12GF$F.,&F-F)F 2F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$a31G6\",$*(,.*(I$a23GF$\"\" \"I$a32GF$F*I$t12GF$F*F**(F)F*F+F*I$t32GF$F*!\"\"*(F,F*I$t22GF$F*I$t30 GF$F*F**(F,F*F2F*F.F*F/*(F1F*F2F*F.F*F/*&F2F*F.\"\"#F*F*I$a13GF$F/,&F1 F*F.F/F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_sy slibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-F,6%-F,6%-I# miGF$6&Q)λF'/%'italicGQ&falseF'/%+foregroundGQ([0,0,0]F'/%,math variantGQ'normalF'-I#moGF$6-Q1⁢F'FE/%&fenceGFA/%*separa torGFA/%)stretchyGFA/%*symmetricGFA/%(largeopGFA/%.movablelimitsGFA/%' accentGFA/%'lspaceGQ&0.0emF'/%'rspaceGFfn-F<6&Q$t12F'/F@Q%trueF'FB/FFQ 'italicF'-FI6.Q\"+F'FBFEFLFNFPFRFTFVFX/FenQ,0.2222222emF'/FhnFdo-F<6&Q $t11F'F\\oFBF^o/%)rowalignGQ!F'/%,columnalignGF[p/%+groupalignGF[p/%(r owspanGQ\"1F'/%+columnspanGFbp-F56(-F<6&Q$a12F'F\\oFBF^oFioF\\pF^pF`pF cp-F56(-F<6&Q$a13F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-I&mfr acGF$6)-F,6%-F#6%-F,6%Fin-FI6.Q(−F'FBFEFLFNFPFRFTFVFXFcoFeo-F<6& Q$t22F'F\\oFBF^oFBFEFH-F#6%-F,6%-F,6%-F#6%-F,6&-FI6.Q*&uminus0;F'FBFEF LFNFPFRFTFVFXFcoFeoF_rF`o-F<6&Q$t32F'F\\oFBF^oFBFEFH-F<6&Q$t20F'F\\oFB F^oF`o-F,6%-F<6&Q$a23F'F\\oFBF^oFH-F<6&Q$a32F'F\\oFBF^oFBFE-F,6%FgpFH- F#6%-F,6%F_rF\\rF_sFBFE/%.linethicknessGFbp/%+denomalignGQ'centerF'/%) numalignGFgt/%)bevelledGFAFBFioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FHF_rF`o- F<6&Q$t21F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(FgsFioF\\pF^pF`pFcpFioF\\pF^p -F26(-F56(-F,6$F\\s-Fdq6)-F,6%-F#6%-F,6%FinF\\rF_sFBFEFH-F#6%-F,6%-F,6 %-F<6&Q$t30F'F\\oFBF^oFHF_tF`oFesFBFE-F,6%F\\qFHF_tFctFetFhtFjtFBFioF \\pF^pF`pFcp-F56(FjsFioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FHF_sF`o-F<6&Q$t3 1F'F\\oFBF^oFioF\\pF^pF`pFcpFioF\\pF^p/%&alignGQ%axisF'/FjoQ)baselineF '/F]pFgt/F_pQ'|frleft|hrF'/%/alignmentscopeGF]o/%,columnwidthGQ%autoF' /%&widthGFgx/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlin esGQ%noneF'/%,columnlinesGFby/%&frameGFby/%-framespacingGQ,0.4em~0.5ex F'/%*equalrowsGFA/%-equalcolumnsGFA/%-displaystyleGFA/%%sideGQ&rightF' /%0minlabelspacingGF_yFBFE/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 279 196 "Definition of the Darboux coordinates t o end the expression of the Lax matrices and gauge matrices. \nThe coo rdinate q was introduced earlier in the oper gauge transform as the ap parent singularity" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "Condi tionp:=unapply(factor(Determinant(Psing*IdentityMatrix(3)-tdL)),lambda ):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "Ps ing:=(a12^2*a23*t32+a12*a13*t22*t31-a12*a13*t32*t21-a13^2*a32*t22)/(a1 2*(t22-t32)*a13);\n" }{MPLTEXT 1 0 27 "factor(Conditionp(Qsing));\n" } {MPLTEXT 1 0 9 "Qsing=q;\n" }{MPLTEXT 1 0 9 "Psing=p;\n" }{MPLTEXT 1 0 36 "solve(\{Qsing-q,Psing-p\},\{a23,a32\});\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "a23 := -a13*(-q*t22+p-t21)/a12;\n" }{MPLTEXT 1 0 32 "a32 := -a12*(-q*t32+p-t31)/a13;\n" }{MPLTEXT 1 0 19 "simplify(Qsing-q );\n" }{MPLTEXT 1 0 18 "simplify(Psing-p);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&PsingG6\"**,**(I$a12GF$\"\"#I$a23GF$\"\"\"I$t32GF$F+F+ **F(F+I$a13GF$F+I$t21GF$F+F,F+!\"\"**F(F+F.F+I$t22GF$F+I$t31GF$F+F+*(F .F)I$a32GF$F+F2F+F0F+F(F0F.F0,&F2F+F,F0F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "/**,**&I$a12G6\"\" \"#I$a23GF'\"\"\"F**(F&F*I$a13GF'F*I$t21GF'F*!\"\"*(F&F*F,F*I$t31GF'F* F**&F,F(I$a32GF'F*F.F*F&F.F,F.,&I$t22GF'F*I$t32GF'F.F.I\"qGF'" }} {PARA 11 "" 1 "" {XPPMATH 20 "/**,**(I$a12G6\"\"\"#I$a23GF'\"\"\"I$t32 GF'F*F***F&F*I$a13GF'F*I$t21GF'F*F+F*!\"\"**F&F*F-F*I$t22GF'F*I$t31GF' F*F**(F-F(I$a32GF'F*F1F*F/F*F&F/F-F/,&F1F*F+F/F/I\"pGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "<$/I$a23G6\",$*(I$a12GF%!\"\"I$a13GF%\"\"\",(*&I\"q GF%F+I$t22GF%F+F)I\"pGF%F+I$t21GF%F)F+F)/I$a32GF%,$*(F(F+,(*&F.F+I$t32 GF%F+F)F0F+I$t31GF%F)F+F*F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$a23G 6\",$*(I$a12GF$!\"\"I$a13GF$\"\"\",(*&I\"qGF$F*I$t22GF$F*F(I\"pGF$F*I$ t21GF$F(F*F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$a32G6\",$*(I$a12GF$\" \"\",(*&I\"qGF$F(I$t32GF$F(!\"\"I\"pGF$F(I$t31GF$F-F(I$a13GF$F-F-" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "g132:=solve(" } {MPLTEXT 1 0 65 "simplify(residue(ToCancel2[1,3]/lambda^0,lambda=infin ity)),g132);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 78 "g221:=solve(simpl ify(residue(ToCancel2[1,2]/lambda^0,lambda=infinity)),g221);\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 51 "simplify(residue(ToCancel2[1,1], lambda=infinity));\n" }{MPLTEXT 1 0 51 "simplify(residue(ToCancel2[1,2 ],lambda=infinity));\n" }{MPLTEXT 1 0 50 "simplify(residue(ToCancel2[1 ,3],lambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 51 "simplif y(residue(ToCancel2[2,1],lambda=infinity));\n" }{MPLTEXT 1 0 51 "simpl ify(residue(ToCancel2[2,2],lambda=infinity));\n" }{MPLTEXT 1 0 51 "sim plify(residue(ToCancel2[2,3],lambda=infinity));\n" }{MPLTEXT 1 0 51 "s implify(residue(ToCancel2[3,1],lambda=infinity));\n" }{MPLTEXT 1 0 51 "simplify(residue(ToCancel2[3,2],lambda=infinity));\n" }{MPLTEXT 1 0 50 "simplify(residue(ToCancel2[3,3],lambda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g132G6\",$**,D*(I\"qGF$\"\"#I$t12GF$\"\"\"I$t22GF $F,F,*(I\"pGF$F,F)F,F+F,!\"\"*(F/F,F)F,F-F,F0*(F)F,I$t11GF$F,F-F,F,*(F )F,F+F,I$t21GF$F,F,*(F)F,F+F,F-F,F0*(F)F,F-F,I$t32GF$F,F,*$F/F*F,*&F/F ,F3F,F0*&F/F,F+F,F,*&F/F,F5F,F0*&F/F,F8F,F0*&F3F,F5F,F,*&F+F,I$t20GF$F ,F,*&F+F,F5F,F0*&F@F,F-F,F0*&F5F,F8F,F,F,I$a13GF$F,,&F+F,F8F0!\"#,(*&F )F,F-F,F0F/F,F5F0F0F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%g221G6\"**,B **I$a12GF$\"\"\"I\"qGF$F)I$t12GF$F)I$t32GF$F)!\"\"**F(F)F*F)I$t22GF$F) F,F)F)*(I%g122GF$F)F+\"\"#F/F)F-*(F1F)F+F2F,F)F)*(F1F)F+F)F/F2F2**F1F) F+F)F/F)F,F)!\"#*&F1F)F/\"\"$F-*(F1F)F/F2F,F)F)*(F(F)I\"pGF$F)F+F)F)*( F(F)F;F)F/F)F-*(F(F)I$t11GF$F)F/F)F)*(F(F)F>F)F,F)F-*(F(F)F+F)I$t31GF$ F)F-*(F(F)I$t21GF$F)F/F)F-*(F(F)FCF)F,F)F)*(F(F)F/F)FAF)F)F),&F+F)F/F- F-,&F/F)F,F-F-F(F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "u11:=solve( simplify(residue(ToCancel2[1,1]*lambda,lambda=infinity )),u11):\n" }{MPLTEXT 1 0 57 "simplify(residue(ToCancel2[1,1]*lambda,l ambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 75 "u22:=solve( \+ simplify(residue(ToCancel2[2,2]*lambda,lambda=infinity)),u22):\n" } {MPLTEXT 1 0 58 "simplify(residue(ToCancel2[2,2]*lambda,lambda=infinit y));\n" }{MPLTEXT 1 0 75 "u33:=solve( simplify(residue(ToCancel2[3,3]* lambda,lambda=infinity)),u33):\n" }{MPLTEXT 1 0 57 "simplify(residue(T oCancel2[3,3]*lambda,lambda=infinity));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 280 59 "Summary of the formulas for Lax matrices and gauge matrices" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "tdL:=simplify(tdL):" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 10 "tdL[1,1];\n" }{MPLTEXT 1 0 10 "t dL[1,2];\n" }{MPLTEXT 1 0 10 "tdL[1,3];\n" }{MPLTEXT 1 0 10 "tdL[2,1]; \n" }{MPLTEXT 1 0 120 "tdL21bis:=(t12-t22)/a12/(t22-t32)*(p^2-(q*(t22+ t32)+t21+t31)*p+t32*t22*q^2+(t22*t31+t32*t21)*q+(t32-t22)*t20+t21*t31 \+ );\n" }{MPLTEXT 1 0 21 "factor(series(factor(" }{MPLTEXT 1 0 9 "tdL[2, 1]-" }{MPLTEXT 1 0 16 "tdL21bis),q=0));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 10 "tdL[2,2];\n" }{MPLTEXT 1 0 10 "tdL[2,3];\n" }{MPLTEXT 1 0 10 "tdL[3,1];\n" }{MPLTEXT 1 0 121 "tdL31bis:=(t12-t32)*(p^2-(q*( t22+t32)+t21+t31)*p+t22*t32*q^2+(t22*t31+t32*t21)*q+((t22-t32)*t30+t21 *t31) )/a13/(t32-t22);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "factor( series(factor(" }{MPLTEXT 1 0 25 "tdL[3,1]-tdL31bis),q=0));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 10 "tdL[3,2];\n" }{MPLTEXT 1 0 10 "tdL[3,3]; \n" }{MPLTEXT 1 0 4 "tdL;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I'lambd aG6\"\"\"\"I$t12GF%F&F&I$t11GF%F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$a 12G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$a13G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "**,&I$t12G6\"\"\"\"I$t22GF%!\"\"F&,(*&,**&I\"qGF%\"\"#I$t 32GF%F&F&*&I\"pGF%F&F-F&F(*&F-F&I$t31GF%F&F&I$t20GF%F(F&F'F&F&*&,(F0F( *&F-F&I$t21GF%F&F&F4F&F&F/F&F&*&,&F1F&F3F(F&,&F1F&F8F(F&F&F&I$a12GF%F( ,&F'F&F/F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdL21bisG6\"**,&I$t12 GF$\"\"\"I$t22GF$!\"\"F(I$a12GF$F*,&F)F(I$t32GF$F*F*,.*$I\"pGF$\"\"#F( *&,(*&I\"qGF$F(,&F)F(F-F(F(F(I$t21GF$F(I$t31GF$F(F(F0F(F**(F5F1F)F(F-F (F(*&,&*&F7F(F-F(F(*&F)F(F8F(F(F(F5F(F(*&,&F)F*F-F(F(I$t20GF$F(F(*&F7F (F8F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I'lambdaG6\"\"\"\"I$t22GF%F&F&I$t21GF%F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(I$a12G6\"!\"\"I$a13GF%\"\"\",(*&I\"qGF%F(I$t2 2GF%F(F&I\"pGF%F(I$t21GF%F&F(F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**, &I$t12G6\"\"\"\"I$t32GF&!\"\"F',(*&,**&I\"qGF&\"\"#I$t22GF&F'F'*&I\"pG F&F'F.F'F)*&F.F'I$t21GF&F'F'I$t30GF&F)F'F(F'F'*&,(F1F)*&F.F'I$t31GF&F' F'F5F'F'F0F'F'*&,&F2F'F9F)F',&F2F'F4F)F'F'F'I$a13GF&F),&F0F'F(F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdL31bisG6\"**,&I$t12GF$\"\"\"I$t32 GF$!\"\"F(,.*$I\"pGF$\"\"#F(*&,(*&I\"qGF$F(,&I$t22GF$F(F)F(F(F(I$t21GF $F(I$t31GF$F(F(F-F(F**(F2F.F4F(F)F(F(*&,&*&F5F(F)F(F(*&F4F(F6F(F(F(F2F (F(*&I$t30GF$F(,&F4F(F)F*F(F(*&F5F(F6F(F(F(I$a13GF$F*,&F4F*F)F(F*" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ", $*(I$a12G6\"\"\"\",(*&I\"qGF%F&I$t32GF%F&!\"\"I\"pGF%F&I$t31GF%F+F&I$a 13GF%F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I'lambdaG6\"\"\"\"I$t32 GF%F&F&I$t31GF%F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+mod ulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mt rGF$6(-I$mtdGF$6(-F,6%-F,6%-I#miGF$6&Q)λF'/%'italicGQ&falseF'/% +foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'-I#moGF$6-Q1&Invisible Times;F'FE/%&fenceGFA/%*separatorGFA/%)stretchyGFA/%*symmetricGFA/%(la rgeopGFA/%.movablelimitsGFA/%'accentGFA/%'lspaceGQ&0.0emF'/%'rspaceGFf n-F<6&Q$t12F'/F@Q%trueF'FB/FFQ'italicF'-FI6.Q\"+F'FBFEFLFNFPFRFTFVFX/F enQ,0.2222222emF'/FhnFdo-F<6&Q$t11F'F\\oFBF^o/%)rowalignGQ!F'/%,column alignGF[p/%+groupalignGF[p/%(rowspanGQ\"1F'/%+columnspanGFbp-F56(-F<6& Q$a12F'F\\oFBF^oFioF\\pF^pF`pFcp-F56(-F<6&Q$a13F'F\\oFBF^oFioF\\pF^pF` pFcpFioF\\pF^p-F26(-F56(-I&mfracGF$6)-F,6%-F#6%-F,6%Fin-FI6.Q(−F 'FBFEFLFNFPFRFTFVFXFcoFeo-F<6&Q$t22F'F\\oFBF^oFBFEFH-F#6%-F,6'-F,6%-F# 6%-F,6)-F,6%-I%msupGF$6%-F<6&Q\"qF'F\\oFBF^o-I#mnGF$6%Q\"2F'FBFE/%1sup erscriptshiftGQ\"0F'FH-F<6&Q$t32F'F\\oFBF^oF\\r-F,6%-F<6&Q\"pF'F\\oFBF ^oFHFasF`o-F,6%FasFH-F<6&Q$t31F'F\\oFBF^oF\\r-F<6&Q$t20F'F\\oFBF^oFBFE FHF_rF`o-F,6%-F#6%-F,6(-FI6.Q*&uminus0;F'FBFEFLFNFPFRFTFVFXFcoFeoF^tF` o-F,6%FasFH-F<6&Q$t21F'F\\oFBF^oF`oFhtFBFEFHF[tF`o-F,6%-F#6%-F,6%F`tF \\rFetFBFEFH-F#6%-F,6%F`tF\\rFfuFBFEFBFE-F,6%FgpFH-F#6%-F,6%F_rF\\rF[t FBFE/%.linethicknessGFbp/%+denomalignGQ'centerF'/%)numalignGF]w/%)beve lledGFAFBFioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FHF_rF`oFfuFioF\\pF^pF`pFcp- F56(-F,6$Fau-Fdq6)-F,6%F\\qFH-F#6%-F,6(Fau-F,6%FasFHF_rF`oF`tF\\rFfuFB FE-F,6#FgpFivF[wF^wF`wFBFioF\\pF^pF`pFcpFioF\\pF^p-F26(-F56(-F,6$Fau-F dq6)-F,6%-F#6%-F,6%FinF\\rF[tFBFEFH-F#6%-F,6'-F,6%-F#6%-F,6)-F,6%F^sFH F_rF\\rF^tF`oFduF\\r-F<6&Q$t30F'F\\oFBF^oFBFEFHF[tF`o-F,6%-F#6%-F,6(Fa uF^tF`oFctF`oFbzFBFEFHF_rF`oFiuFBFE-F,6%F\\qFHFevFivF[wF^wF`wFBFioF\\p F^pF`pFcp-F56(-F,6$Fau-Fdq6)-F,6%FgpFH-F#6%-F,6(Fau-F,6%FasFHF[tF`oF`t F\\rFetFBFE-F,6#F\\qFivF[wF^wF`wFBFioF\\pF^pF`pFcp-F56(-F,6%-F,6%F;FHF [tF`oFetFioF\\pF^pF`pFcpFioF\\pF^p/%&alignGQ%axisF'/FjoQ)baselineF'/F] pF]w/F_pQ'|frleft|hrF'/%/alignmentscopeGF]o/%,columnwidthGQ%autoF'/%&w idthGF_]l/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesG Q%noneF'/%,columnlinesGFj]l/%&frameGFj]l/%-framespacingGQ,0.4em~0.5exF '/%*equalrowsGFA/%-equalcolumnsGFA/%-displaystyleGFA/%%sideGQ&rightF'/ %0minlabelspacingGFg]lFBFE/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "L33ter:=h/(lambda-q)+(t12+t22+t32)* lambda+t11+t21+t31;\n" }{MPLTEXT 1 0 25 "simplify(L33bis-L33ter);\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 198 "L32ter:=h*(-(t12+t22+t32)*q+p-t 11-t21-t31)/(lambda-q)-(t12*t22+t12*t32+t22*t32)*lambda^2-(t12*(t21+t3 1)+t22*(t11+t31)+t32*(t11+t21))*lambda+ t12*t10+t22*t20+t32*t30-t11*t2 1-t11*t31-t21*t31 +h*t12 ;\n" }{MPLTEXT 1 0 14 "factor(series(" } {MPLTEXT 1 0 35 "simplify(L32bis-L32ter),lambda=0));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 12 "L31ter:=h*( " }{MPLTEXT 1 0 113 "p^2-(t11+t21+t31+q*(t12+t22+t32))*p+ (t12*t22+t12*t32+t22*t32)* q^2+(t12*(t21+t31)+t22*(t11+t31)+t32*(t11+t21))*q " }{MPLTEXT 1 0 9 "- t12*t10 " }{MPLTEXT 1 0 61 "-t22*t20-t32*t30+t11*t31+t11*t21+t21*t31 - h*t12 )/(lambda-q)\n" }{MPLTEXT 1 0 69 "+t12*t22*t32*lambda^3+(t22*t12 *t31+t12*t32*t21+t22*t32*t11)*lambda^2\n" }{MPLTEXT 1 0 34 "+((t30-h)* t22*t12+(t20-h)*t32*t12+" }{MPLTEXT 1 0 12 "t10*t22*t32 " }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 4 "t12*" }{MPLTEXT 1 0 8 "t21*t31+" }{MPLTEXT 1 0 4 "t22*" }{MPLTEXT 1 0 8 "t11*t31+" }{MPLTEXT 1 0 4 "t32*" }{MPLTEXT 1 0 16 "t11*t21)*lambda\n" }{MPLTEXT 1 0 39 "+p^3-((t12+t22+t32)*q+t2 1+t31+t11)*p^2\n" }{MPLTEXT 1 0 2 "+(" }{MPLTEXT 1 0 51 "q^2*(t12*t22+ t12*t32+t22*t32)+ (t12*(t21+t31)+t22*(" }{MPLTEXT 1 0 3 "t11" } {MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 6 "t31)+ " }{MPLTEXT 1 0 26 "t32*(t11 +t21))*q-(t10*t12+" }{MPLTEXT 1 0 8 "t20*t22+" }{MPLTEXT 1 0 9 "t30*t3 2)+" }{MPLTEXT 1 0 25 " t11*t21+t11*t31+t21*t31 " }{MPLTEXT 1 0 11 "-h *t12 )*p\n" }{MPLTEXT 1 0 30 "-q^3*t12*t22*t32-(t22*t32*t11+" } {MPLTEXT 1 0 12 "t12*t32*t21+" }{MPLTEXT 1 0 11 "t12*t22*t31" } {MPLTEXT 1 0 6 ")*q^2\n" }{MPLTEXT 1 0 2 "-(" }{MPLTEXT 1 0 12 "t21*t3 1*t12+" }{MPLTEXT 1 0 82 "t11*t31*t22+t11*t21*t32 +t10*t22*t32+ t20*t1 2*t32+t30*t12*t22 -h*(t22+t32)*t12)*q;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 "series(" }{MPLTEXT 1 0 51 "simplify(series(simplify(L31bis-L31 ter),q=0)),q=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'L33terG6\",,*&I\" hGF$\"\"\",&I'lambdaGF$F(I\"qGF$!\"\"F,F(*&,(I$t12GF$F(I$t22GF$F(I$t32 GF$F(F(F*F(F(I$t11GF$F(I$t21GF$F(I$t31GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'L32terG6\",6*(I \"hGF$\"\"\",,*&,(I$t12GF$F(I$t22GF$F(I$t32GF$F(F(I\"qGF$F(!\"\"I\"pGF $F(I$t11GF$F0I$t21GF$F0I$t31GF$F0F(,&I'lambdaGF$F(F/F0F0F(*&,(*&F,F(F- F(F(*&F,F(F.F(F(*&F-F(F.F(F(F(F6\"\"#F0*&,(*&F,F(,&F3F(F4F(F(F(*&F-F(, &F2F(F4F(F(F(*&F.F(,&F2F(F3F(F(F(F(F6F(F0*&F,F(,&I$t20GF$F0I$t30GF$F0F (F(*&FGF(F-F(F(*&FHF(F.F(F(*&F2F(F3F(F0*&F2F(F4F(F0*&F3F(F4F(F0*&F'F(F ,F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'L31terG6\",6*(I\"hGF$\"\"\",8*$I\"pGF$\"\"#F(*&,*I$t11 GF$F(I$t21GF$F(I$t31GF$F(*&,(I$t12GF$F(I$t22GF$F(I$t32GF$F(F(I\"qGF$F( F(F(F+F(!\"\"*&,(*&F4F(F5F(F(*&F4F(F6F(F(*&F5F(F6F(F(F(F7F,F(*&,(*&F4F (,&F0F(F1F(F(F(*&F5F(,&F/F(F1F(F(F(*&F6F(,&F/F(F0F(F(F(F(F7F(F(*&F4F(, &I$t20GF$F8I$t30GF$F8F(F8*&FHF(F5F(F8*&FIF(F6F(F8*&F/F(F1F(F(*&F/F(F0F (F(*&F0F(F1F(F(*&F'F(F4F(F8F(,&I'lambdaGF$F(F7F8F8F(**F4F(F5F(F6F(FQ\" \"$F(*&,(*(F/F(F5F(F6F(F(*(F4F(F0F(F6F(F(*(F4F(F5F(F1F(F(F(FQF,F(*&,.* (,&F'F8FIF(F(F5F(F4F(F(*(,&F'F8FHF(F(F6F(F4F(F(*(FGF(F5F(F6F(F(*(F4F(F 0F(F1F(F(*(F5F(F/F(F1F(F(*(F6F(F/F(F0F(F(F(FQF(F(*$F+FSF(*&F.F(F+F,F8* &,4F9F(F>F(FFF8FJF8FKF8FMF(FLF(FNF(FOF8F(F+F(F(**F7FSF4F(F5F(F6F(F8*&F UF(F7F,F8*&,0FjnF(F[oF(F\\oF(FinF(*(F4F(FHF(F6F(F(*(F4F(F5F(FIF(F(*(F' F(,&F5F(F6F(F(F4F(F8F(F7F(F8" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "G:=simplify(G):\n" } {MPLTEXT 1 0 18 "simplify(G[1,1]);\n" }{MPLTEXT 1 0 18 "simplify(G[1,2 ]);\n" }{MPLTEXT 1 0 17 "simplify(G[1,3]);" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 18 "simplify(G[2,1]);\n" }{MPLTEXT 1 0 17 "simplify(G[2,2 ]);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 17 "simplify(G[2,3]);" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "simplify(G[3,3]);\n" }{MPLTEXT 1 0 18 "simplify(G[3,2]);\n" }{MPLTEXT 1 0 17 "simplify(G[3,1]):" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 128 "G31bis:=(t12*lambda+t11)^2-p^2+ (q*(t22+t32)+t21+t31)*p- t22*t32*q^2-(t22*t31+t32*t21)*q- t21*t31+t10* t12+t20*t22+t30*t32+h*t12;\n" }{MPLTEXT 1 0 53 "G33bis:=a13*( (t12+t32 )*lambda-p+t22*q+t11+t21+t31);\n" }{MPLTEXT 1 0 25 "simplify(G[3,3]-G3 3bis);\n" }{MPLTEXT 1 0 53 "G32bis:=a12*( (t12+t22)*lambda-p+t32*q+t11 +t21+t31);\n" }{MPLTEXT 1 0 25 "simplify(G[3,2]-G32bis);\n" }{MPLTEXT 1 0 36 "series(simplify(G[3,1]-G31bis),q=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I'lam bdaG6\"\"\"\"I$t12GF%F&F&I$t11GF%F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "I $a12G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$a13G6\"" }}{PARA 11 "" 1 " " {XPPMATH 20 ",$*&I$a13G6\"\"\"\",.*&,&I$t12GF%!\"\"I$t32GF%F+F&I'lam bdaGF%F&F&*&I\"qGF%F&I$t22GF%F&F+I\"pGF%F&I$t11GF%F+I$t21GF%F+I$t31GF% F+F&F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,.*&,&I$t12G6\"!\"\"I$t22G F(F)\"\"\"I'lambdaGF(F+F+*&I\"qGF(F+I$t32GF(F+F)I\"pGF(F+I$t11GF(F)I$t 21GF(F)I$t31GF(F)F+I$a12GF(F+F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'G3 1bisG6\",6*$,&*&I'lambdaGF$\"\"\"I$t12GF$F*F*I$t11GF$F*\"\"#F**$I\"pGF $F-!\"\"*&,(*&I\"qGF$F*,&I$t22GF$F*I$t32GF$F*F*F*I$t21GF$F*I$t31GF$F*F *F/F*F**(F4F-F6F*F7F*F0*&,&*&F8F*F7F*F**&F6F*F9F*F*F*F4F*F0*&F8F*F9F*F 0*&F+F*,&I$t20GF$F0I$t30GF$F0F*F**&FBF*F6F*F**&FCF*F7F*F**&I\"hGF$F*F+ F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'G33bisG6\"*&I$a13GF$\"\"\",.* &,&I$t12GF$F'I$t32GF$F'F'I'lambdaGF$F'F'I\"pGF$!\"\"*&I\"qGF$F'I$t22GF $F'F'I$t11GF$F'I$t21GF$F'I$t31GF$F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'G32bisG6\"*&I$a12GF$\"\"\", .*&,&I$t12GF$F'I$t22GF$F'F'I'lambdaGF$F'F'I\"pGF$!\"\"*&I\"qGF$F'I$t32 GF$F'F'I$t11GF$F'I$t21GF$F'I$t31GF$F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Gnorm:=simplify(Gnorm);\n" }{MPLTEXT 1 0 15 " J:=simplify(J);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 41 "simplify(Gnorm -Multiply(G^(-1),J^(-1)));\n" }{MPLTEXT 1 0 35 "simplify(G^(-1)-Multip ly(Gnorm,J));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "J[3,3];\n" } {MPLTEXT 1 0 7 "J[3,2];" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 "J[3,1]; " }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 196 "J31bis:=1/(lambda-q)*(p^2-p* ((t12+t22+t32)*q+t31+t11+t21) +(t12*t22+t12*t32+t22*t32)*q^2 + (t12*(t 21+t31)+ t22*(t11+t31)+ t32*(t21+t11))*q -t12*t10-t22*t20-t32*t30+t11* t21+t11*t31+t21*t31-h*t12):\n" }{MPLTEXT 1 0 49 "series(simplify((lamb da-q)*(J[3,1]-J31bis)),q=0);" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$67-I$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:-F56(-F86%Q\"0F'F ;F>FAFDFFFHFJFLFAFDFF-F26(-F56(-I&mfracGF$6)-F,6#-F,6%-F,6%-F#6%-F,6+- F,6%-F#6%-F,6%-I#miGF$6&Q)λF'/%'italicGQ&falseF'F;F>-I#moGF$6.Q \"+F'F;F>/%&fenceGFho/%*separatorGFho/%)stretchyGFho/%*symmetricGFho/% (largeopGFho/%.movablelimitsGFho/%'accentGFho/%'lspaceGQ,0.2222222emF' /%'rspaceGF]q-Fco6&Q\"qF'/FgoQ%trueF'F;/F?Q'italicF'F;F>-Fjo6-Q1&Invis ibleTimes;F'F>F]pF_pFapFcpFepFgpFip/F\\qQ&0.0emF'/F_qF[r-Fco6&Q$t32F'F cqF;FeqFio-F,6%F`qFgq-Fco6&Q$t22F'FcqF;Feq-Fjo6.Q(−F'F;F>F]pF_pF apFcpFepFgpFipF[qF^q-Fco6&Q\"pF'FcqF;FeqFio-Fco6&Q$t21F'FcqF;FeqFio-Fc o6&Q$t31F'FcqF;FeqF;F>Fgq-Fco6&Q$t12F'FcqF;FeqFio-F,6%-Fco6&Q$t11F'Fcq F;FeqFgqF]r-F,6%-Fco6&Q$a12F'FcqF;FeqFgq-F#6%-F,6%FbrFerF]rF;F>/%.line thicknessGF:/%+denomalignGQ'centerF'/%)numalignGFft/%)bevelledGFhoF;FA FDFFFHFJ-F56(-FV6)-F,6#-F,6&-Fjo6.Q*&uminus0;F'F;F>F]pF_pFapFcpFepFgpF ipF[qF^qFasFerF]rFisFbtFdtFgtFitF;FAFDFFFHFJ-F56(-FV6)F7FisFbtFdtFgtFi tF;FAFDFFFHFJFAFDFF-F26(-F56(-FV6)-F,6#-F,6%-F,6%-F#6%-F,6+-F,6%-F#6%- F,6&FcuFboFerF`qF;F>FgqFbrFer-F,6%F`qFgqF]rFioFhrFerF[sFerF^sF;F>FgqFa sFer-F,6%FfsFgqFbr-F,6%-Fco6&Q$a13F'FcqF;FeqFgqF^tFbtFdtFgtFitF;FAFDFF FHFJ-F56(-FV6)-F,6#-F,6%FasFioFbrFdwFbtFdtFgtFitF;FAFDFFFHFJ-F56(-F,6$ Fcu-FV6)F7FdwFbtFdtFgtFitF;FAFDFFFHFJFAFDFF/%&alignGQ%axisF'/FBQ)basel ineF'/FEFft/FGQ'|frleft|hrF'/%/alignmentscopeGFdq/%,columnwidthGQ%auto F'/%&widthGFcy/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowl inesGQ%noneF'/%,columnlinesGF^z/%&frameGF^z/%-framespacingGQ,0.4em~0.5 exF'/%*equalrowsGFho/%-equalcolumnsGFho/%-displaystyleGFho/%%sideGQ&ri ghtF'/%0minlabelspacingGF[zF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI( _syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6% Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ! F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGF:/%+columnspanGF:-F56(- F86%Q\"0F'F;F>FAFDFFFHFJFLFAFDFF-F26(FLF4FLFAFDFF-F26(-F56(-I&mfracGF$ 6)-F,6#-F,63-F,6%-F#6%-F,6%-F,6%-F#6%-F,6%-I#miGF$6&Q$t22F'/%'italicGQ %trueF'F;/F?Q'italicF'-I#moGF$6.Q\"+F'F;F>/%&fenceGQ&falseF'/%*separat orGFcp/%)stretchyGFcp/%*symmetricGFcp/%(largeopGFcp/%.movablelimitsGFc p/%'accentGFcp/%'lspaceGQ,0.2222222emF'/%'rspaceGFbq-Feo6&Q$t32F'FhoF; F[pF;F>-F^p6-Q1⁢F'F>FapFdpFfpFhpFjpF\\qF^q/FaqQ&0.0emF' /FdqF\\r-Feo6&Q$t12F'FhoF;F[pF]p-F,6%FdoFhqFeqF;F>Fhq-I%msupGF$6%-Feo6 &Q\"qF'FhoF;F[p-F86%Q\"2F'F;F>/%1superscriptshiftGFPF]p-F,6%-F#6%-F,6) -F,6%-F#6%-F,6'-Feo6&Q$t31F'FhoF;F[p-F^p6.Q(−F'F;F>FapFdpFfpFhpF jpF\\qF^qF`qFcq-Feo6&Q\"pF'FhoF;F[pF]p-Feo6&Q$t21F'FhoF;F[pF;F>FhqF^rF ]p-F,6%-F#6%-F,6&-F^p6.Q*&uminus0;F'F;F>FapFdpFfpFhpFjpF\\qF^qF`qFcqFd oF]tFeqF;F>FhqF`tF]p-F,6%FdoFhq-F#6%-F,6%-Feo6&Q$t11F'FhoF;F[pF]pFjsF; F>F]p-F,6%FeqFhq-F#6%-F,6%FeuF]pFctF;F>F;F>FhqFfrF]p-F,6%-F#6%-F,6(F \\u-Feo6&Q\"hF'FhoF;F[pF]p-Feo6&Q$t20F'FhoF;F[pF]p-Feo6&Q$t30F'FhoF;F[ pF;F>FhqF^rF]p-F,6#-Fdr6%F`tFirF\\sF]p-F,6%-F#6%-F,6(F\\uFjsF]tFeuF]tF ctF;F>FhqF`tF]t-F,6%FgvFhqFdoF]t-F,6%FjvFhqFeqF]p-F,6%FeuFhq-F#6%-F,6% FctF]pFjsF;F>F]p-F,6%FctFhqFjs-F,6#-F,6%-Feo6&Q)λF'/FioFcpF;F>F ]tFfr/%.linethicknessGF:/%+denomalignGQ'centerF'/%)numalignGF_y/%)beve lledGFcpF;FAFDFFFHFJ-F56(-FX6)-F,6#-F,6+-F,6%-F#6%-F,6'F^rF]pFdoF]pFeq F;F>FhqFfrF]tF`tF]pFeuF]pFctF]pFjs-F,6#-F,6&F\\uFgxF]pFfrF[yF]yF`yFbyF ;FAFDFFFHFJ-F56(-FX6)F7FcxF[yF]yF`yFbyF;FAFDFFFHFJFAFDFF/%&alignGQ%axi sF'/FBQ)baselineF'/FEF_y/FGQ'|frleft|hrF'/%/alignmentscopeGFjo/%,colum nwidthGQ%autoF'/%&widthGFf[l/%+rowspacingGQ&1.0exF'/%.columnspacingGQ& 0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFa\\l/%&frameGFa\\l/%-frames pacingGQ,0.4em~0.5exF'/%*equalrowsGFcp/%-equalcolumnsGFcp/%-displaysty leGFcp/%%sideGQ&rightF'/%0minlabelspacingGF^\\lF;F>/%%openGQ\"[F'/%&cl oseGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(- I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'no rmalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGQ\"1 F'/%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&r ightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%auto F'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowl inesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5 exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sid eGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI( _syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6% Q\"0F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ! F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4 F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|h rF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFen/%+row spacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,colu mnlinesGF`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&f alseF'/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minlabelspaci ngGF]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$,&I'lambdaG6\"\"\"\"I\"qGF%!\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,,*&,(I$t12G6\"\"\"\"I$t22GF'F(I$t32GF'F(F(I\"qGF'F(F(I\"pGF'!\" \"I$t11GF'F(I$t21GF'F(I$t31GF'F(F(,&I'lambdaGF'F-F+F(F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,4*&,&*&,&I$t22G6\"\"\"\"I$t32GF)F*F*I$t12GF)F*F* *&F(F*F+F*F*F*I\"qGF)\"\"#F**&,**&,(I$t31GF)F*I\"pGF)!\"\"I$t21GF)F*F* F,F*F**&,&F(F6F+F6F*F5F*F**&F(F*,&I$t11GF)F*F4F*F*F**&F+F*,&F " 0 " " {MPLTEXT 1 0 55 "P1:=unapply( (t12+t22+t32)*lambda+t11+t21+t31,lambd a);\n" }{MPLTEXT 1 0 157 "P2:=unapply( (t12*t22+t12*t32+t22*t32)*lambd a^2+((t21+t31)*t12+(t11+t31)*t22+t32*(t11+t21))*lambda-t10*t12-t20*t22 -t30*t32+t21*t11 +t31*t11+t21*t31,lambda);\n" }{MPLTEXT 1 0 58 "P3:=un apply(t12*t22*t32*lambda^3+(t12*t22*t31+t12*t32*t21+" }{MPLTEXT 1 0 8 "t22*t32*" }{MPLTEXT 1 0 39 "t11)*lambda^2+(t12*t22*t30+t12*t32*t20+" }{MPLTEXT 1 0 13 "t22*t32*t10 " }{MPLTEXT 1 0 54 "+t12*t21*t31+t22*t1 1*t31+t32*t11*t21)*lambda,lambda);\n" }{MPLTEXT 1 0 16 "L:=simplify(L) :\n" }{MPLTEXT 1 0 42 "simplify(L[3,3]-h/(lambda-q)-P1(lambda));\n" } {MPLTEXT 1 0 60 "simplify(L[3,2]-(h*(p-P1(q))/(lambda-q)-P2(lambda)+h* t12));\n" }{MPLTEXT 1 0 8 "series( " }{MPLTEXT 1 0 56 "simplify(L[3,1] -(h*(p^2-P1(q)*p+P2(q)-h*t12)/(lambda-q) " }{MPLTEXT 1 0 75 "+p^3-P1(q )*p^2+(P2(q)-h*t12)*p-P3(q)+P3(lambda)-h*(t22+t32)*t12*(lambda-q) " } {MPLTEXT 1 0 13 ")),lambda=0);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 54 "simplify(J31bis-(p^2-P1(q)*p+P2(q)-h*t12)/(lambda-q));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P1G6\"f*6#I'lambdaGF$F$6$I)operatorGF$I&arrowGF$ F$,**&,(I$t12GF$\"\"\"I$t22GF$F/I$t32GF$F/F/9$F/F/I$t11GF$F/I$t21GF$F/ I$t31GF$F/F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P2G6\"f*6#I'lambd aGF$F$6$I)operatorGF$I&arrowGF$F$,2*&,(*&I$t12GF$\"\"\"I$t22GF$F0F0*&F /F0I$t32GF$F0F0*&F1F0F3F0F0F09$\"\"#F0*&,(*&F/F0,&I$t21GF$F0I$t31GF$F0 F0F0*&F1F0,&I$t11GF$F0FI#P3G6\"f*6#I'la mbdaGF$F$6$I)operatorGF$I&arrowGF$F$,(**I$t12GF$\"\"\"I$t22GF$F.I$t32G F$F.9$\"\"$F.*&,(*(I$t11GF$F.F/F.F0F.F.*(F-F.I$t21GF$F.F0F.F.*(F-F.F/F .I$t31GF$F.F.F.F1\"\"#F.*&,.*(,&I$t20GF$!\"\"I$t30GF$FAF.F/F.F0F.F.*(F 0F.F6F.F8F.F.*(F/F.F6F.F:F.F.*(F-F.F@F.F0F.F.*(F-F.F8F.F:F.F.