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{TEXT 231 239 "In this Maple file, we \+ compute the evolution equations for the Painlev\351 24equation using t he compatibility equation of the Lax system. We also obtain the expres sion of the Lax matrices in the geometric gauge without apparent singu larities." }{TEXT 231 0 "" }}{PARA 0 "" 0 "" {TEXT 231 28 "The deforma tion operator is " }{TEXT 231 42 "h*(alpha12 \\partial_\{t_\{\\infty^ \{(1)\},2\}\}+ " }{TEXT 231 7 "alpha22" }{TEXT 231 31 " \\partial_\{t_ \{\\infty^\{(2)\},2\}\}+" }{TEXT 231 7 "alpha11" }{TEXT 231 31 "\\part ial_\{t_\{\\infty^\{(1)\},1\}\}+ " }{TEXT 231 7 "alpha21" }{TEXT 231 29 "\\partial_\{t_\{\\infty^\{(2)\},1\}\}" }{TEXT 231 16 " +Lt *partia l_t)" }{TEXT 231 3 ") \n" }{TEXT 230 114 "For convenience the irregula r times and monodromies are denoted t_\{i,j\} at lambda=infinity and s _\{i,j\} at lambda=t" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 102 "Summary of previous files: We have the expression for some coefficients of t he Lax matrix L and of A." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart:\n" }{MPLTEXT 1 0 20 "with(LinearAlgebra):" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 15 "P011:=s10+s20;\n" }{MPLTEXT 1 0 15 "P022:=s10*s2 0;\n" }{MPLTEXT 1 0 20 "Pinfty11:=-t12-t22;\n" }{MPLTEXT 1 0 20 "Pinft y01:=-t11-t21;\n" }{MPLTEXT 1 0 19 "Pinfty22:=t12*t22;\n" }{MPLTEXT 1 0 27 "Pinfty12:=t11*t22+t12*t21;\n" }{MPLTEXT 1 0 35 "Pinfty02:=t12*t2 0+t10*t22+t11*t21;\n" }{MPLTEXT 1 0 36 "CoherenceEquation:=t10+t20+s10 +s20;\n" }{MPLTEXT 1 0 2 " \n" }{MPLTEXT 1 0 40 "P1:=x-> P011/(x-t)+Pi nfty01+Pinfty11*x;\n" }{MPLTEXT 1 0 66 "P2:=x-> P022/(x-t)^2+P012/(x-t )+Pinfty02+Pinfty12*x+Pinfty22*x^2;\n" }{MPLTEXT 1 0 25 "tdP2:=unapply (P2(lambda)-" }{MPLTEXT 1 0 24 "P012/(lambda-t),lambda);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 48 "c2bis:=(alpha12*t22-al pha22*t12)/(2*(t12-t22));\n" }{MPLTEXT 1 0 99 "c1bis:=(1/2)*(t12*t21-t 11*t22)/(t12-t22)^2*(alpha12-alpha22)+ (alpha11*t22-alpha21*t12)/(t12- t22);\n" }{MPLTEXT 1 0 7 "mubis:=" }{MPLTEXT 1 0 109 "(1/2)*(t*(t12-t2 2)-t11+t21)*(q-t)/(-t22+t12)^2*(alpha12-alpha22)+(alpha11-alpha21)*(q- t)/(t12-t22)+(q-t)*Lt/h" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 13 "nuMin us1bis:=" }{MPLTEXT 1 0 34 "(alpha12-alpha22)/(2*(-t22+t12));\n" } {MPLTEXT 1 0 8 "nu0bis:=" }{MPLTEXT 1 0 74 "(1/2)*(t21-t11)/(t12-t22)^ 2*(alpha12-alpha22)+(alpha11-alpha21)/(t12-t22);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 53 "dP1dlambd a:=unapply(diff(P1(lambda),lambda),lambda):\n" }{MPLTEXT 1 0 53 "dP2dl ambda:=unapply(diff(P2(lambda),lambda),lambda):\n" }{MPLTEXT 1 0 18 "L :=Matrix(2,2,0):\n" }{MPLTEXT 1 0 11 "L[1,1]:=0:\n" }{MPLTEXT 1 0 11 " L[1,2]:=1:\n" }{MPLTEXT 1 0 74 "L[2,1]:=-P2(lambda)+P012/(lambda-t) +C /(lambda-t) -h*t12 -h*p/(lambda-q):\n" }{MPLTEXT 1 0 47 "L[2,2]:= P1(l ambda)-h/(lambda-t)+h/(lambda-q):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "C01:=C:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "A:=Matrix(2,2,0 ):\n" }{MPLTEXT 1 0 52 "A[1,1]:= c2*lambda^2+ c1*lambda +c0+rho/(lambd a-q):\n" }{MPLTEXT 1 0 43 "A[1,2]:=nuMinus1*lambda+nu0+mu/(lambda-q): \n" }{MPLTEXT 1 0 23 "A[2,1]:= AA21(lambda):\n" }{MPLTEXT 1 0 23 "A[2, 2]:= AA22(lambda):\n" }{MPLTEXT 1 0 26 "dAdlambda:=Matrix(2,2,0):\n" } {MPLTEXT 1 0 87 "for i from 1 to 2 do for j from 1 to 2 do dAdlambda[i ,j]:=diff(A[i,j],lambda): od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 3 "L;\n" }{MPLTEXT 1 0 3 "A;\n" }{MPLTEXT 1 0 4 "Q2:=" }{MPLTEXT 1 0 25 "unapply(-p*(q-t),lambda):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "J:=Matrix(2,2,0):\n" }{MPLTEXT 1 0 11 "J[1,1]:= 1:\n" }{MPLTEXT 1 0 11 "J[1,2]:=0:\n" }{MPLTEXT 1 0 31 "J[2,1]:=Q2(lam bda)/(lambda-q):\n" }{MPLTEXT 1 0 33 "J[2,2]:=(lambda-t)^1/(lambda-q): \n" }{MPLTEXT 1 0 3 "J;\n" }{MPLTEXT 1 0 26 "dJdlambda:=Matrix(2,2,0): \n" }{MPLTEXT 1 0 87 "for i from 1 to 2 do for j from 1 to 2 do dJdlam bda[i,j]:=diff(J[i,j],lambda): od: od:\n" }{MPLTEXT 1 0 3 "J:\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "LJ:=Matrix(2,2,0):\n" }{MPLTEXT 1 0 12 "LJ[1,1]:=0:\n" }{MPLTEXT 1 0 12 "LJ[1,2]:=0:\n" }{MPLTEXT 1 0 66 "LJ[2,2]:=diff(J[2,2],q)*Lq+diff(J[2,2],p)*Lp+h*diff(J[2,2],t)*Lt: \n" }{MPLTEXT 1 0 66 "LJ[2,1]:=diff(J[2,1],q)*Lq+diff(J[2,1],p)*Lp+h*d iff(J[2,1],t)*Lt:\n" }{MPLTEXT 1 0 4 "LJ:\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 79 "checkL:=simplify(Multiply(Multiply(J,L),J^(-1))+h*Mul tiply(dJdlambda,J^(-1))):\n" }{MPLTEXT 1 0 69 "checkA:=simplify(Multip ly(Multiply(J,A),J^(-1))+Multiply(LJ,J^(-1))):" }{MPLTEXT 1 0 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%P011G6\",&I$s10GF$\"\"\"I$s20GF$F'" } }{PARA 11 "" 1 "" {XPPMATH 20 ">I%P022G6\"*&I$s10GF$\"\"\"I$s20GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty11G6\",&I$t12GF$!\"\"I$t22GF$ F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty01G6\",&I$t11GF$!\"\"I$t2 1GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty22G6\"*&I$t12GF$\"\" \"I$t22GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty12G6\",&*&I$t11 GF$\"\"\"I$t22GF$F(F(*&I$t12GF$F(I$t21GF$F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty02G6\",(*&I$t10GF$\"\"\"I$t22GF$F(F(*&I$t11GF$F( I$t21GF$F(F(*&I$t12GF$F(I$t20GF$F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I2CoherenceEquationG6\",*I$t10GF$\"\"\"I$t20GF$F'I$s10GF$F'I$s20GF$F' " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P1G6\"f*6#I\"xGF$F$6$I)operatorGF $I&arrowGF$F$,(*&I%P011GF$\"\"\",&9$F.I\"tGF$!\"\"F2F.I)Pinfty01GF$F.* &I)Pinfty11GF$F.F0F.F.F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P2G6 \"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$,,*&I%P022GF$\"\"\",&9$F.I\" tGF$!\"\"!\"#F.*&I%P012GF$F.F/F2F.I)Pinfty02GF$F.*&I)Pinfty12GF$F.F0F. F.*&I)Pinfty22GF$F.F0\"\"#F.F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I %tdP2G6\"f*6#I'lambdaGF$F$6$I)operatorGF$I&arrowGF$F$,.*(I$s10GF$\"\" \"I$s20GF$F.,&9$F.I\"tGF$!\"\"!\"#F.*&I$t10GF$F.I$t22GF$F.F.*&I$t11GF$ F.I$t21GF$F.F.*&I$t12GF$F.I$t20GF$F.F.*&,&*&F9F.F7F.F.*&FI&c2bi sG6\"*&,&*&I(alpha12GF$\"\"\"I$t22GF$F)F)*&I(alpha22GF$F)I$t12GF$F)!\" \"F),&F-\"\"#F*!\"#F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&c1bisG6\",&* (,&*&I$t11GF$\"\"\"I$t22GF$F*!\"\"*&I$t12GF$F*I$t21GF$F*F*F*,&F.F*F+F, !\"#,&I(alpha12GF$F*I(alpha22GF$F,F*#F*\"\"#*&,&*&I(alpha11GF$F*F+F*F* *&I(alpha21GF$F*F.F*F,F*F0F,F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&mub isG6\",(**,(*&I\"tGF$\"\"\",&I$t12GF$F*I$t22GF$!\"\"F*F*I$t11GF$F.I$t2 1GF$F*F*,&I\"qGF$F*F)F.F*F+!\"#,&I(alpha12GF$F*I(alpha22GF$F.F*#F*\"\" #*(,&I(alpha11GF$F*I(alpha21GF$F.F*F1F*F+F.F**(F1F*I#LtGF$F*I\"hGF$F.F *" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,nuMinus1bisG6\"*&,&I(alpha12GF$ \"\"\"I(alpha22GF$!\"\"F(,&I$t12GF$\"\"#I$t22GF$!\"#F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'nu0bisG6\",&*(,&I$t21GF$\"\"\"I$t11GF$!\"\"F),&I$ t12GF$F)I$t22GF$F+!\"#,&I(alpha12GF$F)I(alpha22GF$F+F)#F)\"\"#*&,&I(al pha11GF$F)I(alpha21GF$F+F)F,F+F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(m fencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'm tableGF$66-I$mtrGF$6'-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0 ]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupa lignGFC/%(rowspanGQ\"1F'/%+columnspanGFJ-F56(-F86%FJF;F>FAFDFFFHFKFAFD FF-F26'-F56(-F,64-I#moGF$6.Q*&uminus0;F'F;F>/%&fenceGQ&falseF'/%*separ atorGFgn/%)stretchyGFgn/%*symmetricGFgn/%(largeopGFgn/%.movablelimitsG Fgn/%'accentGFgn/%'lspaceGQ,0.2222222emF'/%'rspaceGFfo-I&mfracGF$6)-F, 6%-I#miGF$6&Q$s10F'/%'italicGQ%trueF'F;/F?Q'italicF'-FX6-Q1&InvisibleT imes;F'F>FenFhnFjnF\\oF^oF`oFbo/FeoQ&0.0emF'/FhoF[q-F_p6&Q$s20F'FbpF;F ep-F,6#-I%msupGF$6%-F#6%-F,6%-F_p6&Q)λF'/FcpFgnF;F>-FX6.Q(&minu s;F'F;F>FenFhnFjnF\\oF^oF`oFboFdoFgo-F_p6&Q\"tF'FbpF;FepF;F>-F86%Q\"2F 'F;F>/%1superscriptshiftGF:/%.linethicknessGFJ/%+denomalignGQ'centerF' /%)numalignGF\\s/%)bevelledGFgnF;F]r-F,6%-F_p6&Q$t10F'FbpF;FepFgp-F_p6 &Q$t22F'FbpF;FepF]r-F,6%-F_p6&Q$t11F'FbpF;FepFgp-F_p6&Q$t21F'FbpF;FepF ]r-F,6%-F_p6&Q$t12F'FbpF;FepFgp-F_p6&Q$t20F'FbpF;FepF]r-F,6%-F#6%-F,6% -F,6%F[tFgpFfs-FX6.Q\"+F'F;F>FenFhnFjnF\\oF^oF`oFboFdoFgo-F,6%FctFgpF^ tF;F>FgpFiqF]r-F,6'FctFgpFfsFgp-Fcq6%FiqFcrFfrFau-Fjo6)-F,6#-F_p6&Q\"C F'FbpF;Fep-F,6#FgqFhrFjrF]sF_sF;F]r-F,6%-F_p6&Q\"hF'FbpF;FepFgpFctF]r- Fjo6)-F,6%FevFgp-F_p6&Q\"pF'FbpF;Fep-F,6#-F,6%FiqF]r-F_p6&Q\"qF'FbpF;F epFhrFjrF]sF_sF;FAFDFFFHFK-F56(-F,6--Fjo6)-F,6#-F,6%F^pFauF]qFavFhrFjr F]sF_sF;F]rF[tF]rF^tFau-F,6%-F#6%-F,6&FWFctF]rFfsF;F>FgpFiqF]r-Fjo6)-F ,6#FevFavFhrFjrF]sF_sF;Fau-Fjo6)FhxF_wFhrFjrF]sF_sF;FAFDFFFHFKFAFDFF/% &alignGQ%axisF'/FBQ)baselineF'/FEF\\s/FGQ'|frleft|hrF'/%/alignmentscop eGFdp/%,columnwidthGQ%autoF'/%&widthGFhy/%+rowspacingGQ&1.0exF'/%.colu mnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFcz/%&frameGFcz/ %-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFgn/%-equalcolumnsGFgn/%-di splaystyleGFgn/%%sideGQ&rightF'/%0minlabelspacingGF`zF;F>/%%openGQ\"[F '/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modu lenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$66-I$mtr GF$6'-I$mtdGF$6(-F,6)-F,6%-I#miGF$6&Q#c2F'/%'italicGQ%trueF'/%+foregro undGQ([0,0,0]F'/%,mathvariantGQ'italicF'-I#moGF$6-Q1⁢F' /FFQ'normalF'/%&fenceGQ&falseF'/%*separatorGFP/%)stretchyGFP/%*symmetr icGFP/%(largeopGFP/%.movablelimitsGFP/%'accentGFP/%'lspaceGQ&0.0emF'/% 'rspaceGFin-I%msupGF$6%-F<6&Q)λF'/F@FPFBFL-I#mnGF$6%Q\"2F'FBFL/ %1superscriptshiftGQ\"0F'-FI6.Q\"+F'FBFLFNFQFSFUFWFYFen/FhnQ,0.2222222 emF'/F[oF^p-F,6%-F<6&Q#c1F'F?FBFEFHF_oFjo-F<6&Q#c0F'F?FBFEFjo-I&mfracG F$6)-F,6#-F<6&Q&ρF'FboFBFL-F,6#-F,6%F_o-FI6.Q(−F'FBFLFNFQFSF UFWFYFenF]pF_p-F<6&Q\"qF'F?FBFE/%.linethicknessGQ\"1F'/%+denomalignGQ' centerF'/%)numalignGF_r/%)bevelledGFPFB/%)rowalignGQ!F'/%,columnalignG Ffr/%+groupalignGFfr/%(rowspanGF\\r/%+columnspanGF\\r-F56(-F,6'-F,6%-F <6&Q)nuMinus1F'F?FBFEFHF_oFjo-F<6&Q&ν0F'F?FBFEFjo-Fip6)-F,6#-F<6&Q% μF'FboFBFLF`qFjqF]rF`rFbrFBFdrFgrFirF[sF]sFdrFgrFir-F26'-F56(-F,6%- F<6&Q%AA21F'F?FBFE-FI6-Q0⁡F'FLFNFQFSFUFWFYFenFgnFjn-F#6% -F,6#F_oFBFLFdrFgrFirF[sF]s-F56(-F,6%-F<6&Q%AA22F'F?FBFEF[uF^uFdrFgrFi rF[sF]sFdrFgrFir/%&alignGQ%axisF'/FerQ)baselineF'/FhrF_r/FjrQ'|frleft| hrF'/%/alignmentscopeGFA/%,columnwidthGQ%autoF'/%&widthGFev/%+rowspaci ngGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlin esGF`w/%&frameGF`w/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFP/%-equ alcolumnsGFP/%-displaystyleGFP/%%sideGQ&rightF'/%0minlabelspacingGF]wF BFL/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(m fencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'm tableGF$66-I$mtrGF$6'-I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0 ]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupa lignGFC/%(rowspanGF:/%+columnspanGF:-F56(-F86%Q\"0F'F;F>FAFDFFFHFJFAFD FF-F26'-F56(-F,6$-I#moGF$6.Q*&uminus0;F'F;F>/%&fenceGQ&falseF'/%*separ atorGFgn/%)stretchyGFgn/%*symmetricGFgn/%(largeopGFgn/%.movablelimitsG Fgn/%'accentGFgn/%'lspaceGQ,0.2222222emF'/%'rspaceGFfo-I&mfracGF$6)-F, 6%-I#miGF$6&Q\"pF'/%'italicGQ%trueF'F;/F?Q'italicF'-FX6-Q1&InvisibleTi mes;F'F>FenFhnFjnF\\oF^oF`oFbo/FeoQ&0.0emF'/FhoF[q-F#6%-F,6%-F_p6&Q\"q F'FbpF;Fep-FX6.Q(−F'F;F>FenFhnFjnF\\oF^oF`oFboFdoFgo-F_p6&Q\"tF' FbpF;FepF;F>-F,6#-F,6%-F_p6&Q)λF'/FcpFgnF;F>FdqFaq/%.linethickn essGF:/%+denomalignGQ'centerF'/%)numalignGFfr/%)bevelledGFgnF;FAFDFFFH FJ-F56(-Fjo6)-F,6#-F,6%F^rFdqFgqFjqFbrFdrFgrFirF;FAFDFFFHFJFAFDFF/%&al ignGQ%axisF'/FBQ)baselineF'/FEFfr/FGQ'|frleft|hrF'/%/alignmentscopeGFd p/%,columnwidthGQ%autoF'/%&widthGF_t/%+rowspacingGQ&1.0exF'/%.columnsp acingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFjt/%&frameGFjt/%-fr amespacingGQ,0.4em~0.5exF'/%*equalrowsGFgn/%-equalcolumnsGFgn/%-displa ystyleGFgn/%%sideGQ&rightF'/%0minlabelspacingGFgtF;F>/%%openGQ\"[F'/%& closeGQ\"]F'" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 232 73 "Solving the com patibility equations to obtain the Hamiltonian evolutions." }{TEXT 232 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 231 69 "The compatibility equa tion is \\mathcal\{L\}L=h\\partial_\\lambda A+[A,L]\n" }{TEXT 231 111 "Since the first line of L is trivial, we may easily obtain A[2,1] et \+ A[2,2] to obtain the full expression for A" }{TEXT 231 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "LL:=h*dAdlambda+(Multiply(A,L)-Mult iply(L,A)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "Entry11:=LL[1,1] :\n" }{MPLTEXT 1 0 18 "Entry12:=LL[1,2]:\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 53 "AA21:=unapply(solve(Entry11=0,AA21(lambda)),lambda): \n" }{MPLTEXT 1 0 41 "AA21bis:=h*dAdlambda[1,1]+A[1,2]*L[2,1]:\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "simplify(AA21(lambda)-AA21bis); \n" }{MPLTEXT 1 0 53 "AA22:=unapply(solve(Entry12=0,AA22(lambda)),lamb da):\n" }{MPLTEXT 1 0 47 "AA22bis:=h*dAdlambda[1,2]+A[1,1]+A[1,2]*L[2, 2]:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "simpl ify(AA22(lambda)-AA22bis);\n" }{MPLTEXT 1 0 19 "simplify(Entry11);\n" }{MPLTEXT 1 0 19 "simplify(Entry12);\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 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 231 95 "We now compute the act ion of \\mathcal\{L\} on L[2,2] et L[2,1] to obtain the evolution equ ations" }{TEXT 231 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 26 "Evolut ion of entry L_\{2,2\}" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "E ntry22:=simplify(LL[2,2]);\n" }{MPLTEXT 1 0 77 "Entry22TermLambdaMinus qCube:=factor(residue(Entry22*(lambda-q)^2,lambda=q));\n" }{MPLTEXT 1 0 77 "Entry22TermLambdaMinusqSquare:=factor(residue(Entry22*(lambda-q) ,lambda=q));\n" }{MPLTEXT 1 0 60 "Entry22TermLambdaMinusq:=factor(resi due(Entry22,lambda=q));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 77 "Entr y22TermLambdaInfty4:=factor(-residue(Entry22/lambda^5,lambda=infinity) );\n" }{MPLTEXT 1 0 77 "Entry22TermLambdaInfty3:=factor(-residue(Entry 22/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 77 "Entry22TermLambdaI nfty2:=factor(-residue(Entry22/lambda^3,lambda=infinity));\n" } {MPLTEXT 1 0 77 "Entry22TermLambdaInfty1:=factor(-residue(Entry22/lamb da^2,lambda=infinity));\n" }{MPLTEXT 1 0 75 "Entry22TermLambdaInfty0:= factor(-residue(Entry22/lambda,lambda=infinity));\n" }{MPLTEXT 1 0 81 "Entry22TermLambdaInftyMinus1:=factor(-residue(Entry22/lambda^2,lambda =infinity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 81 "Entry22TermLambda InftyMinus2:=factor(-residue(Entry22/lambda^3,lambda=infinity));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 60 "Entry22TermLambdaTMinus1:=factor (residue(Entry22,lambda=t));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 71 "E ntry22TermLambdaTMinus2:=factor(residue(Entry22*(lambda-t),lambda=t)); " }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 97 "simplify ( Entry22-(Entry22TermLambdaMinusqSquare/(lambda-q)^2+Entry22TermLambd aMinusq/(lambda-q)\n" }{MPLTEXT 1 0 155 "+Entry22TermLambdaInfty0+Entr y22TermLambdaInfty1*lambda+Entry22TermLambdaInfty2*lambda^2+Entry22Ter mLambdaInfty3*lambda^3+Entry22TermLambdaInfty4*lambda^4+" }{MPLTEXT 1 0 36 "Entry22TermLambdaTMinus1/(lambda-t)+" }{MPLTEXT 1 0 37 "Entry22T ermLambdaTMinus2/(lambda-t)^2" }{MPLTEXT 1 0 5 ") );\n" }{MPLTEXT 1 0 8 "L[2,2];\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(Entry22G6\",$**,2*&,&*&,&I$t12GF$\"\"#I$t22GF$F- \"\"\"I)nuMinus1GF$F/F/I#c2GF$!\"%F/I'lambdaGF$\"\"&F/*&,,*&,&*&,&F,F2 F.F2F/F0F/F/F1\"\")F/I\"tGF$F/F/*&F8F/I\"qGF$F/F/*&,&I$t21GF$F/I$t11GF $F/F/F0F/F/*&,&F,F/F.F/F/I$nu0GF$F/F/I#c1GF$!\"#F/F3\"\"%F/*&,(*&F)F/F F/F/*&,&FBFGFAFGF/F0F/F/*&,& F,FGF.FGF/FEF/F/FFFHF/FF/ F/F?F/FCF/FFFGF/F>F/FGF/F3\"\"$F/*&,0*&,*F=F/F?F/FCF/FFFGF/FF-F/*&,(*&,&FBFHFAFHF/F0F/F/*&,&F,FHF.FHF/FEF/F/FF!\")F/F>F/F/* &F0F/,(I\"hGF$F/I$s20GF$FgnI$s10GF$FgnF/FgnF/FF-F/*&,&*&FioF/F0F/F/*&I#muGF$F/FDF/FgnF/F>F/F/*&,&F[pF/FjoF/F/FEF/F/ *&,&FBFgnFAFgnF/FbpF/F/I$rhoGF$F-F/F3F-F/*&,(*(FXF/F>F/FF-F/*&,&*&,&FjoFGF[pFGF/F0F/F/FapF-F/F>F/F/*&FioF/FEF/F G*&,&FBF-FAF-F/FbpF/F/FgpF2F/FF/F/FbpFgnF/FhoF/F-F/F3 F/F/*&,,F\\pF/F^pF/FcqF/FepF/FgpF-F/FF-F0F/F/FbpFgnF/FhoF /FF/FgqF/FhoF/FgnF/FioF/,&F3F/F>FgnFG,&F3F/FII>Entry22TermLambdaMinusqSquareG6\"* (,D*(I\"hGF$\"\"\"I\"qGF$\"\"#I)nuMinus1GF$F)!\"\"**F(F)F*F)I\"tGF$F)F ,F)F)*(I#muGF$F)F*F+I$t12GF$F)F)*(F1F)F*F+I$t22GF$F)F)**F1F)F*F)F/F)F2 F)F-**F1F)F*F)F/F)F4F)F-*(F(F)I$nu0GF$F)F*F)F-*(F(F)F8F)F/F)F)*(F1F)F* F)I$t11GF$F)F)*(F1F)F*F)I$t21GF$F)F)*(F1F)F/F)F;F)F-*(F1F)F/F)F=F)F-*& F(F)F1F)F)*&F1F)I$s10GF$F)F-*&F1F)I$s20GF$F)F-*&F*F)I$rhoGF$F)!\"#*&FF F)F/F)F+F)F(F),&F*F)F/F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry22 TermLambdaMinusqG6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry22T ermLambdaInfty4G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry22Te rmLambdaInfty3G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry22Ter mLambdaInfty2G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry22Term LambdaInfty1G6\",$*&,(*&I$t12GF$\"\"\"I)nuMinus1GF$F*!\"\"*&I$t22GF$F* F+F*F,I#c2GF$\"\"#F*I\"hGF$F*F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8En try22TermLambdaInfty0G6\"*&I\"hGF$\"\"\",,*&I$nu0GF$F'I$t12GF$F'!\"\"* &F*F'I$t22GF$F'F,*&I$t11GF$F'I)nuMinus1GF$F'F,*&I$t21GF$F'F1F'F,I#c1GF $\"\"#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I=Entry22TermLambdaInftyMin us1G6\",$*&,(*&I$t12GF$\"\"\"I)nuMinus1GF$F*!\"\"*&I$t22GF$F*F+F*F,I#c 2GF$\"\"#F*I\"hGF$F*F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I=Entry22Term LambdaInftyMinus2G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I9Entry22 TermLambdaTMinus1G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I9Entry22 TermLambdaTMinus2G6\",$**I\"hGF$\"\"\",,*(I\"qGF$F(I\"tGF$F(I)nuMinus1 GF$F(!\"\"*&F,\"\"#F-F(F(*&I$nu0GF$F(F+F(F.*&F2F(F,F(F(I#muGF$F(F(,(F' F(I$s20GF$F.I$s10GF$F.F(,&F+F(F,F.F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.*&,&I$s10G6\"\"\"\"I$s20GF& F'F',&I'lambdaGF&F'I\"tGF&!\"\"F,F'I$t11GF&F,I$t21GF&F,*&,&I$t12GF&F,I $t22GF&F,F'F*F'F'*&I\"hGF&F'F)F,F,*&F4F',&F*F'I\"qGF&F,F,F'" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 231 35 "Since the deformation operator is " }{TEXT 231 80 "\\hbar (alpha12\\partial_\{t_\{\\infty^\{(1)\},2\} \+ +alpha22\\partial_\{t_\{\\infty^\{(2)\},2\}+" }{TEXT 231 7 "alpha11" } {TEXT 231 30 "\\partial_\{t_\{\\infty^\{(1)\},1\} +" }{TEXT 231 7 "alp ha21" }{TEXT 231 28 "\\partial_\{t_\{\\infty^\{(2)\},1\}" }{TEXT 231 22 ")) we can obtain L[q]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "nu0:=solve(" }{MPLTEXT 1 0 45 "Entry22TermLambdaTMinus2=(s10+s20-h )*Lt,nu0);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$nu0G6\",$*(,,**I\"hGF$ \"\"\"I\"qGF$F*I\"tGF$F*I)nuMinus1GF$F*F**(F)F*F,\"\"#F-F*!\"\"*&I#LtG F$F*F+F*F**&F2F*F,F*F0*&F)F*I#muGF$F*F0F*,&F+F*F,F0F0F)F0F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "L22OrderLambda2:=-residue(L[ 2,2]/lambda^3,lambda=infinity);\n" }{MPLTEXT 1 0 60 "L22OrderLambda1:= -residue(L[2,2]/lambda^2,lambda=infinity);\n" }{MPLTEXT 1 0 60 "L22Ord erLambda0:=-residue(L[2,2]/lambda^1,lambda=infinity);\n" }{MPLTEXT 1 0 64 "L22OrderLambdaMinus1:=-residue(L[2,2]/lambda^2,lambda=infinity); " }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 37 "L22OrderT1:=residue(L[2,2],la mbda=t):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 87 "factor(simplify(h*(al pha12*diff(L22OrderLambda2,t12)+alpha22*diff(L22OrderLambda2,t22)\n" } {MPLTEXT 1 0 35 "+alpha11*diff(L22OrderLambda2,t11)+" }{MPLTEXT 1 0 7 "alpha21" }{MPLTEXT 1 0 32 "*diff(L22OrderLambda2,t21) +Lt*" } {MPLTEXT 1 0 23 "diff(L22OrderLambda2,t)" }{MPLTEXT 1 0 2 " )" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 28 "- Entry22TermLambdaInfty2));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "Equation1:= " }{MPLTEXT 1 0 87 "factor(simplify(h*(alpha12*diff(L22OrderLambda1,t1 2)+alpha22*diff(L22OrderLambda1,t22)\n" }{MPLTEXT 1 0 35 "+alpha11*dif f(L22OrderLambda1,t11)+" }{MPLTEXT 1 0 7 "alpha21" }{MPLTEXT 1 0 26 "* diff(L22OrderLambda1,t21)" }{MPLTEXT 1 0 4 "+Lt*" }{MPLTEXT 1 0 23 "di ff(L22OrderLambda1,t)" }{MPLTEXT 1 0 2 ")\n" }{MPLTEXT 1 0 28 "- Entry 22TermLambdaInfty1));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 98 "Equation2:=factor(simplify(h*(alpha12*diff(L22OrderLa mbda0,t12)+alpha22*diff(L22OrderLambda0,t22)\n" }{MPLTEXT 1 0 1 "+" } {MPLTEXT 1 0 67 "alpha11*diff(L22OrderLambda0,t11)+alpha21*diff(L22Ord erLambda0,t21)" }{MPLTEXT 1 0 4 "+Lt*" }{MPLTEXT 1 0 23 "diff(L22Order Lambda0,t)" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 29 "- Entry22TermLambdaInfty0));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "Equation3:=factor(simplify(h*(alpha12*diff(L22OrderLambda" } {MPLTEXT 1 0 6 "Minus1" }{MPLTEXT 1 0 33 ",t12)+alpha22*diff(L22OrderL ambda" }{MPLTEXT 1 0 6 "Minus1" }{MPLTEXT 1 0 6 ",t22)\n" }{MPLTEXT 1 0 28 "+alpha11*diff(L22OrderLambda" }{MPLTEXT 1 0 6 "Minus1" }{MPLTEXT 1 0 33 ",t11)+alpha21*diff(L22OrderLambda" }{MPLTEXT 1 0 6 "Minus1" } {MPLTEXT 1 0 5 ",t21)" }{MPLTEXT 1 0 4 "+Lt*" }{MPLTEXT 1 0 28 "diff(L 22OrderLambdaMinus1,t)" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 24 "- Entry22TermLambdaInfty" }{MPLTEXT 1 0 6 "Minus1" } {MPLTEXT 1 0 3 "));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 46 "Equation3bis:=factor(simplify(h*(alpha12*diff(" } {MPLTEXT 1 0 10 "L22OrderT1" }{MPLTEXT 1 0 19 ",t12)+alpha22*diff(" } {MPLTEXT 1 0 10 "L22OrderT1" }{MPLTEXT 1 0 6 ",t22)\n" }{MPLTEXT 1 0 14 "+alpha11*diff(" }{MPLTEXT 1 0 10 "L22OrderT1" }{MPLTEXT 1 0 19 ",t 11)+alpha21*diff(" }{MPLTEXT 1 0 10 "L22OrderT1" }{MPLTEXT 1 0 5 ",t21 )" }{MPLTEXT 1 0 4 "+Lt*" }{MPLTEXT 1 0 5 "diff(" }{MPLTEXT 1 0 10 "L2 2OrderT1" }{MPLTEXT 1 0 3 ",t)" }{MPLTEXT 1 0 2 ")\n" }{MPLTEXT 1 0 2 "- " }{MPLTEXT 1 0 24 "Entry22TermLambdaTMinus1" }{MPLTEXT 1 0 3 "));" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0L22OrderLambd a2G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0L22OrderLambda1G6\",&I $t12GF$!\"\"I$t22GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0L22OrderLam bda0G6\",&I$t11GF$!\"\"I$t21GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5 L22OrderLambdaMinus1G6\",&I$t12GF$!\"\"I$t22GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Equation1G6\",$ *&I\"hGF$\"\"\",,*&I$t12GF$F(I)nuMinus1GF$F(!\"#*&I$t22GF$F(F,F(F-I(al pha12GF$F(I(alpha22GF$F(I#c2GF$\"\"%F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Equation2G6\",$*&,J*,I\"hGF$\"\"\"I\"qGF$F*I\"tGF$F*I$ t12GF$F*I)nuMinus1GF$F*F**,F)F*F+F*F,F*I$t22GF$F*F.F*F***F)F*F,\"\"#F- F*F.F*!\"\"**F)F*F,F2F0F*F.F*F3**F)F*F+F*I$t11GF$F*F.F*F3**F)F*F+F*I$t 21GF$F*F.F*F3**F)F*F,F*F6F*F.F*F***F)F*F,F*F8F*F.F*F**(I#LtGF$F*F+F*F- F*F**(FI*Equation3G6\",$ *&I\"hGF$\"\"\",,*&I$t12GF$F(I)nuMinus1GF$F(!