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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT 257 68 "Method 1: Comparing the
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" {TEXT 249 29 "Loading the gl_2 side results" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 9 "restart:\n" }{MPLTEXT 1 0 25 "checkQfunction:=S2*
Q+S1;\n" }{MPLTEXT 1 0 35 "checkPfunction=1/S2*(P-1/2*R1(Q));\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 23 "SolQ:=-(S1-checkQ)/S2;\n" }
{MPLTEXT 1 0 43 "SolP:=checkP*S2+(1/2)*R1(-(S1-checkQ)/S2);\n" }
{MPLTEXT 1 0 31 "simplify(checkQ-(S2*SolQ+S1));\n" }{MPLTEXT 1 0 45 "s
implify(checkP-(1/S2*(SolP-1/2*R1(SolQ))));\n" }{MPLTEXT 1 0 26 "Sinft
y2function:=s12+s22;\n" }{MPLTEXT 1 0 26 "Sinfty1function:=s11+s21;\n"
 }{MPLTEXT 1 0 35 "S2function:=sqrt(s12-s22)/sqrt(2);\n" }{MPLTEXT 1 
0 45 "S1function:=(s11-s21)/sqrt(2)/sqrt(s12-s22);\n" }{MPLTEXT 1 0 
40 "tdX1function:=X1*S2function+S1function;\n" }{MPLTEXT 1 0 67 "solve
( \{s12+s22=Sinfty2,s11+s21=Sinfty1, S2=sqrt(s12-s22)/sqrt(2),\n" }
{MPLTEXT 1 0 36 "S1=(s11-s21)/sqrt(2)/sqrt(s12-s22),\n" }{MPLTEXT 1 0 
55 "tdX1=X1*S2function+S1function\},\{s12,s22,s11,s21,X1\}); \n" }
{MPLTEXT 1 0 67 "X1function := unapply( -(S1-tdX1)/S2 ,Sinfty1,Sinfty2
,S1,S2,tdX1);\n" }{MPLTEXT 1 0 73 "s11function:= unapply( S2*S1+(1/2)*
Sinfty1, Sinfty1,Sinfty2,S1,S2,tdX1);\n" }{MPLTEXT 1 0 72 "s12function
:= unapply( S2^2+(1/2)*Sinfty2, Sinfty1,Sinfty2,S1,S2,tdX1);\n" }
{MPLTEXT 1 0 74 "s21function:= unapply( -S2*S1+(1/2)*Sinfty1, Sinfty1,
Sinfty2,S1,S2,tdX1);\n" }{MPLTEXT 1 0 74 "s22function:= unapply( -S2^2
+(1/2)*Sinfty2, Sinfty1,Sinfty2,S1,S2,tdX1 );\n" }{MPLTEXT 1 0 90 "sim
plify(X1function(Sinfty1function,Sinfty2function,S1function,S2function
,tdX1function));\n" }{MPLTEXT 1 0 91 "simplify(s11function(Sinfty1func
tion,Sinfty2function,S1function,S2function,tdX1function));\n" }
{MPLTEXT 1 0 91 "simplify(s12function(Sinfty1function,Sinfty2function,
S1function,S2function,tdX1function));\n" }{MPLTEXT 1 0 91 "simplify(s2
1function(Sinfty1function,Sinfty2function,S1function,S2function,tdX1fu
nction));\n" }{MPLTEXT 1 0 91 "simplify(s22function(Sinfty1function,Si
nfty2function,S1function,S2function,tdX1function));\n" }{MPLTEXT 1 0 
94 "partialtdX1function:=simplify(diff(s11function(Sinfty1,Sinfty2,S1,
S2,tdX1),tdX1))*partials11+\n" }{MPLTEXT 1 0 72 "simplify(diff(s21func
tion(Sinfty1,Sinfty2,S1,S2,tdX1),tdX1))*partials21\n" }{MPLTEXT 1 0 
73 "+simplify(diff(s12function(Sinfty1,Sinfty2,S1,S2,tdX1),tdX1))*part
ials12\n" }{MPLTEXT 1 0 73 "+simplify(diff(s22function(Sinfty1,Sinfty2
,S1,S2,tdX1),tdX1))*partials22\n" }{MPLTEXT 1 0 72 "+simplify(diff(X1f
unction(Sinfty1,Sinfty2,S1,S2,tdX1),tdX1))*partialX1;\n" }{MPLTEXT 1 
0 1 "\n" }{MPLTEXT 1 0 143 "K0OldCoordinates := unapply( (1/2)*(sX10+s
20)*(sX10+s10)*ln((s12-s22)/2)+(1/2)*X1*((X1*s12+2*s11)*s10+s20*(X1*s2
2+2*s21)),s11,s21,s12,s22,X1);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 
93 "K0NewCoordinates2:=unapply((sX10+s20)*(sX10+s10)*ln(S2)-(1/2)*(S1-
tdX1)*(s10+s20)*Sinfty1/S2\n" }{MPLTEXT 1 0 78 "+(1/4)*(S1-tdX1)^2*(s1
0+s20)*Sinfty2/S2^2-(1/2)*(S1-tdX1)*(s10-s20)*(S1+tdX1)\n" }{MPLTEXT 
1 0 30 ",Sinfty1,Sinfty2,S1,S2,tdX1);\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 153 "dtdX1function:=diff(tdX1function,s11)*ds11+diff(tdX1
function,s21)*ds21+diff(tdX1function,s12)*ds12+diff(tdX1function,s22)*
ds22+diff(tdX1function,X1)*dX1;" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 ""
 {XPPMATH 20 ">I/checkQfunctionG6\",&*&I\"QGF$\"\"\"I#S2GF$F(F(I#S1GF$
F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I/checkPfunctionG6\"*&I#S2GF$!\"
\",&I\"PGF$\"\"\"-I#R1GF$6#I\"QGF$#F'\"\"#F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I%SolQG6\",$*&,&I#S1GF$\"\"\"I'checkQGF$!\"\"F)I#S2GF$F+
F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%SolPG6\",&*&I'checkPGF$\"\"\"I#
S2GF$F(F(-I#R1GF$6#,$*&,&I#S1GF$F(I'checkQGF$!\"\"F(F)F2F2#F(\"\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0Sinfty2functionG6\",&I$s12GF
$\"\"\"I$s22GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0Sinfty1functionG
6\",&I$s11GF$\"\"\"I$s21GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+S2fu
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"" 1 "" {XPPMATH 20 ">I+S1functionG6\",$*(,&I$s11GF$\"\"\"I$s21GF$!\"
\"F)\"\"##F)F,,&I$s12GF$F)I$s22GF$F+#F+F,F-" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I-tdX1functionG6\",&*(I#X1GF$\"\"\",&I$s12GF$F(I$s22GF$!
\"\"#F(\"\"#F.F-F-*(,&I$s11GF$F(I$s21GF$F,F(F.F-F)#F,F.F-" }}{PARA 11 
"" 1 "" {XPPMATH 20 "<'/I#X1G6\",$*&I#S2GF%!\"\",&I#S1GF%\"\"\"I%tdX1G
F%F)F,F)/I$s11GF%,&*&F+F,F(F,F,I(Sinfty1GF%#F,\"\"#/I$s12GF%,&*$F(F4F,
I(Sinfty2GF%F3/I$s21GF%,&F1F)F2F3/I$s22GF%,&F8F)F9F3" }}{PARA 11 "" 1 
"" {XPPMATH 20 ">I+X1functionG6\"f*6'I(Sinfty1GF$I(Sinfty2GF$I#S1GF$I#
S2GF$I%tdX1GF$F$6$I)operatorGF$I&arrowGF$F$,$*&9'!\"\",&9&\"\"\"9(F2F5
F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,s11functionG6\"f*6'I(Sinf
ty1GF$I(Sinfty2GF$I#S1GF$I#S2GF$I%tdX1GF$F$6$I)operatorGF$I&arrowGF$F$
,&*&9&\"\"\"9'F2F29$#F2\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
,s12functionG6\"f*6'I(Sinfty1GF$I(Sinfty2GF$I#S1GF$I#S2GF$I%tdX1GF$F$6
$I)operatorGF$I&arrowGF$F$,&*$9'\"\"#\"\"\"9%#F3F2F$F$F$" }}{PARA 11 "
" 1 "" {XPPMATH 20 ">I,s21functionG6\"f*6'I(Sinfty1GF$I(Sinfty2GF$I#S1
GF$I#S2GF$I%tdX1GF$F$6$I)operatorGF$I&arrowGF$F$,&*&9&\"\"\"9'F2!\"\"9
$#F2\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,s22functionG6\"f*6
'I(Sinfty1GF$I(Sinfty2GF$I#S1GF$I#S2GF$I%tdX1GF$F$6$I)operatorGF$I&arr
owGF$F$,&*$9'\"\"#!\"\"9%#\"\"\"F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "I#X1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$s11G6\"" }}{PARA 11 ""
 1 "" {XPPMATH 20 "I$s12G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$s21G6
\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$s22G6\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I4partialtdX1functionG6\"*&I#S2GF$!\"\"I*partialX1GF$\"
\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I1K0OldCoordinatesG6\"f*6'I$s11
GF$I$s21GF$I$s12GF$I$s22GF$I#X1GF$F$6$I)operatorGF$I&arrowGF$F$,&*(,&I