*(F-F.F/F .FBF.F.F.F1F.F.F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Gnormalized:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 21 "Gnor malized[1,1]:=1:\n" }{MPLTEXT 1 0 21 "Gnormalized[2,2]:=1:\n" } {MPLTEXT 1 0 20 "Gnormalized[3,3]:=1:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "Gnormalized[3,1]:=" }{MPLTEXT 1 0 13 "(t12-t32)/a13" }{MPLTEXT 1 0 9 "*lambda:\n" }{MPLTEXT 1 0 12 "Gnormalized;" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 36 "dGnormalizeddlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do " }{MPLTEXT 1 0 31 "dGnormalizeddlambda[i,j]:=diff(" }{MPLTEXT 1 0 34 "Gnormalized[i,j],l ambda): od: od:\n" }{MPLTEXT 1 0 29 "LGnormalized:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 361 "for i from 1 to 3 do for j from 1 to 3 do LGnormaliz ed[i,j]:=simplify( h*diff(Gnormalized[i,j],t12)*dott12+h*diff(Gnormali zed[i,j],t22)*dott22+h*diff(Gnormalized[i,j],t32)*dott32+h*diff(Gnorma lized[i,j],t11)*dott11+h*diff(Gnormalized[i,j],t21)*dott21+h*diff(Gnor malized[i,j],t31)*dott31+h*diff(Gnormalized[i,j],a12)*dota12+h*diff(Gn ormalized[i,j],a13)*dota13):\n" }{MPLTEXT 1 0 9 "od: od: \n" }{MPLTEXT 1 0 67 "Lnew:=simplify(Multiply(Multiply(Gnormalized,tdL),Gnormalized ^(-1))" }{MPLTEXT 1 0 49 "+h*Multiply(dGnormalizeddlambda,Gnormalized^ (-1))" }{MPLTEXT 1 0 2 "):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "Multiply(" }{MPLTEXT 1 0 20 "dGnormalizeddlambda," } {MPLTEXT 1 0 18 "Gnormalized^(-1));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "Multiply(Gnormalized^(-1)," }{MPLTEXT 1 0 19 "dGnormalizeddlambd a" }{MPLTEXT 1 0 2 ");" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "simplif y(tdL[1,2]*tdL[2,3]-" }{MPLTEXT 1 0 19 "tdL[2,2]*tdL[1,3]);" }{MPLTEXT 1 0 1 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG 6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I $mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'nor malF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGF:/%+ columnspanGF:-F56(-F86%Q\"0F'F;F>FAFDFFFHFJFLFAFDFF-F26(FLF4FLFAFDFF-F 26(-F56(-I&mfracGF$6)-F,6%-F#6%-F,6%-I#miGF$6&Q$t12F'/%'italicGQ%trueF 'F;/F?Q'italicF'-I#moGF$6.Q(−F'F;F>/%&fenceGQ&falseF'/%*separato rGFio/%)stretchyGFio/%*symmetricGFio/%(largeopGFio/%.movablelimitsGFio /%'accentGFio/%'lspaceGQ,0.2222222emF'/%'rspaceGFhp-F[o6&Q$t32F'F^oF;F aoF;F>-Fdo6-Q1⁢F'F>FgoFjoF\\pF^pF`pFbpFdp/FgpQ&0.0emF'/ FjpFbq-F[o6&Q)λF'/F_oFioF;F>-F,6#-F[o6&Q$a13F'F^oF;Fao/%.lineth icknessGF:/%+denomalignGQ'centerF'/%)numalignGFar/%)bevelledGFioF;FAFD FFFHFJFLF4FAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEFar/FGQ'|frleft|hrF '/%/alignmentscopeGF`o/%,columnwidthGQ%autoF'/%&widthGFbs/%+rowspacing GQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlines GF]t/%&frameGF]t/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFio/%-equa lcolumnsGFio/%-displaystyleGFio/%%sideGQ&rightF'/%0minlabelspacingGFjs F;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I( mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I' mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0, 0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+group alignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1-F26(-F56(-I&mfra cGF$6)-F,6#-F,6%-I#miGF$6&Q$t12F'/%'italicGQ%trueF'F;/F?Q'italicF'-I#m oGF$6.Q(−F'F;F>/%&fenceGQ&falseF'/%*separatorGFao/%)stretchyGFao /%*symmetricGFao/%(largeopGFao/%.movablelimitsGFao/%'accentGFao/%'lspa ceGQ,0.2222222emF'/%'rspaceGF`p-FY6&Q$t32F'FfnF;Fin-F,6#-FY6&Q$a13F'Ff nF;Fin/%.linethicknessGFJ/%+denomalignGQ'centerF'/%)numalignGF_q/%)bev elledGFaoF;FAFDFFFHFKF4F4FAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEF_q/ FGQ'|frleft|hrF'/%/alignmentscopeGFhn/%,columnwidthGQ%autoF'/%&widthGF `r/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF '/%,columnlinesGF[s/%&frameGF[s/%-framespacingGQ,0.4em~0.5exF'/%*equal rowsGFao/%-equalcolumnsGFao/%-displaystyleGFao/%%sideGQ&rightF'/%0minl abelspacingGFhrF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$67-I$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'/%+columnspanGFJF4F4FAFDFFF1- F26(-F56(-I&mfracGF$6)-F,6#-F,6%-I#miGF$6&Q$t12F'/%'italicGQ%trueF'F;/ F?Q'italicF'-I#moGF$6.Q(−F'F;F>/%&fenceGQ&falseF'/%*separatorGFa o/%)stretchyGFao/%*symmetricGFao/%(largeopGFao/%.movablelimitsGFao/%'a ccentGFao/%'lspaceGQ,0.2222222emF'/%'rspaceGF`p-FY6&Q$t32F'FfnF;Fin-F, 6#-FY6&Q$a13F'FfnF;Fin/%.linethicknessGFJ/%+denomalignGQ'centerF'/%)nu malignGF_q/%)bevelledGFaoF;FAFDFFFHFKF4F4FAFDFF/%&alignGQ%axisF'/FBQ)b aselineF'/FEF_q/FGQ'|frleft|hrF'/%/alignmentscopeGFhn/%,columnwidthGQ% autoF'/%&widthGF`r/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%) rowlinesGQ%noneF'/%,columnlinesGF[s/%&frameGF[s/%-framespacingGQ,0.4em ~0.5exF'/%*equalrowsGFao/%-equalcolumnsGFao/%-displaystyleGFao/%%sideG Q&rightF'/%0minlabelspacingGFhrF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }} {PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&*&,&I'lambdaG6\"\"\"\"I\"qGF(!\"\" F)I$t22GF(F)F)I\"pGF(F)F)I$a13GF(F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "GeneralSpectralCurve:=Determinant(y*IdentityMatrix(3) -tdL);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5GeneralSpectralCurveG6\",ds **I'lambdaGF$\"\"$I$t12GF$\"\"\"I$t22GF$F*I$t32GF$F*!\"\"**I\"qGF$F(F) F*F+F*F,F*F***F'\"\"#I$t11GF$F*F+F*F,F*F-**F'F1F)F*I$t21GF$F*F,F*F-**F 'F1F)F*F+F*I$t31GF$F*F-**F'F1F)F*F+F*I\"yGF$F*F***F'F1F)F*F,F*F8F*F*** F'F1F+F*F,F*F8F*F***I\"pGF$F*F/F1F)F*F+F*F-**F " 0 "" {MPLTEXT 1 0 34 "ExpLambdaInfinity:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 60 "ExpLambdaInfinity[1,1]:=exp((t11*lambda+t12/2*lambda^2)/h):\n" } {MPLTEXT 1 0 60 "ExpLambdaInfinity[2,2]:=exp((t21*lambda+t22/2*lambda^ 2)/h):\n" }{MPLTEXT 1 0 60 "ExpLambdaInfinity[3,3]:=exp((t31*lambda+t3 2/2*lambda^2)/h):\n" }{MPLTEXT 1 0 19 "ExpLambdaInfinity;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "LambdaInfinity:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 48 "LambdaInfinity[1,1]:=t11*lambda+t12/2*lambda^2:\n" } {MPLTEXT 1 0 48 "LambdaInfinity[2,2]:=t21*lambda+t22/2*lambda^2:\n" } {MPLTEXT 1 0 48 "LambdaInfinity[3,3]:=t31*lambda+t32/2*lambda^2:\n" } {MPLTEXT 1 0 16 "LambdaInfinity:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 39 "dLambdaInfinitydlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 113 "for i from 1 to 3 do for j from 1 to 3 do dLambdaInfinitydlambda[i,j]:=di ff(LambdaInfinity[i,j],lambda): od: od:\n" }{MPLTEXT 1 0 24 "dLambdaIn finitydlambda:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "ExpMonodromie s:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 44 "ExpMonodromies[1,1]:=exp(t10*ln (lambda)/h):\n" }{MPLTEXT 1 0 44 "ExpMonodromies[2,2]:=exp(t20*ln(lamb da)/h):\n" }{MPLTEXT 1 0 44 "ExpMonodromies[3,3]:=exp(t30*ln(lambda)/h ):\n" }{MPLTEXT 1 0 16 "ExpMonodromies;\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 28 "Monodromies:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 30 "Mono dromies[1,1]:=t10/lambda:\n" }{MPLTEXT 1 0 30 "Monodromies[2,2]:=t20/l ambda:\n" }{MPLTEXT 1 0 30 "Monodromies[3,3]:=t30/lambda:\n" }{MPLTEXT 1 0 13 "Monodromies:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "F1:=Ma trix(3,3,0):\n" }{MPLTEXT 1 0 19 "F2:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 19 "F3:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 19 "F4:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 20 "FF5:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 61 "for i from 1 to 3 do for j from 1 to 3 do F1[i,j]:=f1[i,j]: \n" }{MPLTEXT 1 0 18 " F2[i,j]:=f2[i,j]:\n" }{MPLTEXT 1 0 18 "F3[i,j]:=f3[i,j]:\n" }{MPLTEXT 1 0 18 "F4[i,j]:=f4[i,j]:\n" }{MPLTEXT 1 0 20 "FF5[i,j]:=ff5[i,j]:\n" }{MPLTEXT 1 0 8 "od: od:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 3 "Hat" }{MPLTEXT 1 0 87 "PsiReg:=IdentityMatrix(3)+F1/l ambda+F2/lambda^2+F3/lambda^3+F4/lambda^4+ FF5/lambda^5:\n" }{MPLTEXT 1 0 35 "tdPsi:=Multiply(Multiply(HatPsiReg," }{MPLTEXT 1 0 19 "ExpLamb daInfinity)," }{MPLTEXT 1 0 16 "ExpMonodromies):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "d" }{MPLTEXT 1 0 9 "HatPsiReg" }{MPLTEXT 1 0 24 "dlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i f rom 1 to 3 do for j from 1 to 3 do " }{MPLTEXT 1 0 10 "dHatPsiReg" } {MPLTEXT 1 0 7 "dlambda" }{MPLTEXT 1 0 12 "[i,j]:=diff(" }{MPLTEXT 1 0 9 "HatPsiReg" }{MPLTEXT 1 0 22 "[i,j],lambda): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "d" }{MPLTEXT 1 0 5 "tdP si" }{MPLTEXT 1 0 24 "dlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do " }{MPLTEXT 1 0 6 "dtdPsi" } {MPLTEXT 1 0 7 "dlambda" }{MPLTEXT 1 0 12 "[i,j]:=diff(" }{MPLTEXT 1 0 5 "tdPsi" }{MPLTEXT 1 0 23 "[i,j],lambda): od: od:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 34 "dLambdaInfinitydt:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do " }{MPLTEXT 1 0 39 "dLambdaInfinitydt[i,j]:= simplify(diff(" }{MPLTEXT 1 0 30 "La mbdaInfinity[i,j],t11)*dt11+" }{MPLTEXT 1 0 19 "diff(LambdaInfinity" } {MPLTEXT 1 0 5 "[i,j]" }{MPLTEXT 1 0 11 ",t21)*dt21+" }{MPLTEXT 1 0 19 "diff(LambdaInfinity" }{MPLTEXT 1 0 5 "[i,j]" }{MPLTEXT 1 0 11 ",t3 1)*dt31+" }{MPLTEXT 1 0 19 "diff(LambdaInfinity" }{MPLTEXT 1 0 5 "[i,j ]" }{MPLTEXT 1 0 11 ",t12)*dt12+" }{MPLTEXT 1 0 19 "diff(LambdaInfinit y" }{MPLTEXT 1 0 5 "[i,j]" }{MPLTEXT 1 0 11 ",t22)*dt22+" }{MPLTEXT 1 0 19 "diff(LambdaInfinity" }{MPLTEXT 1 0 5 "[i,j]" }{MPLTEXT 1 0 21 ", t32)*dt32): od: od:\n" }{MPLTEXT 1 0 18 "dLambdaInfinitydt:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 45 "omegaJMU:=-h*residu e(Trace(Multiply(Multiply(" }{MPLTEXT 1 0 15 "HatPsiReg^(-1)," } {MPLTEXT 1 0 10 "dHatPsiReg" }{MPLTEXT 1 0 10 "dlambda), " }{MPLTEXT 1 0 19 "dLambdaInfinitydt))" }{MPLTEXT 1 0 18 ",lambda=infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I%m supGF$6%-I#moGF$6.Q/ⅇF'/%+foregroundGQ([0,0,0]F'/%,mathva riantGQ'normalF'/%&fenceGQ&falseF'/%*separatorGFF/%)stretchyGFF/%*symm etricGFF/%(largeopGFF/%.movablelimitsGFF/%'accentGFF/%'lspaceGQ&0.0emF '/%'rspaceGQ,0.1111111emF'-I&mfracGF$6)-F,6#-F,6%-F,6%-I#miGF$6&Q)&lam bda;F'/%'italicGFFF>FA-F;6-Q1⁢F'FAFDFGFIFKFMFOFQFS/FWFU -F]o6&Q$t11F'/FaoQ%trueF'F>/FBQ'italicF'-F;6.Q\"+F'F>FAFDFGFIFKFMFOFQ/ FTQ,0.2222222emF'/FWFap-F,6%-FZ6)-I#mnGF$6%Q\"1F'F>FA-Fhp6%Q\"2F'F>FA/ %.linethicknessGFjp/%+denomalignGQ'centerF'/%)numalignGFbq/%)bevelledG FFF>Fbo-F,6%-F]o6&Q$t12F'FioF>F[pFbo-F86%F\\oF[q/%1superscriptshiftGQ \"0F'-F,6#-F]o6&Q\"hF'FioF>F[pF^qF`qFcqFeqF>F^r/%)rowalignGQ!F'/%,colu mnalignGFhr/%+groupalignGFhr/%(rowspanGFjp/%+columnspanGFjp-F56(-Fhp6% F`rF>FAFfrFirF[sF]sF_sFasFfrFirF[s-F26(Fas-F56(-F86%F:-FZ6)-F,6#-F,6%- F,6%-F]o6&Q$t21F'FioF>F[pFboF\\oF]p-F,6%FepFbo-F,6%-F]o6&Q$t22F'FioF>F [pFboF\\rFarF^qF`qFcqFeqF>F^rFfrFirF[sF]sF_sFasFfrFirF[s-F26(FasFas-F5 6(-F86%F:-FZ6)-F,6#-F,6%-F,6%-F]o6&Q$t31F'FioF>F[pFboF\\oF]p-F,6%FepFb o-F,6%F\\rFbo-F]o6&Q$t32F'FioF>F[pFarF^qF`qFcqFeqF>F^rFfrFirF[sF]sF_sF frFirF[s/%&alignGQ%axisF'/FgrQ)baselineF'/FjrFbq/F\\sQ'|frleft|hrF'/%/ alignmentscopeGFjo/%,columnwidthGQ%autoF'/%&widthGFaw/%+rowspacingGQ&1 .0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF \\x/%&frameGF\\x/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFF/%-equal columnsGFF/%-displaystyleGFF/%%sideGQ&rightF'/%0minlabelspacingGFiwF>F A/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfe ncedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mta bleGF$67-I$mtrGF$6(-I$mtdGF$6(-I%msupGF$6%-I#moGF$6.Q/ⅇF' /%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/% *separatorGFF/%)stretchyGFF/%*symmetricGFF/%(largeopGFF/%.movablelimit sGFF/%'accentGFF/%'lspaceGQ&0.0emF'/%'rspaceGQ,0.1111111emF'-I&mfracGF $6)-F,6%-F#6%-F,6&-F;6.Q*&uminus0;F'F>FAFDFGFIFKFMFOFQ/FTQ,0.2222222em F'/FWF`o-I#miGF$6&Q$t20F'/%'italicGQ%trueF'F>/FBQ'italicF'-F;6.Q(&minu s;F'F>FAFDFGFIFKFMFOFQF_oFao-Fco6&Q$t30F'FfoF>FioF>FA-F;6-Q1&Invisible Times;F'FAFDFGFIFKFMFOFQFS/FWFU-F,6%-Fco6&Q#lnF'/FgoFFF>FA-F;6-Q0&Appl yFunction;F'FAFDFGFIFKFMFOFQFSFdp-F#6%-F,6#-Fco6&Q)λF'FjpF>FAF> FA-F,6#-Fco6&Q\"hF'FfoF>Fio/%.linethicknessGQ\"1F'/%+denomalignGQ'cent erF'/%)numalignGF_r/%)bevelledGFFF>/%1superscriptshiftGQ\"0F'/%)rowali gnGQ!F'/%,columnalignGFir/%+groupalignGFir/%(rowspanGF\\r/%+columnspan GF\\r-F56(-I#mnGF$6%FfrF>FAFgrFjrF\\sF^sF`sFbsFgrFjrF\\s-F26(Fbs-F56(- F86%F:-FZ6)-F,6%FboFapFepFeqFjqF]rF`rFbrF>FdrFgrFjrF\\sF^sF`sFbsFgrFjr F\\s-F26(FbsFbs-F56(-F86%F:-FZ6)-F,6%F^pFapFepFeqFjqF]rF`rFbrF>FdrFgrF jrF\\sF^sF`sFgrFjrF\\s/%&alignGQ%axisF'/FhrQ)baselineF'/F[sF_r/F]sQ'|f rleft|hrF'/%/alignmentscopeGFho/%,columnwidthGQ%autoF'/%&widthGFgu/%+r owspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,co lumnlinesGFbv/%&frameGFbv/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGF F/%-equalcolumnsGFF/%-displaystyleGFF/%%sideGQ&rightF'/%0minlabelspaci ngGF_vF>FA/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)omegaJMUG6\",$*&I\"hGF$\"\"\",.*&&I#f1GF$6$F(F(F(I%dt11GF$F(F(* &,**$F+\"\"#F(*&&F,6$F(F2F(&F,6$F2F(F(F(*&&F,6$F(\"\"$F(&F,6$F;F(F(F(& I#f2GF$F-!\"#F(I%dt12GF$F(#!\"\"F2*&&F,6$F2F2F(I%dt21GF$F(F(*&,*F3F(*$ FEF2F(*&&F,6$F2F;F(&F,6$F;F2F(F(&F?FFF@F(I%dt22GF$F(FB*&&F,6$F;F;F(I%d t31GF$F(F(*&,*F8F(FKF(*$FSF2F(&F?FTF@F(I%dt32GF$F(FBF(FC" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "ToCancel0:=simplify(h*" }{MPLTEXT 1 0 6 "dtdPsi" }{MPLTEXT 1 0 7 "dlambda" }{MPLTEXT 1 0 14 "-Multiply(t dL," }{MPLTEXT 1 0 5 "tdPsi" }{MPLTEXT 1 0 3 ")):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 168 "Cancel11:=series(simplify(series( simplify( ToCancel0[1,1]*exp(-((-2*t20-2*t30)*ln(lambda)+t12*lambda^2+2*lambda* t11)/(2*h)) ),lambda=infinity,10)),lambda=infinity);\n" }{MPLTEXT 1 0 23 "f1[3,1]:=solve(residue(" }{MPLTEXT 1 0 8 "Cancel11" }{MPLTEXT 1 0 29 " ,lambda=infinity),f1[3,1]);\n" }{MPLTEXT 1 0 23 "f2[3,1]:=solve (residue(" }{MPLTEXT 1 0 8 "Cancel11" }{MPLTEXT 1 0 36 "*lambda ,lambd a=infinity),f2[3,1]);\n" }{MPLTEXT 1 0 23 "f3[3,1]:=solve(residue(" } {MPLTEXT 1 0 8 "Cancel11" }{MPLTEXT 1 0 37 "*lambda^2 ,lambda=infinity ),f3[3,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Cancel11G6\",.*&,**&I$ a12GF$\"\"\"&I#f1GF$6$\"\"#F*F*!\"\"*&I$a13GF$F*&F,6$\"\"$F*F*F/I$t20G F$F/I$t30GF$F/F*I'lambdaGF$F/F**&,,*&F)F*&I#f2GF$F-F*F/*&F1F*&F&I#f1G6\"6$\" \"$\"\"\",$*&,(*&I$a12GF%F(&F$6$\"\"#F(F(F(I$t20GF%F(I$t30GF%F(F(I$a13 GF%!\"\"F4" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f2G6\"6$\"\"$\"\"\",$* &,**&I$a12GF%F(&F$6$\"\"#F(F(F(*&I\"hGF%F(&I#f1GF%6$F(F(F(F(*&I$t20GF% F(F3F(F(*&I$t30GF%F(F3F(F(F(I$a13GF%!\"\"F;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f3G6\"6$\"\"$\"\"\",$*&,**&I$a12GF%F(&F$6$\"\"#F(F(F( *&I\"hGF%F(&I#f2GF%6$F(F(F(F0*&I$t20GF%F(F3F(F(*&I$t30GF%F(F3F(F(F(I$a 13GF%!\"\"F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "Cancel12:= series(simplify(series( simplify( ToCancel0[1,2]*exp(-(lambda^2*t22+2* t20*ln(lambda)+2*lambda*t21)/(2*h))\n" }{MPLTEXT 1 0 43 " ),lambda=i nfinity,10)),lambda=infinity):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "f1[1,2]:=solve(residue(" }{MPLTEXT 1 0 8 "Cancel12" }{MPLTEXT 1 0 7 " /lambda" }{MPLTEXT 1 0 28 ",lambda=infinity),f1[1,2]);\n" }{MPLTEXT 1 0 23 "f2[1,2]:=solve(residue(" }{MPLTEXT 1 0 8 "Cancel12" }{MPLTEXT 1 0 27 ",lambda=infinity),f2[1,2]);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "f3[1,2]:=solve(residue(" }{MPLTEXT 1 0 8 "Cancel12" }{MPLTEXT 1 0 7 "*lambda" }{MPLTEXT 1 0 27 ",lambda=infinity),f3[1,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"\"\"\"#,$*&I$a12GF%F',&I$t12GF%F' I$t22GF%!\"\"F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f2G6\"6$\"\"\" \"\"#*&,.*(I$a12GF%F'I$t12GF%F'&I#f1GF%6$F(F(F'!\"\"*(F,F'I$t22GF%F'F. F'F'*(I$a13GF%F'F-F'&F/6$\"\"$F(F'F1*(F5F'F3F'F6F'F'*&F,F'I$t11GF%F'F' *&F,F'I$t21GF%F'F1F',&F-F'F3F1!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">& I#f3G6\"6$\"\"\"\"\"#*&,L**I$a12GF%F'I$t11GF%F'I$t12GF%F'&I#f1GF%6$F(F (F'F'**F,F'F-F'I$t22GF%F'F/F'!\"\"*(F,F'F.F(&I#f2GF%F1F'F4**F,F'F.F'I$ t21GF%F'F/F'F4**F,F'F.F'F3F'F6F'F(**F,F'F9F'F3F'F/F'F'*(F,F'F3F(F6F'F4 **I$a13GF%F'F-F'F.F'&F06$\"\"$F(F'F'**F>F'F-F'F3F'F?F'F4*(F>F'F.F(&F7F @F'F4**F>F'F.F'F9F'F?F'F4**F>F'F.F'F3F'FDF'F(**F>F'F9F'F3F'F?F'F'*(F>F 'F3F(FDF'F4*(F,F'I\"hGF%F'F.F'F'*(F,F'FJF'F3F'F4*&F,F'F-F(F4*(F,F'F-F' F9F'F(*(F,F'F.F'I$t20GF%F'F4*(F,F'FOF'F3F'F'*&F,F'F9F(F4F',&F.F'F3F4! \"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "Cancel13:=series(si mplify(series( simplify( ToCancel0[1,3]*exp(-(lambda^2*t32+2*t30*ln(la mbda)+2*lambda*t31)/(2*h))\n" }{MPLTEXT 1 0 44 " ),lambda=infinity,1 0)),lambda=infinity);\n" }{MPLTEXT 1 0 23 "f1[1,3]:=solve(residue(" } {MPLTEXT 1 0 8 "Cancel13" }{MPLTEXT 1 0 7 "/lambda" }{MPLTEXT 1 0 27 " ,lambda=infinity),f1[1,3]);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "f2[ 1,3]:=" }{MPLTEXT 1 0 14 "solve(residue(" }{MPLTEXT 1 0 8 "Cancel13" } {MPLTEXT 1 0 28 ",lambda=infinity),f2[1,3]);\n" }{MPLTEXT 1 0 23 "f3[1 ,3]:=solve(residue(" }{MPLTEXT 1 0 8 "Cancel13" }{MPLTEXT 1 0 7 "*lamb da" }{MPLTEXT 1 0 27 ",lambda=infinity),f3[1,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Cancel13G6\",2*&,&I$t12GF$!\"\"I$t32GF$\"\"\"F+&I#f1GF $6$F+\"\"$F+F+I$a13GF$F)*&,**&,&I$t11GF$F)I$t31GF$F+F+F,F+F+*&F'F+&I#f 2GF$F.F+F+*&I$a12GF$F+&F-6$\"\"#F/F+F)*&&F-6$F/F/F+F0F+F)F+I'lambdaGF$ F)F+*&,,*&,&I\"hGF$F)I$t30GF$F+F+F,F+F+*&F4F+F8F+F+*&F'F+&I#f3GF$F.F+F +*&F;F+&F9F=F+F)*&&F9FAF+F0F+F)F+FB!\"#F+*&,,*&,&FGFQFHF+F+F8F+F+*&F4F +FKF+F+*&F'F+&I#f4GF$F.F+F+*&F;F+&FLF=F+F)*&&FLFAF+F0F+F)F+FB!\"$F+*&, ,*&F'F+&I$ff5GF$F.F+F+*&,&FGFhnFHF+F+FKF+F+*&F4F+FXF+F+*&F;F+&FYF=F+F) *&&FYFAF+F0F+F)F+FB!\"%F+*&,**&F4F+F\\oF+F+*&,&FGFeoFHF+F+FXF+F+*&F;F+ &F]oF=F+F)*&F0F+&F]oFAF+F)F+FB!\"&F+-I\"OG6$%*protectedGI(_syslibGF$6# *$FB!\"'F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"\"\"\"$,$* &I$a13GF%F',&I$t12GF%F'I$t32GF%!\"\"F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f2G6\"6$\"\"\"\"\"$,$*&,.*(I$a12GF%F'I$t12GF%F'&I#f1GF%6$\"\"# F(F'F'*(F-F'I$t32GF%F'F/F'!\"\"*(I$a13GF%F'F.F'&F06$F(F(F'F'*(F7F'F4F' F8F'F5*&F7F'I$t11GF%F'F5*&F7F'I$t31GF%F'F'F',&F.F'F4F5!\"#F5" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f3G6\"6$\"\"\"\"\"$*&,L**I$a12GF%F'I$t11GF %F'I$t12GF%F'&I#f1GF%6$\"\"#F(F'F'**F,F'F-F'I$t32GF%F'F/F'!\"\"*(F,F'F .F2&I#f2GF%F1F'F5**F,F'F.F'I$t31GF%F'F/F'F5**F,F'F.F'F4F'F7F'F2**F,F'F :F'F4F'F/F'F'*(F,F'F4F2F7F'F5**I$a13GF%F'F-F'F.F'&F06$F(F(F'F'**F?F'F- F'F4F'F@F'F5*(F?F'F.F2&F8FAF'F5**F?F'F.F'F:F'F@F'F5**F?F'F.F'F4F'FDF'F 2**F?F'F:F'F4F'F@F'F'*(F?F'F4F2FDF'F5*(F?F'I\"hGF%F'F.F'F'*(F?F'FJF'F4 F'F5*&F?F'F-F2F5*(F?F'F-F'F:F'F2*(F?F'F.F'I$t30GF%F'F5*(F?F'FOF'F4F'F' *&F?F'F:F2F5F',&F.F'F4F5!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "Cancel21:=series(simplify(series( simplify( ToCancel0[2,1]*exp( -((-2*t20-2*t30)*ln(lambda)+lambda^2*t12+2*lambda*t11)/(2*h))" } {MPLTEXT 1 0 41 "),lambda=infinity,10)),lambda=infinity):\n" }{MPLTEXT 1 0 34 "f1[2,1]:=simplify(solve( residue(" }{MPLTEXT 1 0 8 "Cancel21 " }{MPLTEXT 1 0 7 "/lambda" }{MPLTEXT 1 0 28 ",lambda=infinity),f1[2,1 ]));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 34 "f2[2,1]:=simplify(solve( \+ residue(" }{MPLTEXT 1 0 8 "Cancel21" }{MPLTEXT 1 0 28 ",lambda=infini ty),f2[2,1]));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 34 "f3[2,1]:=simpli fy(solve( residue(" }{MPLTEXT 1 0 8 "Cancel21" }{MPLTEXT 1 0 7 "*lamb da" }{MPLTEXT 1 0 28 ",lambda=infinity),f3[2,1])):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"#\"\"\"*(,(*&,**&I\"qGF%F'I$t32GF%F(F(*& I\"pGF%F(F.F(!\"\"*&F.F(I$t31GF%F(F(I$t20GF%F2F(I$t22GF%F(F(*&,(F0F2*& F.F(I$t21GF%F(F(F5F(F(F/F(F(*&,&F1F(F4F2F(,&F1F(F:F2F(F(F(I$a12GF%F2,& F6F(F/F2F2" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f2G6\"6$\"\"#\"\"\"**, 4*&,,*(I\"qGF%F(,&&I#f1GF%6$F(F(F(F.F(F(I\"pGF%F(!\"\"*&I$t32GF%F(F.\" \"$F(*&,&*&F6F(F0F(F(I$t31GF%F(F(F.F'F(*&,&*&F;F(F0F(F(I$t30GF%F(F(F.F (F(*&F0F(I$t20GF%F(F4F(I$t22GF%F'F(*&,0*&,&F0F(F.F'F(F3F'F(*&,**&F.F'F 6F(!\"#*&,**&,&I$t12GF%F(F6F4F(F0F(F(F;FJI$t11GF%F4I$t21GF%F4F(F.F(F(* &,&F;F4FQF4F(F0F(F(F?F4F(F3F(F(*(F6F(,(*&FOF(F0F(F(FPF4FQF4F(F.F'F4*&, (*&,&*&FOF(F;F(F4*&FQF(F6F(F(F(F0F(F(*&F?F(F6F(F4*&F;F(,&FPF(FQF(F(F(F (F.F(F(*&,(*&FOF(FAF(F(*&FAF(F6F(F(*&FQF(F;F(F(F(F0F(F(*&FQF(,&FAF(F?F (F(F(*&FPF(FAF(F4F(FBF(F(*$F3F7F4*&,,*&F.F(F6F(F(FVF4FPF(FQF(F;F(F(F3F 'F(*&,,*(F6F(FUF(F.F(F(*(FOF(,&FQF(F;F(F(F0F(F(FgnF(*&,&FPF4F;F4F(FQF( F(*&FPF(F;F(F4F(F3F(F(**FQF(F6F(,&FVF(FPF4F(F.F(F4*(FOF(,&F]oF(F^oF(F( F0F(F4*&,&*&,&FAF4F?F4F(FQF(F(FaoF(F(F6F(F(*(FPF(FQF(F;F(F(F(I$a12GF%F 4,&FBF4F6F(F4,&FOF(FBF4F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "Cancel22:=series(simplify(series( simplify( ToCancel0[2,2]*exp(-( lambda^2*t22+2*t20*ln(lambda)+2*lambda*t21)/(2*h))\n" }{MPLTEXT 1 0 44 " ),lambda=infinity,10)),lambda=infinity):\n" }{MPLTEXT 1 0 32 "f 1[3,2]:=simplify(solve(residue(" }{MPLTEXT 1 0 8 "Cancel22" }{MPLTEXT 1 0 1 "," }{MPLTEXT 1 0 27 "lambda=infinity),f1[3,2]));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "f2[3,2]:=simplify(solve(residue(" }{MPLTEXT 1 0 8 "Cancel22" }{MPLTEXT 1 0 8 "*lambda," }{MPLTEXT 1 0 27 "lambda= infinity),f2[3,2]));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "f3[3,2]:= simplify(solve(residue(" }{MPLTEXT 1 0 8 "Cancel22" }{MPLTEXT 1 0 10 " *lambda^2," }{MPLTEXT 1 0 27 "lambda=infinity),f3[3,2])):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"$\"\"#,$**I$a12GF%\"\"\",(*&I\"qG F%F,I$t32GF%F,!\"\"I\"pGF%F,I$t31GF%F1F,I$a13GF%F1,&I$t22GF%F,F0F1F1F1 " }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f2G6\"6$\"\"$\"\"#,$*.I$a12GF%\" \"\",.*(&I#f1GF%6$F(F(F,,(*&I\"qGF%F(I$t32GF%F,!\"\"*&,&I\"pGF%F,I$t31 GF%F6F,F4F,F,I\"hGF%F,F,I$t22GF%F'F,*&,2*(F4F(,&F/F,F4F6F,F5F(F,*&,(*& ,,*&I$t12GF%F,F/F,F,F9F(I$t11GF%F6I$t21GF%F,F:!\"#F,F4F(F,*&,(*&FHF,F/ F,F6*&F:F,F/F,F,I$t20GF%F,F,F4F,F,*&F;F,F/F,FIF,F5F,F,*(,&F9F6F:F,F,,, FEF6F9F6FGF,FHF6F:F,F,F4F,F6*&F/F,F9F(F6*&,(FLF,FMF,FNF6F,F9F,F,*&,&FM F6FNF6F,FHF,F,*(F;F,F/F,FFF,F6*&FNF,,&FGF,F:F,F,F,F,F " 0 "" {MPLTEXT 1 0 116 "Cancel 23:=series(simplify(series( simplify( ToCancel0[2,3]*exp(-(lambda^2*t3 2+2*t30*ln(lambda)+2*lambda*t31)/(2*h))\n" }{MPLTEXT 1 0 44 " ),lamb da=infinity,10)),lambda=infinity):\n" }{MPLTEXT 1 0 33 "f1[2,3]:=simpl ify(solve( residue(" }{MPLTEXT 1 0 8 "Cancel23" }{MPLTEXT 1 0 35 "/lam bda,lambda=infinity),f1[2,3]));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 33 "f2[2,3]:=simplify(solve( residue(" }{MPLTEXT 1 0 8 "Cancel23" } {MPLTEXT 1 0 28 ",lambda=infinity),f2[2,3]));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 33 "f3[2,3]:=simplify(solve( residue(" }{MPLTEXT 1 0 8 "C ancel23" }{MPLTEXT 1 0 35 "*lambda,lambda=infinity),f3[2,3])):" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"#\"\"$**I$a12GF%!\"\"I$a 13GF%\"\"\",(*&I\"qGF%F-I$t22GF%F-F+I\"pGF%F-I$t21GF%F+F-,&F1F-I$t32GF %F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f2G6\"6$\"\"#\"\"$,$*,I$a13 GF%\"\"\",,*&,,*(I\"qGF%F,,&&I#f1GF%6$F(F(F,F1!\"\"F,I$t32GF%F,F,*(F3F ,F1F,I$t12GF%F,F6*&I\"pGF%F,F1F,F,*&F1F,I$t31GF%F,F6I$t20GF%F,F,I$t22G F%F'F,*&,**(F7F'F3F,F1F,F6*&,,*(F1F,,&F3F,F1F,F,F9F,F,*&,&F3F6F1F,F,F; F,F,*&,&I$t21GF%!\"#F=F,F,F1F,F,*&F3F,FKF,F,F>F6F,F7F,F,*&,**&F2F,F;F, F,FMF6*&F1F,FKF,F,F>F6F,F9F,F,*&,&F;F,F=F6F,,&F;F,FKF6F,F6F,F?F,F,*(F3 F,FTF,F7F'F,*&,&*&,**&,&F3F6F1F6F,F;F,F,FMF,FQF,F>F,F,F9F,F,*&,&FKF,F= F6F,FTF,F,F,F7F,F,*&F9F,FTF'F,F,I$a12GF%F6,&F9F6F7F,F6,&F?F6F7F,FLF6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "Cancel31:=series(simplif y(series( simplify( ToCancel0[3,1]*exp(-((-2*t20-2*t30)*ln(lambda)+lam bda^2*t12+2*lambda*t11)/(2*h))" }{MPLTEXT 1 0 41 "),lambda=infinity,10 )),lambda=infinity):\n" }{MPLTEXT 1 0 41 "f1[1,1]:=simplify(solve(simp lify(residue(" }{MPLTEXT 1 0 8 "Cancel31" }{MPLTEXT 1 0 29 ",lambda=in finity)),f1[1,1]));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 41 "f2[1,1]:=s implify(solve(simplify(residue(" }{MPLTEXT 1 0 8 "Cancel31" }{MPLTEXT 1 0 37 "*lambda,lambda=infinity)),f2[1,1])):\n" }{MPLTEXT 1 0 41 "f3[1 ,1]:=simplify(solve(simplify(residue(" }{MPLTEXT 1 0 8 "Cancel31" } {MPLTEXT 1 0 38 "*lambda^2,lambda=infinity)),f3[1,1])):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"\"F'**,6*$I\"pGF%\"\"$F'*&,**&,(I$t 12GF%!\"\"I$t22GF%F2I$t32GF%F2F'I\"qGF%F'F'I$t31GF%F2I$t11GF%F2I$t21GF %F2F'F+\"\"#F'*&,0*&,&*&,&F3F'F4F'F'F1F'F'*&F3F'F4F'F'F'F5F9F'*&,(*&F1 F',&F8F'F6F'F'F'*&F3F',&F7F'F6F'F'F'*&F4F',&F7F'F8F'F'F'F'F5F'F'*&,&I$ t20GF%F'I$t30GF%F'F'F1F'F'*&FKF'F3F'F2*&FLF'F4F'F2*&F7F'FDF'F'*&F8F'F6 F'F'F'F+F'F'**F5F,F1F'F3F'F4F'F2*&,&*&,&*&F8F'F4F'F2*&F3F'F6F'F2F'F1F' F'*(F3F'F4F'F7F'F2F'F5F9F'*&,(*&,(*&FKF'F4F'F2FPF2*&F3F'FLF'F2F'F1F'F' *&,&*&FJF'F4F'F'*&F7F'F6F'F2F'F3F'F'*(F4F'F7F'F8F'F2F'F5F'F'*(FJF',(F6 F'F7F2F8F'F'F1F'F2*&,&*&F7F'FLF'F2*&F6F'FJF'F'F'F3F'F'*&,&*&F8F'FJF'F' *&F7F'FKF'F2F'F4F'F'*(F7F'F8F'F6F'F2F',&F1F'F3F2F2,&F1F2F4F'F2I\"hGF%F 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "Cancel32:=series(simp lify(series( simplify( ToCancel0[3,2]*exp(-(lambda^2*t22+2*t20*ln(lamb da)+2*lambda*t21)/(2*h))\n" }{MPLTEXT 1 0 44 " ),lambda=infinity,10) ),lambda=infinity):\n" }{MPLTEXT 1 0 32 "f1[2,2]:=solve(simplify(resid ue(" }{MPLTEXT 1 0 8 "Cancel32" }{MPLTEXT 1 0 28 ",lambda=infinity)),f 1[2,2]);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "f2[2,2]:=solve(simpli fy(residue(" }{MPLTEXT 1 0 8 "Cancel32" }{MPLTEXT 1 0 7 "*lambda" } {MPLTEXT 1 0 28 ",lambda=infinity)),f2[2,2]):" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 32 "f3[2,2]:=solve(simplify(residue(" }{MPLTEXT 1 0 8 "Ca ncel32" }{MPLTEXT 1 0 9 "*lambda^2" }{MPLTEXT 1 0 28 ",lambda=infinity )),f3[2,2]):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"#F'**,bp **I\"qGF%\"\"$I$t12GF%\"\"\"I$t22GF%F.I$t32GF%F.!\"\"**I\"pGF%F.F+F'F- F.F/F.F.**F3F.F+F'F-F.F0F.F.**F3F.F+F'F/F.F0F.F.**F+F'I$t11GF%F.F/F.F0 F.F1**F+F'F-F.I$t21GF%F.F0F.F1**F+F'F-F.F/F.I$t31GF%F.F1*(F3F'F+F.F-F. F1*(F3F'F+F.F/F.F1*(F3F'F+F.F0F.F1**F3F.F+F.F7F.F/F.F.**F3F.F+F.F7F.F0 F.F.**F3F.F+F.F-F.F9F.F.**F3F.F+F.F-F.F;F.F.**F3F.F+F.F9F.F0F.F.**F3F. F+F.F/F.F;F.F.**F+F.F7F.F9F.F0F.F1**F+F.F7F.F/F.F;F.F1**F+F.F-F.I$t20G F%F.F0F.F1**F+F.F-F.F9F.F;F.F1**F+F.F-F.F/F.I$t30GF%F.F1**F+F.FHF.F/F. F0F.F.**F+F.F/F.FKF.F0F.F.*$F3F,F.*&F3F'F7F.F1*&F3F'F9F.F1*&F3F'F;F.F1 *(F3F.F7F.F9F.F.*(F3F.F7F.F;F.F.*(F3F.F-F.FHF.F.*(F3F.F-F.FKF.F.*(F3F. FHF.F/F.F1*(F3F.F9F.F;F.F.*(F3F.FKF.F0F.F1*(F7F.FHF.F/F.F.*(F7F.FHF.F0 F.F1*(F7F.F9F.F;F.F1*(F-F.FHF.F;F.F1*(F-F.F9F.FKF.F1*(FHF.F9F.F/F.F1*( FHF.F9F.F0F.F.*(FHF.F/F.F;F.F.