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0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 221 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 222 "T imes" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 223 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 224 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 225 "Times" 1 16 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "" -1 226 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "" -1 227 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 211 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "" -1 228 "Times" 1 16 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 210 153 "In this Maple file we c ompute the Lax pair in the oper gauge in terms of the irregular times \+ at infinity. We check the results with the theoretical ones." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart:\n" }{MPLTEXT 1 0 21 "with(LinearAlgebra):\n" }{MPLTEXT 1 0 11 "rinfty:=4:\n" }{MPLTEXT 1 0 13 "g:=rinfty-2:\n" }{MPLTEXT 1 0 21 "tinfty27:=-tinfty17:\n" } {MPLTEXT 1 0 21 "tinfty25:=-tinfty15:\n" }{MPLTEXT 1 0 21 "tinfty23:=- tinfty13:\n" }{MPLTEXT 1 0 21 "tinfty21:=-tinfty11:\n" }{MPLTEXT 1 0 20 "tinfty20:=-tinfty10:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "tinft y26:=tinfty16:\n" }{MPLTEXT 1 0 20 "tinfty24:=tinfty14:\n" }{MPLTEXT 1 0 20 "tinfty22:=tinfty12:\n" }{MPLTEXT 1 0 12 "tinfty10:=0:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "Pinfty01 := -tinfty12;\n" } {MPLTEXT 1 0 23 "Pinfty11 := -tinfty14;\n" }{MPLTEXT 1 0 23 "Pinfty21 \+ := -tinfty16;\n" }{MPLTEXT 1 0 103 "Pinfty22 := -(1/2)*tinfty11*tinfty 17+(1/2)*tinfty12*tinfty16-(1/2)*tinfty13*tinfty15+(1/4)*tinfty14^2;\n " }{MPLTEXT 1 0 79 "Pinfty32 := -(1/2)*tinfty13*tinfty17+(1/2)*tinfty1 4*tinfty16-(1/4)*tinfty15^2;\n" }{MPLTEXT 1 0 55 "Pinfty42 := -(1/2)*t infty15*tinfty17+(1/4)*tinfty16^2;\n" }{MPLTEXT 1 0 31 "Pinfty52 := -( 1/4)*tinfty17^2;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 42 "P1:=x-> Pin fty01+Pinfty11*x+Pinfty21*x^2;\n" }{MPLTEXT 1 0 81 "P2:=x-> Pinfty02+P infty12*x+Pinfty22*x^2+Pinfty32*x^3+Pinfty42*x^4+Pinfty52*x^5;\n" } {MPLTEXT 1 0 14 "tdP2:=unapply(" }{MPLTEXT 1 0 55 "Pinfty22*x^2+Pinfty 32*x^3+Pinfty42*x^4+Pinfty52*x^5,x);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "Unknownn:=-" }{MPLTEXT 1 0 9 "Unknown:\n" }{MPLTEXT 1 0 1 "L" }{MPLTEXT 1 0 12 "Unknownn:=-L" }{MPLTEXT 1 0 8 " Unknown:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "Unknownn2:=" } {MPLTEXT 1 0 10 "Unknown2:\n" }{MPLTEXT 1 0 1 "L" }{MPLTEXT 1 0 22 "Un knownn2:=LUnknown2:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "L" } {MPLTEXT 1 0 21 "tinfty27:=-Ltinfty17;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "L" }{MPLTEXT 1 0 22 "tinfty25:=-Ltinfty15;\n" }{MPLTEXT 1 0 1 "L" }{MPLTEXT 1 0 22 "tinfty23:=-Ltinfty13;\n" }{MPLTEXT 1 0 1 "L" } {MPLTEXT 1 0 22 "tinfty21:=-Ltinfty11;\n" }{MPLTEXT 1 0 1 "L" } {MPLTEXT 1 0 22 "tinfty20:=-Ltinfty10;\n" }{MPLTEXT 1 0 1 "L" } {MPLTEXT 1 0 20 "tinfty26:=Ltinfty16;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "L" }{MPLTEXT 1 0 21 "tinfty24:=Ltinfty14;\n" }{MPLTEXT 1 0 1 "L " }{MPLTEXT 1 0 21 "tinfty22:=Ltinfty12;\n" }{MPLTEXT 1 0 1 "L" } {MPLTEXT 1 0 12 "tinfty10:=0:" }}{PARA 0 "" 0 "" {TEXT 229 0 "" } {MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty01G6\",$I )tinfty12GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty11G6\",$I) tinfty14GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty21G6\",$I)t infty16GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty22G6\",**&I) tinfty11GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty12GF$F(I)tinfty16 GF$F(#F(F,*&I)tinfty13GF$F(I)tinfty15GF$F(F**$I)tinfty14GF$F,#F(\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty32G6\",(*&I)tinfty13GF$\"\" \"I)tinfty17GF$F(#!\"\"\"\"#*&I)tinfty14GF$F(I)tinfty16GF$F(#F(F,*$I)t infty15GF$F,#F+\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty42G6\", &*&I)tinfty15GF$\"\"\"I)tinfty17GF$F(#!\"\"\"\"#*$I)tinfty16GF$F,#F(\" \"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty52G6\",$*$I)tinfty17GF$ \"\"##!\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P1G6\"f*6#I\"xGF$ F$6$I)operatorGF$I&arrowGF$F$,(I)Pinfty01GF$\"\"\"*&I)Pinfty11GF$F-9$F -F-*&I)Pinfty21GF$F-F0\"\"#F-F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "> I#P2G6\"f*6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$,.I)Pinfty02GF$\"\"\"* &I)Pinfty12GF$F-9$F-F-*&I)Pinfty22GF$F-F0\"\"#F-*&I)Pinfty32GF$F-F0\" \"$F-*&I)Pinfty42GF$F-F0\"\"%F-*&I)Pinfty52GF$F-F0\"\"&F-F$F$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%tdP2G6\"f*6#I\"xGF$F$6$I)operatorGF$I &arrowGF$F$,**&9$\"\"&I)tinfty17GF$\"\"##!\"\"\"\"%*&F-F3,&*&I)tinfty1 5GF$\"\"\"F/F8#F2F0*$I)tinfty16GF$F0#F8F3F8F8*&F-\"\"$,(*&I)tinfty13GF $F8F/F8F9*&I)tinfty14GF$F8F;F8#F8F0*$F7F0F1F8F8*&F-F0,**&I)tinfty11GF$ F8F/F8F9*&I)tinfty12GF$F8F;F8FD*&FAF8F7F8F9*$FCF0FI*Ltinfty27G6\",$I*Ltinfty17GF$!\"\"" } }{PARA 11 "" 1 "" {XPPMATH 20 ">I*Ltinfty25G6\",$I*Ltinfty15GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Ltinfty23G6\",$I*Ltinfty13GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Ltinfty21G6\",$I*Ltinfty11GF$!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Ltinfty20G6\",$I*Ltinfty10GF$!\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Ltinfty26G6\"I*Ltinfty16GF$" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I*Ltinfty24G6\"I*Ltinfty14GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Ltinfty22G6\"I*Ltinfty12GF$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 155 "We have recopied the results regarding \+ the coefficients of the classical spectral curve and adapted the defor mation parameters according to the symmetries." }}}{EXCHG {PARA 210 "" 0 "" {TEXT 230 17 "Study at infinity" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "logPsi1Infty:=" }{MPLTEXT 1 0 22 "-1/7*tinfty17/h*lam bda" }{MPLTEXT 1 0 6 "^(7/2)" }{MPLTEXT 1 0 22 "-1/6*tinfty16/h*lambda " }{MPLTEXT 1 0 2 "^3" }{MPLTEXT 1 0 16 "-1/5*tinfty15/h*" }{MPLTEXT 1 0 6 "lambda" }{MPLTEXT 1 0 22 "^(5/2)-1/4*tinfty14/h*" }{MPLTEXT 1 0 6 "lambda" }{MPLTEXT 1 0 18 "^2-1/3*tinfty13/h*" }{MPLTEXT 1 0 6 "la mbda" }{MPLTEXT 1 0 22 "^(3/2)-1/2*tinfty12/h*" }{MPLTEXT 1 0 6 "lambd a" }{MPLTEXT 1 0 14 "^1-tinfty11/h*" }{MPLTEXT 1 0 6 "lambda" } {MPLTEXT 1 0 66 "^(1/2)-1/4*ln(lambda)+A10+ Unknown/lambda^(1/2)+ Unkn own2/lambda;\n" }{MPLTEXT 1 0 14 "logPsi2Infty:=" }{MPLTEXT 1 0 52 "-1 /7*tinfty27/h*lambda^(7/2)-1/6*tinfty26/h*lambda^3" }{MPLTEXT 1 0 122 "-1/5*tinfty25/h*lambda^(5/2)-1/4*tinfty24/h*lambda^2-1/3*tinfty23/h*l ambda^(3/2)-1/2*tinfty22/h*lambda^1-tinfty21/h*lambda" }{MPLTEXT 1 0 21 "^(1/2)-1/4*ln(lambda)" }{MPLTEXT 1 0 4 "+A20" }{MPLTEXT 1 0 42 "+ \+ Unknownn/lambda^(1/2)+ Unknownn2/lambda;" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "CurlyLlogps i1Infty:=" }{MPLTEXT 1 0 29 "-1/7*Ltinfty17/h*lambda^(7/2)" }{MPLTEXT 1 0 25 "-1/6*Ltinfty16/h*lambda^3" }{MPLTEXT 1 0 127 "-1/5*Ltinfty15/h *lambda^(5/2)-1/4*Ltinfty14/h*lambda^2-1/3*Ltinfty13/h*lambda^(3/2)-1/ 2*Ltinfty12/h*lambda^1-Ltinfty11/h*lambda" }{MPLTEXT 1 0 6 "^(1/2)" } {MPLTEXT 1 0 5 "+LA10" }{MPLTEXT 1 0 41 "+ LUnknown/lambda^(1/2)+ LUnk nown2/lambda" }{MPLTEXT 1 0 4 " ;\n" }{MPLTEXT 1 0 20 "CurlyLlogpsi2I nfty:=" }{MPLTEXT 1 0 54 "-1/7*Ltinfty27/h*lambda^(7/2)-1/6*Ltinfty26/ h*lambda^3" }{MPLTEXT 1 0 127 "-1/5*Ltinfty25/h*lambda^(5/2)-1/4*Ltinf ty24/h*lambda^2-1/3*Ltinfty23/h*lambda^(3/2)-1/2*Ltinfty22/h*lambda^1- Ltinfty21/h*lambda" }{MPLTEXT 1 0 6 "^(1/2)" }{MPLTEXT 1 0 5 "+LA20" } {MPLTEXT 1 0 44 "+ LUnknownn/lambda^(1/2)+ LUnknownn2/lambda;" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "CurlyLpsi1I nfty := exp(" }{MPLTEXT 1 0 52 "-1/7*tinfty17/h*lambda^(7/2)-1/6*tinft y16/h*lambda^3" }{MPLTEXT 1 0 122 "-1/5*tinfty15/h*lambda^(5/2)-1/4*ti nfty14/h*lambda^2-1/3*tinfty13/h*lambda^(3/2)-1/2*tinfty12/h*lambda^1- tinfty11/h*lambda" }{MPLTEXT 1 0 26 "^(1/2)-1/4*ln(lambda)+A10+" } {MPLTEXT 1 0 38 " Unknown/lambda^(1/2)+ Unknown2/lambda" }{MPLTEXT 1 0 3 ")*(" }{MPLTEXT 1 0 54 "-1/7*Ltinfty17/h*lambda^(7/2)-1/6*Ltinfty1 6/h*lambda^3" }{MPLTEXT 1 0 180 "-1/5*Ltinfty15/h*lambda^(5/2)-1/4*Lti nfty14/h*lambda^2-1/3*Ltinfty13/h*lambda^(3/2)-1/2*Ltinfty12/h*lambda^ 1-Ltinfty11/h*lambda^(1/2)+LA10+ LUnknown/lambda^(1/2)+ LUnknown2/lamb da)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 23 "CurlyLpsi2Infty := exp(" }{MPLTEXT 1 0 52 "-1/7*tinfty27/h*lambda^(7/2)-1/6*tinfty26/h*lambda^3 " }{MPLTEXT 1 0 191 "-1/5*tinfty25/h*lambda^(5/2)-1/4*tinfty24/h*lambd a^2-1/3*tinfty23/h*lambda^(3/2)-1/2*tinfty22/h*lambda^1-tinfty21/h*lam bda^(1/2)-1/4*ln(lambda)+A20+ Unknownn/lambda^(1/2)+ Unknownn2/lambda) *(" }{MPLTEXT 1 0 54 "-1/7*Ltinfty27/h*lambda^(7/2)-1/6*Ltinfty26/h*la mbda^3" }{MPLTEXT 1 0 182 "-1/5*Ltinfty25/h*lambda^(5/2)-1/4*Ltinfty24 /h*lambda^2-1/3*Ltinfty23/h*lambda^(3/2)-1/2*Ltinfty22/h*lambda^1-Ltin fty21/h*lambda^(1/2)+LA20+ LUnknownn/lambda^(1/2)+ LUnknownn2/lambda)" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 30 "psi1Infty:=exp(logPsi1Infty);\n" }{MPLTEXT 1 0 30 "ps i2Infty:=exp(logPsi2Infty);\n" }{MPLTEXT 1 0 43 "dpsi1dlambdaInfty:=di ff(psi1Infty,lambda):\n" }{MPLTEXT 1 0 43 "dpsi2dlambdaInfty:=diff(psi 2Infty,lambda):\n" }{MPLTEXT 1 0 47 "d2psi1dlambda2Infty:=diff(psi1Inf ty,lambda$2):\n" }{MPLTEXT 1 0 47 "d2psi2dlambda2Infty:=diff(psi2Infty ,lambda$2):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 89 "WronskianLambdaInfty:=h*factor(psi1Infty*dpsi2dlambdaInfty-psi2I nfty*dpsi1dlambdaInfty):\n" }{MPLTEXT 1 0 132 "WronskianLambdabisInfty :=h*simplify(factor( (diff(logPsi2Infty,lambda)-diff(logPsi1Infty,lamb da))*exp(logPsi1Infty+logPsi2Infty))):\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 116 "WronskianTildeLambdaInfty:=h^3*factor(dpsi2dlambdaIn fty*d2psi1dlambda2Infty-dpsi1dlambdaInfty*d2psi2dlambda2Infty):\n" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I-logPsi1InftyG6\",8*(I)tinfty17GF$\"\" \"I\"hGF$!\"\"I'lambdaGF$#\"\"(\"\"##F*F-*(I)tinfty16GF$F(F)F*F+\"\"$# F*\"\"'*(I)tinfty15GF$F(F)F*F+#\"\"&F.#F*F8*(I)tinfty14GF$F(F)F*F+F.#F *\"\"%*(I)tinfty13GF$F(F)F*F+#F2F.#F*F2*(I)tinfty12GF$F(F)F*F+F(#F*F.* (I)tinfty11GF$F(F)F*F+#F(F.F*-I#lnG6$%*protectedGI(_syslibGF$6#F+FI-logPsi2InftyG6\",8*(I)tinfty17GF$\"\"\"I\"hGF$!\"\" I'lambdaGF$#\"\"(\"\"##F(F-*(I)tinfty16GF$F(F)F*F+\"\"$#F*\"\"'*(I)tin fty15GF$F(F)F*F+#\"\"&F.#F(F8*(I)tinfty14GF$F(F)F*F+F.#F*\"\"%*(I)tinf ty13GF$F(F)F*F+#F2F.#F(F2*(I)tinfty12GF$F(F)F*F+F(#F*F.*(I)tinfty11GF$ F(F)F*F+#F(F.F(-I#lnG6$%*protectedGI(_syslibGF$6#F+FI3CurlyLlogpsi1InftyG6\",6*(I*Ltinfty17GF$\"\"\"I\"hGF$!\"\"I'lambd aGF$#\"\"(\"\"##F*F-*(I*Ltinfty16GF$F(F)F*F+\"\"$#F*\"\"'*(I*Ltinfty15 GF$F(F)F*F+#\"\"&F.#F*F8*(I*Ltinfty14GF$F(F)F*F+F.#F*\"\"%*(I*Ltinfty1 3GF$F(F)F*F+#F2F.#F*F2*(I*Ltinfty12GF$F(F)F*F+F(#F*F.*(I*Ltinfty11GF$F (F)F*F+#F(F.F*I%LA10GF$F(*&I)LUnknownGF$F(F+FDF(*&I*LUnknown2GF$F(F+F* F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3CurlyLlogpsi2InftyG6\",6*(I*Lti nfty17GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$#\"\"(\"\"##F(F-*(I*Ltinfty16GF$ F(F)F*F+\"\"$#F*\"\"'*(I*Ltinfty15GF$F(F)F*F+#\"\"&F.#F(F8*(I*Ltinfty1 4GF$F(F)F*F+F.#F*\"\"%*(I*Ltinfty13GF$F(F)F*F+#F2F.#F(F2*(I*Ltinfty12G F$F(F)F*F+F(#F*F.*(I*Ltinfty11GF$F(F)F*F+#F(F.F(I%LA20GF$F(*&I)LUnknow nGF$F(F+FDF**&I*LUnknown2GF$F(F+F*F(" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I0CurlyLpsi1InftyG6\"*&-I$expG6$%*protectedGI(_syslibGF$6#,8*(I)tinft y17GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$#\"\"(\"\"##F1F4*(I)tinfty16GF$F/F0 F1F2\"\"$#F1\"\"'*(I)tinfty15GF$F/F0F1F2#\"\"&F5#F1F?*(I)tinfty14GF$F/ F0F1F2F5#F1\"\"%*(I)tinfty13GF$F/F0F1F2#F9F5#F1F9*(I)tinfty12GF$F/F0F1 F2F/#F1F5*(I)tinfty11GF$F/F0F1F2#F/F5F1-I#lnGF(6#F2FCI$A10GF$F/*&I(Unk nownGF$F/F2FKF/*&I)Unknown2GF$F/F2F1F/F/,6*(I*Ltinfty17GF$F/F0F1F2F3F6 *(I*Ltinfty16GF$F/F0F1F2F9F:*(I*Ltinfty15GF$F/F0F1F2F>F@*(I*Ltinfty14G F$F/F0F1F2F5FC*(I*Ltinfty13GF$F/F0F1F2FGFH*(I*Ltinfty12GF$F/F0F1F2F/FK *(I*Ltinfty11GF$F/F0F1F2FNF1I%LA10GF$F/*&I)LUnknownGF$F/F2FKF/*&I*LUnk nown2GF$F/F2F1F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0CurlyLpsi2Infty G6\"*&-I$expG6$%*protectedGI(_syslibGF$6#,8*(I)tinfty17GF$\"\"\"I\"hGF $!\"\"I'lambdaGF$#\"\"(\"\"##F/F4*(I)tinfty16GF$F/F0F1F2\"\"$#F1\"\"'* (I)tinfty15GF$F/F0F1F2#\"\"&F5#F/F?*(I)tinfty14GF$F/F0F1F2F5#F1\"\"%*( I)tinfty13GF$F/F0F1F2#F9F5#F/F9*(I)tinfty12GF$F/F0F1F2F/#F1F5*(I)tinft y11GF$F/F0F1F2#F/F5F/-I#lnGF(6#F2FCI$A20GF$F/*&I(UnknownGF$F/F2FKF1*&I )Unknown2GF$F/F2F1F/F/,6*(I*Ltinfty17GF$F/F0F1F2F3F6*(I*Ltinfty16GF$F/ F0F1F2F9F:*(I*Ltinfty15GF$F/F0F1F2F>F@*(I*Ltinfty14GF$F/F0F1F2F5FC*(I* Ltinfty13GF$F/F0F1F2FGFH*(I*Ltinfty12GF$F/F0F1F2F/FK*(I*Ltinfty11GF$F/ F0F1F2FNF/I%LA20GF$F/*&I)LUnknownGF$F/F2FKF1*&I*LUnknown2GF$F/F2F1F/F/ " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*psi1InftyG6\"-I$expG6$%*protected GI(_syslibGF$6#,8*(I)tinfty17GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$#\"\"(\" \"##F0F3*(I)tinfty16GF$F.F/F0F1\"\"$#F0\"\"'*(I)tinfty15GF$F.F/F0F1#\" \"&F4#F0F>*(I)tinfty14GF$F.F/F0F1F4#F0\"\"%*(I)tinfty13GF$F.F/F0F1#F8F 4#F0F8*(I)tinfty12GF$F.F/F0F1F.#F0F4*(I)tinfty11GF$F.F/F0F1#F.F4F0-I#l nGF'6#F1FBI$A10GF$F.*&I(UnknownGF$F.F1FJF.*&I)Unknown2GF$F.F1F0F." }} {PARA 11 "" 1 "" {XPPMATH 20 ">I*psi2InftyG6\"-I$expG6$%*protectedGI(_ syslibGF$6#,8*(I)tinfty17GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$#\"\"(\"\"##F .F3*(I)tinfty16GF$F.F/F0F1\"\"$#F0\"\"'*(I)tinfty15GF$F.F/F0F1#\"\"&F4 #F.F>*(I)tinfty14GF$F.F/F0F1F4#F0\"\"%*(I)tinfty13GF$F.F/F0F1#F8F4#F.F 8*(I)tinfty12GF$F.F/F0F1F.#F0F4*(I)tinfty11GF$F.F/F0F1#F.F4F.-I#lnGF'6 #F1FBI$A20GF$F.*&I(UnknownGF$F.F1FJF0*&I)Unknown2GF$F.F1F0F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "L21Infty:=factor(simplify(Wr onskianTildeLambdaInfty/WronskianLambdabisInfty)):\n" }{MPLTEXT 1 0 74 "L21InftyOrdrelambda6:=factor(-residue(L21Infty/lambda^7,lambda=inf inity));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 75 "L21InftyOrdrelambda5: =factor(-residue(L21Infty/lambda^6,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L21InftyOrdrelambda4:=factor(-residue(L21Infty/lambda^5,lambda=i nfinity));\n" }{MPLTEXT 1 0 75 "L21InftyOrdrelambda3:=factor(-residue( L21Infty/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L21InftyOrdr elambda2:=factor(-residue(L21Infty/lambda^3,lambda=infinity));\n" } {MPLTEXT 1 0 75 "L21InftyOrdrelambda1:=factor(-residue(L21Infty/lambda ^2,lambda=infinity));\n" }{MPLTEXT 1 0 74 "L21InftyOrdrelambda0:=facto r(-residue(L21Infty/lambda^1,lambda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrdrelambda6G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrdrelambda5G6\",$*$I)tinfty17GF$\"\"##\"\"\" \"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrdrelambda4G6\",&*& I)tinfty15GF$\"\"\"I)tinfty17GF$F(#F(\"\"#*$I)tinfty16GF$F+#!\"\"\"\"% " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrdrelambda3G6\",(*&I)tin fty13GF$\"\"\"I)tinfty17GF$F(#F(\"\"#*&I)tinfty14GF$F(I)tinfty16GF$F(# !\"\"F+*$I)tinfty15GF$F+#F(\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L 21InftyOrdrelambda2G6\",**&I)tinfty11GF$\"\"\"I)tinfty17GF$F(#F(\"\"#* &I)tinfty12GF$F(I)tinfty16GF$F(#!\"\"F+*&I)tinfty13GF$F(I)tinfty15GF$F (F**$I)tinfty14GF$F+#F0\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21In ftyOrdrelambda1G6\",**(I(UnknownGF$\"\"\"I\"hGF$F(I)tinfty17GF$F(#F(\" \"#*&I)tinfty11GF$F(I)tinfty15GF$F(F+*&I)tinfty12GF$F(I)tinfty14GF$F(# !\"\"F,*$I)tinfty13GF$F,#F(\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L 21InftyOrdrelambda0G6\",$*&,.**I(UnknownGF$\"\"\"I\"hGF$F*I)tinfty15GF $F*I)tinfty17GF$F*\"\"#**F+F*I)Unknown2GF$F*I)tinfty16GF$F*F-F*!\"%*(F +F*I)tinfty14GF$F*F-F*F.*(F+F*F,F*F1F*!\"#*(I)tinfty11GF$F*I)tinfty13G F$F*F-F*F.*&I)tinfty12GF$F.F-F*!\"\"F*F-F<#F*\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "factor(simplify(" }{MPLTEXT 1 0 20 "L21Inft yOrdrelambda5" }{MPLTEXT 1 0 10 "*lambda^5+" }{MPLTEXT 1 0 20 "L21Inft yOrdrelambda4" }{MPLTEXT 1 0 10 "*lambda^4+" }{MPLTEXT 1 0 20 "L21Inft yOrdrelambda3" }{MPLTEXT 1 0 10 "*lambda^3+" }{MPLTEXT 1 0 20 "L21Inft yOrdrelambda2" }{MPLTEXT 1 0 10 "*lambda^2+" }{MPLTEXT 1 0 20 "L21Inft yOrdrelambda1" }{MPLTEXT 1 0 27 "*lambda- (-tdP2(lambda))));" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,**(I(UnknownG6\"\"\"\"I\"hGF'F(I)tinfty17 GF'F(\"\"#*&I)tinfty11GF'F(I)tinfty15GF'F(F+*&I)tinfty12GF'F(I)tinfty1 4GF'F(!\"#*$I)tinfty13GF'F+F(F(I'lambdaGF'F(#F(\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 90 "We deduce that L_\{2,1\} behaves at infinity l ike -tdP2(\\lambda)+C_1*lambda+C_0+ O(1/lambda)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "L22Infty:=factor(h*simplify(diff(WronskianLamb dabisInfty,lambda)/WronskianLambdabisInfty)):\n" }{MPLTEXT 1 0 74 "L22 InftyOrdrelambda6:=factor(-residue(L22Infty/lambda^7,lambda=infinity)) ;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 75 "L22InftyOrdrelambda5:=factor (-residue(L22Infty/lambda^6,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L2 2InftyOrdrelambda4:=factor(-residue(L22Infty/lambda^5,lambda=infinity) );\n" }{MPLTEXT 1 0 75 "L22InftyOrdrelambda3:=factor(-residue(L22Infty /lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L22InftyOrdrelambda2 :=factor(-residue(L22Infty/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L22InftyOrdrelambda1:=factor(-residue(L22Infty/lambda^2,lambda=i nfinity));\n" }{MPLTEXT 1 0 75 "L22InftyOrdrelambda0:=factor(-residue( L22Infty/lambda^1,lambda=infinity));\n" }{MPLTEXT 1 0 80 "L22InftyOrdr elambdaMinus1:=factor(-residue(L22Infty/lambda^0,lambda=infinity));\n" }{MPLTEXT 1 0 82 "L22InftyOrdrelambdaMinus2:=factor(-residue(L22Infty /lambda^(-1),lambda=infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L2 2InftyOrdrelambda6G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L22Inf tyOrdrelambda5G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L22InftyOr drelambda4G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L22InftyOrdrel ambda3G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L22InftyOrdrelambd a2G6\",$I)tinfty16GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L22Inft yOrdrelambda1G6\",$I)tinfty14GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L22InftyOrdrelambda0G6\",$I)tinfty12GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I:L22InftyOrdrelambdaMinus1G6\",$I\"hGF$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I:L22InftyOrdrelambdaMinus2G6\",$*(I\"hGF$\" \"\",&*&I)Unknown2GF$F(I)tinfty17GF$F(\"\"#I)tinfty15GF$F(F(F,!\"\"F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "simplify(L22InftyOrdrel ambda2*lambda^2+L22InftyOrdrelambda1*lambda+L22InftyOrdrelambda0-P1(la mbda));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 2 47 "We deduce that L_\{2,2\} behaves at infinity like" } {TEXT 2 19 " -tinfty16*lambda^2" }{TEXT 2 88 "-tinfty14*lambda -tinfty 12+2*h/lambda +O(1/lambda^2) =P1(lambda) +h/lambda+O(1/lambda^2)" }}} {EXCHG {PARA 209 "" 0 "" {TEXT 2 37 "Thus we get the form of the matri x L:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 215 37 "L_\{2,2\}= P_1(lambda) \+ +h/(lambda-q1)" }{TEXT 2 1 " " }{TEXT 216 14 "+h/(lambda-q2)" }{TEXT 2 2 " \n" }{TEXT 217 7 "L_\{2,1\}" }{TEXT 218 2 "= " }{TEXT 219 6 "-td P_2" }{TEXT 220 8 "(lambda)" }{TEXT 221 4 "+C1*" }{TEXT 222 6 "lambda" }{TEXT 223 3 "+C0" }{TEXT 224 36 " -h*p1/(lambda-q1)-h*p2/(lambda-q2 )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "L21Form:=-tdP2(lambda) - h*p1/(lambda-q1)-h*" }{MPLTEXT 1 0 14 "p2/(lambda-q2)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 35 "L22Form:=P1(lambda) +h/(lambda-q1)" } {MPLTEXT 1 0 14 "+h/(lambda-q2)" }{MPLTEXT 1 0 2 ";\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(L21FormG6\",.*&I'lambdaGF$\"\"&I)tinfty17GF$\"\"## \"\"\"\"\"%*&F'F-,&*&I)tinfty15GF$F,F)F,#!\"\"F**$I)tinfty16GF$F*F+F,F 3*&F'\"\"$,(*&I)tinfty13GF$F,F)F,F2*&I)tinfty14GF$F,F5F,#F,F**$F1F*#F3 F-F,F3*&F'F*,**&I)tinfty11GF$F,F)F,F2*&I)tinfty12GF$F,F5F,F=*&F:F,F1F, F2*$FI(L22FormG6\",,*&I )tinfty16GF$\"\"\"I'lambdaGF$\"\"#!\"\"*&I)tinfty14GF$F(F)F(F+I)tinfty 12GF$F+*&I\"hGF$F(,&F)F(I#q1GF$F+F+F(*&F0F(,&F)F(I#q2GF$F+F+F(" }}} {EXCHG {PARA 209 "" 0 "" {TEXT 225 37 "Computation of the Auxiliary ma trix A" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 2 91 "We define the deformatio n operator \\mathcal\{L\}=\\hbar (alpha7*\\partial_\{t_\{\\infty^\{(1) \},7\} +" }{TEXT 2 47 "alpha6*\\partial_\{t_\{\\infty^\{(1)\},6\}+... \+ alpha1*" }{TEXT 2 28 "\\partial_\{t_\{\\infty^\{(1)\},1\}" }{TEXT 2 1 ")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "WronskianCurlyLInfty: =factor(psi1Infty*CurlyLpsi2Infty-psi2Infty*CurlyLpsi1Infty):\n" } {MPLTEXT 1 0 71 "A12Infty:=factor(simplify(WronskianCurlyLInfty/Wronsk ianLambdaInfty)):\n" }{MPLTEXT 1 0 48 "Y1Infty:=h*factor(dpsi1dlambdaI nfty/psi1Infty):\n" }{MPLTEXT 1 0 48 "Y2Infty:=h*factor(dpsi2dlambdaIn fty/psi2Infty):\n" }{MPLTEXT 1 0 44 "Z1Infty:=factor(CurlyLpsi1Infty/p si1Infty):\n" }{MPLTEXT 1 0 44 "Z2Infty:=factor(CurlyLpsi2Infty/psi2In fty):\n" }{MPLTEXT 1 0 68 "A12bisInfty:=factor(simplify((Z2Infty-Z1Inf ty)/(Y2Infty-Y1Infty))):\n" }{MPLTEXT 1 0 83 "A11Infty:=factor(simplif y( (Y2Infty*Z1Infty-Y1Infty*Z2Infty)/(Y2Infty-Y1Infty) )):\n" } {MPLTEXT 1 0 39 "factor(simplify(A12bisInfty-A12Infty));" }}{PARA 11 " " 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Ltinfty17:=h*alpha7:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "Ltinf ty16:=h*alpha6:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "Ltinfty15:=h*a lpha5:\n" }{MPLTEXT 1 0 21 "Ltinfty14:=h*alpha4:\n" }{MPLTEXT 1 0 13 " Ltinfty13:=h*" }{MPLTEXT 1 0 6 "alpha3" }{MPLTEXT 1 0 2 ":\n" } {MPLTEXT 1 0 13 "Ltinfty12:=h*" }{MPLTEXT 1 0 6 "alpha2" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 13 "Ltinfty11:=h*" }{MPLTEXT 1 0 6 "alpha1" } {MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 14 "Ltinfty10:=0 :\n" }{MPLTEXT 1 0 14 "Ltinfty20:=0:\n" }{MPLTEXT 1 0 11 "LA20:=LA10:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "A12InftyLambda4:=factor( -residue(A12Infty/lambda^5,lambda=infinity));" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 70 "A12InftyLambda3:=factor(-residue(A12Infty/lambda^4,la mbda=infinity));\n" }{MPLTEXT 1 0 70 "A12InftyLambda2:=factor(-residue (A12Infty/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 70 "A12InftyLam bda1:=factor(-residue(A12Infty/lambda^2,lambda=infinity));\n" } {MPLTEXT 1 0 70 "A12InftyLambda0:=factor(-residue(A12Infty/lambda^1,la mbda=infinity));\n" }{MPLTEXT 1 0 75 "A12InftyLambdaMinus1:=factor(-re sidue(A12Infty/lambda^0,lambda=infinity));\n" }{MPLTEXT 1 0 77 "A12Inf tyLambdaMinus2:=factor(-residue(A12Infty/lambda^(-1),lambda=infinity)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda4G6\"\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda3G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda2G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda1G6\",$*&I'alpha7GF$\"\"\"I)tinfty17GF$! \"\"#\"\"#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda0G6 \",$*&,&*&I'alpha5GF$\"\"\"I)tinfty17GF$F*\"\"(*&I'alpha7GF$F*I)tinfty 15GF$F*!\"&F*F+!\"##\"\"#\"#N" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5A12I nftyLambdaMinus1G6\",$*&,**&I'alpha3GF$\"\"\"I)tinfty17GF$\"\"#\"#N*(I 'alpha5GF$F*I)tinfty15GF$F*F+F*!#@*(I'alpha7GF$F*I)tinfty13GF$F*F+F*!# :*&F3F*F0F,\"#:F*F+!\"$#F,\"$0\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5A 12InftyLambdaMinus2G6\",$*&,0*&I'alpha1GF$\"\"\"I)tinfty17GF$\"\"$\"$0 \"*(I'alpha3GF$F*I)tinfty15GF$F*F+\"\"#!#N*(I'alpha5GF$F*I)tinfty13GF$ F*F+F1!#@*(F4F*F0F1F+F*\"#@*(I'alpha7GF$F*I)tinfty11GF$F*F+F1!#:**F:F* F5F*F0F*F+F*\"#I*&F:F*F0F,F " 0 "" {MPLTEXT 1 0 64 "A12Form:=2*nuMinus1*lambda+nu0+ mu1/(lambda -q1)+ mu2/(lambda-q2)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 27 "nuMinus 1:=A12InftyLambda1;\n" }{MPLTEXT 1 0 21 "nu0:=A12InftyLambda0;" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 33 "Equation1:=A12InftyLambdaMinus1- (" }{MPLTEXT 1 0 33 "-residue(A12Form,lambda=infinity)" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 33 "Equation2:=A12InftyLambdaMinus2-(" } {MPLTEXT 1 0 40 "-residue(A12Form*lambda,lambda=infinity)" }{MPLTEXT 1 0 2 ");" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(A12FormG6\",**&I)nuMinus1GF$\"\"\"I'lambdaGF$F(\"\"#I$ nu0GF$F(*&I$mu1GF$F(,&F)F(I#q1GF$!\"\"F0F(*&I$mu2GF$F(,&F)F(I#q2GF$F0F 0F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)nuMinus1G6\",$*&I'alpha7GF$\" \"\"I)tinfty17GF$!\"\"#\"\"#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$ nu0G6\",$*&,&*&I'alpha5GF$\"\"\"I)tinfty17GF$F*\"\"(*&I'alpha7GF$F*I)t infty15GF$F*!\"&F*F+!\"##\"\"#\"#N" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I *Equation1G6\",(*&,**&I'alpha3GF$\"\"\"I)tinfty17GF$\"\"#\"#N*(I'alpha 5GF$F*I)tinfty15GF$F*F+F*!#@*(I'alpha7GF$F*I)tinfty13GF$F*F+F*!#:*&F3F *F0F,\"#:F*F+!\"$#F,\"$0\"I$mu1GF$!\"\"I$mu2GF$F<" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*Equation2G6\",(*&,0*&I'alpha1GF$\"\"\"I)tinfty17GF$\" \"$\"$0\"*(I'alpha3GF$F*I)tinfty15GF$F*F+\"\"#!#N*(I'alpha5GF$F*I)tinf ty13GF$F*F+F1!#@*(F4F*F0F1F+F*\"#@*(I'alpha7GF$F*I)tinfty11GF$F*F+F1!# :**F:F*F5F*F0F*F+F*\"#I*&F:F*F0F,F " 0 "" {MPLTEXT 1 0 359 "mu1:=2*(-35*alpha3*q2*tinfty17^3+21*alpha5*q2*tinfty15*tinfty17^2 +15*alpha7*q2*tinfty13*tinfty17^2-15*alpha7*q2*tinfty15^2*tinfty17+105 *alpha1*tinfty17^3-35*alpha3*tinfty15*tinfty17^2-21*alpha5*tinfty13*ti nfty17^2+21*alpha5*tinfty15^2*tinfty17-15*alpha7*tinfty11*tinfty17^2+3 0*alpha7*tinfty13*tinfty15*tinfty17-15*alpha7*tinfty15^3)/(105*tinfty1 7^4*(q1-q2));\n" }{MPLTEXT 1 0 363 "mu2:=-1/(105*tinfty17^4*(q1-q2))* \+ 2*(-35*alpha3*q1*tinfty17^3+21*alpha5*q1*tinfty15*tinfty17^2+15*alpha7 *q1*tinfty13*tinfty17^2-15*alpha7*q1*tinfty15^2*tinfty17+105*alpha1*ti nfty17^3-35*alpha3*tinfty15*tinfty17^2-21*alpha5*tinfty13*tinfty17^2+2 1*alpha5*tinfty15^2*tinfty17-15*alpha7*tinfty11*tinfty17^2+30*alpha7*t infty13*tinfty15*tinfty17-15*alpha7*tinfty15^3);\n" }{MPLTEXT 1 0 21 " simplify(Equation1);\n" }{MPLTEXT 1 0 20 "simplify(Equation2);" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I$mu1G6\",$*(,8*(I'alpha3GF$\"\"\"I#q2G F$F*I)tinfty17GF$\"\"$!#N**I'alpha5GF$F*F+F*I)tinfty15GF$F*F,\"\"#\"#@ **I'alpha7GF$F*F+F*I)tinfty13GF$F*F,F2\"#:**F5F*F+F*F1F2F,F*!#:*&I'alp ha1GF$F*F,F-\"$0\"*(F)F*F1F*F,F2F.*(F0F*F6F*F,F2!#@*(F0F*F1F2F,F*F3*(F 5F*I)tinfty11GF$F*F,F2F9**F5F*F6F*F1F*F,F*\"#I*&F5F*F1F-F9F*F,!\"%,&I# q1GF$F*F+!\"\"FI#F2F<" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$mu2G6\",$*(I )tinfty17GF$!\"%,&I#q1GF$\"\"\"I#q2GF$!\"\"F-,8*(I'alpha3GF$F+F*F+F'\" \"$!#N**I'alpha5GF$F+F*F+I)tinfty15GF$F+F'\"\"#\"#@**I'alpha7GF$F+F*F+ I)tinfty13GF$F+F'F6\"#:**F9F+F*F+F5F6F'F+!#:*&I'alpha1GF$F+F'F1\"$0\"* (F0F+F5F+F'F6F2*(F4F+F:F+F'F6!#@*(F4F+F5F6F'F+F7*(F9F+I)tinfty11GF$F+F 'F6F=**F9F+F:F+F5F+F'F+\"#I*&F9F+F5F1F=F+#!\"#F@" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 68 "We compute the values of nu_\{\\infty,k \} using the theoretical results" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Minfty:=Matrix(rinfty," }{MPLTEXT 1 0 6 "rinfty" }{MPLTEXT 1 0 5 ",0):\n" }{MPLTEXT 1 0 12 "2*rinfty-1;\n" }{MPLTEXT 1 0 23 "Minfty [1,1]:=tinfty17:\n" }{MPLTEXT 1 0 23 "Minfty[2,2]:=tinfty17:\n" } {MPLTEXT 1 0 23 "Minfty[3,3]:=tinfty17:\n" }{MPLTEXT 1 0 22 "Minfty[4, 4]:=tinfty17:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "Minfty[2,1]:=tin fty15:\n" }{MPLTEXT 1 0 23 "Minfty[3,2]:=tinfty15:\n" }{MPLTEXT 1 0 22 "Minfty[4,3]:=tinfty15:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "Min fty[3,1]:=tinfty13:\n" }{MPLTEXT 1 0 22 "Minfty[4,2]:=tinfty13:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "Minfty[4,1]:=tinfty11:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "Minfty;\n" }{MPLTEXT 1 0 31 "RHSM atrix:=Matrix(rinfty,1,0):\n" }{MPLTEXT 1 0 28 "RHSMatrix[1,1]:=2*alph a7/7:\n" }{MPLTEXT 1 0 28 "RHSMatrix[2,1]:=2*alpha5/5:\n" }{MPLTEXT 1 0 28 "RHSMatrix[3,1]:=2*alpha3/3:\n" }{MPLTEXT 1 0 28 "RHSMatrix[4,1]: =2*alpha1/1:\n" }{MPLTEXT 1 0 11 "RHSMatrix;\n" }{MPLTEXT 1 0 43 "NuVe ctor:=Multiply(Minfty^(-1),RHSMatrix):\n" }{MPLTEXT 1 0 14 "nuMinus1Th eo:=" }{MPLTEXT 1 0 15 "NuVector[1,1];\n" }{MPLTEXT 1 0 9 "nu0Theo:=" }{MPLTEXT 1 0 15 "NuVector[2,1];\n" }{MPLTEXT 1 0 24 "nu1Theo:=NuVecto r[3,1];\n" }{MPLTEXT 1 0 23 "nu2Theo:=NuVector[4,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I +modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$68- I$mtrGF$6)-I$mtdGF$6(-I#miGF$6&Q)tinfty17F'/%'italicGQ%trueF'/%+foregr oundGQ([0,0,0]F'/%,mathvariantGQ'italicF'/%)rowalignGQ!F'/%,columnalig nGFF/%+groupalignGFF/%(rowspanGQ\"1F'/%+columnspanGFM-F56(-I#mnGF$6%Q \"0F'F>/FBQ'normalF'FDFGFIFKFNFPFPFDFGFI-F26)-F56(-F86&Q)tinfty15F'F;F >FAFDFGFIFKFNF4FPFPFDFGFI-F26)-F56(-F86&Q)tinfty13F'F;F>FAFDFGFIFKFNFZ F4FPFDFGFI-F26)-F56(-F86&Q)tinfty11F'F;F>FAFDFGFIFKFNF[oFZF4FDFGFI/%&a lignGQ%axisF'/FEQ)baselineF'/FHQ'centerF'/FJQ'|frleft|hrF'/%/alignment scopeGF=/%,columnwidthGQ%autoF'/%&widthGFdp/%+rowspacingGQ&1.0exF'/%.c olumnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF_q/%&frameGF _q/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumns GFiq/%-displaystyleGFiq/%%sideGQ&rightF'/%0minlabelspacingGF\\qF>FV/%% openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfenced G6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableG F$68-I$mtrGF$6&-I$mtdGF$6(-F,6%-I&mfracGF$6)-I#mnGF$6%Q\"2F'/%+foregro undGQ([0,0,0]F'/%,mathvariantGQ'normalF'-F=6%Q\"7F'F@FC/%.linethicknes sGQ\"1F'/%+denomalignGQ'centerF'/%)numalignGFN/%)bevelledGQ&falseF'F@- I#moGF$6-Q1⁢F'FC/%&fenceGFS/%*separatorGFS/%)stretchyGF S/%*symmetricGFS/%(largeopGFS/%.movablelimitsGFS/%'accentGFS/%'lspaceG Q&0.0emF'/%'rspaceGFbo-F,6#-I#miGF$6&Q)α7F'/%'italicGQ%trueF'F@/ FDQ'italicF'/%)rowalignGQ!F'/%,columnalignGFbp/%+groupalignGFbp/%(rows panGFK/%+columnspanGFKF`pFcpFep-F26&-F56(-F,6%-F:6)F<-F=6%Q\"5F'F@FCFI FLFOFQF@FT-F,6#-Fho6&Q)α5F'F[pF@F^pF`pFcpFepFgpFipF`pFcpFep-F26& -F56(-F,6%-F:6)F<-F=6%Q\"3F'F@FCFIFLFOFQF@FT-F,6#-Fho6&Q)α3F'F[p F@F^pF`pFcpFepFgpFipF`pFcpFep-F26&-F56(-F,6%FI-nuMinus1TheoG6\",$*&I'alpha7GF$\"\"\"I)tinfty17GF$!\" \"#\"\"#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(nu0TheoG6\",&*(I)tin fty15GF$\"\"\"I)tinfty17GF$!\"#I'alpha7GF$F(#F*\"\"(*&F)!\"\"I'alpha5G F$F(#\"\"#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(nu1TheoG6\",(*(,&* &I)tinfty13GF$\"\"\"I)tinfty17GF$F*F**$I)tinfty15GF$\"\"#!\"\"F*F+!\"$ I'alpha7GF$F*#!\"#\"\"(*(F-F*F+F3I'alpha5GF$F*#F3\"\"&*&F+F/I'alpha3GF $F*#F.\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(nu2TheoG6\",**(,(*&I)t infty11GF$\"\"\"I)tinfty17GF$\"\"#F**(I)tinfty13GF$F*I)tinfty15GF$F*F+ F*!\"#*$F/\"\"$F*F*F+!\"%I'alpha7GF$F*#F0\"\"(*(,&*&F.F*F+F*F**$F/F,! \"\"F*F+!\"$I'alpha5GF$F*#F0\"\"&*(F/F*F+F0I'alpha3GF$F*#F0F2*&F+F;I'a lpha1GF$F*F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 102 "We check agreem ent between theoretical formulas and practical one for nu_\{infty,-1\} and \\nu_\{\\infty,0\}" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " simplify(nuMinus1-nuMinus1Theo);\n" }{MPLTEXT 1 0 22 "simplify(nu0-nu0 Theo);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 125 "We check \+ theoretical formulas giving the relations between the mu's and the nu' s and with the deformation parameters alpha's." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Vinfty:=Matrix(g,g,0):\n" }{MPLTEXT 1 0 16 "Vin fty[1,1]:=1:\n" }{MPLTEXT 1 0 16 "Vinfty[1,2]:=1:\n" }{MPLTEXT 1 0 17 "Vinfty[2,1]:=q1:\n" }{MPLTEXT 1 0 17 "Vinfty[2,2]:=q2:\n" }{MPLTEXT 1 0 8 "Vinfty;\n" }{MPLTEXT 1 0 25 "muVector:=Matrix(g,1,0):\n" } {MPLTEXT 1 0 20 "muVector[1,1]:=mu1:\n" }{MPLTEXT 1 0 20 "muVector[2,1 ]:=mu2:\n" }{MPLTEXT 1 0 36 "nuVectorReducedTheo:=Matrix(g,1,0):\n" } {MPLTEXT 1 0 15 "nuVectorReduced" }{MPLTEXT 1 0 4 "Theo" }{MPLTEXT 1 0 10 "[1,1]:=nu1" }{MPLTEXT 1 0 4 "Theo" }{MPLTEXT 1 0 2 ":\n" } {MPLTEXT 1 0 15 "nuVectorReduced" }{MPLTEXT 1 0 4 "Theo" }{MPLTEXT 1 0 10 "[2,1]:=nu2" }{MPLTEXT 1 0 4 "Theo" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 35 "simplify(Multiply(Vinfty,muVector)-" } {MPLTEXT 1 0 21 "nuVectorReducedTheo);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 30 "BigMatrix:=Matrix(g+2,g+2,0):\n" } {MPLTEXT 1 0 19 "BigMatrix[1,1]:=1:\n" }{MPLTEXT 1 0 19 "BigMatrix[2,2 ]:=1:\n" }{MPLTEXT 1 0 46 "for i from 3 to g+2 do for j from 3 to g+2 \+ do\n" }{MPLTEXT 1 0 41 "BigMatrix[i,j]:=Vinfty[i-2,j-2]: od: od:\n" } {MPLTEXT 1 0 11 "BigMatrix;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 28 " BigVector:=Matrix(g+2,1,0):\n" }{MPLTEXT 1 0 26 "BigVector[1,1]:=nuMin us1:\n" }{MPLTEXT 1 0 21 "BigVector[2,1]:=nu0:\n" }{MPLTEXT 1 0 20 "Bi gVector[3,1]:=mu1:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "BigVector[4 ,1]:=mu2:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 10 "BigVector:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 44 "simplify(Mu ltiply(Minfty,Multiply(BigMatrix," }{MPLTEXT 1 0 12 "BigVector))-" } {MPLTEXT 1 0 12 "RHSMatrix);\n" }{MPLTEXT 1 0 14 "nu1:=nu1Theo:\n" } {MPLTEXT 1 0 13 "nu2:=nu2Theo:" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfe ncedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mta bleGF$66-I$mtrGF$6'-I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F '/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupali gnGFC/%(rowspanGF:/%+columnspanGF:F4FAFDFF-F26'-F56(-I#miGF$6&Q#q1F'/% 'italicGQ%trueF'F;/F?Q'italicF'FAFDFFFHFJ-F56(-FQ6&Q#q2F'FTF;FWFAFDFFF HFJFAFDFF/%&alignGQ%axisF'/FBQ)baselineF'/FEQ'centerF'/FGQ'|frleft|hrF '/%/alignmentscopeGFV/%,columnwidthGQ%autoF'/%&widthGFeo/%+rowspacingG Q&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesG F`p/%&frameGF`p/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/% -equalcolumnsGFjp/%-displaystyleGFjp/%%sideGQ&rightF'/%0minlabelspacin gGF]pF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$ 6#-I'mtableGF$66-I$mtrGF$6&-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ( [0,0,0]F'/%,mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+ groupalignGFC/%(rowspanGQ\"1F'/%+columnspanGFJFAFDFFF1/%&alignGQ%axisF '/FBQ)baselineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF '/%,columnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnsp acingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-fr amespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%- displaystyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&c loseGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenam eG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6) -I$mtdGF$6(-I#mnGF$6%Q\"1F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'n ormalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGF:/ %+columnspanGF:-F56(-F86%Q\"0F'F;F>FAFDFFFHFJFLFLFAFDFF-F26)FLF4FLFLFA FDFF-F26)FLFLF4F4FAFDFF-F26)FLFL-F56(-I#miGF$6&Q#q1F'/%'italicGQ%trueF 'F;/F?Q'italicF'FAFDFFFHFJ-F56(-FZ6&Q#q2F'FgnF;FjnFAFDFFFHFJFAFDFF/%&a lignGQ%axisF'/FBQ)baselineF'/FEQ'centerF'/FGQ'|frleft|hrF'/%/alignment scopeGFin/%,columnwidthGQ%autoF'/%&widthGF^p/%+rowspacingGQ&1.0exF'/%. columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFip/%&frameG Fip/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumn sGFcq/%-displaystyleGFcq/%%sideGQ&rightF'/%0minlabelspacingGFfpF;F>/%% openGQ\"[F'/%&closeGQ\"]F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfenced G6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableG F$68-I$mtrGF$6&-I$mtdGF$6(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%, mathvariantGQ'normalF'/%)rowalignGQ!F'/%,columnalignGFC/%+groupalignGF C/%(rowspanGQ\"1F'/%+columnspanGFJFAFDFFF1F1F1/%&alignGQ%axisF'/FBQ)ba selineF'/FEQ&rightF'/FGQ'|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,colu mnwidthGQ%autoF'/%&widthGFen/%+rowspacingGQ&1.0exF'/%.columnspacingGQ& 0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF`o/%&frameGF`o/%-framespaci ngGQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFjo/%-displays tyleGFjo/%%sideGFS/%0minlabelspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\" ]F'" }}}{EXCHG {PARA 211 "" 0 "" {TEXT 210 25 "We now deal with A_\{1 ,1\}" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "A11InftyLambda5:=fa ctor(-residue(A11Infty/lambda^6,lambda=infinity));" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 70 "A11InftyLambda4:=factor(-residue(A11Infty/lambda ^5,lambda=infinity));\n" }{MPLTEXT 1 0 70 "A11InftyLambda3:=factor(-re sidue(A11Infty/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 70 "A11Inf tyLambda2:=factor(-residue(A11Infty/lambda^3,lambda=infinity));\n" } {MPLTEXT 1 0 70 "A11InftyLambda1:=factor(-residue(A11Infty/lambda^2,la mbda=infinity));\n" }{MPLTEXT 1 0 70 "A11InftyLambda0:=factor(-residue (A11Infty/lambda^1,lambda=infinity));\n" }{MPLTEXT 1 0 75 "A11InftyLam bdaMinus1:=factor(-residue(A11Infty/lambda^0,lambda=infinity)):\n" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda5G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda4G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda3G6\",$*&,&*&I'alpha6GF$\"\"\"I)tinfty17 GF$F*\"\"(*&I'alpha7GF$F*I)tinfty16GF$F*!\"'F*F+!\"\"#F1\"#U" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda2G6\",$*&,**&I'alpha4GF$\"\" \"I)tinfty17GF$\"\"#\"#N*(I'alpha5GF$F*I)tinfty16GF$F*F+F*!#G*(I'alpha 7GF$F*I)tinfty14GF$F*F+F*!#?*(F3F*I)tinfty15GF$F*F0F*\"#?F*F+!\"##!\" \"\"$S\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda1G6\",$*&,2 *&I'alpha2GF$\"\"\"I)tinfty17GF$\"\"$\"$0\"*(I'alpha3GF$F*I)tinfty16GF $F*F+\"\"#!#q*(I'alpha5GF$F*I)tinfty14GF$F*F+F1!#U**F4F*I)tinfty15GF$F *F0F*F+F*\"#U*(I'alpha7GF$F*I)tinfty12GF$F*F+F1!#I**F;F*I)tinfty13GF$F *F0F*F+F*\"#I**F;F*F5F*F8F*F+F*F@*(F;F*F8F1F0F*F=F*F+!\"$#!\"\"\"$5#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda0G6\",$*&,@*&I%LA10GF $\"\"\"I)tinfty17GF$\"\"%\"$5#*(I'alpha1GF$F*I)tinfty16GF$F*F+\"\"$F-* (I'alpha3GF$F*I)tinfty14GF$F*F+F1\"#q**F3F*I)tinfty15GF$F*F0F*F+\"\"#! #q*(I'alpha5GF$F*I)tinfty12GF$F*F+F1\"#U**F;F*I)tinfty13GF$F*F0F*F+F8! #U**F;F*F4F*F7F*F+F8F@**F;F*F7F8F0F*F+F*F=*(I'alpha7GF$F*I\"hGF$F*F+F1 \"#:**FDF*I)tinfty11GF$F*F0F*F+F8!#I**FDF*F " 0 "" {MPLTEXT 1 0 21 "A11Form:=c3*lambda^3+" }{MPLTEXT 1 0 2 "c2" }{MPLTEXT 1 0 40 "*lambda^2+c1*lambda+c0+ rho1/(lambda-q1)" }{MPLTEXT 1 0 18 "+ rho2/(lambda-q2)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 71 "simplify(-residue(A11Form/lambda^4,lambda=infinity)-A 11InftyLambda3); \n" }{MPLTEXT 1 0 8 "solve(\{\n" }{MPLTEXT 1 0 67 "fa ctor(-residue(A11Form/lambda^4,lambda=infinity))=A11InftyLambda3," } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 68 "factor(-residue(A11Form/lambda^3 ,lambda=infinity))=A11InftyLambda2,\n" }{MPLTEXT 1 0 80 "factor(-resid ue(A11Form/lambda^2,lambda=infinity))=A11InftyLambda1\},\{c1,c2,c3\}): " }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(A11FormG6\",.*&I#c3GF$\"\"\"I'lam bdaGF$\"\"$F(*&I#c2GF$F(F)\"\"#F(*&I#c1GF$F(F)F(F(I#c0GF$F(*&I%rho1GF$ F(,&F)F(I#q1GF$!\"\"F5F(*&I%rho2GF$F(,&F)F(I#q2GF$F5F5F(" }}{PARA 11 " " 1 "" {XPPMATH 20 ",$*&,&*&,&I#c3G6\"\"#UI'alpha6GF(\"\"(\"\"\"I)tinf ty17GF(F,F,*&I'alpha7GF(F,I)tinfty16GF(F,!\"'F,F-!\"\"#F,F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 280 "c1 := -(105*alpha2*tinfty17 ^3-70*alpha3*tinfty16*tinfty17^2-42*alpha5*tinfty14*tinfty17^2+42*alph a5*tinfty15*tinfty16*tinfty17-30*alpha7*tinfty12*tinfty17^2+30*alpha7* tinfty13*tinfty16*tinfty17+30*alpha7*tinfty14*tinfty15*tinfty17-30*alp ha7*tinfty15^2*tinfty16)/(210*tinfty17^3):\n" }{MPLTEXT 1 0 132 "c2 := -(35*alpha4*tinfty17^2-28*alpha5*tinfty16*tinfty17-20*alpha7*tinfty14 *tinfty17+20*alpha7*tinfty15*tinfty16)/(140*tinfty17^2):\n" }{MPLTEXT 1 0 60 "c3 := -(7*alpha6*tinfty17-6*alpha7*tinfty16)/(42*tinfty17):\n" }{MPLTEXT 1 0 68 "factor(-residue(A11Form/lambda^4,lambda=infinity)-A 11InftyLambda3);\n" }{MPLTEXT 1 0 68 "factor(-residue(A11Form/lambda^3 ,lambda=infinity)-A11InftyLambda2);\n" }{MPLTEXT 1 0 67 "factor(-resid ue(A11Form/lambda^2,lambda=infinity)-A11InftyLambda1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 93 "We check the result for (c_\{\\infty,k\})_\{1\\leq k\\leq r_ \\infty-1\} with the theoretical formulas" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "cVectorTheo:=Matrix(rinfty-1,1,0):\n" }{MPLTEXT 1 0 26 "cVectorTheo[1,1]:=c3Theo:\n" }{MPLTEXT 1 0 26 "cVectorTheo[2,1]:=c 2Theo:\n" }{MPLTEXT 1 0 25 "cVectorTheo[3,1]:=c1Theo:" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 12 "cVectorTheo;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 44 "MinftyReduced:=Matrix(rinfty-1,rinfty-1,0):\n" }{MPLTEXT 1 0 13 "MinftyReduced" }{MPLTEXT 1 0 17 "[1,1]:=tinfty17:\n" }{MPLTEXT 1 0 13 "MinftyReduced" }{MPLTEXT 1 0 17 "[2,2]:=tinfty17:\n" }{MPLTEXT 1 0 13 "MinftyReduced" }{MPLTEXT 1 0 17 "[3,3]:=tinfty17:\n" }{MPLTEXT 1 0 13 "MinftyReduced" }{MPLTEXT 1 0 17 "[2,1]:=tinfty15:\n" } {MPLTEXT 1 0 13 "MinftyReduced" }{MPLTEXT 1 0 17 "[3,2]:=tinfty15:\n" }{MPLTEXT 1 0 13 "MinftyReduced" }{MPLTEXT 1 0 16 "[3,1]:=tinfty13:" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 14 "MinftyReduced;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 31 "RHSTheo:=Matrix(rinfty-1,1 ,0):\n" }{MPLTEXT 1 0 32 "RHSTheo[1,1]:=alpha7/7*tinfty16-" }{MPLTEXT 1 0 19 "alpha6/6*tinfty17:\n" }{MPLTEXT 1 0 32 "RHSTheo[2,1]:=alpha7/7 *tinfty14-" }{MPLTEXT 1 0 18 "alpha6/6*tinfty15+" }{MPLTEXT 1 0 18 "al pha5/5*tinfty16-" }{MPLTEXT 1 0 17 "alpha4/4*tinfty17" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 50 "RHSTheo[3,1]:=alpha7/7*tinfty12-alpha6/6*tin fty13+" }{MPLTEXT 1 0 18 "alpha5/5*tinfty14-" }{MPLTEXT 1 0 18 "alpha4 /4*tinfty15+" }{MPLTEXT 1 0 18 "alpha3/3*tinfty16-" }{MPLTEXT 1 0 17 " alpha2/2*tinfty17" }{MPLTEXT 1 0 1 ":" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6'-I%mrowGF$6 #-I'mtableGF$67-I$mtrGF$6&-I$mtdGF$6(-I#miGF$6&Q'c3TheoF'/%'italicGQ%t rueF'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'italicF'/%)rowalignGQ!F '/%,columnalignGFF/%+groupalignGFF/%(rowspanGQ\"1F'/%+columnspanGFMFDF GFI-F26&-F56(-F86&Q'c2TheoF'F;F>FAFDFGFIFKFNFDFGFI-F26&-F56(-F86&Q'c1T heoF'F;F>FAFDFGFIFKFNFDFGFI/%&alignGQ%axisF'/FEQ)baselineF'/FHQ'center F'/FJQ'|frleft|hrF'/%/alignmentscopeGF=/%,columnwidthGQ%autoF'/%&width GFeo/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%non eF'/%,columnlinesGF`p/%&frameGF`p/%-framespacingGQ,0.4em~0.5exF'/%*equ alrowsGQ&falseF'/%-equalcolumnsGFjp/%-displaystyleGFjp/%%sideGQ&rightF '/%0minlabelspacingGF]pF>/FBQ'normalF'/%%openGQ\"[F'/%&closeGQ\"]F'" } }{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Typeset tingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$67-I$mtrGF$6(-I$mtdGF$6(-I# miGF$6&Q)tinfty17F'/%'italicGQ%trueF'/%+foregroundGQ([0,0,0]F'/%,mathv ariantGQ'italicF'/%)rowalignGQ!F'/%,columnalignGFF/%+groupalignGFF/%(r owspanGQ\"1F'/%+columnspanGFM-F56(-I#mnGF$6%Q\"0F'F>/FBQ'normalF'FDFGF IFKFNFPFDFGFI-F26(-F56(-F86&Q)tinfty15F'F;F>FAFDFGFIFKFNF4FPFDFGFI-F26 (-F56(-F86&Q)tinfty13F'F;F>FAFDFGFIFKFNFZF4FDFGFI/%&alignGQ%axisF'/FEQ )baselineF'/FHQ'centerF'/FJQ'|frleft|hrF'/%/alignmentscopeGF=/%,column widthGQ%autoF'/%&widthGF]p/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0. 8emF'/%)rowlinesGQ%noneF'/%,columnlinesGFhp/%&frameGFhp/%-framespacing GQ,0.4em~0.5exF'/%*equalrowsGQ&falseF'/%-equalcolumnsGFbq/%-displaysty leGFbq/%%sideGQ&rightF'/%0minlabelspacingGFepF>FV/%%openGQ\"[F'/%&clos eGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "cVectorTheo:=" }{MPLTEXT 1 0 28 "Multiply(MinftyReduced^(-1)," }{MPLTEXT 1 0 10 "RHST heo):\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 22 "cVectorTheo[1,1 ]-c3);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 22 "cVectorTheo[2, 1]-c2);\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 21 "cVectorTheo[3 ,1]-c1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 228 27 "Summary of all coefficients" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "c3;\n" }{MPLTEXT 1 0 4 "c2;\n" } {MPLTEXT 1 0 3 "c1;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&*&I'alpha6G 6\"\"\"\"I)tinfty17GF'F(\"\"(*&I'alpha7GF'F(I)tinfty16GF'F(!\"'F(F)!\" \"#F/\"#U" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,**&I'alpha4G6\"\"\"\"I )tinfty17GF'\"\"#\"#N*(I'alpha5GF'F(I)tinfty16GF'F(F)F(!#G*(I'alpha7GF 'F(I)tinfty14GF'F(F)F(!#?*(F1F(I)tinfty15GF'F(F.F(\"#?F(F)!\"##!\"\"\" $S\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,2*&I'alpha2G6\"\"\"\"I)tinf ty17GF'\"\"$\"$0\"*(I'alpha3GF'F(I)tinfty16GF'F(F)\"\"#!#q*(I'alpha5GF 'F(I)tinfty14GF'F(F)F/!#U**F2F(I)tinfty15GF'F(F.F(F)F(\"#U*(I'alpha7GF 'F(I)tinfty12GF'F(F)F/!#I**F9F(I)tinfty13GF'F(F.F(F)F(\"#I**F9F(F3F(F6 F(F)F(F>*(F9F(F6F/F.F(F;F(F)!\"$#!\"\"\"$5#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nuMinus1;\n" }{MPLTEXT 1 0 5 "nu0;\n" }{MPLTEXT 1 0 5 "nu1;\n" }{MPLTEXT 1 0 4 "nu2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$ *&I'alpha7G6\"\"\"\"I)tinfty17GF%!\"\"#\"\"#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&,&*&I'alpha5G6\"\"\"\"I)tinfty17GF'F(\"\"(*&I'alpha7G F'F(I)tinfty15GF'F(!\"&F(F)!\"##\"\"#\"#N" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*(,&*&I)tinfty13G6\"\"\"\"I)tinfty17GF'F(F(*$I)tinfty15 GF'\"\"#!\"\"F(F)!\"$I'alpha7GF'F(#!\"#\"\"(*(F+F(F)F1I'alpha5GF'F(#F1 \"\"&*&F)F-I'alpha3GF'F(#F,\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**( ,(*&I)tinfty11G6\"\"\"\"I)tinfty17GF'\"\"#F(*(I)tinfty13GF'F(I)tinfty1 5GF'F(F)F(!\"#*$F-\"\"$F(F(F)!\"%I'alpha7GF'F(#F.\"\"(*(,&*&F,F(F)F(F( *$F-F*!\"\"F(F)!\"$I'alpha5GF'F(#F.\"\"&*(F-F(F)F.I'alpha3GF'F(#F.F0*& F)F9I'alpha1GF'F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "mu1; \n" }{MPLTEXT 1 0 4 "mu2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(,8*(I'a lpha3G6\"\"\"\"I#q2GF'F(I)tinfty17GF'\"\"$!#N**I'alpha5GF'F(F)F(I)tinf ty15GF'F(F*\"\"#\"#@**I'alpha7GF'F(F)F(I)tinfty13GF'F(F*F0\"#:**F3F(F) F(F/F0F*F(!#:*&I'alpha1GF'F(F*F+\"$0\"*(F&F(F/F(F*F0F,*(F.F(F4F(F*F0!# @*(F.F(F/F0F*F(F1*(F3F(I)tinfty11GF'F(F*F0F7**F3F(F4F(F/F(F*F(\"#I*&F3 F(F/F+F7F(F*!\"%,&I#q1GF'F(F)!\"\"FG#F0F:" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(I)tinfty17G6\"!\"%,&I#q1GF%\"\"\"I#q2GF%!\"\"F+,8*(I' alpha3GF%F)F(F)F$\"\"$!#N**I'alpha5GF%F)F(F)I)tinfty15GF%F)F$\"\"#\"#@ **I'alpha7GF%F)F(F)I)tinfty13GF%F)F$F4\"#:**F7F)F(F)F3F4F$F)!#:*&I'alp ha1GF%F)F$F/\"$0\"*(F.F)F3F)F$F4F0*(F2F)F8F)F$F4!#@*(F2F)F3F4F$F)F5*(F 7F)I)tinfty11GF%F)F$F4F;**F7F)F8F)F3F)F$F)\"#I*&F7F)F3F/F;F)#!\"#F>" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }