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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 208 174 "In this Maple sheet, we
 compute the Lax matrices using the asymptotics of the wave functions \+
and the local diagonalization for the second element of the Painlev\35
1 2 hierarchy." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 232 65 "Loading previ
ous results on the coefficient of the spectral curve" }}{EXCHG {PARA 0
 "" 0 "" {TEXT 208 118 "We first use the expression of the coefficient
s of the spectral curve in terms of the irregular times and monodromie
s." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart:\n" }{MPLTEXT 
1 0 40 "CoherenceEquation1 :=tinfty10+tinfty20;\n" }{MPLTEXT 1 0 21 "t
infty20:=-tinfty10:\n" }{MPLTEXT 1 0 32 "Pinfty01 := -tinfty11-tinfty2
1;\n" }{MPLTEXT 1 0 32 "Pinfty11 := -tinfty12-tinfty22;\n" }{MPLTEXT 
1 0 32 "Pinfty21 := -tinfty13-tinfty23;\n" }{MPLTEXT 1 0 32 "Pinfty31 \+
:= -tinfty14-tinfty24;\n" }{MPLTEXT 1 0 31 "Pinfty62 := tinfty14*tinft
y24;\n" }{MPLTEXT 1 0 49 "Pinfty52 := tinfty13*tinfty24+tinfty14*tinft
y23;\n" }{MPLTEXT 1 0 67 "Pinfty42 := tinfty12*tinfty24+tinfty13*tinft
y23+tinfty14*tinfty22;\n" }{MPLTEXT 1 0 85 "Pinfty32 := tinfty11*tinft
y24+tinfty12*tinfty23+tinfty13*tinfty22+tinfty14*tinfty21;\n" }
{MPLTEXT 1 0 103 "Pinfty22 := tinfty20*tinfty14+tinfty10*tinfty24+tinf
ty11*tinfty23+tinfty12*tinfty22+tinfty13*tinfty21;\n" }{MPLTEXT 1 0 
55 "P1:=x-> Pinfty01+Pinfty11*x+Pinfty21*x^2+Pinfty31*x^3:\n" }
{MPLTEXT 1 0 93 "P2:=x-> Pinfty02+Pinfty12*x+Pinfty22*x^2+Pinfty32*x^3
+Pinfty42*x^4+Pinfty52*x^5+Pinfty62*x^6:" }}{PARA 0 "" 0 "" {MPLTEXT 
1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3CoherenceEquation1G6\",&
I)tinfty10GF$\"\"\"I)tinfty20GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
)Pinfty01G6\",&I)tinfty11GF$!\"\"I)tinfty21GF$F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I)Pinfty11G6\",&I)tinfty12GF$!\"\"I)tinfty22GF$F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty21G6\",&I)tinfty13GF$!\"\"I)tin
fty23GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty31G6\",&I)tinfty1
4GF$!\"\"I)tinfty24GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty62G
6\"*&I)tinfty14GF$\"\"\"I)tinfty24GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I)Pinfty52G6\",&*&I)tinfty13GF$\"\"\"I)tinfty24GF$F(F(*&I)tinfty1
4GF$F(I)tinfty23GF$F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty42G6
\",(*&I)tinfty12GF$\"\"\"I)tinfty24GF$F(F(*&I)tinfty13GF$F(I)tinfty23G
F$F(F(*&I)tinfty14GF$F(I)tinfty22GF$F(F(" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I)Pinfty32G6\",**&I)tinfty11GF$\"\"\"I)tinfty24GF$F(F(*&I)tinfty1
2GF$F(I)tinfty23GF$F(F(*&I)tinfty13GF$F(I)tinfty22GF$F(F(*&I)tinfty14G
F$F(I)tinfty21GF$F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Pinfty22G6\"
,,*&I)tinfty10GF$\"\"\"I)tinfty14GF$F(!\"\"*&F'F(I)tinfty24GF$F(F(*&I)
tinfty11GF$F(I)tinfty23GF$F(F(*&I)tinfty12GF$F(I)tinfty22GF$F(F(*&I)ti
nfty13GF$F(I)tinfty21GF$F(F(" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 232 
30 "Expression of the Lax matrix L" }{TEXT 232 0 "" }}{EXCHG {PARA 210
 "" 0 "" {TEXT 233 36 "Study of the asymptotics at infinity" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 266 "logPsi1Infty:=-tinfty14/4/h
*lambda^4-tinfty13/3/h*lambda^3-tinfty12/2/h*lambda^2-tinfty11/h*lambd
a-tinfty10/h*ln(lambda)+A10-A12/(2-1)/lambda^(2-1)-A13/(3-1)/lambda^(3
-1)-A14/(4-1)/lambda^(4-1)-A15/(5-1)/lambda^(5-1)-A16/(6-1)/lambda^(6-
1)-A17/(7-1)/lambda^(7-1)  ;\n" }{MPLTEXT 1 0 279 "logPsi2Infty:=-tinf
ty24/4/h*lambda^4-tinfty23/3/h*lambda^3-tinfty22/2/h*lambda^2-tinfty21
/h*lambda-tinfty20/h*ln(lambda)-1*ln(lambda)+A20-A22/(2-1)/lambda^(2-1
)-A23/(3-1)/lambda^(3-1)-A24/(4-1)/lambda^(4-1)-A25/(5-1)/lambda^(5-1)
-A26/(6-1)/lambda^(6-1)-A27/(7-1)/lambda^(7-1)  ;\n" }{MPLTEXT 1 0 
279 "Llogpsi1Infty:=-Ltinfty14/4/h*lambda^4-Ltinfty13/3/h*lambda^3-Lti
nfty12/2/h*lambda^2-Ltinfty11/h*lambda-Ltinfty10/h*ln(lambda)+LA10-LA1
2/(2-1)/lambda^(2-1)-LA13/(3-1)/lambda^(3-1)-LA14/(4-1)/lambda^(4-1)-L
A15/(5-1)/lambda^(5-1)-LA16/(6-1)/lambda^(6-1)-LA17/(7-1)/lambda^(7-1)
  ;\n" }{MPLTEXT 1 0 279 "Llogpsi2Infty:=-Ltinfty24/4/h*lambda^4-Ltinf
ty23/3/h*lambda^3-Ltinfty22/2/h*lambda^2-Ltinfty21/h*lambda-Ltinfty20/
h*ln(lambda)+LA20-LA22/(2-1)/lambda^(2-1)-LA23/(3-1)/lambda^(3-1)-LA24
/(4-1)/lambda^(4-1)-LA25/(5-1)/lambda^(5-1)-LA26/(6-1)/lambda^(6-1)-LA
27/(7-1)/lambda^(7-1)  ;\n" }{MPLTEXT 1 0 466 "Lpsi1Infty := exp(1/h*(
-tinfty14/4*lambda^4-tinfty13/3*lambda^3-tinfty12/2*lambda^2-tinfty11*
lambda-tinfty10*ln(lambda)+h*A10-h*A12/lambda-1/2*h*A13/lambda^2-1/3*h
*A14/lambda^3-1/4*h*A15/lambda^4-1/5*h*A16/lambda^5-1/6*h*A17/lambda^6
))*1/h*(-Ltinfty14/4*lambda^4-Ltinfty13/3*lambda^3-Ltinfty12/2*lambda^
2-Ltinfty11*lambda-Ltinfty10*ln(lambda)+h*LA10-h*LA12/lambda-1/2*h*LA1
3/lambda^2-1/3*h*LA14/lambda^3-1/4*h*LA15/lambda^4-1/5*h*LA16/lambda^5
-1/6*h*LA17/lambda^6);\n" }{MPLTEXT 1 0 479 "Lpsi2Infty := exp(1/h*(-t
infty24/4*lambda^4-tinfty23/3*lambda^3-tinfty22/2*lambda^2-tinfty21*la
mbda-tinfty20*ln(lambda)-h*ln(lambda)+h*A20-h*A22/lambda-1/2*h*A23/lam
bda^2-1/3*h*A24/lambda^3-1/4*h*A25/lambda^4-1/5*h*A26/lambda^5-1/6*h*A
27/lambda^6))*1/h*(-Ltinfty24/4*lambda^4-Ltinfty23/3*lambda^3-Ltinfty2
2/2*lambda^2-Ltinfty21*lambda-Ltinfty20*ln(lambda)+h*LA20-h*LA22/lambd
a-1/2*h*LA23/lambda^2-1/3*h*LA24/lambda^3-1/4*h*LA25/lambda^4-1/5*h*LA
26/lambda^5-1/6*h*LA27/lambda^6);\n" }{MPLTEXT 1 0 30 "psi1Infty:=exp(
logPsi1Infty);\n" }{MPLTEXT 1 0 30 "psi2Infty:=exp(logPsi2Infty);\n" }
{MPLTEXT 1 0 43 "dpsi1dlambdaInfty:=diff(psi1Infty,lambda):\n" }
{MPLTEXT 1 0 43 "dpsi2dlambdaInfty:=diff(psi2Infty,lambda):\n" }
{MPLTEXT 1 0 47 "d2psi1dlambda2Infty:=diff(psi1Infty,lambda$2):\n" }
{MPLTEXT 1 0 47 "d2psi2dlambda2Infty:=diff(psi2Infty,lambda$2):\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 89 "WronskianLa
mbdaInfty:=h*factor(psi1Infty*dpsi2dlambdaInfty-psi2Infty*dpsi1dlambda
Infty):\n" }{MPLTEXT 1 0 132 "WronskianLambdabisInfty:=h*simplify(fact
or( (diff(logPsi2Infty,lambda)-diff(logPsi1Infty,lambda))*exp(logPsi1I
nfty+logPsi2Infty))):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 116 "Wrons
kianTildeLambdaInfty:=h^3*factor(dpsi2dlambdaInfty*d2psi1dlambda2Infty
-dpsi1dlambdaInfty*d2psi2dlambda2Infty):\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I-logPsi1InftyG6\",:*(I)tinfty14GF$\"\"\"I\"hGF$!\"\"I'l
ambdaGF$\"\"%#F*F,*(I)tinfty13GF$F(F)F*F+\"\"$#F*F0*(I)tinfty12GF$F(F)
F*F+\"\"##F*F4*(I)tinfty11GF$F(F)F*F+F(F**(I)tinfty10GF$F(F)F*-I#lnG6$
%*protectedGI(_syslibGF$6#F+F(F*I$A10GF$F(*&I$A12GF$F(F+F*F**&I$A13GF$
F(F+!\"#F5*&I$A14GF$F(F+!\"$F1*&I$A15GF$F(F+!\"%F-*&I$A16GF$F(F+!\"&#F
*\"\"&*&I$A17GF$F(F+!\"'#F*\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-l
ogPsi2InftyG6\",<*(I)tinfty24GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$\"\"%#F*F
,*(I)tinfty23GF$F(F)F*F+\"\"$#F*F0*(I)tinfty22GF$F(F)F*F+\"\"##F*F4*(I
)tinfty21GF$F(F)F*F+F(F**(I)tinfty10GF$F(F)F*-I#lnG6$%*protectedGI(_sy
slibGF$6#F+F(F(F:F*I$A20GF$F(*&I$A22GF$F(F+F*F**&I$A23GF$F(F+!\"#F5*&I
$A24GF$F(F+!\"$F1*&I$A25GF$F(F+!\"%F-*&I$A26GF$F(F+!\"&#F*\"\"&*&I$A27
GF$F(F+!\"'#F*\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I.Llogpsi1InftyG
6\",:*(I*Ltinfty14GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$\"\"%#F*F,*(I*Ltinft
y13GF$F(F)F*F+\"\"$#F*F0*(I*Ltinfty12GF$F(F)F*F+\"\"##F*F4*(I*Ltinfty1
1GF$F(F)F*F+F(F**(I*Ltinfty10GF$F(F)F*-I#lnG6$%*protectedGI(_syslibGF$
6#F+F(F*I%LA10GF$F(*&I%LA12GF$F(F+F*F**&I%LA13GF$F(F+!\"#F5*&I%LA14GF$
F(F+!\"$F1*&I%LA15GF$F(F+!\"%F-*&I%LA16GF$F(F+!\"&#F*\"\"&*&I%LA17GF$F
(F+!\"'#F*\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I.Llogpsi2InftyG6\",
:*(I*Ltinfty24GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$\"\"%#F*F,*(I*Ltinfty23G
F$F(F)F*F+\"\"$#F*F0*(I*Ltinfty22GF$F(F)F*F+\"\"##F*F4*(I*Ltinfty21GF$
F(F)F*F+F(F**(I*Ltinfty20GF$F(F)F*-I#lnG6$%*protectedGI(_syslibGF$6#F+
F(F*I%LA20GF$F(*&I%LA22GF$F(F+F*F**&I%LA23GF$F(F+!\"#F5*&I%LA24GF$F(F+
!\"$F1*&I%LA25GF$F(F+!\"%F-*&I%LA26GF$F(F+!\"&#F*\"\"&*&I%LA27GF$F(F+!