*(F9F.FKF.F0F.F.F.,&F-F.F/F1F1,&F/F.F0F1 F1I\"hGF%F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "Cancel33:=s eries(simplify(series( simplify( ToCancel0[3,3]*exp(-(lambda^2*t32+2*t 30*ln(lambda)+2*lambda*t31)/(2*h))\n" }{MPLTEXT 1 0 44 " ),lambda=in finity,10)),lambda=infinity):\n" }{MPLTEXT 1 0 32 "f1[3,3]:=solve(simp lify(residue(" }{MPLTEXT 1 0 8 "Cancel33" }{MPLTEXT 1 0 35 "*lambda,la mbda=infinity)),f1[3,3]);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "f2[3 ,3]:=solve(simplify(residue(" }{MPLTEXT 1 0 8 "Cancel33" }{MPLTEXT 1 0 38 "*lambda^2,lambda=infinity)),f2[3,3]):\n" }{MPLTEXT 1 0 32 "f3[3, 3]:=solve(simplify(residue(" }{MPLTEXT 1 0 8 "Cancel33" }{MPLTEXT 1 0 37 "*lambda^3,lambda=infinity)),f3[3,3]):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#f1G6\"6$\"\"$F',$**,bp**I\"qGF%F'I$t12GF%\"\"\"I$t22G F%F.I$t32GF%F.!\"\"**I\"pGF%F.F,\"\"#F-F.F/F.F.**F3F.F,F4F-F.F0F.F.**F 3F.F,F4F/F.F0F.F.**F,F4I$t11GF%F.F/F.F0F.F1**F,F4F-F.I$t21GF%F.F0F.F1* *F,F4F-F.F/F.I$t31GF%F.F1*(F3F4F,F.F-F.F1*(F3F4F,F.F/F.F1*(F3F4F,F.F0F .F1**F3F.F,F.F8F.F/F.F.**F3F.F,F.F8F.F0F.F.**F3F.F,F.F-F.F:F.F.**F3F.F ,F.F-F.F " 0 "" {MPLTEXT 1 0 19 "omegaJMU:=simplify(" }{MPLTEXT 1 0 10 "om egaJMU):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "OmegaJMUdt11:=simplify(residue(omegaJMU/dt11^2,dt11=0)):\n" } {MPLTEXT 1 0 14 "OmegaJMUdt21:=" }{MPLTEXT 1 0 43 "simplify(residue(om egaJMU/dt21^2,dt21=0)):\n" }{MPLTEXT 1 0 14 "OmegaJMUdt31:=" }{MPLTEXT 1 0 43 "simplify(residue(omegaJMU/dt31^2,dt31=0)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 14 "OmegaJMUdt12:=" }{MPLTEXT 1 0 43 "simplify(re sidue(omegaJMU/dt12^2,dt12=0)):\n" }{MPLTEXT 1 0 14 "OmegaJMUdt22:=" } {MPLTEXT 1 0 43 "simplify(residue(omegaJMU/dt22^2,dt22=0)):\n" } {MPLTEXT 1 0 14 "OmegaJMUdt32:=" }{MPLTEXT 1 0 43 "simplify(residue(om egaJMU/dt32^2,dt32=0)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 443 "omegaJMUdt11:=1/((t12-t22)*(-t12+t32))*(-p^3+(t11+t2 1+t31+(t12+t22+t32)*q)*p^2+(((-t22-t32)*t12-t22*t32)*q^2+((-t31-t21)*t 12+(-t11-t31)*t22-t32*(t11+t21))*q+t12*(-t20-t30)+t22*t20+t30*t32+(-t3 1-t21)*t11-t21*t31)*p+q^3*t12*t22*t32+((t21*t32+t22*t31)*t12+t22*t32*t 11)*q^2+((t20*t32+t21*t31+t22*t30)*t12+((-t20-t30)*t32+t11*t31)*t22+t3 2*t11*t21)*q+(t20+t30)*(t31-t11+t21)*t12+(t11*t30-t31*(t20+t30))*t22+( t11*t20-t21*(t20+t30))*t32+t11*t21*t31);\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 428 "omegaJMUdt21:=1/((t12-t22)*(-t22+t32))*(p^3+((-t12-t 22-t32)*q-t31-t11-t21)*p^2+(((t12+t32)*t22+t12*t32)*q^2+(t12*(t21+t31) +t22*(t11+t31)+t32*(t11+t21))*q-t22*t20-t30*t32+(t20+t30)*t12+(t11+t31 )*t21+t11*t31)*p-q^3*t12*t22*t32+((-t11*t32-t12*t31)*t22-t32*t12*t21)* q^2+(((t20+t30)*t32-t11*t31-t12*t30)*t22+(-t11*t21-t12*t20)*t32-t12*t2 1*t31)*q+t20*(t31+t11-t21)*t22+(t21*(t20+t30)-t11*t20)*t32+(-t20*t31-t 21*t30)*t12-t11*t21*t31);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 430 "o megaJMUdt31:=1/((-t22+t32)*(-t12+t32))*(p^3+((-t12-t22-t32)*q-t31-t11- t21)*p^2+(((t12+t22)*t32+t12*t22)*q^2+(t12*(t21+t31)+t22*(t11+t31)+t32 *(t11+t21))*q-t30*t32-t22*t20+(t20+t30)*t12+t31*(t11+t21)+t11*t21)*p-q ^3*t12*t22*t32+((-t11*t22-t12*t21)*t32-t31*t12*t22)*q^2+(((t20+t30)*t2 2-t11*t21-t12*t20)*t32+(-t11*t31-t12*t30)*t22-t12*t21*t31)*q-t30*(t31- t11-t21)*t32+(-t11*t30+t31*(t20+t30))*t22+(-t20*t31-t21*t30)*t12-t11*t 21*t31);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1734 "omegaJMUdt12:=1/( 2*(t12-t22)^2*(-t12+t32)^2)*(-(t20+t30)^2*t12^3+((-q^3*(t31-2*t11+t21) *t32+2*q*((-p+t31)*q+t30)*t11-(t21+t31)*(-p+t31)*q^2-t30*(t21+t31)*q+( t20+2*t30)*(t20+t30))*t22+(-2*q*((p-t21)*q-t20)*t11+(p-t21)*(t21+t31)* q^2-t20*(t21+t31)*q+2*t20^2+3*t30*t20+t30^2)*t32+(-t20-t30)*t11^2+(-(2 *(p-t21))*(-p+t31)*q+(2*(t20+t30))*(t31-p+t21))*t11+(p-t21)*(t21+t31)* (-p+t31)*q-(t20+t30)*((-t31-t21)*p+t31^2+t21*t31+t21^2))*t12^2+((q^3*( -t11+t31)*t32-q*((-p+t31)*q+t30)*t11+t31*(-p+t31)*q^2+t31*t30*q-t30*(t 20+t30))*t22^2+(-q^3*(t11-t21)*t32^2+(2*q^2*t11^2-2*q*((t21+t31)*q+3*t 20*(1/2)+3*t30*(1/2))*t11+2*q^2*t21*t31+((t20+2*t30)*t21+2*t31*(t20+(1 /2)*t30))*q-2*(t20+t30)^2)*t32+((2*t31-2*p)*q+2*t30)*t11^2+(-(-p+t31)* (t31+2*t21+p)*q+(t30+3*t20)*p-t21*t30-(3*(t20+4*t30*(1/3)))*t31)*t11+( -p^2*t21+t21*t31^2)*q+(-t21*t20-2*t31*(t20+(1/2)*t30))*p+(2*(t20+t30)) *t31*((1/2)*t21+t31))*t22+(q*((p-t21)*q-t20)*t11-(p-t21)*t21*q^2+t21*t 20*q-t20*(t20+t30))*t32^2+(((-2*p+2*t21)*q+2*t20)*t11^2+((2*(p-t21))*( (1/2)*p+t31+(1/2)*t21)*q+(t20+3*t30)*p+(-4*t20-3*t30)*t21-t31*t20)*t11 +(-p^2*t31+t21^2*t31)*q+((-t20-2*t30)*t21-t31*t30)*p+t21*(t20+t30)*(t3 1+2*t21))*t32-(p-t21)*(p-t11)*(t31-2*t11+t21)*(-p+t31))*t12+((-q^2*t11 ^2+q*((t31+p)*q+t20+t30)*t11-q^2*p*t31-(t20+t30)*t31*q+t30*(t20+t30))* t32-(-t11+t31)*(((p-t31)*q-t30)*t11+p*(-p+t31)*q-p*t20+t31*(t20+t30))) *t22^2+((-q^2*t11^2+((p+t21)*q+t20+t30)*q*t11-q^2*p*t21-t21*(t20+t30)* q+t20*(t20+t30))*t32^2+(-q*(t31-2*p+t21)*t11^2+((-2*p^2+2*t21*t31)*q+( -t20-t30)*p+t31*t20+t21*t30)*t11+((t21+t31)*p-2*t21*t31)*p*q+(t20*t21+ t30*t31)*p-t31*t21*(t20+t30))*t32+(p-t11)*(-t11+t31)*(-p+t31)*(p-t21)) *t22-((((-p+t21)*q+t20)*t11+p*(p-t21)*q+p*t30-t21*(t20+t30))*t32+(p-t2 1)*(p-t11)*(-p+t31))*(t11-t21)*t32);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1659 "omegaJMUdt22:=1/(2*(t12-t22)^2*(-t22+t32)^2)*(-t20^2*t22^3+ ((-q^3*(t31+t11-2*t21)*t12-2*q*((p-t11)*q+t20+t30)*t21+(p-t11)*(t11+t3 1)*q^2+(t20+t30)*(t11+t31)*q+2*t20^2+t30*t20)*t32+(2*q*((-p+t31)*q+t30 )*t21-(t11+t31)*(-p+t31)*q^2-t30*(t11+t31)*q+t20*(t20-t30))*t12+t20*t2 1^2+(-(2*(p-t11))*(-p+t31)*q-2*t20*(t31-p+t11))*t21+(p-t11)*(t11+t31)* (-p+t31)*q+t20*((-t11-t31)*p+t31^2+t11*t31+t11^2))*t22^2+((q^3*(t11-t2 1)*t12+q*((p-t11)*q+t20+t30)*t21-(p-t11)*t11*q^2-t11*(t20+t30)*q-t20*( t20+t30))*t32^2+(q^3*(-t21+t31)*t12^2+(2*q^2*t21^2-(2*((t11+t31)*q-3*t 20*(1/2)))*q*t21+2*q^2*t11*t31+(t11*(-t20+t30)-2*t31*(t20+(1/2)*t30))* q-2*t20^2)*t12+((-2*p+2*t11)*q-2*t20-2*t30)*t21^2+((2*((1/2)*p+t31+(1/ 2)*t11))*(p-t11)*q+(2*t30-t20)*p+(t30+4*t20)*t11+t31*(t20+t30))*t21+(- p^2*t31+t11^2*t31)*q+((t20-t30)*t11-t31*t30)*p-t11*t20*(t31+2*t11))*t3 2+(-q*((-p+t31)*q+t30)*t21+t31*(-p+t31)*q^2+t31*t30*q+t30*t20)*t12^2+( ((2*t31-2*p)*q+2*t30)*t21^2+(-(-p+t31)*(t31+2*t11+p)*q+(-2*t30-3*t20)* p-t11*t30+3*t31*(t20-(1/3)*t30))*t21+(-p^2*t11+t11*t31^2)*q+((t20+t30) *t11+2*t31*(t20+(1/2)*t30))*p-(2*(t31+(1/2)*t11))*t31*t20)*t12-(p-t21) *(p-t11)*(t31+t11-2*t21)*(-p+t31))*t22+((-q^2*t21^2+((p+t11)*q-t20)*q* t21-q^2*p*t11+t20*t11*q+t20*(t20+t30))*t12+(t11-t21)*(((-p+t11)*q-t20- t30)*t21+p*(p-t11)*q+p*t30+t11*t20))*t32^2+((-q^2*t21^2+q*((t31+p)*q-t 20)*t21-q^2*p*t31+t31*t20*q-t30*t20)*t12^2+(-q*(-2*p+t31+t11)*t21^2+(( -2*p^2+2*t11*t31)*q+p*t20+t11*t30-t31*(t20+t30))*t21+((t11+t31)*p-2*t1 1*t31)*p*q+((-t20-t30)*t11+t31*t30)*p+t31*t11*t20)*t12+(t11-t21)*(p-t2 1)*(p-t11)*(-p+t31))*t32+t12*((((-p+t31)*q+t30)*t21-p*(-p+t31)*q+(-t20 -t30)*p+t31*t20)*t12+(p-t21)*(p-t11)*(-p+t31))*(-t21+t31));\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1656 "omegaJMUdt32:=1/(2*(-t12+t32)^ 2*(-t22+t32)^2)*(-t30^2*t32^3+((2*q^3*(t31-(1/2)*t11-(1/2)*t21)*t12-2* q*((p-t11)*q+t20+t30)*t31+(t11+t21)*(p-t11)*q^2+(t20+t30)*(t11+t21)*q+ t30*(t20+2*t30))*t22+(-2*q*((p-t21)*q-t20)*t31+(t11+t21)*(p-t21)*q^2-t 20*(t11+t21)*q-t30*(t20-t30))*t12+t30*t31^2+((2*(p-t21))*(p-t11)*q+2*t 30*(p-t11-t21))*t31-(t11+t21)*(p-t21)*(p-t11)*q-t30*((t11+t21)*p-t11^2 -t11*t21-t21^2))*t32^2+((-q^3*(-t11+t31)*t12+q*((p-t11)*q+t20+t30)*t31 -(p-t11)*t11*q^2-t11*(t20+t30)*q-t30*(t20+t30))*t22^2+(-q^3*(-t21+t31) *t12^2+(2*q^2*t31^2-2*q*((t11+t21)*q-3*t30*(1/2))*t31+2*q^2*t11*t21+(( t20-t30)*t11-(t20+2*t30)*t21)*q-2*t30^2)*t12+((-2*p+2*t11)*q-2*t20-2*t 30)*t31^2+((p-t11)*(p+t11+2*t21)*q+(-t30+2*t20)*p+t11*(4*t30+t20)+t21* (t20+t30))*t31+(-p^2*t21+t11^2*t21)*q+(t11*(-t20+t30)-t21*t20)*p-(2*(t 11+(1/2)*t21))*t11*t30)*t22+(q*((p-t21)*q-t20)*t31-(p-t21)*t21*q^2+t21 *t20*q+t30*t20)*t12^2+(((-2*p+2*t21)*q+2*t20)*t31^2+((p-t21)*(p+2*t11+ t21)*q+(-2*t20-3*t30)*p-t11*t20-t21*(t20-3*t30))*t31+(-p^2*t11+t11*t21 ^2)*q+((t20+t30)*t11+(t20+2*t30)*t21)*p-t30*t21*(t11+2*t21))*t12+(2*(t 31-(1/2)*t11-(1/2)*t21))*(-p+t31)*(p-t21)*(p-t11))*t32+((-q^2*t31^2+q* ((p+t11)*q-t30)*t31-q^2*p*t11+t30*t11*q+t30*(t20+t30))*t12+(-t11+t31)* (((p-t11)*q+t20+t30)*t31-p*(p-t11)*q-p*t20-t11*t30))*t22^2+((-q^2*t31^ 2+q*((p+t21)*q-t30)*t31-q^2*p*t21+t30*t21*q-t30*t20)*t12^2+(2*q*(p-(1/ 2)*t11-(1/2)*t21)*t31^2+((-2*p^2+2*t11*t21)*q+p*t30+t11*t20-t21*(t20+t 30))*t31+((t11+t21)*p-2*t11*t21)*p*q+((-t20-t30)*t11+t21*t20)*p+t21*t1 1*t30)*t12-(p-t11)*(-t11+t31)*(-p+t31)*(p-t21))*t22-t12*((((-p+t21)*q+ t20)*t31+p*(p-t21)*q+(-t20-t30)*p+t21*t30)*t12+(p-t21)*(p-t11)*(-p+t31 ))*(-t21+t31));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 37 "simplify(Ome gaJMUdt11-omegaJMUdt11);\n" }{MPLTEXT 1 0 37 "simplify(OmegaJMUdt21-om egaJMUdt21);\n" }{MPLTEXT 1 0 37 "simplify(OmegaJMUdt31-omegaJMUdt31); \n" }{MPLTEXT 1 0 37 "simplify(OmegaJMUdt12-omegaJMUdt12);\n" } {MPLTEXT 1 0 37 "simplify(OmegaJMUdt22-omegaJMUdt22);\n" }{MPLTEXT 1 0 36 "simplify(OmegaJMUdt32-omegaJMUdt32);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-omegaJMUdt11G6\"*(,&I$t12GF$\"\"\"I$t22GF$!\"\"F*,&F'F *I$t32GF$F(F*,6*$I\"pGF$\"\"$F**&,*I$t11GF$F(I$t21GF$F(I$t31GF$F(*&,(F 'F(F)F(F,F(F(I\"qGF$F(F(F(F/\"\"#F(*&,0*&,&*&,&F)F*F,F*F(F'F(F(*&F)F(F ,F(F*F(F8F9F(*&,(*&,&F5F*F4F*F(F'F(F(*&,&F3F*F5F*F(F)F(F(*&F,F(,&F3F(F 4F(F(F*F(F8F(F(*&F'F(,&I$t20GF$F*I$t30GF$F*F(F(*&FKF(F)F(F(*&FLF(F,F(F (*&FDF(F3F(F(*&F4F(F5F(F*F(F/F(F(**F8F0F'F(F)F(F,F(F(*&,&*&,&*&F4F(F,F (F(*&F)F(F5F(F(F(F'F(F(*(F)F(F,F(F3F(F(F(F8F9F(*&,(*&,(*&FKF(F,F(F(FPF (*&F)F(FLF(F(F(F'F(F(*&,&*&FJF(F,F(F(*&F3F(F5F(F(F(F)F(F(*(F,F(F3F(F4F (F(F(F8F(F(*(,&FKF(FLF(F(,(F5F(F3F*F4F(F(F'F(F(*&,&*&F3F(FLF(F(*&F5F(F _oF(F*F(F)F(F(*&,&*&F3F(FKF(F(*&F4F(F_oF(F*F(F,F(F(*(F3F(F4F(F5F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-omegaJMUdt21G6\"*(,6*$I\"pGF$\"\"$ \"\"\"*&,**&,(I$t12GF$!\"\"I$t22GF$F0I$t32GF$F0F*I\"qGF$F*F*I$t31GF$F0 I$t11GF$F0I$t21GF$F0F*F(\"\"#F**&,0*&,&*&,&F/F*F2F*F*F1F*F**&F/F*F2F*F *F*F3F7F**&,(*&F/F*,&F6F*F4F*F*F**&F1F*,&F5F*F4F*F*F**&F2F*,&F5F*F6F*F *F*F*F3F*F**&I$t20GF$F*F1F*F0*&I$t30GF$F*F2F*F0*&,&FHF*FJF*F*F/F*F**&F DF*F6F*F**&F5F*F4F*F*F*F(F*F***F3F)F/F*F1F*F2F*F0*&,&*&,&*&F5F*F2F*F0* &F/F*F4F*F0F*F1F*F**(F/F*F6F*F2F*F0F*F3F7F**&,(*&,(*&FLF*F2F*F*FNF0*&F /F*FJF*F0F*F1F*F**&,&*&F5F*F6F*F0*&F/F*FHF*F0F*F2F*F**(F/F*F6F*F4F*F0F *F3F*F**(FHF*,(F4F*F5F*F6F0F*F1F*F**&,&*&F6F*FLF*F**&F5F*FHF*F0F*F2F*F **&,&*&FHF*F4F*F0*&F6F*FJF*F0F*F/F*F**(F5F*F6F*F4F*F0F*,&F/F*F1F0F0,&F 1F0F2F*F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-omegaJMUdt31G6\"*(,&I$t2 2GF$!\"\"I$t32GF$\"\"\"F(,&I$t12GF$F(F)F*F(,6*$I\"pGF$\"\"$F**&,**&,(F ,F(F'F(F)F(F*I\"qGF$F*F*I$t31GF$F(I$t11GF$F(I$t21GF$F(F*F/\"\"#F**&,0* &,&*&,&F,F*F'F*F*F)F*F**&F,F*F'F*F*F*F5F9F**&,(*&F,F*,&F8F*F6F*F*F**&F 'F*,&F7F*F6F*F*F**&F)F*,&F7F*F8F*F*F*F*F5F*F**&I$t30GF$F*F)F*F(*&I$t20 GF$F*F'F*F(*&,&FLF*FJF*F*F,F*F**&F6F*FHF*F**&F7F*F8F*F*F*F/F*F***F5F0F ,F*F'F*F)F*F(*&,&*&,&*&F7F*F'F*F(*&F,F*F8F*F(F*F)F*F**(F6F*F,F*F'F*F(F *F5F9F**&,(*&,(*&FNF*F'F*F*FPF(*&FLF*F,F*F(F*F)F*F**&,&*&F7F*F6F*F(*&F ,F*FJF*F(F*F'F*F**(F,F*F8F*F6F*F(F*F5F*F**(FJF*,(F6F*F7F(F8F(F*F)F*F(* &,&*&F7F*FJF*F(*&F6F*FNF*F*F*F'F*F**&,&*&FLF*F6F*F(*&F8F*FJF*F(F*F,F*F **(F7F*F8F*F6F*F(F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-omegaJMUdt12G6 \",$*(,&I$t12GF$\"\"\"I$t22GF$!\"\"!\"#,&F(F+I$t32GF$F)F,,.*&,&I$t20GF $F)I$t30GF$F)\"\"#F(\"\"$F+*&,.*&,,*(I\"qGF$F5,(I$t31GF$F)I$t11GF$F,I$ t21GF$F)F)F.F)F+*(F;F),&*&,&I\"pGF$F+F=F)F)F;F)F)F3F)F)F>F)F4*(,&F?F)F =F)F)FCF)F;F4F+*(F3F)FFF)F;F)F+*&,&F2F)F3F4F)F1F)F)F)F*F)F)*&,.*(F;F), &*&,&FDF)F?F+F)F;F)F)F2F+F)F>F)F,*(FFF)FOF)F;F4F)*(FFF)F2F)F;F)F+*$F2F 4F4*&F3F)F2F)F5*$F3F4F)F)F.F)F)*&,&F2F+F3F+F)F>F4F)*&,&*(FOF)FCF)F;F)F ,*&F1F),(F=F)FDF+F?F)F)F4F)F>F)F)**FOF)FFF)FCF)F;F)F)*&F1F),**&,&F=F+F ?F+F)FDF)F)*$F=F4F)*&F?F)F=F)F)*$F?F4F)F)F+F)F(F4F)*&,,*&,,*(F;F5,&F>F +F=F)F)F.F)F)F@F+*(F=F)FCF)F;F4F)*(F=F)F3F)F;F)F)*&F3F)F1F)F+F)F*F4F)* &,0*(F;F5,&F>F)F?F+F)F.F4F+*&,,*&F>F4F;F4F4*(F;F),(*&FFF)F;F)F)F2#F5F4 F3FapF)F>F)F,*(F;F4F?F)F=F)F4*&,&*&FIF)F?F)F)*&F=F),&F2F)F3#F)F4F)F4F) F;F)F)*$F1F4F,F)F.F)F)*&,&*&,&F=F4FDF,F)F;F)F)F3F4F)F>F4F)*&,**(FCF),( FDF)F?F4F=F)F)F;F)F+*&,&F3F)F2F5F)FDF)F)*&F?F)F3F)F+*&F=F),&F2F)F3#\" \"%F5F)!\"$F)F>F)F)*&,&*&FDF4F?F)F+*&F?F)F=F4F)F)F;F)F)*&,&*&F?F)F2F)F +FfpF,F)FDF)F)*(F1F)F=F),&F=F)F?FhpF)F4F)F*F)F)*&,*FLF)*(FOF)F?F)F;F4F +*(F?F)F2F)F;F)F)*&F2F)F1F)F+F)F.F4F)*&,,*&,&*&,&FDF,F?F4F)F;F)F)F2F4F )F>F4F)*&,**(FOF),(FDFhpF=F)F?FhpF)F;F)F4*&,&F2F)F3F5F)FDF)F)*&,&F2!\" %F3FiqF)F?F)F)*&F=F)F2F)F+F)F>F)F)*&,&*&FDF4F=F)F+*&F?F4F=F)F)F)F;F)F) *&,&*&,&F2F+F3F,F)F?F)F)*&F=F)F3F)F+F)FDF)F)*(F?F)F1F),&F=F)F?F4F)F)F) F.F)F)**FOF),&FDF)F>F+F)FF)F)*(F=F)F;F4FDF)F+*(F=F)F1F)F;F)F+FfoF)F)F. F)F)*&FcoF),**&,&*&,&FDF)F=F+F)F;F)F)F3F+F)F>F)F)*(FDF)FCF)F;F)F)*&F2F )FDF)F+*&F=F)F1F)F)F)F+F)F*F4F)*&,(*&,,F]pF+*(F;F),(*&,&FDF)F?F)F)F;F) F)F2F)F3F)F)F>F)F)*(F?F)F;F4FDF)F+*(F?F)F1F)F;F)F+FgrF)F)F.F4F)*&,,*(F ;F),(F=F)FDF,F?F)F)F>F4F+*&,**&,&*$FDF4F,F\\oF4F)F;F)F)*&FVF)FDF)F)Fgs F)FdqF)F)F>F)F)*(,&*&FFF)FDF)F)F\\oF,F)FDF)F;F)F)*&,&*&F2F)F?F)F)*&F3F )F=F)F)F)FDF)F)*(F?F)F=F)F1F)F+F)F.F)F)**FdtF)FcoF)FCF)FOF)F)F)F*F)F)* (,&*&,**&,&*&,&FDF+F?F)F)F;F)F)F2F)F)F>F)F)*(FDF)FOF)F;F)F)*&FDF)F3F)F )*&F?F)F1F)F+F)F.F)F)*(FOF)FdtF)FCF)F)F)FjoF)F.F)F+F)Fhp" }}{PARA 11 " " 1 "" {XPPMATH 20 ">I-omegaJMUdt22G6\",$*(,&I$t12GF$\"\"\"I$t22GF$!\" \"!\"#,&F*F+I$t32GF$F)F,,.*&I$t20GF$\"\"#F*\"\"$F+*&,.*&,.*(I\"qGF$F3, (I$t11GF$F)I$t21GF$F,I$t31GF$F)F)F(F)F+*(,(*&,&I\"pGF$F)F;F+F)F9F)F)F1 F)I$t30GF$F)F)F9F)FF)*(F;F)FAF)F9F2F+*(F;F)FGF)F9 F)F+*&F1F)FGF)F+F)F.F2F)*&,0*(F9F3,&FI-omegaJMUdt32G6\",$*(,&I$t12GF$!\"\"I$t32GF$\"\"\"!\"#,&I$t22GF$F)F* F+F,,.*&F*\"\"$I$t30GF$\"\"#F)*&,.*&,,*(I\"qGF$F1,(I$t31GF$F+I$t11GF$# F)F3I$t21GF$F=F+F(F+F3*(,(*&,&I\"pGF$F+FF+F+FBF+F9F3F+*(,&FDF+F2F+F+FFF+F9F+F+*&F2F+,&FDF+F2F 3F+F+F+F.F+F+*&,**(F9F+,&*&,&FCF+F>F)F+F9F+F+FDF)F+F;F+F,*(FFF+FPF+F9F 3F+*(FDF+FFF+F9F+F)*&F2F+,&FDF+F2F)F+F)F+F(F+F+*&F;F3F2F+F+*&,&*(FPF+F BF+F9F+F3*&F2F+,(FCF+FF)F+F3F+F;F+F+**FFF+FPF+FBF+F9F+F)*&,**&FFF +FCF+F+*$FF+F)*$F>F3F)F+F2F+F)F+F*F3F+*&,,*&,,*(F9F1,&FF)F;F+F+F(F3F)*&,,*&F;F3F9F3F3*(F9F+,&*&FFF+F9F+F+F2#!\"$ F3F+F;F+F,*(F>F+FF+F)F+F9F+F+*$F2F3F, F+F(F+F+*&,(*&,&FCF,FF3F< F+F+F9F+F+*&,&F2F)FDF3F+FCF+F+*&FF+FHF+F+F+F;F +F+*&,&*&FCF3F>F+F)*&FF+F+F+F9F+F+*&,&*&FF+F DF+F)F+FCF+F+*(F2F+F#F+F3F+F,F+F.F+F+*&,*FMF+*(FPF+F>F+F9F3 F)*(F>F+FDF+F9F+F+*&F2F+FDF+F+F+F(F3F+*&,,*&,&*&,&FCF,F>F3F+F9F+F+FDF3 F+F;F3F+*&,**(FPF+,(FCF+FF+F+F9F+F+*&,&FDF,F2F`pF+FCF+F+*&FF+,&FDF+F2F`pF+F)F+F;F+F+*&,&*&FCF3FF3F+F+F9F+F+*& ,&*&FHF+FF+,&FF3F+F)F+F(F+F+**FPF+F:F+F BF+,&FCF)F;F+F+F3F+F*F+F+*&,&*&,,F[pF)*(F9F+,&*&,&FCF+FF+F+F9F+F+F2F)F+F9F+F;F+F+*(F>F+F9F3FCF+F)*(F2F+F>F+F9F+F +FerF)F+F(F3F+*&,,*(F9F+,(FCF+FF=F+F;F3F3*&,**&,&*$FCF3F,FjnF3F+F 9F+F+*&FCF+F2F+F+FbsF+FdqF)F+F;F+F+*(FCF+,&FhnF+FjnF,F+F9F+F+*&,&*&,&F DF)F2F)F+FF+FF+F+F9F+F+FDF+F+F;F+F+*(FCF+FPF+ F9F+F+*&FivF+FCF+F+*&F>F+F2F+F+F+F(F+F+*(FPF+FBF+F_tF+F+F+FhoF+F)F+F`r " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "simplify(Trace(2*F2-F1^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"! " }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 290 94 "Computation of the general auxiliary matrix \\td\{A\} and of the Hamiltonian evolutions for (q,p )" }}{EXCHG {PARA 0 "" 0 "" {TEXT 218 106 "The evolutions relatively t o the irregular times are denoted dott12, dott22, dott32, dott11, dott 21,dott31" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "tdA:=Matrix(3, 3,0):\n" }{MPLTEXT 1 0 49 "tdA[1,1]:=tdA112*lambda^2+tdA111*lambda+tdA 110: \n" }{MPLTEXT 1 0 48 "tdA[1,2]:=tdA122*lambda^2+tdA121*lambda+tdA 120:\n" }{MPLTEXT 1 0 48 "tdA[1,3]:=tdA132*lambda^2+tdA131*lambda+tdA1 30:\n" }{MPLTEXT 1 0 49 "tdA[2,1]:=tdA212*lambda^2+tdA211*lambda+tdA21 0: \n" }{MPLTEXT 1 0 48 "tdA[2,2]:=tdA222*lambda^2+tdA221*lambda+tdA22 0:\n" }{MPLTEXT 1 0 48 "tdA[2,3]:=tdA232*lambda^2+tdA231*lambda+tdA230 :\n" }{MPLTEXT 1 0 49 "tdA[3,1]:=tdA312*lambda^2+tdA311*lambda+tdA310: \n" }{MPLTEXT 1 0 48 "tdA[3,2]:=tdA322*lambda^2+tdA321*lambda+tdA320: \n" }{MPLTEXT 1 0 48 "tdA[3,3]:=tdA332*lambda^2+tdA331*lambda+tdA330: \n" }{MPLTEXT 1 0 5 "tdA;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "td Adt:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 57 "tdAdt[1,1]:=tdAdt112*lambda^2 +tdAdt111*lambda+tdAdt110: \n" }{MPLTEXT 1 0 56 "tdAdt[1,2]:=tdAdt122* lambda^2+tdAdt121*lambda+tdAdt120:\n" }{MPLTEXT 1 0 56 "tdAdt[1,3]:=td Adt132*lambda^2+tdAdt131*lambda+tdAdt130:\n" }{MPLTEXT 1 0 57 "tdAdt[2 ,1]:=tdAdt212*lambda^2+tdAdt211*lambda+tdAdt210: \n" }{MPLTEXT 1 0 56 "tdAdt[2,2]:=tdAdt222*lambda^2+tdAdt221*lambda+tdAdt220:\n" }{MPLTEXT 1 0 56 "tdAdt[2,3]:=tdAdt232*lambda^2+tdAdt231*lambda+tdAdt230:\n" } {MPLTEXT 1 0 57 "tdAdt[3,1]:=tdAdt312*lambda^2+tdAdt311*lambda+tdAdt31 0: \n" }{MPLTEXT 1 0 56 "tdAdt[3,2]:=tdAdt322*lambda^2+tdAdt321*lambda +tdAdt320:\n" }{MPLTEXT 1 0 56 "tdAdt[3,3]:=tdAdt332*lambda^2+tdAdt331 *lambda+tdAdt330:\n" }{MPLTEXT 1 0 7 "tdAdt;\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 27 "tdAdlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 90 "for i from 1 to 3 do for j from 1 to 3 do tdAdlambda[i,j]:=diff(tdA[i,j],la mbda): od: od:\n" }{MPLTEXT 1 0 11 "tdAdlambda;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 109 "Anew:=simplify(Multiply(Multip ly(Gnormalized,tdA),Gnormalized^(-1))+Multiply(LGnormalized,Gnormalize d^(-1))):" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG 6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I $mtdGF$6(-F,6'-F,6%-I%msupGF$6%-I#miGF$6&Q)λF'/%'italicGQ&false F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'-I#mnGF$6%Q\"2F'FE FH/%1superscriptshiftGQ\"0F'-I#moGF$6-Q1⁢F'FH/%&fenceGF D/%*separatorGFD/%)stretchyGFD/%*symmetricGFD/%(largeopGFD/%.movableli mitsGFD/%'accentGFD/%'lspaceGQ&0.0emF'/%'rspaceGF`o-F?6&Q'tdA112F'/FCQ %trueF'FE/FIQ'italicF'-FS6.Q\"+F'FEFHFVFXFZFfnFhnFjnF\\o/F_oQ,0.222222 2emF'/FboF^p-F,6%F>FR-F?6&Q'tdA111F'FfoFEFhoFjo-F?6&Q'tdA110F'FfoFEFho /%)rowalignGQ!F'/%,columnalignGFjp/%+groupalignGFjp/%(rowspanGQ\"1F'/% +columnspanGFaq-F56(-F,6'-F,6%F;FR-F?6&Q'tdA122F'FfoFEFhoFjo-F,6%F>FR- F?6&Q'tdA121F'FfoFEFhoFjo-F?6&Q'tdA120F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F ,6'-F,6%F;FR-F?6&Q'tdA132F'FfoFEFhoFjo-F,6%F>FR-F?6&Q'tdA131F'FfoFEFho Fjo-F?6&Q'tdA130F'FfoFEFhoFhpF[qF]qF_qFbqFhpF[qF]q-F26(-F56(-F,6'-F,6% F;FR-F?6&Q'tdA212F'FfoFEFhoFjo-F,6%F>FR-F?6&Q'tdA211F'FfoFEFhoFjo-F?6& Q'tdA210F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F,6'-F,6%F;FR-F?6&Q'tdA222F'Ffo FEFhoFjo-F,6%F>FR-F?6&Q'tdA221F'FfoFEFhoFjo-F?6&Q'tdA220F'FfoFEFhoFhpF [qF]qF_qFbq-F56(-F,6'-F,6%F;FR-F?6&Q'tdA232F'FfoFEFhoFjo-F,6%F>FR-F?6& Q'tdA231F'FfoFEFhoFjo-F?6&Q'tdA230F'FfoFEFhoFhpF[qF]qF_qFbqFhpF[qF]q-F 26(-F56(-F,6'-F,6%F;FR-F?6&Q'tdA312F'FfoFEFhoFjo-F,6%F>FR-F?6&Q'tdA311 F'FfoFEFhoFjo-F?6&Q'tdA310F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F,6'-F,6%F;FR -F?6&Q'tdA322F'FfoFEFhoFjo-F,6%F>FR-F?6&Q'tdA321F'FfoFEFhoFjo-F?6&Q'td A320F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F,6'-F,6%F;FR-F?6&Q'tdA332F'FfoFEFh oFjo-F,6%F>FR-F?6&Q'tdA331F'FfoFEFhoFjo-F?6&Q'tdA330F'FfoFEFhoFhpF[qF] qF_qFbqFhpF[qF]q/%&alignGQ%axisF'/FipQ)baselineF'/F\\qQ'centerF'/F^qQ' |frleft|hrF'/%/alignmentscopeGFgo/%,columnwidthGQ%autoF'/%&widthGF][l/ %+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/% ,columnlinesGFh[l/%&frameGFh[l/%-framespacingGQ,0.4em~0.5exF'/%*equalr owsGFD/%-equalcolumnsGFD/%-displaystyleGFD/%%sideGQ&rightF'/%0minlabel spacingGFe[lFEFH/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-F,6'-F,6%-I%msupGF$6 %-I#miGF$6&Q)λF'/%'italicGQ&falseF'/%+foregroundGQ([0,0,0]F'/%, mathvariantGQ'normalF'-I#mnGF$6%Q\"2F'FEFH/%1superscriptshiftGQ\"0F'-I #moGF$6-Q1⁢F'FH/%&fenceGFD/%*separatorGFD/%)stretchyGFD /%*symmetricGFD/%(largeopGFD/%.movablelimitsGFD/%'accentGFD/%'lspaceGQ &0.0emF'/%'rspaceGF`o-F?6&Q)tdAdt112F'/FCQ%trueF'FE/FIQ'italicF'-FS6.Q \"+F'FEFHFVFXFZFfnFhnFjnF\\o/F_oQ,0.2222222emF'/FboF^p-F,6%F>FR-F?6&Q) tdAdt111F'FfoFEFhoFjo-F?6&Q)tdAdt110F'FfoFEFho/%)rowalignGQ!F'/%,colum nalignGFjp/%+groupalignGFjp/%(rowspanGQ\"1F'/%+columnspanGFaq-F56(-F,6 '-F,6%F;FR-F?6&Q)tdAdt122F'FfoFEFhoFjo-F,6%F>FR-F?6&Q)tdAdt121F'FfoFEF hoFjo-F?6&Q)tdAdt120F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F,6'-F,6%F;FR-F?6&Q )tdAdt132F'FfoFEFhoFjo-F,6%F>FR-F?6&Q)tdAdt131F'FfoFEFhoFjo-F?6&Q)tdAd t130F'FfoFEFhoFhpF[qF]qF_qFbqFhpF[qF]q-F26(-F56(-F,6'-F,6%F;FR-F?6&Q)t dAdt212F'FfoFEFhoFjo-F,6%F>FR-F?6&Q)tdAdt211F'FfoFEFhoFjo-F?6&Q)tdAdt2 10F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F,6'-F,6%F;FR-F?6&Q)tdAdt222F'FfoFEFh oFjo-F,6%F>FR-F?6&Q)tdAdt221F'FfoFEFhoFjo-F?6&Q)tdAdt220F'FfoFEFhoFhpF [qF]qF_qFbq-F56(-F,6'-F,6%F;FR-F?6&Q)tdAdt232F'FfoFEFhoFjo-F,6%F>FR-F? 6&Q)tdAdt231F'FfoFEFhoFjo-F?6&Q)tdAdt230F'FfoFEFhoFhpF[qF]qF_qFbqFhpF[ qF]q-F26(-F56(-F,6'-F,6%F;FR-F?6&Q)tdAdt312F'FfoFEFhoFjo-F,6%F>FR-F?6& Q)tdAdt311F'FfoFEFhoFjo-F?6&Q)tdAdt310F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F ,6'-F,6%F;FR-F?6&Q)tdAdt322F'FfoFEFhoFjo-F,6%F>FR-F?6&Q)tdAdt321F'FfoF EFhoFjo-F?6&Q)tdAdt320F'FfoFEFhoFhpF[qF]qF_qFbq-F56(-F,6'-F,6%F;FR-F?6 &Q)tdAdt332F'FfoFEFhoFjo-F,6%F>FR-F?6&Q)tdAdt331F'FfoFEFhoFjo-F?6&Q)td Adt330F'FfoFEFhoFhpF[qF]qF_qFbqFhpF[qF]q/%&alignGQ%axisF'/FipQ)baselin eF'/F\\qQ'centerF'/F^qQ'|frleft|hrF'/%/alignmentscopeGFgo/%,columnwidt hGQ%autoF'/%&widthGF][l/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8em F'/%)rowlinesGQ%noneF'/%,columnlinesGFh[l/%&frameGFh[l/%-framespacingG Q,0.4em~0.5exF'/%*equalrowsGFD/%-equalcolumnsGFD/%-displaystyleGFD/%%s ideGQ&rightF'/%0minlabelspacingGFe[lFEFH/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Types ettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(- F,6%-F,6'-I#mnGF$6%Q\"2F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'nor malF'-I#moGF$6-Q1⁢F'FB/%&fenceGQ&falseF'/%*separatorGFK /%)stretchyGFK/%*symmetricGFK/%(largeopGFK/%.movablelimitsGFK/%'accent GFK/%'lspaceGQ&0.0emF'/%'rspaceGFZ-I#miGF$6&Q)λF'/%'italicGFKF? FBFE-Fhn6&Q'tdA112F'/F\\oQ%trueF'F?/FCQ'italicF'-FF6.Q\"+F'F?FBFIFLFNF PFRFTFV/FYQ,0.2222222emF'/FfnFho-Fhn6&Q'tdA111F'F`oF?Fbo/%)rowalignGQ! F'/%,columnalignGF_p/%+groupalignGF_p/%(rowspanGQ\"1F'/%+columnspanGFf p-F56(-F,6%-F,6'F;FEFgnFE-Fhn6&Q'tdA122F'F`oF?FboFdo-Fhn6&Q'tdA121F'F` oF?FboF]pF`pFbpFdpFgp-F56(-F,6%-F,6'F;FEFgnFE-Fhn6&Q'tdA132F'F`oF?FboF do-Fhn6&Q'tdA131F'F`oF?FboF]pF`pFbpFdpFgpF]pF`pFbp-F26(-F56(-F,6%-F,6' F;FEFgnFE-Fhn6&Q'tdA212F'F`oF?FboFdo-Fhn6&Q'tdA211F'F`oF?FboF]pF`pFbpF dpFgp-F56(-F,6%-F,6'F;FEFgnFE-Fhn6&Q'tdA222F'F`oF?FboFdo-Fhn6&Q'tdA221 F'F`oF?FboF]pF`pFbpFdpFgp-F56(-F,6%-F,6'F;FEFgnFE-Fhn6&Q'tdA232F'F`oF? FboFdo-Fhn6&Q'tdA231F'F`oF?FboF]pF`pFbpFdpFgpF]pF`pFbp-F26(-F56(-F,6%- F,6'F;FEFgnFE-Fhn6&Q'tdA312F'F`oF?FboFdo-Fhn6&Q'tdA311F'F`oF?FboF]pF`p FbpFdpFgp-F56(-F,6%-F,6'F;FEFgnFE-Fhn6&Q'tdA322F'F`oF?FboFdo-Fhn6&Q'td A321F'F`oF?FboF]pF`pFbpFdpFgp-F56(-F,6%-F,6'F;FEFgnFE-Fhn6&Q'tdA332F'F `oF?FboFdo-Fhn6&Q'tdA331F'F`oF?FboF]pF`pFbpFdpFgpF]pF`pFbp/%&alignGQ%a xisF'/F^pQ)baselineF'/FapQ'centerF'/FcpQ'|frleft|hrF'/%/alignmentscope GFao/%,columnwidthGQ%autoF'/%&widthGFjw/%+rowspacingGQ&1.0exF'/%.colum nspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFex/%&frameGFex/% -framespacingGQ,0.4em~0.5exF'/%*equalrowsGFK/%-equalcolumnsGFK/%-displ aystyleGFK/%%sideGQ&rightF'/%0minlabelspacingGFbxF?FB/%%openGQ\"[F'/%& closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "dtdLdt:=Mat rix(3,3,0):\n" }{MPLTEXT 1 0 55 "for i from 1 to 3 do for j from 1 to \+ 3 do dtdLdt[i,j]:=" }{MPLTEXT 1 0 26 "diff(tdL[i,j],t12)*dott12+" } {MPLTEXT 1 0 53 "diff(tdL[i,j],t22)*dott22+ diff(tdL[i,j],t32)*dott32+ " }{MPLTEXT 1 0 52 "diff(tdL[i,j],a12)*dota12+diff(tdL[i,j],a13)*dota1 3\n" }{MPLTEXT 1 0 46 "+diff(tdL[i,j],q)*dotq+ diff(tdL[i,j],p)*dotp\n " }{MPLTEXT 1 0 26 "+diff(tdL[i,j],t11)*dott11" }{MPLTEXT 1 0 64 "+ di ff(tdL[i,j],t21)*dott21+diff(tdL[i,j],t31)*dott31: od: od: \n" } {MPLTEXT 1 0 9 "dtdLdt: \n" }{MPLTEXT 1 0 55 "Compatibilite:=simplify( h*tdAdlambda-h*dtdLdt+Multiply(" }{MPLTEXT 1 0 4 "tdA," }{MPLTEXT 1 0 14 "tdL)-Multiply(" }{MPLTEXT 1 0 4 "tdL," }{MPLTEXT 1 0 6 "tdA)):" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 89 "Solving the \+ compatibility equations to obtain \\td\{A\} and the general evolutions for (q,p)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compa tibilite[1,1]*(lambda-q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compa tibilite[1,1],lambda=q);\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibi lite[1,1]/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 68 "Eq1:= facto r(residue(Compatibilite[1,1]/lambda^3,lambda=infinity)):\n" }{MPLTEXT 1 0 68 "Eq2:= factor(residue(Compatibilite[1,1]/lambda^2,lambda=infini ty)):\n" }{MPLTEXT 1 0 67 "Eq3:= factor(residue(Compatibilite[1,1]/lam bda^1,lambda=infinity)):" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatibil ite[1,2]*(lambda-q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compatibil ite[1,2],lambda=q);\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[ 1,2]/lambda^5,lambda=infinity));\n" }{MPLTEXT 1 0 10 "tdA122:=0;" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[1,2 ]/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 68 "Eq4:= factor(residu e(Compatibilite[1,2]/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 68 " Eq5:= factor(residue(Compatibilite[1,2]/lambda^2,lambda=infinity));\n" }{MPLTEXT 1 0 67 "Eq6:= factor(residue(Compatibilite[1,2]/lambda^1,la mbda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I'tdA122G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq4G6\",$*&,2** I$a12GF$\"\"\"I\"qGF$F*I$t32GF$F*I'tdA132GF$F*F**(F)F*I$a13GF$F*I'tdA1 12GF$F*F**(F)F*F/F*I'tdA222GF$F*!\"\"*(F)F*I\"pGF$F*F-F*F3*(F)F*I$t31G F$F*F-F*F**&F/\"\"#I'tdA322GF$F*F3*(F/F*I$t12GF$F*I'tdA121GF$F*F3*(F/F *I$t22GF$F*F=F*F*F*F/F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq5G6\", $*&,6**I$a12GF$\"\"\"I\"qGF$F*I$t32GF$F*I'tdA131GF$F*F**(F)F*I$a13GF$F *I'tdA111GF$F*F**(F)F*F/F*I'tdA221GF$F*!