%sX10GF$\"\"\"I$s20GF$F3F3,&F2F3I$s10GF$F3F3-I#lnG6$%*protectedGI(_sys
libGF$6#,&9&#F3\"\"#9'#!\"\"F@F3F?*&9(F3,&*&,&*&FEF3F>F3F39$F@F3F6F3F3
*&F4F3,&*&FEF3FAF3F39%F@F3F3F3F?F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I2K0NewCoordinates2G6\"f*6'I(Sinfty1GF$I(Sinfty2GF$I#S1GF$I#S2GF$I%
tdX1GF$F$6$I)operatorGF$I&arrowGF$F$,**(,&I%sX10GF$\"\"\"I$s20GF$F3F3,
&F2F3I$s10GF$F3F3-I#lnG6$%*protectedGI(_syslibGF$6#9'F3F3**,&9&F39(!\"
\"F3,&F6F3F4F3F39$F3F=FB#FB\"\"#**F?FFFCF39%F3F=!\"##F3\"\"%*(F?F3,&F6
F3F4FBF3,&F@F3FAF3F3FEF$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I.dtdX1
functionG6\",,*(\"\"##\"\"\"F',&I$s12GF$F)I$s22GF$!\"\"#F-F'I%ds11GF$F
)F(*(F'F(F*F.I%ds21GF$F)F.*&,&*(I#X1GF$F)F*F.F'F(#F)\"\"%*(,&I$s11GF$F
)I$s21GF$F-F)F'F(F*#!\"$F'#F-F7F)I%ds12GF$F)F)*&,&F4F>F8F6F)I%ds22GF$F
)F)*(F*F(F'F(I$dX1GF$F)F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 250 29 "Loa
ding the gl_3 side results" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "t10:=-t20-t30;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 55 "P1:=unapp
ly( (t12+t22+t32)*lambda+t11+t21+t31,lambda);\n" }{MPLTEXT 1 0 157 "P2
:=unapply( (t12*t22+t12*t32+t22*t32)*lambda^2+((t21+t31)*t12+(t11+t31)
*t22+t32*(t11+t21))*lambda-t10*t12-t20*t22-t30*t32+t21*t11 +t31*t11+t2
1*t31,lambda);\n" }{MPLTEXT 1 0 172 "P3:=unapply(t12*t22*t32*lambda^3+
(t12*t22*t31+t12*t32*t21+t22*t32*t11)*lambda^2+(t12*t22*t30+t12*t32*t2
0+t22*t32*t10  +t12*t21*t31+t22*t11*t31+t32*t11*t21)*lambda,lambda);\n
" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 132 "taufunction:=unapply(  ((t21
-t31)*t12+(t31-t11)*t22+(t11-t21)*t32)/(sqrt((t22-t12)*(t12-t32)*(t32-
t22))) ,t11,t21,t31,t12,t22,t32);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 84 "checkqfunction:=unapply( sqrt((t12-t32)/((t22-t12)*(t32-t22)))*(
-p+t22*q+t21),q,p);\n" }{MPLTEXT 1 0 83 "checkpfunction:=unapply( sqrt
((t32-t22)/((t12-t32)*(t22-t12)))*(p-t12*q-t11),q,p);\n" }{MPLTEXT 1 
0 51 "TT1:=unapply(t12+t22+t32,t11,t21,t31,t12,t22,t32);\n" }{MPLTEXT 
1 0 51 "TT2:=unapply(t11+t21+t31,t11,t21,t31,t12,t22,t32);\n" }
{MPLTEXT 1 0 43 "TT3:=unapply(t22,t11,t21,t31,t12,t22,t32);\n" }
{MPLTEXT 1 0 43 "TT4:=unapply(t11,t11,t21,t31,t12,t22,t32);\n" }
{MPLTEXT 1 0 43 "TT5:=unapply(t32,t11,t21,t31,t12,t22,t32);\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 238 "solve(\{TT1(t11,t21,t31,t12,t22
,t32)=T1,TT2(t11,t21,t31,t12,t22,t32)=T2,TT3(t11,t21,t31,t12,t22,t32)=
T3,TT4(t11,t21,t31,t12,t22,t32)=T4,TT5(t11,t21,t31,t12,t22,t32)=T5,tau
function(t11,t21,t31,t12,t22,t32)=tau \},\{t11,t21,t31,t12,t22,t32\});
\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "t11function := T4;\n" }
{MPLTEXT 1 0 26 "t12function := -T3-T5+T1;\n" }{MPLTEXT 1 0 115 "t21fu
nction := (tau*sqrt((-2*T3-T5+T1)*(-T3-2*T5+T1)*(T3-T5))+T1*T2-T1*T4-2
*T3*T2-T5*T2+3*T4*T3)/(2*T1-3*T3-3*T5);\n" }{MPLTEXT 1 0 19 "t22functi
on := T3;\n" }{MPLTEXT 1 0 116 "t31function := -(tau*sqrt((-2*T3-T5+T1
)*(-T3-2*T5+T1)*(T3-T5))-T1*T2+T1*T4+T3*T2+2*T5*T2-3*T4*T5)/(2*T1-3*T3
-3*T5);\n" }{MPLTEXT 1 0 19 "t32function := T5;\n" }{MPLTEXT 1 0 88 "s
implify(TT1(t11function,t21function,t31function,t12function,t22functio
n,t32function));\n" }{MPLTEXT 1 0 88 "simplify(TT2(t11function,t21func
tion,t31function,t12function,t22function,t32function));\n" }{MPLTEXT 
1 0 88 "simplify(TT3(t11function,t21function,t31function,t12function,t
22function,t32function));\n" }{MPLTEXT 1 0 88 "simplify(TT4(t11functio
n,t21function,t31function,t12function,t22function,t32function));\n" }
{MPLTEXT 1 0 88 "simplify(TT5(t11function,t21function,t31function,t12f
unction,t22function,t32function));\n" }{MPLTEXT 1 0 96 "simplify(taufu
nction(t11function,t21function,t31function,t12function,t22function,t32
function));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 76 "SOLL:=solve(\{ch
eckqfunction(q,p)=checkq,checkpfunction(q,p)=checkp\},\{q,p\}):\n" }
{MPLTEXT 1 0 30 "Solp:=simplify(rhs(SOLL[1])):\n" }{MPLTEXT 1 0 31 "So
lq:=simplify(rhs(SOLL[2])): \n" }{MPLTEXT 1 0 44 "simplify(checkqfunct
ion(Solq,Solp)-checkq);\n" }{MPLTEXT 1 0 43 "simplify(checkpfunction(S
olq,Solp)-checkp);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 130 "HamtaucheckCoordinatesTheo:=una
pply(-(checkq*checkp^2+checkq^2*checkp-tau*checkq*checkp-t20*checkp+(t
10+h)*checkq),checkq,checkp);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 94 "
GSolOldCoordinatesbis:= 1/2*(t30*t10*ln(-t12+t32)  +t10*t20*ln(t22-t12
)+ln(-t32+t22)*t20*t30)\n" }{MPLTEXT 1 0 45 "-t10*t11^2/2/(t12-t32)-t2
0*t21^2/2/(t22-t32)\n" }{MPLTEXT 1 0 23 "+t30*t31^2/2/(t12-t32)\n" }
{MPLTEXT 1 0 49 "-(1/2)*(t12-t22)*t31^2*t20/((t22-t32)*(t12-t32))\n" }
{MPLTEXT 1 0 45 "+t31*t11*t10/(t12-t32)+t20*t31*t21/(t22-t32);" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 84 "GSolbis:=1/
2*(-(t20+t30)*(t20*ln(2*T3+T5-T1)+t30*ln(T3+2*T5-T1))+t20*t30*ln(T3-T5
))\n" }{MPLTEXT 1 0 72 "+(T2-3*T4)^2*((T1-2*T3-T5)*t20+t30*(T1-T3-2*T5
))/(2*(2*T1-3*T3-3*T5)^2)\n" }{MPLTEXT 1 0 90 "+sqrt(T1-T3-2*T5)*sqrt(
T1-2*T3-T5)*sqrt(T3-T5)*(T2-3*T4)*(t20-t30)*tau/(2*T1-3*T3-3*T5)^2\n" 
}{MPLTEXT 1 0 77 "-(((4*T1-5*T3-7*T5)*t20-t30*(T3-T5)))*(T1-2*T3-T5)*t
au^2/2/(2*T1-3*T3-3*T5)^2" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I$t10G6\",&I$t20GF$!\"\"I$t30GF$F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I#P1G6\"f*6#I'lambdaGF$F$6$I)operatorGF
$I&arrowGF$F$,**&,(I$t12GF$\"\"\"I$t22GF$F/I$t32GF$F/F/9$F/F/I$t11GF$F
/I$t21GF$F/I$t31GF$F/F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P2G6\"
f*6#I'lambdaGF$F$6$I)operatorGF$I&arrowGF$F$,2*&,(*&I$t12GF$\"\"\"I$t2
2GF$F0F0*&F/F0I$t32GF$F0F0*&F1F0F3F0F0F09$\"\"#F0*&,(*&,&I$t21GF$F0I$t
31GF$F0F0F/F0F0*&,&I$t11GF$F0F<F0F0F1F0F0*&F3F0,&F?F0F;F0F0F0F0F5F0F0*
&,&I$t20GF$!\"\"I$t30GF$FEF0F/F0FE*&FDF0F1F0FE*&FFF0F3F0FE*&F;F0F?F0F0
*&F<F0F?F0F0*&F;F0F<F0F0F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P3G
6\"f*6#I'lambdaGF$F$6$I)operatorGF$I&arrowGF$F$,(**I$t12GF$\"\"\"I$t22
GF$F.I$t32GF$F.9$\"\"$F.*&,(*(I$t11GF$F.F/F.F0F.F.*(F-F.I$t21GF$F.F0F.
F.*(F-F.F/F.I$t31GF$F.F.F.F1\"\"#F.*&,.*(,&I$t20GF$!\"\"I$t30GF$FAF.F/
F.F0F.F.*(F0F.F6F.F8F.F.*(F/F.F6F.F:F.F.*(F-F.F0F.F@F.F.*(F-F.F8F.F:F.
F.*(F-F.F/F.FBF.F.F.F1F.F.F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t
aufunctionG6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$
I)operatorGF$I&arrowGF$F$*&,(*&,&9%\"\"\"9&!\"\"F59'F5F5*&,&F6F59$F7F5
9(F5F5*&,&F;F5F4F7F59)F5F5F5*(,&F<F5F8F7F5,&F8F5F?F7F5,&F?F5F<F7F5#F7
\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I/checkqfunctionG6\"f*6$
I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$*&*(,&I$t12GF$\"\"\"I$t32GF
$!\"\"F0,&I$t22GF$F0F/F2F2,&F1F0F4F2F2#F0\"\"#,(*&9$F0F4F0F09%F2I$t21G
F$F0F0F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I/checkpfunctionG6\"f*6
$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$*&*(,&I$t32GF$\"\"\"I$t22G
F$!\"\"F0,&F1F0I$t12GF$F2F2,&F4F0F/F2F2#F0\"\"#,(*&9$F0F4F0F29%F0I$t11
GF$F2F0F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT1G6\"f*6(I$t11GF$I
$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF$I&arrowGF$F$,(
9'\"\"\"9(F29)F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT2G6\"f*6(
I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF$I&arr
owGF$F$,(9$\"\"\"9%F29&F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT
3G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operato
rGF$I&arrowGF$F$9(F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT4G6\"f*
6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF$I&a
rrowGF$F$9$F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT5G6\"f*6(I$t11
GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF$I&arrowGF$
F$9)F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<(/I$t11G6\"I#T4GF%/I$t12G
F%,(I#T3GF%!\"\"I#T5GF%F+I#T1GF%\"\"\"/I$t21GF%*&,.*&I$tauGF%F.*(,(F*!
\"#F,F+F-F.F.,(F*F+F,F7F-F.F.,&F,F+F*F.F.#F.\"\"#F.*&F-F.I#T2GF%F.F.*&
F-F.F&F.F+*&F*F.F=F.F7*&F,F.F=F.F+*&F*F.F&F.\"\"$F.,(F-F;F*!\"$F,FDF+/
I$t22GF%F*/I$t31GF%,$*&,.F3F.F<F+F>F.F?F.F@F;*&F,F.F&F.FDF.FCF+F+/I$t3
2GF%F," }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t11functionG6\"I#T4GF$" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I,t12functionG6\",(I#T3GF$!\"\"I#T5GF$F
'I#T1GF$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t21functionG6\"*&,.
*&I$tauGF$\"\"\"*(,(I#T3GF$!\"#I#T5GF$!\"\"I#T1GF$F)F),(F,F/F.F-F0F)F)
,&F.F/F,F)F)#F)\"\"#F)*&F0F)I#T2GF$F)F)*&F0F)I#T4GF$F)F/*&F,F)F6F)F-*&
F.F)F6F)F/*&F,F)F8F)\"\"$F),(F0F4F,!\"$F.F>F/" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I,t22functionG6\"I#T3GF$" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I,t31functionG6\",$*&,.*&I$tauGF$\"\"\"*(,(I#T3GF$!\"#I#T5GF$!\"\"I
#T1GF$F*F*,(F-F0F/F.F1F*F*,&F/F0F-F*F*#F*\"\"#F**&F1F*I#T2GF$F*F0*&F1F
*I#T4GF$F*F**&F-F*F7F*F**&F/F*F7F*F5*&F/F*F9F*!\"$F*,(F1F5F-F=F/F=F0F0
" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t32functionG6\"I#T5GF$" }}{PARA 
11 "" 1 "" {XPPMATH 20 "I#T1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#T2
G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#T3G6\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "I#T4G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#T5G6\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "I$tauG6\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I;HamtaucheckCoordinatesTheoG6\"f*6$I'checkqGF$I'checkpG
F$F$6$I)operatorGF$I&arrowGF$F$,,*&9$\"\"\"9%\"\"#!\"\"*&F.F1F0F/F2*(I
$tauGF$F/F.F/F0F/F/*&I$t20GF$F/F0F/F/*&,(F7F2I$t30GF$F2I\"hGF$F/F/F.F/
F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I6GSolOldCoordinatesbisG6\"
,4*(I$t30GF$\"\"\",&I$t20GF$!\"\"F'F+F(-I#lnG6$%*protectedGI(_syslibGF
$6#,&I$t12GF$F+I$t32GF$F(F(#F(\"\"#*(F)F(F*F(-F-6#,&I$t22GF$F(F3F+F(F5
*(-F-6#,&F4F+F;F(F(F*F(F'F(F5*(F)F(I$t11GF$F6,&F3F(F4F+F+#F+F6*(F*F(I$
t21GF$F6F?F+FC*(F'F(I$t31GF$F6FBF+F5*,,&F;F+F3F(F(FGF6F*F(F?F+FBF+FC**
FGF(FAF(F)F(FBF+F(**F*F(FGF(FEF(F?F+F(" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I(GSolbisG6\",,*&,&I$t20GF$\"\"\"I$t30GF$F)F),&*&F(F)-I#lnG6$%*prot
ectedGI(_syslibGF$6#,(I#T3GF$\"\"#I#T5GF$F)I#T1GF$!\"\"F)F)*&F*F)-F.6#
,(F4F)F6F5F7F8F)F)F)#F8F5*(F(F)F*F)-F.6#,&F6F8F4F)F)#F)F5*(,&I#T2GF$F)
I#T4GF$!\"$F5,&*&,(F4!\"#F6F8F7F)F)F(F)F)*&F*F),(F4F8F6FKF7F)F)F)F),(F
7F5F4FGF6FGFKFB*0FMFBFJFBFAFBFDF),&F(F)F*F8F)I$tauGF$F)FNFKF)**,&*&,(F
7\"\"%F4!\"&F6!\"(F)F(F)F)*&F*F)FAF)F8F)FJF)FQF5FNFKF=" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 251 43 "Loading the spectral duality corresponde
nce" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "t11functionduality:=
-s21/s22;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 24 "t21functionduality:=
X1;\n" }{MPLTEXT 1 0 29 "t31functionduality:=-s11/s12;" }{MPLTEXT 1 0 
1 "\n" }{MPLTEXT 1 0 30 "t12functionduality:=t22-1/s22;" }{MPLTEXT 1 
0 1 "\n" }{MPLTEXT 1 0 25 "t22functionduality:=t22;\n" }{MPLTEXT 1 0 
30 "t32functionduality:=t22-1/s12;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 30 "t20functionduality:=-s10-s20;\n" }{MPLTEXT 1 0 25 "t30functiondu
ality:=s10;\n" }{MPLTEXT 1 0 18 "dt11duality:=diff(" }{MPLTEXT 1 0 29 
"t11functionduality,s11)*ds11+" }{MPLTEXT 1 0 5 "diff(" }{MPLTEXT 1 0 
29 "t11functionduality,s21)*ds21+" }{MPLTEXT 1 0 5 "diff(" }{MPLTEXT 
1 0 29 "t11functionduality,s12)*ds12+" }{MPLTEXT 1 0 5 "diff(" }
{MPLTEXT 1 0 29 "t11functionduality,s22)*ds22+" }{MPLTEXT 1 0 5 "diff(
" }{MPLTEXT 1 0 26 "t11functionduality,X1)*dX1" }{MPLTEXT 1 0 1 "+" }
{MPLTEXT 1 0 5 "diff(" }{MPLTEXT 1 0 28 "t11functionduality,t22)*dt22"
 }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 18 "dt21dualit
y:=diff(" }{MPLTEXT 1 0 162 "t21functionduality,s11)*ds11+diff(t21func
tionduality,s21)*ds21+diff(t21functionduality,s12)*ds12+diff(t21functi
onduality,s22)*ds22+diff(t21functionduality,X1)*dX1" }{MPLTEXT 1 0 34 
"+diff(t21functionduality,t22)*dt22" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 
0 1 "\n" }{MPLTEXT 1 0 18 "dt31duality:=diff(" }{MPLTEXT 1 0 162 "t31f
unctionduality,s11)*ds11+diff(t31functionduality,s21)*ds21+diff(t31fun
ctionduality,s12)*ds12+diff(t31functionduality,s22)*ds22+diff(t31funct
ionduality,X1)*dX1" }{MPLTEXT 1 0 34 "+diff(t31functionduality,t22)*dt
22" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 18 "dt12duality:=diff(" }
{MPLTEXT 1 0 162 "t12functionduality,s11)*ds11+diff(t12functionduality
,s21)*ds21+diff(t12functionduality,s12)*ds12+diff(t12functionduality,s
22)*ds22+diff(t12functionduality,X1)*dX1" }{MPLTEXT 1 0 34 "+diff(t12f
unctionduality,t22)*dt22" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 180 "dt22duality:=diff(t22functionduality,s11)*ds11+diff(
t22functionduality,s21)*ds21+diff(t22functionduality,s12)*ds12+diff(t2
2functionduality,s22)*ds22+diff(t22functionduality,X1)*dX1" }{MPLTEXT 
1 0 34 "+diff(t22functionduality,t22)*dt22" }{MPLTEXT 1 0 1 ";" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 215 "dt32duality:=diff(t32functiondu
ality,s11)*ds11+diff(t32functionduality,s21)*ds21+diff(t32functiondual
ity,s12)*ds12+diff(t32functionduality,s22)*ds22+diff(t32functiondualit
y,X1)*dX1+diff(t32functionduality,t22)*dt22;" }{MPLTEXT 1 0 1 "\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I3t11functiondualityG6\",$*&I$s21GF$\"
\"\"I$s22GF$!\"\"F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3t21functiondua
lityG6\"I#X1GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3t31functionduality
G6\",$*&I$s11GF$\"\"\"I$s12GF$!\"\"F*" }}{PARA 11 "" 1 "" {XPPMATH 20 
">I3t12functiondualityG6\",&I$t22GF$\"\"\"*$I$s22GF$!\"\"F*" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I3t22functiondualityG6\"I$t22GF$" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I3t32functiondualityG6\",&I$t22GF$\"\"\"*$I$s12G
F$!\"\"F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3t20functiondualityG6\",&
I$s10GF$!\"\"I$s20GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3t30functio
ndualityG6\"I$s10GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dt11dualityG6
\",&*&I$s22GF$!\"\"I%ds21GF$\"\"\"F(*(I$s21GF$F*F'!\"#I%ds22GF$F*F*" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dt21dualityG6\"I$dX1GF$" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I,dt31dualityG6\",&*&I$s12GF$!\"\"I%ds11GF$\"\"
\"F(*(I$s11GF$F*F'!\"#I%ds12GF$F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">
I,dt12dualityG6\",&*&I$s22GF$!\"#I%ds22GF$\"\"\"F*I%dt22GF$F*" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I,dt22dualityG6\"I%dt22GF$" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I,dt32dualityG6\",&*&I$s12GF$!\"#I%ds12GF$\"\"\"
F*I%dt22GF$F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 252 49 "Decomposing the
 dG_0 term in the dual coordinates" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "dG0:=unapply( diff(" }{MPLTEXT 1 0 32 "GSolOldCoordin
atesbis,t11)*dt11+" }{MPLTEXT 1 0 37 "diff(GSolOldCoordinatesbis,t21)*
dt21+" }{MPLTEXT 1 0 38 "diff(GSolOldCoordinatesbis,t31)*dt31+\n" }
{MPLTEXT 1 0 37 "diff(GSolOldCoordinatesbis,t12)*dt12+" }{MPLTEXT 1 0 
37 "diff(GSolOldCoordinatesbis,t22)*dt22+" }{MPLTEXT 1 0 38 "diff(GSol
OldCoordinatesbis,t32)*dt32,\n" }{MPLTEXT 1 0 63 "t11,t21,t31,t12,t22,
t32,dt11,dt21,dt31,dt12,dt22,dt32,t20,t30);" }{MPLTEXT 1 0 2 "\n\n" }
{MPLTEXT 1 0 265 "dG0Intermediate:=unapply(simplify(dG0(t11functiondua
lity,t21functionduality,t31functionduality,t12functionduality,t22funct
ionduality,t32functionduality,dt11duality,dt21duality,dt31duality,dt12
duality,dt22duality,dt32duality,t20functionduality,t30functionduality \+
))\n" }{MPLTEXT 1 0 22 ",s11,s21,s12,s22,X1):\n" }{MPLTEXT 1 0 83 "dG0
Termds11:=simplify(residue(dG0Intermediate(s11,s21,s12,s22,X1)/ds11^2,
ds11=0));\n" }{MPLTEXT 1 0 83 "dG0Termds21:=simplify(residue(dG0Interm
ediate(s11,s21,s12,s22,X1)/ds21^2,ds21=0));\n" }{MPLTEXT 1 0 83 "dG0Te
rmds12:=simplify(residue(dG0Intermediate(s11,s21,s12,s22,X1)/ds12^2,ds
12=0));\n" }{MPLTEXT 1 0 83 "dG0Termds22:=simplify(residue(dG0Intermed
iate(s11,s21,s12,s22,X1)/ds22^2,ds22=0));\n" }{MPLTEXT 1 0 80 "dG0Term
dX1:=simplify(residue(dG0Intermediate(s11,s21,s12,s22,X1)/dX1^2,dX1=0)
);\n" }{MPLTEXT 1 0 82 "dG0Termdt22:=simplify(residue(dG0Intermediate(
s11,s21,s12,s22,X1)/dt22^2,dt22=0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "
>I$dG0G6\"f*60I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$I%dt11GF
$I%dt21GF$I%dt31GF$I%dt12GF$I%dt22GF$I%dt32GF$I$t20GF$I$t30GF$F$6$I)op
eratorGF$I&arrowGF$F$,.*&,&*(,&90!\"\"91F>\"\"\"9$F@,&9'F@9)F>F>F>*(9&
F@F<F@FBF>F@F@9*F@F@*&,&*(F=F@9%F@,&FDF>9(F@F>F>*(F=F@FFF@FLF>F@F@9+F@
F@*&,**(F?F@FFF@FBF>F@*,,&FMF>FCF@F@FFF@F=F@FLF>FBF>F>F;F@FJF@F@9,F@F@
*&,0*(F?F@F<F@,&FCF>FDF@F>#F>\"\"#*(F<F@F=F@,&FMF@FCF>F>FZ*(F<F@FAFenF
B!\"##F@Fen*(F?F@FFFenFBFinFZ**FFFenF=F@FLF>FBF>FZ*,FTF@FFFenF=F@FLF>F
BFinFjn**FFF@FAF@F<F@FBFinF>F@9-F@F@*&,.FfnFjn*(FLF>F=F@F?F@Fjn*(F=F@F
KFenFLFinFjnF\\oFjn*,FTF@FFFenF=F@FLFinFBF>Fjn**F=F@FFF@FKF@FLFinF>F@9
.F@F@*&,4FXFjnFboFZFhnFZFcoFZF[oFjnFdoFZF]oFZF^oF@FeoF@F@9/F@F@F$F$F$"
 }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dG0Termds11G6\"*(,(*(I#X1GF$\"\"\"
,&I$s10GF$F)I$s20GF$F)F)I$s12GF$\"\"#F)*&,&*&,&*&F(F)I$s22GF$F)!\"\"I$
s11GF$F)F)F+F)F)*&F,F),(F3F)F6F5I$s21GF$F)F)F5F)F-F)F)*(F+F)F6F)F4F)F5
F)F-F5,&F-F)F4F5F5" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dG0Termds21G6\"
,$**,&*&I$s11GF$\"\"\"I$s22GF$F*F**&I$s12GF$F*I$s21GF$F*!\"\"F*I$s20GF
$F*F+F/,&F-F*F+F/F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dG0Termds12G
6\",$*(,,*(I#X1GF$\"\"#,&I$s10GF$\"\"\"I$s20GF$F-F-I$s12GF$\"\"%F-*(,&
*&F)F*I$s22GF$F-F-F,#!\"\"F*F-F+F-F/\"\"$!\"#*&,(*&F4F-F,F*F8*&,(*&F)F
*F4F*F-*$I$s11GF$F*F6*&F.F-F4F-F6F-F,F-F-*(F.F-,(*&F)F-F4F-F-F@F6I$s21
GF$F-F-,(FDF-F@F-FEF6F-F-F-F/F*F-*&,&*&F,F*F4F*F-*(F,F-F@F*F4F-F*F-F/F
-F-*(F,F-F@F*F4F*F6F-F/F8,&F/F-F4F6F8#F-F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I,dG0Termds22G6\",$**I$s20GF$\"\"\",**&,&I$s10GF$!\"\"F'
F-F(I$s22GF$\"\"$F(*&,&*&,&F,F(F'\"\"#F(I$s12GF$F(F(*&I$s11GF$F(,&F7F(
I$s21GF$!\"#F(F-F(F.F4F(*&,&*&F5F4F'F(F-*&F5F(F9F4F:F(F.F(F(*&F9F4F5F4
F(F(F.F:,&F5F(F.F-F:#F-F4" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+dG0Termd
X1G6\"*&,&I$s10GF$\"\"\"I$s20GF$F(F(,&*&I#X1GF$F(I$s12GF$F(F(I$s11GF$F
(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dG0Termdt22G6\"\"\"!" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 253 30 "Computing the dK0 differential" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "dK0:=unapply( simplify(dif
f(" }{MPLTEXT 1 0 48 "K0OldCoordinates(s11,s21,s12,s22,X1),s11)*ds11+ 
" }{MPLTEXT 1 0 52 "diff(K0OldCoordinates(s11,s21,s12,s22,X1),s21)*ds2
1+" }{MPLTEXT 1 0 52 "diff(K0OldCoordinates(s11,s21,s12,s22,X1),s12)*d
s12+" }{MPLTEXT 1 0 52 "diff(K0OldCoordinates(s11,s21,s12,s22,X1),s22)
*ds22+" }{MPLTEXT 1 0 72 "diff(K0OldCoordinates(s11,s21,s12,s22,X1),X1
)*dX1,s11,s21,s12,s22,X1)):\n" }{MPLTEXT 1 0 71 "dK0Termds11:=simplify
(residue(dK0(s11,s21,s12,s22,X1)/ds11^2,ds11=0));\n" }{MPLTEXT 1 0 71 
"dK0Termds21:=simplify(residue(dK0(s11,s21,s12,s22,X1)/ds21^2,ds21=0))
;\n" }{MPLTEXT 1 0 71 "dK0Termds12:=simplify(residue(dK0(s11,s21,s12,s
22,X1)/ds12^2,ds12=0));\n" }{MPLTEXT 1 0 71 "dK0Termds22:=simplify(res
idue(dK0(s11,s21,s12,s22,X1)/ds22^2,ds22=0));\n" }{MPLTEXT 1 0 68 "dK0
TermdX1:=simplify(residue(dK0(s11,s21,s12,s22,X1)/dX1^2,dX1=0));\n" }
{MPLTEXT 1 0 70 "dK0Termdt22:=simplify(residue(dK0(s11,s21,s12,s22,X1)
/dt22^2,dt22=0));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dK0Termds11G6\"*
&I$s10GF$\"\"\"I#X1GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dK0Termds
21G6\"*&I$s20GF$\"\"\"I#X1GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dK
0Termds12G6\"*&,&*&,**&I#X1GF$\"\"#I$s12GF$\"\"\"F-*&F*F+I$s22GF$F-!\"
\"I$s20GF$F-I%sX10GF$F-F-I$s10GF$F-F-*&F2F-,&F2F-F1F-F-F-F-,&F,F+F/!\"
#F0" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,dK0Termds22G6\"*&,&*&,**&I#X1G
F$\"\"#I$s12GF$\"\"\"F-*&F*F+I$s22GF$F-!\"\"I$s10GF$F0I%sX10GF$F0F-I$s
20GF$F-F-*&F2F-,&F2F-F1F-F-F0F-,&F,F+F/!\"#F0" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I+dK0TermdX1G6\",&*&,&*&I#X1GF$\"\"\"I$s12GF$F*F*I$s11GF
$F*F*I$s10GF$F*F**&I$s20GF$F*,&*&F)F*I$s22GF$F*F*I$s21GF$F*F*F*" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I,dK0Termdt22G6\"\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 254 63 "Comparing the difference of the JMU diff
erentials on both sides" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
dG0MinusdK0:=" }{MPLTEXT 1 0 15 "dG0Intermediate" }{MPLTEXT 1 0 1 "(" 
}{MPLTEXT 1 0 20 "s11,s21,s12,s22,X1)-" }{MPLTEXT 1 0 4 "dK0(" }
{MPLTEXT 1 0 20 "s11,s21,s12,s22,X1):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 
1 0 25 "omegaJMUMinusomegaJMUP4:=" }{MPLTEXT 1 0 14 "dG0MinusdK0-2*" }
{MPLTEXT 1 0 32 "s20*tdX1function*dtdX1function:\n" }{MPLTEXT 1 0 23 "
omegaJMUMinusomegaJMUP4" }{MPLTEXT 1 0 27 "Termds11:=simplify(residue(
" }{MPLTEXT 1 0 23 "omegaJMUMinusomegaJMUP4" }{MPLTEXT 1 0 18 "/ds11^2
,ds11=0));\n" }{MPLTEXT 1 0 23 "omegaJMUMinusomegaJMUP4" }{MPLTEXT 1 
0 27 "Termds21:=simplify(residue(" }{MPLTEXT 1 0 23 "omegaJMUMinusomeg
aJMUP4" }{MPLTEXT 1 0 18 "/ds21^2,ds21=0));\n" }{MPLTEXT 1 0 23 "omega
JMUMinusomegaJMUP4" }{MPLTEXT 1 0 27 "Termds12:=simplify(residue(" }
{MPLTEXT 1 0 23 "omegaJMUMinusomegaJMUP4" }{MPLTEXT 1 0 18 "/ds12^2,ds
12=0));\n" }{MPLTEXT 1 0 23 "omegaJMUMinusomegaJMUP4" }{MPLTEXT 1 0 
27 "Termds22:=simplify(residue(" }{MPLTEXT 1 0 23 "omegaJMUMinusomegaJ
MUP4" }{MPLTEXT 1 0 18 "/ds22^2,ds22=0));\n" }{MPLTEXT 1 0 23 "omegaJM
UMinusomegaJMUP4" }{MPLTEXT 1 0 26 "TermdX1:=simplify(residue(" }
{MPLTEXT 1 0 23 "omegaJMUMinusomegaJMUP4" }{MPLTEXT 1 0 16 "/dX1^2,dX1
=0));\n" }{MPLTEXT 1 0 23 "omegaJMUMinusomegaJMUP4" }{MPLTEXT 1 0 27 "
Termdt22:=simplify(residue(" }{MPLTEXT 1 0 23 "omegaJMUMinusomegaJMUP4
" }{MPLTEXT 1 0 17 "/dt22^2,dt22=0));" }}{PARA 11 "" 1 "" {XPPMATH 20 
">I@omegaJMUMinusomegaJMUP4Termds11G6\"*(I$s10GF$\"\"\"I$s11GF$F'I$s12
GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I@omegaJMUMinusomegaJMUP4Te
rmds21G6\"*(I$s20GF$\"\"\"I$s21GF$F'I$s22GF$!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I@omegaJMUMinusomegaJMUP4Termds12G6\",$*(,(*&,(*$I$s10GF
$\"\"#\"\"\"*&I%sX10GF$F-F+F-!\"\"*&F/F-,&F/F-I$s20GF$F-F-F0F-I$s12GF$
F,F-*&,&*&F+F,I$s22GF$F-F0*&F+F-I$s11GF$F,F0F-F4F-F-*(F+F-F:F,F8F-F-F-
,&F4F-F8F0F0F4!\"##F-F," }}{PARA 11 "" 1 "" {XPPMATH 20 ">I@omegaJMUMi
nusomegaJMUP4Termds22G6\",$*(,(*&,(*$I$s20GF$\"\"#!\"\"*&F+\"\"\"I%sX1
0GF$F/F/*&F0F/,&F0F/I$s10GF$F/F/F/F/I$s22GF$F,F/*&,&*&I$s12GF$F/F+F,F/
*&F+F/I$s21GF$F,F/F/F4F/F/*(F8F/F+F/F:F,F-F/,&F8F/F4F-F-F4!\"##F/F," }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I?omegaJMUMinusomegaJMUP4TermdX1G6\"\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I@omegaJMUMinusomegaJMUP4Termdt2
2G6\"\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 255 50 "Imposing sX20=0 an
d obtaining the differential df " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
 1 0 21 "sX20:=-sX10-s20-s10:\n" }{MPLTEXT 1 0 15 "sX10:=-s10-s20:" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 75 "pdsolve(\{d
iff(ff(s11,s21,s12,s22,X1),s11)=omegaJMUMinusomegaJMUP4Termds11,\n" }
{MPLTEXT 1 0 66 "diff(ff(s11,s21,s12,s22,X1),s21)=omegaJMUMinusomegaJM
UP4Termds21,\n" }{MPLTEXT 1 0 66 "diff(ff(s11,s21,s12,s22,X1),s12)=ome
gaJMUMinusomegaJMUP4Termds12,\n" }{MPLTEXT 1 0 66 "diff(ff(s11,s21,s12
,s22,X1),s22)=omegaJMUMinusomegaJMUP4Termds22,\n" }{MPLTEXT 1 0 62 "di
ff(ff(s11,s21,s12,s22,X1),X1)=omegaJMUMinusomegaJMUP4TermdX1" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 3 "\},\{" }{MPLTEXT 1 0 25 "ff(s11,s
21,s12,s22,X1)\});" }{MPLTEXT 1 0 3 " \n\n" }{MPLTEXT 1 0 109 "f:=unap
ply(s10*s11^2/(2*s12)+s20*s21^2/(2*s22)+(1/2)*s10^2*ln(s12)+(1/2)*s20^
2*ln(s22) ,s11,s21,s12,s22,X1);\n" }{MPLTEXT 1 0 217 "df:=unapply( dif
f(f(s11,s21,s12,s22,X1),s11)*ds11+ diff(f(s11,s21,s12,s22,X1),s21)*ds2
1+diff(f(s11,s21,s12,s22,X1),s12)*ds12+diff(f(s11,s21,s12,s22,X1),s22)
*ds22+diff(f(s11,s21,s12,s22,X1),X1)*dX1,s11,s21,s12,s22,X1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "<#/-I#ffG6\"6'I$s11G6\"I$s21G6\"I$s12G6
\"I$s22G6\"I#X1G6\",,*(I$s10G6\"\"\"\"I$s11G6\"\"\"#I$s12G6\"!\"\"#\"
\"\"\"\"#*(I$s20G6\"\"\"\"I$s21G6\"\"\"#I$s22G6\"!\"\"#\"\"\"\"\"#*&I$
s10G6\"\"\"#-I#lnG6$%*protectedGI(_syslibG6\"6#I$s12G6\"\"\"\"#\"\"\"
\"\"#*&I$s20G6\"\"\"#-I#lnG6$%*protectedGI(_syslibG6\"6#I$s22G6\"\"\"
\"#\"\"\"\"\"#I$_C1G6\"\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"fG6
\"f*6'I$s11GF$I$s21GF$I$s12GF$I$s22GF$I#X1GF$F$6$I)operatorGF$I&arrowG
F$F$,**(I$s10GF$\"\"\"9$\"\"#9&!\"\"#F2F4*(I$s20GF$F29%F49'F6F7*&F1F4-
I#lnG6$%*protectedGI(_syslibGF$6#F5F2F7*&F9F4-F>6#F;F2F7F$F$F$" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I#dfG6\"f*6'I$s11GF$I$s21GF$I$s12GF$I$s
22GF$I#X1GF$F$6$I)operatorGF$I&arrowGF$F$,***I$s10GF$\"\"\"9$F29&!\"\"
I%ds11GF$F2F2**I$s20GF$F29%F29'F5I%ds21GF$F2F2*&,&*&F1\"\"#F4F5#F2F?*(
F1F2F4!\"#F3F?#F5F?F2I%ds12GF$F2F2*&,&*&F8F?F:F5F@*(F8F2F:FBF9F?FCF2I%
ds22GF$F2F2F$F$F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 51 "Rewriting f
 and df in terms of the gl_3 coordinates" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "solve(\{t11functionduality=t11," }{MPLTEXT 1 0 23 "t2
1functionduality=t21," }{MPLTEXT 1 0 23 "t31functionduality=t31," }
{MPLTEXT 1 0 23 "t12functionduality=t12," }{MPLTEXT 1 0 47 "t32functio
nduality=t32\},\{s11,s21,s12,s22,X1\});\n" }{MPLTEXT 1 0 18 "X1duality
 := t21;\n" }{MPLTEXT 1 0 19 "s11duality:= -t31/(" }{MPLTEXT 1 0 3 "t2
2" }{MPLTEXT 1 0 7 "-t32);\n" }{MPLTEXT 1 0 16 "s12duality:= 1/(" }
{MPLTEXT 1 0 3 "t22" }{MPLTEXT 1 0 7 "-t32);\n" }{MPLTEXT 1 0 18 "s21d
uality:= t11/(" }{MPLTEXT 1 0 3 "t12" }{MPLTEXT 1 0 7 "-t22);\n" }
{MPLTEXT 1 0 17 "s22duality:= -1/(" }{MPLTEXT 1 0 3 "t12" }{MPLTEXT 1 
0 7 "-t22);\n" }{MPLTEXT 1 0 18 "t22duality:= t22;\n" }{MPLTEXT 1 0 7 
"solve(\{" }{MPLTEXT 1 0 23 "t20functionduality=t20," }{MPLTEXT 1 0 
36 "t30functionduality=t30\},\{s10,s20\});\n" }{MPLTEXT 1 0 18 "s10dua
lity:= t30;\n" }{MPLTEXT 1 0 19 "s20duality:= t10;\n\n" }{MPLTEXT 1 0 
95 "ftCoordinates:=f(s11duality,s21duality,s12duality,s22duality,X1dua
lity,s10duality,s20duality);\n" }{MPLTEXT 1 0 100 "ftCoordinatesbis:=1
/2*(s10*t31^2/(t22-t32)-s20*t11^2/(t12-t22)-s10^2*ln(t22-t32)-s20^2*ln
(t12-t22));" }}{PARA 11 "" 1 "" {XPPMATH 20 "<'/I#X1G6\"I$t21GF%/I$s11
GF%,$*&I$t31GF%\"\"\",&I$t32GF%!\"\"I$t22GF%F,F/F//I$s12GF%*$F-F//I$s2
1GF%*&I$t11GF%F,,&F0F/I$t12GF%F,F//I$s22GF%,$*$F8F/F/" }}{PARA 11 "" 1
 "" {XPPMATH 20 ">I*X1dualityG6\"I$t21GF$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I+s11dualityG6\",$*&I$t31GF$\"\"\",&I$t32GF$!\"\"I$t22GF
$F(F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+s12dualityG6\"*$,&I$t32GF$
!\"\"I$t22GF$\"\"\"F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+s21dualityG6
\"*&I$t11GF$\"\"\",&I$t22GF$!\"\"I$t12GF$F'F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I+s22dualityG6\",$*$,&I$t22GF$!\"\"I$t12GF$\"\"\"F)F)" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I+t22dualityG6\"I$t22GF$" }}{PARA 11 "
" 1 "" {XPPMATH 20 "<$/I$s10G6\"I$t30GF%/I$s20GF%,&I$t20GF%!\"\"F&F+" 
}}{PARA 11 "" 1 "" {XPPMATH 20 ">I+s10dualityG6\"I$t30GF$" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I+s20dualityG6\",&I$t20GF$!\"\"I$t30GF$F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I.ftCoordinatesG6\",**(I$s10GF$\"\"\"I$
t31GF$\"\"#,&I$t32GF$!\"\"I$t22GF$F(F-#F(F**(I$s20GF$F(I$t11GF$F*,&F.F
-I$t12GF$F(F-#F-F**&F'F*-I#lnG6$%*protectedGI(_syslibGF$6#*$F+F-F(F/*&
F1F*-F86#,$*$F3F-F-F(F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I1ftCoordina
tesbisG6\",**(I$s10GF$\"\"\"I$t31GF$\"\"#,&I$t32GF$!\"\"I$t22GF$F(F-#F
(F**(I$s20GF$F(I$t11GF$F*,&F.F-I$t12GF$F(F-#F-F**&F'F*-I#lnG6$%*protec
tedGI(_syslibGF$6#F+F(F5*&F1F*-F86#F3F(F5" }}}{EXCHG {PARA 0 "> " 0 ""
 {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT 257 62 "Method 2: Direct verifications f
rom the full JMU differentials" }{TEXT 257 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 443 "omegaJMUdt11:=1/((t12-t22)*(-t12+t32))*(-p^3+(t
11+t21+t31+(t12+t22+t32)*q)*p^2+(((-t22-t32)*t12-t22*t32)*q^2+((-t31-t
21)*t12+(-t11-t31)*t22-t32*(t11+t21))*q+t12*(-t20-t30)+t22*t20+t30*t32
+(-t31-t21)*t11-t21*t31)*p+q^3*t12*t22*t32+((t21*t32+t22*t31)*t12+t22*
t32*t11)*q^2+((t20*t32+t21*t31+t22*t30)*t12+((-t20-t30)*t32+t11*t31)*t
22+t32*t11*t21)*q+(t20+t30)*(t31-t11+t21)*t12+(t11*t30-t31*(t20+t30))*
t22+(t11*t20-t21*(t20+t30))*t32+t11*t21*t31):\n" }{MPLTEXT 1 0 1 "\n" 
}{MPLTEXT 1 0 428 "omegaJMUdt21:=1/((t12-t22)*(-t22+t32))*(p^3+((-t12-
t22-t32)*q-t31-t11-t21)*p^2+(((t12+t32)*t22+t12*t32)*q^2+(t12*(t21+t31
)+t22*(t11+t31)+t32*(t11+t21))*q-t22*t20-t30*t32+(t20+t30)*t12+(t11+t3
1)*t21+t11*t31)*p-q^3*t12*t22*t32+((-t11*t32-t12*t31)*t22-t32*t12*t21)
*q^2+(((t20+t30)*t32-t11*t31-t12*t30)*t22+(-t11*t21-t12*t20)*t32-t12*t
21*t31)*q+t20*(t31+t11-t21)*t22+(t21*(t20+t30)-t11*t20)*t32+(-t20*t31-
t21*t30)*t12-t11*t21*t31):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 430 "
omegaJMUdt31:=1/((-t22+t32)*(-t12+t32))*(p^3+((-t12-t22-t32)*q-t31-t11
-t21)*p^2+(((t12+t22)*t32+t12*t22)*q^2+(t12*(t21+t31)+t22*(t11+t31)+t3
2*(t11+t21))*q-t30*t32-t22*t20+(t20+t30)*t12+t31*(t11+t21)+t11*t21)*p-
q^3*t12*t22*t32+((-t11*t22-t12*t21)*t32-t31*t12*t22)*q^2+(((t20+t30)*t
22-t11*t21-t12*t20)*t32+(-t11*t31-t12*t30)*t22-t12*t21*t31)*q-t30*(t31
-t11-t21)*t32+(-t11*t30+t31*(t20+t30))*t22+(-t20*t31-t21*t30)*t12-t11*
t21*t31):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1734 "omegaJMUdt12:=1/
(2*(t12-t22)^2*(-t12+t32)^2)*(-(t20+t30)^2*t12^3+((-q^3*(t31-2*t11+t21
)*t32+2*q*((-p+t31)*q+t30)*t11-(t21+t31)*(-p+t31)*q^2-t30*(t21+t31)*q+
(t20+2*t30)*(t20+t30))*t22+(-2*q*((p-t21)*q-t20)*t11+(p-t21)*(t21+t31)
*q^2-t20*(t21+t31)*q+2*t20^2+3*t30*t20+t30^2)*t32+(-t20-t30)*t11^2+(-(
2*(p-t21))*(-p+t31)*q+(2*(t20+t30))*(t31-p+t21))*t11+(p-t21)*(t21+t31)
*(-p+t31)*q-(t20+t30)*((-t31-t21)*p+t31^2+t21*t31+t21^2))*t12^2+((q^3*
(-t11+t31)*t32-q*((-p+t31)*q+t30)*t11+t31*(-p+t31)*q^2+t31*t30*q-t30*(
t20+t30))*t22^2+(-q^3*(t11-t21)*t32^2+(2*q^2*t11^2-2*q*((t21+t31)*q+3*
t20*(1/2)+3*t30*(1/2))*t11+2*q^2*t21*t31+((t20+2*t30)*t21+2*t31*(t20+(
1/2)*t30))*q-2*(t20+t30)^2)*t32+((2*t31-2*p)*q+2*t30)*t11^2+(-(-p+t31)
*(t31+2*t21+p)*q+(t30+3*t20)*p-t21*t30-(3*(t20+4*t30*(1/3)))*t31)*t11+
(-p^2*t21+t21*t31^2)*q+(-t21*t20-2*t31*(t20+(1/2)*t30))*p+(2*(t20+t30)
)*t31*((1/2)*t21+t31))*t22+(q*((p-t21)*q-t20)*t11-(p-t21)*t21*q^2+t21*
t20*q-t20*(t20+t30))*t32^2+(((-2*p+2*t21)*q+2*t20)*t11^2+((2*(p-t21))*
((1/2)*p+t31+(1/2)*t21)*q+(t20+3*t30)*p+(-4*t20-3*t30)*t21-t31*t20)*t1
1+(-p^2*t31+t21^2*t31)*q+((-t20-2*t30)*t21-t31*t30)*p+t21*(t20+t30)*(t
31+2*t21))*t32-(p-t21)*(p-t11)*(t31-2*t11+t21)*(-p+t31))*t12+((-q^2*t1
1^2+q*((t31+p)*q+t20+t30)*t11-q^2*p*t31-(t20+t30)*t31*q+t30*(t20+t30))
*t32-(-t11+t31)*(((p-t31)*q-t30)*t11+p*(-p+t31)*q-p*t20+t31*(t20+t30))
)*t22^2+((-q^2*t11^2+((p+t21)*q+t20+t30)*q*t11-q^2*p*t21-t21*(t20+t30)
*q+t20*(t20+t30))*t32^2+(-q*(t31-2*p+t21)*t11^2+((-2*p^2+2*t21*t31)*q+
(-t20-t30)*p+t31*t20+t21*t30)*t11+((t21+t31)*p-2*t21*t31)*p*q+(t20*t21
+t30*t31)*p-t31*t21*(t20+t30))*t32+(p-t11)*(-t11+t31)*(-p+t31)*(p-t21)
)*t22-((((-p+t21)*q+t20)*t11+p*(p-t21)*q+p*t30-t21*(t20+t30))*t32+(p-t
21)*(p-t11)*(-p+t31))*(t11-t21)*t32):\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 1659 "omegaJMUdt22:=1/(2*(t12-t22)^2*(-t22+t32)^2)*(-t20^
2*t22^3+((-q^3*(t31+t11-2*t21)*t12-2*q*((p-t11)*q+t20+t30)*t21+(p-t11)
*(t11+t31)*q^2+(t20+t30)*(t11+t31)*q+2*t20^2+t30*t20)*t32+(2*q*((-p+t3
1)*q+t30)*t21-(t11+t31)*(-p+t31)*q^2-t30*(t11+t31)*q+t20*(t20-t30))*t1
2+t20*t21^2+(-(2*(p-t11))*(-p+t31)*q-2*t20*(t31-p+t11))*t21+(p-t11)*(t
11+t31)*(-p+t31)*q+t20*((-t11-t31)*p+t31^2+t11*t31+t11^2))*t22^2+((q^3
*(t11-t21)*t12+q*((p-t11)*q+t20+t30)*t21-(p-t11)*t11*q^2-t11*(t20+t30)
*q-t20*(t20+t30))*t32^2+(q^3*(-t21+t31)*t12^2+(2*q^2*t21^2-(2*((t11+t3
1)*q-3*t20*(1/2)))*q*t21+2*q^2*t11*t31+(t11*(-t20+t30)-2*t31*(t20+(1/2
)*t30))*q-2*t20^2)*t12+((-2*p+2*t11)*q-2*t20-2*t30)*t21^2+((2*((1/2)*p
+t31+(1/2)*t11))*(p-t11)*q+(2*t30-t20)*p+(t30+4*t20)*t11+t31*(t20+t30)
)*t21+(-p^2*t31+t11^2*t31)*q+((t20-t30)*t11-t31*t30)*p-t11*t20*(t31+2*
t11))*t32+(-q*((-p+t31)*q+t30)*t21+t31*(-p+t31)*q^2+t31*t30*q+t30*t20)
*t12^2+(((2*t31-2*p)*q+2*t30)*t21^2+(-(-p+t31)*(t31+2*t11+p)*q+(-2*t30
-3*t20)*p-t11*t30+3*t31*(t20-(1/3)*t30))*t21+(-p^2*t11+t11*t31^2)*q+((
t20+t30)*t11+2*t31*(t20+(1/2)*t30))*p-(2*(t31+(1/2)*t11))*t31*t20)*t12
-(p-t21)*(p-t11)*(t31+t11-2*t21)*(-p+t31))*t22+((-q^2*t21^2+((p+t11)*q
-t20)*q*t21-q^2*p*t11+t20*t11*q+t20*(t20+t30))*t12+(t11-t21)*(((-p+t11
)*q-t20-t30)*t21+p*(p-t11)*q+p*t30+t11*t20))*t32^2+((-q^2*t21^2+q*((t3
1+p)*q-t20)*t21-q^2*p*t31+t31*t20*q-t30*t20)*t12^2+(-q*(-2*p+t31+t11)*
t21^2+((-2*p^2+2*t11*t31)*q+p*t20+t11*t30-t31*(t20+t30))*t21+((t11+t31
)*p-2*t11*t31)*p*q+((-t20-t30)*t11+t31*t30)*p+t31*t11*t20)*t12+(t11-t2
1)*(p-t21)*(p-t11)*(-p+t31))*t32+t12*((((-p+t31)*q+t30)*t21-p*(-p+t31)
*q+(-t20-t30)*p+t31*t20)*t12+(p-t21)*(p-t11)*(-p+t31))*(-t21+t31)):\n"
 }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1656 "omegaJMUdt32:=1/(2*(-t12+t32
)^2*(-t22+t32)^2)*(-t30^2*t32^3+((2*q^3*(t31-(1/2)*t11-(1/2)*t21)*t12-
2*q*((p-t11)*q+t20+t30)*t31+(t11+t21)*(p-t11)*q^2+(t20+t30)*(t11+t21)*
q+t30*(t20+2*t30))*t22+(-2*q*((p-t21)*q-t20)*t31+(t11+t21)*(p-t21)*q^2
-t20*(t11+t21)*q-t30*(t20-t30))*t12+t30*t31^2+((2*(p-t21))*(p-t11)*q+2
*t30*(p-t11-t21))*t31-(t11+t21)*(p-t21)*(p-t11)*q-t30*((t11+t21)*p-t11
^2-t11*t21-t21^2))*t32^2+((-q^3*(-t11+t31)*t12+q*((p-t11)*q+t20+t30)*t
31-(p-t11)*t11*q^2-t11*(t20+t30)*q-t30*(t20+t30))*t22^2+(-q^3*(-t21+t3
1)*t12^2+(2*q^2*t31^2-2*q*((t11+t21)*q-3*t30*(1/2))*t31+2*q^2*t11*t21+
((t20-t30)*t11-(t20+2*t30)*t21)*q-2*t30^2)*t12+((-2*p+2*t11)*q-2*t20-2
*t30)*t31^2+((p-t11)*(p+t11+2*t21)*q+(-t30+2*t20)*p+t11*(4*t30+t20)+t2
1*(t20+t30))*t31+(-p^2*t21+t11^2*t21)*q+(t11*(-t20+t30)-t21*t20)*p-(2*
(t11+(1/2)*t21))*t11*t30)*t22+(q*((p-t21)*q-t20)*t31-(p-t21)*t21*q^2+t
21*t20*q+t30*t20)*t12^2+(((-2*p+2*t21)*q+2*t20)*t31^2+((p-t21)*(p+2*t1
1+t21)*q+(-2*t20-3*t30)*p-t11*t20-t21*(t20-3*t30))*t31+(-p^2*t11+t11*t
21^2)*q+((t20+t30)*t11+(t20+2*t30)*t21)*p-t30*t21*(t11+2*t21))*t12+(2*
(t31-(1/2)*t11-(1/2)*t21))*(-p+t31)*(p-t21)*(p-t11))*t32+((-q^2*t31^2+
q*((p+t11)*q-t30)*t31-q^2*p*t11+t30*t11*q+t30*(t20+t30))*t12+(-t11+t31
)*(((p-t11)*q+t20+t30)*t31-p*(p-t11)*q-p*t20-t11*t30))*t22^2+((-q^2*t3
1^2+q*((p+t21)*q-t30)*t31-q^2*p*t21+t30*t21*q-t30*t20)*t12^2+(2*q*(p-(
1/2)*t11-(1/2)*t21)*t31^2+((-2*p^2+2*t11*t21)*q+p*t30+t11*t20-t21*(t20
+t30))*t31+((t11+t21)*p-2*t11*t21)*p*q+((-t20-t30)*t11+t21*t20)*p+t21*
t11*t30)*t12-(p-t11)*(-t11+t31)*(-p+t31)*(p-t21))*t22-t12*((((-p+t21)*
q+t20)*t31+p*(p-t21)*q+(-t20-t30)*p+t21*t30)*t12+(p-t21)*(p-t11)*(-p+t
31))*(-t21+t31)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 118 "omegaJMU:
=omegaJMUdt11*dt11+omegaJMUdt21*dt21+omegaJMUdt31*dt31+omegaJMUdt12*dt
12+omegaJMUdt22*dt22+omegaJMUdt32*dt32:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3458 "omegaJMUP4:= ((2*(-(1/2)*(ds12-ds22)*(-s12+s22)*X1+
dX1*s12^2+(-2*dX1*s22+ds11-ds21)*s12+dX1*s22^2+(-ds11+ds21)*s22-(1/2)*
(-s21+s11)*(ds12-ds22)))*s22*s12*Q^4+(2*(-(1/2)*(ds12-ds22)*(-s12+s22)
*X1+dX1*s12^2+(-2*dX1*s22+ds11-ds21)*s12+dX1*s22^2+(-ds11+ds21)*s22-(1
/2)*(-s21+s11)*(ds12-ds22)))*(-2*X1*s12*s22+(s21+P)*s12+s22*(P+s11))*Q
^3+(2*(-(1/2)*(ds12-ds22)*(-s12+s22)*X1+dX1*s12^2+(-2*dX1*s22+ds11-ds2
1)*s12+dX1*s22^2+(-ds11+ds21)*s22-(1/2)*(-s21+s11)*(ds12-ds22)))*(X1^2
*s12*s22+((-2*P-2*s21)*s12-2*s22*(P+s11))*X1+s12*s20+s10*s22+(P+s11)*(
s21+P))*Q^2+(-(-s12+s22)*((s21+P)*s12+s22*(P+s11))*(ds12-ds22)*X1^3+(2
*dX1*(s21+P)*s12^3+(-2*dX1*(P-s11+2*s21)*s22+(2*ds11-2*ds21)*P+(2*ds11
-2*ds21)*s21+(s10-s20)*ds12+2*ds22*s20)*s12^2+(-2*dX1*(P+2*s11-s21)*s2
2^2+((2*ds11-2*ds21)*s11+(-2*ds11+2*ds21)*s21+(-3*s10+s20)*ds12+ds22*(
s10-3*s20))*s22-(2*(P+3*s11*(1/2)-(1/2)*s21))*(ds12-ds22)*(s21+P))*s12
+2*s22*(dX1*(P+s11)*s22^2+((-ds11+ds21)*P+(-ds11+ds21)*s11+ds12*s10-(1
/2)*ds22*(s10-s20))*s22+(P-(1/2)*s11+3*s21*(1/2))*(ds12-ds22)*(P+s11))
)*X1^2+(2*dX1*(s10-s20)*s12^3+(-6*dX1*(s10-s20)*s22-4*P^2*dX1-4*dX1*(s
21+s11)*P-4*dX1*s11*s21+2*ds11*s10-2*s20*(ds11-2*ds21))*s12^2+(6*dX1*(
s10-s20)*s22^2+(8*P^2*dX1+8*dX1*(s21+s11)*P+8*dX1*s11*s21+(-6*ds11+2*d
s21)*s10+2*s20*(ds11-3*ds21))*s22+(-4*ds11+4*ds21)*P^2+((-4*ds11+4*ds2
1)*s11+(-4*ds11+4*ds21)*s21+(s10+s20)*(ds12-ds22))*P+((-4*ds11+4*ds21)
*s21+2*s20*(ds12-ds22))*s11+s21*(s10-s20)*(ds12-ds22))*s12-2*dX1*(s10-
s20)*s22^3+(-4*P^2*dX1-4*dX1*(s21+s11)*P-4*dX1*s11*s21+(4*ds11-2*ds21)
*s10+2*ds21*s20)*s22^2+((4*ds11-4*ds21)*P^2+((4*ds11-4*ds21)*s11+(4*ds
11-4*ds21)*s21-(s10+s20)*(ds12-ds22))*P+((4*ds11-4*ds21)*s21+(s10-s20)
*(ds12-ds22))*s11-2*s21*s10*(ds12-ds22))*s22+(2*(-s21+s11))*(s21+P)*(P
+s11)*(ds12-ds22))*X1+2*dX1*(s10+s20)*(P+s11+s21)*s12^2+(-4*dX1*(s10+s
20)*(P+s11+s21)*s22+(2*(s10+s20))*(ds11-ds21)*P+2*s20*(ds11-ds21)*s11+
2*s10*(ds11-ds21)*s21+(sX10+s20)*(sX10+s10)*(ds12-ds22))*s12+2*dX1*(s1
0+s20)*(P+s11+s21)*s22^2+(-(2*(s10+s20))*(ds11-ds21)*P-2*s20*(ds11-ds2
1)*s11-2*s10*(ds11-ds21)*s21-(sX10+s20)*(sX10+s10)*(ds12-ds22))*s22-(d
s12-ds22)*((s10+s20)*P+s21*s10+s11*s20)*(-s21+s11))*Q-(-s12+s22)*((-ds
12*s10-ds22*s20)*s12+(ds12*s10+ds22*s20)*s22+(s21+P)*(P+s11)*(ds12-ds2
2))*X1^3+(-2*dX1*s10*s12^3+((4*(s10-(1/2)*s20))*dX1*s22+2*P^2*dX1+2*dX
1*(s21+s11)*P+2*dX1*s11*s21-2*ds11*s10-2*ds21*s20)*s12^2+(-2*dX1*(s10-
2*s20)*s22^2+(-4*P^2*dX1-4*dX1*(s21+s11)*P-4*dX1*s11*s21+4*ds11*s10+4*
ds21*s20)*s22+(2*ds11-2*ds21)*P^2+((2*ds11-2*ds21)*s11+(2*ds11-2*ds21)
*s21-(s10+s20)*(ds12-ds22))*P+((2*ds11-2*ds21)*s21-s20*(ds12-ds22))*s1
1-s21*s10*(ds12-ds22))*s12-2*s22^3*dX1*s20+(2*P^2*dX1+2*dX1*(s21+s11)*
P+2*dX1*s11*s21-2*ds11*s10-2*ds21*s20)*s22^2+((-2*ds11+2*ds21)*P^2+((-
2*ds11+2*ds21)*s11+(-2*ds11+2*ds21)*s21+(s10+s20)*(ds12-ds22))*P+((-2*
ds11+2*ds21)*s21+s20*(ds12-ds22))*s11+s21*s10*(ds12-ds22))*s22-(-s21+s
11)*(s21+P)*(P+s11)*(ds12-ds22))*X1^2+(-2*dX1*(s10+s20)*(P+s11+s21)*s1
2^2+(4*dX1*(s10+s20)*(P+s11+s21)*s22-(2*(s10+s20))*(ds11-ds21)*P-2*s20
*(ds11-ds21)*s11-2*s10*(ds11-ds21)*s21-(2*((sX10+(1/2)*s20)*s10+sX10*(
sX10+s20)))*(ds12-ds22))*s12-2*dX1*(s10+s20)*(P+s11+s21)*s22^2+((2*(s1
0+s20))*(ds11-ds21)*P+2*s20*(ds11-ds21)*s11+2*s10*(ds11-ds21)*s21+(2*(
(sX10+(1/2)*s20)*s10+sX10*(sX10+s20)))*(ds12-ds22))*s22+(ds12-ds22)*((
s10+s20)*P+s21*s10+s11*s20)*(-s21+s11))*X1-2*sX10*(sX10+s10+s20)*(dX1*
s12^2+(-2*dX1*s22+ds11-ds21)*s12+dX1*s22^2+(-ds11+ds21)*s22-(1/2)*(-s2
1+s11)*(ds12-ds22)))/((2*(Q-X1))*(-s12+s22)^2):" }}}{EXCHG {PARA 0 "> 
" 0 "" {MPLTEXT 1 0 41 "omegaJMUfunction:=unapply(omegaJMU,q,p):\n" }
{MPLTEXT 1 0 129 "omegaJMUfunction2:=unapply(simplify(omegaJMUfunction
(P,Q+t22*P)),t11,t21,t31,t12,t22,t32,t20,t30,dt11,dt21,dt31,dt12,dt22,
dt32):\n" }{MPLTEXT 1 0 270 "omegaJMUduality:=simplify(omegaJMUfunctio
n2(t11functionduality,t21functionduality,t31functionduality,t12functio
nduality,t22functionduality,t32functionduality,t20functionduality,t30f
unctionduality,dt11duality,dt21duality,dt31duality,dt12duality,dt22dua
lity,dt32duality)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "Diff
erenceomegaJMU:=simplify(omegaJMUduality-omegaJMUP4):\n" }{MPLTEXT 1 
0 67 "DifferenceomegaJMUds11:=residue(DifferenceomegaJMU/ds11^2,ds11=0
);\n" }{MPLTEXT 1 0 67 "DifferenceomegaJMUds21:=residue(Differenceomeg
aJMU/ds21^2,ds21=0);\n" }{MPLTEXT 1 0 77 "DifferenceomegaJMUds12:=simp
lify(residue(DifferenceomegaJMU/ds12^2,ds12=0));\n" }{MPLTEXT 1 0 77 "
DifferenceomegaJMUds22:=simplify(residue(DifferenceomegaJMU/ds22^2,ds2
2=0));\n" }{MPLTEXT 1 0 74 "DifferenceomegaJMUdX1:=simplify(residue(Di
fferenceomegaJMU/dX1^2,dX1=0));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 
53 "simplify(DifferenceomegaJMU-omegaJMUMinusomegaJMUP4);" }}{PARA 11 
"" 1 "" {XPPMATH 20 ">I7DifferenceomegaJMUds11G6\"*(I$s10GF$\"\"\"I$s1
1GF$F'I$s12GF$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I7Differenceomeg
aJMUds21G6\"*(I$s20GF$\"\"\"I$s21GF$F'I$s22GF$!\"\"" }}{PARA 11 "" 1 "
" {XPPMATH 20 ">I7DifferenceomegaJMUds12G6\",$*(I$s10GF$\"\"\",&*&F'F(
I$s12GF$F(F(*$I$s11GF$\"\"#!\"\"F(F+!\"##F(F." }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I7DifferenceomegaJMUds22G6\",$*(I$s20GF$\"\"\",&*&F'F(I$
s22GF$F(F(*$I$s21GF$\"\"#!\"\"F(F+!\"##F(F." }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I6DifferenceomegaJMUdX1G6\"\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "pdsol
ve(\{DifferenceomegaJMUds11=diff(gg(s11,s21,s12,s22,X1),s11),\n" }
{MPLTEXT 1 0 57 "DifferenceomegaJMUds21=diff(gg(s11,s21,s12,s22,X1),s2
1),\n" }{MPLTEXT 1 0 57 "DifferenceomegaJMUds12=diff(gg(s11,s21,s12,s2
2,X1),s12),\n" }{MPLTEXT 1 0 57 "DifferenceomegaJMUds22=diff(gg(s11,s2
1,s12,s22,X1),s22),\n" }{MPLTEXT 1 0 54 "DifferenceomegaJMUdX1=diff(gg
(s11,s21,s12,s22,X1),X1)\n" }{MPLTEXT 1 0 29 "\},\{gg(s11,s21,s12,s22,
X1)\});\n" }{MPLTEXT 1 0 116 "g:=unapply(s10*s11^2/(2*s12)+s20*s21^2/(
2*s22)+(1/2)*s10^2*ln(s12)+(1/2)*s20^2*ln(s22),s11,s21,s12,s22,X1,s10,
s20);\n" }{MPLTEXT 1 0 258 "dg:=unapply( diff(g(s11,s21,s12,s22,X1,s10
,s20),s11)*ds11+ diff(g(s11,s21,s12,s22,X1,s10,s20),s21)*ds21+diff(g(s
11,s21,s12,s22,X1,s10,s20),s12)*ds12+diff(g(s11,s21,s12,s22,X1,s10,s20
),s22)*ds22+diff(g(s11,s21,s12,s22,X1,s10,s20),X1)*dX1,s11,s21,s12,s22
,X1):\n" }{MPLTEXT 1 0 60 "simplify(omegaJMUduality-omegaJMUP4-dg(s11,
s21,s12,s22,X1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "<#/-I#ggG6\"6'I$s11
G6\"I$s21G6\"I$s12G6\"I$s22G6\"I#X1G6\",,*(I$s10G6\"\"\"\"I$s11G6\"\"
\"#I$s12G6\"!\"\"#\"\"\"\"\"#*(I$s20G6\"\"\"\"I$s21G6\"\"\"#I$s22G6\"!
\"\"#\"\"\"\"\"#*&I$s10G6\"\"\"#-I#lnG6$%*protectedGI(_syslibG6\"6#I$s
12G6\"\"\"\"#\"\"\"\"\"#*&I$s20G6\"\"\"#-I#lnG6$%*protectedGI(_syslibG
6\"6#I$s22G6\"\"\"\"#\"\"\"\"\"#I$_C1G6\"\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I\"gG6\"f*6)I$s11GF$I$s21GF$I$s12GF$I$s22GF$I#X1GF$I$s10
GF$I$s20GF$F$6$I)operatorGF$I&arrowGF$F$,**(9)\"\"\"9$\"\"#9&!\"\"#F4F
6*(9*F49%F69'F8F9*&F3F6-I#lnG6$%*protectedGI(_syslibGF$6#F7F4F9*&F;F6-
F@6#F=F4F9F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "gtcoordinates:=g(s11duality,s21dual
ity,s12duality,s22duality,X1duality,s10duality,s20duality);\n" }
{MPLTEXT 1 0 99 "gtcoordinates:= 1/2* (t30*t31^2/(t22-t32)-t10*t11^2/(
t12-t22)-t30^2*ln(t22-t32)-t10^2*ln(t12-t22));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I.gtcoordinatesG6\",**(I$t30GF$\"\"\"I$t31GF$\"\"#,&I$t3
2GF$!\"\"I$t22GF$F(F-#F(F**(,&I$t20GF$F-F'F-F(I$t11GF$F*,&F.F-I$t12GF$
F(F-#F-F**&F'F*-I#lnG6$%*protectedGI(_syslibGF$6#*$F+F-F(F/*&F1F*-F96#
,$*$F4F-F-F(F/" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I.gtcoordinatesG6\",*
*(I$t30GF$\"\"\"I$t31GF$\"\"#,&I$t32GF$!\"\"I$t22GF$F(F-#F(F**(,&I$t20
GF$F-F'F-F(I$t11GF$F*,&F.F-I$t12GF$F(F-#F-F**&F'F*-I#lnG6$%*protectedG
I(_syslibGF$6#F+F(F6*&F1F*-F96#F4F(F6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 72 "simplify(g(s11, s21, s12, s22, X1, s10, s20)-f(s11, s
21, s12, s22, X1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 89 100 1803 1 1 1 1 }{PAGENUMBERS 0 
1 2 33 1 1 }