\"'#F*\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+Lpsi1InftyG6\"*(-I$exp
G6$%*protectedGI(_syslibGF$6#*&I\"hGF$!\"\",:*&I)tinfty14GF$\"\"\"I'la
mbdaGF$\"\"%#F.F4*&I)tinfty13GF$F2F3\"\"$#F.F8*&I)tinfty12GF$F2F3\"\"#
#F.F<*&I)tinfty11GF$F2F3F2F.*&I)tinfty10GF$F2-I#lnGF(6#F3F2F.*&F-F2I$A
10GF$F2F2*(F-F2I$A12GF$F2F3F.F.*(F-F2I$A13GF$F2F3!\"#F=*(F-F2I$A14GF$F
2F3!\"$F9*(F-F2I$A15GF$F2F3!\"%F5*(F-F2I$A16GF$F2F3!\"&#F.\"\"&*(F-F2I
$A17GF$F2F3!\"'#F.\"\"'F2F2F-F.,:*&I*Ltinfty14GF$F2F3F4F5*&I*Ltinfty13
GF$F2F3F8F9*&I*Ltinfty12GF$F2F3F<F=*&I*Ltinfty11GF$F2F3F2F.*&I*Ltinfty
10GF$F2FBF2F.*&F-F2I%LA10GF$F2F2*(F-F2I%LA12GF$F2F3F.F.*(F-F2I%LA13GF$
F2F3FKF=*(F-F2I%LA14GF$F2F3FNF9*(F-F2I%LA15GF$F2F3FQF5*(F-F2I%LA16GF$F
2F3FTFU*(F-F2I%LA17GF$F2F3FYFZF2" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+L
psi2InftyG6\"*(-I$expG6$%*protectedGI(_syslibGF$6#*&I\"hGF$!\"\",<*&I)
tinfty24GF$\"\"\"I'lambdaGF$\"\"%#F.F4*&I)tinfty23GF$F2F3\"\"$#F.F8*&I
)tinfty22GF$F2F3\"\"##F.F<*&I)tinfty21GF$F2F3F2F.*&I)tinfty10GF$F2-I#l
nGF(6#F3F2F2*&F-F2FBF2F.*&F-F2I$A20GF$F2F2*(F-F2I$A22GF$F2F3F.F.*(F-F2
I$A23GF$F2F3!\"#F=*(F-F2I$A24GF$F2F3!\"$F9*(F-F2I$A25GF$F2F3!\"%F5*(F-
F2I$A26GF$F2F3!\"&#F.\"\"&*(F-F2I$A27GF$F2F3!\"'#F.\"\"'F2F2F-F.,:*&I*
Ltinfty24GF$F2F3F4F5*&I*Ltinfty23GF$F2F3F8F9*&I*Ltinfty22GF$F2F3F<F=*&
I*Ltinfty21GF$F2F3F2F.*&I*Ltinfty20GF$F2FBF2F.*&F-F2I%LA20GF$F2F2*(F-F
2I%LA22GF$F2F3F.F.*(F-F2I%LA23GF$F2F3FLF=*(F-F2I%LA24GF$F2F3FOF9*(F-F2
I%LA25GF$F2F3FRF5*(F-F2I%LA26GF$F2F3FUFV*(F-F2I%LA27GF$F2F3FZFenF2" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I*psi1InftyG6\"-I$expG6$%*protectedGI(_
syslibGF$6#,:*(I)tinfty14GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$\"\"%#F0F2*(I
)tinfty13GF$F.F/F0F1\"\"$#F0F6*(I)tinfty12GF$F.F/F0F1\"\"##F0F:*(I)tin
fty11GF$F.F/F0F1F.F0*(I)tinfty10GF$F.F/F0-I#lnGF'6#F1F.F0I$A10GF$F.*&I
$A12GF$F.F1F0F0*&I$A13GF$F.F1!\"#F;*&I$A14GF$F.F1!\"$F7*&I$A15GF$F.F1!
\"%F3*&I$A16GF$F.F1!\"&#F0\"\"&*&I$A17GF$F.F1!\"'#F0\"\"'" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I*psi2InftyG6\"-I$expG6$%*protectedGI(_syslibGF$
6#,<*(I)tinfty24GF$\"\"\"I\"hGF$!\"\"I'lambdaGF$\"\"%#F0F2*(I)tinfty23
GF$F.F/F0F1\"\"$#F0F6*(I)tinfty22GF$F.F/F0F1\"\"##F0F:*(I)tinfty21GF$F
.F/F0F1F.F0*(I)tinfty10GF$F.F/F0-I#lnGF'6#F1F.F.F@F0I$A20GF$F.*&I$A22G
F$F.F1F0F0*&I$A23GF$F.F1!\"#F;*&I$A24GF$F.F1!\"$F7*&I$A25GF$F.F1!\"%F3
*&I$A26GF$F.F1!\"&#F0\"\"&*&I$A27GF$F.F1!\"'#F0\"\"'" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 79 "L21Infty:=factor(simplify(WronskianTildeL
ambdaInfty/WronskianLambdabisInfty)):\n" }{MPLTEXT 1 0 75 "L21InftyOrd
erlambda7:=factor(-residue(L21Infty/lambda^8,lambda=infinity));\n" }
{MPLTEXT 1 0 75 "L21InftyOrderlambda6:=factor(-residue(L21Infty/lambda
^7,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L21InftyOrderlambda5:=facto
r(-residue(L21Infty/lambda^6,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L
21InftyOrderlambda4:=factor(-residue(L21Infty/lambda^5,lambda=infinity
));\n" }{MPLTEXT 1 0 75 "L21InftyOrderlambda3:=factor(-residue(L21Inft
y/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L21InftyOrderlambda
2:=factor(-residue(L21Infty/lambda^3,lambda=infinity));\n" }{MPLTEXT 
1 0 75 "L21InftyOrderlambda1:=factor(-residue(L21Infty/lambda^2,lambda
=infinity));\n" }{MPLTEXT 1 0 75 "L21InftyOrderlambda0:=factor(-residu
e(L21Infty/lambda^1,lambda=infinity));\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 228 "factor(simplify(L21InftyOrderlambda6*lambda^6+L21Inf
tyOrderlambda5*lambda^5+L21InftyOrderlambda4*lambda^4+L21InftyOrderlam
bda3*lambda^3+L21InftyOrderlambda2*lambda^2- (-P2(lambda)+Pinfty02+Pin
fty12*lambda-h*lambda^2*tinfty14)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "
>I5L21InftyOrderlambda7G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L
21InftyOrderlambda6G6\",$*&I)tinfty14GF$\"\"\"I)tinfty24GF$F(!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrderlambda5G6\",&*&I)tinfty1
3GF$\"\"\"I)tinfty24GF$F(!\"\"*&I)tinfty14GF$F(I)tinfty23GF$F(F*" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrderlambda4G6\",(*&I)tinfty1
2GF$\"\"\"I)tinfty24GF$F(!\"\"*&I)tinfty13GF$F(I)tinfty23GF$F(F**&I)ti
nfty14GF$F(I)tinfty22GF$F(F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21In
ftyOrderlambda3G6\",**&I)tinfty11GF$\"\"\"I)tinfty24GF$F(!\"\"*&I)tinf
ty12GF$F(I)tinfty23GF$F(F**&I)tinfty13GF$F(I)tinfty22GF$F(F**&I)tinfty
14GF$F(I)tinfty21GF$F(F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyO
rderlambda2G6\",.*&I\"hGF$\"\"\"I)tinfty14GF$F(!\"\"*&I)tinfty10GF$F(F
)F(F(*&F,F(I)tinfty24GF$F(F**&I)tinfty11GF$F(I)tinfty23GF$F(F**&I)tinf
ty12GF$F(I)tinfty22GF$F(F**&I)tinfty13GF$F(I)tinfty21GF$F(F*" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrderlambda1G6\"*&,>**I$A12GF$\"\"
\"I\"hGF$F)I)tinfty14GF$F)I)tinfty24GF$F)F)*(F(F)F*F)F,\"\"#!\"\"*(I$A
22GF$F)F*F)F+F.F)**F1F)F*F)F+F)F,F)F/*(F*F)I)tinfty13GF$F)F+F)F/*(F*F)
F+F)I)tinfty23GF$F)F)*(I)tinfty10GF$F)F4F)F+F)F)*(F8F)F4F)F,F)F/*(F8F)
F+F)F6F)F/*(F8F)F6F)F,F)F)*(I)tinfty11GF$F)F+F)I)tinfty22GF$F)F/*(F=F)
F>F)F,F)F)*(I)tinfty12GF$F)F+F)I)tinfty21GF$F)F/*(FAF)FBF)F,F)F)F),&F,
F/F+F)F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L21InftyOrderlambda0G6\"*
&,fn**I$A12GF$\"\"\"I\"hGF$F)I)tinfty14GF$\"\"#I)tinfty23GF$F)F)*,F(F)
F*F)F+F)F-F)I)tinfty24GF$F)!\"#**F(F)F*F)F-F)F/F,F)**I$A13GF$F)F*F)F+F
,F/F)F)**F3F)F*F)F+F)F/F,F0*(F3F)F*F)F/\"\"$F)**I$A22GF$F)F*F)I)tinfty
13GF$F)F+F,F)*,F8F)F*F)F9F)F+F)F/F)F0**F8F)F*F)F9F)F/F,F)*(I$A23GF$F)F
*F)F+F6F)**F=F)F*F)F+F,F/F)F0**F=F)F*F)F+F)F/F,F)*(F*F)I)tinfty12GF$F)
F+F,!\"\"*(F*F)FAF)F/F,F)*(F*F)F9F,F/F)F)**F*F)F9F)F+F)F-F)FB**F*F)F9F
)F-F)F/F)FB*(F*F)F+F,I)tinfty22GF$F)F,**F*F)F+F)FHF)F/F)F0*(F*F)F+F)F-
F,F)*(I)tinfty10GF$F)FAF)F+F,F)**FLF)FAF)F+F)F/F)F0*(FLF)FAF)F/F,F)*(F
LF)F+F,FHF)FB**FLF)F+F)FHF)F/F)F,*(FLF)FHF)F/F,FB*(I)tinfty11GF$F)F+F,
I)tinfty21GF$F)FB**FSF)F+F)FTF)F/F)F,*(FSF)FTF)F/F,FBF),&F/FBF+F)F0" }
}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
234 45 "We get that L_\{2,1\}behaves at infinity like  " }}{PARA 0 "" 
0 "" {TEXT 216 43 "L21(lambda)= -(tinfty14*tinfty24)*lambda^6\n" }
{TEXT 217 48 "-(tinfty13*tinfty24+tinfty14*tinfty23)*lambda^5\n" }
{TEXT 218 66 "-(tinfty12*tinfty24+tinfty13*tinfty23+tinfty14*tinfty22)
*lambda^4\n" }{TEXT 219 84 "-(tinfty11*tinfty24+tinfty12*tinfty23+tinf
ty13*tinfty22+tinfty14*tinfty21)*lambda^3\n" }{TEXT 220 112 "-(tinfty2
