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{SECT 0 {EXCHG {PARA 11 "" 1 "" {XPPMATH 20 "%#%?G" }}}{EXCHG {PARA 0
 "" 0 "" {TEXT 215 149 "In this Maple file, we compute the Casimir coe
fficients of the Lax matrix L associated to the Painlev\351 5 equation
 in relation with the spectral curve" }{TEXT 210 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "restart:\n" }{MPLTEXT 1 0 27 "P1:=x-> P011
/x+P121/(x-1)^2" }{MPLTEXT 1 0 13 "+P111/(x-1);\n" }{MPLTEXT 1 0 23 "P
2:=x-> P022/x^2+P012/x" }{MPLTEXT 1 0 13 "+P142/(x-1)^4" }{MPLTEXT 1 
0 13 "+P132/(x-1)^3" }{MPLTEXT 1 0 26 "+P122/(x-1)^2+P112/(x-1);\n" }
{MPLTEXT 1 0 45 "SpectralCurve:=unapply( y^2-P1(x)*y+P2(x),y);" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I#P1G6\"f*6#I\"xGF$F$6$I)operatorGF$I&a
rrowGF$F$,(*&I%P011GF$\"\"\"F'!\"\"F.*&I%P121GF$F.),&F'F.F.F/\"\"#F/F.
*&I%P111GF$F.F3F/F.F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P2G6\"f*
6#I\"xGF$F$6$I)operatorGF$I&arrowGF$F$,.*&I%P022GF$\"\"\")F'\"\"#!\"\"
F.*&I%P012GF$F.F'F1F.*&I%P142GF$F.),&F'F.F.F1\"\"%F1F.*&I%P132GF$F.)F7
\"\"$F1F.*&I%P122GF$F.)F7F0F1F.*&I%P112GF$F.F7F1F.F$F$F$" }}{PARA 11 "
" 1 "" {XPPMATH 20 ">I.SpectralCurveG6\"f*6#I\"yGF$F$6$I)operatorGF$I&
arrowGF$F$,2*$)F'\"\"#\"\"\"F/*&,(*&I%P011GF$F/I\"xGF$!\"\"F/*&I%P121G
F$F/),&F4F/F/F5F.F5F/*&I%P111GF$F/F9F5F/F/F'F/F5*&I%P022GF$F/)F4F.F5F/
*&I%P012GF$F/F4F5F/*&I%P142GF$F/)F9\"\"%F5F/*&I%P132GF$F/)F9\"\"$F5F/*
&I%P122GF$F/F8F5F/*&I%P112GF$F/F9F5F/F$F$F$" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 42 "DiaginftySheet1:=-tinfty10/x+Unknown/x^2;\n" }
{MPLTEXT 1 0 43 "DiaginftySheet2:=-tinfty20/x+Unknown2/x^2;\n" }
{MPLTEXT 1 0 30 "Diag0Sheet1:=t010/x+Unknown3;\n" }{MPLTEXT 1 0 30 "Di
ag0Sheet2:=t020/x+Unknown4;\n" }{MPLTEXT 1 0 47 "Diag1Sheet1:=t111/(x-
1)^2+t110/(x-1)+Unknown5;\n" }{MPLTEXT 1 0 13 "Diag1Sheet2:=" }
{MPLTEXT 1 0 13 "t121/(x-1)^2+" }{MPLTEXT 1 0 20 "t120/(x-1)+Unknown6;
" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0DiaginftyShe
et1G6\",&*&I)tinfty10GF$\"\"\"I\"xGF$!\"\"F**&I(UnknownGF$F()F)\"\"#F*
F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0DiaginftySheet2G6\",&*&I)tinfty
20GF$\"\"\"I\"xGF$!\"\"F**&I)Unknown2GF$F()F)\"\"#F*F(" }}{PARA 11 "" 
1 "" {XPPMATH 20 ">I,Diag0Sheet1G6\",&*&I%t010GF$\"\"\"I\"xGF$!\"\"F(I
)Unknown3GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,Diag0Sheet2G6\",&*&
I%t020GF$\"\"\"I\"xGF$!\"\"F(I)Unknown4GF$F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I,Diag1Sheet1G6\",(*&I%t111GF$\"\"\"),&I\"xGF$F(F(!\"\"
\"\"#F,F(*&I%t110GF$F(F*F,F(I)Unknown5GF$F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I,Diag1Sheet2G6\",(*&I%t121GF$\"\"\"),&I\"xGF$F(F(!\"\"
\"\"#F,F(*&I%t120GF$F(F*F,F(I)Unknown6GF$F(" }}}{EXCHG {PARA 0 "" 0 ""