\"#*&I$t22GF$F(F,F(F-I(al pha12GF$F(I(alpha22GF$F(I#c2GF$\"\"%F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-Equation3bisG6\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Lq:=factor(Entry22TermLambdaMinusqSquare/h):\n" } {MPLTEXT 1 0 24 "Lqbis:=-2*rho-mu*q*P1(q)" }{MPLTEXT 1 0 38 "-(1/2)*h* q/(t12-t22)*(alpha12-alpha22)" }{MPLTEXT 1 0 2 ":\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 231 34 "We now look at \\mathcal\{L\}[L[2,1]]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Entry21:=simplify(LL[2,1]): \n" }{MPLTEXT 1 0 77 "Entry21TermLambdaMinusqCube:=factor(residue(Entr y21*(lambda-q)^2,lambda=q));\n" }{MPLTEXT 1 0 77 "Entry21TermLambdaMin usqSquare:=factor(residue(Entry21*(lambda-q),lambda=q));\n" }{MPLTEXT 1 0 59 "Entry21TermLambdaMinusq:=factor(residue(Entry21,lambda=q));" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 76 "Entry21TermLambdaInfty2:=factor( -residue(Entry21/lambda^3,lambda=infinity));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 77 "Entry21TermLambdaInfty1:=factor(-residue(Entry21/lamb da^2,lambda=infinity));\n" }{MPLTEXT 1 0 74 "Entry21TermLambdaInfty0:= factor(-residue(Entry21/lambda,lambda=infinity));" }{MPLTEXT 1 0 1 "\n " }{MPLTEXT 1 0 55 "Entry21TermLambdaT1:=factor(residue(Entry21,lambda =t));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "Entry21TermLambdaT2:=fac tor(residue(Entry21*(lambda-t),lambda=t));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 138 "simplify( Entry21-(Entry21TermL ambdaMinusqCube/(lambda-q)^3+Entry21TermLambdaMinusqSquare/(lambda-q)^ 2+Entry21TermLambdaMinusq/(lambda-q)\n" }{MPLTEXT 1 0 56 "+Entry21Term LambdaInfty0+Entry21TermLambdaInfty1*lambda+" }{MPLTEXT 1 0 32 "Entry2 1TermLambdaInfty2*lambda^2" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "+" } {MPLTEXT 1 0 31 "Entry21TermLambdaT1/(lambda-t)\n" }{MPLTEXT 1 0 5 ") \+ );\n" }{MPLTEXT 1 0 8 "L[2,1];\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">II>Entry21TermLambdaMinusqSquareG6\",$*(,bq**I#muGF$\"\" \"I\"qGF$\"\"%I$t12GF$F*I$t22GF$F*!\"#*,F)F*F+\"\"$I\"tGF$F*F-F*F.F*F, *,F)F*F+\"\"#F2F4F-F*F.F*F/**I\"hGF$F*I\"pGF$F*F+F1I)nuMinus1GF$F*!\" \"*,F6F*F7F*F+F4F2F*F8F*F1*,F6F*F7F*F+F*F2F4F8F*!\"$**F6F*F7F*F2F1F8F* F***F)F*F+F1I$t11GF$F*F.F*F/**F)F*F+F1F-F*I$t21GF$F*F/*,F)F*F+F4F2F*F? F*F.F*F,*,F)F*F+F4F2F*F-F*FAF*F,*,F)F*F+F*F2F4F?F*F.F*F/*,F)F*F+F*F2F4 F-F*FAF*F/**F6F*F)F*F+F4F-F*F/*,F6F*F)F*F+F*F2F*F-F*F,**F6F*F)F*F2F4F- F*F/**F)F*F+F4I$t10GF$F*F.F*F/**F)F*F+F4F?F*FAF*F/**F)F*F+F4F-F*I$t20G F$F*F/*,F)F*F+F*F2F*FJF*F.F*F,*,F)F*F+F*F2F*F?F*FAF*F,*,F)F*F+F*F2F*F- F*FMF*F,**F)F*F2F4FJF*F.F*F/**F)F*F2F4F?F*FAF*F/**F)F*F2F4F-F*FMF*F/*( F+F1I$rhoGF$F*F-F*F**(F+F1FUF*F.F*F***F+F4FUF*F2F*F-F*F/**F+F4FUF*F2F* F.F*F/**F+F*FUF*F2F4F-F*F***F+F*FUF*F2F4F.F*F**(I#LtGF$F*F7F*F+F4F***F fnF*F7F*F+F*F2F*F/*(FfnF*F7F*F2F4F***F6F*F)F*F7F*F+F*F9**F6F*F)F*F7F*F 2F*F**(F+F4FUF*F?F*F**(F+F4FUF*FAF*F***F+F*FUF*F2F*F?F*F/**F+F*FUF*F2F *FAF*F/*(FUF*F2F4F?F*F**(FUF*F2F4FAF*F**(I\"CGF$F*F)F*F+F*F4*(FboF*F)F *F2F*F/*(F6F*F+F*FUF*F**(F6F*FUF*F2F*F9*(F)F*I$s10GF$F*I$s20GF$F*F/*(F +F*FUF*FgoF*F9*(F+F*FUF*FhoF*F9*(FUF*FgoF*F2F*F**(FUF*FhoF*F2F*F*F*F6F *,&F+F*F2F9F/F9" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry21TermLambdaM inusqG6\"*(I\"hGF$\"\"\",^p**I#muGF$F'I\"qGF$\"\"%I$t12GF$F'I$t22GF$F' \"\"#*,F*F'F+\"\"$I\"tGF$F'F-F'F.F'!\"'*,F*F'F+F/F2F/F-F'F.F'\"\"'*,F* F'F+F'F2F1F-F'F.F'!\"#*(I#c2GF$F'F&F'F+F,F7**F9F'F&F'F+F1F2F'F5**F9F'F &F'F+F/F2F/F3**F9F'F&F'F+F'F2F1F/**F&F'I\"pGF$F'F+F1I)nuMinus1GF$F'!\" \"*,F&F'F>F'F+F/F2F'F?F'F1*,F&F'F>F'F+F'F2F/F?F'!\"$**F&F'F>F'F2F1F?F' F'**F*F'F+F1I$t11GF$F'F.F'F'**F*F'F+F1F-F'I$t21GF$F'F'*,F*F'F+F/F2F'FF F'F.F'FC*,F*F'F+F/F2F'F-F'FHF'FC*,F*F'F+F'F2F/FFF'F.F'F1*,F*F'F+F'F2F/ F-F'FHF'F1**F*F'F2F1FFF'F.F'F@**F*F'F2F1F-F'FHF'F@*(I#c1GF$F'F&F'F+F1F @**FPF'F&F'F+F/F2F'F1**FPF'F&F'F+F'F2F/FC*(FPF'F&F'F2F1F'*(F+F1I$rhoGF $F'F-F'F@*(F+F1FUF'F.F'F@**F+F/FUF'F2F'F-F'F1**F+F/FUF'F2F'F.F'F1**F+F 'FUF'F2F/F-F'FC**F+F'FUF'F2F/F.F'FC*(FUF'F2F1F-F'F'*(FUF'F2F1F.F'F'*(I \"CGF$F'F*F'F+F'F'*(FhnF'F*F'F2F'F@*(F&F'F+F'FUF'F'*(F&F'FUF'F2F'F@*(F *F'I$s10GF$F'I$s20GF$F'F7*(F+F'FUF'F]oF'F@*(F+F'FUF'F^oF'F@*(FUF'F]oF' F2F'F'*(FUF'F^oF'F2F'F'F',&F+F'F2F@FC" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry21TermLambdaInfty2G6\",$*&,(*(I$t12GF$\"\"\"I$t22GF$F*I)nuMin us1GF$F*!\"#*&I#c2GF$F*F)F*F**&F/F*F+F*F*F*I\"hGF$F*\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8Entry21TermLambdaInfty1G6\"*&,D*.I\"hGF$\"\"\" I\"qGF$F)I\"tGF$F)I$t12GF$F)I$t22GF$F)I)nuMinus1GF$F)\"\"#*,F(F)F+F/F, F)F-F)F.F)!\"#*,F(F)F*F)I$t11GF$F)F-F)F.F)!\"$*,F(F)F*F)F,F)I$t21GF$F) F.F)F4*,F(F)F+F)F3F)F-F)F.F)\"\"$*,F(F)F+F)F,F)F6F)F.F)F8**I#LtGF$F)F* F)F,F)F-F)F/**F;F)F+F)F,F)F-F)F1**I#c1GF$F)F(F)F*F)F,F)F)**F>F)F(F)F*F )F-F)F)**F>F)F(F)F+F)F,F)!\"\"**F>F)F(F)F+F)F-F)FA**I#c2GF$F)F(F)F*F)F 3F)F/**FDF)F(F)F*F)F6F)F/**FDF)F(F)F+F)F3F)F1**FDF)F(F)F+F)F6F)F1**F(F )I#muGF$F)F,F)F-F)F1F),&F*F)F+FAFA" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I 8Entry21TermLambdaInfty0G6\"*&,Z*.I\"hGF$\"\"\"I\"qGF$F)I\"tGF$F)I$t11 GF$F)I$t22GF$F)I)nuMinus1GF$F)F)*.F(F)F*F)F+F)I$t12GF$F)I$t21GF$F)F.F) F)*,F(F)F+\"\"#F,F)F-F)F.F)!\"\"*,F(F)F+F3F0F)F1F)F.F)F4**F(F3F*F)F0F) F.F)!\"#**F(F3F+F)F0F)F.F)F3*,F(F)F*F)I$t10GF$F)F-F)F.F)F7*,F(F)F*F)F, F)F1F)F.F)F7*,F(F)F*F)F0F)I$t20GF$F)F.F)F7*,F(F)F+F)F:F)F-F)F.F)F3*,F( F)F+F)F,F)F1F)F.F)F3*,F(F)F+F)F0F)F=F)F.F)F3**I#LtGF$F)F*F)F,F)F-F)F)* *FBF)F*F)F0F)F1F)F)**FBF)F+F)F,F)F-F)F4**FBF)F+F)F0F)F1F)F4**I#c1GF$F) F(F)F*F)F,F)F)**FGF)F(F)F*F)F1F)F)**FGF)F(F)F+F)F,F)F4**FGF)F(F)F+F)F1 F)F4*(I#c2GF$F)F(F3F*F)F3*(FLF)F(F3F+F)F7**FLF)F(F)F*F)I$s10GF$F)F7**F LF)F(F)F*F)I$s20GF$F)F7**FLF)F(F)FOF)F+F)F3**FLF)F(F)FQF)F+F)F3**F(F)I #muGF$F)F,F)F-F)F4**F(F)FUF)F0F)F1F)F4F),&F*F)F+F4F4" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I4Entry21TermLambdaT1G6\",$*(,fo**I#c2GF$\"\"\"I\"hGF $F*I\"qGF$\"\"$I\"tGF$F*!\"#**F)F*F+F*F,\"\"#F.F1\"\"'**F)F*F+F*F,F*F. F-!\"'*(F)F*F+F*F.\"\"%F1**F)F*F,F-I$s10GF$F*F.F*F1**F)F*F,F-I$s20GF$F *F.F*F1**F)F*F,F1F8F*F.F1F4**F)F*F,F1F:F*F.F1F4**F)F*F,F*F8F*F.F-F2**F )F*F,F*F:F*F.F-F2*(F)F*F8F*F.F6F/*(F)F*F:F*F.F6F/*(I\"CGF$F*F,F-I)nuMi nus1GF$F*!\"\"**FBF*F,F1F.F*FCF*F-**FBF*F,F*F.F1FCF*!\"$*(FBF*F.F-FCF* F**(I#c1GF$F*F+F*F,F-FD**FJF*F+F*F,F1F.F*F-**FJF*F+F*F,F*F.F1FG*(FJF*F +F*F.F-F**(FJF*F,F-F8F*F**(FJF*F,F-F:F*F***FJF*F,F1F8F*F.F*FG**FJF*F,F 1F:F*F.F*FG**FJF*F,F*F8F*F.F1F-**FJF*F,F*F:F*F.F1F-*(FJF*F8F*F.F-FD*(F JF*F:F*F.F-FD*(FBF*I#muGF$F*F,F*F**(FBF*FWF*F.F*FD*(F+F*F,F*I$rhoGF$F* F**(F+F*FZF*F.F*FD*(FWF*F8F*F:F*F/*(F,F*FZF*F8F*FD*(F,F*FZF*F:F*FD*(FZ F*F8F*F.F*F**(FZF*F:F*F.F*F*F*F+F*,&F,F*F.FDFGFD" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I4Entry21TermLambdaT2G6\"*&I\"CGF$\"\"\"I#LtGF$F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "*(,&*&,&I\"tG6\"\"\"\"I'lambdaGF'!\"\"F( I\"CGF'F(F(*&I$s10GF'F(I$s20GF'F(\"\"#F(I#LtGF'F(F%!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",4*(I$s10G6\"\"\"\"I$s20GF%F&,&I'lambdaGF%F&I\"tGF% !\"\"!\"#F+*&I$t10GF%F&I$t22GF%F&F+*&I$t11GF%F&I$t21GF%F&F+*&I$t12GF%F &I$t20GF%F&F+*&,&*&F1F&F/F&F&*&F4F&F2F&F&F&F)F&F+*(F4F&F/F&F)\"\"#F+*& I\"CGF%F&F(F+F&*&I\"hGF%F&F4F&F+*(F?F&I\"pGF%F&,&F)F&I\"qGF%F+F+F+" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "rho:=factor(solve(Entry21Te rmLambdaMinusqCube,rho));\n" }{MPLTEXT 1 0 25 "simplify(rho-(-p*q*mu)) ;\n" }{MPLTEXT 1 0 39 "simplify(Entry21TermLambdaMinusqCube);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I$rhoG6\",$*&I\"pGF$\"\"\"I#muGF$F(!\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(I\"pG6\"\"\"\"I#muGF$F%,&I\"qGF$ F%!\"\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "L21OrderLambda3:=-residue(L[2,1]/lambda^4,l ambda=infinity);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 59 "L21OrderLambd a2:=-residue(L[2,1]/lambda^3,lambda=infinity);" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 60 "L21OrderLambda1:=-residue(L[2,1]/lambda^2,lambda=infi nity);\n" }{MPLTEXT 1 0 60 "L21OrderLambda0:=-residue(L[2,1]/lambda^1, lambda=infinity);\n" }{MPLTEXT 1 0 64 "L21OrderLambdaMinus1:=-residue( L[2,1]/lambda^2,lambda=infinity);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 64 "L21OrderLambdaMinus2:=-residue(L[2,1]/lambda^3,lambda=infinity);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "L21TOrder2:=factor(" }{MPLTEXT 1 0 37 "residue(L[2,1]*(lambda-t),lambda=t));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 12 "L21TOrder1:=" }{MPLTEXT 1 0 25 "residue(L[2,1],lambda =t);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "Equation4:=" }{MPLTEXT 1 0 80 "simplify(h*(alpha12*diff(L21OrderLambda2,t12)+alpha22*diff(L21Or derLambda2,t22)+" }{MPLTEXT 1 0 66 "alpha11*diff(L21OrderLambda2,t11)+ alpha21*diff(L21OrderLambda2,t21" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 27 "+Lt*diff(L21OrderLambda2,t)" }{MPLTEXT 1 0 29 ")- Entry21TermLambd aInfty2);\n" }{MPLTEXT 1 0 11 "Equation5:=" }{MPLTEXT 1 0 12 "simplify (h*(" }{MPLTEXT 1 0 68 "alpha12*diff(L21OrderLambda1,t12)+alpha22*diff (L21OrderLambda1,t22)+" }{MPLTEXT 1 0 66 "alpha11*diff(L21OrderLambda1 ,t11)+alpha21*diff(L21OrderLambda1,t21" }{MPLTEXT 1 0 1 ")" }{MPLTEXT 1 0 27 "+Lt*diff(L21OrderLambda1,t)" }{MPLTEXT 1 0 20 ")- Entry21TermL ambda" }{MPLTEXT 1 0 6 "Infty1" }{MPLTEXT 1 0 2 ");" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 36 "Equation6:=simplify(h*(alpha12*diff(" }{MPLTEXT 1 0 10 "L21TOrder2" }{MPLTEXT 1 0 19 ",t12)+alpha22*diff(" }{MPLTEXT 1 0 10 "L21TOrder2" }{MPLTEXT 1 0 19 ",t22)+alpha11*diff(" }{MPLTEXT 1 0 10 "L21TOrder2" }{MPLTEXT 1 0 19 ",t11)+alpha21*diff(" }{MPLTEXT 1 0 10 "L21TOrder2" }{MPLTEXT 1 0 5 ",t21)" }{MPLTEXT 1 0 22 "+Lt*diff (L21TOrder2,t)" }{MPLTEXT 1 0 3 ")- " }{MPLTEXT 1 0 19 "Entry21TermLam bdaT2" }{MPLTEXT 1 0 2 ");" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0L21OrderLambda 3G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0L21OrderLambda2G6\",$*& I$t12GF$\"\"\"I$t22GF$F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0L21O rderLambda1G6\",&*&I$t11GF$\"\"\"I$t22GF$F(!\"\"*&I$t12GF$F(I$t21GF$F( F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0L21OrderLambda0G6\",**&I\"hGF$ \"\"\"I$t12GF$F(!\"\"*&I$t10GF$F(I$t22GF$F(F**&I$t11GF$F(I$t21GF$F(F** &F)F(I$t20GF$F(F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21OrderLambdaMi nus1G6\",&*&I$t11GF$\"\"\"I$t22GF$F(!\"\"*&I$t12GF$F(I$t21GF$F(F*" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I5L21OrderLambdaMinus2G6\",$*&I$t12GF$ \"\"\"I$t22GF$F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+L21TOrder2G6 \",$*&I$s10GF$\"\"\"I$s20GF$F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I+L21TOrder1G6\"*&,&*&I\"CGF$\"\"\"I\"qGF$F)!\"\"*&F(F)I\"tGF$F)F)F),& F*F+F-F)F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Equation4G6\",$*&,&*&,( *&I$t22GF$\"\"\"I)nuMinus1GF$F,!\"#I#c2GF$F,I(alpha22GF$#F,\"\"#F,I$t1 2GF$F,F,*&F+F,,&F/F,I(alpha12GF$F1F,F,F,I\"hGF$F,F." }}{PARA 11 "" 1 " " {XPPMATH 20 ">I*Equation5G6\"*&,&*&,***I$t22GF$\"\"\"I)nuMinus1GF$F+ I$t12GF$F+I\"tGF$\"\"#F/*&,,**F-F+F*F+F,F+I\"qGF$F+!\"#*&,(*&I$t21GF$F +F,F+!\"$I(alpha21GF$F+I#c1GF$F+F+F-F+F+*&,(*&I$t11GF$F+F,F+F9I(alpha1 1GF$F+F;F+F+F*F+F+*&,&I(alpha22GF$F+I#c2GF$F/F+F?F+F+*&F8F+,&I(alpha12 GF$F+FDF/F+F+F+F.F+F+*&,**&,(F7\"\"$F:!\"\"F;FMF+F-F+F+*&,(F>FLF@FMF;F MF+F*F+F+*&,&FCFMFDF4F+F?F+F+FEFMF+F3F+F+*(F-F+F*F+I#muGF$F+F/F+I\"hGF $F+F+**F-F+F*F+I#LtGF$F+,&F3F+F.FMF+F4F+FWFM" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Equation6G6\",$*&I\"CGF$\"\"\"I#LtGF$F(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "c2:=factor(solve(Equation1,c 2));\n" }{MPLTEXT 1 0 33 "mu:=factor(solve(Equation2,mu));\n" } {MPLTEXT 1 0 45 "nuMinus1:=factor(solve(Equation4,nuMinus1));\n" } {MPLTEXT 1 0 33 "c1:=factor(solve(Equation5,c1));\n" }{MPLTEXT 1 0 18 "c2:=simplify(c2);\n" }{MPLTEXT 1 0 15 "mu:=factor(mu);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#c2G6\",**&I$t12GF$\"\"\"I)nuMinus1GF$F(#F(\"\"#* &I$t22GF$F(F)F(F*I(alpha12GF$#!\"\"\"\"%I(alpha22GF$F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#muG6\"**,4**I\"hGF$\"\"\"I\"tGF$F)I$t12GF$F)I)nuM inus1GF$F)F)**F(F)F*F)I$t22GF$F)F,F)F)*(F(F)I$t11GF$F)F,F)!\"\"*(F(F)I $t21GF$F)F,F)F1*&I#LtGF$F)F+F)F)*&F5F)F.F)F)*&I(alpha11GF$F)F(F)F)*&I( alpha21GF$F)F(F)F)*&I#c1GF$F)F(F)\"\"#F),&I\"qGF$F)F*F1F)F(F1,&F+F)F.F )F1" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)nuMinus1G6\",$*&,&I(alpha12GF$ \"\"\"I(alpha22GF$!\"\"F),&I$t12GF$F)I$t22GF$F+F+#F)\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#c1G6\",$*&,2*(I(alpha11GF$\"\"\"I$t12GF$F*I$t2 2GF$F*\"\"#*&F)F*F,F-!\"#*(I(alpha12GF$F*I$t11GF$F*F,F*!\"\"*(F1F*F+F* I$t21GF$F*F**&I(alpha21GF$F*F+F-F/*(F7F*F+F*F,F*F-*(I(alpha22GF$F*F2F* F,F*F**(F:F*F+F*F5F*F3F*,&F+F*F,F3F/#F*F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#c2G6\"*&,&*&I(alpha12GF$\"\"\"I$t22GF$F)F)*&I(alpha22G F$F)I$t12GF$F)!\"\"F),&F-\"\"#F*!\"#F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#muG6\",$**,&I\"qGF$\"\"\"I\"tGF$!\"\"F),@**I(alpha12GF$F)I\"hGF$F )F*F)I$t12GF$F)F)**F.F)F/F)F*F)I$t22GF$F)F+**I(alpha22GF$F)F/F)F*F)F0F )F+**F4F)F/F)F*F)F2F)F)*&I#LtGF$F)F0\"\"#F8*(F7F)F0F)F2F)!\"%*&F7F)F2F 8F8*(I(alpha11GF$F)F/F)F0F)F8*(F=F)F/F)F2F)!\"#*(F.F)F/F)I$t11GF$F)F+* (F.F)F/F)I$t21GF$F)F)*(I(alpha21GF$F)F/F)F0F)F?*(FEF)F/F)F2F)F8*(F4F)F /F)FAF)F)*(F4F)F/F)FCF)F+F)F/F+,&F0F)F2F+F?#F)F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "simplify(Equation1);\n" }{MPLTEXT 1 0 9 "simp lify(" }{MPLTEXT 1 0 12 "Equation2);\n" }{MPLTEXT 1 0 9 "simplify(" } {MPLTEXT 1 0 12 "Equation3);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 12 "Equation4);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 12 "E quation5);\n" }{MPLTEXT 1 0 20 "simplify(c1-c1bis);\n" }{MPLTEXT 1 0 20 "simplify(c2-c2bis);\n" }{MPLTEXT 1 0 20 "simplify(mu-mubis);\n" } {MPLTEXT 1 0 22 "simplify(nu0-nu0bis);\n" }{MPLTEXT 1 0 31 "simplify(n uMinus1-nuMinus1bis);" }}{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 50 "simplify(Entry21TermLambdaMi nusqSquare-(-p*h*Lq)):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Lpfunction:=unapply(-Entry21TermLambdaMinusq/h,C):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "Equation7:=unapply( simpl ify(Entry21TermLambdaMinusqSquare-(-p*h*Lq)),C):\n" }{MPLTEXT 1 0 503 "Cter:=(q^4*t12*t22-2*q^3*t*t12*t22+q^2*t^2*t12*t22+p*q^3*t12+p*q^3*t2 2-2*p*q^2*t*t12-2*p*q^2*t*t22+p*q*t^2*t12+p*q*t^2*t22+q^3*t11*t22+q^3* t12*t21-2*q^2*t*t11*t22-2*q^2*t*t12*t21+q*t^2*t11*t22+q*t^2*t12*t21+h* q^2*t12-2*h*q*t*t12+h*t^2*t12+p^2*q^2-2*p^2*q*t+p^2*t^2+p*q^2*t11+p*q^ 2*t21-2*p*q*t*t11-2*p*q*t*t21+p*t^2*t11+p*t^2*t21+q^2*t10*t22+q^2*t11* t21+q^2*t12*t20-2*q*t*t10*t22-2*q*t*t11*t21-2*q*t*t12*t20+t^2*t10*t22+ t^2*t11*t21+t^2*t12*t20+h*p*q-h*p*t-p*q*s10-p*q*s20+p*s10*t+p*s20*t+s1 0*s20)/(q-t):\n" }{MPLTEXT 1 0 27 "simplify(Equation7(Cter));\n" } {MPLTEXT 1 0 23 "solve(Equation7(C),C):\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 15 "Cbis:=(q-t)*p^2" }{MPLTEXT 1 0 4 "+h*p" }{MPLTEXT 1 0 44 "-(q-t)*P1(q)*p+(q-t)*P2(q)-P012+h*t12*(q-t);" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 27 "simplify(Equation7(Cbis));\n" }{MPLTEXT 1 0 31 " simplify(series(Cter-Cbis,p));\n" }{MPLTEXT 1 0 8 "C:=Cbis:" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Cbis G6\",.*&,&I\"qGF$\"\"\"I\"tGF$!\"\"F)I\"pGF$\"\"#F)*&I\"hGF$F)F,F)F)*( F'F),**&,&I$s10GF$F)I$s20GF$F)F)F'F+F)I$t11GF$F+I$t21GF$F+*&,&I$t12GF$ F+I$t22GF$F+F)F(F)F)F)F,F)F+*&F'F),0*(F4F)F5F)F'!\"#F)*&I%P012GF$F)F'F +F)*&I$t10GF$F)F;F)F)*&F6F)F7F)F)*&F:F)I$t20GF$F)F)*&,&*&F6F)F;F)F)*&F :F)F7F)F)F)F(F)F)*(F:F)F;F)F(F-F)F)F)FAF+*(F/F)F:F)F'F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Lp:=factor(simplify(Lpfuncti on(" }{MPLTEXT 1 0 4 "Cbis" }{MPLTEXT 1 0 5 "))):\n" }{MPLTEXT 1 0 99 "Lpbis:=mu*(p*diff(P1(q),q)+p*h*1/(q-t)^2-diff(tdP2(q),q)- C01/(q-t)^2 )+h*nuMinus1*p +h*c1+2*h*c2*q:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 32 "factor(series(Lp-Lpbis,P012=0));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Lqter:=" }{MPLTEXT 1 0 30 "2*mu*(p-P1(q)/2+1/2*h*1 /(q-t))" }{MPLTEXT 1 0 20 "-h*nu0-h*nuMinus1*q:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "simplify(Lq-Lqter);" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nuMinus1:=" }{MPLTEXT 1 0 8 "nuMinus1" }{MPLTEXT 1 0 2 ";\n" } {MPLTEXT 1 0 10 "nu0:=nu0;\n" }{MPLTEXT 1 0 8 "c1:=c1;\n" }{MPLTEXT 1 0 7 "c2:=c2;" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)nu Minus1G6\",$*&,&I(alpha12GF$\"\"\"I(alpha22GF$!\"\"F),&I$t12GF$F)I$t22 GF$F+F+#F)\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$nu0G6\",$*(,,*,I\" hGF$\"\"\"I\"qGF$F*I\"tGF$F*,&I(alpha12GF$F*I(alpha22GF$!\"\"F*,&I$t12 GF$F*I$t22GF$F0F0#F*\"\"#**F)F*F,F5F-F*F1F0#F0F5*&I#LtGF$F*F+F*F**&F9F *F,F*F0*(,&F+F*F,F0F*,@**F.F*F)F*F,F*F2F*F***F.F*F)F*F,F*F3F*F0**F/F*F )F*F,F*F2F*F0**F/F*F)F*F,F*F3F*F**&F9F*F2F5F5*(F9F*F2F*F3F*!\"%*&F9F*F 3F5F5*(I(alpha11GF$F*F)F*F2F*F5*(FGF*F)F*F3F*!\"#*(F.F*F)F*I$t11GF$F*F 0*(F.F*F)F*I$t21GF$F*F**(I(alpha21GF$F*F)F*F2F*FI*(FOF*F)F*F3F*F5*(F/F *F)F*FKF*F**(F/F*F)F*FMF*F0F*F1FIF7F*FI#c1G6\",$*&,2*(I(alpha11GF$\"\"\"I$t12GF$F*I$t22GF$F*\" \"#*&F)F*F,F-!\"#*(I(alpha12GF$F*I$t11GF$F*F,F*!\"\"*(F1F*F+F*I$t21GF$ F*F**&I(alpha21GF$F*F+F-F/*(F7F*F+F*F,F*F-*(I(alpha22GF$F*F2F*F,F*F**( F:F*F+F*F5F*F3F*,&F+F*F,F3F/#F*F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I# c2G6\"*&,&*&I(alpha12GF$\"\"\"I$t22GF$F)F)*&I(alpha22GF$F)I$t12GF$F)! \"\"F),&F-\"\"#F*!\"#F." }}}{EXCHG {PARA 209 "" 0 "" {TEXT 212 17 "We \+ thus get that\n" }{TEXT 212 5 "L[q]=" }{TEXT 212 62 "2*mu*q*(p-P1(q)/2 )-(1/2)*h*q/(t12-t22)*(alpha12-alpha22) -h*mu" }}{PARA 210 "" 0 "" {TEXT 212 7 "L[p] = " }{TEXT 212 98 "-mu*p^2+mu*diff(p*q*P1(q)-q*P2(q) ,q)-h*t12*mu +1/2*h*(alpha12-alpha22)/(t12-t22)*p+ h*c1+2*h*c2*q\n" } {TEXT 212 6 "with \n" }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi (\"nuMinus1\", bold = \"true\", italic = \"true\", mathvariant = \"bol d-italic\", fontweight = \"bold\"), Typesetting:-mo(\"≔\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \" false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting: -mfrac(Typesetting:-mrow(Typesetting:-mi(\"α12\", bold = \"true \", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"b old\"), Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \" bold\", fontweight = \"bold\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em \", rspace = \"0.2222222em\"), Typesetting:-mi(\"α22\", bold = \+ \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mrow(Typesetting:-mn(\"2\", bold = \"true \", mathvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\" ⁢\", mathvariant = \"normal\", fence = \"false\", separ ator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+ \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow (Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", mathvari ant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"&minu s;\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", \+ fence = \"false\", separator = \"false\", stretchy = \"false\", symmet ric = \"false\", largeop = \"false\", movablelimits = \"false\", accen t = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Ty pesetting:-mi(\"t22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), bold = \"true\", mathvari ant = \"bold\", fontweight = \"bold\")), linethickness = \"1\", denoma lign = \"center\", numalign = \"center\", bevelled = \"false\"));" "-I %mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6'Q)nuMin us1F'/%%boldGQ%trueF'/%'italicGF1/%,mathvariantGQ,bold-italicF'/%+font weightGQ%boldF'-I#moGF$6/Q)≔F'F//F5F9F7/%&fenceGQ&falseF'/%*sep aratorGFA/%)stretchyGFA/%*symmetricGFA/%(largeopGFA/%.movablelimitsGFA /%'accentGFA/%'lspaceGQ,0.2777778emF'/%'rspaceGFP-I&mfracGF$6(-F#6%-F, 6'Q*α12F'F/F2F4F7-F;6/Q(−F'F/F>F7F?FBFDFFFHFJFL/FOQ,0.2222 222emF'/FRFin-F,6'Q*α22F'F/F2F4F7-F#6%-I#mnGF$6&Q\"2F'F/F>F7-F;6 -Q1⁢F'/F5Q'normalF'F?FBFDFFFHFJFL/FOQ&0.0emF'/FRFjo-I(m fencedGF$6&-F#6%-F,6'Q$t12F'F/F2F4F7Fen-F,6'Q$t22F'F/F2F4F7F/F>F7/%.li nethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGF\\q/%)bevelledG FA" }{TEXT 212 1 "\n" }{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi (\"ν0\", bold = \"true\", italic = \"true\", mathvariant = \"bold-i talic\", fontweight = \"bold\"), Typesetting:-mo(\"≔\", bold = \+ \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"fal se\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mr ow(Typesetting:-mi(\"\"), Typesetting:-mo(\"&uminus0;\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fa lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f alse\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.222 2222em\"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mfrac(Typ esetting:-mrow(Typesetting:-mi(\"h\", bold = \"true\", italic = \"true \", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting :-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\" , separator = \"false\", stretchy = \"false\", symmetric = \"false\", \+ largeop = \"false\", movablelimits = \"false\", accent = \"false\", ls pace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"q\", bold = \+ \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"no rmal\", fence = \"false\", separator = \"false\", stretchy = \"false\" , symmetric = \"false\", largeop = \"false\", movablelimits = \"false \", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Types etting:-mi(\"t\", bold = \"true\", italic = \"true\", mathvariant = \" bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"&InvisibleTim es;\", mathvariant = \"normal\", fence = \"false\", separator = \"fals e\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rs pace = \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting: -mi(\"α12\", bold = \"true\", italic = \"true\", mathvariant = \+ \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"−\", \+ bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence \+ = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \+ \"false\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesett ing:-mi(\"α22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), bold = \"true\", mathvari ant = \"bold\", fontweight = \"bold\")), Typesetting:-mrow(Typesetting :-mn(\"2\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bo ld\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symme tric = \"false\", largeop = \"false\", movablelimits = \"false\", acce nt = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:- mfenced(Typesetting:-mrow(Typesetting:-mi(\"t12\", bold = \"true\", it alic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\") , Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \"bold\" , fontweight = \"bold\", fence = \"false\", separator = \"false\", str etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable limits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspa ce = \"0.2222222em\"), Typesetting:-mi(\"t22\", bold = \"true\", itali c = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), \+ bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\")), line thickness = \"1\", denomalign = \"center\", numalign = \"center\", bev elled = \"false\"), Typesetting:-mo(\"−\", bold = \"true\", math variant = \"bold\", fontweight = \"bold\", fence = \"false\", separato r = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0 .2222222em\", rspace = \"0.2222222em\"), Typesetting:-mfrac(Typesettin g:-mrow(Typesetting:-mi(\"h\", bold = \"true\", italic = \"true\", mat hvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\" ⁢\", mathvariant = \"normal\", fence = \"false\", separ ator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+ \"0.0em\", rspace = \"0.0em\"), Typesetting:-msup(Typesetting:-mi(\"t \", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mn(\"2\", bold = \"true\", mathv ariant = \"bold\", fontweight = \"bold\"), superscriptshift = \"0\"), \+ Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence \+ = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \+ \"false\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced (Typesetting:-mrow(Typesetting:-mi(\"α12\", bold = \"true\", ita lic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"false\", stre tchy = \"false\", symmetric = \"false\", largeop = \"false\", movablel imits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspac e = \"0.2222222em\"), Typesetting:-mi(\"α22\", bold = \"true\", \+ italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold \")), bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\")) , Typesetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvarian t = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"&InvisibleTime s;\", mathvariant = \"normal\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp ace = \"0.0em\"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:- mi(\"t12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-i talic\", fontweight = \"bold\"), Typesetting:-mo(\"−\", bold = \+ \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"fal se\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mi (\"t22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-ita lic\", fontweight = \"bold\")), bold = \"true\", mathvariant = \"bold \", fontweight = \"bold\")), linethickness = \"1\", denomalign = \"cen ter\", numalign = \"center\", bevelled = \"false\"), Typesetting:-mo( \"+\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bo ld\", fence = \"false\", separator = \"false\", stretchy = \"false\", \+ symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em \"), Typesetting:-mrow(Typesetting:-mi(\"Lt\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Ty pesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \+ \"false\", separator = \"false\", stretchy = \"false\", symmetric = \" false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"q\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fo ntweight = \"bold\")), Typesetting:-mo(\"−\", bold = \"true\", m athvariant = \"bold\", fontweight = \"bold\", fence = \"false\", separ ator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+ \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesett ing:-mi(\"Lt\", bold = \"true\", italic = \"true\", mathvariant = \"bo ld-italic\", fontweight = \"bold\"), Typesetting:-mo(\"&InvisibleTimes ;\", mathvariant = \"normal\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp ace = \"0.0em\"), Typesetting:-mi(\"t\", bold = \"true\", italic = \"t rue\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typeset ting:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontwei ght = \"bold\", fence = \"false\", separator = \"false\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0 .2222222em\"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mfenc ed(Typesetting:-mrow(Typesetting:-mi(\"q\", bold = \"true\", italic = \+ \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Types etting:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontw eight = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits \+ = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \" 0.2222222em\"), Typesetting:-mi(\"t\", bold = \"true\", italic = \"tru e\", mathvariant = \"bold-italic\", fontweight = \"bold\")), bold = \" true\", mathvariant = \"bold\", fontweight = \"bold\"), Typesetting:-m o(\"⁢\", mathvariant = \"normal\", fence = \"false\", s eparator = \"false\", stretchy = \"false\", symmetric = \"false\", lar geop = \"false\", movablelimits = \"false\", accent = \"false\", lspac e = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mfenced(Typesetting:- mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mi(\"&alpha ;12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic \", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", math variant = \"normal\", fence = \"false\", separator = \"false\", stretc hy = \"false\", symmetric = \"false\", largeop = \"false\", movablelim its = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0. 0em\"), Typesetting:-mi(\"h\", bold = \"true\", italic = \"true\", mat hvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\" ⁢\", mathvariant = \"normal\", fence = \"false\", separ ator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \+ \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"t\", bold = \"true\" , italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bol d\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", \+ fence = \"false\", separator = \"false\", stretchy = \"false\", symmet ric = \"false\", largeop = \"false\", movablelimits = \"false\", accen t = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-m i(\"t12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-it alic\", fontweight = \"bold\")), Typesetting:-mo(\"−\", bold = \+ \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"fal se\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mr ow(Typesetting:-mi(\"α12\", bold = \"true\", italic = \"true\", \+ mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo (\"⁢\", mathvariant = \"normal\", fence = \"false\", se parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", bold = \"tru e\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \" bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin g:-mi(\"t\", bold = \"true\", italic = \"true\", mathvariant = \"bold- italic\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\" , mathvariant = \"normal\", fence = \"false\", separator = \"false\", \+ stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace \+ = \"0.0em\"), Typesetting:-mi(\"t22\", bold = \"true\", italic = \"tru e\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesetti ng:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontweigh t = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.22 22222em\"), Typesetting:-mrow(Typesetting:-mi(\"α22\", bold = \" true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"norm al\", fence = \"false\", separator = \"false\", stretchy = \"false\", \+ symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesett ing:-mi(\"h\", bold = \"true\", italic = \"true\", mathvariant = \"bol d-italic\", fontweight = \"bold\"), Typesetting:-mo(\"⁢ \", mathvariant = \"normal\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspac e = \"0.0em\"), Typesetting:-mi(\"t\", bold = \"true\", italic = \"tru e\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesettin g:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false \", separator = \"false\", stretchy = \"false\", symmetric = \"false\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontwei ght = \"bold\")), Typesetting:-mo(\"+\", bold = \"true\", mathvar iant = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"f alse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.22 22222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-m i(\"α22\", bold = \"true\", italic = \"true\", mathvariant = \"b old-italic\", fontweight = \"bold\"), Typesetting:-mo(\"&InvisibleTime s;\", mathvariant = \"normal\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp ace = \"0.0em\"), Typesetting:-mi(\"h\", bold = \"true\", italic = \"t rue\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesett ing:-mo(\"⁢\", mathvariant = \"normal\", fence = \"fals e\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"t\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontwei ght = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \+ \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fal se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa lse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Ty pesetting:-mi(\"t22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"+ \", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fe nce = \"false\", separator = \"false\", stretchy = \"false\", symmetri c = \"false\", largeop = \"false\", movablelimits = \"false\", accent \+ = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Type setting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \" bold\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", \+ mathvariant = \"normal\", fence = \"false\", separator = \"false\", st retchy = \"false\", symmetric = \"false\", largeop = \"false\", movabl elimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \+ \"0.0em\"), Typesetting:-mi(\"Lt\", bold = \"true\", italic = \"true\" , mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:- mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", \+ separator = \"false\", stretchy = \"false\", symmetric = \"false\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa ce = \"0.0em\", rspace = \"0.0em\"), Typesetting:-msup(Typesetting:-mi (\"t12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-ita lic\", fontweight = \"bold\"), Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), superscriptshift = \" 0\")), Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \"b old\", fontweight = \"bold\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-mn(\"4\", b old = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), Typese tting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"fa lse\", separator = \"false\", stretchy = \"false\", symmetric = \"fals e\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"Lt\", b old = \"true\", italic = \"true\", mathvariant = \"bold-italic\", font weight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), \+ Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", mathvaria nt = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"&Invis ibleTimes;\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"f alse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0e m\", rspace = \"0.0em\"), Typesetting:-mi(\"t22\", bold = \"true\", it alic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\") ), Typesetting:-mo(\"+\", bold = \"true\", mathvariant = \"bold\" , fontweight = \"bold\", fence = \"false\", separator = \"false\", str etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable limits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspa ce = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), Typesetting :-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\" , separator = \"false\", stretchy = \"false\", symmetric = \"false\", \+ largeop = \"false\", movablelimits = \"false\", accent = \"false\", ls pace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-msup(Typesetting:- mi(\"t22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-i talic\", fontweight = \"bold\"), Typesetting:-mn(\"2\", bold = \"true \", mathvariant = \"bold\", fontweight = \"bold\"), superscriptshift = \"0\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin g:-mi(\"Lt\", bold = \"true\", italic = \"true\", mathvariant = \"bold -italic\", fontweight = \"bold\")), Typesetting:-mo(\"+\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"fa lse\", separator = \"false\", stretchy = \"false\", symmetric = \"fals e\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:- mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \"bold\", f ontweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvaria nt = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\" ), Typesetting:-mi(\"α11\", bold = \"true\", italic = \"true\", \+ mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo (\"⁢\", mathvariant = \"normal\", fence = \"false\", se parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", bold = \"tru e\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \" bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin g:-mi(\"t12\", bold = \"true\", italic = \"true\", mathvariant = \"bol d-italic\", fontweight = \"bold\")), Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \" false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting: -mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \"bold\", \+ fontweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvari ant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits \+ = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em \"), Typesetting:-mi(\"α11\", bold = \"true\", italic = \"true\" , mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:- mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", \+ separator = \"false\", stretchy = \"false\", symmetric = \"false\", la rgeop = \"false\", movablelimits = \"false\", accent = \"false\", lspa ce = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", bold = \"t rue\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \+ \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"norma l\", fence = \"false\", separator = \"false\", stretchy = \"false\", s ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+ accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetti ng:-mi(\"t22\", bold = \"true\", italic = \"true\", mathvariant = \"bo ld-italic\", fontweight = \"bold\")), Typesetting:-mo(\"−\", bol d = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \+ \"false\", separator = \"false\", stretchy = \"false\", symmetric = \" false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesettin g:-mrow(Typesetting:-mi(\"α12\", bold = \"true\", italic = \"tru e\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesettin g:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false \", separator = \"false\", stretchy = \"false\", symmetric = \"false\" , largeop = \"false\", movablelimits = \"false\", accent = \"false\", \+ lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweigh t = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"n ormal\", fence = \"false\", separator = \"false\", stretchy = \"false \", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Type setting:-mi(\"t11\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"+\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typese tting:-mrow(Typesetting:-mi(\"α12\", bold = \"true\", italic = \+ \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Types etting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"f alse\", separator = \"false\", stretchy = \"false\", symmetric = \"fal se\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", bo ld = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontw eight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fa lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f alse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), T ypesetting:-mi(\"t21\", bold = \"true\", italic = \"true\", mathvarian t = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"&minus ;\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", f ence = \"false\", separator = \"false\", stretchy = \"false\", symmetr ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typ esetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \+ \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\" , mathvariant = \"normal\", fence = \"false\", separator = \"false\", \+ stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace \+ = \"0.0em\"), Typesetting:-mi(\"α21\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Type setting:-mo(\"⁢\", mathvariant = \"normal\", fence = \" false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", b old = \"true\", italic = \"true\", mathvariant = \"bold-italic\", font weight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), \+ Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", mathvaria nt = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"&plus ;\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", f ence = \"false\", separator = \"false\", stretchy = \"false\", symmetr ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typ esetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \+ \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\" , mathvariant = \"normal\", fence = \"false\", separator = \"false\", \+ stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace \+ = \"0.0em\"), Typesetting:-mi(\"α21\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Type setting:-mo(\"⁢\", mathvariant = \"normal\", fence = \" false\", separator = \"false\", stretchy = \"false\", symmetric = \"fa lse\", largeop = \"false\", movablelimits = \"false\", accent = \"fals e\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", b old = \"true\", italic = \"true\", mathvariant = \"bold-italic\", font weight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant \+ = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), \+ Typesetting:-mi(\"t22\", bold = \"true\", italic = \"true\", mathvaria nt = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"&plus ;\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", f ence = \"false\", separator = \"false\", stretchy = \"false\", symmetr ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typ esetting:-mrow(Typesetting:-mi(\"α22\", bold = \"true\", italic \+ = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typ esetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \+ \"false\", separator = \"false\", stretchy = \"false\", symmetric = \" false\", largeop = \"false\", movablelimits = \"false\", accent = \"fa lse\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"h\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fo ntweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvarian t = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\" ), Typesetting:-mi(\"t11\", bold = \"true\", italic = \"true\", mathva riant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"&m inus;\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\") , Typesetting:-mrow(Typesetting:-mi(\"α22\", bold = \"true\", it alic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\") , Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fenc e = \"false\", separator = \"false\", stretchy = \"false\", symmetric \+ = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\" h\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\" , fontweight = \"bold\"), Typesetting:-mo(\"⁢\", mathva riant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit s = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0e m\"), Typesetting:-mi(\"t21\", bold = \"true\", italic = \"true\", mat hvariant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mi( \"\")), bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\" )), Typesetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvari ant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"&InvisibleTi mes;\", mathvariant = \"normal\", fence = \"false\", separator = \"fal se\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\" , movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", r space = \"0.0em\"), Typesetting:-msup(Typesetting:-mfenced(Typesetting :-mrow(Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", ma thvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo( \"−\", bold = \"true\", mathvariant = \"bold\", fontweight = \"b old\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\" , accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em \"), Typesetting:-mi(\"t22\", bold = \"true\", italic = \"true\", math variant = \"bold-italic\", fontweight = \"bold\")), bold = \"true\", m athvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mn(\"2\", \+ bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), super scriptshift = \"0\")), linethickness = \"1\", denomalign = \"center\", numalign = \"center\", bevelled = \"false\")), Typesetting:-mrow(Type setting:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"q\", bold = \"tru e\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \" bold\"), Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \+ \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"fals e\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em \", rspace = \"0.2222222em\"), Typesetting:-mi(\"t\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold \")), bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\" h\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\" , fontweight = \"bold\")), linethickness = \"1\", denomalign = \"cente r\", numalign = \"center\", bevelled = \"false\")), Typesetting:-mi(\" \"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6&-I#miGF $6'Q&ν0F'/%%boldGQ%trueF'/%'italicGF1/%,mathvariantGQ,bold-italicF' /%+fontweightGQ%boldF'-I#moGF$6/Q)≔F'F//F5F9F7/%&fenceGQ&falseF '/%*separatorGFA/%)stretchyGFA/%*symmetricGFA/%(largeopGFA/%.movableli mitsGFA/%'accentGFA/%'lspaceGQ,0.2777778emF'/%'rspaceGFP-F#6%-F,6#Q!F' -F;6-Q*&uminus0;F'/F5Q'normalF'F?FBFDFFFHFJFL/FOQ,0.2222222emF'/FRFhn- I&mfracGF$6(-F#6+-F[o6(-F#6)-F,6'Q\"hF'F/F2F4F7-F;6-Q1⁢ F'FenF?FBFDFFFHFJFL/FOQ&0.0emF'/FRFjo-F,6'Q\"qF'F/F2F4F7Ffo-F,6'Q\"tF' F/F2F4F7Ffo-I(mfencedGF$6&-F#6%-F,6'Q*α12F'F/F2F4F7-F;6/Q(&minus ;F'F/F>F7F?FBFDFFFHFJFLFgnFin-F,6'Q*α22F'F/F2F4F7F/F>F7-F#6%-I#m nGF$6&Q\"2F'F/F>F7Ffo-Fcp6&-F#6%-F,6'Q$t12F'F/F2F4F7Fjp-F,6'Q$t22F'F/F 2F4F7F/F>F7/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignG Fer/%)bevelledGFAFjp-F[o6(-F#6'FcoFfo-I%msupGF$6%F_pFbq/%1superscripts hiftGQ\"0F'FfoFbpF`qF`rFcrFfrFhr-F;6/Q'+F'F/F>F7F?FBFDFFFHFJFLFgn Fin-F#6%-F,6'Q#LtF'F/F2F4F7FfoF\\pFjp-F#6%FisFfoF_pFjp-F[o6(-F#6%-Fcp6 &-F#6%F\\pFjpF_pF/F>F7Ffo-Fcp6&-F#6AFU-F#6)FgpFfoFcoFfoF_pFfoFjqFjp-F# 6)FgpFfoFcoFfoF_pFfoF]rFjp-F#6)F]qFfoFcoFfoF_pFfoFjqFds-F#6)F]qFfoFcoF foF_pFfoF]rFds-F#6'FbqFfoFisFfo-F_s6%FjqFbqFasFjp-F#6)-Fcq6&Q\"4F'F/F> F7FfoFisFfoFjqFfoF]rFds-F#6'FbqFfo-F_s6%F]rFbqFasFfoFisFds-F#6)FbqFfo- F,6'Q*α11F'F/F2F4F7FfoFcoFfoFjqFjp-F#6)FbqFfoFavFfoFcoFfoF]rFjp- F#6'FgpFfoFcoFfo-F,6'Q$t11F'F/F2F4F7Fds-F#6'FgpFfoFcoFfo-F,6'Q$t21F'F/ F2F4F7Fjp-F#6)FbqFfo-F,6'Q*α21F'F/F2F4F7FfoFcoFfoFjqFds-F#6)FbqF foFbwFfoFcoFfoF]rFds-F#6'F]qFfoFcoFfoFhvFjp-F#6'F]qFfoFcoFfoF]wFUF/F>F 7-F#6%FbqFfo-F_s6%FfqFbqFasF`rFcrFfrFhr-F#6%FbtFfoFcoF`rFcrFfrFhrFU" } }{PARA 0 "" 0 "" {XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"c1 \", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"≔\", bold = \"true\" , mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", se parator = \"false\", stretchy = \"false\", symmetric = \"false\", larg eop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mfrac(Type setting:-mrow(Typesetting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mn (\"2\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\" ), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fen ce = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi( \"t12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-ital ic\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", ma thvariant = \"normal\", fence = \"false\", separator = \"false\", stre tchy = \"false\", symmetric = \"false\", largeop = \"false\", movablel imits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \" 0.0em\"), Typesetting:-mi(\"α11\", bold = \"true\", italic = \"t rue\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesett ing:-mo(\"⁢\", mathvariant = \"normal\", fence = \"fals e\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"t22\", bo ld = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontw eight = \"bold\")), Typesetting:-mo(\"−\", bold = \"true\", math variant = \"bold\", fontweight = \"bold\", fence = \"false\", separato r = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0 .2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting :-mn(\"2\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bo ld\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symme tric = \"false\", largeop = \"false\", movablelimits = \"false\", acce nt = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:- msup(Typesetting:-mi(\"t22\", bold = \"true\", italic = \"true\", math variant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mn(\"2 \", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), s uperscriptshift = \"0\"), Typesetting:-mo(\"⁢\", mathva riant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit s = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0e m\"), Typesetting:-mi(\"α11\", bold = \"true\", italic = \"true \", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesettin g:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"fa lse\", symmetric = \"false\", largeop = \"false\", movablelimits = \"f alse\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.222 2222em\"), Typesetting:-mrow(Typesetting:-mi(\"t11\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold \"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", f ence = \"false\", separator = \"false\", stretchy = \"false\", symmetr ic = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi (\"α12\", bold = \"true\", italic = \"true\", mathvariant = \"bo ld-italic\", fontweight = \"bold\"), Typesetting:-mo(\"&InvisibleTimes ;\", mathvariant = \"normal\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp ace = \"0.0em\"), Typesetting:-mi(\"t22\", bold = \"true\", italic = \+ \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Type setting:-mo(\"+\", bold = \"true\", mathvariant = \"bold\", fontw eight = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits \+ = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \" 0.2222222em\"), Typesetting:-mrow(Typesetting:-mi(\"t21\", bold = \"tr ue\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \+ \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"norma l\", fence = \"false\", separator = \"false\", stretchy = \"false\", s ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+ accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetti ng:-mi(\"α12\", bold = \"true\", italic = \"true\", mathvariant \+ = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"&Invisibl eTimes;\", mathvariant = \"normal\", fence = \"false\", separator = \" false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fals e\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\" , rspace = \"0.0em\"), Typesetting:-mi(\"t12\", bold = \"true\", itali c = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), \+ Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", \+ fontweight = \"bold\", fence = \"false\", separator = \"false\", stret chy = \"false\", symmetric = \"false\", largeop = \"false\", movableli mits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-mn(\"2\", bold = \+ \"true\", mathvariant = \"bold\", fontweight = \"bold\"), Typesetting: -mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", l argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp ace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-msup(Typesetting:-m i(\"t12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-it alic\", fontweight = \"bold\"), Typesetting:-mn(\"2\", bold = \"true\" , mathvariant = \"bold\", fontweight = \"bold\"), superscriptshift = \+ \"0\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\" , fence = \"false\", separator = \"false\", stretchy = \"false\", symm etric = \"false\", largeop = \"false\", movablelimits = \"false\", acc ent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting: -mi(\"α21\", bold = \"true\", italic = \"true\", mathvariant = \+ \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"+\", \+ bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence \+ = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \+ \"false\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesett ing:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \"bold \", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", math variant = \"normal\", fence = \"false\", separator = \"false\", stretc hy = \"false\", symmetric = \"false\", largeop = \"false\", movablelim its = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0. 0em\"), Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", m athvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo( \"⁢\", mathvariant = \"normal\", fence = \"false\", sep arator = \"false\", stretchy = \"false\", symmetric = \"false\", large op = \"false\", movablelimits = \"false\", accent = \"false\", lspace \+ = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"α21\", bold \+ = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweig ht = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \" normal\", fence = \"false\", separator = \"false\", stretchy = \"false \", symmetric = \"false\", largeop = \"false\", movablelimits = \"fals e\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Type setting:-mi(\"t22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"+\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \+ \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typese tting:-mrow(Typesetting:-mi(\"t11\", bold = \"true\", italic = \"true \", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting :-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\" , separator = \"false\", stretchy = \"false\", symmetric = \"false\", \+ largeop = \"false\", movablelimits = \"false\", accent = \"false\", ls pace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"α22\", \+ bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fon tweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \" false\", symmetric = \"false\", largeop = \"false\", movablelimits = \+ \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\") , Typesetting:-mi(\"t22\", bold = \"true\", italic = \"true\", mathvar iant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"&mi nus;\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\" , fence = \"false\", separator = \"false\", stretchy = \"false\", symm etric = \"false\", largeop = \"false\", movablelimits = \"false\", acc ent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), \+ Typesetting:-mrow(Typesetting:-mi(\"t21\", bold = \"true\", italic = \+ \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Types etting:-mo(\"⁢\", mathvariant = \"normal\", fence = \"f alse\", separator = \"false\", stretchy = \"false\", symmetric = \"fal se\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"α 22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic \", fontweight = \"bold\"), Typesetting:-mo(\"⁢\", math variant = \"normal\", fence = \"false\", separator = \"false\", stretc hy = \"false\", symmetric = \"false\", largeop = \"false\", movablelim its = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0. 0em\"), Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", m athvariant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mi (\"\")), Typesetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mat hvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"&Invisi bleTimes;\", mathvariant = \"normal\", fence = \"false\", separator = \+ \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em \", rspace = \"0.0em\"), Typesetting:-msup(Typesetting:-mfenced(Typese tting:-mrow(Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true \", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting :-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontweight \+ = \"bold\", fence = \"false\", separator = \"false\", stretchy = \"fal se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa lse\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222 222em\"), Typesetting:-mi(\"t22\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), bold = \"true \", mathvariant = \"bold\", fontweight = \"bold\"), Typesetting:-mn(\" 2\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\"), \+ superscriptshift = \"0\")), linethickness = \"1\", denomalign = \"cent er\", numalign = \"center\", bevelled = \"false\"));" "-I%mrowG6#/I+mo dulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6'Q#c1F'/%%boldGQ%true F'/%'italicGF1/%,mathvariantGQ,bold-italicF'/%+fontweightGQ%boldF'-I#m oGF$6/Q)≔F'F//F5F9F7/%&fenceGQ&falseF'/%*separatorGFA/%)stretch yGFA/%*symmetricGFA/%(largeopGFA/%.movablelimitsGFA/%'accentGFA/%'lspa ceGQ,0.2777778emF'/%'rspaceGFP-I&mfracGF$6(-F#63-F,6#Q!F'-F#6)-I#mnGF$ 6&Q\"2F'F/F>F7-F;6-Q1⁢F'/F5Q'normalF'F?FBFDFFFHFJFL/FOQ &0.0emF'/FRFao-F,6'Q$t12F'F/F2F4F7F[o-F,6'Q*α11F'F/F2F4F7F[o-F,6 'Q$t22F'F/F2F4F7-F;6/Q(−F'F/F>F7F?FBFDFFFHFJFL/FOQ,0.2222222emF' /FRF`p-F#6'FgnF[o-I%msupGF$6%FioFgn/%1superscriptshiftGQ\"0F'F[oFfoF \\p-F#6'-F,6'Q$t11F'F/F2F4F7F[o-F,6'Q*α12F'F/F2F4F7F[oFio-F;6/Q' +F'F/F>F7F?FBFDFFFHFJFLF_pFap-F#6'-F,6'Q$t21F'F/F2F4F7F[oF_qF[oFc oF\\p-F#6'FgnF[o-Fep6%FcoFgnFgpF[o-F,6'Q*α21F'F/F2F4F7Fbq-F#6)Fg nF[oFcoF[oF^rF[oFioFbq-F#6'F\\qF[o-F,6'Q*α22F'F/F2F4F7F[oFioF\\p -F#6'FgqF[oFerF[oFcoFX-F#6%FgnF[o-Fep6%-I(mfencedGF$6&-F#6%FcoF\\pFioF /F>F7FgnFgp/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignG Fhs/%)bevelledGFA" }}{PARA 0 "" 0 "" {XPPEDIT 2 0 "Typesetting:-mrow(T ypesetting:-mi(\"c2\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-mo(\"≔ \", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fe nce = \"false\", separator = \"false\", stretchy = \"false\", symmetri c = \"false\", largeop = \"false\", movablelimits = \"false\", accent \+ = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Type setting:-mfrac(Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-m row(Typesetting:-mi(\"α12\", bold = \"true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\"), Typesetting:-m o(\"⁢\", mathvariant = \"normal\", fence = \"false\", s eparator = \"false\", stretchy = \"false\", symmetric = \"false\", lar geop = \"false\", movablelimits = \"false\", accent = \"false\", lspac e = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"t22\", bold = \" true\", italic = \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"−\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold\", fence = \"false\", separator = \"f alse\", stretchy = \"false\", symmetric = \"false\", largeop = \"false \", movablelimits = \"false\", accent = \"false\", lspace = \"0.222222 2em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typesetting:-mi(\" α22\", bold = \"true\", italic = \"true\", mathvariant = \"bold- italic\", fontweight = \"bold\"), Typesetting:-mo(\"⁢\" , mathvariant = \"normal\", fence = \"false\", separator = \"false\", \+ stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mova blelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace \+ = \"0.0em\"), Typesetting:-mi(\"t12\", bold = \"true\", italic = \"tru e\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Typesetti ng:-mi(\"\")), Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-m row(Typesetting:-mn(\"2\", bold = \"true\", mathvariant = \"bold\", fo ntweight = \"bold\"), Typesetting:-mo(\"⁢\", mathvarian t = \"normal\", fence = \"false\", separator = \"false\", stretchy = \+ \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\" ), Typesetting:-mi(\"t12\", bold = \"true\", italic = \"true\", mathva riant = \"bold-italic\", fontweight = \"bold\")), Typesetting:-mo(\"&m inus;\", bold = \"true\", mathvariant = \"bold\", fontweight = \"bold \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\") , Typesetting:-mrow(Typesetting:-mn(\"2\", bold = \"true\", mathvarian t = \"bold\", fontweight = \"bold\"), Typesetting:-mo(\"&InvisibleTime s;\", mathvariant = \"normal\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp ace = \"0.0em\"), Typesetting:-mi(\"t22\", bold = \"true\", italic = \+ \"true\", mathvariant = \"bold-italic\", fontweight = \"bold\")), Type setting:-mi(\"\")), linethickness = \"1\", denomalign = \"center\", nu malign = \"center\", bevelled = \"false\"));" "-I%mrowG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6'Q#c2F'/%%boldGQ%trueF'/%'ita licGF1/%,mathvariantGQ,bold-italicF'/%+fontweightGQ%boldF'-I#moGF$6/Q) ≔F'F//F5F9F7/%&fenceGQ&falseF'/%*separatorGFA/%)stretchyGFA/%*s ymmetricGFA/%(largeopGFA/%.movablelimitsGFA/%'accentGFA/%'lspaceGQ,0.2 777778emF'/%'rspaceGFP-I&mfracGF$6(-F#6'-F,6#Q!F'-F#6%-F,6'Q*α12 F'F/F2F4F7-F;6-Q1⁢F'/F5Q'normalF'F?FBFDFFFHFJFL/FOQ&0.0 emF'/FRF`o-F,6'Q$t22F'F/F2F4F7-F;6/Q(−F'F/F>F7F?FBFDFFFHFJFL/FOQ ,0.2222222emF'/FRFio-F#6%-F,6'Q*α22F'F/F2F4F7Fjn-F,6'Q$t12F'F/F2 F4F7FX-F#6'FX-F#6%-I#mnGF$6&Q\"2F'F/F>F7FjnF`pFeo-F#6%FgpFjnFboFX/%.li nethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFbq/%)bevelledGF A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Hamiltonian:= " } {MPLTEXT 1 0 22 "mu*(p^2-P1(q)*p+P2(q))" }{MPLTEXT 1 0 38 "-1/2*h*(alp ha12-alpha22)/(t12-t22)*p*q" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 8 "h*t1 2*mu" }{MPLTEXT 1 0 77 " -h*c1*q-h*c2*q^2+p*((2*Lt*t12-2*Lt*t22+h*t*(a lpha12-alpha22))/(2*t12-2*t22))" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 37 "simplify(Lp-(-diff(Hamiltonian,q)));\n" } {MPLTEXT 1 0 36 "simplify(Lq-(diff(Hamiltonian,p)));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 104 "Hamiltonianbis:= mu*(p^2-P1(q)*p+h*p*1/(q-t) +tdP2(q)+h*t12 )-h*nu0*p-h*nuMinus1*q*p-h*c1*q-h*c2*q^2 :\n" } {MPLTEXT 1 0 48 "factor(simplify(Lp-(-diff(Hamiltonianbis,q))));\n" } {MPLTEXT 1 0 38 "simplify(Lq-(diff(Hamiltonianbis,p)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 232 81 "Expression of the Lax matrix in the geometric gauge and normalisation at infinity" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "simplify(checkL[1,1]);\n" } {MPLTEXT 1 0 23 "simplify(checkL[1,2]);\n" }{MPLTEXT 1 0 44 "checkL22b is:=P1(lambda)-p*(q-t)/(lambda-t);\n" }{MPLTEXT 1 0 35 "simplify(check L[2,2]-checkL22bis);\n" }{MPLTEXT 1 0 31 "checkL21:=factor(checkL[2,1] );\n" }{MPLTEXT 1 0 40 "simplify(series(checkL[2,1],lambda=t)):\n" } {MPLTEXT 1 0 203 "checkL21bis:=(p*(q-t)-s10)*(p*(q-t)-s20)/((q-t)*(lam bda-t))-t12*t22*lambda^2+(((-q+t)*t22-t21)*t12-t11*t22)*lambda+((-q^2+ q*t)*t22+(-t21-p)*q+(t21+p)*t-h-t20)*t12+((-p-t11)*q+(t11+p)*t-t10)*t2 2-t11*t21:\n" }{MPLTEXT 1 0 32 "simplify(checkL21-checkL21bis);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "*(I\"pG6\"\"\"\",&I\"qGF$F%I\"tGF$!\"\"F %,&I'lambdaGF$F%F(F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,&I'lambdaG6 \"!\"\"I\"qGF%\"\"\"F(,&I\"tGF%F(F$F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,checkL22bisG6\",,*&,&I$s10GF$\"\"\"I$s20GF$F)F),&I'lambdaGF$F)I \"tGF$!\"\"F.F)I$t11GF$F.I$t21GF$F.*&,&I$t12GF$F.I$t22GF$F.F)F,F)F)*(I \"pGF$F),&I\"qGF$F)F-F.F)F+F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"! " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)checkL21G6\",$*(,\\s**I'lambdaGF$ \"\"$I\"qGF$\"\"\"I$t12GF$F,I$t22GF$F,F,**F)F*I\"tGF$F,F-F,F.F,!\"\"** F)\"\"#F+F3F-F,F.F,F,*,F)F3F+F,F0F,F-F,F.F,!\"$**F)F3F0F3F-F,F.F,F3**F )F,F+F*F-F,F.F,F,*,F)F,F+F3F0F,F-F,F.F,F5*,F)F,F+F,F0F3F-F,F.F,F***F)F ,F0F*F-F,F.F,F1**F+F*F0F,F-F,F.F,F1**F+F3F0F3F-F,F.F,F3**F+F,F0F*F-F,F .F,F1**F)F3F+F,I$t11GF$F,F.F,F,**F)F3F+F,F-F,I$t21GF$F,F,**F)F3F0F,F?F ,F.F,F1**F)F3F0F,F-F,FAF,F1**F)F,I\"pGF$F,F+F3F-F,F,**F)F,FEF,F+F3F.F, F,*,F)F,FEF,F+F,F0F,F-F,!\"#*,F)F,FEF,F+F,F0F,F.F,FH**F)F,FEF,F0F3F-F, F,**F)F,FEF,F0F3F.F,F,**F)F,F+F3F?F,F.F,F,**F)F,F+F3F-F,FAF,F,*,F)F,F+ F,F0F,F?F,F.F,F5*,F)F,F+F,F0F,F-F,FAF,F5**F)F,F0F3F?F,F.F,F3**F)F,F0F3 F-F,FAF,F3**FEF,F+F3F0F,F-F,F1**FEF,F+F3F0F,F.F,F1**FEF,F+F,F0F3F-F,F3 **FEF,F+F,F0F3F.F,F3*(FEF,F0F*F-F,F1*(FEF,F0F*F.F,F1**F+F3F0F,F?F,F.F, F1**F+F3F0F,F-F,FAF,F1**F+F,F0F3F?F,F.F,F3**F+F,F0F3F-F,FAF,F3*(F0F*F? F,F.F,F1*(F0F*F-F,FAF,F1**I\"hGF$F,F)F,F+F,F-F,F,**FinF,F)F,F0F,F-F,F1 **FinF,F+F,F0F,F-F,F1*(FinF,F0F3F-F,F,**F)F,F+F,I$t10GF$F,F.F,F,**F)F, F+F,F?F,FAF,F,**F)F,F+F,F-F,I$t20GF$F,F,**F)F,F0F,F^oF,F.F,F1**F)F,F0F ,F?F,FAF,F1**F)F,F0F,F-F,FaoF,F1*&FEF3F+F3F1*(FEF3F+F,F0F,F3*&FEF3F0F3 F1**F+F,F0F,F^oF,F.F,F1**F+F,F0F,F?F,FAF,F1**F+F,F0F,F-F,FaoF,F1*(F0F3 F^oF,F.F,F,*(F0F3F?F,FAF,F,*(F0F3F-F,FaoF,F,*(FEF,F+F,I$s10GF$F,F,*(FE F,F+F,I$s20GF$F,F,*(FEF,F_pF,F0F,F1*(FEF,FapF,F0F,F1*&F_pF,FapF,F1F,,& F)F,F0F1F1,&F+F,F0F1F1F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "G1:=Matrix(2,2,0):\n" } {MPLTEXT 1 0 12 "G1[1,1]:=1:\n" }{MPLTEXT 1 0 12 "G1[2,2]:=1:\n" } {MPLTEXT 1 0 12 "G1[1,2]:=0:\n" }{MPLTEXT 1 0 26 "G1[2,1]:=t12*lambda+ eta0:\n" }{MPLTEXT 1 0 8 "g1:=t12:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "eta0:=(q-t)*t12+t11;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 27 "d G1dlambda:=Matrix(2,2,0):\n" }{MPLTEXT 1 0 88 "for i from 1 to 2 do fo r j from 1 to 2 do dG1dlambda[i,j]:=diff(G1[i,j],lambda): od: od:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 85 "tdL:=simpli fy(Multiply(Multiply(G1,checkL),G1^(-1))+h*Multiply(dG1dlambda,G1^(-1) )):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 15 "simplify(tdL);\n" } {MPLTEXT 1 0 36 "series(tdL[1,1],lambda=infinity,1);\n" }{MPLTEXT 1 0 36 "series(tdL[1,2],lambda=infinity,1);\n" }{MPLTEXT 1 0 35 "series(td L[2,1],lambda=infinity,1);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%eta0G6\",&*&,&I\"qGF$\"\"\"I\"tGF$!\" \"F)I$t12GF$F)F)I$t11GF$F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfenced G6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableG F$66-I$mtrGF$6'-I$mtdGF$6(-I&mfracGF$6)-F,6#-F,6+-F,6%-I%msupGF$6%-I#m iGF$6&Q)λF'/%'italicGQ&falseF'/%+foregroundGQ([0,0,0]F'/%,mathv ariantGQ'normalF'-I#mnGF$6%Q\"2F'FJFM/%1superscriptshiftGQ\"0F'-I#moGF $6-Q1⁢F'FM/%&fenceGFI/%*separatorGFI/%)stretchyGFI/%*sy mmetricGFI/%(largeopGFI/%.movablelimitsGFI/%'accentGFI/%'lspaceGQ&0.0e mF'/%'rspaceGFeo-FD6&Q$t12F'/FHQ%trueF'FJ/FNQ'italicF'-FX6.Q\"+F'FJFMF enFgnFinF[oF]oF_oFao/FdoQ,0.2222222emF'/FgoFcp-F,6%-F#6%-F,6&-FX6.Q*&u minus0;F'FJFMFenFgnFinF[oF]oF_oFaoFbpFdp-F,6%-FD6&Q\"tF'F[pFJF]pFWFhoF _p-FD6&Q$t11F'F[pFJF]pFJFMFWFC-FX6.Q(−F'FJFMFenFgnFinF[oF]oF_oFa oFbpFdp-F,6'-FD6&Q\"qF'F[pFJF]pFW-F#6%-F,6%F[rFfqF`qFJFMFWFhoF_p-F,6%- F#6%-F,6&F[q-FD6&Q\"pF'F[pFJF]pFfqFcqFJFMFWF[rF_p-F,6%FhrFWF`q-F,6#-F, 6%F`qFfqFC/%.linethicknessGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGF fs/%)bevelledGFIFJ/%)rowalignGQ!F'/%,columnalignGF]t/%+groupalignGF]t/ %(rowspanGFcs/%+columnspanGFcs-F56(-F86)-F,6#-F,6&F[qFCF_pF[rF]sFasFds FgsFisFJF[tF^tF`tFbtFdtF[tF^tF`t-F26'-F56(-F86)-F,6#-F,61-F,6'-F#6%-F, 6&F[qFhoF_p-FD6&Q$t22F'F[pFJF]pFJFMFW-F#6%-F,6'-F,6%F[rFWFhoF_pFhrF_pF cqFJFMFW-FA6%F`q-FQ6%Q\"3F'FJFMFTF_p-F,6%-F#6%-F,61-F,6%-F#6%-F,6%-F,6 %FivFW-FA6%FhoFPFTFfq-F,6'FPFWFhoFWF^vFJFMFW-FA6%F[rFPFTF_p-F,6%-F#6%- 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$t12G6\"\"\"\"I'lambdaGF%F&!\"\"I$t11GF%F(-I\"OG6$%*protectedGI(_sysli bGF%6#*$F'F(F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"\"F#-I\"OG6$%*pr otectedGI(_syslibG6\"6#*$I'lambdaGF)!\"\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&,,*&,(*&,&*$I$t12G6\"\"\"#\"\"\"*&F*F-I$t22GF+F-!\"\" F-I\"qGF+F-F-*&,&I$t11GF+F-I\"pGF+F-F-F*F-F-*&F/F-F3F-F0F-I\"tGF+F,F-* &,**&,&F)!\"#F.F,F-F1F,F-*&,&*&,&F5F " 0 "" {MPLTEXT 1 0 19 "s20:=-s10-t10-t20:\n" }{MPLTEXT 1 0 11 "t21:=-t11:\n" }{MPLTEXT 1 0 10 "t22:=-t12:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "t 11:=0:\n" }{MPLTEXT 1 0 8 "t12:=1:\n" }{MPLTEXT 1 0 12 "alpha12:=0:\n" }{MPLTEXT 1 0 12 "alpha22:=0:\n" }{MPLTEXT 1 0 7 "alpha11" }{MPLTEXT 1 0 5 ":=0:\n" }{MPLTEXT 1 0 7 "alpha21" }{MPLTEXT 1 0 12 ":=-alpha11: \n" }{MPLTEXT 1 0 7 "Lt:=1:\n" }{MPLTEXT 1 0 11 "mu:=mubis;\n" } {MPLTEXT 1 0 19 "nuMinus1:=nuMinus1;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "c1:=c1bis;\n" }{MPLTEXT 1 0 11 "c2:=c2bis;\n" }{MPLTEXT 1 0 6 "c0:=0:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "c heckL:=simplify(checkL):\n" }{MPLTEXT 1 0 19 "tdL:=simplify(tdL):" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "dG1dt:=Matr ix(2,2,0):\n" }{MPLTEXT 1 0 121 "for i from 1 to 2 do for j from 1 to \+ 2 do dG1dt[i,j]:=diff(G1[i,j],t)+diff(G1[i,j],q)*dqdt+diff(G1[i,j],p)* dpdt : od: od:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 12 "dqdt:=Lq/h:\n" }{MPLTEXT 1 0 1 "d" }{MPLTEXT 1 0 10 "pdt:=Lp/h:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "q:=checkq:\n" }{MPLTEXT 1 0 11 "p:=checkp:\n" }{MPLTEXT 1 0 41 "tdA:=simplify(Multiply(Multiply(G1 ,checkA" }{MPLTEXT 1 0 39 "),G1^(-1))+h*Multiply(dG1dt,G1^(-1))):\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "checkL:=" }{MPLTEXT 1 0 17 "simpl ify(checkL);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "tdL:=simplify(tdL );" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "checkA:=" }{MPLTEXT 1 0 9 "s implify(" }{MPLTEXT 1 0 8 "checkA);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "tdA:=simplify(tdA);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 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