0*tinfty14+tinfty10*tinfty24+tinfty11*tinfty23+tinfty12*tinfty22+tinft
y13*tinfty21+h*tinfty14)*lambda^2" }{TEXT 221 10 "+O(lambda)" }{TEXT 
234 1 "\n" }{TEXT 234 6 "i..e.\n" }{TEXT 222 88 "L_\{2,1\}= -P_2(lambd
a)+Pinfty02+Pinfty12*lambda  +C1*lambda+C0 -h*lambda^2*tinfty14 +o(1)"
 }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 22 "Computation of L_\{2,2\}" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "L22Infty:=factor(h*simplify(
diff(WronskianLambdabisInfty,lambda)/WronskianLambdabisInfty)):\n" }
{MPLTEXT 1 0 75 "L22InftyOrderlambda7:=factor(-residue(L22Infty/lambda
^8,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L22InftyOrderlambda6:=facto
r(-residue(L22Infty/lambda^7,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L
22InftyOrderlambda5:=factor(-residue(L22Infty/lambda^6,lambda=infinity
));\n" }{MPLTEXT 1 0 75 "L22InftyOrderlambda4:=factor(-residue(L22Inft
y/lambda^5,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L22InftyOrderlambda
3:=factor(-residue(L22Infty/lambda^4,lambda=infinity));\n" }{MPLTEXT 
1 0 75 "L22InftyOrderlambda2:=factor(-residue(L22Infty/lambda^3,lambda
=infinity));\n" }{MPLTEXT 1 0 75 "L22InftyOrderlambda1:=factor(-residu
e(L22Infty/lambda^2,lambda=infinity));\n" }{MPLTEXT 1 0 75 "L22InftyOr
derlambda0:=factor(-residue(L22Infty/lambda^1,lambda=infinity));\n" }
{MPLTEXT 1 0 80 "L22InftyOrderlambdaMinus1:=factor(-residue(L22Infty/l
ambda^0,lambda=infinity));\n" }{MPLTEXT 1 0 82 "L22InftyOrderlambdaMin
us2:=factor(-residue(L22Infty/lambda^(-1),lambda=infinity));" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I5L22InftyOrderlambda7G6\"\"\"!" }}{PARA 11 "
" 1 "" {XPPMATH 20 ">I5L22InftyOrderlambda6G6\"\"\"!" }}{PARA 11 "" 1 
"" {XPPMATH 20 ">I5L22InftyOrderlambda5G6\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I5L22InftyOrderlambda4G6\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I5L22InftyOrderlambda3G6\",&I)tinfty14GF$!\"\"I)tinfty24
GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L22InftyOrderlambda2G6\",&I)
tinfty13GF$!\"\"I)tinfty23GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5L2
2InftyOrderlambda1G6\",&I)tinfty12GF$!\"\"I)tinfty22GF$F'" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I5L22InftyOrderlambda0G6\",&I)tinfty11GF$!\"\"I)
tinfty21GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I:L22InftyOrderlambdaM
inus1G6\",$I\"hGF$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I:L22InftyOr
derlambdaMinus2G6\"*(I\"hGF$\"\"\",.*&I$A12GF$F'I)tinfty14GF$F'F'*&F*F
'I)tinfty24GF$F'!\"\"*&I$A22GF$F'F+F'F'*&F0F'F-F'F.I)tinfty13GF$F.I)ti
nfty23GF$F'F',&F-F.F+F'F." }}}{EXCHG {PARA 211 "" 0 "" {TEXT 208 47 "W
e deduce that L_\{2,2\} behaves at infinity like" }}{PARA 212 "" 0 "" 
{TEXT 208 18 "L_\{2,2\}(lambda)=  " }{TEXT 208 86 "-(tinfty14+tinfty24
)*lambda^3-(tinfty13+tinfty23)*lambda^2 -(tinfty12+tinfty22)*lambda" }
{TEXT 208 47 "-(tinfty11+tinfty21)+2*h/lambda +O(1/lambda^2) " }}
{PARA 213 "" 0 "" {TEXT 208 37 "=P1(lambda) +2*h/lambda+O(1/lambda^2)"
 }}}{EXCHG {PARA 209 "" 0 "" {TEXT 235 32 "Formulas for L_\{2,2\} and \+
L_\{2,1\}" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 223 37 "L_\{2,2\}=  P_1(lam
bda)  +h/(lambda-q1)" }{TEXT 224 14 "+h/(lambda-q2)" }{TEXT 234 1 " " 
}{TEXT 225 1 "\n" }{TEXT 226 7 "L_\{2,1\}" }{TEXT 227 1 "=" }{TEXT 
228 1 " " }{TEXT 229 105 "-P2(lambda)+Pinfty02+Pinfty12*lambda +C1*lam
bda+C0 -h*lambda^2*tinfty14-p1*h/(lambda-q1)-p2*h/(lambda-q2)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "L21Form:=-P2(lambda)+Pinfty
02+Pinfty12*lambda +C1*lambda+C0 -h*lambda^2*tinfty14-p1*h/(lambda-q1)
-p2*h/(lambda-q2);\n" }{MPLTEXT 1 0 51 "L22Form:=P1(lambda)  +h/(lambd
a-q1)+h/(lambda-q2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(L21FormG6\"
,6*&,,*&I)tinfty10GF$\"\"\"I)tinfty14GF$F*!\"\"*&F)F*I)tinfty24GF$F*F*
*&I)tinfty11GF$F*I)tinfty23GF$F*F**&I)tinfty12GF$F*I)tinfty22GF$F*F**&
I)tinfty13GF$F*I)tinfty21GF$F*F*F*I'lambdaGF$\"\"#F,*&,**&F0F*F.F*F**&
F3F*F1F*F**&F6F*F4F*F**&F+F*F7F*F*F*F8\"\"$F,*&,(*&F3F*F.F*F**&F6F*F1F
*F**&F+F*F4F*F*F*F8\"\"%F,*&,&*&F6F*F.F*F**&F+F*F1F*F*F*F8\"\"&F,*(F+F
*F.F*F8\"\"'F,*&I#C1GF$F*F8F*F*I#C0GF$F**(I\"hGF$F*F8F9F+F*F,*(I#p1GF$
F*FRF*,&F8F*I#q1GF$F,F,F,*(I#p2GF$F*FRF*,&F8F*I#q2GF$F,F,F," }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I(L22FormG6\",0I)tinfty11GF$!\"\"I)tinfty21GF
$F'*&,&I)tinfty12GF$F'I)tinfty22GF$F'\"\"\"I'lambdaGF$F-F-*&,&I)tinfty
13GF$F'I)tinfty23GF$F'F-F.\"\"#F-*&,&I)tinfty14GF$F'I)tinfty24GF$F'F-F
.\"\"$F-*&I\"hGF$F-,&F.F-I#q1GF$F'F'F-*&F:F-,&F.F-I#q2GF$F'F'F-" }}}}
{SECT 0 {PARA 3 "" 0 "" {TEXT 232 18 "Auxiliary matrix A" }{TEXT 232 
0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 234 29 "The deformation operator i
s \n" }{TEXT 234 167 "\\mathcal\{L\}=\\hbar (alpha14\\partial_\{t_\{
\\infty^\{(1)\},4\} +alpha24\\partial_\{t_\{\\infty^\{(2)\},4\}+alpha1
3*\\partial_\{t_\{\\infty^\{(1)\},3\} +alpha23*\\partial_\{t_\{\\infty
^\{(2)\},3\}\n" }{TEXT 234 150 "+alpha12*\\partial_\{t_\{\\infty^\{(1)
\},2\} +alpha22*\\partial_\{t_\{\\infty^\{(2)\},2\}+alpha11*\\partial_
\{t_\{\\infty^\{(1)\},1\} +alpha21*\\partial_\{t_\{\\infty^\{(2)\},1\}
" }{TEXT 234 1 ")" }}}{EXCHG {PARA 214 "" 0 "" {TEXT 208 22 "Computati
on of A_\{1,2\}" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "Wronskia
nLInfty:=factor(psi1Infty*Lpsi2Infty-psi2Infty*Lpsi1Infty):\n" }
{MPLTEXT 1 0 66 "A12Infty:=factor(simplify(WronskianLInfty/WronskianLa
mbdaInfty)):\n" }{MPLTEXT 1 0 48 "Y1Infty:=h*factor(dpsi1dlambdaInfty/
psi1Infty):\n" }{MPLTEXT 1 0 48 "Y2Infty:=h*factor(dpsi2dlambdaInfty/p
si2Infty):\n" }{MPLTEXT 1 0 39 "Z1Infty:=factor(Lpsi1Infty/psi1Infty):
\n" }{MPLTEXT 1 0 39 "Z2Infty:=factor(Lpsi2Infty/psi2Infty):\n" }
{MPLTEXT 1 0 68 "A12bisInfty:=factor(simplify((Z2Infty-Z1Infty)/(Y2Inf
ty-Y1Infty))):\n" }{MPLTEXT 1 0 83 "A11Infty:=factor(simplify( (Y2Inft
y*Z1Infty-Y1Infty*Z2Infty)/(Y2Infty-Y1Infty) )):\n" }{MPLTEXT 1 0 39 "
factor(simplify(A12bisInfty-A12Infty));" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "Ltinfty14:=h*alpha14:\n" }{MPLTEXT 1 0 22 "Ltinfty24:=h*alpha24:
\n" }{MPLTEXT 1 0 13 "Ltinfty13:=h*" }{MPLTEXT 1 0 7 "alpha13" }
{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 13 "Ltinfty23:=h*" }{MPLTEXT 1 0 7 
"alpha23" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 13 "Ltinfty12:=h*" }
{MPLTEXT 1 0 7 "alpha12" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 13 "Ltinf
ty22:=h*" }{MPLTEXT 1 0 7 "alpha22" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 
0 13 "Ltinfty11:=h*" }{MPLTEXT 1 0 7 "alpha11" }{MPLTEXT 1 0 2 ":\n" }
{MPLTEXT 1 0 13 "Ltinfty21:=h*" }{MPLTEXT 1 0 7 "alpha21" }{MPLTEXT 1 
0 2 ":\n" }{MPLTEXT 1 0 14 "Ltinfty10:=0:\n" }{MPLTEXT 1 0 14 "Ltinfty
20:=0:\n" }{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 70 "A12InftyLambda4:=factor(-residue(A12Infty/lambda^5,lambda=infini
ty));\n" }{MPLTEXT 1 0 70 "A12InftyLambda3:=factor(-residue(A12Infty/l
ambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 70 "A12InftyLambda2:=facto
r(-residue(A12Infty/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 70 "A
12InftyLambda1:=factor(-residue(A12Infty/lambda^2,lambda=infinity));\n
" }{MPLTEXT 1 0 70 "A12InftyLambda0:=factor(-residue(A12Infty/lambda^1
,lambda=infinity));\n" }{MPLTEXT 1 0 75 "A12InftyLambdaMinus1:=factor(
-residue(A12Infty/lambda^0,lambda=infinity));\n" }{MPLTEXT 1 0 78 "A12
InftyLambdaMinus2:=factor(-residue(A12Infty/lambda^(-1),lambda=infinit
y));\n" }{MPLTEXT 1 0 78 "A12InftyLambdaMinus3:=factor(-residue(A12Inf
ty/lambda^(-2),lambda=infinity)):\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">
I0A12InftyLambda4G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12Inft
yLambda3G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda2G
6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda1G6\",$*&,&
I(alpha14GF$\"\"\"I(alpha24GF$!\"\"F),&I)tinfty24GF$F+I)tinfty14GF$F)F
+#F)\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A12InftyLambda0G6\",$*&,
2*&I(alpha13GF$\"\"\"I)tinfty14GF$F*\"\"%*&F)F*I)tinfty24GF$F*!\"%*&I(
alpha14GF$F*I)tinfty13GF$F*!\"$*&F1F*I)tinfty23GF$F*\"\"$*&I(alpha23GF
$F*F+F*F/*&F8F*F.F*F,*&I(alpha24GF$F*F2F*F6*&F;F*F5F*F3F*,&F.!\"\"F+F*
!\"##F*\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I5A12InftyLambdaMinus1G6
\",$*&,Z*&I(alpha12GF$\"\"\"I)tinfty14GF$\"\"#\"\"'*(F)F*F+F*I)tinfty2
4GF$F*!#7*&F)F*F/F,F-*(I(alpha13GF$F*I)tinfty13GF$F*F+F*!\"%*(F3F*F4F*
F/F*\"\"%*(F3F*F+F*I)tinfty23GF$F*F7*(F3F*F9F*F/F*F5*(I(alpha14GF$F*I)
tinfty12GF$F*F+F*!\"$*(F<F*F=F*F/F*\"\"$*&F<F*F4F,F@*(F<F*F4F*F9F*!\"'
*(F<F*F+F*I)tinfty22GF$F*F@*(F<F*FEF*F/F*F>*&F<F*F9F,F@*&I(alpha22GF$F
*F+F,FC*(FIF*F+F*F/F*\"#7*&FIF*F/F,FC*(I(alpha23GF$F*F4F*F+F*F7*(FNF*F
4F*F/F*F5*(FNF*F+F*F9F*F5*(FNF*F9F*F/F*F7*(I(alpha24GF$F*F=F*F+F*F@*(F
SF*F=F*F/F*F>*&FSF*F4F,F>*(FSF*F4F*F9F*F-*(FSF*F+F*FEF*F>*(FSF*FEF*F/F
*F@*&FSF*F9F,F>F*,&F/!\"\"F+F*F>#F*FK" }}{PARA 11 "" 1 "" {XPPMATH 20 
">I5A12InftyLambdaMinus2G6\",$*&,\\u*&I(alpha11GF$\"\"\"I)tinfty14GF$
\"\"$\"#7*(F)F*F+\"\"#I)tinfty24GF$F*!#O*(F)F*F+F*F0F/\"#O*&F)F*F0F,!#
7*(I(alpha12GF$F*I)tinfty13GF$F*F+F/!\"'**F7F*F8F*F+F*F0F*F-*(F7F*F8F*
F0F/F9*(F7F*F+F/I)tinfty23GF$F*\"\"'**F7F*F+F*F=F*F0F*F5*(F7F*F=F*F0F/
F>*(I(alpha13GF$F*I)tinfty12GF$F*F+F/!\"%**FBF*FCF*F+F*F0F*\"\")*(FBF*
FCF*F0F/FD*(FBF*F8F/F+F*\"\"%*(FBF*F8F/F0F*FD**FBF*F8F*F+F*F=F*!\")**F
BF*F8F*F=F*F0F*FF*(FBF*F+F/I)tinfty22GF$F*FI**FBF*F+F*FOF*F0F*FL*(FBF*
F+F*F=F/FI*(FBF*FOF*F0F/FI*(FBF*F=F/F0F*FD*(I(alpha14GF$F*I)tinfty11GF
$F*F+F/!\"$**FUF*FVF*F+F*F0F*F>*(FUF*FVF*F0F/FW**FUF*FCF*F8F*F+F*F>**F
UF*FCF*F8F*F0F*F9**FUF*FCF*F+F*F=F*F9**FUF*FCF*F=F*F0F*F>*&FUF*F8F,FW*
(FUF*F8F/F=F*\"\"***FUF*F8F*F+F*FOF*F9**FUF*F8F*FOF*F0F*F>*(FUF*F8F*F=
F/!\"**(FUF*F+F/I)tinfty21GF$F*F,**FUF*F+F*F`oF*F0F*F9**FUF*F+F*FOF*F=
F*F>*(FUF*F`oF*F0F/F,**FUF*FOF*F=F*F0F*F9*&FUF*F=F,F,*&I(alpha21GF$F*F
+F,F5*(FgoF*F+F/F0F*F3*(FgoF*F+F*F0F/F1*&FgoF*F0F,F-*(I(alpha22GF$F*F8
F*F+F/F>**F\\pF*F8F*F+F*F0F*F5*(F\\pF*F8F*F0F/F>*(F\\pF*F+F/F=F*F9**F
\\pF*F+F*F=F*F0F*F-*(F\\pF*F=F*F0F/F9*(I(alpha23GF$F*FCF*F+F/FI**FcpF*
FCF*F+F*F0F*FL*(FcpF*FCF*F0F/FI*(FcpF*F8F/F+F*FD*(FcpF*F8F/F0F*FI**Fcp
F*F8F*F+F*F=F*FF**FcpF*F8F*F=F*F0F*FL*(FcpF*F+F/FOF*FD**FcpF*F+F*FOF*F
0F*FF*(FcpF*F+F*F=F/FD*(FcpF*FOF*F0F/FD*(FcpF*F=F/F0F*FI*(I(alpha24GF$
F*FVF*F+F/F,**F`qF*FVF*F+F*F0F*F9*(F`qF*FVF*F0F/F,**F`qF*FCF*F8F*F+F*F
9**F`qF*FCF*F8F*F0F*F>**F`qF*FCF*F+F*F=F*F>**F`qF*FCF*F=F*F0F*F9*&F`qF
*F8F,F,*(F`qF*F8F/F=F*F^o**F`qF*F8F*F+F*FOF*F>**F`qF*F8F*FOF*F0F*F9*(F
`qF*F8F*F=F/Fjn*(F`qF*F+F/F`oF*FW**F`qF*F+F*F`oF*F0F*F>**F`qF*F+F*FOF*
F=F*F9*(F`qF*F`oF*F0F/FW**F`qF*FOF*F=F*F0F*F>*&F`qF*F=F,FWF*,&F0!\"\"F
+F*FD#F*F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 234 12 "We get that " }
{TEXT 230 74 "A_\{1,2\}=(alpha14-alpha24)/4/(tinfty14-tinfty24)*lambda
+nu+mu1/(lambda-q1)+" }{TEXT 231 15 "mu2/(lambda-q2)" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 95 "A12Form:=(alpha14-alpha24)/4/(-tinfty24+t
infty14)*lambda+nu+ mu1/(lambda-q1)+ mu2/(lambda-q2);\n" }{MPLTEXT 1 
0 116 "A12Formbis:=(alpha14-alpha24)/4/(-tinfty24+tinfty14)*lambda+nu+
 (nu1*(lambda-(q1+q2))+nu2)/(lambda-q1)/(lambda-q2);\n" }{MPLTEXT 1 0 
69 "Equationmu1:=-residue(A12Form,lambda=infinity)-A12InftyLambdaMinus
1:\n" }{MPLTEXT 1 0 76 "Equationmu2:=-residue(A12Form*lambda,lambda=in
finity)-A12InftyLambdaMinus2:\n" }{MPLTEXT 1 0 29 "mu1:= -(nu1*q2-nu2)
/(q1-q2);\n" }{MPLTEXT 1 0 28 "mu2:= (nu1*q1-nu2)/(q1-q2);\n" }
{MPLTEXT 1 0 71 "simplify(-residue(A12Form/lambda^2,lambda=infinity)-A
12InftyLambda1); \n" }{MPLTEXT 1 0 38 "factor(simplify(A12Form-A12Form
bis));\n" }{MPLTEXT 1 0 80 "solve(\{factor(-residue(A12Form/lambda,lam
bda=infinity))=A12InftyLambda0\},\{nu\});\n" }{MPLTEXT 1 0 209 "nu:=-(
3*alpha14*tinfty13-3*alpha14*tinfty23-3*alpha24*tinfty13+3*alpha24*tin
fty23-4*alpha13*tinfty14+4*alpha13*tinfty24+4*alpha23*tinfty14-4*alpha
23*tinfty24)/(12*(tinfty14^2-2*tinfty14*tinfty24+tinfty24^2)):\n" }
{MPLTEXT 1 0 117 "nubis:=-(1/4)*(tinfty13-tinfty23)/(tinfty14-tinfty24
)^2*(alpha14-alpha24)+1/3*(alpha13-alpha23)/(tinfty14-tinfty24);\n" }
{MPLTEXT 1 0 17 "factor(nu-nubis);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(A12FormG6\",**(,&I(alpha14
GF$\"\"\"I(alpha24GF$!\"\"F),&I)tinfty24GF$F+I)tinfty14GF$F)F+I'lambda
GF$F)#F)\"\"%I#nuGF$F)*&I$mu1GF$F),&F/F)I#q1GF$F+F+F)*&I$mu2GF$F),&F/F
)I#q2GF$F+F+F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+A12FormbisG6\",(*(,
&I(alpha14GF$\"\"\"I(alpha24GF$!\"\"F),&I)tinfty24GF$F+I)tinfty14GF$F)
F+I'lambdaGF$F)#F)\"\"%I#nuGF$F)*(,&*&I$nu1GF$F),(F/F)I#q1GF$F+I#q2GF$
F+F)F)I$nu2GF$F)F),&F/F)F8F+F+,&F/F)F9F+F+F)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I$mu1G6\",$*&,&*&I$nu1GF$\"\"\"I#q2GF$F*F*I$nu2GF$!\"\"F
*,&I#q1GF$F*F+F-F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$mu2G6\"*&,&*&
I$nu1GF$\"\"\"I#q1GF$F)F)I$nu2GF$!\"\"F),&F*F)I#q2GF$F,F," }}{PARA 11 
"" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "<#/I#nuG6\",$*&,2*&I(alpha13G6\"\"\"\"I)
tinfty14G6\"\"\"\"\"\"%*&I(alpha13G6\"\"\"\"I)tinfty24G6\"\"\"\"!\"%*&
I(alpha14G6\"\"\"\"I)tinfty13G6\"\"\"\"!\"$*&I(alpha14G6\"\"\"\"I)tinf
ty23G6\"\"\"\"\"\"$*&I(alpha23G6\"\"\"\"I)tinfty14G6\"\"\"\"!\"%*&I(al
pha23G6\"\"\"\"I)tinfty24G6\"\"\"\"\"\"%*&I(alpha24G6\"\"\"\"I)tinfty1
3G6\"\"\"\"\"\"$*&I(alpha24G6\"\"\"\"I)tinfty23G6\"\"\"\"!\"$\"\"\",&I
)tinfty24G6\"!\"\"I)tinfty14G6\"\"\"\"!\"##\"\"\"\"#7" }}{PARA 11 "" 1
 "" {XPPMATH 20 ">I&nubisG6\",&*(,&I)tinfty23GF$!\"\"I)tinfty13GF$\"\"
\"F+,&I)tinfty24GF$F)I)tinfty14GF$F+!\"#,&I(alpha14GF$F+I(alpha24GF$F)
F+#F)\"\"%*&,&I(alpha13GF$F+I(alpha23GF$F)F+F,F)#F+\"\"$" }}{PARA 11 "
" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "nu1:=A12InftyLambdaMinus1:\n" }{MPLTEXT 1 0 27 "nu2:=A12InftyLambd
aMinus2:\n" }{MPLTEXT 1 0 23 "simplify(Equationmu1);\n" }{MPLTEXT 1 0 
22 "simplify(Equationmu2);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "A12InftyLambdaMinus1bis:=-(1/4)*((
tinfty12-tinfty22)*(tinfty14-tinfty24) -(tinfty13-tinfty23)^2 )/(tinft
y14-tinfty24)^3*(alpha14-alpha24)\n" }{MPLTEXT 1 0 67 "-(1/3)*(tinfty1
3-tinfty23)/(tinfty14-tinfty24)^2*(alpha13-alpha23)\n" }{MPLTEXT 1 0 
44 "+(alpha12-alpha22)/(2*(tinfty14-tinfty24));\n" }{MPLTEXT 1 0 72 "f
actor(series(A12InftyLambdaMinus1-A12InftyLambdaMinus1bis,alpha13=0));
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I8A12InftyLambdaMinus1bisG6\",(*(
,&*&,&I)tinfty22GF$!\"\"I)tinfty12GF$\"\"\"F-,&I)tinfty24GF$F+I)tinfty
14GF$F-F-F-*$,&I)tinfty23GF$F+I)tinfty13GF$F-\"\"#F+F-F.!\"$,&I(alpha1
4GF$F-I(alpha24GF$F+F-#F+\"\"%*(F2F-F.!\"#,&I(alpha13GF$F-I(alpha23GF$
F+F-#F+\"\"$*&,&I(alpha12GF$F-I(alpha22GF$F+F-,&F/F=F0F5F+F-" }}{PARA 
11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 201 "A12InftyLambdaMinus2bis:=-(1/4)*((tinfty11-tinfty21)*(tinfty14-
tinfty24)^2-2*(tinfty12-tinfty22)*(tinfty14-tinfty24)*(tinfty13-tinfty
23) +(tinfty13-tinfty23)^3)/(tinfty14-tinfty24)^4*(alpha14-alpha24)\n"
 }{MPLTEXT 1 0 112 "-(1/3)*((tinfty12-tinfty22)*(tinfty14-tinfty24) -(
tinfty13-tinfty23)^2)/(tinfty14-tinfty24)^3*(alpha13-alpha23)\n" }
{MPLTEXT 1 0 68 "-(1/2)*(-tinfty23+tinfty13)/(tinfty14-tinfty24)^2*(al
pha12-alpha22)\n" }{MPLTEXT 1 0 39 "+(alpha11-alpha21)/(tinfty14-tinft
y24);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 65 "factor(series(A12InftyLa
mbdaMinus2-A12InftyLambdaMinus2bis,g=0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I8A12InftyLambdaMinus2bisG6\",**(,(*&,&I)tinfty21GF$!\"
\"I)tinfty11GF$\"\"\"F-,&I)tinfty24GF$F+I)tinfty14GF$F-\"\"#F-*(,&I)ti
nfty22GF$F+I)tinfty12GF$F-F-F.F-,&I)tinfty23GF$F+I)tinfty13GF$F-F-!\"#
*$F6\"\"$F-F-F.!\"%,&I(alpha14GF$F-I(alpha24GF$F+F-#F+\"\"%*(,&*&F3F-F
.F-F-*$F6F1F+F-F.!\"$,&I(alpha13GF$F-I(alpha23GF$F+F-#F+F;*(F6F-F.F9,&
I(alpha12GF$F-I(alpha22GF$F+F-#F+F1*&,&I(alpha11GF$F-I(alpha21GF$F+F-F
.F+F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 215 "" 0
 "" {TEXT 208 22 "Computation of A_\{1,1\}" }{TEXT 208 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "A11InftyLambda6:=factor(-residue(A1
1Infty/lambda^7,lambda=infinity));\n" }{MPLTEXT 1 0 70 "A11InftyLambda
5:=factor(-residue(A11Infty/lambda^6,lambda=infinity));\n" }{MPLTEXT 
1 0 70 "A11InftyLambda4:=factor(-residue(A11Infty/lambda^5,lambda=infi
nity));\n" }{MPLTEXT 1 0 70 "A11InftyLambda3:=factor(-residue(A11Infty
/lambda^4,lambda=infinity));\n" }{MPLTEXT 1 0 70 "A11InftyLambda2:=fac
tor(-residue(A11Infty/lambda^3,lambda=infinity));\n" }{MPLTEXT 1 0 70 
"A11InftyLambda1:=factor(-residue(A11Infty/lambda^2,lambda=infinity));
\n" }{MPLTEXT 1 0 70 "A11InftyLambda0:=factor(-residue(A11Infty/lambda
^1,lambda=infinity)):\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLa
mbda6G6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda5G6\"
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLambda4G6\",$*&,&*&I
(alpha14GF$\"\"\"I)tinfty24GF$F*F**&I(alpha24GF$F*I)tinfty14GF$F*!\"\"
F*,&F+F/F.F*F/#F*\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0A11InftyLam
bda3G6\",$*&,2*(I(alpha13GF$\"\"\"I)tinfty14GF$F*I)tinfty24GF$F*\"\"%*
&F)F*F,\"\"#!\"%*(I(alpha14GF$F*I)tinfty13GF$F*F,F*!\"$*(F2F*F+F*I)tin
fty23GF$F*\"\"$*&I(alpha23GF$F*F+F/F0*(F9F*F+F*F,F*F-*(I(alpha24GF$F*F
3F*F,F*F7*(F<F*F+F*F6F*F4F*,&F,!\"\"F+F*!\"##F*\"#7" }}{PARA 11 "" 1 "
" {XPPMATH 20 ">I0A11InftyLambda2G6\",$*&,hn*(I(alpha12GF$\"\"\"I)tinf
ty14GF$\"\"#I)tinfty24GF$F*\"\"'*(F)F*F+F*F-F,!#7*&F)F*F-\"\"$F.**I(al
pha13GF$F*I)tinfty13GF$F*F+F*F-F*!\"%*(F4F*F5F*F-F,\"\"%*(F4F*F+F,I)ti
nfty23GF$F*F8**F4F*F+F*F:F*F-F*F6**I(alpha14GF$F*I)tinfty12GF$F*F+F*F-
F*!\"$*(F=F*F>F*F-F,F2*(F=F*F5F,F-F*F2**F=F*F5F*F+F*F:F*F?**F=F*F5F*F:
F*F-F*F?*(F=F*F+F,I)tinfty22GF$F*F2**F=F*F+F*FEF*F-F*F?*(F=F*F+F*F:F,F
2*&I(alpha22GF$F*F+F2!\"'*(FIF*F+F,F-F*\"#7*(FIF*F+F*F-F,FJ**I(alpha23
GF$F*F5F*F+F*F-F*F8*(FOF*F5F*F-F,F6*(FOF*F+F,F:F*F6**FOF*F+F*F:F*F-F*F
8**I(alpha24GF$F*F>F*F+F*F-F*F2*(FTF*F>F*F-F,F?*(FTF*F5F,F-F*F?**FTF*F
5F*F+F*F:F*F2**FTF*F5F*F:F*F-F*F2*(FTF*F+F,FEF*F?**FTF*F+F*FEF*F-F*F2*
(FTF*F+F*F:F,F?F*,&F-!\"\"F+F*F?#F*FL" }}{PARA 11 "" 1 "" {XPPMATH 20 
">I0A11InftyLambda1G6\",$*&,du*(I(alpha11GF$\"\"\"I)tinfty14GF$\"\"$I)
tinfty24GF$F*\"#7*(F)F*F+\"\"#F-F0!#O*(F)F*F+F*F-F,\"#O*&F)F*F-\"\"%!#
7**I(alpha12GF$F*I)tinfty13GF$F*F+F0F-F*!\"'**F8F*F9F*F+F*F-F0F.*(F8F*
F9F*F-F,F:*(F8F*F+F,I)tinfty23GF$F*\"\"'**F8F*F+F0F>F*F-F*F6**F8F*F+F*
F>F*F-F0F?**I(alpha13GF$F*I)tinfty12GF$F*F+F0F-F*!\"%**FCF*FDF*F+F*F-F
0\"\")*(FCF*FDF*F-F,FE**FCF*F9F0F+F*F-F*F5*(FCF*F9F0F-F0FE**FCF*F9F*F+
F0F>F*FE**FCF*F9F*F>F*F-F0F5*(FCF*F+F,I)tinfty22GF$F*F5**FCF*F+F0FNF*F
-F*!\")*(FCF*F+F0F>F0F5**FCF*F+F*FNF*F-F0F5**FCF*F+F*F>F0F-F*FE**I(alp
ha14GF$F*I)tinfty11GF$F*F+F0F-F*!\"$**FUF*FVF*F+F*F-F0F?*(FUF*FVF*F-F,
FW*,FUF*FDF*F9F*F+F*F-F*F?**FUF*FDF*F9F*F-F0F:**FUF*FDF*F+F0F>F*FW**FU
F*FDF*F>F*F-F0F,*(FUF*F9F,F-F*FW**FUF*F9F0F+F*F>F*F,**FUF*F9F0F>F*F-F*
F?**FUF*F9F*F+F0FNF*FW**FUF*F9F*F+F*F>F0F:**FUF*F9F*FNF*F-F0F,**FUF*F9
F*F>F0F-F*FW*(FUF*F+F,I)tinfty21GF$F*F,**FUF*F+F0F`oF*F-F*F:**FUF*F+F0
FNF*F>F*F?**FUF*F+F*F`oF*F-F0F,*,FUF*F+F*FNF*F>F*F-F*F:*(FUF*F+F*F>F,F
,*&I(alpha21GF$F*F+F5F6*(FgoF*F+F,F-F*F3*(FgoF*F+F0F-F0F1*(FgoF*F+F*F-
F,F.**I(alpha22GF$F*F9F*F+F0F-F*F?**F\\pF*F9F*F+F*F-F0F6*(F\\pF*F9F*F-
F,F?*(F\\pF*F+F,F>F*F:**F\\pF*F+F0F>F*F-F*F.**F\\pF*F+F*F>F*F-F0F:**I(
alpha23GF$F*FDF*F+F0F-F*F5**FcpF*FDF*F+F*F-F0FP*(FcpF*FDF*F-F,F5**FcpF
*F9F0F+F*F-F*FE*(FcpF*F9F0F-F0F5**FcpF*F9F*F+F0F>F*F5**FcpF*F9F*F>F*F-
F0FE*(FcpF*F+F,FNF*FE**FcpF*F+F0FNF*F-F*FG*(FcpF*F+F0F>F0FE**FcpF*F+F*
FNF*F-F0FE**FcpF*F+F*F>F0F-F*F5**I(alpha24GF$F*FVF*F+F0F-F*F,**F`qF*FV
F*F+F*F-F0F:*(F`qF*FVF*F-F,F,*,F`qF*FDF*F9F*F+F*F-F*F:**F`qF*FDF*F9F*F
-F0F?**F`qF*FDF*F+F0F>F*F,**F`qF*FDF*F>F*F-F0FW*(F`qF*F9F,F-F*F,**F`qF
*F9F0F+F*F>F*FW**F`qF*F9F0F>F*F-F*F:**F`qF*F9F*F+F0FNF*F,**F`qF*F9F*F+
F*F>F0F?**F`qF*F9F*FNF*F-F0FW**F`qF*F9F*F>F0F-F*F,*(F`qF*F+F,F`oF*FW**
F`qF*F+F0F`oF*F-F*F?**F`qF*F+F0FNF*F>F*F:**F`qF*F+F*F`oF*F-F0FW*,F`qF*
F+F*FNF*F>F*F-F*F?*(F`qF*F+F*F>F,FWF*,&F-!\"\"F+F*FE#F*F." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 208 162 "We get that A_\{1,1\}=1/4*(alpha14*tinf
ty24-alpha24*tinfty14)/(tinfty14-tinfty24)*lambda^4+c3*lambda^3+c2*lam
bda^2+c1*lambda +c0+ rho1/(lambda-q1)+ rho2/(lambda-q2)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "A11Form:=1/4*(alpha14*tinfty24-alp
ha24*tinfty14)/(tinfty14-tinfty24)*lambda^4+c3*lambda^3+c2*lambda^2+c1
*lambda +c0+ rho1/(lambda-q1)+rho2/(lambda-q2);\n" }{MPLTEXT 1 0 1 "\n
" }{MPLTEXT 1 0 71 "simplify(-residue(A11Form/lambda^5,lambda=infinity
)-A11InftyLambda4); \n" }{MPLTEXT 1 0 221 "solve(\{factor(-residue(A11
Form/lambda^4,lambda=infinity))=A11InftyLambda3,factor(-residue(A11For
m/lambda^3,lambda=infinity))=A11InftyLambda2,factor(-residue(A11Form/l
ambda^2,lambda=infinity))=A11InftyLambda1\},\{c3,c2,c1\}):" }}{PARA 11
 "" 1 "" {XPPMATH 20 ">I(A11FormG6\",0*(,&*&I(alpha14GF$\"\"\"I)tinfty
24GF$F*F**&I(alpha24GF$F*I)tinfty14GF$F*!\"\"F*,&F+F/F.F*F/I'lambdaGF$
\"\"%#F*F2*&I#c3GF$F*F1\"\"$F**&I#c2GF$F*F1\"\"#F**&I#c1GF$F*F1F*F*I#c
0GF$F**&I%rho1GF$F*,&F1F*I#q1GF$F/F/F**&I%rho2GF$F*,&F1F*I#q2GF$F/F/F*
" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3164 "c1:= -(3*alpha14*tinfty11*tinfty14^2*tinfty24-6*alp
ha14*tinfty11*tinfty14*tinfty24^2+3*alpha14*tinfty11*tinfty24^3-6*alph
a14*tinfty12*tinfty13*tinfty14*tinfty24+6*alpha14*tinfty12*tinfty13*ti
nfty24^2+3*alpha14*tinfty12*tinfty14^2*tinfty23-3*alpha14*tinfty12*tin
fty23*tinfty24^2+3*alpha14*tinfty13^3*tinfty24-3*alpha14*tinfty13^2*ti
nfty14*tinfty23-6*alpha14*tinfty13^2*tinfty23*tinfty24+3*alpha14*tinft
y13*tinfty14^2*tinfty22+6*alpha14*tinfty13*tinfty14*tinfty23^2-3*alpha
14*tinfty13*tinfty22*tinfty24^2+3*alpha14*tinfty13*tinfty23^2*tinfty24
-3*alpha14*tinfty14^3*tinfty21+6*alpha14*tinfty14^2*tinfty21*tinfty24-
6*alpha14*tinfty14^2*tinfty22*tinfty23-3*alpha14*tinfty14*tinfty21*tin
fty24^2+6*alpha14*tinfty14*tinfty22*tinfty23*tinfty24-3*alpha14*tinfty
14*tinfty23^3-3*alpha24*tinfty11*tinfty14^2*tinfty24+6*alpha24*tinfty1
1*tinfty14*tinfty24^2-3*alpha24*tinfty11*tinfty24^3+6*alpha24*tinfty12
*tinfty13*tinfty14*tinfty24-6*alpha24*tinfty12*tinfty13*tinfty24^2-3*a
lpha24*tinfty12*tinfty14^2*tinfty23+3*alpha24*tinfty12*tinfty23*tinfty
24^2-3*alpha24*tinfty13^3*tinfty24+3*alpha24*tinfty13^2*tinfty14*tinft
y23+6*alpha24*tinfty13^2*tinfty23*tinfty24-3*alpha24*tinfty13*tinfty14
^2*tinfty22-6*alpha24*tinfty13*tinfty14*tinfty23^2+3*alpha24*tinfty13*
tinfty22*tinfty24^2-3*alpha24*tinfty13*tinfty23^2*tinfty24+3*alpha24*t
infty14^3*tinfty21-6*alpha24*tinfty14^2*tinfty21*tinfty24+6*alpha24*ti
nfty14^2*tinfty22*tinfty23+3*alpha24*tinfty14*tinfty21*tinfty24^2-6*al
pha24*tinfty14*tinfty22*tinfty23*tinfty24+3*alpha24*tinfty14*tinfty23^
3+4*alpha13*tinfty12*tinfty14^2*tinfty24-8*alpha13*tinfty12*tinfty14*t
infty24^2+4*alpha13*tinfty12*tinfty24^3-4*alpha13*tinfty13^2*tinfty14*
tinfty24+4*alpha13*tinfty13^2*tinfty24^2+4*alpha13*tinfty13*tinfty14^2
*tinfty23-4*alpha13*tinfty13*tinfty23*tinfty24^2-4*alpha13*tinfty14^3*
tinfty22+8*alpha13*tinfty14^2*tinfty22*tinfty24-4*alpha13*tinfty14^2*t
infty23^2-4*alpha13*tinfty14*tinfty22*tinfty24^2+4*alpha13*tinfty14*ti
nfty23^2*tinfty24-4*alpha23*tinfty12*tinfty14^2*tinfty24+8*alpha23*tin
fty12*tinfty14*tinfty24^2-4*alpha23*tinfty12*tinfty24^3+4*alpha23*tinf
ty13^2*tinfty14*tinfty24-4*alpha23*tinfty13^2*tinfty24^2-4*alpha23*tin
fty13*tinfty14^2*tinfty23+4*alpha23*tinfty13*tinfty23*tinfty24^2+4*alp
ha23*tinfty14^3*tinfty22-8*alpha23*tinfty14^2*tinfty22*tinfty24+4*alph
a23*tinfty14^2*tinfty23^2+4*alpha23*tinfty14*tinfty22*tinfty24^2-4*alp
ha23*tinfty14*tinfty23^2*tinfty24+6*alpha12*tinfty13*tinfty14^2*tinfty
24-12*alpha12*tinfty13*tinfty14*tinfty24^2+6*alpha12*tinfty13*tinfty24
^3-6*alpha12*tinfty14^3*tinfty23+12*alpha12*tinfty14^2*tinfty23*tinfty
24-6*alpha12*tinfty14*tinfty23*tinfty24^2-6*alpha22*tinfty13*tinfty14^
2*tinfty24+12*alpha22*tinfty13*tinfty14*tinfty24^2-6*alpha22*tinfty13*
tinfty24^3+6*alpha22*tinfty14^3*tinfty23-12*alpha22*tinfty14^2*tinfty2
3*tinfty24+6*alpha22*tinfty14*tinfty23*tinfty24^2-12*alpha11*tinfty14^
3*tinfty24+36*alpha11*tinfty14^2*tinfty24^2-36*alpha11*tinfty14*tinfty
24^3+12*alpha11*tinfty24^4+12*alpha21*tinfty14^4-36*alpha21*tinfty14^3
*tinfty24+36*alpha21*tinfty14^2*tinfty24^2-12*alpha21*tinfty14*tinfty2
4^3)/(12*(tinfty14^4-4*tinfty14^3*tinfty24+6*tinfty14^2*tinfty24^2-4*t
infty14*tinfty24^3+tinfty24^4)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 1049 "c2:= -(3*alpha14*tinfty12*tinfty14*tinfty24-3*alpha14*tinfty12
*tinfty24^2-3*alpha14*tinfty13^2*tinfty24+3*alpha14*tinfty13*tinfty14*
tinfty23+3*alpha14*tinfty13*tinfty23*tinfty24-3*alpha14*tinfty14^2*tin
fty22+3*alpha14*tinfty14*tinfty22*tinfty24-3*alpha14*tinfty14*tinfty23
^2-3*alpha24*tinfty12*tinfty14*tinfty24+3*alpha24*tinfty12*tinfty24^2+
3*alpha24*tinfty13^2*tinfty24-3*alpha24*tinfty13*tinfty14*tinfty23-3*a
lpha24*tinfty13*tinfty23*tinfty24+3*alpha24*tinfty14^2*tinfty22-3*alph
a24*tinfty14*tinfty22*tinfty24+3*alpha24*tinfty14*tinfty23^2+4*alpha13
*tinfty13*tinfty14*tinfty24-4*alpha13*tinfty13*tinfty24^2-4*alpha13*ti
nfty14^2*tinfty23+4*alpha13*tinfty14*tinfty23*tinfty24-4*alpha23*tinft
y13*tinfty14*tinfty24+4*alpha23*tinfty13*tinfty24^2+4*alpha23*tinfty14
^2*tinfty23-4*alpha23*tinfty14*tinfty23*tinfty24-6*alpha12*tinfty14^2*
tinfty24+12*alpha12*tinfty14*tinfty24^2-6*alpha12*tinfty24^3+6*alpha22
*tinfty14^3-12*alpha22*tinfty14^2*tinfty24+6*alpha22*tinfty14*tinfty24
^2)/(12*(tinfty14^3-3*tinfty14^2*tinfty24+3*tinfty14*tinfty24^2-tinfty
24^3)):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 267 "
c3:=-(3*alpha14*tinfty13*tinfty24-3*alpha14*tinfty14*tinfty23-3*alpha2
4*tinfty13*tinfty24+3*alpha24*tinfty14*tinfty23-4*alpha13*tinfty14*tin
fty24+4*alpha13*tinfty24^2+4*alpha23*tinfty14^2-4*alpha23*tinfty14*tin
fty24)/(12*(tinfty14^2-2*tinfty14*tinfty24+tinfty24^2)):\n" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 47 "c4:=(1/4)*(alpha14*tinfty24-alpha24*tinft
y14)/(" }{MPLTEXT 1 0 8 "tinfty14" }{MPLTEXT 1 0 12 "-tinfty24):\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 69 "fact
or(-residue(A11Form/lambda^4,lambda=infinity))-A11InftyLambda3);\n" }
{MPLTEXT 1 0 78 "simplify(factor(-residue(A11Form/lambda^3,lambda=infi
nity))-A11InftyLambda2);\n" }{MPLTEXT 1 0 77 "simplify(factor(-residue
(A11Form/lambda^2,lambda=infinity))-A11InftyLambda1);" }{MPLTEXT 1 0 
1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "c3bis:=-(1/4)*(tinfty13*tinfty24-ti
nfty14*tinfty23)/(" }{MPLTEXT 1 0 8 "tinfty14" }{MPLTEXT 1 0 31 "-tinf
ty24)^2*(alpha14-alpha24)\n" }{MPLTEXT 1 0 42 "+1/3*(alpha13*tinfty24-
alpha23*tinfty14)/(" }{MPLTEXT 1 0 8 "tinfty14" }{MPLTEXT 1 0 12 "-tin
fty24);\n" }{MPLTEXT 1 0 35 "factor(series(c3-c3bis,alpha14=0));" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I&c3bisG6\",&*(,&*&I)tinfty13GF$\"\"\"I
)tinfty24GF$F*F**&I)tinfty14GF$F*I)tinfty23GF$F*!\"\"F*,&F+F/F-F*!\"#,
&I(alpha14GF$F*I(alpha24GF$F/F*#F/\"\"%*&,&*&I(alpha13GF$F*F+F*F**&I(a
lpha23GF$F*F-F*F/F*F0F/#F*\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "c2bis:=-(1/4)*(" }
{MPLTEXT 1 0 116 "(tinfty14-tinfty24)*(tinfty24*tinfty12-tinfty14*tinf
ty22)-(-tinfty23+tinfty13)*(tinfty13*tinfty24-tinfty14*tinfty23)" }
{MPLTEXT 1 0 3 ")/(" }{MPLTEXT 1 0 8 "tinfty14" }{MPLTEXT 1 0 31 "-tin
fty24)^3*(alpha14-alpha24)\n" }{MPLTEXT 1 0 46 "-(1/3)*(tinfty13*tinft
y24-tinfty14*tinfty23)/(" }{MPLTEXT 1 0 8 "tinfty14" }{MPLTEXT 1 0 31 
"-tinfty24)^2*(alpha13-alpha23)\n" }{MPLTEXT 1 0 41 "+(alpha12*tinfty2
4-alpha22*tinfty14)/(2*(" }{MPLTEXT 1 0 8 "tinfty14" }{MPLTEXT 1 0 13 
"-tinfty24));\n" }{MPLTEXT 1 0 35 "factor(series(c2-c2bis,alpha14=0));
" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I&c2bisG6\",(*(,&*&,&I)tinfty24GF$!\"\"I)tinfty14GF$\"\"\"F-,&*&I
)tinfty12GF$F-F*F-F-*&F,F-I)tinfty22GF$F-F+F-F-*&,&I)tinfty23GF$F+I)ti
nfty13GF$F-F-,&*&F6F-F*F-F-*&F,F-F5F-F+F-F+F-F)!\"$,&I(alpha14GF$F-I(a
lpha24GF$F+F-#F+\"\"%*(F7F-F)!\"#,&I(alpha13GF$F-I(alpha23GF$F+F-#F+\"
\"$*&,&*&I(alpha12GF$F-F*F-F-*&I(alpha22GF$F-F,F-F+F-,&F*FAF,\"\"#F+F-
" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "c1bis:=(tinfty24*alpha11-tinfty14*alpha21)/(" }
{MPLTEXT 1 0 8 "tinfty14" }{MPLTEXT 1 0 11 "-tinfty24)\n" }{MPLTEXT 1 
0 46 "-(1/2)*(tinfty13*tinfty24-tinfty14*tinfty23)/(" }{MPLTEXT 1 0 8 
"tinfty14" }{MPLTEXT 1 0 31 "-tinfty24)^2*(alpha12-alpha22)\n" }
{MPLTEXT 1 0 8 "-(1/3)*(" }{MPLTEXT 1 0 116 "(tinfty14-tinfty24)*(tinf
ty24*tinfty12-tinfty14*tinfty22)-(-tinfty23+tinfty13)*(tinfty13*tinfty
24-tinfty14*tinfty23)" }{MPLTEXT 1 0 3 ")/(" }{MPLTEXT 1 0 8 "tinfty14
" }{MPLTEXT 1 0 31 "-tinfty24)^3*(alpha13-alpha23)\n" }{MPLTEXT 1 0 6 
"-1/4*(" }{MPLTEXT 1 0 83 "tinfty24*tinfty13^3-tinfty14*tinfty23^3+ (2
*tinfty14+tinfty24)*tinfty13*tinfty23^2-" }{MPLTEXT 1 0 42 "(2*tinfty2
4+tinfty14)*tinfty13^2*tinfty23\n" }{MPLTEXT 1 0 88 "-(tinfty14-tinfty
24)*(2*tinfty12*tinfty24-tinfty14*tinfty22-tinfty22*tinfty24)*tinfty13
\n" }{MPLTEXT 1 0 88 "-(tinfty14-tinfty24)*(2*tinfty22*tinfty14-tinfty
14*tinfty12-tinfty12*tinfty24)*tinfty23\n" }{MPLTEXT 1 0 10 "+(tinfty1
4" }{MPLTEXT 1 0 50 "-tinfty24)^2*(tinfty11*tinfty24-tinfty14*tinfty21
)" }{MPLTEXT 1 0 42 ")/(tinfty14-tinfty24)^4*(alpha14-alpha24)\n" }
{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 29 "factor(series(c1-c1bis,e=0));" 
}{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&c1bisG6\",**&,&*
&I(alpha11GF$\"\"\"I)tinfty24GF$F*F**&I(alpha21GF$F*I)tinfty14GF$F*!\"
\"F*,&F+F/F.F*F/F**(,&*&I)tinfty13GF$F*F+F*F**&F.F*I)tinfty23GF$F*F/F*
F0!\"#,&I(alpha12GF$F*I(alpha22GF$F/F*#F/\"\"#*(,&*&F0F*,&*&I)tinfty12
GF$F*F+F*F**&F.F*I)tinfty22GF$F*F/F*F**&,&F6F/F4F*F*F2F*F/F*F0!\"$,&I(
alpha13GF$F*I(alpha23GF$F/F*#F/\"\"$*(,0*&F+F*F4FLF**&F.F*F6FLF/*(,&F.
F<F+F*F*F4F*F6F<F**(,&F+F<F.F*F*F4F<F6F*F/*(F0F*,(FAF<FCF/*&FDF*F+F*F/
F*F4F*F/*(F0F*,(*&FBF*F.F*F/FAF/FCF<F*F6F*F/*&F0F<,&*&I)tinfty11GF$F*F
+F*F**&F.F*I)tinfty21GF$F*F/F*F*F*F0!\"%,&I(alpha14GF$F*I(alpha24GF$F/
F*#F/\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 39 "c1function:=unapply(c1,alpha14,alpha24," }
{MPLTEXT 1 0 7 "alpha13" }{MPLTEXT 1 0 1 "," }{MPLTEXT 1 0 7 "alpha23"
 }{MPLTEXT 1 0 1 "," }{MPLTEXT 1 0 7 "alpha12" }{MPLTEXT 1 0 1 "," }
{MPLTEXT 1 0 7 "alpha22" }{MPLTEXT 1 0 1 "," }{MPLTEXT 1 0 7 "alpha11"
 }{MPLTEXT 1 0 1 "," }{MPLTEXT 1 0 7 "alpha21" }{MPLTEXT 1 0 3 "):\n" 
}{MPLTEXT 1 0 23 "c2function:=unapply(c2," }{MPLTEXT 1 0 16 "alpha14,a
lpha24," }{MPLTEXT 1 0 47 "alpha13,alpha23,alpha12,alpha22,alpha11,alp
ha21" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 23 "c3function:=unapply(c3,
" }{MPLTEXT 1 0 16 "alpha14,alpha24," }{MPLTEXT 1 0 47 "alpha13,alpha2
3,alpha12,alpha22,alpha11,alpha21" }{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 
0 23 "nufunction:=unapply(nu," }{MPLTEXT 1 0 16 "alpha14,alpha24," }
{MPLTEXT 1 0 47 "alpha13,alpha23,alpha12,alpha22,alpha11,alpha21" }
{MPLTEXT 1 0 3 "):\n" }{MPLTEXT 1 0 134 "nu1function:=unapply(-(1/4)*(
(tinfty12-tinfty22)*(tinfty14-tinfty24) -(tinfty13-tinfty23)^2 )/(tinf
ty14-tinfty24)^3*(alpha14-alpha24)\n" }{MPLTEXT 1 0 67 "-(1/3)*(tinfty
13-tinfty23)/(tinfty14-tinfty24)^2*(alpha13-alpha23)\n" }{MPLTEXT 1 0 
109 "+(alpha12-alpha22)/(2*(tinfty14-tinfty24)),alpha14,alpha24,alpha1
3,alpha23,alpha12,alpha22,alpha11,alpha21);\n" }{MPLTEXT 1 0 197 "nu2f
unction:=unapply(-(1/4)*((tinfty11-tinfty21)*(tinfty14-tinfty24)^2-2*(
tinfty12-tinfty22)*(tinfty14-tinfty24)*(tinfty13-tinfty23) +(tinfty13-
tinfty23)^3)/(tinfty14-tinfty24)^4*(alpha14-alpha24)\n" }{MPLTEXT 1 0 
112 "-(1/3)*((tinfty12-tinfty22)*(tinfty14-tinfty24) -(tinfty13-tinfty
23)^2)/(tinfty14-tinfty24)^3*(alpha13-alpha23)\n" }{MPLTEXT 1 0 68 "-(
1/2)*(-tinfty23+tinfty13)/(tinfty14-tinfty24)^2*(alpha12-alpha22)\n" }
{MPLTEXT 1 0 104 "+(alpha11-alpha21)/(tinfty14-tinfty24),alpha14,alpha
24,alpha13,alpha23,alpha12,alpha22,alpha11,alpha21);" }}{PARA 11 "" 1 
"" {XPPMATH 20 ">I,nu1functionG6\"f*6*I(alpha14GF$I(alpha24GF$I(alpha1
3GF$I(alpha23GF$I(alpha12GF$I(alpha22GF$I(alpha11GF$I(alpha21GF$F$6$I)
operatorGF$I&arrowGF$F$,(*(,&*&,&I)tinfty22GF$!\"\"I)tinfty12GF$\"\"\"
F:,&I)tinfty24GF$F8I)tinfty14GF$F:F:F:*$,&I)tinfty23GF$F8I)tinfty13GF$
F:\"\"#F8F:F;!\"$,&9$F:9%F8F:#F8\"\"%*(F?F:F;!\"#,&9&F:9'F8F:#F8\"\"$*
&,&9(F:9)F8F:,&F<FJF=FBF8F:F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,
nu2functionG6\"f*6*I(alpha14GF$I(alpha24GF$I(alpha13GF$I(alpha23GF$I(a
lpha12GF$I(alpha22GF$I(alpha11GF$I(alpha21GF$F$6$I)operatorGF$I&arrowG
F$F$,**(,(*&,&I)tinfty21GF$!\"\"I)tinfty11GF$\"\"\"F:,&I)tinfty24GF$F8
I)tinfty14GF$F:\"\"#F:*(,&I)tinfty22GF$F8I)tinfty12GF$F:F:F;F:,&I)tinf
ty23GF$F8I)tinfty13GF$F:F:!\"#*$FC\"\"$F:F:F;!\"%,&9$F:9%F8F:#F8\"\"%*
(,&*&F@F:F;F:F:*$FCF>F8F:F;!\"$,&9&F:9'F8F:#F8FH*(FCF:F;FF,&9(F:9)F8F:
#F8F>*&,&9*F:9+F8F:F;F8F:F$F$F$" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
232 59 "Verification of the theoretical formulas for c1, c2, c3, c4" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "with(LinearAlgebra):\n" }
{MPLTEXT 1 0 6 "m:=4:\n" }{MPLTEXT 1 0 19 "M0:=Matrix(m,m,0):\n" }
{MPLTEXT 1 0 55 "for i from 1 to m do M0[i,i]:=(tinfty14-tinfty24): od
:\n" }{MPLTEXT 1 0 28 "M0[2,1]:=tinfty13-tinfty23:\n" }{MPLTEXT 1 0 
28 "M0[3,1]:=tinfty12-tinfty22:\n" }{MPLTEXT 1 0 28 "M0[3,2]:=tinfty13
-tinfty23:\n" }{MPLTEXT 1 0 28 "M0[4,1]:=tinfty11-tinfty21:\n" }
{MPLTEXT 1 0 28 "M0[4,2]:=tinfty12-tinfty22:\n" }{MPLTEXT 1 0 28 "M0[4
,3]:=tinfty13-tinfty23:\n" }{MPLTEXT 1 0 3 "M0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6
'-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6)-I$mtdGF$6(-F,6&-I#moGF$6.Q*&umi
nus0;F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%&fenceGQ&fa
lseF'/%*separatorGFE/%)stretchyGFE/%*symmetricGFE/%(largeopGFE/%.movab
lelimitsGFE/%'accentGFE/%'lspaceGQ,0.2222222emF'/%'rspaceGFT-I#miGF$6&
Q)tinfty24F'/%'italicGQ%trueF'F=/FAQ'italicF'-F:6.Q\"+F'F=F@FCFFFHFJFL
FNFPFRFU-FX6&Q)tinfty14F'FenF=Fhn/%)rowalignGQ!F'/%,columnalignGFbo/%+
groupalignGFbo/%(rowspanGQ\"1F'/%+columnspanGFio-F56(-I#mnGF$6%Q\"0F'F
=F@F`oFcoFeoFgoFjoF\\pF\\pF`oFcoFeo-F26)-F56(-F,6&F9-FX6&Q)tinfty23F'F
enF=FhnFjn-FX6&Q)tinfty13F'FenF=FhnF`oFcoFeoFgoFjoF4F\\pF\\pF`oFcoFeo-
F26)-F56(-F,6&F9-FX6&Q)tinfty22F'FenF=FhnFjn-FX6&Q)tinfty12F'FenF=FhnF
`oFcoFeoFgoFjoFdpF4F\\pF`oFcoFeo-F26)-F56(-F,6&F9-FX6&Q)tinfty21F'FenF
=FhnFjn-FX6&Q)tinfty11F'FenF=FhnF`oFcoFeoFgoFjoF`qFdpF4F`oFcoFeo/%&ali
gnGQ%axisF'/FaoQ)baselineF'/FdoQ'centerF'/FfoQ'|frleft|hrF'/%/alignmen
tscopeGFgn/%,columnwidthGQ%autoF'/%&widthGFcs/%+rowspacingGQ&1.0exF'/%
.columnspacingGQ&0.8emF'/%)rowlinesGQ%noneF'/%,columnlinesGF^t/%&frame
GF^t/%-framespacingGQ,0.4em~0.5exF'/%*equalrowsGFE/%-equalcolumnsGFE/%
-displaystyleGFE/%%sideGQ&rightF'/%0minlabelspacingGF[tF=F@/%%openGQ\"
[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "c3bis
:=-(1/4)*(tinfty13*tinfty24-tinfty14*tinfty23)/(tinfty14-tinfty24)^2*(
alpha14-alpha24)\n" }{MPLTEXT 1 0 62 "+1/3*(alpha13*tinfty24-alpha23*t
infty14)/(tinfty14-tinfty24):\n" }{MPLTEXT 1 0 173 "c2bis:=-(1/4)*((ti
nfty14-tinfty24)*(tinfty24*tinfty12-tinfty14*tinfty22)-(-tinfty23+tinf
ty13)*(tinfty13*tinfty24-tinfty14*tinfty23))/(tinfty14-tinfty24)^3*(al
pha14-alpha24)\n" }{MPLTEXT 1 0 68 "-(1/3)*(tinfty13*tinfty24-tinfty14
*tinfty23)/(tinfty14-tinfty24)^2*(" }{MPLTEXT 1 0 7 "alpha13" }
{MPLTEXT 1 0 1 "-" }{MPLTEXT 1 0 7 "alpha23" }{MPLTEXT 1 0 2 ")\n" }
{MPLTEXT 1 0 62 "+(alpha12*tinfty24-alpha22*tinfty14)/(2*(tinfty14-tin
fty24)):\n" }{MPLTEXT 1 0 17 "c1bis:=(tinfty24*" }{MPLTEXT 1 0 7 "alph
a11" }{MPLTEXT 1 0 10 "-tinfty14*" }{MPLTEXT 1 0 7 "alpha21" }{MPLTEXT
 1 0 22 ")/(tinfty14-tinfty24)\n" }{MPLTEXT 1 0 68 "-(1/2)*(tinfty13*t
infty24-tinfty14*tinfty23)/(tinfty14-tinfty24)^2*(" }{MPLTEXT 1 0 7 "a
lpha12" }{MPLTEXT 1 0 1 "-" }{MPLTEXT 1 0 7 "alpha22" }{MPLTEXT 1 0 2 
")\n" }{MPLTEXT 1 0 149 "-(1/3)*((tinfty14-tinfty24)*(tinfty24*tinfty1
2-tinfty14*tinfty22)-(-tinfty23+tinfty13)*(tinfty13*tinfty24-tinfty14*
tinfty23))/(tinfty14-tinfty24)^3*(" }{MPLTEXT 1 0 7 "alpha13" }
{MPLTEXT 1 0 1 "-" }{MPLTEXT 1 0 7 "alpha23" }{MPLTEXT 1 0 2 ")\n" }
{MPLTEXT 1 0 131 "-1/4*(tinfty24*tinfty13^3-tinfty14*tinfty23^3+ (2*ti
nfty14+tinfty24)*tinfty13*tinfty23^2-(2*tinfty24+tinfty14)*tinfty13^2*
tinfty23\n" }{MPLTEXT 1 0 88 "-(tinfty14-tinfty24)*(2*tinfty12*tinfty2
4-tinfty14*tinfty22-tinfty22*tinfty24)*tinfty13\n" }{MPLTEXT 1 0 88 "-
(tinfty14-tinfty24)*(2*tinfty22*tinfty14-tinfty14*tinfty12-tinfty12*ti
nfty24)*tinfty23\n" }{MPLTEXT 1 0 103 "+(tinfty14-tinfty24)^2*(tinfty1
1*tinfty24-tinfty14*tinfty21))/(tinfty14-tinfty24)^4*(alpha14-alpha24)
:\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 67 "c4bis:=1/4*(alpha14*tinfty
24-alpha24*tinfty14)/(tinfty14-tinfty24):" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 24 "cvector:=Matrix(4,1,0):\n" }{MPLTEXT 1 0 21 "cvector[
1,1]:=c4bis:\n" }{MPLTEXT 1 0 21 "cvector[2,1]:=c3bis:\n" }{MPLTEXT 1 
0 21 "cvector[3,1]:=c2bis:\n" }{MPLTEXT 1 0 20 "cvector[4,1]:=c1bis:" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "RHSTheo:=Multiply(M0,cvec
tor):\n" }{MPLTEXT 1 0 25 "RHSTheo2:=Matrix(4,1,0):\n" }{MPLTEXT 1 0 
54 "RHSTheo2[1,1]:=(tinfty24*alpha14-tinfty14*alpha24)/4:\n" }{MPLTEXT
 1 0 92 "RHSTheo2[2,1]:=(tinfty24*alpha13-tinfty14*alpha23)/3+(tinfty2
3*alpha14-tinfty13*alpha24)/4:\n" }{MPLTEXT 1 0 130 "RHSTheo2[3,1]:=(t
infty24*alpha12-tinfty14*alpha22)/2+(tinfty23*alpha13-tinfty13*alpha23
)/3+(tinfty22*alpha14-tinfty12*alpha24)/4:\n" }{MPLTEXT 1 0 168 "RHSTh
eo2[4,1]:=(tinfty24*alpha11-tinfty14*alpha21)/1+(tinfty23*alpha12-tinf
ty13*alpha22)/2+(tinfty22*alpha13-tinfty12*alpha23)/3+(tinfty21*alpha1
4-tinfty11*alpha24)/4:\n" }{MPLTEXT 1 0 27 "simplify(RHSTheo-RHSTheo2)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,Typ
esettingGI(_syslibGF'6'-I%mrowGF$6#-I'mtableGF$68-I$mtrGF$6&-I$mtdGF$6
(-I#mnGF$6%Q\"0F'/%+foregroundGQ([0,0,0]F'/%,mathvariantGQ'normalF'/%)
rowalignGQ!F'/%,columnalignGFC/%+groupalignGFC/%(rowspanGQ\"1F'/%+colu
mnspanGFJFAFDFFF1F1F1/%&alignGQ%axisF'/FBQ)baselineF'/FEQ&rightF'/FGQ'
|frleft|hrF'/%/alignmentscopeGQ%trueF'/%,columnwidthGQ%autoF'/%&widthG
Fen/%+rowspacingGQ&1.0exF'/%.columnspacingGQ&0.8emF'/%)rowlinesGQ%none
F'/%,columnlinesGF`o/%&frameGF`o/%-framespacingGQ,0.4em~0.5exF'/%*equa
lrowsGQ&falseF'/%-equalcolumnsGFjo/%-displaystyleGFjo/%%sideGFS/%0minl
abelspacingGF]oF;F>/%%openGQ\"[F'/%&closeGQ\"]F'" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}}
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