 {TEXT 216 67 "Expression of P_1 in terms of the diagonal expansion in
 both sheets" }{TEXT 216 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 58 "series(DiaginftySheet1+DiaginftySheet2-P1(x),x=infinity);\n" }
{MPLTEXT 1 0 46 "series(Diag0Sheet1+Diag0Sheet2-P1(x),x=0,10);\n" }
{MPLTEXT 1 0 45 "series(Diag1Sheet1+Diag1Sheet2-P1(x),x=1,10);" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 17 "P011:=t010+t020;\n" }{MPLTEXT 1 
0 17 "P121:=t111+t121;\n" }{MPLTEXT 1 0 17 "P111:=t110+t120;\n" }
{MPLTEXT 1 0 48 "CoherenceEquation1:=tinfty10+tinfty20+P011+P111;" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",.*&,*I)tinfty10G6\"!\"\"I)tinfty20GF&F'
I%P011GF&F'I%P111GF&F'\"\"\"I\"xGF&F'F+*&,*I(UnknownGF&F+I)Unknown2GF&
F+I%P121GF&F'F*F'F+)F,\"\"#F'F+*&,&*&F3F+F1F+F'F*F'F+)F,\"\"$F'F+*&,&*
&F8F+F1F+F'F*F'F+)F,\"\"%F'F+*&,&*&F=F+F1F+F'F*F'F+)F,\"\"&F'F+-I\"OG6
$%*protectedGI(_syslibGF&6#*$)F,\"\"'F'F+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "+;I\"xG6\",(I%t010GF$\"\"\"I%t020GF$F'I%P011GF$!\"\"F*,*I
)Unknown3GF$F'I)Unknown4GF$F'I%P121GF$F*I%P111GF$F'\"\"!,&*&\"\"#F'F.F
'F*F/F'F',&*&\"\"$F'F.F'F*F/F'F3,&*&\"\"%F'F.F'F*F/F'F6,&*&\"\"&F'F.F'
F*F/F'F9,&*&\"\"'F'F.F'F*F/F'F<,&*&\"\"(F'F.F'F*F/F'F?,&*&\"\")F'F.F'F
*F/F'FB,&*&\"\"*F'F.F'F*F/F'FE,&*&\"#5F'F.F'F*F/F'FH-I\"OG6$%*protecte
dGI(_syslibGF$6#F'FK" }}{PARA 11 "" 1 "" {XPPMATH 20 "+=,&I\"xG6\"\"\"
\"F&!\"\",(I%t111GF%F&I%t121GF%F&I%P121GF%F'!\"#,(I%t110GF%F&I%t120GF%
F&I%P111GF%F'F',(I)Unknown5GF%F&I)Unknown6GF%F&I%P011GF%F'\"\"!F4F&,$F
4F'\"\"#F4\"\"$F6\"\"%F4\"\"&F6\"\"'F4\"\"(F6\"\")F4\"\"*-I\"OG6$%*pro
tectedGI(_syslibGF%6#F&\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P011G6
\",&I%t010GF$\"\"\"I%t020GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P12
1G6\",&I%t111GF$\"\"\"I%t121GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%
P111G6\",&I%t110GF$\"\"\"I%t120GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "
>I3CoherenceEquation1G6\",.I)tinfty10GF$\"\"\"I)tinfty20GF$F'I%t010GF$
F'I%t020GF$F'I%t110GF$F'I%t120GF$F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
216 10 "Study at 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "facto
r(series(SpectralCurve(Diag0Sheet1),x=0)):\n" }{MPLTEXT 1 0 48 "factor
(series(SpectralCurve(Diag0Sheet2),x=0)):\n" }{MPLTEXT 1 0 51 "EQ01:=r
esidue(x^3*SpectralCurve(Diag0Sheet1),x=0);\n" }{MPLTEXT 1 0 51 "EQ02:
=residue(x^3*SpectralCurve(Diag0Sheet2),x=0);\n" }{MPLTEXT 1 0 51 "EQ0
3:=residue(x^2*SpectralCurve(Diag0Sheet1),x=0);\n" }{MPLTEXT 1 0 51 "E
Q04:=residue(x^2*SpectralCurve(Diag0Sheet2),x=0);\n" }{MPLTEXT 1 0 49 
"EQ05:=residue(x*SpectralCurve(Diag0Sheet1),x=0);\n" }{MPLTEXT 1 0 49 
"EQ06:=residue(x*SpectralCurve(Diag0Sheet2),x=0);\n" }{MPLTEXT 1 0 51 
"EQ07:=residue(x^0*SpectralCurve(Diag0Sheet1),x=0);\n" }{MPLTEXT 1 0 
51 "EQ08:=residue(x^0*SpectralCurve(Diag0Sheet2),x=0);\n" }{MPLTEXT 1 
0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ01G
6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ02G6\"\"\"!" }}{PARA 11
 "" 1 "" {XPPMATH 20 ">I%EQ03G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I%EQ04G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ05G6\",&*&I%t
010GF$\"\"\"I%t020GF$F(!\"\"I%P022GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I%EQ06G6\",&*&I%t010GF$\"\"\"I%t020GF$F(!\"\"I%P022GF$F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ07G6\",0*&I%t010GF$\"\"\"I%t110GF$F
(F(*&F'F(I%t111GF$F(!\"\"*&F'F(I%t120GF$F(F(*&F'F(I%t121GF$F(F,*&F'F(I
)Unknown3GF$F(F(*&I%t020GF$F(F2F(F,I%P012GF$F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I%EQ08G6\",0*&I%t010GF$\"\"\"I)Unknown4GF$F(!\"\"*&I%t02
0GF$F(I%t110GF$F(F(*&F,F(I%t111GF$F(F**&F,F(I%t120GF$F(F(*&F,F(I%t121G
F$F(F**&F,F(F)F(F(I%P012GF$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "P022:=solve(EQ05,P022);\n" }{MPLTEXT 1 0 16 "simplify(EQ05);\n" 
}{MPLTEXT 1 0 16 "simplify(EQ06);\n" }{MPLTEXT 1 0 16 "simplify(EQ07);
\n" }{MPLTEXT 1 0 15 "simplify(EQ08);" }}{PARA 11 "" 1 "" {XPPMATH 20 
">I%P022G6\"*&I%t010GF$\"\"\"I%t020GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",(*&,,I%t110G6\"\"\"\"I%t111GF&!\"\"I%t120GF&F'I%t121GF&F
)I)Unknown3GF&F'F'I%t010GF&F'F'*&F,F'I%t020GF&F'F)I%P012GF&F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",(*&,,I%t110G6\"\"\"\"I%t111GF&!\"\"I%t1
20GF&F'I%t121GF&F)I)Unknown4GF&F'F'I%t020GF&F'F'*&F,F'I%t010GF&F'F)I%P
012GF&F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 216 17 "Study at infinity" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "series(SpectralCurve(Diagi
nftySheet1),x=infinity):\n" }{MPLTEXT 1 0 51 "series(SpectralCurve(Dia
ginftySheet2),x=infinity):\n" }{MPLTEXT 1 0 78 "EQinftDiag1Sheet1:=res
idue(x^(-2)*SpectralCurve(DiaginftySheet1),x=infinity);\n" }{MPLTEXT 
1 0 69 "EQinfty2:=residue(x^(-2)*SpectralCurve(DiaginftySheet2),x=infi
nity);\n" }{MPLTEXT 1 0 69 "EQinfty3:=residue(x^(-1)*SpectralCurve(Dia
ginftySheet1),x=infinity);\n" }{MPLTEXT 1 0 69 "EQinfty4:=residue(x^(-
1)*SpectralCurve(DiaginftySheet2),x=infinity);\n" }{MPLTEXT 1 0 68 "EQ
infty5:=residue(x^(0)*SpectralCurve(DiaginftySheet1),x=infinity);\n" }
{MPLTEXT 1 0 68 "EQinfty6:=residue(x^(0)*SpectralCurve(DiaginftySheet2
),x=infinity);\n" }{MPLTEXT 1 0 68 "EQinfty7:=residue(x^(1)*SpectralCu
rve(DiaginftySheet1),x=infinity);\n" }{MPLTEXT 1 0 68 "EQinfty8:=resid
ue(x^(1)*SpectralCurve(DiaginftySheet2),x=infinity);\n" }}{PARA 11 "" 
1 "" {XPPMATH 20 ">I2EQinftDiag1Sheet1G6\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I)EQinfty2G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)
EQinfty3G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty4G6\"\"\"
!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty5G6\",&I%P012GF$!\"\"I%P1
12GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty6G6\",&I%P012GF$!\"
\"I%P112GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)EQinfty7G6\",,*$)I)t
infty10GF$\"\"#\"\"\"!\"\"*&,*I%t010GF$F*I%t020GF$F*I%t110GF$F*I%t120G
F$F*F*F(F*F+*&F.F*F/F*F+I%P122GF$F+I%P112GF$F+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I)EQinfty8G6\",,*$)I)tinfty20GF$\"\"#\"\"\"!\"\"*&,*I%t0
10GF$F*I%t020GF$F*I%t110GF$F*I%t120GF$F*F*F(F*F+*&F.F*F/F*F+I%P122GF$F
+I%P112GF$F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "CoherenceEq
uation2:=-EQinfty5;\n" }{MPLTEXT 1 0 31 "CoherenceEquation3:=-EQinfty7
;\n" }{MPLTEXT 1 0 31 "CoherenceEquation4:=-EQinfty8;\n" }{MPLTEXT 1 
0 58 "simplify(CoherenceEquation3-CoherenceEquation1*tinfty10);\n" }
{MPLTEXT 1 0 20 "CoherenceEquation5:=" }{MPLTEXT 1 0 57 "simplify(Cohe
renceEquation4-CoherenceEquation1*tinfty20);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I3CoherenceEquation2G6\",&I%P012GF$\"\"\"I%P112GF$F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I3CoherenceEquation3G6\",,*$)I)tinfty10
GF$\"\"#\"\"\"F**&,*I%t010GF$F*I%t020GF$F*I%t110GF$F*I%t120GF$F*F*F(F*
F**&F-F*F.F*F*I%P122GF$F*I%P112GF$F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "
>I3CoherenceEquation4G6\",,*$)I)tinfty20GF$\"\"#\"\"\"F**&,*I%t010GF$F
*I%t020GF$F*I%t110GF$F*I%t120GF$F*F*F(F*F**&F-F*F.F*F*I%P122GF$F*I%P11
2GF$F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&I%t010G6\"\"\"\"I%t020GF%F
&F&*&I)tinfty10GF%F&I)tinfty20GF%F&!\"\"I%P112GF%F&I%P122GF%F&" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I3CoherenceEquation5G6\",**&I%t010GF$\"
\"\"I%t020GF$F(F(*&I)tinfty10GF$F(I)tinfty20GF$F(!\"\"I%P112GF$F(I%P12
2GF$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "CoherenceEquation
1;\n" }{MPLTEXT 1 0 20 "CoherenceEquation2;\n" }{MPLTEXT 1 0 19 "Coher
enceEquation5;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.I)tinfty10G6\"\"\"\"
I)tinfty20GF$F%I%t010GF$F%I%t020GF$F%I%t110GF$F%I%t120GF$F%" }}{PARA 
11 "" 1 "" {XPPMATH 20 ",&I%P012G6\"\"\"\"I%P112GF$F%" }}{PARA 11 "" 1
 "" {XPPMATH 20 ",**&I%t010G6\"\"\"\"I%t020GF%F&F&*&I)tinfty10GF%F&I)t
infty20GF%F&!\"\"I%P112GF%F&I%P122GF%F&" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 216 10 "Study at 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 
"series(SpectralCurve(Diag1Sheet1),x=1):\n" }{MPLTEXT 1 0 40 "series(S
pectralCurve(Diag1Sheet2),x=1):\n" }{MPLTEXT 1 0 57 "EQ19:=residue((x-
1)^(3)*SpectralCurve(Diag1Sheet1),x=1);\n" }{MPLTEXT 1 0 56 "EQ20:=res
idue((x-1)^(3)*SpectralCurve(Diag1Sheet2),x=1);" }{MPLTEXT 1 0 1 "\n" 
}{MPLTEXT 1 0 57 "EQ21:=residue((x-1)^(4)*SpectralCurve(Diag1Sheet1),x
=1);\n" }{MPLTEXT 1 0 56 "EQ22:=residue((x-1)^(4)*SpectralCurve(Diag1S
heet2),x=1);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 57 "EQ11:=residue((x-
1)^(2)*SpectralCurve(Diag1Sheet1),x=1);\n" }{MPLTEXT 1 0 57 "EQ12:=res
idue((x-1)^(2)*SpectralCurve(Diag1Sheet2),x=1);\n" }{MPLTEXT 1 0 57 "E
Q13:=residue((x-1)^(1)*SpectralCurve(Diag1Sheet1),x=1);\n" }{MPLTEXT 
1 0 57 "EQ14:=residue((x-1)^(1)*SpectralCurve(Diag1Sheet2),x=1);\n" }
{MPLTEXT 1 0 57 "EQ15:=residue((x-1)^(0)*SpectralCurve(Diag1Sheet1),x=
1);\n" }{MPLTEXT 1 0 57 "EQ16:=residue((x-1)^(0)*SpectralCurve(Diag1Sh
eet2),x=1);\n" }{MPLTEXT 1 0 58 "EQ17:=residue((x-1)^(-1)*SpectralCurv
e(Diag1Sheet1),x=1);\n" }{MPLTEXT 1 0 58 "EQ18:=residue((x-1)^(-1)*Spe
ctralCurve(Diag1Sheet2),x=1);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ
19G6\",&*&I%t111GF$\"\"\"I%t121GF$F(!\"\"I%P142GF$F(" }}{PARA 11 "" 1 
"" {XPPMATH 20 ">I%EQ20G6\",&*&I%t111GF$\"\"\"I%t121GF$F(!\"\"I%P142GF
$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ21G6\"\"\"!" }}{PARA 11 "" 1
 "" {XPPMATH 20 ">I%EQ22G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%
EQ11G6\",(*&I%t110GF$\"\"\"I%t121GF$F(!\"\"*&I%t111GF$F(I%t120GF$F(F*I
%P132GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ12G6\",(*&I%t110GF$\"
\"\"I%t121GF$F(!\"\"*&I%t111GF$F(I%t120GF$F(F*I%P132GF$F(" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I%EQ13G6\",.*&I%t010GF$\"\"\"I%t111GF$F(!\"\"*&I
%t020GF$F(F)F(F**&I%t110GF$F(I%t120GF$F(F**&F)F(I)Unknown5GF$F(F(*&I%t
121GF$F(F1F(F*I%P122GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ14G6\"
,.*&I%t010GF$\"\"\"I%t121GF$F(!\"\"*&I%t020GF$F(F)F(F**&I%t110GF$F(I%t
120GF$F(F**&I%t111GF$F(I)Unknown6GF$F(F**&F)F(F2F(F(I%P122GF$F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ15G6\",0*&I%t010GF$\"\"\"I%t110GF$F
(!\"\"*&F'F(I%t111GF$F(F(*&I%t020GF$F(F)F(F**&F.F(F,F(F(*&F)F(I)Unknow
n5GF$F(F(*&I%t120GF$F(F1F(F*I%P112GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I%EQ16G6\",0*&I%t010GF$\"\"\"I%t120GF$F(!\"\"*&F'F(I%t121GF$F(F(*
&I%t020GF$F(F)F(F**&F.F(F,F(F(*&I%t110GF$F(I)Unknown6GF$F(F**&F)F(F2F(
F(I%P112GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ17G6\",4*&I%t010GF
$\"\"\"I%t020GF$F(F(*&F'F(I%t110GF$F(F(*&F'F(I%t111GF$F(!\"\"*&F'F(I)U
nknown5GF$F(F.*&F)F(F+F(F(*&F)F(F-F(F.*&F)F(F0F(F.*$)F0\"\"#F(F(I%P012
GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%EQ18G6\",4*&I%t010GF$\"\"\"I
%t020GF$F(F(*&F'F(I%t120GF$F(F(*&F'F(I%t121GF$F(!\"\"*&F'F(I)Unknown6G
F$F(F.*&F)F(F+F(F(*&F)F(F-F(F.*&F)F(F0F(F.*$)F0\"\"#F(F(I%P012GF$F(" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "P142:=solve(EQ19,P142);\n"
 }{MPLTEXT 1 0 16 "simplify(EQ19);\n" }{MPLTEXT 1 0 16 "simplify(EQ20)
;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P142G6\"*&I%t111GF$\"\"\"I%t12
1GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "P132:
=solve(EQ11,P132);\n" }{MPLTEXT 1 0 16 "simplify(EQ11);\n" }{MPLTEXT 
1 0 16 "simplify(EQ12);\n" }{MPLTEXT 1 0 15 "simplify(EQ13);" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I%P132G6\",&*&I%t110GF$\"\"\"I%t121GF$F(F(*&I
%t111GF$F(I%t120GF$F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",
**&,(I%t010G6\"!\"\"I%t020GF&F'I)Unknown5GF&\"\"\"F*I%t111GF&F*F**&I%t
110GF&F*I%t120GF&F*F'*&I%t121GF&F*F)F*F'I%P122GF&F*" }}}{EXCHG {PARA 0
 "" 0 "" {TEXT 216 135 "Summary of coefficients and additional coheren
ce relations (sum of residues is null and P112+P012= tinfty21*tinfty10
+tinfty11*tinfty20)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "P011
:=P011;\n" }{MPLTEXT 1 0 11 "P111:=P111;" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 11 "P121:=P121;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n
" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 11 "P142:=P142;" }{MPLTEXT 1 0 1 
"\n" }{MPLTEXT 1 0 11 "P132:=P132;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 12 "P122:=P122;\n" }{MPLTEXT 1 0 12 "P112:=P112;\n" }{MPLTEXT 1 0 1 
"\n" }{MPLTEXT 1 0 11 "P022:=P022;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 11 "P012:=P012;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT
 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "CoherenceEquation1;
\n" }{MPLTEXT 1 0 20 "CoherenceEquation2;\n" }{MPLTEXT 1 0 19 "Coheren
ceEquation5;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P011G6\",&I%t010GF$\"
\"\"I%t020GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P111G6\",&I%t110GF
$\"\"\"I%t120GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P121G6\",&I%t11
1GF$\"\"\"I%t121GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P142G6\"*&I%
t111GF$\"\"\"I%t121GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P132G6\",
&*&I%t110GF$\"\"\"I%t121GF$F(F(*&I%t111GF$F(I%t120GF$F(F(" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I%P122G6\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
%P112G6\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P022G6\"*&I%t010GF$\"
\"\"I%t020GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%P012G6\"F#" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",.I)tinfty10G6\"\"\"\"I)tinfty20GF$F%I%t
010GF$F%I%t020GF$F%I%t110GF$F%I%t120GF$F%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",&I%P012G6\"\"\"\"I%P112GF$F%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",**&I%t010G6\"\"\"\"I%t020GF%F&F&*&I)tinfty10GF%F&I)tinft
y20GF%F&!\"\"I%P112GF%F&I%P122GF%F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
216 107 "There are 3 unknown coefficients but two additional relations
, thus only one remaining unknown coefficient " }}}{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 }