\"\"*(F)F*I\"pGF$F*F-F*F3*(F)F *I$t31GF$F*F-F*F**&F/\"\"#I'tdA321GF$F*F3*(F/F*I$t11GF$F*I'tdA121GF$F* F3*(F/F*I$t12GF$F*I'tdA120GF$F*F3*(F/F*I$t21GF$F*F=F*F**(F/F*I$t22GF$F *F@F*F*F*F/F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq6G6\",$*&,6**I$a 12GF$\"\"\"I\"qGF$F*I$t32GF$F*I'tdA130GF$F*F**(F)F*I$a13GF$F*I'tdA110G F$F*F**(F)F*F/F*I'tdA220GF$F*!\"\"*(F)F*I\"pGF$F*F-F*F3*(F)F*I$t31GF$F *F-F*F**&F/\"\"#I'tdA320GF$F*F3*(F/F*I'dota12GF$F*I\"hGF$F*F3*(F/F*F=F *I'tdA121GF$F*F**(F/F*I$t11GF$F*I'tdA120GF$F*F3*(F/F*I$t21GF$F*FBF*F*F *F/F3F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatib ilite[1,3]*(lambda-q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compatib ilite[1,3],lambda=q);\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilit e[1,3]/lambda^5,lambda=infinity));\n" }{MPLTEXT 1 0 10 "tdA132:=0;" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[1,3 ]/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 68 "Eq7:= factor(residu e(Compatibilite[1,3]/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 68 " Eq8:= factor(residue(Compatibilite[1,3]/lambda^2,lambda=infinity));\n" }{MPLTEXT 1 0 67 "Eq9:= factor(residue(Compatibilite[1,3]/lambda^1,la mbda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I'tdA132G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq7G6\",,*&I$a1 2GF$\"\"\"I'tdA232GF$F(F(*&I$a13GF$F(I'tdA112GF$F(!\"\"*&F+F(I'tdA332G F$F(F(*&I$t12GF$F(I'tdA131GF$F(F(*&I$t32GF$F(F2F(F-" }}{PARA 11 "" 1 " " {XPPMATH 20 ">I$Eq8G6\"*&,6**I$a13GF$\"\"\"I\"qGF$F)I$t22GF$F)I'tdA1 21GF$F)!\"\"*&I$a12GF$\"\"#I'tdA231GF$F)F)*(F/F)F(F)I'tdA111GF$F)F-*(F /F)F(F)I'tdA331GF$F)F)*(F/F)I$t11GF$F)I'tdA131GF$F)F)*(F/F)I$t12GF$F)I 'tdA130GF$F)F)*(F/F)I$t31GF$F)F8F)F-*(F/F)I$t32GF$F)F;F)F-*(F(F)I\"pGF $F)F,F)F)*(F(F)I$t21GF$F)F,F)F-F)F/F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq9G6\"*&,6**I$a13GF$\"\"\"I\"qGF$F)I$t22GF$F)I'tdA120GF$F)!\"\"*& I$a12GF$\"\"#I'tdA230GF$F)F)*(F/F)F(F)I'tdA110GF$F)F-*(F/F)F(F)I'tdA33 0GF$F)F)*(F/F)I'dota13GF$F)I\"hGF$F)F)*(F/F)F8F)I'tdA131GF$F)F-*(F/F)I $t11GF$F)I'tdA130GF$F)F)*(F/F)I$t31GF$F)F=F)F-*(F(F)I\"pGF$F)F,F)F)*(F (F)I$t21GF$F)F,F)F-F)F/F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatibilite[2,1]*(lambda-q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compatibilite[2,1],lambda=q);\n" }{MPLTEXT 1 0 62 "factor( residue(Compatibilite[2,1]/lambda^5,lambda=infinity));\n" }{MPLTEXT 1 0 10 "tdA212:=0;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 61 "factor(residu e(Compatibilite[2,1]/lambda^4,lambda=infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 69 "Eq10:= factor(residue(Compatibilite[2,1]/lambda^3,l ambda=infinity)):\n" }{MPLTEXT 1 0 69 "Eq11:= factor(residue(Compatibi lite[2,1]/lambda^2,lambda=infinity)):\n" }{MPLTEXT 1 0 68 "Eq12:= fact or(residue(Compatibilite[2,1]/lambda^1,lambda=infinity)):" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I'tdA212G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatibilite[2,2]*(lambda- q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compatibilite[2,2],lambda=q );\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[2,2]/lambda^5,lam bda=infinity));\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[2,2] /lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 69 "Eq13:= factor(residu e(Compatibilite[2,2]/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 69 " Eq14:= factor(residue(Compatibilite[2,2]/lambda^2,lambda=infinity));\n " }{MPLTEXT 1 0 68 "Eq15:= factor(residue(Compatibilite[2,2]/lambda^1, lambda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I%Eq13G6\"*(,.**I$a12GF$\"\"#I\"qGF$\"\"\"I$t32GF$F+I'tdA232GF$F+!\"\" **I$a13GF$F)F*F+I$t22GF$F+I'tdA322GF$F+F+*(F(F)I\"pGF$F+F-F+F+*(F(F)I$ t31GF$F+F-F+F.*(F0F)F4F+F2F+F.*(F0F)I$t21GF$F+F2F+F+F+F0F.F(F." }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq14G6\",$**,\\p*.I$a13GF$\"\"\"I\"qG F$\"\"#I$t12GF$F*I$t22GF$F*I$t32GF$F*I'tdA121GF$F*!\"\"*,F)F*F+F,F.F,F /F*F0F*F**,I$a12GF$F,F+F*F.F*F/F*I'tdA231GF$F*F***F4F,F+F*F/F,F5F*F1** F)F,F+F*F.F,I'tdA321GF$F*F1*,F)F,F+F*F.F*F/F*F8F*F**.F)F*I\"pGF$F*F+F* F-F*F.F*F0F*F**.F)F*F;F*F+F*F-F*F/F*F0F*F**,F)F*F;F*F+F*F.F,F0F*F1*.F) F*F;F*F+F*F.F*F/F*F0F*F1*.F)F*F+F*F-F*I$t21GF$F*F/F*F0F*F1*.F)F*F+F*F- F*F.F*I$t31GF$F*F0F*F1*.F)F*F+F*F@F*F.F*F/F*F0F*F**,F)F*F+F*F.F,FBF*F0 F*F***F4F,F)F*F.F*I'tdA211GF$F*F***F4F,F)F*F/F*FFF*F1**F4F,F;F*F.F*F5F *F1**F4F,F;F*F/F*F5F*F***F4F,F.F*FBF*F5F*F***F4F,FBF*F/F*F5F*F1*,F4F*F )F*I'dott22GF$F*I\"hGF$F*F.F*F1*,F4F*F)F*FMF*FNF*F/F*F**,F4F*F)F*FNF*F .F*I'tdA222GF$F*F,*,F4F*F)F*FNF*F/F*FQF*!\"#**F)F,F;F*F.F*F8F*F***F)F, F;F*F/F*F8F*F1**F)F,F@F*F.F*F8F*F1**F)F,F@F*F/F*F8F*F***F)F*F;F,F-F*F0 F*F1**F)F*F;F,F.F*F0F*F**,F)F*F;F*F-F*F@F*F0F*F**,F)F*F;F*F-F*FBF*F0F* F**,F)F*F;F*F@F*F.F*F0F*F1*,F)F*F;F*F.F*FBF*F0F*F1*,F)F*F-F*I$t20GF$F* F.F*F0F*F**,F)F*F-F*FinF*F/F*F0F*F1*,F)F*F-F*F@F*FBF*F0F*F1**F)F*FinF* F.F,F0F*F1*,F)F*FinF*F.F*F/F*F0F*F**,F)F*F@F*F.F*FBF*F0F*F*F*F4F1,&F.F *F/F1F1F)F1F1" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq15G6\",$**,\\p*.I$ a13GF$\"\"\"I\"qGF$\"\"#I$t12GF$F*I$t22GF$F*I$t32GF$F*I'tdA120GF$F*!\" \"*,F)F*F+F,F.F,F/F*F0F*F**,I$a12GF$F,F+F*F.F*F/F*I'tdA230GF$F*F***F4F ,F+F*F/F,F5F*F1**F)F,F+F*F.F,I'tdA320GF$F*F1*,F)F,F+F*F.F*F/F*F8F*F**. F)F*I\"pGF$F*F+F*F-F*F.F*F0F*F**.F)F*F;F*F+F*F-F*F/F*F0F*F**,F)F*F;F*F +F*F.F,F0F*F1*.F)F*F;F*F+F*F.F*F/F*F0F*F1*.F)F*F+F*F-F*I$t21GF$F*F/F*F 0F*F1*.F)F*F+F*F-F*F.F*I$t31GF$F*F0F*F1*.F)F*F+F*F@F*F.F*F/F*F0F*F**,F )F*F+F*F.F,FBF*F0F*F***F4F,F)F*F.F*I'tdA210GF$F*F***F4F,F)F*F/F*FFF*F1 **F4F,F;F*F.F*F5F*F1**F4F,F;F*F/F*F5F*F***F4F,F.F*FBF*F5F*F***F4F,FBF* F/F*F5F*F1*,F4F*F)F*I'dott21GF$F*I\"hGF$F*F.F*F1*,F4F*F)F*FMF*FNF*F/F* F**,F4F*F)F*FNF*F.F*I'tdA221GF$F*F**,F4F*F)F*FNF*F/F*FQF*F1**F)F,F;F*F .F*F8F*F***F)F,F;F*F/F*F8F*F1**F)F,F@F*F.F*F8F*F1**F)F,F@F*F/F*F8F*F** *F)F*F;F,F-F*F0F*F1**F)F*F;F,F.F*F0F*F**,F)F*F;F*F-F*F@F*F0F*F**,F)F*F ;F*F-F*FBF*F0F*F**,F)F*F;F*F@F*F.F*F0F*F1*,F)F*F;F*F.F*FBF*F0F*F1*,F)F *F-F*I$t20GF$F*F.F*F0F*F**,F)F*F-F*FhnF*F/F*F0F*F1*,F)F*F-F*F@F*FBF*F0 F*F1**F)F*FhnF*F.F,F0F*F1*,F)F*FhnF*F.F*F/F*F0F*F**,F)F*F@F*F.F*FBF*F0 F*F*F*F4F1,&F.F*F/F1F1F)F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatibilite[2,3]*(lambda-q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compatibilite[2,3],lambda=q);\n" }{MPLTEXT 1 0 62 "facto r(residue(Compatibilite[2,3]/lambda^5,lambda=infinity));\n" }{MPLTEXT 1 0 10 "tdA232:=0;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 62 "factor(resi due(Compatibilite[2,3]/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 69 "Eq16:= factor(residue(Compatibilite[2,3]/lambda^3,lambda=infinity) );\n" }{MPLTEXT 1 0 69 "Eq17:= factor(residue(Compatibilite[2,3]/lambd a^2,lambda=infinity)):\n" }{MPLTEXT 1 0 68 "Eq18:= factor(residue(Comp atibilite[2,3]/lambda^1,lambda=infinity)):" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'tdA232G 6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq16G6\"*&,2**I$a13GF$\"\"\"I\"qGF$F)I$t22GF$F)I'tdA22 2GF$F)!\"\"**F(F)F*F)F+F)I'tdA332GF$F)F)*(I$a12GF$F)F+F)I'tdA231GF$F)F )*(F1F)I$t32GF$F)F2F)F-*(F(F)I\"pGF$F)F,F)F)*(F(F)F6F)F/F)F-*(F(F)I$t2 1GF$F)F,F)F-*(F(F)F9F)F/F)F)F)F1F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatibilite[3,1]*(lambda-q),lambda=q);\n" } {MPLTEXT 1 0 38 "residue(Compatibilite[3,1],lambda=q);\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[3,1]/lambda^5,lambda=infinity));\n" }{MPLTEXT 1 0 10 "tdA312:=0;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 62 " factor(residue(Compatibilite[3,1]/lambda^4,lambda=infinity));\n" } {MPLTEXT 1 0 69 "Eq19:= factor(residue(Compatibilite[3,1]/lambda^3,lam bda=infinity)):\n" }{MPLTEXT 1 0 69 "Eq20:= factor(residue(Compatibili te[3,1]/lambda^2,lambda=infinity)):\n" }{MPLTEXT 1 0 68 "Eq21:= factor (residue(Compatibilite[3,1]/lambda^1,lambda=infinity)):" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I'tdA312G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatibilite[3,2]*(lambda- q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compatibilite[3,2],lambda=q );\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[3,2]/lambda^5,lam bda=infinity));\n" }{MPLTEXT 1 0 10 "tdA322:=0;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[3,2]/lambda^4,lambda=in finity));\n" }{MPLTEXT 1 0 69 "Eq22:= factor(residue(Compatibilite[3,2 ]/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 69 "Eq23:= factor(resid ue(Compatibilite[3,2]/lambda^2,lambda=infinity)):\n" }{MPLTEXT 1 0 68 "Eq24:= factor(residue(Compatibilite[3,2]/lambda^1,lambda=infinity)):" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I'tdA322G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq22G6\",$*&,2* *I$a12GF$\"\"\"I\"qGF$F*I$t32GF$F*I'tdA222GF$F*!\"\"**F)F*F+F*F,F*I'td A332GF$F*F**(F)F*I\"pGF$F*F-F*F**(F)F*F2F*F0F*F.*(F)F*I$t31GF$F*F-F*F. *(F)F*F5F*F0F*F**(I$a13GF$F*I$t22GF$F*I'tdA321GF$F*F**(F8F*F,F*F:F*F.F *F8F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "residue(Compatib ilite[3,3]*(lambda-q),lambda=q);\n" }{MPLTEXT 1 0 38 "residue(Compatib ilite[3,3],lambda=q);\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilit e[3,3]/lambda^5,lambda=infinity));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[3,3]/lambda^4,lambda=infinity)); \n" }{MPLTEXT 1 0 62 "factor(residue(Compatibilite[3,3]/lambda^3,lambd a=infinity));\n" }{MPLTEXT 1 0 69 "Eq25:= factor(residue(Compatibilite [3,3]/lambda^2,lambda=infinity));\n" }{MPLTEXT 1 0 68 "Eq26:= factor(r esidue(Compatibilite[3,3]/lambda^1,lambda=infinity));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq25G6\",$**,\\p*.I$a12GF$\"\"\"I\"qG F$\"\"#I$t12GF$F*I$t22GF$F*I$t32GF$F*I'tdA131GF$F*F**,F)F*F+F,F.F*F/F, F0F*!\"\"*,F)F,F+F*F.F*F/F*I'tdA231GF$F*F2**F)F,F+F*F/F,F4F*F**.F)F*I \"pGF$F*F+F*F-F*F.F*F0F*F2*.F)F*F7F*F+F*F-F*F/F*F0F*F2*.F)F*F7F*F+F*F. F*F/F*F0F*F**,F)F*F7F*F+F*F/F,F0F*F**.F)F*F+F*F-F*I$t21GF$F*F/F*F0F*F* *.F)F*F+F*F-F*F.F*I$t31GF$F*F0F*F**,F)F*F+F*FF*F/F*F0F*F2**I$a13GF$F,F+F*F.F,I'tdA321GF$F*F**,FBF,F+F*F.F*F/F*F CF*F2**F)F,F7F*F.F*F4F*F***F)F,F7F*F/F*F4F*F2**F)F,F.F*F>F*F4F*F2**F)F ,F>F*F/F*F4F*F***F)F*FBF,F.F*I'tdA311GF$F*F***F)F*FBF,F/F*FJF*F2*,F)F* FBF*I'dott32GF$F*I\"hGF$F*F.F*F2*,F)F*FBF*FMF*FNF*F/F*F**,F)F*FBF*FNF* F.F*I'tdA332GF$F*F,*,F)F*FBF*FNF*F/F*FQF*!\"#**F)F*F7F,F-F*F0F*F***F)F *F7F,F/F*F0F*F2*,F)F*F7F*F-F*FF*F0F*F2*,F)F*F 7F*FF*F/F*F0F*F**,F)F*F-F*FF*F0F*F**,F)F *F-F*F.F*I$t30GF$F*F0F*F**,F)F*F-F*FfnF*F/F*F0F*F2*,F)F*FF*F/F*F0 F*F2*,F)F*F.F*FfnF*F/F*F0F*F2**F)F*FfnF*F/F,F0F*F***FBF,F7F*F.F*FCF*F2 **FBF,F7F*F/F*FCF*F***FBF,FI%Eq26G6\",$**,\\p*.I $a12GF$\"\"\"I\"qGF$\"\"#I$t12GF$F*I$t22GF$F*I$t32GF$F*I'tdA130GF$F*F* *,F)F*F+F,F.F*F/F,F0F*!\"\"*,F)F,F+F*F.F*F/F*I'tdA230GF$F*F2**F)F,F+F* F/F,F4F*F**.F)F*I\"pGF$F*F+F*F-F*F.F*F0F*F2*.F)F*F7F*F+F*F-F*F/F*F0F*F 2*.F)F*F7F*F+F*F.F*F/F*F0F*F**,F)F*F7F*F+F*F/F,F0F*F**.F)F*F+F*F-F*I$t 21GF$F*F/F*F0F*F**.F)F*F+F*F-F*F.F*I$t31GF$F*F0F*F**,F)F*F+F*FF*F/F*F0F*F2**I$a13GF$F,F+F*F.F,I'tdA320GF$F*F**, FBF,F+F*F.F*F/F*FCF*F2**F)F,F7F*F.F*F4F*F***F)F,F7F*F/F*F4F*F2**F)F,F. F*F>F*F4F*F2**F)F,F>F*F/F*F4F*F***F)F*FBF,F.F*I'tdA310GF$F*F***F)F*FBF ,F/F*FJF*F2*,F)F*FBF*I'dott31GF$F*I\"hGF$F*F.F*F2*,F)F*FBF*FMF*FNF*F/F *F**,F)F*FBF*FNF*F.F*I'tdA331GF$F*F**,F)F*FBF*FNF*F/F*FQF*F2**F)F*F7F, F-F*F0F*F***F)F*F7F,F/F*F0F*F2*,F)F*F7F*F-F*F F*F0F*F2*,F)F*F7F*FF*F/F*F0F*F**,F)F*F-F*FF*F0F*F**,F)F*F-F*F.F*I$t30GF$F*F0F*F**,F)F*F-F*FenF*F/F*F0F*F2*,F)F *FF*F/F*F0F*F2*,F)F*F.F*FenF*F/F*F0F*F2**F)F*FenF*F/F,F0F*F***FBF ,F7F*F.F*FCF*F2**FBF,F7F*F/F*FCF*F***FBF,F " 0 "" {MPLTEXT 1 0 20 "Eq1:=simplify(Eq1):\n" }{MPLTEXT 1 0 20 "Eq2:=simplify(Eq2):\n" }{MPLTEXT 1 0 20 "Eq3:=simplify(Eq3):\n" }{MPLTEXT 1 0 20 "Eq4:=simpli fy(Eq4):\n" }{MPLTEXT 1 0 20 "Eq5:=simplify(Eq5):\n" }{MPLTEXT 1 0 20 "Eq6:=simplify(Eq6):\n" }{MPLTEXT 1 0 20 "Eq7:=simplify(Eq7):\n" } {MPLTEXT 1 0 20 "Eq8:=simplify(Eq8):\n" }{MPLTEXT 1 0 20 "Eq9:=simplif y(Eq9):\n" }{MPLTEXT 1 0 22 "Eq10:=simplify(Eq10):\n" }{MPLTEXT 1 0 22 "Eq11:=simplify(Eq11):\n" }{MPLTEXT 1 0 22 "Eq12:=simplify(Eq12):\n " }{MPLTEXT 1 0 22 "Eq13:=simplify(Eq13):\n" }{MPLTEXT 1 0 22 "Eq14:=s implify(Eq14):\n" }{MPLTEXT 1 0 22 "Eq15:=simplify(Eq15):\n" }{MPLTEXT 1 0 22 "Eq16:=simplify(Eq16):\n" }{MPLTEXT 1 0 22 "Eq17:=simplify(Eq1 7):\n" }{MPLTEXT 1 0 22 "Eq18:=simplify(Eq18):\n" }{MPLTEXT 1 0 22 "Eq 19:=simplify(Eq19):\n" }{MPLTEXT 1 0 22 "Eq20:=simplify(Eq20):\n" } {MPLTEXT 1 0 22 "Eq21:=simplify(Eq21):\n" }{MPLTEXT 1 0 22 "Eq22:=simp lify(Eq22):\n" }{MPLTEXT 1 0 22 "Eq23:=simplify(Eq23):\n" }{MPLTEXT 1 0 22 "Eq24:=simplify(Eq24):\n" }{MPLTEXT 1 0 22 "Eq25:=simplify(Eq25): \n" }{MPLTEXT 1 0 21 "Eq26:=simplify(Eq26):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "tdA131:=a13*(tdA112-tdA332)/(t12-t32):\n" } {MPLTEXT 1 0 15 "simplify(Eq7);\n" }{MPLTEXT 1 0 331 "tdA130:=-(-q*a13 *t12*t22*tdA121+q*a13*t22*t32*tdA121+p*a13*t12*tdA121-p*a13*t32*tdA121 +a12^2*t12*tdA231-a12^2*t32*tdA231-a12*a13*t12*tdA111+a12*a13*t12*tdA3 31+a12*a13*t32*tdA111-a12*a13*t32*tdA331+a12*a13*t11*tdA112-a12*a13*t1 1*tdA332-a12*a13*t31*tdA112+a12*a13*t31*tdA332-a13*t12*t21*tdA121+a13* t32*t21*tdA121)/((t12-t32)^2*a12):\n" }{MPLTEXT 1 0 15 "simplify(Eq8); \n" }{MPLTEXT 1 0 297 "tdA321:=-(-q*a12*t32*tdA112+q*a12*t32*tdA332+p* a12*tdA112-p*a12*tdA332-a12*t12*tdA111+a12*t12*tdA221+a12*t32*tdA111-a 12*t32*tdA221-a12*t31*tdA112+a12*t31*tdA332+t12^2*tdA120-t12*t22*tdA12 0-t12*t32*tdA120+t12*t11*tdA121-t12*t21*tdA121+t22*t32*tdA120-t32*t11* tdA121+t32*t21*tdA121)/((t12-t32)*a13):\n" }{MPLTEXT 1 0 14 "simplify( Eq5);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "tdA121:=a12*(tdA11 2-tdA222)/(t12-t22):\n" }{MPLTEXT 1 0 14 "simplify(Eq4);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 981 "tdA320:=((((tdA110-tdA220)*t12^3+((q*(tdA1 11-tdA331)-2*tdA110+2*tdA220)*t32+(-tdA110+tdA220)*t22+(-tdA111+tdA331 )*p+(tdA111-tdA331)*t31+h*(tdA112-tdA222))*t12^2+(((-tdA111+tdA331)*q+ tdA110-tdA220)*t32^2+(((tdA112-tdA222)*q^2+(-tdA111+tdA331)*q+2*tdA110 -2*tdA220)*t22+((-tdA112+tdA222)*q+tdA111-tdA331)*p+((tdA112-tdA332)*t 31+(-t11+t21)*tdA112-tdA222*t21+tdA332*t11)*q+(-tdA111+tdA331)*t31-2*h *(tdA112-tdA222))*t32+(((-tdA112+tdA222)*q+tdA111-tdA331)*t22+(tdA112- tdA222)*p+(-tdA112+tdA332)*t31+(t11-t21)*tdA112+tdA222*t21-tdA332*t11) *(p-t31))*t12+(((-tdA112+tdA222)*q^2+q*(tdA111-tdA331)-tdA110+tdA220)* t22+(tdA112-tdA222)*(p*q-q*t21+h))*t32^2+((((tdA112-tdA222)*q-tdA111+t dA331)*p+((-2*tdA112+tdA222+tdA332)*t31+t11*(tdA112-tdA332))*q+(tdA111 -tdA331)*t31)*t22-(tdA112-tdA222)*(p-t31)*(p-t21))*t32+t22*(tdA112-tdA 332)*(-t11+t31)*(p-t31))*a12+(t12-t32)^2*(t12-t22)*(-dota12*h-t11*tdA1 20+t21*tdA120))*a13+tdA231*a12^2*(t12-t32)*(t12-t22)*(-q*t32+p-t31))/( (t12-t22)*(t12-t32)^2*a13^2):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 15 " simplify(Eq6);\n" }{MPLTEXT 1 0 272 "tdA211:=((-q^2*(tdA222-tdA332)*t3 2+(p*q-q*t31+t20)*tdA222+(-p*q+q*t31+t30)*tdA332+(-t30+2*h-t20)*tdA112 -dott12*h-tdA311*a13)*t22+((p*q-q*t21-t20)*tdA222+(-p*q+q*t21-t30)*tdA 332+(t30-2*h+t20)*tdA112+dott12*h+tdA311*a13)*t32-(tdA222-tdA332)*(p-t 21)*(p-t31))/((t22-t32)*a12):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 14 " simplify(Eq2);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2818 "tdA 210:=(-tdA310*(t22-t32)*a13^2*(t12-t22)*(t12-t32)*a12+((((((-tdA112+td A222)*q+tdA111-tdA331)*q^2*t32-((-tdA112+tdA222)*q+tdA111-tdA331)*q*p- t31*(tdA112-tdA222)*q^2+((tdA111-tdA331)*t31-t30*(tdA112-tdA222))*q+t3 0*(tdA111-tdA331)+h*(dott11-tdA111))*t12-((-tdA112+tdA222)*q+tdA111-td A331)*q^2*t32^2+(((-tdA112+tdA222)*q+tdA111-tdA331)*q*p+((2*tdA112-tdA 222-tdA332)*t31-t11*(tdA112-tdA332))*q^2+((-tdA111+tdA331)*t31+t30*(td A112-tdA222))*q+(-tdA111+tdA331)*t30-h*(dott11-tdA111))*t32-(tdA112-td A332)*(-t11+t31)*(p*q-q*t31-t30))*t22^2+((-q^2*(tdA111-tdA331)*t32+q*( tdA111-tdA331)*p-t31*(tdA111-tdA331)*q+(-tdA111+tdA331)*t30-h*(dott11- tdA111))*t12^2+(q^2*(tdA111-tdA331)*t32^2-2*q*(((-tdA112+tdA222)*q+tdA 111-tdA331)*p+(((1/2)*tdA112-(1/2)*tdA332)*t31+(tdA112-tdA222)*t21-(1/ 2)*t11*(tdA112-tdA332))*q+(-(1/2)*tdA111+(1/2)*tdA331)*t31+(-(1/2)*tdA 111+(1/2)*tdA331)*t21-(1/2)*t30*(tdA112-tdA222))*t32+((-2*tdA112+2*tdA 222)*q+tdA111-tdA331)*p^2+(((3*tdA112-2*tdA222-tdA332)*t31+(2*tdA112-2 *tdA222)*t21-t11*(tdA112-tdA332))*q+(-tdA111+tdA331)*t31+(-tdA111+tdA3 31)*t21+t30*(tdA112-tdA222))*p-2*t31*(((1/2)*tdA112-(1/2)*tdA332)*t31+ (tdA112-tdA222)*t21-(1/2)*t11*(tdA112-tdA332))*q+((tdA111-tdA331)*t21- t30*(tdA112-tdA332))*t31-t30*((tdA112-tdA222)*t21-t11*(tdA112-tdA332)) )*t12+(q*((-2*tdA112+2*tdA222)*q+tdA111-tdA331)*p+(2*(tdA112-tdA222))* t21*q^2+((-tdA111+tdA331)*t21-t30*(tdA112-tdA222))*q+t30*(tdA111-tdA33 1)+h*(dott11-tdA111))*t32^2+(((2*tdA112-2*tdA222)*q-tdA111+tdA331)*p^2 +(((-3*tdA112+2*tdA222+tdA332)*t31+(-2*tdA112+2*tdA222)*t21+t11*(tdA11 2-tdA332))*q+(tdA111-tdA331)*t31+(tdA111-tdA331)*t21-t30*(tdA112-tdA22 2))*p+3*t21*((tdA112-2*tdA222*(1/3)-(1/3)*tdA332)*t31-(1/3)*t11*(tdA11 2-tdA332))*q+((-tdA111+tdA331)*t21-t30*(tdA112-tdA332))*t31+t30*((tdA1 12-tdA222)*t21+t11*(tdA112-tdA332)))*t32+(tdA112-tdA332)*(-t11+t31)*(p -t31)*(p-t21))*t22+((q*(tdA111-tdA331)*p-t21*(tdA111-tdA331)*q+t30*(td A111-tdA331)+h*(dott11-tdA111))*t32-(tdA111-tdA331)*(p-t31)*(p-t21))*t 12^2+((-q*(tdA111-tdA331)*p+t21*(tdA111-tdA331)*q+(-tdA111+tdA331)*t30 -h*(dott11-tdA111))*t32^2+(((-tdA112+tdA222)*q+tdA111-tdA331)*p^2+(((t dA112-tdA332)*t31+(2*tdA112-2*tdA222)*t21-t11*(tdA112-tdA332))*q+(-tdA 111+tdA331)*t31+(-tdA111+tdA331)*t21-t30*(tdA112-tdA222))*p-((tdA112-t dA332)*t31+(tdA112-tdA222)*t21-t11*(tdA112-tdA332))*t21*q+((tdA111-tdA 331)*t21+t30*(tdA112-tdA332))*t31+t30*((tdA112-tdA222)*t21-t11*(tdA112 -tdA332)))*t32+(p-t21)*(p-t31)*((tdA112-tdA222)*p+(-tdA112+tdA332)*t31 +(-tdA112+tdA222)*t21+t11*(tdA112-tdA332)))*t12-(tdA112-tdA222)*((-p*q +q*t21-t30)*t32+(p-t31)*(p-t21))*(p-t21)*t32)*a12+((q^2*t32-p*q+q*t31- t20)*t22+(-p*q+q*t21+t20)*t32+(p-t31)*(p-t21))*(t12-t32)*(t12-t22)^2*t dA120)*a13+tdA231*a12^2*(t12-t32)*(t12-t22)*((q^2*t32-p*q+q*t31+t30)*t 22+(-p*q+q*t21-t30)*t32+(p-t31)*(p-t21)))/(a12^2*(t12-t22)*(t12-t32)*a 13*(t22-t32)):\n" }{MPLTEXT 1 0 15 "simplify(Eq3);\n" }{MPLTEXT 1 0 14 "simplify(Eq1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 796 "tdA230:=((((tdA110-tdA330)*t12^3+((-2*tdA110+2*tdA330)*t32+(-tdA1 10+tdA330)*t22+(-tdA111+tdA331)*t11+(tdA111-tdA331)*t31+h*(tdA112-tdA3 32))*t12^2+((tdA110-tdA330)*t32^2+((2*tdA110-2*tdA330)*t22+(tdA111-tdA 331)*t11+(-tdA111+tdA331)*t31-h*(tdA112-tdA332))*t32+((-q*tdA112+q*tdA 222+tdA111-tdA331)*t11+(q*tdA112-q*tdA222-tdA111+tdA331)*t31-h*(tdA112 -tdA332))*t22-(t11*(tdA112-tdA332)+(-tdA112+tdA332)*t31+(tdA112-tdA222 )*(p-t21))*(-t11+t31))*t12-t22*(tdA110-tdA330)*t32^2+(((q*tdA112-q*tdA 222-tdA111+tdA331)*t11+(-q*tdA112+q*tdA222+tdA111-tdA331)*t31+h*(tdA11 2-tdA332))*t22+(tdA112-tdA222)*(-t11+t31)*(p-t21))*t32-t22*(-t11+t31)^ 2*(tdA112-tdA332))*a12-tdA120*(t12-t32)^2*(t12-t22)*(-q*t22+p-t21))*a1 3-(t12-t32)*a12*(tdA231*(-t11+t31)*a12+dota13*h*(t12-t32))*(t12-t22))/ ((t12-t22)*(t12-t32)^2*a12^2):\n" }{MPLTEXT 1 0 15 "simplify(Eq9);\n" }{MPLTEXT 1 0 202 "tdA311:=(((-q^2*t32+p*q-q*t31+2*h-t30)*t22+(p*q-q*t 21-2*h+t30)*t32-(p-t31)*(p-t21))*tdA112+((q^2*t32-p*q+q*t31+t30)*t22+( -p*q+q*t21-t30)*t32+(p-t31)*(p-t21))*tdA332-dott12*h*(t22-t32))/(a13*( t22-t32)):\n" }{MPLTEXT 1 0 16 "simplify(Eq10);\n" }{MPLTEXT 1 0 61 "t dA231:=-(tdA222-tdA332)*(-q*t22+p-t21)*a13/(a12*(t22-t32)):\n" } {MPLTEXT 1 0 16 "simplify(Eq16);\n" }{MPLTEXT 1 0 22 "tdA112:=(1/2)*do tt12:\n" }{MPLTEXT 1 0 16 "simplify(Eq19);\n" }{MPLTEXT 1 0 589 "tdA12 0:=-((((q*dott12-2*q*tdA222-2*tdA111+2*tdA221)*t12+(-q*dott12+2*q*tdA2 22+2*tdA111-2*tdA221)*t22+(t11-t21)*(dott12-2*tdA222))*t32^2+((2*q*tdA 222-2*q*tdA332+2*tdA111-2*tdA221)*t12^2+(-q*(dott12+2*tdA222-4*tdA332) *t22-(dott12-2*tdA222)*(p-t31+t11-t21))*t12+((q*dott12-2*q*tdA332-2*td A111+2*tdA221)*t22+(dott12-2*tdA222)*(p-t31-t11+t21))*t22)*t32+((-2*td A111+2*tdA221)*t22-(2*(tdA222-tdA332))*(p-t31))*t12^2+((2*tdA111-2*tdA 221)*t22+(p-t31+t11-t21)*dott12+(2*p-2*t31-2*t11+2*t21)*tdA222-4*tdA33 2*(p-t31))*t22*t12-t22^2*(dott12-2*tdA332)*(p-t31))*a12)/(2*(t12-t22)^ 2*(t12-t32)*(t22-t32)):\n" }{MPLTEXT 1 0 16 "simplify(Eq22);\n" } {MPLTEXT 1 0 22 "tdA332:=(1/2)*dott32:\n" }{MPLTEXT 1 0 16 "simplify(E q25);\n" }{MPLTEXT 1 0 22 "tdA222:=(1/2)*dott22:\n" }{MPLTEXT 1 0 16 " simplify(Eq14);\n" }{MPLTEXT 1 0 48 "tdA220:=simplify(solve(simplify(E q23),tdA220)):\n" }{MPLTEXT 1 0 16 "simplify(Eq23);\n" }{MPLTEXT 1 0 46 "tdA310:=factor(solve(simplify(Eq20),tdA310)):\n" }{MPLTEXT 1 0 16 "simplify(Eq20);\n" }{MPLTEXT 1 0 16 "tdA111:=dott11:\n" }{MPLTEXT 1 0 16 "simplify(Eq11);\n" }{MPLTEXT 1 0 46 "tdA330:=factor(solve(simpli fy(Eq17),tdA330)):\n" }{MPLTEXT 1 0 16 "simplify(Eq17);\n" }{MPLTEXT 1 0 16 "tdA331:=dott31:\n" }{MPLTEXT 1 0 16 "simplify(Eq26);\n" } {MPLTEXT 1 0 16 "tdA221:=dott21:\n" }{MPLTEXT 1 0 15 "simplify(Eq15);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Eq1:=simplify(Eq1);\n" }{MPLTEXT 1 0 20 "Eq2:=simplify(Eq2);\n" } {MPLTEXT 1 0 20 "Eq3:=simplify(Eq3);\n" }{MPLTEXT 1 0 20 "Eq4:=simplif y(Eq4);\n" }{MPLTEXT 1 0 20 "Eq5:=simplify(Eq5);\n" }{MPLTEXT 1 0 20 " Eq6:=simplify(Eq6);\n" }{MPLTEXT 1 0 20 "Eq7:=simplify(Eq7);\n" } {MPLTEXT 1 0 20 "Eq8:=simplify(Eq8);\n" }{MPLTEXT 1 0 20 "Eq9:=simplif y(Eq9);\n" }{MPLTEXT 1 0 22 "Eq10:=simplify(Eq10);\n" }{MPLTEXT 1 0 22 "Eq11:=simplify(Eq11);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "Eq 13:=simplify(Eq13);\n" }{MPLTEXT 1 0 22 "Eq14:=simplify(Eq14);\n" } {MPLTEXT 1 0 22 "Eq15:=simplify(Eq15);\n" }{MPLTEXT 1 0 22 "Eq16:=simp lify(Eq16);\n" }{MPLTEXT 1 0 22 "Eq17:=simplify(Eq17);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "Eq19:=simplify(Eq19);\n" }{MPLTEXT 1 0 22 " Eq20:=simplify(Eq20);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "Eq22:= simplify(Eq22);\n" }{MPLTEXT 1 0 22 "Eq23:=simplify(Eq23);\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "Eq25:=simplify(Eq25);\n" } {MPLTEXT 1 0 21 "Eq26:=simplify(Eq26);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq1G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I$Eq2G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq3G6\"\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq4G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq5G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq6G6 \"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$Eq7G6\"\"\"!" }}{PARA 11 " " 1 "" {XPPMATH 20 ">I$Eq8G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I$Eq9G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq10G6\"\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq11G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq13G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq14 G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq15G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq16G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq17G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq19G6\"\"\"! " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq20G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq22G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq2 3G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq25G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Eq26G6\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Eq12:=simplify(Eq12):\n" }{MPLTEXT 1 0 22 "Eq18:=simp lify(Eq18):\n" }{MPLTEXT 1 0 22 "Eq21:=simplify(Eq21):\n" }{MPLTEXT 1 0 21 "Eq24:=simplify(Eq24):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 284 153 "There are only 4 remaining non trivial equations. S olving the first two gives the evolutions for (q,p) and we check that \+ these evolutions are Hamiltonian" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "dotq:=factor(solve(simplify(Eq12),dotq)):\n" }{MPLTEXT 1 0 15 "simplify(Eq12);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 34 "dotp:=solv e(simplify(Eq18),dotp):\n" }{MPLTEXT 1 0 16 "simplify(Eq18);\n" } {MPLTEXT 1 0 16 "simplify(Eq21);\n" }{MPLTEXT 1 0 16 "simplify(Eq24); \n" }{MPLTEXT 1 0 29 "dotq:=factor(simplify(dotq)):" }}{PARA 11 "" 1 " " {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "H:=unapply( int(h*dotq,p) ,q,p):\n" }{MPLTEXT 1 0 74 "f:=unapply( factor(-simplify(int(simplify( diff(H(q,p),q)+h*dotp),q))), q):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 49 "Hamiltonian:=unapply(simplify(H(q,p)+f(q)),q,p):\n" }{MPLTEXT 1 0 43 "simplify(diff(Hamiltonian(q,p),p)-h*dotq);\n" }{MPLTEXT 1 0 42 "si mplify(diff(Hamiltonian(q,p),q)+h*dotp);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "dotqfunction:=unapply(dotq,t12,t22,t32,t11,t2 1,t31,dott12,dott22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 27 "dotpfunction:=unapply(dotp," }{MPLTEXT 1 0 65 "t12,t22,t32,t11,t21,t3 1,dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" } {MPLTEXT 1 0 38 "P1function:=unapply(P1(lambda),lambda," }{MPLTEXT 1 0 23 "t12,t22,t32,t11,t21,t31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 40 "dP1function:=unapply(dP1(lambda),lambda," }{MPLTEXT 1 0 65 "t12,t2 2,t32,t11,t21,t31,dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 2 "):" }{MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 290 66 "Expression of the Hamiltonian evolutions in the trivial directions " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "factor(h*dotqfunction(t1 2,t22,t32,t11,t21,t31,0,0,0,1,1,1));\n" }{MPLTEXT 1 0 60 "factor(h*dot pfunction(t12,t22,t32,t11,t21,t31,0,0,0,1,1,1));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "Hamv1:=(q,p)->-h*q;\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 74 "h*dotqfunction(t12,t22,t32,t11,t21,t31,0,0,0,1,1,1)- diff(Hamv1(q,p),p));\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 73 "h*dotpfunction(t12,t22,t32,t11,t21,t31,0,0,0,1,1,1)+ diff(Hamv1(q,p), q));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"hG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&Hamv1G6\"f*6 $I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,$*&I\"hGF$\"\"\"9$F/!\"\" F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "facto r(h*dotqfunction(t12,t22,t32,t11,t21,t31,1,1,1," }{MPLTEXT 1 0 5 "0,0, 0" }{MPLTEXT 1 0 4 "));\n" }{MPLTEXT 1 0 52 "factor(h*dotpfunction(t12 ,t22,t32,t11,t21,t31,1,1,1," }{MPLTEXT 1 0 5 "0,0,0" }{MPLTEXT 1 0 3 " ));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 24 "Hamv2:=(q,p)->-h*q^2/2;\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 39 "h*dotqfunction(t12,t22, t32,t11,t21,t31," }{MPLTEXT 1 0 6 "1,1,1," }{MPLTEXT 1 0 5 "0,0,0" } {MPLTEXT 1 0 24 ")- diff(Hamv2(q,p),p));\n" }{MPLTEXT 1 0 48 "simplify (h*dotpfunction(t12,t22,t32,t11,t21,t31," }{MPLTEXT 1 0 6 "1,1,1," } {MPLTEXT 1 0 5 "0,0,0" }{MPLTEXT 1 0 23 ")+ diff(Hamv2(q,p),q));" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "* &I\"hG6\"\"\"\"I\"qGF$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&Hamv2G6\" f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,$*&I\"hGF$\"\"\"9$\"\" ##!\"\"F1F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " simplify(h*dotqfunction" }{MPLTEXT 1 0 46 "(t12,t22,t32,t11,t21,t31,0, 0,0,t12,t22,t32));\n" }{MPLTEXT 1 0 68 "simplify(h*dotpfunction(t12,t2 2,t32,t11,t21,t31,0,0,0,t12,t22,t32));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "Hamu1:=(q,p)->-h*p;\n" }{MPLTEXT 1 0 24 "simplify(h*dotqfunct ion(" }{MPLTEXT 1 0 65 "t12,t22,t32,t11,t21,t31,0,0,0,t12,t22,t32)- di ff(Hamu1(q,p),p));\n" }{MPLTEXT 1 0 24 "simplify(h*dotpfunction(" } {MPLTEXT 1 0 64 "t12,t22,t32,t11,t21,t31,0,0,0,t12,t22,t32)+ diff(Hamu 1(q,p),q));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$I\"hG6\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&Hamu 1G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,$*&I\"hGF$\"\"\"9 %F/!\"\"F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "s implify(h*dotqfunction(t12,t22,t32,t11,t21,t31,2*t12,2*t22,2*t32,t11,t 21,t31));\n" }{MPLTEXT 1 0 80 "simplify(h*dotpfunction(t12,t22,t32,t11 ,t21,t31,2*t12,2*t22,2*t32,t11,t21,t31));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 22 "Hamu2:=(q,p)->-h*q*p;\n" }{MPLTEXT 1 0 24 "simplify(h *dotqfunction(" }{MPLTEXT 1 0 53 "t12,t22,t32,t11,t21,t31,2*t12,2*t22, 2*t32,t11,t21,t31" }{MPLTEXT 1 0 24 ")- diff(Hamu2(q,p),p));\n" } {MPLTEXT 1 0 24 "simplify(h*dotpfunction(" }{MPLTEXT 1 0 53 "t12,t22,t 32,t11,t21,t31,2*t12,2*t22,2*t32,t11,t21,t31" }{MPLTEXT 1 0 23 ")+ dif f(Hamu2(q,p),q));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&I\"hG6\"\"\"\"I \"qGF%F&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&I\"pG6\"\"\"\"I\"hGF$ F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&Hamu2G6\"f*6$I\"qGF$I\"pGF$F$6$ I)operatorGF$I&arrowGF$F$,$*(I\"hGF$\"\"\"9$F/9%F/!\"\"F$F$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "simplify(h*dotqfun ction(t12,t22,t32,t11,t21,t31," }{MPLTEXT 1 0 21 "2*(t12-t32)*(t12-t22 )" }{MPLTEXT 1 0 5 ",0,0," }{MPLTEXT 1 0 39 "t12*(3*t11-t21-t31)-(t12+ t22+t32)*t11+ " }{MPLTEXT 1 0 15 "t22*t31+t32*t21" }{MPLTEXT 1 0 8 ",0 ,0));\n" }{MPLTEXT 1 0 48 "simplify(h*dotpfunction(t12,t22,t32,t11,t21 ,t31," }{MPLTEXT 1 0 21 "2*(t12-t32)*(t12-t22)" }{MPLTEXT 1 0 5 ",0,0, " }{MPLTEXT 1 0 53 "t12*(3*t11-t21-t31)-(t12+t22+t32)*t11+t22*t31+t32* t21" }{MPLTEXT 1 0 8 ",0,0));\n" }{MPLTEXT 1 0 49 "Hama1:=(q,p)->h*( ( t22+t32)*q*p-p^2+(t21+t31)*p -" }{MPLTEXT 1 0 8 "t32*t22*" }{MPLTEXT 1 0 27 "q^2 -(t22*t31+t32*t21)*q);\n" }{MPLTEXT 1 0 24 "simplify(h*dot qfunction(" }{MPLTEXT 1 0 24 "t12,t22,t32,t11,t21,t31," }{MPLTEXT 1 0 80 "2*(t12-t32)*(t12-t22),0,0,t12*(3*t11-t21-t31)-(t12+t22+t32)*t11+ t 22*t31+t32*t21" }{MPLTEXT 1 0 4 ",0,0" }{MPLTEXT 1 0 24 ")- diff(Hama1 (q,p),p));\n" }{MPLTEXT 1 0 24 "simplify(h*dotpfunction(" }{MPLTEXT 1 0 24 "t12,t22,t32,t11,t21,t31," }{MPLTEXT 1 0 80 "2*(t12-t32)*(t12-t22 ),0,0,t12*(3*t11-t21-t31)-(t12+t22+t32)*t11+ t22*t31+t32*t21" } {MPLTEXT 1 0 4 ",0,0" }{MPLTEXT 1 0 23 ")+ diff(Hama1(q,p),q));" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*(,&I$t22G6\"\"\"\"I$t32GF&F'F'I\"hGF& F'I\"qGF&F'F'*&,(I$t31GF&!\"\"I\"pGF&\"\"#I$t21GF&F.F'F)F'F." }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&I\"hG6\"\"\"\",&*&,(*&I\"qGF%F&I$t32GF%F&! \"#I\"pGF%F&I$t31GF%!\"\"F&I$t22GF%F&F&*&F,F&,&F.F&I$t21GF%F0F&F&F&F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&Hama1G6\"f*6$I\"qGF$I\"pGF$F$6$I)o peratorGF$I&arrowGF$F$*&I\"hGF$\"\"\",,*(,&I$t22GF$F.I$t32GF$F.F.9$F.9 %F.F.*$F5\"\"#!\"\"*&,&I$t21GF$F.I$t31GF$F.F.F5F.F.*(F3F.F2F.F4F7F8*&, &*&F;F.F3F.F.*&F2F.F " 0 "" {MPLTEXT 1 0 50 "simplify(h*dotqfunction(t12,t22,t32 ,t11,t21,t31,0," }{MPLTEXT 1 0 21 "2*(t22-t12)*(t22-t32)" }{MPLTEXT 1 0 1 "," }{MPLTEXT 1 0 1 "0" }{MPLTEXT 1 0 3 ",0," }{MPLTEXT 1 0 11 "t2 2*(3*t21-" }{MPLTEXT 1 0 7 "t11-t31" }{MPLTEXT 1 0 2 ")-" }{MPLTEXT 1 0 2 " (" }{MPLTEXT 1 0 38 "t12+t22+t32)*t21+t12*t31+t32*t11,0));\n" } {MPLTEXT 1 0 98 "simplify(h*dotpfunction(t12,t22,t32,t11,t21,t31,0,2*( t22-t12)*(t22-t32),0,0,t22*(3*t21-t11-t31)- (" }{MPLTEXT 1 0 37 "t12+t 22+t32)*t21+t12*t31+t32*t11,0));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 84 "Hama2:=(q,p)->h*( (t12+t32)*q*p-p^2+(t11+t31)*p -t32*t12*q^2 -(t12 *t31+t32*t11)*q);\n" }{MPLTEXT 1 0 24 "simplify(h*dotqfunction(" } {MPLTEXT 1 0 26 "t12,t22,t32,t11,t21,t31,0," }{MPLTEXT 1 0 48 "2*(t22- t12)*(t22-t32),0,0,t22*(3*t21-t11-t31)- (" }{MPLTEXT 1 0 34 "t12+t22+t 32)*t21+t12*t31+t32*t11,0" }{MPLTEXT 1 0 24 ")- diff(Hama2(q,p),p));\n " }{MPLTEXT 1 0 24 "simplify(h*dotpfunction(" }{MPLTEXT 1 0 26 "t12,t2 2,t32,t11,t21,t31,0," }{MPLTEXT 1 0 48 "2*(t22-t12)*(t22-t32),0,0,t22* (3*t21-t11-t31)- (" }{MPLTEXT 1 0 34 "t12+t22+t32)*t21+t12*t31+t32*t11 ,0" }{MPLTEXT 1 0 23 ")+ diff(Hama2(q,p),q));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(,&I$t12G6\"\"\"\"I$t32GF&F'F'I\"hGF&F'I\"qGF&F'F'*&,( I$t31GF&!\"\"I\"pGF&\"\"#I$t11GF&F.F'F)F'F." }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&I\"hG6\"\"\"\",&*&,(*&I\"qGF%F&I$t32GF%F&!\"#I\"pGF%F &I$t31GF%!\"\"F&I$t12GF%F&F&*&F,F&,&F.F&I$t11GF%F0F&F&F&F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&Hama2G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I &arrowGF$F$*&I\"hGF$\"\"\",,*(,&I$t12GF$F.I$t32GF$F.F.9$F.9%F.F.*$F5\" \"#!\"\"*&,&I$t11GF$F.I$t31GF$F.F.F5F.F.*(F3F.F2F.F4F7F8*&,&*&F;F.F3F. F.*&F2F.F " 0 "" {MPLTEXT 1 0 136 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0,0, 2*(t32-t12)*(t32-t22),0,0,t32*(3*t31-t11-t21)- (t12+t22+t32)*t31+t12*t 21+t22*t11));\n" }{MPLTEXT 1 0 135 "simplify(h*dotpfunction(t12,t22,t3 2,t11,t21,t31,0,0,2*(t32-t12)*(t32-t22),0,0,t32*(3*t31-t11-t21)- (t12+ t22+t32)*t31+t12*t21+t22*t11));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 84 "Hama3:=(q,p)->h*( (t12+t22)*q*p-p^2+(t11+t21)*p -t22*t12*q^2 -(t12 *t21+t22*t11)*q);\n" }{MPLTEXT 1 0 24 "simplify(h*dotqfunction(" } {MPLTEXT 1 0 108 "t12,t22,t32,t11,t21,t31,0,0,2*(t32-t12)*(t32-t22),0, 0,t32*(3*t31-t11-t21)- (t12+t22+t32)*t31+t12*t21+t22*t11" }{MPLTEXT 1 0 24 ")- diff(Hama3(q,p),p));\n" }{MPLTEXT 1 0 24 "simplify(h*dotpfunc tion(" }{MPLTEXT 1 0 108 "t12,t22,t32,t11,t21,t31,0,0,2*(t32-t12)*(t32 -t22),0,0,t32*(3*t31-t11-t21)- (t12+t22+t32)*t31+t12*t21+t22*t11" } {MPLTEXT 1 0 23 ")+ diff(Hama3(q,p),q));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(,&I$t12G6\"\"\"\"I$t22GF&F'F'I\"hGF&F'I\"qGF&F'F'*&,(I\"pGF&\" \"#I$t11GF&!\"\"I$t21GF&F0F'F)F'F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$ *&I\"hG6\"\"\"\",&*&,(*&I\"qGF%F&I$t22GF%F&!\"#I\"pGF%F&I$t21GF%!\"\"F &I$t12GF%F&F&*&F,F&,&F.F&I$t11GF%F0F&F&F&F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&Hama3G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$ F$*&I\"hGF$\"\"\",,*(,&I$t12GF$F.I$t22GF$F.F.9$F.9%F.F.*$F5\"\"#!\"\"* &,&I$t11GF$F.I$t21GF$F.F.F5F.F.*(F3F.F2F.F4F7F8*&,&*&F;F.F3F.F.*&F2F.F " 0 "" {MPLTEXT 1 0 63 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0,0,0,1,0,0));\n " }{MPLTEXT 1 0 63 "simplify(h*dotpfunction(t12,t22,t32,t11,t21,t31,0, 0,0,1,0,0));\n" }{MPLTEXT 1 0 353 "Hame11 := unapply( (-p^3+((t12+t22+ t32)*q+t11+t21+t31)*p^2+(((-t22-t32)*t12-t22*t32)*q^2+((-t31-t21)*t12+ (-t11-t31)*t22-t32*(t11+t21))*q+t12*(-t20-t30)+t22*t20+t32*t30+(-t31-t 21)*t11-t21*t31)*p+q*(q^2*t12*t22*t32+((t22*t31+t32*t21)*t12+t22*t32*t 11)*q+(t22*t30+t32*t20+t21*t31)*t12+((-t20-t30)*t32+t11*t31)*t22+t32*t 11*t21))/((t12-t32)*(t12-t22)) ,q,p);\n" }{MPLTEXT 1 0 84 "simplify(h* dotqfunction(t12,t22,t32,t11,t21,t31,0,0,0,1,0,0)- diff(Hame11(q,p),p) );\n" }{MPLTEXT 1 0 83 "simplify(h*dotpfunction(t12,t22,t32,t11,t21,t3 1,0,0,0,1,0,0)+ diff(Hame11(q,p),q));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 79 "simplify( Hame11(q,p)-1/((t32-t12)*(t22-t 12))*(-p^3+ P1(q)*p^2-P2(q)*p+P3(q)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,4*&,&*&,&I$t22G6\"\"\"\"I$t32GF)F*F*I$t12GF)F*F**&F(F*F+F*F*F*I\" qGF)\"\"#F**&,(*&,(I$t31GF)F*I\"pGF)!\"#I$t21GF)F*F*F,F*F**&,(F5F6F4F* I$t11GF)F*F*F(F*F**&,(F5F*F:#!\"\"F/F7F=F*F+F*F6F*F.F*F**&,&I$t20GF)F* I$t30GF)F*F*F,F*F**&FAF*F(F*F>*&FBF*F+F*F>*$F5F/\"\"$*&,(F4F6F:F6F7F6F *F5F*F**&F:F*,&F7F*F4F*F*F**&F7F*F4F*F*F*,&F,F>F+F*F>,&F,F*F(F>F>" }} {PARA 11 "" 1 "" {XPPMATH 20 "*(,(*&,(*&,**&I\"qG6\"\"\"#I$t32GF*\"\" \"\"\"$*&I\"pGF*F-F)F-!\"#*&F)F-I$t31GF*F-F+I$t30GF*F-F-I$t22GF*F-F-*& ,(F/F1*&F)F-I$t21GF*F-F+I$t20GF*F-F-F,F-F-*&,&F0F-F3!\"\"F-,&F0F-F9F=F -F-F-I$t12GF*F-F-*&,&*&,*F/F1*&F)F-I$t11GF*F-F+F:F=F4F=F-F,F-F-*&FF-FGF-F-F-,&F?F=F,F-F=,&F?F-F5F=F=" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame11G6\"f*6$I\"qGF$I\"pGF$F$6$I)ope ratorGF$I&arrowGF$F$*(,**$9%\"\"$!\"\"*&,**&,(I$t12GF$\"\"\"I$t22GF$F7 I$t32GF$F7F79$F7F7I$t11GF$F7I$t21GF$F7I$t31GF$F7F7F/\"\"#F7*&,0*&,&*&, &F8F1F9F1F7F6F7F7*&F8F7F9F7F1F7F:F>F7*&,(*&,&F=F1FF6F7F8F7F9F7F7*&,&*&,&*&F " 0 "" {MPLTEXT 1 0 63 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0 ,0,0,0,1,0));\n" }{MPLTEXT 1 0 63 "simplify(h*dotpfunction(t12,t22,t32 ,t11,t21,t31,0,0,0,0,1,0));\n" }{MPLTEXT 1 0 359 "Hame21:= unapply( (p ^3+((-t12-t22-t32)*q-t31-t11-t21)*p^2+(((t12+t32)*t22+t12*t32)*q^2+(t1 2*(t21+t31)+t22*(t11+t31)+t32*(t11+t21))*q+(h-t20)*t22+(t30-h+t20)*t12 -t32*t30+t11*(t21+t31)+t21*t31)*p-q*(q^2*t12*t22*t32+((t12*t31+t32*t11 )*t22+t12*t32*t21)*q+(t12*t30+(-t30+h-t20)*t32+t11*t31)*t22+((-h+t20)* t32+t21*t31)*t12+t32*t11*t21))/((t22-t32)*(t12-t22)),q,p);\n" } {MPLTEXT 1 0 84 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0,0,0 ,0,1,0)- diff(Hame21(q,p),p));\n" }{MPLTEXT 1 0 83 "simplify(h*dotpfun ction(t12,t22,t32,t11,t21,t31,0,0,0,0,1,0)+ diff(Hame21(q,p),q));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "simplify( H ame21(q,p)- (1/" }{MPLTEXT 1 0 21 "((t32-t22)*(t12-t22))" }{MPLTEXT 1 0 37 "*(-p^3+ P1(q)*p^2-P2(q)*p+P3(q)) +(p-" }{MPLTEXT 1 0 23 "q*t32)* h/(t32-t22)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,4*&,&*&,&I$t22G6 \"!\"\"I$t32GF)F*\"\"\"I$t12GF)F,F,*&F(F,F+F,F*F,I\"qGF)\"\"#F,*&,(*&, (I$t31GF)F*I\"pGF)F0I$t21GF)F*F,F-F,F,*&,(F5F*F6F0I$t11GF)F*F,F(F,F,*& ,(F6F,F:#F*F0F7F=F,F+F,F0F,F/F,F,*&,(I\"hGF)F,I$t20GF)F*I$t30GF)F*F,F- F,F,*&,&F@F*FAF,F,F(F,F,*&FBF,F+F,F,*$F6F0!\"$*&,(F5F0F:F0F7F0F,F6F,F, *&,&F5F*F7F*F,F:F,F,*&F7F,F5F,F*F,,&F(F*F+F,F*,&F-F,F(F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,(*&,(*&,.*&I\"qG6\"\"\"#I$t12GF*\"\"\"!\"$*&I \"pGF*F-F)F-F+*&F)F-I$t11GF*F-!\"#I\"hGF*!\"\"I$t20GF*F-I$t30GF*F-F-I$ t32GF*F-F-*&,(F/F+*&F)F-I$t31GF*F-F3F7F5F-F,F-F-*&,&F0F-F2F5F-,&F0F5F< F-F-F-F-I$t22GF*F-F-*&,&*&,*F/F+*&F)F-I$t21GF*F-F3F4F-F6F5F-F,F-F-*&,& F0F-FFF5F-F>F-F5F-F8F-F-*(F,F-FHF-F?F-F-F-,&F@F5F8F-F5,&F,F-F@F5F5" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame21G6\"f*6$I\"qGF$I\"pGF$F$6$I)ope ratorGF$I&arrowGF$F$*(,**$9%\"\"$\"\"\"*&,**&,(I$t12GF$!\"\"I$t22GF$F7 I$t32GF$F7F19$F1F1I$t31GF$F7I$t11GF$F7I$t21GF$F7F1F/\"\"#F1*&,0*&,&*&, &F6F1F9F1F1F8F1F1*&F6F1F9F1F1F1F:F>F1*&,(*&F6F1,&F=F1F;F1F1F1*&F8F1,&F F6F1F8F1F9F1F1*&,&*&,&*&F " 0 "" {MPLTEXT 1 0 63 "simpl ify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0,0,0,0,0,1));\n" }{MPLTEXT 1 0 63 "simplify(h*dotpfunction(t12,t22,t32,t11,t21,t31,0,0,0,0,0,1)) ;\n" }{MPLTEXT 1 0 363 "Hame31:=unapply((-p^3+(t11+t21+t31+(t12+t22+t3 2)*q)*p^2+(((-t12-t22)*t32-t12*t22)*q^2+((-t21-t11)*t32+(-t31-t21)*t12 -t22*(t11+t31))*q+(-h+t30)*t32+(-t30+h-t20)*t12+t22*t20+(-t31-t21)*t11 -t21*t31)*p+q*(t12*t22*t32*q^2+((t12*t21+t22*t11)*t32+t31*t12*t22)*q+( t12*t20+(-t30+h-t20)*t22+t11*t21)*t32+((-h+t30)*t22+t21*t31)*t12+t22*t 11*t31))/((t22-t32)*(t12-t32)),q,p);\n" }{MPLTEXT 1 0 84 "simplify(h*d otqfunction(t12,t22,t32,t11,t21,t31,0,0,0,0,0,1)- diff(Hame31(q,p),p)) ;\n" }{MPLTEXT 1 0 83 "simplify(h*dotpfunction(t12,t22,t32,t11,t21,t31 ,0,0,0,0,0,1)+ diff(Hame31(q,p),q));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 107 "simplify( Hame31(q,p)- (1/((t22-t32)*(t1 2-t32))*(-p^3+ P1(q)*p^2-P2(q)*p+P3(q)) -(p-q*t22)*h/(t32-t22)) );" } }{PARA 11 "" 1 "" {XPPMATH 20 "*(,4*&,&*&,&I$t22G6\"!\"\"I$t32GF)F*\" \"\"I$t12GF)F,F,*&F(F,F+F,F*F,I\"qGF)\"\"#F,*&,(*&,(I$t31GF)F*I\"pGF)F 0I$t21GF)F*F,F-F,F,*&F+F,,(F6F0I$t11GF)F*F7F*F,F,*&,(F6!\"#F5F,F:F,F,F (F,F*F,F/F,F,*&,(I\"hGF)F,I$t20GF)F*I$t30GF)F*F,F-F,F,*&,&F@F*FBF,F,F+ F,F,*&FAF,F(F,F,*$F6F0!\"$*&,(F5F0F:F0F7F0F,F6F,F,*&,&F5F*F7F*F,F:F,F, *&F7F,F5F,F*F,,&F(F*F+F,F*,&F-F*F+F,F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,(*&,(*&,.*&I\"qG6\"\"\"#I$t12GF*\"\"\"!\"$*&I\"pGF*F-F)F-F+*&F)F- I$t11GF*F-!\"#I\"hGF*!\"\"I$t20GF*F-I$t30GF*F-F-I$t32GF*F-F-*&,*F/F+*& F)F-I$t31GF*F-F3F4F-F7F5F-F,F-F-*&,&F0F-F2F5F-,&F0F5FF-F5F-F8 F-F-*(F,F-FHF-F?F-F-F-,&F@F5F8F-F5,&F,F5F8F-F5" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame31G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF $F$*(,**$9%\"\"$!\"\"*&,**&,(I$t12GF$\"\"\"I$t22GF$F7I$t32GF$F7F79$F7F 7I$t11GF$F7I$t21GF$F7I$t31GF$F7F7F/\"\"#F7*&,0*&,&*&,&F6F1F8F1F7F9F7F7 *&F6F7F8F7F1F7F:F>F7*&,(*&,&FF6F7F8F7F9F7F7*&,&*&,&*&F;F7F8F7F7*&F6F7F " 0 "" {MPLTEXT 1 0 105 "simplify(Hame31(q,p)- (t12/(t12-t32)*Hamv1(q,p)+ 1/(t32-t12)*Hamu1(q,p)+(t22-t12)/(t12-t32)*Hame21(q,p)));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31 ,1,0,0,0,0,0)):\n" }{MPLTEXT 1 0 63 "simplify(h*dotpfunction(t12,t22,t 32,t11,t21,t31,1,0,0,0,0,0)):\n" }{MPLTEXT 1 0 1771 "Hame12:=unapply(( (t32*t22*(t21+t31-2*t11)*q^3+(-(t22+t32)*(t21+t31-2*t11)*p+(-h*t32+t31 *(t21+t31-2*t11))*t22+t32*t21*(t21+t31-2*t11))*q^2+((t21+t31-2*t11)*p^ 2+(h*t22+h*t32-(t21+t31)*(t21+t31-2*t11))*p+(-2*t30*t11+t21*t30+(-h+t3 0)*t31)*t22+(-2*t11*t20+(-h+t20)*t21+t31*t20)*t32+t31*t21*(t21+t31-2*t 11))*q-(p*h+(-2*t30-2*t20)*t11+(t21+t31)*(t30-h+t20))*p)*t12^2+(-((-t1 1+t31)*t22-t32*(t11-t21))*t32*t22*q^3+(((-t11+t31)*t22^2-t32^2*(t11-t2 1))*p+(h*t32-t31*(-t11+t31))*t22^2+(2*((1/2)*h*t32+(t11-t21)*(-t11+t31 )))*t32*t22+t21*t32^2*(t11-t21))*q^2+(((-t11+t21)*t22+t32*(-t11+t31))* p^2+(-h*t22^2+(-2*h*t32+2*t11*(t11-t21))*t22-h*t32^2-2*t11*(-t11+t31)* t32)*p+(t30*t11-(-h+t30)*t31)*t22^2+(((3*t20+3*t30)*t11+(h-t20-2*t30)* t21-(-h+2*t20+t30)*t31)*t32+t31*(t11-t21)*(-2*t11+t31))*t22+(2*(((1/2) *t11*t20+(1/2)*(h-t20)*t21)*t32+(-t11+t31)*t21*(-(1/2)*t21+t11)))*t32) *q-p*((t21+t31-2*t11)*p^2+(-h*t22-h*t32-(t11+t21+t31)*(t21+t31-2*t11)) *p+((3*t20+t30)*t11+(h-t20)*t21-(-h+2*t20+t30)*t31)*t22+(t11*(t20+3*t3 0)+(h-t20-2*t30)*t21-(-h+t30)*t31)*t32+(t21+t31-2*t11)*(t11*(t21+t31)+ t21*t31)))*t12+t32*(((-t11+t31)*t22-t32*(t11-t21))*p+(-h*t32-t11*(-t11 +t31))*t22+t32*t11*(t11-t21))*t22*q^2+(-((-t11+t31)*t22-t32*(t11-t21)) *(t22+t32)*p^2+((t32*h-t11^2+t31^2)*t22^2+(h*t32^2+(-2*t11^2+2*t21*t31 )*t32)*t22+(-t11^2+t21^2)*t32^2)*p+(((-t20-t30)*t11+(t30-h+t20)*t31)*t 32-t11*t31*(-t11+t31))*t22^2-t32*((t11*(t20+t30)-(t30-h+t20)*t21)*t32- (t11*(t21+t31)-2*t21*t31)*t11)*t22+t32^2*t11*t21*(t11-t21))*q+p*(((-t1 1+t31)*t22-t32*(t11-t21))*p^2+((-h*t32-(-t11+t31)*(t11+t21+t31))*t22+t 32*(t11-t21)*(t11+t21+t31))*p-t20*(-t11+t31)*t22^2+((t11*(t20+t30)+(h- t20)*t21-(-h+t30)*t31)*t32+(-t11+t31)*(t11*(t21+t31)+t21*t31))*t22+t32 *((-t31-t21)*t11+t32*t30-t21*t31)*(t11-t21)))/(2*(t12-t32)^2*(t12-t22) ^2)\n" }{MPLTEXT 1 0 7 ",q,p);\n" }{MPLTEXT 1 0 84 "simplify(h*dotqfun ction(t12,t22,t32,t11,t21,t31,1,0,0,0,0,0)- diff(Hame12(q,p),p));\n" } {MPLTEXT 1 0 83 "simplify(h*dotpfunction(t12,t22,t32,t11,t21,t31,1,0,0 ,0,0,0)+ diff(Hame12(q,p),q));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Ham e12G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,$*(,,*&,***I$t3 2GF$\"\"\"I$t22GF$F3,(I$t31GF$F3I$t11GF$!\"#I$t21GF$F3F39$\"\"$F3*&,(* (,&F4F3F2F3F3F5F39%F3!\"\"*&,&*&I\"hGF$F3F2F3FA*&F6F3F5F3F3F3F4F3F3*(F 2F3F9F3F5F3F3F3F:\"\"#F3*&,,*&F5F3F@FHF3*&,(*&FEF3F4F3F3FDF3*&,&F9F3F6 F3F3F5F3FAF3F@F3F3*&,(*&F7F3I$t30GF$F3F8*&F9F3FTF3F3*&,&FEFAFTF3F3F6F3 F3F3F4F3F3*&,(*&F7F3I$t20GF$F3F8*&,&FEFAFenF3F3F9F3F3*&F6F3FenF3F3F3F2 F3F3*(F6F3F9F3F5F3F3F3F:F3F3*&,(*&FEF3F@F3F3*&,&FenF8FTF8F3F7F3F3*&FPF 3,(FEFAFenF3FTF3F3F3F3F@F3FAF3I$t12GF$FHF3*&,***,&*&,&F7FAF6F3F3F4F3F3 *&F2F3,&F7F3F9FAF3FAF3F2F3F4F3F:F;FA*&,**&,&*&FgoF3F4FHF3*&F2FHFioF3FA F3F@F3F3*&,&FDF3*&F6F3FgoF3FAF3F4FHF3*(,&FD#F3FH*&FioF3FgoF3F3F3F2F3F4 F3FH*(F9F3F2FHFioF3F3F3F:FHF3*&,,*&,&*&,&F7FAF9F3F3F4F3F3*&F2F3FgoF3F3 F3F@FHF3*&,**&FEF3F4FHFA*&,&FDF8*&F7F3FioF3FHF3F4F3F3*&FEF3F2FHFA*(F7F 3FgoF3F2F3F8F3F@F3F3*&,&FSF3FVFAF3F4FHF3*&,&*&,(*&,&FTF;FenF;F3F7F3F3* &F9F3,(FEF3FenFAFTF8F3F3*&,(FEFAFenFHFTF3F3F6F3FAF3F2F3F3*(F6F3FioF3,& F6F3F7F8F3F3F3F4F3F3*&,&*&,&FZFep*&,&FEF3FenFAF3F9F3FepF3F2F3F3*(FgoF3 F9F3,&F7F3F9#FAFHF3F3F3F2F3FHF3F:F3F3*&F@F3,,FKF3*&,(FNFAFDFA*&,(F7F3F 9F3F6F3F3F5F3FAF3F@F3F3*&,(*&F7F3,&FTF3FenF;F3F3FirF3FarFAF3F4F3F3*&,( *&F7F3,&FenF3FTF;F3F3F_rF3FVFAF3F2F3F3*&F5F3,&*&F7F3FPF3F3*&F9F3F6F3F3 F3F3F3FAF3FaoF3F3**F2F3,(*&FeoF3F@F3F3*&,&FDFA*&F7F3FgoF3FAF3F4F3F3*(F 2F3F7F3FioF3F3F3F4F3F:FHF3*&,,*(FeoF3F?F3F@FHFA*&,(*&,(FDF3*$F7FHFA*$F 6FHF3F3F4FHF3*&,&FeqF3*&,&F^uF8F_tFHF3F2F3F3F3F4F3F3*&,&F^uFA*$F9FHF3F 3F2FHF3F3F@F3F3*&,&*&,&*&,&FenFAFTFAF3F7F3F3*&F`oF3F6F3F3F3F2F3F3*(F7F 3F6F3FgoF3FAF3F4FHF3*(F2F3,&*&,&*&,&FenF3FTF3F3F7F3F3*&F`oF3F9F3FAF3F2 F3F3*&,&F^tF3F_tF8F3F7F3FAF3F4F3FA**F2FHF7F3F9F3FioF3F3F3F:F3F3*&F@F3, ,*&FeoF3F@FHF3*&,&*&,&FDFA*&FgoF3FcsF3FAF3F4F3F3*(F2F3FioF3FcsF3F3F3F@ F3F3*(FenF3FgoF3F4FHFA*&,&*&,(FcvF3FirF3FVFAF3F2F3F3*&FgoF3F]tF3F3F3F4 F3F3*(F2F3,(*&,&F6FAF9FAF3F7F3F3*&FTF3F2F3F3F_tFAF3FioF3F3F3F3F3,&FaoF 3F2FAF8,&FaoF3F4FAF8FepF$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0,1,0 ,0,0,0)):\n" }{MPLTEXT 1 0 63 "simplify(h*dotpfunction(t12,t22,t32,t11 ,t21,t31,0,1,0,0,0,0)):\n" }{MPLTEXT 1 0 1765 "Hame22:=unapply( ((t12* t32*(t11-2*t21+t31)*q^3+(-(t12+t32)*(t11-2*t21+t31)*p+(-h*t12+t11*(t11 -2*t21+t31))*t32+t12*t31*(t11-2*t21+t31))*q^2+((t11-2*t21+t31)*p^2+(h* t32+h*t12-(t11+t31)*(t11-2*t21+t31))*p+((2*t30-2*h+2*t20)*t21+(-t30+h- t20)*t31-t11*(t20+t30))*t32+(-2*t21*t30+(-h+t30)*t31+t30*t11)*t12+t11* t31*(t11-2*t21+t31))*q-(p*h+(-2*h+2*t20)*t21-t20*(t11+t31))*p)*t22^2+( -t12*t32*(t32*(t11-t21)+t12*(-t21+t31))*q^3+((t32^2*(t11-t21)+t12^2*(- t21+t31))*p+(h*t12-t11*(t11-t21))*t32^2-2*t12*(-(1/2)*h*t12+(t11-t21)* (-t21+t31))*t32-t31*(-t21+t31)*t12^2)*q^2+(((-t21+t31)*t32+t12*(t11-t2 1))*p^2+(-h*t32^2+(-2*h*t12-2*t21*(-t21+t31))*t32-t12*(h*t12+2*t21*(t1 1-t21)))*p+((-t30+h-t20)*t21+t11*(t20+t30))*t32^2+(((3*h-3*t20)*t21+(- h+2*t20+t30)*t31-(-t20+t30)*t11)*t12-t11*(-2*t21+t11)*(-t21+t31))*t32- t12*((-t21*t30+(-h+t30)*t31)*t12+t31*(t11-t21)*(t31-2*t21)))*q-((t11-2 *t21+t31)*p^2+(-h*t32-h*t12-(t11+t21+t31)*(t11-2*t21+t31))*p+((2*t30+h -t20)*t21+(h-t30)*t31-(-t20+t30)*t11)*t32+((-2*t30+3*h-3*t20)*t21+(-h+ 2*t20+t30)*t31+t11*(t20+t30))*t12+(t11-2*t21+t31)*((t11+t31)*t21+t11*t 31))*p)*t22+t12*((t32*(t11-t21)+t12*(-t21+t31))*p+(-h*t12-t21*(t11-t21 ))*t32-t12*t21*(-t21+t31))*t32*q^2+(-(t12+t32)*(t32*(t11-t21)+t12*(-t2 1+t31))*p^2+((t12*h+t11^2-t21^2)*t32^2+(h*t12^2+(2*t11*t31-2*t21^2)*t1 2)*t32+t12^2*(-t21^2+t31^2))*p+(((-h+t20)*t21-t11*t20)*t12-t11*t21*(t1 1-t21))*t32^2-t12*(((h-t20)*t21+t31*t20)*t12+(-t11-t31)*t21^2+2*t11*t2 1*t31)*t32-t31*t12^2*t21*(-t21+t31))*q+((t32*(t11-t21)+t12*(-t21+t31)) *p^2+((-h*t12-(t11-t21)*(t11+t21+t31))*t32-t12*(-t21+t31)*(t11+t21+t31 ))*p-t30*(t11-t21)*t32^2+(((h-t20)*t21+(h-t30)*t31+t11*(t20+t30))*t12+ (t11-t21)*((t11+t31)*t21+t11*t31))*t32+t12*((t30-h+t20)*t12+(t11+t31)* t21+t11*t31)*(-t21+t31))*p)/(2*(t22-t32)^2*(t12-t22)^2),q,p);\n" } {MPLTEXT 1 0 84 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0,1,0 ,0,0,0)- diff(Hame22(q,p),p));\n" }{MPLTEXT 1 0 83 "simplify(h*dotpfun ction(t12,t22,t32,t11,t21,t31,0,1,0,0,0,0)+ diff(Hame22(q,p),q));" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame22G6\"f*6$I\" qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,$*(,,*&,***I$t12GF$\"\"\"I$t3 2GF$F3,(I$t11GF$F3I$t21GF$!\"#I$t31GF$F3F39$\"\"$F3*&,(*(,&F2F3F4F3F3F 5F39%F3!\"\"*&,&*&I\"hGF$F3F2F3FA*&F6F3F5F3F3F3F4F3F3*(F2F3F9F3F5F3F3F 3F:\"\"#F3*&,,*&F5F3F@FHF3*&,(*&FEF3F4F3F3FDF3*&,&F6F3F9F3F3F5F3FAF3F@ F3F3*&,(*&,(FEF8I$t30GF$FHI$t20GF$FHF3F7F3F3*&,(FEF3FVFAFUFAF3F9F3F3*& ,&FVF3FUF3F3F6F3FAF3F4F3F3*&,(*&F7F3FUF3F8*&,&FEFAFUF3F3F9F3F3*&F6F3FU F3F3F3F2F3F3*(F6F3F9F3F5F3F3F3F:F3F3*&,(*&FEF3F@F3F3*&,&FEF8FVFHF3F7F3 F3*&FVF3FPF3FAF3F@F3FAF3I$t22GF$FHF3*&,***F2F3F4F3,&*&F4F3,&F6F3F7FAF3 F3*&F2F3,&F7FAF9F3F3F3F3F:F;FA*&,**&,&*&F4FHFhoF3F3*&F2FHFjoF3F3F3F@F3 F3*&,&FDF3*&F6F3FhoF3FAF3F4FHF3*(F2F3,&FD#FAFH*&FhoF3FjoF3F3F3F4F3F8*( F9F3FjoF3F2FHFAF3F:FHF3*&,,*&,&*&FjoF3F4F3F3*&F2F3FhoF3F3F3F@FHF3*&,(* &FEF3F4FHFA*&,&FDF8*&F7F3FjoF3F8F3F4F3F3*&F2F3,&FDF3*&F7F3FhoF3FHF3FAF 3F@F3F3*&,&*&F7F3FXF3F3FYF3F3F4FHF3*&,&*&,(*&,&FEF;FV!\"$F3F7F3F3*&,(F EFAFVFHFUF3F3F9F3F3*&F6F3,&FVFAFUF3F3FAF3F2F3F3*(F6F3,&F6F3F7F8F3FjoF3 FAF3F4F3F3*&F2F3,&*&,&FgnFAFhnF3F3F2F3F3*(F9F3FhoF3,&F7F8F9F3F3F3F3FAF 3F:F3F3*&,,FKF3*&,(FNFAFDFA*&,(F6F3F7F3F9F3F3F5F3FAF3F@F3F3*&,(*&,(FEF 3FUFHFVFAF3F7F3F3*&,&FEF3FUFAF3F9F3F3FdrFAF3F4F3F3*&,(*&,(FUF8FEF;FVFa rF3F7F3F3FbrF3FYF3F3F2F3F3*&F5F3,&*&FPF3F7F3F3*&F6F3F9F3F3F3F3F3F@F3FA F3FboF3F3**F2F3,(*&FfoF3F@F3F3*&,&FDFAFgqFAF3F4F3F3*(F2F3F7F3FjoF3FAF3 F4F3F:FHF3*&,,*(F?F3FfoF3F@FHFA*&,(*&,(FDF3*$F6FHF3*$F7FHFAF3F4FHF3*&, &*&FEF3F2FHF3*&,&FatFHF`uF8F3F2F3F3F3F4F3F3*&F2FH,&F`uFA*$F9FHF3F3F3F3 F@F3F3*&,&*&,&*&,&FEFAFVF3F3F7F3F3*&F6F3FVF3FAF3F2F3F3*(F6F3F7F3FhoF3F AF3F4FHF3*(F2F3,(*&,&*&,&FEF3FVFAF3F7F3F3*&F9F3FVF3F3F3F2F3F3*&,&F6FAF 9FAF3F7FHF3*(F6F3F7F3F9F3FHF3F4F3FA**F9F3F2FHF7F3FjoF3FAF3F:F3F3*&,,*& FfoF3F@FHF3*&,&*&,&FDFA*&FhoF3FcsF3FAF3F4F3F3*(F2F3FjoF3FcsF3FAF3F@F3F 3*(FUF3FhoF3F4FHFA*&,&*&,(FevF3FhsF3FYF3F3F2F3F3*&FhoF3F_tF3F3F3F4F3F3 *(F2F3,(*&,(FEFAFVF3FUF3F3F2F3F3F`tF3FatF3F3FjoF3F3F3F@F3F3F3,&FboF3F4 FAF8,&F2F3FboFAF8#F3FHF$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "simplify(h*dotqfunction(t12,t22,t32,t11,t21,t31,0,0,1 ,0,0,0)):\n" }{MPLTEXT 1 0 63 "simplify(h*dotpfunction(t12,t22,t32,t11 ,t21,t31,0,0,1,0,0,0)):\n" }{MPLTEXT 1 0 1977 "Hame32:=unapply( ((-(2 *(t31-(1/2)*t11-(1/2)*t21))*t12*t22*q^3+((2*(t31-(1/2)*t11-(1/2)*t21)) *(t12+t22)*p+(-h*t12-(2*(t31-(1/2)*t11-(1/2)*t21))*t11)*t22-(2*(t31-(1 /2)*t11-(1/2)*t21))*t12*t21)*q^2+((t11+t21-2*t31)*p^2+(h*t22+h*t12+(2* (t31-(1/2)*t11-(1/2)*t21))*(t11+t21))*p+((2*t30-2*h+2*t20)*t31+(-t30+h -t20)*t21-t11*(t20+t30))*t22+(-2*t31*t20+(-h+t20)*t21+t11*t20)*t12-2*t 21*(t31-(1/2)*t11-(1/2)*t21)*t11)*q-p*(p*h+(2*t30-2*h)*t31-t30*(t11+t2 1)))*t32^2+(t12*((-t11+t31)*t22+t12*(-t21+t31))*t22*q^3+(((t11-t31)*t2 2^2-t12^2*(-t21+t31))*p+(h*t12+t11*(-t11+t31))*t22^2-2*t12*(-(1/2)*h*t 12+(-t21+t31)*(-t11+t31))*t22+t21*t12^2*(-t21+t31))*q^2+(((t21-t31)*t2 2-t12*(-t11+t31))*p^2+(-h*t22^2+(-2*h*t12+2*t31*(-t21+t31))*t22-h*t12^ 2+2*t31*(-t11+t31)*t12)*p+((-t30+h-t20)*t31+t11*(t20+t30))*t22^2+(((-3 *t30+3*h)*t31+(-h+t20+2*t30)*t21+(-t20+t30)*t11)*t12-(2*(-t21+t31))*(- (1/2)*t11+t31)*t11)*t22-2*t12*((-(1/2)*t31*t20-(1/2)*(h-t20)*t21)*t12+ (-t11+t31)*t21*(t31-(1/2)*t21)))*q+(2*((t31-(1/2)*t11-(1/2)*t21)*p^2+( (1/2)*h*t22+(1/2)*h*t12-(t31-(1/2)*t11-(1/2)*t21)*(t11+t21+t31))*p+((- (1/2)*h-t20+(1/2)*t30)*t31+t21*((1/2)*t20-(1/2)*h)-(1/2)*(-t20+t30)*t1 1)*t22+((t20+3*t30*(1/2)-3*h*(1/2))*t31+(-t30+(1/2)*h-(1/2)*t20)*t21-( 1/2)*t11*(t20+t30))*t12+(t31-(1/2)*t11-(1/2)*t21)*((t11+t21)*t31+t11*t 21)))*p)*t32-t12*t22*(((-t11+t31)*t22+t12*(-t21+t31))*p+(h*t12-t31*(-t 11+t31))*t22-t12*t31*(-t21+t31))*q^2+((t12+t22)*((-t11+t31)*t22+t12*(- t21+t31))*p^2+((t12*h+t11^2-t31^2)*t22^2+(h*t12^2+(2*t11*t21-2*t31^2)* t12)*t22+(t21^2-t31^2)*t12^2)*p+(((-h+t30)*t31-t30*t11)*t12+t11*t31*(- t11+t31))*t22^2+((-t21*t30+(-h+t30)*t31)*t12+t31*((t11+t21)*t31-2*t11* t21))*t12*t22+t31*t12^2*t21*(-t21+t31))*q-(((-t11+t31)*t22+t12*(-t21+t 31))*p^2+((h*t12-(-t11+t31)*(t11+t21+t31))*t22-t12*(-t21+t31)*(t11+t21 +t31))*p-t20*(-t11+t31)*t22^2+(((-h+t30)*t31+(-h+t20)*t21-t11*(t20+t30 ))*t12+(-t11+t31)*((t11+t21)*t31+t11*t21))*t22+t12*((t30-h+t20)*t12+(t 11+t21)*t31+t11*t21)*(-t21+t31))*p)/(2*(t22-t32)^2*(t12-t32)^2)\n" } {MPLTEXT 1 0 7 ",q,p);\n" }{MPLTEXT 1 0 84 "simplify(h*dotqfunction(t1 2,t22,t32,t11,t21,t31,0,0,1,0,0,0)- diff(Hame32(q,p),p));\n" }{MPLTEXT 1 0 83 "simplify(h*dotpfunction(t12,t22,t32,t11,t21,t31,0,0,1,0,0,0)+ diff(Hame32(q,p),q));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame32G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF $F$,$*(,,*&,***,(I$t31GF$\"\"\"I$t11GF$#!\"\"\"\"#I$t21GF$F6F4I$t12GF$ F4I$t22GF$F49$\"\"$!\"#*&,(*(F2F4,&F:F4F;F4F49%F4F8*&,&*&I\"hGF$F4F:F4 F7*&F2F4F5F4F>F4F;F4F4*(F2F4F:F4F9F4F>F4FF4FC F8F4*&,(*&FGF4F;F4F4FFF4*&F2F4,&F5F4F9F4F4F8F4FCF4F4*&,(*&,(FGF>I$t30G F$F8I$t20GF$F8F4F3F4F4*&F9F4,(FGF4FXF7FWF7F4F4*&,&FXF4FWF4F4F5F4F7F4F; F4F4*&,(*&F3F4FXF4F>*&,&FGF7FXF4F4F9F4F4*&F5F4FXF4F4F4F:F4F4*(F9F4F2F4 F5F4F>F4FFWF8F4F3F4F4*&FWF4FRF4F7F4F7 F4I$t32GF$F8F4*&,***F:F4,&*&,&F5F7F3F4F4F;F4F4*&F:F4,&F9F7F3F4F4F4F4F; F4F*(F9F4F:F8F\\pF4F4 F4F*&F3F4F\\pF4F8F4F;F4F4*&FGF4F:F8F7*(F3F4FjoF4F:F4F8F4FCF4F4 *&,&*&FZF4F3F4F4FenF4F4F;F8F4*&,&*&,(*&,&FGF=FW!\"$F4F3F4F4*&,(FGF7FXF 4FWF8F4F9F4F4*&F5F4,&FXF7FWF4F4F4F4F:F4F4*(F\\pF4,&F3F4F5F6F4F5F4F>F4F ;F4F4*&F:F4,&*&,&FinF6*&,&FGF4FXF7F4F9F4F6F4F:F4F4*(FjoF4F9F4,&F3F4F9F 6F4F4F4F>F4FF4F:F4F4F4F;F4F4*&,&*$F9F8F4F[vF7F4F:F8F4F4FCF4F4*&,&*&,&*&, &FGF7FWF4F4F3F4F4*&F5F4FWF4F7F4F:F4F4*(F5F4F3F4FjoF4F4F4F;F8F4*(,&*&,& *&F9F4FWF4F7FgvF4F4F:F4F4*&F3F4,&FjtF4F[uF>F4F4F4F:F4F;F4F4**F3F4F:F8F 9F4F\\pF4F4F4F,&F:F4FdoF7F>FgsF$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 13 " Hame21(q,p)-(" }{MPLTEXT 1 0 78 "1/((t32-t22)*(t12-t22))*(-p^3+ P1(q)* p^2-P2(q)*p+P3(q)) +(p-q*t32)*h/(t32-t22)" }{MPLTEXT 1 0 3 "));" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 285 82 "Definition o f the reduced Darboux coordiantes and Hamiltonian in the direction tau " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "TT1:=unapply(t12+t22+t3 2,t11,t21,t31,t12,t22,t32);\n" }{MPLTEXT 1 0 51 "TT2:=unapply(t11+t21+ t31,t11,t21,t31,t12,t22,t32);\n" }{MPLTEXT 1 0 43 "TT3:=unapply(t22,t1 1,t21,t31,t12,t22,t32);\n" }{MPLTEXT 1 0 43 "TT4:=unapply(t11,t11,t21, t31,t12,t22,t32);\n" }{MPLTEXT 1 0 43 "TT5:=unapply(t32,t11,t21,t31,t1 2,t22,t32);\n" }{MPLTEXT 1 0 132 "taufunction:=unapply( ((t21-t31)*t1 2+(t31-t11)*t22+(t11-t21)*t32)/(sqrt((t22-t12)*(t12-t32)*(t32-t22))) , t11,t21,t31,t12,t22,t32);\n" }{MPLTEXT 1 0 238 "solve(\{TT1(t11,t21,t3 1,t12,t22,t32)=T1,TT2(t11,t21,t31,t12,t22,t32)=T2,TT3(t11,t21,t31,t12, t22,t32)=T3,TT4(t11,t21,t31,t12,t22,t32)=T4,TT5(t11,t21,t31,t12,t22,t3 2)=T5,taufunction(t11,t21,t31,t12,t22,t32)=tau \},\{t11,t21,t31,t12,t2 2,t32\});\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "t11function := T4; \n" }{MPLTEXT 1 0 26 "t12function := -T3-T5+T1;\n" }{MPLTEXT 1 0 115 " t21function := (tau*sqrt((-2*T3-T5+T1)*(-T3-2*T5+T1)*(T3-T5))+T1*T2-T1 *T4-2*T3*T2-T5*T2+3*T4*T3)/(2*T1-3*T3-3*T5);\n" }{MPLTEXT 1 0 19 "t22f unction := T3;\n" }{MPLTEXT 1 0 116 "t31function := -(tau*sqrt((-2*T3- T5+T1)*(-T3-2*T5+T1)*(T3-T5))-T1*T2+T1*T4+T3*T2+2*T5*T2-3*T4*T5)/(2*T1 -3*T3-3*T5);\n" }{MPLTEXT 1 0 19 "t32function := T5;\n" }{MPLTEXT 1 0 88 "simplify(TT1(t11function,t21function,t31function,t12function,t22fu nction,t32function));\n" }{MPLTEXT 1 0 88 "simplify(TT2(t11function,t2 1function,t31function,t12function,t22function,t32function));\n" } {MPLTEXT 1 0 88 "simplify(TT3(t11function,t21function,t31function,t12f unction,t22function,t32function));\n" }{MPLTEXT 1 0 88 "simplify(TT4(t 11function,t21function,t31function,t12function,t22function,t32function ));\n" }{MPLTEXT 1 0 88 "simplify(TT5(t11function,t21function,t31funct ion,t12function,t22function,t32function));\n" }{MPLTEXT 1 0 96 "simpli fy(taufunction(t11function,t21function,t31function,t12function,t22func tion,t32function));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 250 "partial taufunction:=unapply( diff(t11function,tau)*partialt11 + diff(t21funct ion,tau)*partialt21+diff(t31function,tau)*partialt31+diff(t12function, tau)*partialt12+diff(t22function,tau)*partialt22+diff(t32function,tau) *partialt32,T1,T2,T3,T4,T5,tau):\n" }{MPLTEXT 1 0 218 "partialtau:=par tialtaufunction(TT1(t11,t21,t31,t12,t22,t32),TT2(t11,t21,t31,t12,t22,t 32),TT3(t11,t21,t31,t12,t22,t32),TT4(t11,t21,t31,t12,t22,t32),TT5(t11, t21,t31,t12,t22,t32),taufunction(t11,t21,t31,t12,t22,t32) ):\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "Coefft21:=residue(partialtau/par tialt21^2,partialt21=0):\n" }{MPLTEXT 1 0 57 "Coefft31:=residue(partia ltau/partialt31^2,partialt31=0):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 76 "Hamtau:= unapply( simplify(Coefft21*Hame21(q,p)+Coefft31*Hame31( q,p)),q,p):\n" }{MPLTEXT 1 0 28 "Ltauq:=diff(Hamtau(q,p),p):\n" } {MPLTEXT 1 0 28 "Ltaup:=-diff(Hamtau(q,p),q):" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 84 "checkqfunction:=unapply( sqrt((t 12-t32)/((t22-t12)*(t32-t22)))*(-p+t22*q+t21),q,p);\n" }{MPLTEXT 1 0 83 "checkpfunction:=unapply( sqrt((t32-t22)/((t12-t32)*(t22-t12)))*(p- t12*q-t11),q,p);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 76 "SOLL:=solve (\{checkqfunction(q,p)=checkq,checkpfunction(q,p)=checkp\},\{q,p\}):\n " }{MPLTEXT 1 0 30 "Solp:=simplify(rhs(SOLL[1])):\n" }{MPLTEXT 1 0 31 "Solq:=simplify(rhs(SOLL[2])): \n" }{MPLTEXT 1 0 44 "simplify(checkqfu nction(Solq,Solp)-checkq);\n" }{MPLTEXT 1 0 44 "simplify(checkpfunctio n(Solq,Solp)-checkp);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 196 "Ltauc heckqfunction:=unapply( simplify( diff(checkqfunction(q,p),q)*Ltauq+di ff(checkqfunction(q,p),p)*Ltaup+Coefft21*h*diff(checkqfunction(q,p),t2 1)+Coefft31*h*diff(checkqfunction(q,p),t31)),q,p):\n" }{MPLTEXT 1 0 195 "Ltaucheckpfunction:=unapply(simplify( diff(checkpfunction(q,p),q) *Ltauq+diff(checkpfunction(q,p),p)*Ltaup+Coefft21*h*diff(checkpfunctio n(q,p),t21)+Coefft31*h*diff(checkpfunction(q,p),t31)),q,p):\n" } {MPLTEXT 1 0 100 "Ltaucheckqfunction2:=unapply(simplify(Ltaucheckqfunc tion(Solq,Solp)),t11, t21, t31, t12, t22, t32):\n" }{MPLTEXT 1 0 100 " Ltaucheckpfunction2:=unapply(simplify(Ltaucheckpfunction(Solq,Solp)),t 11, t21, t31, t12, t22, t32):\n" }{MPLTEXT 1 0 120 "Ltaucheckq:=simpli fy(Ltaucheckqfunction2(t11function,t21function ,t31function ,t12functi on ,t22function ,t32function)):\n" }{MPLTEXT 1 0 119 "Ltaucheckp:=simp lify(Ltaucheckpfunction2(t11function,t21function ,t31function ,t12func tion ,t22function ,t32function)):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 45 "HamtaucheckCoordinates:=unapply(simplify(int(" }{MPLTEXT 1 0 37 "L taucheckq,checkp)-int(simplify(diff(" }{MPLTEXT 1 0 31 "int(Ltaucheckq ,checkp),checkq)+" }{MPLTEXT 1 0 36 "Ltaucheckp),checkq),checkq,checkp )):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 11 "Ltaucheckq-" }{MPLTEXT 1 0 5 "diff(" }{MPLTEXT 1 0 48 "Hamtaucheck Coordinates(checkq,checkp),checkp));\n" }{MPLTEXT 1 0 9 "simplify(" } {MPLTEXT 1 0 16 "Ltaucheckp+diff(" }{MPLTEXT 1 0 47 "HamtaucheckCoordi nates(checkq,checkp),checkq));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT1 G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operator GF$I&arrowGF$F$,(9'\"\"\"9(F29)F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT2G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$ I)operatorGF$I&arrowGF$F$,(9$\"\"\"9%F29&F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT3G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t 32GF$F$6$I)operatorGF$I&arrowGF$F$9(F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT4G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t 32GF$F$6$I)operatorGF$I&arrowGF$F$9$F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT5G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t 32GF$F$6$I)operatorGF$I&arrowGF$F$9)F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,taufunctionG6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t 22GF$I$t32GF$F$6$I)operatorGF$I&arrowGF$F$*&,(*&,&9%\"\"\"9&!\"\"F59'F 5F5*&,&9$F7F6F5F59(F5F5*&9)F5,&F;F5F4F7F5F5F5*(,&F8F7FF7F 5,&FF5F5#F7\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<(/I$t11G 6\"I#T4GF%/I$t12GF%,(I#T3GF%!\"\"I#T5GF%F+I#T1GF%\"\"\"/I$t21GF%*&,.*& I$tauGF%F.*(,(F*F+F,!\"#F-F.F.,&F*F.F,F+F.,(F*F7F,F+F-F.F.#F.\"\"#F.*& F-F.I#T2GF%F.F.*&F-F.F&F.F+*&F*F.F=F.F7*&F,F.F=F.F+*&F&F.F*F.\"\"$F.,( F-F;F*!\"$F,FDF+/I$t22GF%F*/I$t31GF%,$*&,.F3F.FF.F?F.F@F;*&F&F.F, F.FDF.FCF+F+/I$t32GF%F," }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t11functio nG6\"I#T4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t12functionG6\",(I#T3 GF$!\"\"I#T5GF$F'I#T1GF$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t21 functionG6\"*&,.*&I$tauGF$\"\"\"*(,(I#T3GF$!\"\"I#T5GF$!\"#I#T1GF$F)F) ,&F,F)F.F-F),(F,F/F.F-F0F)F)#F)\"\"#F)*&F0F)I#T2GF$F)F)*&F0F)I#T4GF$F) F-*&F,F)F6F)F/*&F.F)F6F)F-*&F8F)F,F)\"\"$F),(F0F4F,!\"$F.F>F-" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I,t22functionG6\"I#T3GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t31functionG6\",$*&,.*&I$tauGF$\"\"\"*(,(I#T3GF$ !\"\"I#T5GF$!\"#I#T1GF$F*F*,&F-F*F/F.F*,(F-F0F/F.F1F*F*#F*\"\"#F**&F1F *I#T2GF$F*F.*&F1F*I#T4GF$F*F**&F-F*F7F*F**&F/F*F7F*F5*&F9F*F/F*!\"$F*, (F1F5F-F=F/F=F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t32functionG6\"I #T5GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#T1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#T2G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#T3G6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "I#T4G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#T5G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$tauG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I/checkqfunctionG6\"f*6$I\"qGF$I\"pGF$F$6$I)operator GF$I&arrowGF$F$*&*(,&I$t12GF$\"\"\"I$t32GF$!\"\"F0,&F/F2I$t22GF$F0F2,& F4F2F1F0F2#F0\"\"#,(*&9$F0F4F0F09%F2I$t21GF$F0F0F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I/checkpfunctionG6\"f*6$I\"qGF$I\"pGF$F$6$I)operato rGF$I&arrowGF$F$*&*(,&I$t22GF$!\"\"I$t32GF$\"\"\"F2,&I$t12GF$F0F/F2F0, &F4F2F1F0F0#F2\"\"#,(*&9$F2F4F2F09%F2I$t11GF$F0F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 286 102 "Verification that the \+ reduced Darboux coordinates have trivial evolutions along the trivial \+ directions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "hdotcheckqfun ction:= unapply(h*simplify(diff(checkqfunction(q,p),q)*dotqfunction(" }{MPLTEXT 1 0 68 "t12,t22,t32,t11,t21,t31,dott12,dott22,dott32,dott11, dott21,dott31)+ " }{MPLTEXT 1 0 109 "diff(checkqfunction(q,p),p)*dotpf unction(t12,t22,t32,t11,t21,t31,dott12,dott22,dott32,dott11,dott21,dot t31)+ " }{MPLTEXT 1 0 30 "diff(checkqfunction(q,p),t12)*" }{MPLTEXT 1 0 7 "dott12+" }{MPLTEXT 1 0 37 "diff(checkqfunction(q,p),t22)*dott22+" }{MPLTEXT 1 0 37 "diff(checkqfunction(q,p),t32)*dott32+" }{MPLTEXT 1 0 37 "diff(checkqfunction(q,p),t11)*dott11+" }{MPLTEXT 1 0 37 "diff(ch eckqfunction(q,p),t21)*dott21+" }{MPLTEXT 1 0 38 "diff(checkqfunction( q,p),t31)*dott31)," }{MPLTEXT 1 0 67 "t12,t22,t32,t11,t21,t31,dott12,d ott22,dott32,dott11,dott21,dott31):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 548 "hdotcheckpfunction:= unapply(h*simplify(diff(checkpfunction(q,p ),q)*dotqfunction(t12,t22,t32,t11,t21,t31,dott12,dott22,dott32,dott11, dott21,dott31)+ diff(checkpfunction(q,p),p)*dotpfunction(t12,t22,t32,t 11,t21,t31,dott12,dott22,dott32,dott11,dott21,dott31)+ diff(checkpfunc tion(q,p),t12)*dott12+diff(checkpfunction(q,p),t22)*dott22+diff(checkp function(q,p),t32)*dott32+diff(checkpfunction(q,p),t11)*dott11+diff(ch eckpfunction(q,p),t21)*dott21+diff(checkpfunction(q,p),t31)*dott31),t1 2,t22,t32,t11,t21,t31,dott12,dott22,dott32,dott11,dott21,dott31):" } {MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "simpl ify(hdotcheckqfunction(" }{MPLTEXT 1 0 38 "t12,t22,t32,t11,t21,t31,1,1 ,1,0,0,0));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" } {MPLTEXT 1 0 58 "hdotcheckqfunction(t12,t22,t32,t11,t21,t31,0,0,0,1,1, 1));\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 43 "hdotcheckqfuncti on(t12,t22,t32,t11,t21,t31," }{MPLTEXT 1 0 29 "2*t12,2*t22,2*t32,t11,t 21,t31" }{MPLTEXT 1 0 4 "));\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 43 "hdotcheckqfunction(t12,t22,t32,t11,t21,t31," }{MPLTEXT 1 0 17 "0,0,0,t12,t22,t32" }{MPLTEXT 1 0 5 ")); \n" }{MPLTEXT 1 0 9 "simplify (" }{MPLTEXT 1 0 43 "hdotcheckqfunction(t12,t22,t32,t11,t21,t31," } {MPLTEXT 1 0 84 "2*(t12-t32)*(t12-t22),0,0,t12*(3*t11-t21-t31)-(t12+t2 2+t32)*t11+ t22*t31+t32*t21,0,0" }{MPLTEXT 1 0 4 ")); " }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 52 "simplify(hdotcheckqfunction(t12,t22,t32,t11,t 21,t31," }{MPLTEXT 1 0 84 "0,2*(t22-t12)*(t22-t32),0,0,t22*(3*t21-t11- t31)- (t12+t22+t32)*t21+t12*t31+t32*t11,0" }{MPLTEXT 1 0 4 ")); " } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 52 "simplify(hdotcheckqfunction(t12, t22,t32,t11,t21,t31," }{MPLTEXT 1 0 84 "0,0,2*(t32-t12)*(t32-t22),0,0, t32*(3*t31-t11-t21)- (t12+t22+t32)*t31+t12*t21+t22*t11" }{MPLTEXT 1 0 5 ")); \n" }{MPLTEXT 1 0 67 "simplify(hdotcheckpfunction(t12,t22,t32,t 11,t21,t31,1,1,1,0,0,0));\n" }{MPLTEXT 1 0 67 "simplify(hdotcheckpfunc tion(t12,t22,t32,t11,t21,t31,0,0,0,1,1,1));\n" }{MPLTEXT 1 0 85 "simpl ify(hdotcheckpfunction(t12,t22,t32,t11,t21,t31,2*t12,2*t22,2*t32,t11,t 21,t31));\n" }{MPLTEXT 1 0 74 "simplify(hdotcheckpfunction(t12,t22,t32 ,t11,t21,t31,0,0,0,t12,t22,t32)); \n" }{MPLTEXT 1 0 141 "simplify(hdot checkpfunction(t12,t22,t32,t11,t21,t31,2*(t12-t32)*(t12-t22),0,0,t12*( 3*t11-t21-t31)-(t12+t22+t32)*t11+ t22*t31+t32*t21,0,0)); \n" }{MPLTEXT 1 0 141 "simplify(hdotcheckpfunction(t12,t22,t32,t11,t21,t31,0,2*(t22 -t12)*(t22-t32),0,0,t22*(3*t21-t11-t31)- (t12+t22+t32)*t21+t12*t31+t32 *t11,0)); \n" }{MPLTEXT 1 0 136 "simplify(hdotcheckpfunction(t12,t22,t 32,t11,t21,t31,0,0,2*(t32-t12)*(t32-t22),0,0,t32*(3*t31-t11-t21)- (t12 +t22+t32)*t31+t12*t21+t22*t11" }{MPLTEXT 1 0 3 "));" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "hdotcheckqtaufunction:=unapp ly(" }{MPLTEXT 1 0 28 "simplify(hdotcheckqfunction(" }{MPLTEXT 1 0 32 "t12,t22,t32,t11,t21,t31,0,0,0,0," }{MPLTEXT 1 0 8 "Coefft21" } {MPLTEXT 1 0 1 "," }{MPLTEXT 1 0 8 "Coefft31" }{MPLTEXT 1 0 8 ")),q,p) :" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 117 "hdotcheckptaufunction:=unap ply(simplify(hdotcheckpfunction(t12,t22,t32,t11,t21,t31,0,0,0,0,Coefft 21,Coefft31)),q,p):\n" }{MPLTEXT 1 0 41 "hdotcheckqtaufunction2:=unapp ly(simplify(" }{MPLTEXT 1 0 60 "hdotcheckqtaufunction(Solq,Solp)),t11, t21,t31,t12,t22,t32):\n" }{MPLTEXT 1 0 74 "hdotcheckptaufunction2:=una pply(simplify(hdotcheckptaufunction(Solq,Solp))" }{MPLTEXT 1 0 24 ",t1 1,t21,t31,t12,t22,t32" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 24 "hdotch eckqtau:=simplify(" }{MPLTEXT 1 0 23 "hdotcheckqtaufunction2(" } {MPLTEXT 1 0 78 "t11function,t21function ,t31function ,t12function ,t2 2function ,t32function));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 126 "hdo tcheckptau:=simplify(hdotcheckptaufunction2(t11function,t21function ,t 31function ,t12function ,t22function ,t32function));\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 14 "hdotcheckqtau-" }{MPLTEXT 1 0 13 "Ltau checkq);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 26 "hdotcheckpta u-Ltaucheckp);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I.hdotcheckqtauG6\"*. *(,(I#T3GF$!\"\"I#T5GF$!\"#I#T1GF$\"\"\"F-,&F(F-F*F)F),(F(F+F*F)F,F-F) #F)\"\"#*(F'F-F.F-F/F-#F-F1,&*(I'checkqGF$F-,&**I'checkpGF$F-F'F-F/F-* (F.F-F'F)F/F)F3F+*&I$tauGF$F-F2F3F-F-F&F3F-*&,&*$F6F1F)I$t20GF$F-F-F'F -F-F-F'F)F.F)F/F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I.hdotcheckptauG6 \"*.,(*.*(,&I#T3GF$\"\"\"I#T5GF$!\"\"F+,(F*F-F,!\"#I#T1GF$F+F-,(F*F/F, F-F0F+F-#F+\"\"#I'checkpGF$F+I'checkqGF$F+F)F+F1F+*(F.F+F)F-F1F-F2F3** F(F2*(F.F+F)F+F1F+F2F4F+I$tauGF$F+F-*&F)F+,**$F4F3F+I\"hGF$F+I$t20GF$F -I$t30GF$F-F+F+F+F8F2F(#F-F3F.F-F)F-F1F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 218 209 "The Hamiltonian in the only non-trivial direction is independent of the values of the trivial times. \nThus, we may tak e some arbitrary values to obtain it since Maple is struggling to simp lify the square roots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "hd otcheckqtauValues:=unapply(" }{MPLTEXT 1 0 30 "hdotcheckqtau,T1,T2,T3, T4,T5):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 60 "hdotcheckptauValues:=u napply(hdotcheckptau,T1,T2,T3,T4,T5):\n" }{MPLTEXT 1 0 20 "hdotcheckqt auFinal:=" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 36 "hdotcheckqtau Values(0,0,0,0,-1/2));\n" }{MPLTEXT 1 0 20 "hdotcheckptauFinal:=" } {MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 36 "hdotcheckptauValues(0,0,0 ,0,-1/2));\n" }{MPLTEXT 1 0 108 "HamtaucheckCoordinatesTheo:=-(checkq* checkp^2+checkq^2*checkp-tau*checkq*checkp-t20*checkp+(t10+h)*checkq); \n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 24 "hdotcheckqtauFinal-d iff(" }{MPLTEXT 1 0 36 "HamtaucheckCoordinatesTheo,checkp));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 60 "hdot checkptauFinal+diff(HamtaucheckCoordinatesTheo,checkq));" }}{PARA 11 " " 1 "" {XPPMATH 20 ">I3hdotcheckqtauFinalG6\",(*$I'checkqGF$\"\"#!\"\" *&,&I$tauGF$\"\"\"I'checkpGF$!\"#F-F'F-F-I$t20GF$F-" }}{PARA 11 "" 1 " " {XPPMATH 20 ">I3hdotcheckptauFinalG6\",,*$I'checkpGF$\"\"#\"\"\"*&,& I$tauGF$!\"\"I'checkqGF$F(F)F'F)F)I\"hGF$F)I$t20GF$F-I$t30GF$F-" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I;HamtaucheckCoordinatesTheoG6\",,*&I'c heckqGF$\"\"\"I'checkpGF$\"\"#!\"\"*&F'F*F)F(F+*(I$tauGF$F(F'F(F)F(F(* &I$t20GF$F(F)F(F(*&,(I\"hGF$F(F0F+I$t30GF$F+F(F'F(F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "S2:=1/sqrt(2)*sqrt(s12-s22); \n" }{MPLTEXT 1 0 4 "S1:=" }{MPLTEXT 1 0 20 "1/sqrt(2)*(s11-s21)/" } {MPLTEXT 1 0 15 "sqrt(s12-s22);\n" }{MPLTEXT 1 0 52 "tdX1function:=una pply(S2*X1+S1,s11,s21,s12,s22,X1);\n" }{MPLTEXT 1 0 167 "RES:=unapply( simplify(series(simplify(tdX1function(t31/(t32-t22),t11/(t12-t22),-1/ (t32-t22),-1/(t12-t22),t21) -1/sqrt(2)*taufunction(t11,t21,t31,t12,t2 2,t32)),t21))," }{MPLTEXT 1 0 24 "t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 3 " ;\n" }{MPLTEXT 1 0 19 "RES(2,4,3,-1,0,1);\n" }{MPLTEXT 1 0 19 "RES(2,4,3,1,0,-1);\n" }{MPLTEXT 1 0 28 "tdX1:=1/sqrt(2)*taufunction(" }{MPLTEXT 1 0 25 "t11,t21,t31,t12,t22,t32):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#S2G6\",$*&\"\"##\"\"\"F',&I$s12GF$F)I$s22GF$!\"\"F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#S1G6\",$*(\"\"##\"\"\"F',&I$s11GF$ F)I$s21GF$!\"\"F),&I$s12GF$F)I$s22GF$F-#F-F'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-tdX1functionG6\"f*6'I$s11GF$I$s21GF$I$s12GF$I$s22GF$I# X1GF$F$6$I)operatorGF$I&arrowGF$F$,&*(\"\"##\"\"\"F1,&9&F39'!\"\"F29(F 3F2*(F1F2,&9$F39%F7F3F4#F7F1F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I$RESG6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)op eratorGF$I&arrowGF$F$+'9%,$*0,&*(,&9(\"\"\"9)!\"\"F8,&9'F8F7F:F8*(,&F< F8F9F:F8F6F:F;F:#F8\"\"#F:*$*(F>F8F6F8F;F8F?F8F8F=#F:F@FBFC,(*&F7F8,&9 $F89&F:F8F8*&FHF8FF8F@F?,& F5F8FAF:F8F=FCFBFCF6F:F;F:FCF8F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "R1:=unapply((sX10+sX20)/(xi-X1) -(s12+s22)*xi-s11 -s21,xi);\n" }{MPLTEXT 1 0 20 "checkqfunction(q,p);" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 58 "checkqidfunction:=unapply(checkqfunction(p,q+t22 *p),q,p):\n" }{MPLTEXT 1 0 28 "checkqidfunction2:=unapply( " }{MPLTEXT 1 0 67 "checkqidfunction((checkq-S1)/S2,S2*checkp+1/2*R1((checkq-S1)/ S2)), " }{MPLTEXT 1 0 31 "s11,s21,s12,s22,X1,sX10,sX20):\n" }{MPLTEXT 1 0 16 "simplify(series(" }{MPLTEXT 1 0 18 "checkqidfunction2(" } {MPLTEXT 1 0 81 "t31/(t32-t22),t11/(t12-t22),-1/(t32-t22),-1/(t12-t22) ,t21,-s10-s20,0),checkq ));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "R ES2:=unapply( simplify(series(" }{MPLTEXT 1 0 18 "checkqidfunction2(" }{MPLTEXT 1 0 111 "t31/(t32-t22),t11/(t12-t22),-1/(t32-t22),-1/(t12-t2 2),t21,-s10-s20,0)- (-sqrt(2)*(checkq-1/sqrt(2)*taufunction(" } {MPLTEXT 1 0 23 "t11,t21,t31,t12,t22,t32" }{MPLTEXT 1 0 3 ")))" } {MPLTEXT 1 0 10 ",checkq=0)" }{MPLTEXT 1 0 3 " )," }{MPLTEXT 1 0 24 "t 11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 20 "RES2( 2,4,3,-1,0,1);\n" }{MPLTEXT 1 0 19 "RES2(2,4,3,1,0,-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#R1G6\"f*6#I#xiGF$F$6$I)operatorGF$I&arrowGF$F$,* *&,&I%sX10GF$\"\"\"I%sX20GF$F/F/,&9$F/I#X1GF$!\"\"F4F/*&,&I$s12GF$F/I$ s22GF$F/F/F2F/F4I$s11GF$F4I$s21GF$F4F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&*(,&I$t12G6\"\"\"\"I$t32GF&!\"\"F',&F%F)I$t22GF&F'F),&F +F)F(F'F)#F'\"\"#,(*&I\"qGF&F'F+F'F'I\"pGF&F)I$t21GF&F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "+'I'checkqG6\",$*(,(*&I$t12GF$\"\"\",&I$t21GF$!\" \"I$t31GF$F*F*F**&,&I$t11GF$F-F,F*F*I$t32GF$F*F**&I$t22GF$F*,&F1F*F.F- F*F*F**(,&F)F*F2F-F*,&F4F*F2F-F-,&F)F*F4F-F-#F*\"\"#F7F-F-\"\"!,$*$F;F :F-F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%RES2G6\"f*6(I$t11GF$I$t21GF$ I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF$I&arrowGF$F$+%I'check qGF$**,(*&*(,&9'\"\"\"9)!\"\"F8,&9(F8F9F:F:,&F7F8FF:F7F8F9F:F8F@#F:F?,(*&F7F8,&9%F:9&F8F8F8*&,&FEF89$F:F8F9F8F8 *&F " 0 "" {MPLTEXT 1 0 21 "checkqfunction(q,p);\n" }{MPLTEXT 1 0 58 "checkp idfunction:=unapply(checkpfunction(p,q+t22*p),q,p):\n" }{MPLTEXT 1 0 126 "checkpidfunction2:=unapply( checkpidfunction((checkq-S1)/S2,S2*ch eckp+1/2*R1((checkq-S1)/S2)), s11,s21,s12,s22,X1,sX10,sX20):\n" } {MPLTEXT 1 0 8 "checkpid" }{MPLTEXT 1 0 2 ":=" }{MPLTEXT 1 0 114 "simp lify(series(checkpidfunction2(t31/(t32-t22),t11/(t12-t22),-1/(t32-t22) ,-1/(t12-t22),t21,-s10-s20,0),checkp ))" }{MPLTEXT 1 0 2 ":\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 69 "checkpidbis:=-1/sqrt(2)*(checkp- (s10+s20)/2/(checkq-tdX1)-checkq );\n" }{MPLTEXT 1 0 41 "simplify(ser ies(simplify(series(simplify(" }{MPLTEXT 1 0 9 "checkpid-" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 49 "checkpidbis),checkp),symbolic),checkq),sym bolic);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&*(,&I$t12G6\"\"\"\"I$t32GF& !\"\"F',&F%F)I$t22GF&F'F),&F+F)F(F'F)#F'\"\"#,(*&I\"qGF&F'F+F'F'I\"pGF &F)I$t21GF&F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,checkpidbisG6\",$* &\"\"##\"\"\"F',(I'checkpGF$F)*&,&I$s10GF$F)I$s20GF$F)F),&I'checkqGF$F )*(F'F(,(*&,&I$t21GF$F)I$t31GF$!\"\"F)I$t12GF$F)F)*&,&I$t11GF$F8F7F)F) I$t22GF$F)F)*&I$t32GF$F),&F " 0 "" {MPLTEXT 1 0 44 "HamtaucheckCoordina tesTheofunction:=unapply(" }{MPLTEXT 1 0 45 "HamtaucheckCoordinatesThe o,checkq,checkp,tau)" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 66 "dtaufunction:=diff(taufunction(t11,t21,t31,t12,t22,t3 2),t11)*dt11+" }{MPLTEXT 1 0 52 "diff(taufunction(t11,t21,t31,t12,t22, t32),t21)*dt21+" }{MPLTEXT 1 0 52 "diff(taufunction(t11,t21,t31,t12,t2 2,t32),t31)*dt31+" }{MPLTEXT 1 0 52 "diff(taufunction(t11,t21,t31,t12, t22,t32),t12)*dt12+" }{MPLTEXT 1 0 52 "diff(taufunction(t11,t21,t31,t1 2,t22,t32),t22)*dt22+" }{MPLTEXT 1 0 53 "diff(taufunction(t11,t21,t31, t12,t22,t32),t32)*dt32:\n" }{MPLTEXT 1 0 5 "delta" }{MPLTEXT 1 0 49 "H amtaucheckCoordinatesTheodeltatau:=unapply(diff(" }{MPLTEXT 1 0 52 "Ha mtaucheckCoordinatesTheo,tau),checkq,checkp,tau):\n" }{MPLTEXT 1 0 18 "OmegaHam:=unapply(" }{MPLTEXT 1 0 53 "HamtaucheckCoordinatesTheofunct ion(checkq,checkp,tau)" }{MPLTEXT 1 0 13 "*dtaufunction" }{MPLTEXT 1 0 21 ",checkq,checkp,tau):\n" }{MPLTEXT 1 0 17 "OmegaR2:=unapply(" } {MPLTEXT 1 0 1 "-" }{MPLTEXT 1 0 109 "int(deltaHamtaucheckCoordinatesT heodeltatau(checkq(s),checkp(s),s),s=0..tau)*dtaufunction,checkq,check p,tau);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "OmegaHambis:=simplify( " }{MPLTEXT 1 0 8 "OmegaHam" }{MPLTEXT 1 0 1 "(" }{MPLTEXT 1 0 52 "che ckqfunction(q,p),checkpfunction(q,p),taufunction(" }{MPLTEXT 1 0 23 "t 11,t21,t31,t12,t22,t32" }{MPLTEXT 1 0 5 "))):\n" }{MPLTEXT 1 0 38 "Ome gaHamNonReduced:=Hame11(q,p)*dt11+ " }{MPLTEXT 1 0 17 "Hame21(q,p)*dt2 1+" }{MPLTEXT 1 0 17 "Hame31(q,p)*dt31+" }{MPLTEXT 1 0 17 "Hame12(q,p) *dt12+" }{MPLTEXT 1 0 17 "Hame22(q,p)*dt22+" }{MPLTEXT 1 0 17 "Hame32( q,p)*dt32:" }}{PARA 11 "" 1 "" {XPPMATH 20 ">ICHamtaucheckCoordinatesT heofunctionG6\"f*6%I'checkqGF$I'checkpGF$I$tauGF$F$6$I)operatorGF$I&ar rowGF$F$,,*&9$\"\"\"9%\"\"#!\"\"*&F/F2F1F0F3*(F/F0F1F09&F0F0*&I$t20GF$ F0F1F0F0*&,(I\"hGF$F0F8F3I$t30GF$F3F0F/F0F3F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(OmegaR2G6\"f*6%I'checkqGF$I'checkpGF$I$tauGF$F$6$I)ope ratorGF$I&arrowGF$F$,$*&-I$intG6$%*protectedGI(_syslibGF$6$*&-9%6#I\"s GF$\"\"\"-9$F8F:/F9;\"\"!9&F:,.*(,&I$t22GF$!\"\"I$t32GF$F:F:*(,&I$t12G F$FEFDF:F:,&FIF:FFFEF:FCF:#FE\"\"#I%dt11GF$F:F:*(FJF:FGFKI%dt21GF$F:F: *(FHF:FGFKI%dt31GF$F:F:*&,&*&,&I$t21GF$F:I$t31GF$FEF:FGFKF:*(,(*&FUF:F IF:F:*&,&I$t11GF$FEFWF:F:FDF:F:*&FFF:,&FgnF:FVFEF:F:F:FG#!\"$FL,&*&FJF :FCF:FE*&FHF:FCF:F:F:FKF:I%dt12GF$F:F:*&,&*&FfnF:FGFKF:*(FYF:FGFjn,&F] oF:*&FHF:FJF:FEF:FKF:I%dt22GF$F:F:*&,&*&FinF:FGFKF:*(FYF:FGFjn,&F^oFEF eoF:F:FKF:I%dt32GF$F:F:F:FEF$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "simplify(residue(simplify(" }{MPLTEXT 1 0 38 "OmegaHa mbis)/dt11^2,dt11=0),symbolic);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "simplify(Hame11(q,p));\n" }{MPLTEXT 1 0 25 "simplify(series(simpli fy(" }{MPLTEXT 1 0 68 "simplify(residue(simplify(OmegaHambis)/dt11^2,d t11=0),symbolic) -( -" }{MPLTEXT 1 0 24 "Hame11(q,p) -h*(p-t22*q)" } {MPLTEXT 1 0 11 "/(t12-t22)+" }{MPLTEXT 1 0 16 "h*t21/(t12-t22)-" } {MPLTEXT 1 0 4 "t11*" }{MPLTEXT 1 0 122 "t21*t31/((t12-t32)*(t12-t22)) +(-t12*t21+(-t11+t21)*t32+t11*t22)*t20/((t12-t32)*(t12-t22)) -t21*t30 /(t12-t22) ) ),t30=0))" }{MPLTEXT 1 0 1 ";" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,4*$I\"pG6\"\"\"$!\"\"*&,*I$t11GF&\"\"\"I$t21GF&F,I$t31 GF&F,*&,(I$t12GF&F,I$t22GF&F,I$t32GF&F,F,I\"qGF&F,F,F,F%\"\"#F,*&,0*&, &*&,&F2F(F3F(F,F1F,F,*&F2F,F3F,F(F,F4F5F,*&,(*&,&F-F(F+F(F,F3F,F,*&,&F .F(F-F(F,F1F,F,*&F2F,,&F+F,F.F,F,F(F,F4F,F,*&,(I\"hGF&F,I$t20GF&F(I$t3 0GF&F(F,F1F,F,*&,&FGF(FIF,F,F3F,F,*&FHF,F2F,F,*&,&F+F(F.F(F,F-F,F,*&F+ F,F.F,F(F,F%F,F,**F4F'F1F,F2F,F3F,F,*&,&*&,&*&F-F,F3F,F,*&F2F,F.F,F,F, F1F,F,*(F2F,F3F,F+F,F,F,F4F5F,*&,(*&,(*&FHF,F3F,F,*&FKF,F2F,F,*&F-F,F. F,F,F,F1F,F,*&,&*&FFF,F2F,F,*&F+F,F-F,F,F,F3F,F,*(F2F,F+F,F.F,F,F,F4F, F,*(F-F,FFF,F1F,F(*&,&*&F-F,FFF,F,*&F+F,FHF,F,F,F3F,F,*&F+F,,&FLF(FhnF ,F,F,F,,&F1F,F2F(F(,&F1F(F3F,F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,** $I\"pG6\"\"\"$\"\"\"*&,**&,(I$t12GF&!\"\"I$t22GF&F.I$t32GF&F.F(I\"qGF& F(F(I$t31GF&F.I$t11GF&F.I$t21GF&F.F(F%\"\"#F(*&,0*&,&*&,&F/F(F0F(F(F-F (F(*&F/F(F0F(F(F(F1F5F(*&,(*&F-F(,&F4F(F2F(F(F(*&F/F(,&F3F(F2F(F(F(*&F 0F(,&F3F(F4F(F(F(F(F1F(F(*&,&I$t20GF&F(I$t30GF&F(F(F-F(F(*&FGF(F/F(F.* &FHF(F0F(F.*&F3F(F@F(F(*&F4F(F2F(F(F(F%F(F(*&F1F(,,**F1F5F-F(F/F(F0F(F (*&,&*&,&*&F4F(F0F(F(*&F/F(F2F(F(F(F-F(F(*(F/F(F0F(F3F(F(F(F1F(F(*&,(* &FGF(F0F(F(FLF(*&F/F(FHF(F(F(F-F(F(*&,&*&,&FGF.FHF.F(F0F(F(*&F3F(F2F(F (F(F/F(F(*(F0F(F3F(F4F(F(F(F.F(,&F-F.F0F(F.,&F-F(F/F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "simplify(residue(simplify(OmegaHambis)/dt21^2,dt21=0),symbolic);\n" } {MPLTEXT 1 0 23 "simplify(Hame21(q,p));\n" }{MPLTEXT 1 0 69 "simplify( series(simplify(residue(simplify(OmegaHambis)/dt21^2,dt21=0)" } {MPLTEXT 1 0 9 ",symbolic" }{MPLTEXT 1 0 19 ") -( -Hame21(q,p) +" } {MPLTEXT 1 0 21 "h*(p-t12*q)/(t12-t22)" }{MPLTEXT 1 0 9 ") ,q=0));" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,4*$I\"pG6\"\"\"$ \"\"\"*&,**&,(I$t12GF&!\"\"I$t22GF&F.I$t32GF&F.F(I\"qGF&F(F(I$t31GF&F. I$t11GF&F.I$t21GF&F.F(F%\"\"#F(*&,0*&,&*&,&F-F(F/F(F(F0F(F(*&F-F(F/F(F (F(F1F5F(*&,(*&F-F(,&F4F(F2F(F(F(*&F/F(,&F3F(F2F(F(F(*&F0F(,&F3F(F4F(F (F(F(F1F(F(*&,&I\"hGF&F(I$t30GF&F.F(F0F(F(*&,(FGF.I$t20GF&F(FHF(F(F-F( F(*&FKF(F/F(F.*&FBF(F4F(F(*&F3F(F2F(F(F(F%F(F(**F1F'F-F(F/F(F0F(F.*&,& *&,&*&F3F(F/F(F.*&F-F(F4F(F.F(F0F(F(*(F2F(F-F(F/F(F.F(F1F5F(*&,(*&,(*& FKF(F-F(F.*&FJF(F/F(F(*&F3F(F4F(F.F(F0F(F(*&,&*&FFF(F/F(F(*&F4F(F2F(F. F(F-F(F(*(F/F(F3F(F2F(F.F(F1F(F(*&,&*&FJF(F4F(F(*&F3F(FKF(F.F(F0F(F(*( F4F(,(FGF(FKF.FHF.F(F-F(F(*&F3F(,&FLF.F[oF(F(F.F(,&F-F(F/F.F.,&F/F.F0F (F." }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,**$I\"pG6\"\"\"$!\"\"*&,*I$t11 GF&\"\"\"I$t21GF&F,I$t31GF&F,*&,(I$t12GF&F,I$t22GF&F,I$t32GF&F,F,I\"qG F&F,F,F,F%\"\"#F,*&,0*&,&*&,&F1F(F3F(F,F2F,F,*&F1F,F3F,F(F,F4F5F,*&,(* &,&F.F(F-F(F,F1F,F,*&,&F+F(F.F(F,F2F,F,*&F3F,,&F+F,F-F,F,F(F,F4F,F,*&, &I\"hGF&F(I$t20GF&F,F,F2F,F,*&,(FGF,FHF(I$t30GF&F(F,F1F,F,*&FKF,F3F,F, *&F@F,F+F,F,*&F-F,F.F,F(F,F%F,F,*&,,**F4F5F1F,F2F,F3F,F(*&,&*&,&*&F+F, F3F,F(*&F1F,F.F,F(F,F2F,F,*(F1F,F-F,F3F,F(F,F4F,F,*&,(*&F1F,FKF,F(*&,( FGF(FHF,FKF,F,F3F,F,*&F+F,F.F,F(F,F2F,F,*&,&*&,&FGF,FHF(F,F3F,F,FNF(F, F1F,F,*(F3F,F+F,F-F,F(F,F4F,F(F,,&F1F,F2F(F(,&F2F(F3F,F(" }}{PARA 11 " " 1 "" {XPPMATH 20 "+%I\"qG6\"*(,&*&,(*&,(I\"hGF$\"\"\"I$t20GF$!\"\"I$ t30GF$F.F,I$t32GF$F,F,*&,(F+F.F-F,F/F,F,I$t12GF$F,F,*&I$t11GF$F,I$t31G F$F,F,F,I$t21GF$F,F,*(F5F,F-F,,&I$t22GF$F,F0F.F,F.F,F9F.,&F3F,F:F.F.\" \"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "simplify(residue(sim plify(OmegaHambis)/dt31^2,dt31=0),symbolic);\n" }{MPLTEXT 1 0 23 "simp lify(Hame31(q,p));\n" }{MPLTEXT 1 0 104 "simplify(series(simplify(resi due(simplify(OmegaHambis)/dt31^2,dt31=0),symbolic) -( -Hame31(q,p)) ,q =0));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,4*$I\"pG6 \"\"\"$\"\"\"*&,**&,(I$t12GF&!\"\"I$t22GF&F.I$t32GF&F.F(I\"qGF&F(F(I$t 31GF&F.I$t11GF&F.I$t21GF&F.F(F%\"\"#F(*&,0*&,&*&,&F-F(F/F(F(F0F(F(*&F- F(F/F(F(F(F1F5F(*&,(*&F-F(,&F4F(F2F(F(F(*&F/F(,&F3F(F2F(F(F(*&F0F(,&F3 F(F4F(F(F(F(F1F(F(*&,&I\"hGF&F(I$t30GF&F.F(F0F(F(*&,(FGF.I$t20GF&F(FHF (F(F-F(F(*&FKF(F/F(F.*&FBF(F4F(F(*&F3F(F2F(F(F(F%F(F(**F1F'F-F(F/F(F0F (F.*&,&*&,&*&F3F(F/F(F.*&F-F(F4F(F.F(F0F(F(*(F2F(F-F(F/F(F.F(F1F5F(*&, (*&,(*&FKF(F-F(F.*&FJF(F/F(F(*&F3F(F4F(F.F(F0F(F(*&,&*&FFF(F/F(F(*&F4F (F2F(F.F(F-F(F(*(F/F(F3F(F2F(F.F(F1F(F(*&,&*&FJF(F4F(F(*&F3F(FKF(F.F(F 0F(F(*(F4F(,(FGF(FKF.FHF.F(F-F(F(*&F3F(,&FLF.F[oF(F(F.F(,&F/F.F0F(F.,& F-F.F0F(F." }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,**$I\"pG6\"\"\"$!\"\"*& ,*I$t11GF&\"\"\"I$t21GF&F,I$t31GF&F,*&,(I$t12GF&F,I$t22GF&F,I$t32GF&F, F,I\"qGF&F,F,F,F%\"\"#F,*&,0*&,&*&,&F1F(F2F(F,F3F,F,*&F1F,F2F,F(F,F4F5 F,*&,(*&,&F-F(F+F(F,F3F,F,*&,&F.F(F-F(F,F1F,F,*&F2F,,&F+F,F.F,F,F(F,F4 F,F,*&,&I\"hGF&F(I$t30GF&F,F,F3F,F,*&,(FGF,I$t20GF&F(FHF(F,F1F,F,*&FKF ,F2F,F,*&FBF,F+F,F,*&F-F,F.F,F(F,F%F,F,*&F4F,,,**F4F5F1F,F2F,F3F,F,*&, &*&,&*&F+F,F2F,F,*&F1F,F-F,F,F,F3F,F,*(F.F,F1F,F2F,F,F,F4F,F,*&,(*&FKF ,F1F,F,*&FJF,F2F,F,*&F+F,F-F,F,F,F3F,F,*&,&*&FFF,F2F,F,FNF,F,F1F,F,*(F 2F,F+F,F.F,F,F,F,F,,&F2F(F3F,F(,&F1F(F3F,F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "+%I\"qG6\"*(,&*&,(*&,(I\"hGF$!\"\"I$t20GF$\"\"\"I$t30GF$F .F.I$t32GF$F.F.*&,(F+F.F-F,F/F,F.I$t12GF$F.F.*&I$t11GF$F.I$t31GF$F.F,F .I$t21GF$F.F.*(F5F.F-F.,&I$t22GF$F.F0F,F.F.F.F9F,,&F3F.F0F,F,\"\"!" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "simplify(residue(simplify(O megaHambis)/dt12^2,dt12=0),symbolic):\n" }{MPLTEXT 1 0 23 "simplify(Ha me12(q,p)):\n" }{MPLTEXT 1 0 384 "simplify(series(simplify(residue(sim plify(OmegaHambis)/dt12^2,dt12=0),symbolic) -( -Hame12(q,p) -(1/2)*h*p ^2/((t12-t22)*(t12-t32))) - (1/2)*(-q*t22^2+(q*t12-q*t32-t11-t21)*t22+ (q*t32+2*t11)*t12-t32*(t11-t21))*h/((t12-t22)^2*(t12-t32))*p +(1/2)*h* t22*t32*q^2/((t12-t22)*(t12-t32)) +(((t11-(1/2)*t21)*t22+(1/2)*t32* t21)*t12-(1/2)*t11*t22*(t22+t32))*h*q/((t12-t22)^2*(t12-t32)),q=0));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "+%I\"qG6\",$**,&*&, (*&,(I\"hGF$!\"\"I$t20GF$\"\"\"I$t30GF$F/F/I$t32GF$F/F/*&,(F,F/F.F-F0F -F/I$t12GF$F/F/*&I$t11GF$F/I$t31GF$F/F-F/I$t21GF$F/F/*(F6F/F.F/,&I$t22 GF$F/F1F-F/F/F/,**&,&F4#F-\"\"#F1#F/F@F/F8F/F/*&,&F6F/F7F?F/F4F/F/*&F6 F/F1F/F?*&F;F/,&F6F/F7F-F/F?F/,&F4F/F1F-!\"#,&F4F/F;F-FHF-\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "simplify(residue(simplify(Om egaHambis)/dt32^2,dt32=0),symbolic):\n" }{MPLTEXT 1 0 23 "simplify(Ham e32(q,p)):\n" }{MPLTEXT 1 0 96 "simplify(series(simplify(residue(simpl ify(OmegaHambis)/dt32^2,dt32=0),symbolic) -( -Hame32(q,p)\n" }{MPLTEXT 1 0 181 "-(1/2)*h*p^2/((t22-t32)*(t12-t32))+(1/2)*((t12+t22)*q+t11+t2 1)*h*p/((t22-t32)*(t12-t32))-(1/2)*h*t12*t22*q^2/((t22-t32)*(t12-t32)) -(1/2)*h*(t11*t22+t12*t21)*q/((t22-t32)*(t12-t32))\n" }{MPLTEXT 1 0 8 "),q=0));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "+%I\"qG6 \",$**,**&,&I$t12GF$\"\"\"I$t32GF$!\"\"F+I$t21GF$F+F+*&,&I$t11GF$F-I$t 31GF$\"\"#F+F,F+F+*&,&F*F-I$t22GF$F-F+F2F+F+*&F1F+F6F+F+F+,&*&,(*&,(I \"hGF$F-I$t20GF$F+I$t30GF$F+F+F,F+F+*&,(F=F+F>F-F?F-F+F*F+F+*&F1F+F2F+ F-F+F.F+F+*(F1F+F>F+,&F6F+F,F-F+F+F+FD!\"#F)FE#F-F3\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 218 94 "We do not care about the term only propo rtional to times. Thus, we find OmegaHambis= - Hame11-" }{TEXT 218 33 "-h*(p-t22*q-t21)/(t12-t22) +times" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "simplify(checkqfunction(q,p)*" }{MPLTEXT 1 0 22 "chec kpfunction(q,p));\n" }{MPLTEXT 1 0 91 "checkqcheckpbis:=-1/(t12-t22)*( p^2- ((t12+t22)*q+(t11+t21))*p +(t12*q+t11)*(t22*q+t21) );\n" } {MPLTEXT 1 0 25 "series(simplify(simplify(" }{MPLTEXT 1 0 50 "checkqfu nction(q,p)*checkpfunction(q,p),symbolic)-" }{MPLTEXT 1 0 1 " " } {MPLTEXT 1 0 22 "checkqcheckpbis),q=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$***(,&I$t12G6\"\"\"\"I$t32GF'!\"\"F(,&I$t22GF'F(F)F*F*,&F&F(F,F* F*#F(\"\"#,(*&I\"qGF'F(F,F(F*I\"pGF'F(I$t21GF'F*F(*(F+F(F%F*F-F*F.,(*& F2F(F&F(F*F3F(I$t11GF'F*F(F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0check qcheckpbisG6\",$*&,&I$t12GF$\"\"\"I$t22GF$!\"\"F+,(*$I\"pGF$\"\"#F)*&, (*&,&F(F)F*F)F)I\"qGF$F)F)I$t11GF$F)I$t21GF$F)F)F.F)F+*&,&*&F4F)F(F)F) F5F)F),&*&F4F)F*F)F)F6F)F)F)F)F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\" !" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "diff(checkqcheckpbis,t 11);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "diff(checkqcheckpbis,t21) ;\n" }{MPLTEXT 1 0 26 "diff(checkqcheckpbis,t31);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&I$t12G6\"\"\"\"I$t22GF&!\"\"F),(*&I\"qGF&F'F(F'F'I \"pGF&F)I$t21GF&F'F'F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&I$t12G6 \"\"\"\"I$t22GF&!\"\"F),(*&I\"qGF&F'F%F'F'I\"pGF&F)I$t11GF&F'F'F)" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 287 63 "Expression of the Lax matrix in the coordinates (checkq,checkp )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "tdL21functioninter:=un apply(tdL[2,1],q,p);\n" }{MPLTEXT 1 0 89 "tdL21function:=unapply(simpl ify(tdL21functioninter(Solq,Solp)),t11,t21,t31,t12,t22,t32):\n" } {MPLTEXT 1 0 26 "tdL21check:=unapply(1/a12*" }{MPLTEXT 1 0 57 "(t22-t1 2)*(-checkq*checkp-checkq^2+tau*checkq+t20),tau):\n" }{MPLTEXT 1 0 16 "simplify(series(" }{MPLTEXT 1 0 23 "tdL21check(taufunction(" } {MPLTEXT 1 0 25 "t11,t21,t31,t12,t22,t32))" }{MPLTEXT 1 0 1 "-" } {MPLTEXT 1 0 14 "tdL21function(" }{MPLTEXT 1 0 46 "t11,t21,t31,t12,t22 ,t32),checkp=0),symbolic);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 43 "t dL23functioninter:=unapply(tdL[2,3],q,p);\n" }{MPLTEXT 1 0 89 "tdL23fu nction:=unapply(simplify(tdL23functioninter(Solq,Solp)),t11,t21,t31,t1 2,t22,t32):\n" }{MPLTEXT 1 0 84 "tdL23check:=unapply(-a13/a12*sqrt(t32 -t22)*sqrt(t22-t12)/sqrt(t12-t32)*checkq,tau):\n" }{MPLTEXT 1 0 125 "s implify(series(tdL23check(taufunction(t11,t21,t31,t12,t22,t32))-tdL23f unction(t11,t21,t31,t12,t22,t32),checkp=0),symbolic);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 43 "tdL31functioninter:=unapply(tdL[3,1],q,p); \n" }{MPLTEXT 1 0 89 "tdL31function:=unapply(simplify(tdL31functionint er(Solq,Solp)),t11,t21,t31,t12,t22,t32):\n" }{MPLTEXT 1 0 26 "tdL31che ck:=unapply( 1/a13" }{MPLTEXT 1 0 11 "*(t12-t32)*" }{MPLTEXT 1 0 1 "(" }{MPLTEXT 1 0 38 "-checkq*checkp-checkq^2+tau*checkq-t30" }{MPLTEXT 1 0 9 ") ,tau):\n" }{MPLTEXT 1 0 125 "simplify(series(tdL31check(taufu nction(t11,t21,t31,t12,t22,t32))-tdL31function(t11,t21,t31,t12,t22,t32 ),checkp=0),symbolic);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 43 "tdL32 functioninter:=unapply(tdL[3,2],q,p);\n" }{MPLTEXT 1 0 89 "tdL32functi on:=unapply(simplify(tdL32functioninter(Solq,Solp)),t11,t21,t31,t12,t2 2,t32):\n" }{MPLTEXT 1 0 29 "tdL32check:=unapply( a12/a13*" }{MPLTEXT 1 0 42 "sqrt(t12-t32)*sqrt(t32-t22)/sqrt(t22-t12)*" }{MPLTEXT 1 0 31 " (checkp+1*checkq+1*tau) ,tau):\n" }{MPLTEXT 1 0 16 "simplify(series(" }{MPLTEXT 1 0 144 "simplify(series(tdL32check(taufunction(t11,t21,t31, t12,t22,t32))-tdL32function(t11,t21,t31,t12,t22,t32),checkp=0),symboli c),checkq=0),symbolic);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3tdL21funct ioninterG6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$**,&I$t12GF $\"\"\"I$t22GF$!\"\"F/,(*&,**&9$\"\"#I$t32GF$F/F/*&9%F/F6F/F1*&F6F/I$t 31GF$F/F/I$t20GF$F1F/F0F/F/*&,(F9F1*&F6F/I$t21GF$F/F/F=F/F/F8F/F/*&,&F :F/FI3tdL23functi oninterG6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,$*(I$a12GF$ !\"\"I$a13GF$\"\"\",(*&9$F1I$t22GF$F1F/9%F1I$t21GF$F/F1F/F$F$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I3tdL31functioninterG6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F $,$**,&I$t12GF$\"\"\"I$t32GF$!\"\"F0,(*&,**&9$\"\"#I$t22GF$F0F0*&9%F0F 7F0F2*&F7F0I$t21GF$F0F0I$t30GF$F2F0F1F0F0*&,(F:F2*&F7F0I$t31GF$F0F0F>F 0F0F9F0F0*&,&F;F0FBF2F0,&F;F0F=F2F0F0F0I$a13GF$F2,&F9F0F1F2F2F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3tdL32functioninterG6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowG F$F$,$*(I$a12GF$\"\"\",(*&9$F/I$t32GF$F/!\"\"9%F/I$t31GF$F4F/I$a13GF$F 4F4F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "+'I'checkqG6\",$**,(*&I$t22 GF$\"\"\",&I$t11GF$F*I$t31GF$!\"\"F*F**&I$t12GF$F*,&I$t21GF$F.F-F*F*F* *&I$t32GF$F*,&F,F*F2F.F*F.F*I$a12GF$F*I$a13GF$F.,&F0F*F)F.F.!\"#\"\"!, $*,F6F*F7F.,&F0F*F4F.#F*\"\"#,&F)F.F4F*F>,&F0F.F)F*#F.F?F9F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "GeneralSpectralCurve:=simpli fy(Determinant(y*IdentityMatrix(3)-tdL)):\n" }{MPLTEXT 1 0 100 "Genera lSpectralCurvebis:=y^3-P1(lambda)*y^2+P2(lambda)*y-P3(lambda)- (p^3-P1 (q)*p^2+P2(q)*p-P3(q)):\n" }{MPLTEXT 1 0 25 "simplify(series(simplify( " }{MPLTEXT 1 0 21 "GeneralSpectralCurve-" }{MPLTEXT 1 0 31 "GeneralSp ectralCurvebis),y=0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT 290 178 "Definition of the auxiliary mat rix A by gauge transformation of \\td\{A\} and verification of the com patibility equation in the oper gauge. Verification of the gauge trans formations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "LalphaG:=Matri x(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 \+ do\n" }{MPLTEXT 1 0 287 " LalphaG[i,j]:=simplify( h*diff(G[i,j],t12)*d ott12+h*diff(G[i,j],t22)*dott22+h*diff(G[i,j],t32)*dott32+h*diff(G[i,j ],t11)*dott11+h*diff(G[i,j],t21)*dott21+h*diff(G[i,j],t31)*dott31+h*di ff(G[i,j],a12)*dota12+h*diff(G[i,j],a13)*dota13+ h*diff(G[i,j],q)*dotq +h*diff(G[i,j],p)*dotp): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "LalphatdL:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do\n" }{MPLTEXT 1 0 309 " L alphatdL[i,j]:=simplify( h*diff(tdL[i,j],t12)*dott12+h*diff(tdL[i,j],t 22)*dott22+h*diff(tdL[i,j],t32)*dott32+h*diff(tdL[i,j],t11)*dott11+h*d iff(tdL[i,j],t21)*dott21+h*diff(tdL[i,j],t31)*dott31+h*diff(tdL[i,j],a 12)*dota12+h*diff(tdL[i,j],a13)*dota13+ h*diff(tdL[i,j],q)*dotq+h*diff (tdL[i,j],p)*dotp): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "LalphaLnew:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do\n" }{MPLTEXT 1 0 7 " Lalpha" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 24 "[i,j]:=simplify( h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 25 "[i,j],t12)*dott12+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 25 "[i,j],t22)*dott22+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 25 "[i,j],t32)*dott32+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 25 "[i,j],t11)*dott11+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 25 "[i,j],t21)*dott21+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 25 "[i,j],t31)*dott31+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 25 "[i,j],a12)*dota12+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 26 "[i,j],a13)*dota13+ h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 21 "[i,j],q)*dotq+h*diff(" } {MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 23 "[i,j],p)*dotp): od: od:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "dGdlambda:= Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 \+ to 3 do\n" }{MPLTEXT 1 0 9 "dGdlambda" }{MPLTEXT 1 0 35 "[i,j]:=diff(G [i,j],lambda): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 28 "dtdAdlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 90 "for \+ i from 1 to 3 do for j from 1 to 3 do dtdAdlambda[i,j]:=diff(tdA[i,j], lambda): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 24 "LalphaL:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do\n" }{MPLTEXT 1 0 287 " LalphaL[i,j]:=simplify ( h*diff(L[i,j],t12)*dott12+h*diff(L[i,j],t22)*dott22+h*diff(L[i,j],t3 2)*dott32+h*diff(L[i,j],t11)*dott11+h*diff(L[i,j],t21)*dott21+h*diff(L [i,j],t31)*dott31+h*diff(L[i,j],a12)*dota12+h*diff(L[i,j],a13)*dota13+ h*diff(L[i,j],q)*dotq+h*diff(L[i,j],p)*dotp): od: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Verification0:= simplify(L- ( Mult iply(Multiply(G,tdL),G^(-1))+h*Multiply(" }{MPLTEXT 1 0 9 "dGdlambda" }{MPLTEXT 1 0 11 ",G^(-1))));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 44 " Verification1:=simplify(LalphatdL-h*dtdLdt);" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 87 "Verification2:=simplify(h*dtdAdlambda-LalphatdL- Mult iply(tdL,tdA)+Multiply(tdA,tdL) );" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "Verification2bis:=simplify(" }{MPLTEXT 1 0 10 "LalphatdL-" } {MPLTEXT 1 0 15 "h*dtdAdlambda-(" }{MPLTEXT 1 0 18 "Multiply(tdA,tdL)- " }{MPLTEXT 1 0 22 " Multiply(tdL,tdA)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6 '-I%mrowGF$6#-I'mtableGF$67-I$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'/%+columnspanGFJF4F4FAFDFFF1F 1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/align mentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1 .0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o /%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-eq ualcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/ %%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfenc edG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtabl eGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/ %,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalign GFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FB Q)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%, columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacin gGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-frames pacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-disp laystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&close GQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6 \"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$ mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'norm alF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGQ\"1F' /%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rig htF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%autoF' /%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlin esGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5ex F'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sideG FS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_sy slibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\" 0F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/ %,columnalignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4F AFDFFF1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF' /%/alignmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFen/%+rowspa cingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnl inesGF`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&fals eF'/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minlabelspacingG F]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "A:=simplify( Multiply(Multiply(G,tdA),G^(-1))+Multipl y(LalphaG,G^(-1))):\n" }{MPLTEXT 1 0 26 "dAdlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 86 "for i from 1 to 3 do for j from 1 to 3 do dAdlambda[ i,j]:=diff(A[i,j],lambda): od: od:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "Verification3:= simplify(A- ( Mult iply(Multiply(G,tdA),G^(-1))+Multiply(" }{MPLTEXT 1 0 7 "LalphaG" } {MPLTEXT 1 0 11 ",G^(-1))));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 76 "V erification4:=simplify(h*dAdlambda-LalphaL- Multiply(L,A)+Multiply(A,L )) ;\n" }{MPLTEXT 1 0 81 "Verification4bis:=simplify( LalphaL-h*dAdlam bda-(Multiply(A,L)- Multiply(L,A)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6 #-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([ 0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+g roupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ% axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ% trueF'/%,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.col umnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o /%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGF jo/%-displaystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F '/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modu lenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtr GF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%,mathvarian tGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspa nGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ)baselineF' /FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthG Q%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/ %)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-framespacingGQ,0.4 em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-displaystyleGFjo /%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#m nGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowal ignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+columnspa nGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|fr left|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFen /%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/ %,columnlinesGF`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equalro wsGQ&falseF'/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minlabe lspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "dAnewdlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do " }{MPLTEXT 1 0 50 "dAne wdlambda[i,j]:=diff(Anew[i,j],lambda): od: od:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 70 "Verification5:= simplify(Anew- ( Multiply(Multiply(Gnormalized,tdA),G" }{MPLTEXT 1 0 10 "normalized" }{MPLTEXT 1 0 18 "^(-1))+Multiply(LG" }{MPLTEXT 1 0 10 "normalized" } {MPLTEXT 1 0 2 ",G" }{MPLTEXT 1 0 10 "normalized" }{MPLTEXT 1 0 10 "^( -1))));\n" }{MPLTEXT 1 0 93 "Verification6:=simplify(h*dAnewdlambda-La lphaLnew- Multiply(Lnew,Anew)+Multiply(Anew,Lnew)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/% +foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,col umnalignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFF F1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/al ignmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingG Q&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesG F`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/% -equalcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF; F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mf encedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mt ableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0] F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupal ignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1F1/%&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'" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 290 78 "Expression of th e auxiliary matrices in the various directions of deformations" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "tdAfunction[1,1]:=unapply(td A[1,1],dott12,dott22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 11 "tdAfunction" }{MPLTEXT 1 0 5 "[1,2]" }{MPLTEXT 1 0 19 ":=unapply(t dA[1,2]," }{MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 11 "tdAfunction" }{MPLTEXT 1 0 5 "[1,3]" }{MPLTEXT 1 0 19 ":=unapply(tdA[1,3]," }{MPLTEXT 1 0 41 "dot t12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" } {MPLTEXT 1 0 11 "tdAfunction" }{MPLTEXT 1 0 5 "[2,1]" }{MPLTEXT 1 0 19 ":=unapply(tdA[2,1]," }{MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11 ,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 11 "tdAfunction" }{MPLTEXT 1 0 5 "[2,2]" }{MPLTEXT 1 0 19 ":=unapply(tdA[2,2]," } {MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 11 "tdAfunction" }{MPLTEXT 1 0 5 "[2,3]" } {MPLTEXT 1 0 19 ":=unapply(tdA[2,3]," }{MPLTEXT 1 0 41 "dott12,dott22, dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 11 " tdAfunction" }{MPLTEXT 1 0 5 "[3,1]" }{MPLTEXT 1 0 19 ":=unapply(tdA[3 ,1]," }{MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" } {MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 11 "tdAfunction" }{MPLTEXT 1 0 5 " [3,2]" }{MPLTEXT 1 0 19 ":=unapply(tdA[3,2]," }{MPLTEXT 1 0 41 "dott12 ,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 11 "tdAfunction" }{MPLTEXT 1 0 5 "[3,3]" }{MPLTEXT 1 0 19 ":=unapp ly(tdA[3,3]," }{MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dot t31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "Afun ction" }{MPLTEXT 1 0 5 "[1,1]" }{MPLTEXT 1 0 17 ":=unapply(A[1,1]," } {MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afunction" }{MPLTEXT 1 0 5 "[1,2]" } {MPLTEXT 1 0 17 ":=unapply(A[1,2]," }{MPLTEXT 1 0 41 "dott12,dott22,do tt32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afu nction" }{MPLTEXT 1 0 5 "[1,3]" }{MPLTEXT 1 0 17 ":=unapply(A[1,3]," } {MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afunction" }{MPLTEXT 1 0 5 "[2,1]" } {MPLTEXT 1 0 17 ":=unapply(A[2,1]," }{MPLTEXT 1 0 41 "dott12,dott22,do tt32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afu nction" }{MPLTEXT 1 0 5 "[2,2]" }{MPLTEXT 1 0 17 ":=unapply(A[2,2]," } {MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afunction" }{MPLTEXT 1 0 5 "[2,3]" } {MPLTEXT 1 0 17 ":=unapply(A[2,3]," }{MPLTEXT 1 0 41 "dott12,dott22,do tt32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afu nction" }{MPLTEXT 1 0 5 "[3,1]" }{MPLTEXT 1 0 17 ":=unapply(A[3,1]," } {MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afunction" }{MPLTEXT 1 0 5 "[3,2]" } {MPLTEXT 1 0 17 ":=unapply(A[3,2]," }{MPLTEXT 1 0 41 "dott12,dott22,do tt32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "Afu nction" }{MPLTEXT 1 0 5 "[3,3]" }{MPLTEXT 1 0 17 ":=unapply(A[3,3]," } {MPLTEXT 1 0 41 "dott12,dott22,dott32,dott11,dott21,dott31" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "Anewfunction[1,1]: =unapply(" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 50 "[1,1],dott12,dott2 2,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 23 "function[1,2]:=unapply(" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 50 "[1,2],dott12,dott22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 23 "function[1,3]:=unapply(" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 50 "[1,3],dott12,dott22,dott32,dott11,dott21,dott 31):\n" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 23 "function[2,1]:=unappl y(" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 50 "[2,1],dott12,dott22,dott3 2,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 23 "f unction[2,2]:=unapply(" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 50 "[2,2] ,dott12,dott22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 23 "function[2,3]:=unapply(" }{MPLTEXT 1 0 4 "Anew" } {MPLTEXT 1 0 50 "[2,3],dott12,dott22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 23 "function[3,1]:=unapply(" } {MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 50 "[3,1],dott12,dott22,dott32,dot t11,dott21,dott31):\n" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 23 "functi on[3,2]:=unapply(" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 50 "[3,2],dott 12,dott22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 4 "Anew" } {MPLTEXT 1 0 23 "function[3,3]:=unapply(" }{MPLTEXT 1 0 4 "Anew" } {MPLTEXT 1 0 47 "[3,3],dott12,dott22,dott32,dott11,dott21,dott31" } {MPLTEXT 1 0 2 "):" }{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 288 151 "Specialisation in different directions of the tangent s pace. We also assume from now on that a_\{1,2\} and a_\{1,3\} are inde pendent to the irregular times" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tdA110:=0:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "dota12:=0; \n" }{MPLTEXT 1 0 11 "dota13:=0;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "tdAvinfty1:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 69 "for i from 1 to \+ 3 do for j from 1 to 3 do tdAvinfty1[i,j]:= simplify(" }{MPLTEXT 1 0 17 "tdAfunction[i,j](" }{MPLTEXT 1 0 11 "0,0,0,1,1,1" }{MPLTEXT 1 0 12 ")): od: od:\n" }{MPLTEXT 1 0 27 "tdAvinfty2:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 60 "for i from 1 to 3 do for j from 1 to 3 do tdAvinfty2[ i,j]:= " }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 18 "tdAfunction[i,j ](1" }{MPLTEXT 1 0 10 ",1,1,0,0,0" }{MPLTEXT 1 0 12 ")): od: od:\n" } {MPLTEXT 1 0 27 "tdAuinfty1:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 86 "for i from 1 to 3 do for j from 1 to 3 do tdAuinfty1[i,j]:= simplify(tdAfun ction[i,j](" }{MPLTEXT 1 0 29 "0,0,0,t12,t22,t32)): od: od:\n" } {MPLTEXT 1 0 27 "tdAuinfty2:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 86 "for i from 1 to 3 do for j from 1 to 3 do tdAuinfty2[i,j]:= simplify(tdAfun ction[i,j](" }{MPLTEXT 1 0 29 "2*t12,2*t22,2*t32,t11,t21,t31" } {MPLTEXT 1 0 11 ")): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "t dAa1:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 81 "for i from 1 to 3 do for j f rom 1 to 3 do tdAa1[i,j]:= simplify(tdAfunction[i,j](" }{MPLTEXT 1 0 84 "2*(t12-t32)*(t12-t22),0,0,t12*(3*t11-t21-t31)-(t12+t22+t32)*t11+ t 22*t31+t32*t21,0,0" }{MPLTEXT 1 0 11 ")): od: od:" }{MPLTEXT 1 0 1 "\n " }{MPLTEXT 1 0 22 "tdAa2:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 81 "for i f rom 1 to 3 do for j from 1 to 3 do tdAa2[i,j]:= simplify(tdAfunction[i ,j](" }{MPLTEXT 1 0 2 "0," }{MPLTEXT 1 0 48 "2*(t22-t12)*(t22-t32),0,0 ,t22*(3*t21-t11-t31)- (" }{MPLTEXT 1 0 34 "t12+t22+t32)*t21+t12*t31+t3 2*t11,0" }{MPLTEXT 1 0 12 ")): od: od:\n" }{MPLTEXT 1 0 22 "tdAa3:=Mat rix(3,3,0):\n" }{MPLTEXT 1 0 81 "for i from 1 to 3 do for j from 1 to \+ 3 do tdAa3[i,j]:= simplify(tdAfunction[i,j](" }{MPLTEXT 1 0 84 "0,0,2* (t32-t12)*(t32-t22),0,0,t32*(3*t31-t11-t21)- (t12+t22+t32)*t31+t12*t21 +t22*t11" }{MPLTEXT 1 0 11 ")): od: od:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 23 "tdAe11:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 104 "for i fr om 1 to 3 do for j from 1 to 3 do tdAe11[i,j]:= simplify(tdAfunction[i ,j](0,0,0,1,0,0)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "tdA e21:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 105 "for i from 1 to 3 do for j f rom 1 to 3 do tdAe21[i,j]:= simplify(tdAfunction[i,j](0,0,0,0,1,0)): o d: od:\n" }{MPLTEXT 1 0 23 "tdAe31:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 104 "for i from 1 to 3 do for j from 1 to 3 do tdAe31[i,j]:= simplify( tdAfunction[i,j](0,0,0,0,0,1)): od: od:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "tdAe12:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 105 "for i from 1 to 3 do for j from 1 to 3 do tdAe12[i,j ]:= simplify(tdAfunction[i,j](1,0,0,0,0,0)): od: od:\n" }{MPLTEXT 1 0 23 "tdAe22:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 105 "for i from 1 to 3 do \+ for j from 1 to 3 do tdAe22[i,j]:= simplify(tdAfunction[i,j](0,1,0,0,0 ,0)): od: od:\n" }{MPLTEXT 1 0 23 "tdAe32:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 104 "for i from 1 to 3 do for j from 1 to 3 do tdAe32[i,j]:= simp lify(tdAfunction[i,j](0,0,1,0,0,0)): od: od:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "tdAtau:=Mat rix(3,3,0):\n" }{MPLTEXT 1 0 100 "for i from 1 to 3 do for j from 1 to 3 do tdAtau[i,j]:= simplify(tdAfunction[i,j](0,0,0,0,Coefftau,-" } {MPLTEXT 1 0 8 "Coefftau" }{MPLTEXT 1 0 11 ")): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "Anewe2:=Matrix(3,3,0): \n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do " } {MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 19 "e2[i,j]:= simplify(" }{MPLTEXT 1 0 4 "Anew" }{MPLTEXT 1 0 36 "function[i,j](0,0,0,0,1,0)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "d" } {MPLTEXT 1 0 6 "tdAtau" }{MPLTEXT 1 0 24 "dlambda:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 43 "for i from 1 to 3 do for j from 1 to 3 do d" } {MPLTEXT 1 0 6 "tdAtau" }{MPLTEXT 1 0 19 "dlambda[i,j]:=diff(" } {MPLTEXT 1 0 6 "tdAtau" }{MPLTEXT 1 0 22 "[i,j],lambda): od: od:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "dtdAe31dlam bda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 96 "for i from 1 to 3 do for j fr om 1 to 3 do dtdAe31dlambda[i,j]:=diff(tdAe31[i,j],lambda): od: od:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "dtdAe21dlam bda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 96 "for i from 1 to 3 do for j fr om 1 to 3 do dtdAe21dlambda[i,j]:=diff(tdAe21[i,j],lambda): od: od:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "dtdAnewdlam bda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j fr om 1 to 3 do " }{MPLTEXT 1 0 14 "dtdAnewdlambda" }{MPLTEXT 1 0 40 "[i, j]:=diff(Anewe2[i,j],lambda): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 25 "Avinfty1:=Matrix(3,3 ,0):\n" }{MPLTEXT 1 0 67 "for i from 1 to 3 do for j from 1 to 3 do Av infty1[i,j]:= simplify(" }{MPLTEXT 1 0 15 "Afunction[i,j](" }{MPLTEXT 1 0 11 "0,0,0,1,1,1" }{MPLTEXT 1 0 12 ")): od: od:\n" }{MPLTEXT 1 0 25 "Avinfty2:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 83 "for i from 1 to 3 do for j from 1 to 3 do Avinfty2[i,j]:= simplify(Afunction[i,j](1" } {MPLTEXT 1 0 10 ",1,1,0,0,0" }{MPLTEXT 1 0 12 ")): od: od:\n" } {MPLTEXT 1 0 25 "Auinfty1:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 111 "for i \+ from 1 to 3 do for j from 1 to 3 do Auinfty1[i,j]:= simplify(Afunction [i,j](0,0,0,t12,t22,t32)): od: od:\n" }{MPLTEXT 1 0 25 "Auinfty2:=Matr ix(3,3,0):\n" }{MPLTEXT 1 0 123 "for i from 1 to 3 do for j from 1 to \+ 3 do Auinfty2[i,j]:= simplify(Afunction[i,j](2*t12,2*t22,2*t32,t11,t21 ,t31)): od: od:\n" }{MPLTEXT 1 0 20 "Aa1:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 173 "for i from 1 to 3 do for j from 1 to 3 do Aa1[i,j]:= simplify (Afunction[i,j](2*(t12-t32)*(t12-t22),0,0,t12*(3*t11-t21-t31)-(t12+t22 +t32)*t11+ t22*t31+t32*t21,0,0)): od: od:\n" }{MPLTEXT 1 0 20 "Aa2:=Ma trix(3,3,0):\n" }{MPLTEXT 1 0 173 "for i from 1 to 3 do for j from 1 t o 3 do Aa2[i,j]:= simplify(Afunction[i,j](0,2*(t22-t12)*(t22-t32),0,0, t22*(3*t21-t11-t31)- (t12+t22+t32)*t21+t12*t31+t32*t11,0)): od: od:\n" }{MPLTEXT 1 0 20 "Aa3:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 173 "for i fro m 1 to 3 do for j from 1 to 3 do Aa3[i,j]:= simplify(Afunction[i,j](0, 0,2*(t32-t12)*(t32-t22),0,0,t32*(3*t31-t11-t21)- (t12+t22+t32)*t31+t12 *t21+t22*t11)): od: od:\n" }{MPLTEXT 1 0 21 "Ae11:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 100 "for i from 1 to 3 do for j from 1 to 3 do Ae11[i,j]: = simplify(Afunction[i,j](0,0,0,1,0,0)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "Ae21:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 101 "for i fr om 1 to 3 do for j from 1 to 3 do Ae21[i,j]:= simplify(Afunction[i,j]( 0,0,0,0,1,0)): od: od:\n" }{MPLTEXT 1 0 21 "Ae31:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 100 "for i from 1 to 3 do for j from 1 to 3 do Ae31[i,j]: = simplify(Afunction[i,j](0,0,0,0,0,1)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "Ae12:=Matrix(3,3,0):\n" } {MPLTEXT 1 0 101 "for i from 1 to 3 do for j from 1 to 3 do Ae12[i,j]: = simplify(Afunction[i,j](1,0,0,0,0,0)): od: od:\n" }{MPLTEXT 1 0 21 " Ae22:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 101 "for i from 1 to 3 do for j \+ from 1 to 3 do Ae22[i,j]:= simplify(Afunction[i,j](0,1,0,0,0,0)): od: \+ od:\n" }{MPLTEXT 1 0 21 "Ae32:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 100 "fo r i from 1 to 3 do for j from 1 to 3 do Ae32[i,j]:= simplify(Afunction [i,j](0,0,1,0,0,0)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n " }{MPLTEXT 1 0 21 "Atau:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 86 "for i fr om 1 to 3 do for j from 1 to 3 do Atau[i,j]:= simplify(Afunction[i,j]( 0,0,0,0," }{MPLTEXT 1 0 8 "Coefftau" }{MPLTEXT 1 0 2 ",-" }{MPLTEXT 1 0 8 "Coefftau" }{MPLTEXT 1 0 11 ")): od: od:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 29 "dAtaudlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 93 "for i from 1 to 3 do for j from 1 to 3 do dAtaudlamb da[i,j]:=diff(Atau[i,j],lambda): od: od:\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 29 "dAe31dlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 91 "for i from 1 to 3 do for j from 1 to 3 do dAe3dlambda[i,j]:=diff(Ae31[i,j ],lambda): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 29 "dAe21dlambda:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 91 "for i from 1 to 3 do for j from 1 to 3 do dAe2dlambda[i,j]:=diff(Ae21[i,j ],lambda): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'dota12G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'dota13G6\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "tdAvinfty1;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "tdAvinfty2 ;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "tdAuinfty1:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "tdAuinfty2:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 "tdAe11:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 "tdAe21:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 "tdAe31:" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 7 "tdAa1:\n" }{MPLTEXT 1 0 6 "tdAa2:" }{MPLTEXT 1 0 1 "\n " }{MPLTEXT 1 0 6 "tdAa3:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 8 "tdAtau:\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG 6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF $67-I$mtrGF$6(-I$mtdGF$6(-I#miGF$6&Q)λF'/%'italicGQ&falseF'/%+f oregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,colum nalignGFF/%+groupalignGFF/%(rowspanGQ\"1F'/%+columnspanGFM-F56(-I#mnGF $6%Q\"0F'F>FAFDFGFIFKFNFPFDFGFI-F26(FPF4FPFDFGFI-F26(FPFPF4FDFGFI/%&al ignGQ%axisF'/FEQ)baselineF'/FHQ'centerF'/FJQ'|frleft|hrF'/%/alignments copeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFbo/%+rowspacingGQ&1.0exF '/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF]p/%&fr ameGF]p/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGF=/%-equalcolumnsGF =/%-displaystyleGF=/%%sideGQ&rightF'/%0minlabelspacingGFjoF>FA/%%openG Q\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I +modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67- I$mtrGF$6(-I$mtdGF$6(-F,6%-I&mfracGF$6)-I#mnGF$6%Q\"1F'/%+foregroundGQ ([0,0,0]F'/%,mathvariantGQ'normalF'-F=6%Q\"2F'F@FC/%.linethicknessGF?/ %+denomalignGQ'centerF'/%)numalignGFM/%)bevelledGQ&falseF'F@-I#moGF$6- Q1⁢F'FC/%&fenceGFR/%*separatorGFR/%)stretchyGFR/%*symme tricGFR/%(largeopGFR/%.movablelimitsGFR/%'accentGFR/%'lspaceGQ&0.0emF' /%'rspaceGFao-F,6#-I%msupGF$6%-I#miGF$6&Q)λF'/%'italicGFRF@FCFF /%1superscriptshiftGQ\"0F'/%)rowalignGQ!F'/%,columnalignGFdp/%+groupal ignGFdp/%(rowspanGF?/%+columnspanGF?-F56(-F=6%FapF@FCFbpFepFgpFipF[qF] qFbpFepFgp-F26(F]qF4F]qFbpFepFgp-F26(F]qF]qF4FbpFepFgp/%&alignGQ%axisF '/FcpQ)baselineF'/FfpFM/FhpQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%, columnwidthGQ%autoF'/%&widthGFbr/%+rowspacingGQ&1.0exF'/%.columnspacin gGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF]s/%&frameGF]s/%-frames pacingGQ,0.4em~0.5exF'/%*equalrowsGFR/%-equalcolumnsGFR/%-displaystyle GFR/%%sideGQ&rightF'/%0minlabelspacingGFjrF@FC/%%openGQ\"[F'/%&closeGQ \"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "simplify(series(td Aa2[1,1],lambda)):\n" }{MPLTEXT 1 0 37 "simplify(series(tdAa2[1,2],lam bda)):\n" }{MPLTEXT 1 0 37 "simplify(series(tdAa2[1,3],lambda)):\n" } {MPLTEXT 1 0 37 "simplify(series(tdAa2[2,1],lambda)):\n" }{MPLTEXT 1 0 37 "simplify(series(tdAa2[2,2],lambda)):\n" }{MPLTEXT 1 0 37 "simpli fy(series(tdAa2[2,3],lambda)):\n" }{MPLTEXT 1 0 37 "simplify(series(td Aa2[3,1],lambda)):\n" }{MPLTEXT 1 0 37 "simplify(series(tdAa2[3,2],lam bda)):\n" }{MPLTEXT 1 0 36 "simplify(series(tdAa2[3,3],lambda)):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 289 82 "Verification for direction \\part ial_\{\\tau\} and \\partial_\{e_31\} and \\partial_\{e_21\}" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "LalphatautdL:=Matrix(3,3,0): \n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do\n" } {MPLTEXT 1 0 86 "LalphatdLfunction:=unapply(LalphatdL[i,j],dott12,dott 22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 85 " LalphatautdL[i, j]:=simplify(LalphatdLfunction(0,0,0,0,Coefftau,-Coefftau)): od: od:\n " }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 29 "Lalphae31tdL:=Matrix(3,3,0): \n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do\n" } {MPLTEXT 1 0 86 "LalphatdLfunction:=unapply(LalphatdL[i,j],dott12,dott 22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 70 " Lalphae31tdL[i, j]:=simplify(LalphatdLfunction(0,0,0,0,0,1)): od: od:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 29 "Lalphae21tdL:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do\n" }{MPLTEXT 1 0 86 "LalphatdLfunction:=unapply(LalphatdL[i,j],dott12,dott22,dott32,dott11 ,dott21,dott31):\n" }{MPLTEXT 1 0 69 " Lalphae21tdL[i,j]:=simplify(Lal phatdLfunction(0,0,0,0,1,0)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 29 "Lalphae2Lnew:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do\n" }{MPLTEXT 1 0 6 "Lalpha" }{MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 24 "function:=unapply(La lpha" }{MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 50 "[i,j],dott12,dott22,dot t32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 10 " Lalphae21" }{MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 22 "[i,j]:=simplify(Lalpha" }{MPLTEXT 1 0 4 "Lnew" }{MPLTEXT 1 0 31 "function(0,0,0,0,1,0)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "LalphatauL:=Matrix(3 ,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to 3 do \n" }{MPLTEXT 1 0 82 "LalphaLfunction:=unapply(LalphaL[i,j],dott12,dot t22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 61 " LalphatauL[i,j ]:=simplify(LalphaLfunction(0,0,0,0,Coefftau,-" }{MPLTEXT 1 0 8 "Coeff tau" }{MPLTEXT 1 0 12 ")): od: od:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "Lalphae31L:=Matrix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 t o 3 do for j from 1 to 3 do\n" }{MPLTEXT 1 0 82 "LalphaLfunction:=unap ply(LalphaL[i,j],dott12,dott22,dott32,dott11,dott21,dott31):\n" } {MPLTEXT 1 0 66 " Lalphae31L[i,j]:=simplify(LalphaLfunction(0,0,0,0,0, 1)): od: od:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "Lalphae21L:=Mat rix(3,3,0):\n" }{MPLTEXT 1 0 42 "for i from 1 to 3 do for j from 1 to \+ 3 do\n" }{MPLTEXT 1 0 82 "LalphaLfunction:=unapply(LalphaL[i,j],dott12 ,dott22,dott32,dott11,dott21,dott31):\n" }{MPLTEXT 1 0 65 " Lalphae21L [i,j]:=simplify(LalphaLfunction(0,0,0,0,1,0)): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 104 "Verificationtau:=simpli fy(LalphatautdL-h*dtdAtaudlambda-(Multiply(tdAtau,tdL)- Multiply(tdL,t dAtau)) );\n" }{MPLTEXT 1 0 103 "Verificatione3:=simplify(Lalphae31tdL -h*dtdAe31dlambda-(Multiply(tdAe31,tdL)- Multiply(tdL,tdAe31)) );\n" } {MPLTEXT 1 0 102 "Verificatione2:=simplify(Lalphae21tdL-h*dtdAe21dlamb da-(Multiply(tdAe21,tdL)- Multiply(tdL,tdAe21)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF' 6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+f oregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,colum nalignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1 F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alig nmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ& 1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF` o/%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-e qualcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F> /%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfen cedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtab leGF$67-I$mtrGF$6(-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F' /%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalig nGFC/%(rowspanGQ\"1F'/%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/F BQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/% ,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspaci ngGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-frame spacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-dis playstyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&clos eGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6 \"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$ mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'norm alF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGQ\"1F' /%+columnspanGFJF4F4FAFDFFF1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rig htF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%autoF' /%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlin esGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5ex F'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sideG FS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 290 96 "Canonical choice of trivial times: t12:=1/2, t22=0, t32=-1/2, \+ t11=0 and t31=-t21 and t21=1/3*tau" }{TEXT 290 0 "" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 4 "TT1(" }{MPLTEXT 1 0 29 "0,1/3*tau,-1/3*tau,1/ 2,0,-1/2" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 4 "TT2(" }{MPLTEXT 1 0 29 "0,1/3*tau,-1/3*tau,1/2,0,-1/2" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 4 "TT3(" }{MPLTEXT 1 0 29 "0,1/3*tau,-1/3*tau,1/2,0,-1/2" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 4 "TT4(" }{MPLTEXT 1 0 29 "0,1/3*tau,-1/3*t au,1/2,0,-1/2" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 4 "TT5(" }{MPLTEXT 1 0 29 "0,1/3*tau,-1/3*tau,1/2,0,-1/2" }{MPLTEXT 1 0 3 ");\n" } {MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 45 "taufunction(0,1/3*tau,-1/ 3*tau,1/2,0,-1/2));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 28 "partialt aufunction:=unapply(" }{MPLTEXT 1 0 34 "partialtau,t11,t21,t31,t12,t22 ,t32" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 18 "partialtaufunction" }{MPLTEXT 1 0 1 "(" }{MPLTEXT 1 0 29 "0,1/3* tau,-1/3*tau,1/2,0,-1/2" }{MPLTEXT 1 0 4 "));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 25 "checkqfunctionT:=unapply(" }{MPLTEXT 1 0 20 "checkqf unction(q,p)," }{MPLTEXT 1 0 24 "t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 3 " ;\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 16 "checkqfunct ionT(" }{MPLTEXT 1 0 29 "0,1/3*tau,-1/3*tau,1/2,0,-1/2" }{MPLTEXT 1 0 4 "));\n" }{MPLTEXT 1 0 72 "checkpfunctionT:=unapply(checkpfunction(q, p),t11,t21,t31,t12,t22,t32) ;\n" }{MPLTEXT 1 0 58 "simplify(checkpfunc tionT(0,1/3*tau,-1/3*tau,1/2,0,-1/2));\n" }{MPLTEXT 1 0 58 "solve(\{-2 *p+2*tau*(1/3)=checkq,-(1/2)*q+p=checkp \},\{q,p\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "#!\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$tauG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I+partialt21 G6\"#\"\"\"\"\"$I+partialt31GF$#!\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0checkqfunctionTG6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$ I$t32GF$F$6$I)operatorGF$I&arrowGF$F$*&*(,&9'\"\"\"9)!\"\"F4,&F3F69(F4 F6,&F8F6F5F4F6#F4\"\"#,(*&I\"qGF$F4F8F4F4I\"pGF$F69%F4F4F$F$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&I\"pG6\"!\"#I$tauGF$#\"\"#\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I0checkpfunctionTG6\"f*6(I$t11GF$I$t21G F$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF$I&arrowGF$F$*&*(,&9 (!\"\"9)\"\"\"F6,&9'F4F3F6F4,&F8F6F5F4F4#F6\"\"#,(*&I\"qGF$F6F8F6F4I\" pGF$F69$F4F6F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"qG6\"#!\"\"\" \"#I\"pGF$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "<$/I\"pG6\",&I$tauGF %#\"\"\"\"\"$I'checkqGF%#!\"\"\"\"#/I\"qGF%,(F'#F.F*F+F-I'checkpGF%!\" #" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a12:=1;\n" }{MPLTEXT 1 0 8 "a13:=1;\n" }{MPLTEXT 1 0 10 "t12:=1/2;\n" }{MPLTEXT 1 0 8 "t22:=0 ;\n" }{MPLTEXT 1 0 11 "t32:=-1/2;\n" }{MPLTEXT 1 0 8 "t11:=0;\n" } {MPLTEXT 1 0 11 "t31:=-t21;\n" }{MPLTEXT 1 0 13 "t21:=1/3*tau;" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$a12G6\"\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I$a13G6\"\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$t12G6\"#\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I$t22G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$t32G6\"#!\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$t11G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$t31G6\",$I$t21GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$t21G6\",$I$tauGF$#\"\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tdL[1,1];\n" }{MPLTEXT 1 0 9 "tdL[2,2];" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "tdL[3,3];" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 16 "tdL21check(tau);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 16 "tdL23ch eck(tau);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 16 "tdL31check(tau);" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 16 "tdL32check(tau);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$I'lambdaG6\"#\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$I$tauG6\"#\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 " ,&I'lambdaG6\"#!\"\"\"\"#I$tauGF$#F&\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&I'checkpG6\"\"\"\"I'checkqGF%F&#F&\"\"#*$F'F)F(*&F'F& I$tauGF%F&#!\"\"F)I$t20GF%F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$I'chec kqG6\"#\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&I'checkpG6\"\" \"\"I'checkqGF%F&!\"\"*$F'\"\"#F(*&F'F&I$tauGF%F&F&I$t30GF%F(" }} {PARA 11 "" 1 "" {XPPMATH 20 ",(I'checkpG6\"\"\"\"I'checkqGF$F%I$tauGF $F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Coefftau:=simplify(C oefft21);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "tdAtau:=" }{MPLTEXT 1 0 18 "simplify(tdAtau):\n" }{MPLTEXT 1 0 26 "tdAtau11function:=unapp ly(" }{MPLTEXT 1 0 18 "tdAtau[1,1],q,p):\n" }{MPLTEXT 1 0 19 "tdAtau11 :=simplify(" }{MPLTEXT 1 0 71 "tdAtau11function(2*tau*(1/3)-checkq-2*c heckp,(1/3)*tau-(1/2)*checkq));\n" }{MPLTEXT 1 0 26 "tdAtau12function: =unapply(" }{MPLTEXT 1 0 18 "tdAtau[1,2],q,p):\n" }{MPLTEXT 1 0 90 "td Atau12:=simplify(tdAtau12function(2*tau*(1/3)-checkq-2*checkp,(1/3)*ta u-(1/2)*checkq));\n" }{MPLTEXT 1 0 26 "tdAtau13function:=unapply(" } {MPLTEXT 1 0 18 "tdAtau[1,3],q,p):\n" }{MPLTEXT 1 0 90 "tdAtau13:=simp lify(tdAtau13function(2*tau*(1/3)-checkq-2*checkp,(1/3)*tau-(1/2)*chec kq));\n" }{MPLTEXT 1 0 26 "tdAtau21function:=unapply(" }{MPLTEXT 1 0 18 "tdAtau[2,1],q,p):\n" }{MPLTEXT 1 0 90 "tdAtau21:=simplify(tdAtau21 function(2*tau*(1/3)-checkq-2*checkp,(1/3)*tau-(1/2)*checkq));\n" } {MPLTEXT 1 0 26 "tdAtau22function:=unapply(" }{MPLTEXT 1 0 18 "tdAtau[ 2,2],q,p):\n" }{MPLTEXT 1 0 90 "tdAtau22:=simplify(tdAtau22function(2* tau*(1/3)-checkq-2*checkp,(1/3)*tau-(1/2)*checkq));\n" }{MPLTEXT 1 0 26 "tdAtau23function:=unapply(" }{MPLTEXT 1 0 18 "tdAtau[2,3],q,p):\n" }{MPLTEXT 1 0 90 "tdAtau23:=simplify(tdAtau23function(2*tau*(1/3)-che ckq-2*checkp,(1/3)*tau-(1/2)*checkq));\n" }{MPLTEXT 1 0 26 "tdAtau31fu nction:=unapply(" }{MPLTEXT 1 0 18 "tdAtau[3,1],q,p):\n" }{MPLTEXT 1 0 90 "tdAtau31:=simplify(tdAtau31function(2*tau*(1/3)-checkq-2*checkp, (1/3)*tau-(1/2)*checkq));\n" }{MPLTEXT 1 0 26 "tdAtau32function:=unapp ly(" }{MPLTEXT 1 0 18 "tdAtau[3,2],q,p):\n" }{MPLTEXT 1 0 90 "tdAtau32 :=simplify(tdAtau32function(2*tau*(1/3)-checkq-2*checkp,(1/3)*tau-(1/2 )*checkq));\n" }{MPLTEXT 1 0 26 "tdAtau33function:=unapply(" }{MPLTEXT 1 0 18 "tdAtau[3,3],q,p):\n" }{MPLTEXT 1 0 89 "tdAtau33:=simplify(tdA tau33function(2*tau*(1/3)-checkq-2*checkp,(1/3)*tau-(1/2)*checkq));" } }{PARA 11 "" 1 "" {XPPMATH 20 ">I)CoefftauG6\"#\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAtau11G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAtau12G6\"#!\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAtau13G6\"#\"\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAt au21G6\",(*$I'checkqGF$\"\"##!\"\"\"\"$*&,&I$tauGF$\"\"\"I'checkpGF$F* F/F'F/#F/F+I$t20GF$F1" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAtau22G6\" ,*I$tauGF$#\"\"(\"\"*I'checkqGF$!\"\"I'checkpGF$F+I'lambdaGF$#\"\"\"\" \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAtau23G6\",$I'checkqGF$#\"\" #\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAtau31G6\",(*$I'checkqGF$ \"\"##!\"\"\"\"$*&,&I$tauGF$\"\"\"I'checkpGF$F*F/F'F/#F/F+I$t30GF$F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAtau32G6\",(I$tauGF$#!\"%\"\"$I'c heckqGF$#\"\"%F)I'checkpGF$F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)tdAt au33G6\",(I$tauGF$#!\"\"\"\"*I'checkqGF$F(I'lambdaGF$#F(\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "P1(lambda);\n" }{MPLTEXT 1 0 12 "P2(lambda);\n" }{MPLTEXT 1 0 11 "P3(lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*$I'lambdaG6\" \"\"##!\"\"\"\"%*&I$tauGF%\"\"\"F$F,#F(\"\"'I$t30GF%F,I$t20GF%#F,F&*$F +F&#F(\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I$tauG6\"\"\"\"I'lamb daGF%\"\"##!\"\"\"#7*&,&I$t20GF%#F*\"\"%*$F$F(#F*\"#=F&F'F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "L[3,3];\n" }{MPLTEXT 1 0 9 "s implify(" }{MPLTEXT 1 0 41 "L[3,2]-(h*p/(lambda-q)-P2(lambda)+h/2));\n " }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 89 "L[3,1]-(h*(p^2+P2(q)-h /2)/(lambda-q)+P3(lambda)+p^3+(P2(q)-h/2)*p-P3(q)+h/4*(lambda-q)));" } }{PARA 11 "" 1 "" {XPPMATH 20 ",$*&I\"hG6\"\"\"\",&I'lambdaGF%!\"\"I\" qGF%F&F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Atau: =simplify(Atau):\n" }{MPLTEXT 1 0 78 "simplify( Atau[1,1]- ( (-2*p^2-2 *P2(q)+h)/(lambda-q)+1/3*lambda+p+1/2*q) );\n" }{MPLTEXT 1 0 49 "sim plify( Atau[1,2]- ( -2*p/(lambda-q)+1/3) );\n" }{MPLTEXT 1 0 43 "sim plify( Atau[1,3]- ( -2/(lambda-q)) );\n" }{MPLTEXT 1 0 103 "simplify ( Atau[2,1]- ( p*(-2*p^2-2*P2(q)+h)/(lambda-q)+1/6*tau*lambda+tau/6*q \+ +tau^2/9+t20/2-h/6 ) );\n" }{MPLTEXT 1 0 67 "simplify( Atau[2,2]- ( - 2*p^2/(lambda-q)-1/6*lambda)-p+1/3*tau );\n" }{MPLTEXT 1 0 50 "simpli fy( Atau[2,3]- ( -2*p/(lambda-q) +1/3) );\n" }{MPLTEXT 1 0 87 "simpl ify( Atau[3,1]- (-1/3*(6*p^2-h)*(p^2+P2(q)-1/2*h)/(lambda-q)-(1/36)*ta u*lambda^2 \n" }{MPLTEXT 1 0 38 "+1/6*(tau*p-tau^2/9-t20/2+h/2)*lambda \n" }{MPLTEXT 1 0 100 "+1/6*(2*p^3-(q^2-4/3*tau*q-8/9*tau^2+8*h-8*t20- 4*t30)*p/2+tau^2/9*q+tau/6*q^2+h*tau -h/2*q+t20/2*q)\n" }{MPLTEXT 1 0 6 ") );" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 97 "simplify( Atau[3,2]- ( p*(-6*p^2+h)/3/(lambda-q)+(1/12)*lambda^2 +(-(1/2)*p+2*tau*(1/9))*l ambda \n" }{MPLTEXT 1 0 50 "+1/6*(8/9*tau^2+(-2*p+q)*tau-3*p*q-h+2*t20 -2*t30)\n" }{MPLTEXT 1 0 6 ") );" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 69 "simplify( Atau[3,3]- ( (-6*p^2+h)/3/(lambda-q) -lambda/6+p-tau/3 ) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 218 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 9 10 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }