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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 279 138 "In this Maple worksheet
 we shall prove that the JMU differentials is related to the evaluatio
n of the Hamiltonian differential at \\hbar=0." }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 9 "restart:\n" }{MPLTEXT 1 0 21 "with(LinearAlgebra
):\n" }{MPLTEXT 1 0 15 "t10:=-t20-t30;\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 55 "P1:=unapply( (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-t
30*t32+t21*t11 +t31*t11+t21*t31,lambda);\n" }{MPLTEXT 1 0 118 "P3:=una
pply(t12*t22*t32*lambda^3+(t12*t22*t31+t12*t32*t21+t22*t32*t11)*lambda
^2+(t12*t22*t30+t12*t32*t20+t22*t32*t10  " }{MPLTEXT 1 0 53 "+t12*t21*
t31+t22*t11*t31+t32*t11*t21)*lambda,lambda);" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 131 "taufunction:=unapply(  ((t21-t3
1)*t12+(t31-t11)*t22+(t11-t21)*t32)/(sqrt((t22-t12)*(t12-t32)*(t32-t22
))) ,t11,t21,t31,t12,t22,t32);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "
\n" }{MPLTEXT 1 0 84 "checkqfunction:=unapply( sqrt((t12-t32)/((t22-t1
2)*(t32-t22)))*(-p+t22*q+t21),q,p);\n" }{MPLTEXT 1 0 82 "checkpfunctio
n:=unapply( sqrt((t32-t22)/((t12-t32)*(t22-t12)))*(p-t12*q-t11),q,p);"
 }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 130 "Hamtauch
eckCoordinatesTheo:=unapply(-(checkq*checkp^2+checkq^2*checkp-tau*chec
kq*checkp-t20*checkp+(t10+h)*checkq),checkq,checkp);" }}{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$t3
1GF$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$\"\"\"I$t22GF$F0F0*&F/F0I
$t32GF$F0F0*&F1F0F3F0F0F09$\"\"#F0*&,(*&,&I$t21GF$F0I$t31GF$F0F0F/F0F0
*&,&I$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#P3G6\"f*6#I'lambd
aGF$F$6$I)operatorGF$I&arrowGF$F$,(**I$t12GF$\"\"\"I$t22GF$F.I$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$FAF.F/F.F0F.F.*(F0F.
F6F.F8F.F.*(F/F.F6F.F:F.F.*(F-F.F0F.F@F.F.*(F-F.F8F.F:F.F.*(F-F.F/F.FB
F.F.F.F1F.F.F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,taufunctionG6\"
f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF$I
&arrowGF$F$*&,(*&,&9%\"\"\"9&!\"\"F59'F5F5*&,&F6F59$F7F59(F5F5*&,&F;F5
F4F7F59)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$!\"\"F0,&I$t22
GF$F0F/F2F2,&F1F0F4F2F2#F0\"\"#,(*&9$F0F4F0F09%F2I$t21GF$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$\"\"\"I$t22GF$!\"\"F0,&F1F0
I$t12GF$F2F2,&F4F0F/F2F2#F0\"\"#,(*&9$F0F4F0F29%F0I$t11GF$F2F0F$F$F$" 
}}{PARA 11 "" 1 "" {XPPMATH 20 ">I;HamtaucheckCoordinatesTheoG6\"f*6$I
'checkqGF$I'checkpGF$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$t30G
F$F2I\"hGF$F/F/F.F/F2F$F$F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 280 44 "L
oading the results on the JMU differentials" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 443 "omegaJMUdt11:=1/((t12-t22)*(-t12+t32))*(-p^3+(t11
+t21+t31+(t12+t22+t32)*q)*p^2+(((-t22-t32)*t12-t22*t32)*q^2+((-t31-t21
)*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*t3
2*t11)*q^2+((t20*t32+t21*t31+t22*t30)*t12+((-t20-t30)*t32+t11*t31)*t22
+t32*t11*t21)*q+(t20+t30)*(t31-t11+t21)*t12+(t11*t30-t31*(t20+t30))*t2
2+(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-t
22-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+t31
)*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*t2
1*t31)*q+t20*(t31+t11-t21)*t22+(t21*(t20+t30)-t11*t20)*t32+(-t20*t31-t
21*t30)*t12-t11*t21*t31);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 430 "o
megaJMUdt31:=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)+t32
*(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)*t2
2-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*t
21*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*(t
20+t30))*t22^2+(-q^3*(t11-t21)*t32^2+(2*q^2*t11^2-2*q*((t21+t31)*q+3*t
20*(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*t
20*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)*t11
+(-p^2*t31+t21^2*t31)*q+((-t20-2*t30)*t21-t31*t30)*p+t21*(t20+t30)*(t3
1+2*t21))*t32-(p-t21)*(p-t11)*(t31-2*t11+t21)*(-p+t31))*t12+((-q^2*t11
^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-t2
1)*(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+t3
1)*q^2+(t20+t30)*(t11+t31)*q+2*t20^2+t30*t20)*t32+(2*q*((-p+t31)*q+t30
)*t21-(t11+t31)*(-p+t31)*q^2-t30*(t11+t31)*q+t20*(t20-t30))*t12+t20*t2
1^2+(-(2*(p-t11))*(-p+t31)*q-2*t20*(t31-p+t11))*t21+(p-t11)*(t11+t31)*
(-p+t31)*q+t20*((-t11-t31)*p+t31^2+t11*t31+t11^2))*t22^2+((q^3*(t11-t2
1)*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+t31)*q-3*t
20*(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))*t3
2+(-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*((t31+p)*q-t
20)*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*t1
1*t31)*p*q+((-t20-t30)*t11+t31*t30)*p+t31*t11*t20)*t12+(t11-t21)*(p-t2
1)*(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 1655 "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-t
20*(t11+t21)*q-t30*(t20-t30))*t12+t30*t31^2+((2*(p-t21))*(p-t11)*q+2*t
30*(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)*t31
-(p-t11)*t11*q^2-t11*(t20+t30)*q-t30*(t20+t30))*t22^2+(-q^3*(-t21+t31)
*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*t
30)*t31^2+((p-t11)*(p+t11+2*t21)*q+(-t30+2*t20)*p+t11*(4*t30+t20)+t21*
(t20+t30))*t31+(-p^2*t21+t11^2*t21)*q+(t11*(-t20+t30)-t21*t20)*p-(2*(t
11+(1/2)*t21))*t11*t30)*t22+(q*((p-t21)*q-t20)*t31-(p-t21)*t21*q^2+t21
*t20*q+t30*t20)*t12^2+(((-2*p+2*t21)*q+2*t20)*t31^2+((p-t21)*(p+2*t11+
t21)*q+(-2*t20-3*t30)*p-t11*t20-t21*(t20-3*t30))*t31+(-p^2*t11+t11*t21
^2)*q+((t20+t30)*t11+(t20+2*t30)*t21)*p-t30*t21*(t11+2*t21))*t12+(2*(t
31-(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*t31^
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+t
30))*t31+((t11+t21)*p-2*t11*t21)*p*q+((-t20-t30)*t11+t21*t20)*p+t21*t1
1*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+t31
))*(-t21+t31));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-omegaJMUdt11G6\"*(
,&I$t22GF$!\"\"I$t12GF$\"\"\"F(,&F)F(I$t32GF$F*F(,6*$I\"pGF$\"\"$F(*&,
*I$t11GF$F*I$t21GF$F*I$t31GF$F**&,(F)F*F'F*F,F*F*I\"qGF$F*F*F*F/\"\"#F
**&,0*&,&*&,&F'F(F,F(F*F)F*F**&F'F*F,F*F(F*F8F9F**&,(*&,&F5F(F4F(F*F)F
*F**&,&F3F(F5F(F*F'F*F**&F,F*,&F3F*F4F*F*F(F*F8F*F**&,&I$t20GF$F(I$t30
GF$F(F*F)F*F**&FKF*F'F*F**&FLF*F,F*F**&FDF*F3F*F**&F4F*F5F*F(F*F/F*F**
*F8F0F)F*F'F*F,F*F**&,&*&,&*&F4F*F,F*F**&F'F*F5F*F*F*F)F*F**(F'F*F,F*F
3F*F*F*F8F9F**&,(*&,(*&FKF*F,F*F*FPF**&F'F*FLF*F*F*F)F*F**&,&*&FJF*F,F
*F**&F5F*F3F*F*F*F'F*F**(F,F*F3F*F4F*F*F*F8F*F**(,&FKF*FLF*F*,(F5F*F3F
(F4F*F*F)F*F**&,&*&F3F*FLF*F**&F5F*F_oF*F(F*F'F*F**&,&*&F3F*FKF*F**&F4
F*F_oF*F(F*F,F*F**(F3F*F4F*F5F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">
I-omegaJMUdt21G6\"*(,&I$t22GF$!\"\"I$t12GF$\"\"\"F(,&I$t32GF$F*F'F(F(,
6*$I\"pGF$\"\"$F**&,**&,(F)F(F'F(F,F(F*I\"qGF$F*F*I$t31GF$F(I$t11GF$F(
I$t21GF$F(F*F/\"\"#F**&,0*&,&*&,&F)F*F,F*F*F'F*F**&F)F*F,F*F*F*F5F9F**
&,(*&,&F8F*F6F*F*F)F*F**&,&F7F*F6F*F*F'F*F**&F,F*,&F7F*F8F*F*F*F*F5F*F
**&I$t20GF$F*F'F*F(*&I$t30GF$F*F,F*F(*&,&FJF*FLF*F*F)F*F**&FFF*F8F*F**
&F6F*F7F*F*F*F/F*F***F5F0F)F*F'F*F,F*F(*&,&*&,&*&F7F*F,F*F(*&F)F*F6F*F
(F*F'F*F**(F)F*F,F*F8F*F(F*F5F9F**&,(*&,(*&FNF*F,F*F*FPF(*&F)F*FLF*F(F
*F'F*F**&,&*&F7F*F8F*F(*&F)F*FJF*F(F*F,F*F**(F)F*F8F*F6F*F(F*F5F*F**(F
JF*,(F6F*F7F*F8F(F*F'F*F**&,&*&F8F*FNF*F**&F7F*FJF*F(F*F,F*F**&,&*&FJF
*F6F*F(*&F8F*FLF*F(F*F)F*F**(F7F*F8F*F6F*F(F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I-omegaJMUdt31G6\"*(,&I$t32GF$\"\"\"I$t22GF$!\"\"F*,&I$t
12GF$F*F'F(F*,6*$I\"pGF$\"\"$F(*&,**&,(F,F*F)F*F'F*F(I\"qGF$F(F(I$t31G
F$F*I$t11GF$F*I$t21GF$F*F(F/\"\"#F(*&,0*&,&*&,&F,F(F)F(F(F'F(F(*&F,F(F
)F(F(F(F5F9F(*&,(*&,&F8F(F6F(F(F,F(F(*&,&F7F(F6F(F(F)F(F(*&F'F(,&F7F(F
8F(F(F(F(F5F(F(*&I$t30GF$F(F'F(F**&I$t20GF$F(F)F(F**&,&FLF(FJF(F(F,F(F
(*&F6F(FHF(F(*&F8F(F7F(F(F(F/F(F(**F5F0F,F(F)F(F'F(F**&,&*&,&*&F7F(F)F
(F**&F,F(F8F(F*F(F'F(F(*(F,F(F)F(F6F(F*F(F5F9F(*&,(*&,(*&FNF(F)F(F(FPF
**&F,F(FLF(F*F(F'F(F(*&,&*&F7F(F6F(F**&F,F(FJF(F*F(F)F(F(*(F,F(F8F(F6F
(F*F(F5F(F(*(FJF(,(F6F(F7F*F8F*F(F'F(F**&,&*&F7F(FJF(F**&F6F(FNF(F(F(F
)F(F(*&,&*&FLF(F6F(F**&F8F(FJF(F*F(F,F(F(*(F7F(F8F(F6F(F*F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I-omegaJMUdt12G6\",$*(,&I$t22GF$!\"\"I$t12GF$
\"\"\"!\"#,&F*F)I$t32GF$F+F,,.*&,&I$t20GF$F+I$t30GF$F+\"\"#F*\"\"$F)*&
,.*&,,*(I\"qGF$F5,(I$t31GF$F+I$t11GF$F,I$t21GF$F+F+F.F+F)*(F;F+,&*&,&I
\"pGF$F)F=F+F+F;F+F+F3F+F+F>F+F4*(,&F?F+F=F+F+FCF+F;F4F)*(F3F+FFF+F;F+
F)*&,&F2F+F3F4F+F1F+F+F+F(F+F+*&,.*(F;F+,&*&,&FDF+F?F)F+F;F+F+F2F)F+F>
F+F,*(FOF+FFF+F;F4F+*(F2F+FFF+F;F+F)*$F2F4F4*&F3F+F2F+F5*$F3F4F+F+F.F+
F+*&,&F2F)F3F)F+F>F4F+*&,&*(FOF+FCF+F;F+F,*&F1F+,(F=F+FDF)F?F+F+F4F+F>
F+F+**FOF+FFF+FCF+F;F+F+*&F1F+,**&,&F=F)F?F)F+FDF+F+*$F=F4F+*&F?F+F=F+
F+*$F?F4F+F+F)F+F*F4F+*&,,*&,,*(F;F5,&F=F+F>F)F+F.F+F+F@F)*(F=F+FCF+F;
F4F+*(F=F+F3F+F;F+F+*&F3F+F1F+F)F+F(F4F+*&,0*(F;F5,&F>F+F?F)F+F.F4F)*&
,,*&F;F4F>F4F4*(F;F+,(*&FFF+F;F+F+F2#F5F4F3FapF+F>F+F,*(F;F4F?F+F=F+F4
*&,&*&FIF+F?F+F+*&F=F+,&F2F+F3#F+F4F+F4F+F;F+F+*$F1F4F,F+F.F+F+*&,&*&,
&F=F4FDF,F+F;F+F+F3F4F+F>F4F+*&,**(FCF+,(F=F+F?F4FDF+F+F;F+F)*&,&F3F+F
2F5F+FDF+F+*&F?F+F3F+F)*&,&F2F+F3#\"\"%F5F+F=F+!\"$F+F>F+F+*&,&*&FDF4F
?F+F)*&F?F+F=F4F+F+F;F+F+*&,&*&F?F+F2F+F)FfpF,F+FDF+F+*(F1F+F=F+,&F?Fh
pF=F+F+F4F+F(F+F+*&,*FLF+*(FOF+F?F+F;F4F)*(F?F+F2F+F;F+F+*&F2F+F1F+F)F
+F.F4F+*&,,*&,&*&,&FDF,F?F4F+F;F+F+F2F4F+F>F4F+*&,**(FOF+,(FDFhpF=F+F?
FhpF+F;F+F4*&,&F2F+F3F5F+FDF+F+*&,&F2!\"%F3FiqF+F?F+F+*&F2F+F=F+F)F+F>
F+F+*&,&*&FDF4F=F+F)*&F?F4F=F+F+F+F;F+F+*&,&*&,&F2F)F3F,F+F?F+F+*&F=F+
F3F+F)F+FDF+F+*(F?F+F1F+,&F=F+F?F4F+F+F+F.F+F+**FOF+,&FDF+F>F)F+F<F+FC
F+F)F+F*F+F+*&,&*&,,F]pF)*(F;F+,(*&,&F=F+FDF+F+F;F+F+F2F+F3F+F+F>F+F+*
(F;F4FDF+F=F+F)*(F1F+F=F+F;F+F)FfoF+F+F.F+F+*&FcoF+,**&,&*&,&FDF+F=F)F
+F;F+F+F3F)F+F>F+F+*(FDF+FCF+F;F+F+*&FDF+F2F+F)*&F=F+F1F+F+F+F)F+F(F4F
+*&,(*&,,F]pF)*(,(*&,&FDF+F?F+F+F;F+F+F2F+F3F+F+F;F+F>F+F+*(F;F4FDF+F?
F+F)*(F?F+F1F+F;F+F)FgrF+F+F.F4F+*&,,*(F;F+,(F=F+FDF,F?F+F+F>F4F)*&,**
&,&*$FDF4F,F\\oF4F+F;F+F+*&FVF+FDF+F+FgsF+FdqF+F+F>F+F+*(,&*&FFF+FDF+F
+F\\oF,F+FDF+F;F+F+*&,&*&F2F+F?F+F+*&F3F+F=F+F+F+FDF+F+*(F=F+F?F+F1F+F
)F+F.F+F+**FdtF+FcoF+FCF+FOF+F+F+F(F+F+*(,&*&,**&,&*&,&FDF)F?F+F+F;F+F
+F2F+F+F>F+F+*(FDF+FOF+F;F+F+*&FDF+F3F+F+*&F?F+F1F+F)F+F.F+F+*(FOF+Fdt
F+FCF+F+F+FjoF+F.F+F)F+Fhp" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-omegaJM
Udt22G6\",$*(,&I$t22GF$!\"\"I$t12GF$\"\"\"!\"#,&I$t32GF$F+F(F)F,,.*&I$
t20GF$\"\"#F(\"\"$F)*&,.*&,.*(I\"qGF$F3,(I$t31GF$F+I$t11GF$F+I$t21GF$F
,F+F*F+F)*(F9F+,(*&,&I\"pGF$F+F<F)F+F9F+F+F1F+I$t30GF$F+F+F=F+F,*(FAF+
,&F<F+F;F+F+F9F2F+*(,&F1F+FCF+F+FEF+F9F+F+*$F1F2F2*&FCF+F1F+F+F+F.F+F+
*&,**(F9F+,&*&,&FBF)F;F+F+F9F+F+FCF+F+F=F+F2*(FEF+FOF+F9F2F)*(FCF+FEF+
F9F+F)*&F1F+,&F1F+FCF)F+F+F+F*F+F+*&F1F+F=F2F+*&,&*(FAF+FOF+F9F+F,*&F1
F+,(F;F+FBF)F<F+F+F,F+F=F+F+**FAF+FEF+FOF+F9F+F+*&F1F+,**&,&F<F)F;F)F+
FBF+F+*$F;F2F+*&F;F+F<F+F+*$F<F2F+F+F+F+F(F2F+*&,,*&,,*(F9F3,&F<F+F=F)
F+F*F+F+F>F+*(FAF+F<F+F9F2F)*(F<F+FGF+F9F+F)*&F1F+FGF+F)F+F.F2F+*&,0*(
F9F3,&F=F)F;F+F+F*F2F+*&,,*&F9F2F=F2F2*(,&*&FEF+F9F+F+F1#!\"$F2F+F9F+F
=F+F,*(F9F2F<F+F;F+F2*&,&*&F<F+,&F1F)FCF+F+F+*&F;F+,&F1F+FC#F+F2F+F,F+
F9F+F+FHF,F+F*F+F+*&,(*&,&FBF,F<F2F+F9F+F+F1F,FCF,F+F=F2F+*&,**(,(FBFh
pF;F+F<FhpF+FAF+F9F+F2*&,&FCF2F1F)F+FBF+F+*&,&FCF+F1\"\"%F+F<F+F+*&F;F
+FGF+F+F+F=F+F+*&,&*&FBF2F;F+F)*&F<F2F;F+F+F+F9F+F+*&,&*&FSF+F<F+F+*&F
;F+FCF+F)F+FBF+F+*(F<F+F1F+,&F;F+F<F2F+F)F+F.F+F+*&,*FLF)*(F;F+FOF+F9F
2F+*(F;F+FCF+F9F+F+FIF+F+F*F2F+*&,,*&,&*&,&F;F2FBF,F+F9F+F+FCF2F+F=F2F
+*&,**(FOF+,(F;F+F<F2FBF+F+F9F+F)*&,&FCF,F1F`pF+FBF+F+*&F<F+FCF+F)*&F;
F+,&F1F+FC#F)F3F+F3F+F=F+F+*&,&*&FBF2F<F+F)*&F<F+F;F2F+F+F9F+F+*&,&*&F
GF+F<F+F+FfpF2F+FBF+F+*(,&F;F+F<FhpF+F;F+F1F+F,F+F*F+F+**,&FBF+F=F)F+F
AF+F:F+FOF+F)F+F(F+F+*&,&*&,,F[pF)*(,&*&,&FBF+F<F+F+F9F+F+F1F)F+F9F+F=
F+F+*(F9F2FBF+F<F+F)*(F1F+F<F+F9F+F+FdoF+F+F*F+F+*&FaoF+,**&,(*&,&FBF)
F<F+F+F9F+F+F1F)FCF)F+F=F+F+*(FBF+FAF+F9F+F+*&FBF+FCF+F+*&F<F+F1F+F+F+
F+F+F.F2F+*&,(*&,,F[pF)*(F9F+,&*&,&F;F+FBF+F+F9F+F+F1F)F+F=F+F+*(F9F2F
BF+F;F+F)*(F;F+F1F+F9F+F+FIF)F+F*F2F+*&,,*(F9F+,(FBF,F;F+F<F+F+F=F2F)*
&,**&,&*$FBF2F,*&F<F+F;F+F2F+F9F+F+*&FBF+F1F+F+FasF+FfqF)F+F=F+F+*(,&*
&FEF+FBF+F+FjnF,F+FBF+F9F+F+*&,&*&,&F1F)FCF)F+F<F+F+F^rF+F+FBF+F+*(F;F
+F<F+F1F+F+F+F*F+F+**FaoF+F_tF+FAF+FOF+F+F+F.F+F+*(F*F+,&*&,**&FMF+F=F
+F+*(FBF+FOF+F9F+F)*&F^wF+FBF+F+*&F1F+F;F+F+F+F*F+F+*(F_tF+FAF+FOF+F+F
+FhoF+F+F+Fhp" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-omegaJMUdt32G6\",$*(
,&I$t12GF$!\"\"I$t32GF$\"\"\"!\"#,&F*F+I$t22GF$F)F,,.*&I$t30GF$\"\"#F*
\"\"$F)*&,.*&,,*(I\"qGF$F3,(I$t31GF$F+I$t11GF$#F)F2I$t21GF$F=F+F(F+F2*
(F9F+,(*&,&I\"pGF$F+F<F)F+F9F+F+I$t20GF$F+F1F+F+F;F+F,*(,&F<F+F>F+F+FB
F+F9F2F+*(,&FDF+F1F+F+FFF+F9F+F+*&F1F+,&FDF+F1F2F+F+F+F.F+F+*&,**(F9F+
,&*&,&FCF+F>F)F+F9F+F+FDF)F+F;F+F,*(FFF+FPF+F9F2F+*(FDF+FFF+F9F+F)*&F1
F+,&FDF+F1F)F+F)F+F(F+F+*&F1F+F;F2F+*&,&*(FPF+FBF+F9F+F2*&F1F+,(FCF+F<
F)F>F)F+F2F+F;F+F+**FFF+FPF+FBF+F9F+F)*&F1F+,**&FFF+FCF+F+*$F<F2F)*&F>
F+F<F+F)*$F>F2F)F+F)F+F*F2F+*&,,*&,,*(F9F3,&F;F+F<F)F+F(F+F)F?F+*(FBF+
F<F+F9F2F)*(F<F+FHF+F9F+F)*&F1F+FHF+F)F+F.F2F+*&,0*(F9F3,&F>F)F;F+F+F(
F2F)*&,,*&F9F2F;F2F2*(F9F+,&*&FFF+F9F+F+F1#!\"$F2F+F;F+F,*(F9F2F<F+F>F
+F2*&,&*&FTF+F<F+F+*&FJF+F>F+F)F+F9F+F+*$F1F2F,F+F(F+F+*&,(*&,&FCF,F<F
2F+F9F+F+FDF,F1F,F+F;F2F+*&,**(FBF+,(FCF+F<F+F>F2F+F9F+F+*&,&F1F)FDF2F
+FCF+F+*&F<F+,&F1\"\"%FDF+F+F+*&F>F+FHF+F+F+F;F+F+*&,&*&FCF2F>F+F)*&F<
F2F>F+F+F+F9F+F+*&,&*&F<F+,&FDF)F1F+F+F+*&F>F+FDF+F)F+FCF+F+*(,&F<F+F>
#F+F2F+F<F+F1F+F,F+F.F+F+*&,*FMF+*(FPF+F>F+F9F2F)*(F>F+FDF+F9F+F+*&F1F
+FDF+F+F+F(F2F+*&,,*&,&*&,&FCF,F>F2F+F9F+F+FDF2F+F;F2F+*&,**(FPF+,(FCF
+F<F2F>F+F+F9F+F+*&,&FDF,F1F`pF+FCF+F+*&F<F+FDF+F)*&F>F+,&FDF+F1F`pF+F
)F+F;F+F+*&,&*&FCF2F<F+F)*&F<F+F>F2F+F+F9F+F+*&,&*&FHF+F<F+F+FepF+F+FC
F+F+*(F1F+F>F+,&F<F+F>F2F+F)F+F(F+F+**F:F+,&FCF)F;F+F+FPF+FBF+F2F+F*F+
F+*&,&*&,,F[pF)*(F9F+,&*&,&FCF+F<F+F+F9F+F+F1F)F+F;F+F+*(F9F2FCF+F<F+F
)*(F1F+F<F+F9F+F+FdoF+F+F(F+F+*&FaoF+,**&F@F+F;F+F+*(FCF+FBF+F9F+F)*&F
CF+FDF+F)*&F<F+F1F+F)F+F+F+F.F2F+*&,(*&,,F[pF)*(F9F+,&*&,&FCF+F>F+F+F9
F+F+F1F)F+F;F+F+*(F9F2FCF+F>F+F)*(F1F+F>F+F9F+F+FerF)F+F(F2F+*&,,*(F9F
+,(FCF+F<F=F>F=F+F;F2F2*&,**&,&*$FCF2F,*&F<F+F>F+F2F+F9F+F+*&FCF+F1F+F
+FbsF+FdqF)F+F;F+F+*(,&FhnF+FjnF,F+FCF+F9F+F+*&,&*&,&FDF)F1F)F+F<F+F+F
]rF+F+FCF+F+*(F>F+F<F+F1F+F+F+F(F+F+**FBF+FaoF+F_tF+FPF+F)F+F.F+F+*(F(
F+,&*&,**&,&*&,&FCF)F>F+F+F9F+F+FDF+F+F;F+F+*(FCF+FPF+F9F+F+*&FjvF+FCF
+F+*&F>F+F1F+F+F+F(F+F+*(FPF+FBF+F_tF+F+F+FhoF+F)F+F`r" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 281 39 "Loading the purely time-dependent terms"
 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "F22:=unapply(0,tt11, tt2
1, tt31, tt12, tt22, tt32);\n" }{MPLTEXT 1 0 52 "F11:=unapply(0,tt11, \+
tt21, tt31, tt12, tt22, tt32);\n" }{MPLTEXT 1 0 131 "F31:=unapply(h/2*
tt21* (-1/(tt22-tt32)-ln(tt22-tt32)/(tt12-tt32)+ln(tt12-tt22)/(tt12-tt
32)),tt11, tt21, tt31, tt12, tt22, tt32);  \n" }{MPLTEXT 1 0 124 "F12:
=unapply( h/2*tt21*tt31*(ln(tt22-tt32)/(tt12-tt32)^2-ln(tt12-tt22)/(tt
12-tt32)^2),tt11, tt21, tt31, tt12, tt22, tt32 );\n" }{MPLTEXT 1 0 
111 "F32:=unapply(h*tt21*tt31/2*((ln(tt12-tt22)-ln(tt22-tt32))/(tt12-t
t32)^2),tt11, tt21, tt31, tt12, tt22, tt32) ;\n" }{MPLTEXT 1 0 92 "F21
:=unapply(h*tt31/2* (1/(tt22-tt32) +ln(tt12-tt22)/(tt12-tt32)-ln(tt22-
tt32)/(tt12-tt32))\n" }{MPLTEXT 1 0 38 ", tt11, tt21, tt31, tt12, tt22
, tt32);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$F22G6
\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%tt22GF$I%tt32GF$F$6$I)oper
atorGF$I&arrowGF$F$\"\"!F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$F11
G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%tt22GF$I%tt32GF$F$6$I)op
eratorGF$I&arrowGF$F$\"\"!F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$F
31G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%tt22GF$I%tt32GF$F$6$I)
operatorGF$I&arrowGF$F$,$*(I\"hGF$\"\"\"9%F3,(*$,&9(F39)!\"\"F:F:*&-I#
lnG6$%*protectedGI(_syslibGF$6#F7F3,&9'F3F9F:F:F:*&-F=6#,&FCF3F8F:F3FB
F:F3F3#F3\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$F12G6\"f*6(I%
tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%tt22GF$I%tt32GF$F$6$I)operatorGF$I
&arrowGF$F$,$**I\"hGF$\"\"\"9%F39&F3,&*&-I#lnG6$%*protectedGI(_syslibG
F$6#,&9(F39)!\"\"F3,&9'F3F@FA!\"#F3*&-F96#,&FCF3F?FAF3FBFDFAF3#F3\"\"#
F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$F32G6\"f*6(I%tt11GF$I%tt21G
F$I%tt31GF$I%tt12GF$I%tt22GF$I%tt32GF$F$6$I)operatorGF$I&arrowGF$F$,$*
,I\"hGF$\"\"\"9%F39&F3,&-I#lnG6$%*protectedGI(_syslibGF$6#,&9'F39(!\"
\"F3-F86#,&F?F39)F@F@F3,&F>F3FDF@!\"##F3\"\"#F$F$F$" }}{PARA 11 "" 1 "
" {XPPMATH 20 ">I$F21G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%tt2
2GF$I%tt32GF$F$6$I)operatorGF$I&arrowGF$F$,$*(I\"hGF$\"\"\"9&F3,(*$,&9
(F39)!\"\"F:F3*&-I#lnG6$%*protectedGI(_syslibGF$6#,&9'F3F8F:F3,&FCF3F9
F:F:F3*&-F=6#F7F3FDF:F:F3#F3\"\"#F$F$F$" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 282 52 "Loading the Hamiltonians in the canonical directions" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 347 "Hame11 := unapply( (-p^3+(
(t12+t22+t32)*q+t11+t21+t31)*p^2+(((-t22-t32)*t12-t22*t32)*q^2+((-t31-
t21)*t12+(-t11-t31)*t22-t32*(t11+t21))*q+t12*(-t20-t30)+t22*t20+t32*t3
0+(-t31-t21)*t11-t21*t31)*p+q*(q^2*t12*t22*t32+((t22*t31+t32*t21)*t12+
t22*t32*t11)*q+(t22*t30+t32*t20+t21*t31)*t12+((-t20-t30)*t32+t11*t31)*
t22+t32*t11*t21))/((t12-t32)*(t12-t22)) \n" }{MPLTEXT 1 0 1 "+" }
{MPLTEXT 1 0 87 "(((t20+t30)*t12+t31*t11-t20*t32-t30*t32)*t21-t11*t20*
(-t32+t22))/((-t22+t12)*(t12-t32))" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 30 "+F11(t11,t21,t31,t12,t22,t32)\n" }{MPLTEXT 1 0 7 ",q,p);\n" }
{MPLTEXT 1 0 353 "Hame21:= unapply( (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*(t
11+t21))*q+(h-t20)*t22+(t30-h+t20)*t12-t32*t30+t11*(t21+t31)+t21*t31)*
p-q*(q^2*t12*t22*t32+((t12*t31+t32*t11)*t22+t12*t32*t21)*q+(t12*t30+(-
t30+h-t20)*t32+t11*t31)*t22+((-h+t20)*t32+t21*t31)*t12+t32*t11*t21))/(
(t22-t32)*(t12-t22))\n" }{MPLTEXT 1 0 91 "+(((-t12+t32)*t20-t31*t11-t1
2*t30+t30*t32)*t21+t11*t20*(-t32+t22))/((-t22+t12)*(-t32+t22))\n" }
{MPLTEXT 1 0 29 "+F21(t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 7 ",q,p);\n" }{MPLTEXT 1 0 357 "Hame31:=unapply((-p^3+(t1
1+t21+t31+(t12+t22+t32)*q)*p^2+(((-t12-t22)*t32-t12*t22)*q^2+((-t21-t1
1)*t32+(-t31-t21)*t12-t22*(t11+t31))*q+(-h+t30)*t32+(-t30+h-t20)*t12+t
22*t20+(-t31-t21)*t11-t21*t31)*p+q*(t12*t22*t32*q^2+((t12*t21+t22*t11)
*t32+t31*t12*t22)*q+(t12*t20+(-t30+h-t20)*t22+t11*t21)*t32+((-h+t30)*t
22+t21*t31)*t12+t22*t11*t31))/((t22-t32)*(t12-t32))\n" }{MPLTEXT 1 0 
90 "+(((-t20-t30)*t32+t31*t11+t12*t20+t12*t30)*t21-t11*t20*(-t32+t22))
/((t12-t32)*(-t32+t22))\n" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 28 "F31(t
11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 ",q,p);
\n" }{MPLTEXT 1 0 1771 "Hame12:=unapply(((t32*t22*(t21+t31-2*t11)*q^3+
(-(t22+t32)*(t21+t31-2*t11)*p+(-h*t32+t31*(t21+t31-2*t11))*t22+t32*t21
*(t21+t31-2*t11))*q^2+((t21+t31-2*t11)*p^2+(h*t22+h*t32-(t21+t31)*(t21
+t31-2*t11))*p+(-2*t30*t11+t21*t30+(-h+t30)*t31)*t22+(-2*t11*t20+(-h+t
20)*t21+t31*t20)*t32+t31*t21*(t21+t31-2*t11))*q-(p*h+(-2*t30-2*t20)*t1
1+(t21+t31)*(t30-h+t20))*p)*t12^2+(-((-t11+t31)*t22-t32*(t11-t21))*t32
*t22*q^3+(((-t11+t31)*t22^2-t32^2*(t11-t21))*p+(h*t32-t31*(-t11+t31))*
t22^2+(2*((1/2)*h*t32+(t11-t21)*(-t11+t31)))*t32*t22+t21*t32^2*(t11-t2
1))*q^2+(((-t11+t21)*t22+t32*(-t11+t31))*p^2+(-h*t22^2+(-2*h*t32+2*t11
*(t11-t21))*t22-h*t32^2-2*t11*(-t11+t31)*t32)*p+(t30*t11-(-h+t30)*t31)
*t22^2+(((3*t20+3*t30)*t11+(h-t20-2*t30)*t21-(-h+2*t20+t30)*t31)*t32+t
31*(t11-t21)*(-2*t11+t31))*t22+(2*(((1/2)*t11*t20+(1/2)*(h-t20)*t21)*t
32+(-t11+t31)*t21*(-(1/2)*t21+t11)))*t32)*q-p*((t21+t31-2*t11)*p^2+(-h
*t22-h*t32-(t11+t21+t31)*(t21+t31-2*t11))*p+((3*t20+t30)*t11+(h-t20)*t
21-(-h+2*t20+t30)*t31)*t22+(t11*(t20+3*t30)+(h-t20-2*t30)*t21-(-h+t30)
*t31)*t32+(t21+t31-2*t11)*(t11*(t21+t31)+t21*t31)))*t12+t32*(((-t11+t3
1)*t22-t32*(t11-t21))*p+(-h*t32-t11*(-t11+t31))*t22+t32*t11*(t11-t21))
*t22*q^2+(-((-t11+t31)*t22-t32*(t11-t21))*(t22+t32)*p^2+((t32*h-t11^2+
t31^2)*t22^2+(h*t32^2+(-2*t11^2+2*t21*t31)*t32)*t22+(-t11^2+t21^2)*t32
^2)*p+(((-t20-t30)*t11+(t30-h+t20)*t31)*t32-t11*t31*(-t11+t31))*t22^2-
t32*((t11*(t20+t30)-(t30-h+t20)*t21)*t32-(t11*(t21+t31)-2*t21*t31)*t11
)*t22+t32^2*t11*t21*(t11-t21))*q+p*(((-t11+t31)*t22-t32*(t11-t21))*p^2
+((-h*t32-(-t11+t31)*(t11+t21+t31))*t22+t32*(t11-t21)*(t11+t21+t31))*p
-t20*(-t11+t31)*t22^2+((t11*(t20+t30)+(h-t20)*t21-(-h+t30)*t31)*t32+(-
t11+t31)*(t11*(t21+t31)+t21*t31))*t22+t32*((-t31-t21)*t11+t32*t30-t21*
t31)*(t11-t21)))/(2*(t12-t32)^2*(t12-t22)^2)\n" }{MPLTEXT 1 0 182 "+((
-(1/2)*t12+(1/2)*t32)*t21+(t11-(1/2)*t31)*t12+(-(1/2)*t22-(1/2)*t32)*t
11+(1/2)*t22*t31)*(((-t20-t30)*t12-t31*t11+(t20+t30)*t32)*t21+t11*t20*
(-t32+t22))/((t12-t32)^2*(-t22+t12)^2)\n" }{MPLTEXT 1 0 1 "+" }
{MPLTEXT 1 0 28 "F12(t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 7 ",q,p);\n" }{MPLTEXT 1 0 1759 "Hame22:=unapply( ((t12*t
32*(t11-2*t21+t31)*q^3+(-(t12+t32)*(t11-2*t21+t31)*p+(-h*t12+t11*(t11-
2*t21+t31))*t32+t12*t31*(t11-2*t21+t31))*q^2+((t11-2*t21+t31)*p^2+(h*t
32+h*t12-(t11+t31)*(t11-2*t21+t31))*p+((2*t30-2*h+2*t20)*t21+(-t30+h-t
20)*t31-t11*(t20+t30))*t32+(-2*t21*t30+(-h+t30)*t31+t30*t11)*t12+t11*t
31*(t11-2*t21+t31))*q-(p*h+(-2*h+2*t20)*t21-t20*(t11+t31))*p)*t22^2+(-
t12*t32*(t32*(t11-t21)+t12*(-t21+t31))*q^3+((t32^2*(t11-t21)+t12^2*(-t
21+t31))*p+(h*t12-t11*(t11-t21))*t32^2-2*t12*(-(1/2)*h*t12+(t11-t21)*(
-t21+t31))*t32-t31*(-t21+t31)*t12^2)*q^2+(((-t21+t31)*t32+t12*(t11-t21
))*p^2+(-h*t32^2+(-2*h*t12-2*t21*(-t21+t31))*t32-t12*(h*t12+2*t21*(t11
-t21)))*p+((-t30+h-t20)*t21+t11*(t20+t30))*t32^2+(((3*h-3*t20)*t21+(-h
+2*t20+t30)*t31-(-t20+t30)*t11)*t12-t11*(-2*t21+t11)*(-t21+t31))*t32-t
12*((-t21*t30+(-h+t30)*t31)*t12+t31*(t11-t21)*(t31-2*t21)))*q-((t11-2*
t21+t31)*p^2+(-h*t32-h*t12-(t11+t21+t31)*(t11-2*t21+t31))*p+((2*t30+h-
t20)*t21+(h-t30)*t31-(-t20+t30)*t11)*t32+((-2*t30+3*h-3*t20)*t21+(-h+2
*t20+t30)*t31+t11*(t20+t30))*t12+(t11-2*t21+t31)*((t11+t31)*t21+t11*t3
1))*p)*t22+t12*((t32*(t11-t21)+t12*(-t21+t31))*p+(-h*t12-t21*(t11-t21)
)*t32-t12*t21*(-t21+t31))*t32*q^2+(-(t12+t32)*(t32*(t11-t21)+t12*(-t21
+t31))*p^2+((t12*h+t11^2-t21^2)*t32^2+(h*t12^2+(2*t11*t31-2*t21^2)*t12
)*t32+t12^2*(-t21^2+t31^2))*p+(((-h+t20)*t21-t11*t20)*t12-t11*t21*(t11
-t21))*t32^2-t12*(((h-t20)*t21+t31*t20)*t12+(-t11-t31)*t21^2+2*t11*t21
*t31)*t32-t31*t12^2*t21*(-t21+t31))*q+((t32*(t11-t21)+t12*(-t21+t31))*
p^2+((-h*t12-(t11-t21)*(t11+t21+t31))*t32-t12*(-t21+t31)*(t11+t21+t31)
)*p-t30*(t11-t21)*t32^2+(((h-t20)*t21+(h-t30)*t31+t11*(t20+t30))*t12+(
t11-t21)*((t11+t31)*t21+t11*t31))*t32+t12*((t30-h+t20)*t12+(t11+t31)*t
21+t11*t31)*(-t21+t31))*p)/(2*(t22-t32)^2*(t12-t22)^2)\n" }{MPLTEXT 1 
0 139 "-((-t31*t11-(t20+t30)*(t12-t32))*t21+t11*t20*(-t32+t22))*((t12-
2*t22+t32)*t21+(t11+t31)*t22-t11*t32-t12*t31)/(2*(-t32+t22)^2*(-t22+t1
2)^2)\n" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 28 "F22(t11,t21,t31,t12,t22
,t32)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 ",q,p);\n" }{MPLTEXT 1 0 
1977 "Hame32:=unapply(  ((-(2*(t31-(1/2)*t11-(1/2)*t21))*t12*t22*q^3+(
(2*(t31-(1/2)*t11-(1/2)*t21))*(t12+t22)*p+(-h*t12-(2*(t31-(1/2)*t11-(1
/2)*t21))*t11)*t22-(2*(t31-(1/2)*t11-(1/2)*t21))*t12*t21)*q^2+((t11+t2
1-2*t31)*p^2+(h*t22+h*t12+(2*(t31-(1/2)*t11-(1/2)*t21))*(t11+t21))*p+(
(2*t30-2*h+2*t20)*t31+(-t30+h-t20)*t21-t11*(t20+t30))*t22+(-2*t31*t20+
(-h+t20)*t21+t11*t20)*t12-2*t21*(t31-(1/2)*t11-(1/2)*t21)*t11)*q-p*(p*
h+(2*t30-2*h)*t31-t30*(t11+t21)))*t32^2+(t12*((-t11+t31)*t22+t12*(-t21
+t31))*t22*q^3+(((t11-t31)*t22^2-t12^2*(-t21+t31))*p+(h*t12+t11*(-t11+
t31))*t22^2-2*t12*(-(1/2)*h*t12+(-t21+t31)*(-t11+t31))*t22+t21*t12^2*(
-t21+t31))*q^2+(((t21-t31)*t22-t12*(-t11+t31))*p^2+(-h*t22^2+(-2*h*t12
+2*t31*(-t21+t31))*t22-h*t12^2+2*t31*(-t11+t31)*t12)*p+((-t30+h-t20)*t
31+t11*(t20+t30))*t22^2+(((-3*t30+3*h)*t31+(-h+t20+2*t30)*t21+(-t20+t3
0)*t11)*t12-(2*(-t21+t31))*(-(1/2)*t11+t31)*t11)*t22-2*t12*((-(1/2)*t3
1*t20-(1/2)*(h-t20)*t21)*t12+(-t11+t31)*t21*(t31-(1/2)*t21)))*q+(2*((t
31-(1/2)*t11-(1/2)*t21)*p^2+((1/2)*h*t22+(1/2)*h*t12-(t31-(1/2)*t11-(1
/2)*t21)*(t11+t21+t31))*p+((-(1/2)*h-t20+(1/2)*t30)*t31+t21*((1/2)*t20
-(1/2)*h)-(1/2)*(-t20+t30)*t11)*t22+((t20+3*t30*(1/2)-3*h*(1/2))*t31+(
-t30+(1/2)*h-(1/2)*t20)*t21-(1/2)*t11*(t20+t30))*t12+(t31-(1/2)*t11-(1
/2)*t21)*((t11+t21)*t31+t11*t21)))*p)*t32-t12*t22*(((-t11+t31)*t22+t12
*(-t21+t31))*p+(h*t12-t31*(-t11+t31))*t22-t12*t31*(-t21+t31))*q^2+((t1
2+t22)*((-t11+t31)*t22+t12*(-t21+t31))*p^2+((t12*h+t11^2-t31^2)*t22^2+
(h*t12^2+(2*t11*t21-2*t31^2)*t12)*t22+(t21^2-t31^2)*t12^2)*p+(((-h+t30
)*t31-t30*t11)*t12+t11*t31*(-t11+t31))*t22^2+((-t21*t30+(-h+t30)*t31)*
t12+t31*((t11+t21)*t31-2*t11*t21))*t12*t22+t31*t12^2*t21*(-t21+t31))*q
-(((-t11+t31)*t22+t12*(-t21+t31))*p^2+((h*t12-(-t11+t31)*(t11+t21+t31)
)*t22-t12*(-t21+t31)*(t11+t21+t31))*p-t20*(-t11+t31)*t22^2+(((-h+t30)*
t31+(-h+t20)*t21-t11*(t20+t30))*t12+(-t11+t31)*((t11+t21)*t31+t11*t21)
)*t22+t12*((t30-h+t20)*t12+(t11+t21)*t31+t11*t21)*(-t21+t31))*p)/(2*(t
22-t32)^2*(t12-t32)^2)\n" }{MPLTEXT 1 0 149 "+(((t20+t30)*t32-t31*t11-
(t20+t30)*t12)*t21+t11*t20*(-t32+t22))*((t12-t32)*t21+(-t11+2*t31)*t32
+(-t12-t22)*t31+t11*t22)/(2*(-t32+t22)^2*(t12-t32)^2)\n" }{MPLTEXT 1 
0 1 "+" }{MPLTEXT 1 0 28 "F32(t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 
1 "\n" }{MPLTEXT 1 0 6 ",q,p);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I'Hame11G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF
$F$,&*(,**$9%\"\"$!\"\"*&,**&,(I$t12GF$\"\"\"I$t22GF$F8I$t32GF$F8F89$F
8F8I$t11GF$F8I$t21GF$F8I$t31GF$F8F8F0\"\"#F8*&,0*&,&*&,&F9F2F:F2F8F7F8
F8*&F9F8F:F8F2F8F;F?F8*&,(*&,&F>F2F=F2F8F7F8F8*&,&F<F2F>F2F8F9F8F8*&F:
F8,&F<F8F=F8F8F2F8F;F8F8*&,&I$t20GF$F2I$t30GF$F2F8F7F8F8*&FQF8F9F8F8*&
FRF8F:F8F8*&FJF8F<F8F8*&F=F8F>F8F2F8F0F8F8*&F;F8,,**F;F?F7F8F9F8F:F8F8
*&,&*&,&*&F=F8F:F8F8*&F9F8F>F8F8F8F7F8F8*(F9F8F:F8F<F8F8F8F;F8F8*&,(*&
FQF8F:F8F8FVF8*&F9F8FRF8F8F8F7F8F8*&,&*&FPF8F:F8F8*&F>F8F<F8F8F8F9F8F8
*(F:F8F<F8F=F8F8F8F8F8,&F9F2F7F8F2,&F7F8F:F2F2F8*(,&*&,**&,&FQF8FRF8F8
F7F8F8FboF8*&F:F8FQF8F2FTF2F8F=F8F8*(F<F8FQF8,&F:F2F9F8F8F2F8FdoF2FeoF
2F8F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame21G6\"f*6$I\"qGF$I\"
pGF$F$6$I)operatorGF$I&arrowGF$F$,(*(,**$9%\"\"$\"\"\"*&,**&,(I$t12GF$
!\"\"I$t22GF$F8I$t32GF$F8F29$F2F2I$t31GF$F8I$t11GF$F8I$t21GF$F8F2F0\"
\"#F2*&,0*&,&*&,&F7F2F:F2F2F9F2F2*&F7F2F:F2F2F2F;F?F2*&,(*&,&F>F2F<F2F
2F7F2F2*&,&F=F2F<F2F2F9F2F2*&F:F2,&F=F2F>F2F2F2F2F;F2F2*&,&I\"hGF$F2I$
t20GF$F8F2F9F2F2*&,(I$t30GF$F2FQF8FRF2F2F7F2F2*&FUF2F:F2F8*&F=F2FJF2F2
*&F>F2F<F2F2F2F0F2F2*&F;F2,,**F;F?F7F2F9F2F:F2F2*&,&*&,&*&F=F2F:F2F2*&
F7F2F<F2F2F2F9F2F2*(F7F2F:F2F>F2F2F2F;F2F2*&,(*&F7F2FUF2F2*&,(FRF8FUF8
FQF2F2F:F2F2*&F<F2F=F2F2F2F9F2F2*&,&*&,&FQF8FRF2F2F:F2F2FXF2F2F7F2F2*(
F:F2F=F2F>F2F2F2F8F2,&F9F8F7F2F8,&F:F8F9F2F8F2*(,&*&,**&,&F7F8F:F2F2FR
F2F2FboF8F_oF8FVF2F2F>F2F2*(F=F2FRF2FioF2F2F2FhoF8FioF8F2*(FQF2F<F2,(*
$FioF8F2*&-I#lnG6$%*protectedGI(_syslibGF$6#FhoF2,&F7F2F:F8F8F2*&-Ffp6
#FioF2F[qF8F8F2#F2F?F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame31G
6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,(*(,**$9%\"\"$!\"\"
*&,**&,(I$t12GF$\"\"\"I$t22GF$F8I$t32GF$F8F89$F8F8I$t11GF$F8I$t21GF$F8
I$t31GF$F8F8F0\"\"#F8*&,0*&,&*&,&F7F2F9F2F8F:F8F8*&F7F8F9F8F2F8F;F?F8*
&,(*&,&F=F2F<F2F8F:F8F8*&,&F>F2F=F2F8F7F8F8*&,&F<F8F>F8F8F9F8F2F8F;F8F
8*&,&I\"hGF$F2I$t30GF$F8F8F:F8F8*&,(I$t20GF$F2FRF2FQF8F8F7F8F8*&FUF8F9
F8F8*&FLF8F<F8F8*&F=F8F>F8F2F8F0F8F8*&F;F8,,**F;F?F7F8F9F8F:F8F8*&,&*&
,&*&F<F8F9F8F8*&F7F8F=F8F8F8F:F8F8*(F7F8F9F8F>F8F8F8F;F8F8*&,(*&F7F8FU
F8F8*&FTF8F9F8F8*&F=F8F<F8F8F8F:F8F8*&,&*&FPF8F9F8F8FXF8F8F7F8F8*(F9F8
F<F8F>F8F8F8F8F8,&F:F2F9F8F2,&F7F8F:F2F2F8*(,&*&,**&,&FUF2FRF2F8F:F8F8
*&F>F8F<F8F8F_oF8*&F7F8FRF8F8F8F=F8F8*(F<F8FUF8FfoF8F2F8FfoF2FgoF2F8*(
FQF8F=F8,(*$FfoF2F2*&-I#lnG6$%*protectedGI(_syslibGF$6#FfoF8FgoF2F2*&-
Ffp6#,&F9F2F7F8F8FgoF2F8F8#F8F?F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 
">I'Hame12G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,(*(,,*&,
***I$t32GF$\"\"\"I$t22GF$F3,(I$t31GF$F3I$t11GF$!\"#I$t21GF$F3F39$\"\"$
F3*&,(*(,&F4F3F2F3F3F5F39%F3!\"\"*&,&*&I\"hGF$F3F2F3FA*&F6F3F5F3F3F3F4
F3F3*(F2F3F9F3F5F3F3F3F:\"\"#F3*&,,*&F5F3F@FHF3*&,(*&FEF3F4F3F3FDF3*&,
&F9F3F6F3F3F5F3FAF3F@F3F3*&,(*&F7F3I$t30GF$F3F8*&F9F3FTF3F3*&,&FEFAFTF
3F3F6F3F3F3F4F3F3*&,(*&F7F3I$t20GF$F3F8*&,&FEFAFenF3F3F9F3F3*&FenF3F6F
3F3F3F2F3F3*(F6F3F9F3F5F3F3F3F:F3F3*&,(*&F@F3FEF3F3*&,&FTF8FenF8F3F7F3
F3*&FPF3,(FTF3FEFAFenF3F3F3F3F@F3FAF3I$t12GF$FHF3*&,***,&*&,&F6F3F7FAF
3F4F3F3*&F2F3,&F7F3F9FAF3FAF3F2F3F4F3F:F;FA*&,**&,&*&FgoF3F4FHF3*&F2FH
FioF3FAF3F@F3F3*&,&FDF3*&F6F3FgoF3FAF3F4FHF3*(,&FD#F3FH*&FioF3FgoF3F3F
3F2F3F4F3FH*(F9F3F2FHFioF3F3F3F:FHF3*&,,*&,&*&,&F7FAF9F3F3F4F3F3*&F2F3
FgoF3F3F3F@FHF3*&,**&FEF3F4FHFA*&,&FDF8*&F7F3FioF3FHF3F4F3F3*&FEF3F2FH
FA*(F7F3FgoF3F2F3F8F3F@F3F3*&,&FSF3FVFAF3F4FHF3*&,&*&,(*&,&FenF;FTF;F3
F7F3F3*&,(FEF3FenFAFTF8F3F9F3F3*&,(FEFAFenFHFTF3F3F6F3FAF3F2F3F3*(F6F3
FioF3,&F7F8F6F3F3F3F3F4F3F3*&,&*&,&FZFep*&,&FEF3FenFAF3F9F3FepF3F2F3F3
*(FgoF3F9F3,&F9#FAFHF7F3F3F3F3F2F3FHF3F:F3F3*&F@F3,,FKF3*&,(FNFAFDFA*&
,(F7F3F9F3F6F3F3F5F3FAF3F@F3F3*&,(*&,&FTF3FenF;F3F7F3F3FirF3FarFAF3F4F
3F3*&,(*&F7F3,&FenF3FTF;F3F3F_rF3FVFAF3F2F3F3*&F5F3,&*&F7F3FPF3F3*&F9F
3F6F3F3F3F3F3FAF3FaoF3F3**F2F3,(*&FeoF3F@F3F3*&,&FDFA*&F7F3FgoF3FAF3F4
F3F3*(F2F3F7F3FioF3F3F3F4F3F:FHF3*&,,*(FeoF3F?F3F@FHFA*&,(*&,(FDF3*$F7
FHFA*$F6FHF3F3F4FHF3*&,&FeqF3*&,&F^uF8F_tFHF3F2F3F3F3F4F3F3*&,&F^uFA*$
F9FHF3F3F2FHF3F3F@F3F3*&,&*&,&*&,&FenFAFTFAF3F7F3F3*&F`oF3F6F3F3F3F2F3
F3*(F7F3F6F3FgoF3FAF3F4FHF3*(F2F3,&*&,&*&,&FenF3FTF3F3F7F3F3*&F`oF3F9F
3FAF3F2F3F3*&,&F^tF3F_tF8F3F7F3FAF3F4F3FA**F2FHF7F3F9F3FioF3F3F3F:F3F3
*&F@F3,,*&FeoF3F@FHF3*&,&*&,&FDFA*&FgoF3FcsF3FAF3F4F3F3*(F2F3FioF3FcsF
3F3F3F@F3F3*(FenF3FgoF3F4FHFA*&,&*&,(FcvF3FirF3FVFAF3F2F3F3*&FgoF3F]tF
3F3F3F4F3F3*(F2F3,(*&,&F6FAF9FAF3F7F3F3*&FTF3F2F3F3F_tFAF3FioF3F3F3F3F
3,&FaoF3F2FAF8,&F4FAFaoF3F8Fep**,**&,&FaoF]sF2FepF3F9F3F3*&,&F7F3F6F]s
F3FaoF3F3*&,&F4F]sF2F]sF3F7F3F3*&F4F3F6F3FepF3,&*&,(*&F\\vF3FaoF3F3*&F
6F3F7F3FA*&FdvF3F2F3F3F3F9F3F3*(F7F3FenF3,&F2FAF4F3F3F3F3F]xF8F^xF8F3*
*FEF3F9F3F6F3,&*&-I#lnG6$%*protectedGI(_syslibGF$6#F_yF3F]xF8F3*&-Fdy6
#F^xF3F]xF8FAF3FepF$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame22G6
\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,&*(,,*&,***I$t12GF$
\"\"\"I$t32GF$F3,(I$t31GF$F3I$t11GF$F3I$t21GF$!\"#F39$\"\"$F3*&,(*(,&F
2F3F4F3F3F5F39%F3!\"\"*&,&*&I\"hGF$F3F2F3FA*&F7F3F5F3F3F3F4F3F3*(F2F3F
6F3F5F3F3F3F:\"\"#F3*&,,*&F5F3F@FHF3*&,(*&FEF3F4F3F3FDF3*&,&F7F3F6F3F3
F5F3FAF3F@F3F3*&,(*&,(I$t30GF$FHFEF9I$t20GF$FHF3F8F3F3*&,(FVFAFUFAFEF3
F3F6F3F3*&,&FVF3FUF3F3F7F3FAF3F4F3F3*&,(*&F8F3FUF3F9*&,&FEFAFUF3F3F6F3
F3*&F7F3FUF3F3F3F2F3F3*(F7F3F6F3F5F3F3F3F:F3F3*&,(*&F@F3FEF3F3*&,&FEF9
FVFHF3F8F3F3*&FVF3FPF3FAF3F@F3FAF3I$t22GF$FHF3*&,***F2F3F4F3,&*&F4F3,&
F7F3F8FAF3F3*&F2F3,&F8FAF6F3F3F3F3F:F;FA*&,**&,&*&F4FHFhoF3F3*&F2FHFjo
F3F3F3F@F3F3*&,&FDF3*&F7F3FhoF3FAF3F4FHF3*(F2F3,&FD#FAFH*&FhoF3FjoF3F3
F3F4F3F9*(F6F3FjoF3F2FHFAF3F:FHF3*&,,*&,&*&FjoF3F4F3F3*&F2F3FhoF3F3F3F
@FHF3*&,(*&FEF3F4FHFA*&,&FDF9*&F8F3FjoF3F9F3F4F3F3*&F2F3,&FDF3*&F8F3Fh
oF3FHF3FAF3F@F3F3*&,&*&FXF3F8F3F3FYF3F3F4FHF3*&,&*&,(*&,&FEF;FV!\"$F3F
8F3F3*&,(FEFAFVFHFUF3F3F6F3F3*&F7F3,&FVFAFUF3F3FAF3F2F3F3*(F7F3,&F8F9F
7F3F3FjoF3FAF3F4F3F3*&F2F3,&*&,&FgnFAFhnF3F3F2F3F3*(F6F3FhoF3,&F6F3F8F
9F3F3F3FAF3F:F3F3*&,,FKF3*&,(FNFAFDFA*&,(F7F3F8F3F6F3F3F5F3FAF3F@F3F3*
&,(*&,(FUFHFEF3FVFAF3F8F3F3*&,&FEF3FUFAF3F6F3F3FdrFAF3F4F3F3*&,(*&,(FU
F9FEF;FVFarF3F8F3F3FbrF3FYF3F3F2F3F3*&F5F3,&*&FPF3F8F3F3*&F6F3F7F3F3F3
F3F3F@F3FAF3FboF3F3**F2F3,(*&FfoF3F@F3F3*&,&FDFAFgqFAF3F4F3F3*(F2F3F8F
3FjoF3FAF3F4F3F:FHF3*&,,*(F?F3FfoF3F@FHFA*&,(*&,(FDF3*$F7FHF3*$F8FHFAF
3F4FHF3*&,&*&FEF3F2FHF3*&,&*&F7F3F6F3FHF`uF9F3F2F3F3F3F4F3F3*&F2FH,&F`
uFA*$F6FHF3F3F3F3F@F3F3*&,&*&,&*&,&FEFAFVF3F3F8F3F3*&F7F3FVF3FAF3F2F3F
3*(F7F3F8F3FhoF3FAF3F4FHF3*(F2F3,(*&,&*&,&FEF3FVFAF3F8F3F3*&FVF3F6F3F3
F3F2F3F3*&,&F7FAF6FAF3F8FHF3*(F7F3F8F3F6F3FHF3F4F3FA**F6F3F2FHF8F3FjoF
3FAF3F:F3F3*&,,*&FfoF3F@FHF3*&,&*&,&FDFA*&FhoF3FcsF3FAF3F4F3F3*(F2F3Fj
oF3FcsF3FAF3F@F3F3*(FUF3FhoF3F4FHFA*&,&*&,(FfvF3FhsF3FYF3F3F2F3F3*&Fho
F3F_tF3F3F3F4F3F3*(F2F3,(*&,(FUF3FEFAFVF3F3F2F3F3F`tF3FatF3F3FjoF3F3F3
F@F3F3F3,&F4FAFboF3F9,&FboFAF2F3F9#F3FH**,&*&,&FatFA*&FZF3,&F2F3F4FAF3
FAF3F8F3F3*(F7F3FVF3F`xF3F3F3,**&,(F2F3FboF9F4F3F3F8F3F3*&FPF3FboF3F3*
&F4F3F7F3FA*&F2F3F6F3FAF3F`xF9FaxF9FfpF$F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I'Hame32G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF
$F$,(*(,,*&,***,(I$t31GF$\"\"\"I$t11GF$#!\"\"\"\"#I$t21GF$F6F4I$t12GF$
F4I$t22GF$F49$\"\"$!\"#*&,(*(F2F4,&F:F4F;F4F49%F4F8*&,&*&I\"hGF$F4F:F4
F7*&F2F4F5F4F>F4F;F4F4*(F2F4F:F4F9F4F>F4F<F8F4*&,,*&,(F5F4F9F4F3F>F4FC
F8F4*&,(*&FGF4F;F4F4FFF4*&F2F4,&F5F4F9F4F4F8F4FCF4F4*&,(*&,(I$t30GF$F8
FGF>I$t20GF$F8F4F3F4F4*&,(FXF7FWF7FGF4F4F9F4F4*&,&FXF4FWF4F4F5F4F7F4F;
F4F4*&,(*&FXF4F3F4F>*&,&FGF7FXF4F4F9F4F4*&F5F4FXF4F4F4F:F4F4*(F9F4F2F4
F5F4F>F4F<F4F4*&FCF4,(*&FCF4FGF4F4*&,&FWF8FGF>F4F3F4F4*&FWF4FRF4F7F4F7
F4I$t32GF$F8F4*&,***F:F4,&*&,&F3F4F5F7F4F;F4F4*&F:F4,&F9F7F3F4F4F4F4F;
F4F<F=F4*&,**&,&*&,&F5F4F3F7F4F;F8F4*&F:F8F\\pF4F7F4FCF4F4*&,&FFF4*&F5
F4FjoF4F4F4F;F8F4*(F:F4,&FFF6*&F\\pF4FjoF4F4F4F;F4F>*(F9F4F:F8F\\pF4F4
F4F<F8F4*&,,*&,&*&,&F9F4F3F7F4F;F4F4*&F:F4FjoF4F7F4FCF8F4*&,**&FGF4F;F
8F7*&,&FFF>*&F3F4F\\pF4F8F4F;F4F4*&FGF4F:F8F7*(F3F4FjoF4F:F4F8F4FCF4F4
*&,&*&FZF4F3F4F4FenF4F4F;F8F4*&,&*&,(*&,&FW!\"$FGF=F4F3F4F4*&,(FGF7FXF
4FWF8F4F9F4F4*&F5F4,&FXF7FWF4F4F4F4F:F4F4*(F\\pF4,&F5F6F3F4F4F5F4F>F4F
;F4F4*&F:F4,&*&,&FinF6*&,&FGF4FXF7F4F9F4F6F4F:F4F4*(FjoF4F9F4,&F3F4F9F
6F4F4F4F>F4F<F4F4*&,,*&F2F4FCF8F4*&,(FP#F4F8FFFgs*&F2F4,(F5F4F9F4F3F4F
4F7F4FCF4F4*&,(*&,(FGF6FXF7FWFgsF4F3F4F4*&F9F4,&FXFgsFGF6F4F4FfrF6F4F;
F4F4*&,(*&,(FXF4FW#F=F8FG#FcrF8F4F3F4F4*&,(FWF7FGFgsFXF6F4F9F4F4FenF6F
4F:F4F4*&F2F4,&*&F3F4FRF4F4*&F9F4F5F4F4F4F4F4FCF4F8F4FdoF4F4**F:F4F;F4
,(*&FhoF4FCF4F4*&,&FFF4*&F3F4FjoF4F7F4F;F4F4*(F:F4F3F4F\\pF4F7F4F<F8F7
*&,,*(FBF4FhoF4FCF8F4*&,(*&,(FFF4*$F5F8F4*$F3F8F7F4F;F8F4*&,&FhqF4*&,&
*&F5F4F9F4F8F[vF>F4F:F4F4F4F;F4F4*&,&*$F9F8F4F[vF7F4F:F8F4F4FCF4F4*&,&
*&,&*&,&FGF7FWF4F4F3F4F4*&F5F4FWF4F7F4F:F4F4*(F5F4F3F4FjoF4F4F4F;F8F4*
(,&*&,&*&F9F4FWF4F7FhvF4F4F:F4F4*&F3F4,&FjtF4F[uF>F4F4F4F:F4F;F4F4**F3
F4F:F8F9F4F\\pF4F4F4F<F4F4*&,,*&FhoF4FCF8F4*&,&*&,&FFF4*&FjoF4FisF4F7F
4F;F4F4*(F:F4F\\pF4FisF4F7F4FCF4F4*(FXF4FjoF4F;F8F7*&,&*&,(FhvF4FjnF4F
enF7F4F:F4F4*&FjoF4FitF4F4F4F;F4F4*(F:F4,(*&,(FWF4FGF7FXF4F4F:F4F4FjtF
4F[uF4F4F\\pF4F4F4FCF4F7F4,&FdoF7F;F4F>,&F:F4FdoF7F>Fgs**,&*&,(*&FfnF4
FdoF4F4*&F3F4F5F4F7*&FfnF4F:F4F7F4F9F4F4*(F5F4FXF4FgxF4F4F4,**&FhxF4F9
F4F4*&,&F5F7F3F8F4FdoF4F4*&,&F:F7F;F7F4F3F4F4*&F;F4F5F4F4F4FgxF>FhxF>F
gs*,FGF4F9F4F3F4,&-I#lnG6$%*protectedGI(_syslibGF$6#,&F;F7F:F4F4-F[z6#
FgxF7F4FhxF>FgsF$F$F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 72 "Matchin
g the JMU tau-function with the Hamiltonians evaluated at \\hbar=0" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Ct11:=" }{MPLTEXT 1 0 33 "si
mplify(omegaJMUdt11 -(-residue(" }{MPLTEXT 1 0 19 "Hame11(q,p)/h,h=0) 
" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 28 "F11(t11,t21,t31,t12,t22,t32)" 
}{MPLTEXT 1 0 3 " ))" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 6 "Ct21:=" }
{MPLTEXT 1 0 24 "simplify(omegaJMUdt21 -(" }{MPLTEXT 1 0 28 "-residue(
Hame21(q,p)/h,h=0) " }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 4 "F21(" }
{MPLTEXT 1 0 24 "t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 4 "  ))" }
{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 6 "Ct31:=" }{MPLTEXT 1 0 24 "simpli
fy(omegaJMUdt31 -(" }{MPLTEXT 1 0 28 "-residue(Hame31(q,p)/h,h=0) " }
{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 4 "F31(" }{MPLTEXT 1 0 24 "t11,t21,t3
1,t12,t22,t32)" }{MPLTEXT 1 0 2 "))" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 29 "Ct12:=simplify(omegaJMUdt12-(" }{MPLTEXT 
1 0 27 "-residue(Hame12(q,p)/h,h=0)" }{MPLTEXT 1 0 37 "  +F12(t11,t21,
t31,t12,t22,t32)  ));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 38 "Ct22:=
simplify(simplify(omegaJMUdt22-(" }{MPLTEXT 1 0 28 "-residue(Hame22(q,
p)/h,h=0) " }{MPLTEXT 1 0 36 "+F22(t11,t21,t31,t12,t22,t32)  )));\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 38 "Ct32:=simplify(simplify(omegaJMU
dt32-(" }{MPLTEXT 1 0 28 "-residue(Hame32(q,p)/h,h=0) " }{MPLTEXT 1 0 
40 "+F32(t11,t21,t31,t12,t22,t32)       )));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I%Ct11G6\"*(,&I$t20GF$\"\"\"I$t30GF$F(F(,&I$t11GF$F(I$t3
1GF$!\"\"F(,&I$t12GF$F(I$t32GF$F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">
I%Ct21G6\",$*(,(**I\"hGF$\"\"\"I$t31GF$F*,&I$t32GF$!\"\"I$t22GF$F*F*-I
#lnG6$%*protectedGI(_syslibGF$6#,&F/F.I$t12GF$F*F*F.**F)F*F+F*F,F*-F16
#F,F*F**&,&F7F*F-F.F*,&*&,&F)F*I$t20GF$!\"#F*F+F*F**&I$t21GF$F*F@F*\"
\"#F*F.F*F,F.F<F.#F*FD" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%Ct31G6\",$*
(,.**I\"hGF$\"\"\"I$t21GF$F*,&I$t32GF$!\"\"I$t22GF$F*F*-I#lnG6$%*prote
ctedGI(_syslibGF$6#,&F/F.I$t12GF$F*F*F.**F)F*F+F*F,F*-F16#F,F*F**&,(*&
,&F)F.I$t20GF$!\"#F*F+F*F**&I$t11GF$F*F?F*\"\"#*&I$t30GF$F*,&FBF*I$t31
GF$F.F*FCF*F-F*F**(F7F*,&F)F*F?FCF*F+F*F**(,&F?F*FEF*F*FFF*F/F*F@*(F7F
*F?F*FGF*F@F*F,F.,&F7F*F-F.F.#F*FC" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
%Ct12G6\",$*(,(*,I\"hGF$\"\"\"I$t21GF$F*I$t31GF$F*,&I$t22GF$!\"\"I$t12
GF$F*F*-I#lnG6$%*protectedGI(_syslibGF$6#F-F*F**,F)F*F+F*F,F*F-F*-F26#
,&I$t32GF$F/F.F*F*F/*&,&I$t20GF$F*I$t30GF$F*F*,,*&F=F*F0\"\"#F**&,(*&,
&F.F/F;F/F*F?F*F**&F;F*F>F*!\"#*$,&I$t11GF$F*F,F/FBF*F*F0F*F**(F.F*F?F
*F;F*F**&F>F*F;FBF**&F.F*FJFBF/F*F/F*,&F0F*F;F/FHF-F/#F*FB" }}{PARA 11
 "" 1 "" {XPPMATH 20 ">I%Ct22G6\",$**I$t20GF$\"\"\",**&F'F(I$t22GF$\"
\"#F(*&,(*&,&F'!\"#I$t30GF$!\"\"F(I$t32GF$F(F(*&I$t12GF$F(F2F(F(*$,&I$
t21GF$F(I$t31GF$F3F,F3F(F+F(F(*&,&*&F2F(F4F(F3F7F(F(F6F(F(*&,&F'F(F2F(
F(F4F,F(F(,&F4F3F+F(F1,&F+F3F6F(F3#F(F," }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I%Ct32G6\",$*(,2*,I\"hGF$\"\"\"I$t21GF$F*I$t31GF$F*,&I$t32GF$!\"
\"I$t22GF$F*\"\"#-I#lnG6$%*protectedGI(_syslibGF$6#,&F0F/I$t12GF$F*F*F
/*,F)F*F+F*F,F*F-F1-F36#F-F*F**&I$t30GF$F1F.\"\"$F/*&,(*(F>F*,&I$t20GF
$F*F>F1F*F0F*F**&,**&,&I$t11GF$!\"#F+F1F*F,F*F**$FIF1F**&F9F*F>F*F/*$F
+F1F/F*FDF*F**&F>F*,*FKF**&FIF*F,F*FJFLF**$F,F1F*F*F*F*F.F1F**&,(*(F>F
*,&FDF*F>F*F*F0F1F/*&,&*&,&FIF*F,F/F1FDF*FJFNFJF*F0F*F**(F9F*FDF*,*FLF
*FMF1*&F+F*F,F*!\"%FQF1F*F*F*F.F*F**(FUF*FOF*F0F1F***F9F1FDF*F0F*F>F*F
/*(F9F1FDF*,&F+F*F,F/F1F/F*F-FJ,&F9F*F.F/FJ#F*F1" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 292 "GSolOldCoordinatesbis:= -t20*t21*(t21-2*t31)
/(2*t22-2*t32)+(t20+t30)*t11*(-2*t31+t11)/(2*t12-2*t32)-t31^2*(t30*t32
+(-t20-t30)*t22+t12*t20)/((2*(-t32+t22))*(t12-t32))+(1/2)*ln(-t32+t22)
*t20*t30-(1/2)*ln(t22-t12)*t20^2-(1/2)*ln(t22-t12)*t20*t30-(1/2)*ln(t1
2-t32)*t20*t30-(1/2)*t30^2*ln(t12-t32)" }{MPLTEXT 1 0 1 ";" }}{PARA 11
 "" 1 "" {XPPMATH 20 ">I6GSolOldCoordinatesbisG6\",2**I$t20GF$\"\"\"I$
t21GF$F(,&F)F(I$t31GF$!\"#F(,&I$t22GF$\"\"#I$t32GF$F,!\"\"F1**,&F'F(I$
t30GF$F(F(I$t11GF$F(,&F+F,F5F(F(,&I$t12GF$F/F0F,F1F(**F+F/,(*&F4F(F0F(
F(*&,&F'F1F4F1F(F.F(F(*&F8F(F'F(F(F(,&F0F1F.F(F1,&F8F(F0F1F1#F1F/*(-I#
lnG6$%*protectedGI(_syslibGF$6#F?F(F'F(F4F(#F(F/*&-FD6#,&F.F(F8F1F(F'F
/FA*(FKF(F'F(F4F(FA*(-FD6#F@F(F'F(F4F(FA*&F4F/FPF(FA" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT 284 69 "We can express the JMU differential using the \+
times (T_1,...,T_5,tau)" }}}{EXCHG {PARA 0 "> " 0 "" {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:=u
napply(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,t3
2)=T4,TT5(t11,t21,t31,t12,t22,t32)=T5,taufunction(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 "t21function := (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 "t22function := 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 "simplify(TT1(t11function,t
21function,t31function,t12function,t22function,t32function));\n" }
{MPLTEXT 1 0 88 "simplify(TT2(t11function,t21function,t31function,t12f
unction,t22function,t32function));\n" }{MPLTEXT 1 0 88 "simplify(TT3(t
11function,t21function,t31function,t12function,t22function,t32function
));\n" }{MPLTEXT 1 0 88 "simplify(TT4(t11function,t21function,t31funct
ion,t12function,t22function,t32function));\n" }{MPLTEXT 1 0 88 "simpli
fy(TT5(t11function,t21function,t31function,t12function,t22function,t32
function));\n" }{MPLTEXT 1 0 96 "simplify(taufunction(t11function,t21f
unction,t31function,t12function,t22function,t32function));\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 250 "partialtaufunction:=unapply( di
ff(t11function,tau)*partialt11 + diff(t21function,tau)*partialt21+diff
(t31function,tau)*partialt31+diff(t12function,tau)*partialt12+diff(t22
function,tau)*partialt22+diff(t32function,tau)*partialt32,T1,T2,T3,T4,
T5,tau):\n" }{MPLTEXT 1 0 218 "partialtau:=partialtaufunction(TT1(t11,
t21,t31,t12,t22,t32),TT2(t11,t21,t31,t12,t22,t32),TT3(t11,t21,t31,t12,
t22,t32),TT4(t11,t21,t31,t12,t22,t32),TT5(t11,t21,t31,t12,t22,t32),tau
function(t11,t21,t31,t12,t22,t32)   ):\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 57 "Coefft21:=residue(partialtau/partialt21^2,partialt21=
0):\n" }{MPLTEXT 1 0 57 "Coefft31:=residue(partialtau/partialt31^2,par
tialt31=0):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 76 "Hamtau:= unapply
( simplify(Coefft21*Hame21(q,p)+Coefft31*Hame31(q,p)),q,p):\n" }
{MPLTEXT 1 0 28 "Ltauq:=diff(Hamtau(q,p),p):\n" }{MPLTEXT 1 0 28 "Ltau
p:=-diff(Hamtau(q,p),q):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 76 "SOLL:=solve(\{checkqfunction(q,p)=checkq,checkpfuncti
on(q,p)=checkp\},\{q,p\}):\n" }{MPLTEXT 1 0 30 "Solp:=simplify(rhs(SOL
L[1])):\n" }{MPLTEXT 1 0 31 "Solq:=simplify(rhs(SOLL[2])): \n" }
{MPLTEXT 1 0 44 "simplify(checkqfunction(Solq,Solp)-checkq);\n" }
{MPLTEXT 1 0 44 "simplify(checkpfunction(Solq,Solp)-checkp);\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 196 "Ltaucheckqfunction:=unapply( si
mplify( diff(checkqfunction(q,p),q)*Ltauq+diff(checkqfunction(q,p),p)*
Ltaup+Coefft21*h*diff(checkqfunction(q,p),t21)+Coefft31*h*diff(checkqf
unction(q,p),t31)),q,p):\n" }{MPLTEXT 1 0 195 "Ltaucheckpfunction:=una
pply(simplify( diff(checkpfunction(q,p),q)*Ltauq+diff(checkpfunction(q
,p),p)*Ltaup+Coefft21*h*diff(checkpfunction(q,p),t21)+Coefft31*h*diff(
checkpfunction(q,p),t31)),q,p):\n" }{MPLTEXT 1 0 100 "Ltaucheckqfuncti
on2:=unapply(simplify(Ltaucheckqfunction(Solq,Solp)),t11, t21, t31, t1
2, t22, t32):\n" }{MPLTEXT 1 0 100 "Ltaucheckpfunction2:=unapply(simpl
ify(Ltaucheckpfunction(Solq,Solp)),t11, t21, t31, t12, t22, t32):\n" }
{MPLTEXT 1 0 120 "Ltaucheckq:=simplify(Ltaucheckqfunction2(t11function
,t21function ,t31function ,t12function ,t22function ,t32function)):\n"
 }{MPLTEXT 1 0 120 "Ltaucheckp:=simplify(Ltaucheckpfunction2(t11functi
on,t21function ,t31function ,t12function ,t22function ,t32function)):
\n" }{MPLTEXT 1 0 150 "HamtaucheckCoordinates:=unapply(simplify(int(Lt
aucheckq,checkp)-int(simplify(diff(int(Ltaucheckq,checkp),checkq)+Ltau
checkp),checkq),checkq,checkp)):\n" }{MPLTEXT 1 0 73 "simplify(Ltauche
ckq-diff(HamtaucheckCoordinates(checkq,checkp),checkp));\n" }{MPLTEXT 
1 0 72 "simplify(Ltaucheckp+diff(HamtaucheckCoordinates(checkq,checkp)
,checkq));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT1G6\"f*6(I$t11GF$I$t2
1GF$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$I&arrow
GF$F$,(9$\"\"\"9%F29&F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT3G
6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorG
F$I&arrowGF$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$I&arr
owGF$F$9$F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT5G6\"f*6(I$t11GF
$I$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$t12GF%
,(I#T3GF%!\"\"I#T5GF%F+I#T1GF%\"\"\"/I$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$t32G
F%F," }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,t11functionG6\"I#T4GF$" }}
{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 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "omegaJMU:=omegaJMUdt11*dt11+" }
{MPLTEXT 1 0 18 "omegaJMUdt21*dt21+" }{MPLTEXT 1 0 18 "omegaJMUdt31*dt
31+" }{MPLTEXT 1 0 18 "omegaJMUdt12*dt12+" }{MPLTEXT 1 0 18 "omegaJMUd
t22*dt22+" }{MPLTEXT 1 0 19 "omegaJMUdt32*dt32:\n" }{MPLTEXT 1 0 27 "o
megaJMUfunction1:=unapply(" }{MPLTEXT 1 0 15 "omegaJMU,q,p):\n" }
{MPLTEXT 1 0 36 "omegaJMUfunction2:=unapply(simplify(" }{MPLTEXT 1 0 
56 "omegaJMUfunction1(Solq,Solp)),t11,t21,t31,t12,t22,t32):\n" }
{MPLTEXT 1 0 36 "omegaJMUfunction3:=unapply(simplify(" }{MPLTEXT 1 0 
123 "omegaJMUfunction2(t11function,t21function,t31function,t12function
,t22function,t32function)),dt11,dt21,dt31,dt12,dt22,dt32):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "dt11function:=simplify(diff(t11func
tion,T1)*dT1+ " }{MPLTEXT 1 0 25 "diff(t11function,T2)*dT2+" }{MPLTEXT
 1 0 25 "diff(t11function,T3)*dT3+" }{MPLTEXT 1 0 25 "diff(t11function
,T4)*dT4+" }{MPLTEXT 1 0 25 "diff(t11function,T5)*dT5+" }{MPLTEXT 1 0 
29 "diff(t11function,tau)*dtau);\n" }{MPLTEXT 1 0 4 "dt21" }{MPLTEXT 
1 0 8 "function" }{MPLTEXT 1 0 2 ":=" }{MPLTEXT 1 0 9 "simplify(" }
{MPLTEXT 1 0 155 "diff(t21function,T1)*dT1+ diff(t21function,T2)*dT2+d
iff(t21function,T3)*dT3+diff(t21function,T4)*dT4+diff(t21function,T5)*
dT5+diff(t21function,tau)*dtau):\n" }{MPLTEXT 1 0 4 "dt31" }{MPLTEXT 
1 0 8 "function" }{MPLTEXT 1 0 2 ":=" }{MPLTEXT 1 0 9 "simplify(" }
{MPLTEXT 1 0 155 "diff(t31function,T1)*dT1+ diff(t31function,T2)*dT2+d
iff(t31function,T3)*dT3+diff(t31function,T4)*dT4+diff(t31function,T5)*
dT5+diff(t31function,tau)*dtau):\n" }{MPLTEXT 1 0 4 "dt12" }{MPLTEXT 
1 0 8 "function" }{MPLTEXT 1 0 2 ":=" }{MPLTEXT 1 0 9 "simplify(" }
{MPLTEXT 1 0 155 "diff(t12function,T1)*dT1+ diff(t12function,T2)*dT2+d
iff(t12function,T3)*dT3+diff(t12function,T4)*dT4+diff(t12function,T5)*
dT5+diff(t12function,tau)*dtau);\n" }{MPLTEXT 1 0 4 "dt22" }{MPLTEXT 
1 0 8 "function" }{MPLTEXT 1 0 2 ":=" }{MPLTEXT 1 0 9 "simplify(" }
{MPLTEXT 1 0 155 "diff(t22function,T1)*dT1+ diff(t22function,T2)*dT2+d
iff(t22function,T3)*dT3+diff(t22function,T4)*dT4+diff(t22function,T5)*
dT5+diff(t22function,tau)*dtau);\n" }{MPLTEXT 1 0 4 "dt32" }{MPLTEXT 
1 0 8 "function" }{MPLTEXT 1 0 2 ":=" }{MPLTEXT 1 0 9 "simplify(" }
{MPLTEXT 1 0 154 "diff(t32function,T1)*dT1+ diff(t32function,T2)*dT2+d
iff(t32function,T3)*dT3+diff(t32function,T4)*dT4+diff(t32function,T5)*
dT5+diff(t32function,tau)*dtau);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-d
t11functionG6\"I$dT4GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-dt12functi
onG6\",(I$dT1GF$\"\"\"I$dT3GF$!\"\"I$dT5GF$F)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I-dt22functionG6\"I$dT3GF$" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I-dt32functionG6\"I$dT5GF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 43 "omegaJMUfunctioncheckCoordinates:=simplify(" }{MPLTEXT 1 0 18 
"omegaJMUfunction3(" }{MPLTEXT 1 0 13 "dt11function," }{MPLTEXT 1 0 
13 "dt21function," }{MPLTEXT 1 0 13 "dt31function," }{MPLTEXT 1 0 13 "
dt12function," }{MPLTEXT 1 0 13 "dt22function," }{MPLTEXT 1 0 15 "dt32
function)):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 101 "omegaJMUfunctioncheckCoordinatesdT1:=simplify(residue(omegaJM
UfunctioncheckCoordinates/dT1^2,dT1=0)):" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 101 "omegaJMUfunctioncheckCoordinatesdT2:=simplify(residu
e(omegaJMUfunctioncheckCoordinates/dT2^2,dT2=0)):" }{MPLTEXT 1 0 1 "\n
" }{MPLTEXT 1 0 101 "omegaJMUfunctioncheckCoordinatesdT3:=simplify(res
idue(omegaJMUfunctioncheckCoordinates/dT3^2,dT3=0)):" }{MPLTEXT 1 0 1 
"\n" }{MPLTEXT 1 0 102 "omegaJMUfunctioncheckCoordinatesdT4:=simplify(
residue(omegaJMUfunctioncheckCoordinates/dT4^2,dT4=0)):\n" }{MPLTEXT 
1 0 101 "omegaJMUfunctioncheckCoordinatesdT5:=simplify(residue(omegaJM
UfunctioncheckCoordinates/dT5^2,dT5=0)):" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 104 "omegaJMUfunctioncheckCoordinatesdtau:=simplify(resid
ue(omegaJMUfunctioncheckCoordinates/dtau^2,dtau=0)):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 53 "omegaJMUfunctioncheckCoordinatesdT1function:=unapply(" }{MPLTEXT
 1 0 56 "omegaJMUfunctioncheckCoordinatesdT1,T1,T2,T3,T4,T5,tau):" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 110 "omegaJMUfunctioncheckCoordinate
sdT2function:=unapply(omegaJMUfunctioncheckCoordinatesdT2,T1,T2,T3,T4,
T5,tau):\n" }{MPLTEXT 1 0 110 "omegaJMUfunctioncheckCoordinatesdT3func
tion:=unapply(omegaJMUfunctioncheckCoordinatesdT3,T1,T2,T3,T4,T5,tau):
\n" }{MPLTEXT 1 0 110 "omegaJMUfunctioncheckCoordinatesdT4function:=un
apply(omegaJMUfunctioncheckCoordinatesdT4,T1,T2,T3,T4,T5,tau):\n" }
{MPLTEXT 1 0 109 "omegaJMUfunctioncheckCoordinatesdT5function:=unapply
(omegaJMUfunctioncheckCoordinatesdT5,T1,T2,T3,T4,T5,tau):" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 54 "omegaJMUfunctioncheckCoordinatesdtaufunct
ion:=unapply(" }{MPLTEXT 1 0 57 "omegaJMUfunctioncheckCoordinatesdtau,
T1,T2,T3,T4,T5,tau):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "t12function-t22function;\n" }{MPLTEXT 1 0 12 "t22func
tion-" }{MPLTEXT 1 0 13 "t32function;\n" }{MPLTEXT 1 0 24 "t12function
-t32function;" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 69 "assume(-2*TTT3-T
TT5+TTT1>0 and TTT3-TTT5>0 and -TTT3-2*TTT5+TTT1>0);\n" }{MPLTEXT 1 0 
34 "TermdT1function:=unapply(simplify(" }{MPLTEXT 1 0 103 "omegaJMUfun
ctioncheckCoordinatesdT1function(TTT1,TTT2,TTT3,TTT4,TTT5,tau)), TTT1,
TTT2,TTT3,TTT4,TTT5):\n" }{MPLTEXT 1 0 137 "TermdT2function:=unapply(s
implify(omegaJMUfunctioncheckCoordinatesdT2function(TTT1,TTT2,TTT3,TTT
4,TTT5,tau)), TTT1,TTT2,TTT3,TTT4,TTT5):\n" }{MPLTEXT 1 0 137 "TermdT3
function:=unapply(simplify(omegaJMUfunctioncheckCoordinatesdT3function
(TTT1,TTT2,TTT3,TTT4,TTT5,tau)), TTT1,TTT2,TTT3,TTT4,TTT5):\n" }
{MPLTEXT 1 0 137 "TermdT4function:=unapply(simplify(omegaJMUfunctionch
eckCoordinatesdT4function(TTT1,TTT2,TTT3,TTT4,TTT5,tau)), TTT1,TTT2,TT
T3,TTT4,TTT5):\n" }{MPLTEXT 1 0 136 "TermdT5function:=unapply(simplify
(omegaJMUfunctioncheckCoordinatesdT5function(TTT1,TTT2,TTT3,TTT4,TTT5,
tau)), TTT1,TTT2,TTT3,TTT4,TTT5):" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(I
#T3G6\"!\"#I#T5GF$!\"\"I#T1GF$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "
,&I#T5G6\"!\"\"I#T3GF$\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(I#T3G6
\"!\"\"I#T5GF$!\"#I#T1GF$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 43 "omegaJMUfunctioncheckCoordinatesdtaubis:=-(" }{MPLTEXT 1 0 16 
"checkp^2*checkq+" }{MPLTEXT 1 0 60 "checkq^2*checkp -checkq*checkp*ta
u-t20*checkp +t10*checkq);\n" }{MPLTEXT 1 0 26 "Termdtaufunction:=unap
ply(" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 74 "omegaJMUfunctionch
eckCoordinatesdtaufunction(TTT1,TTT2,TTT3,TTT4,TTT5,tau)" }{MPLTEXT 1 
0 1 "-" }{MPLTEXT 1 0 68 "omegaJMUfunctioncheckCoordinatesdtaubis),TTT
1,TTT2,TTT3,TTT4,TTT5):\n" }{MPLTEXT 1 0 33 "Termdtaufunction(T1,T2,T3
,T4,T5);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 
1 0 41 "omegaJMUfunctioncheckCoordinatesdtaubis-(" }{MPLTEXT 1 0 54 "H
amtaucheckCoordinatesTheo(checkq,checkp) +h*checkq));" }}{PARA 11 "" 1
 "" {XPPMATH 20 ">IHomegaJMUfunctioncheckCoordinatesdtaubisG6\",,*&I'c
heckpGF$\"\"#I'checkqGF$\"\"\"!\"\"*&F)F(F'F*F+*(F)F*F'F*I$tauGF$F*F**
&I$t20GF$F*F'F*F**&F)F*,&F0F+I$t30GF$F+F*F+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",$*,,(I#T3G6\"!\"#I#T5GF&!\"\"I#T1GF&\"\"\"#F+\"\"#,&*,,(
F%F)F(F'F*F+F,I$tauGF&F+,&F(F)F%F+F,,(*&,&I$t20GF&#!\"&\"\"%I$t30GF&#F
)F9F+F%F+F+*&,&F6#!\"(F9F:#F+F9F+F(F+F+*&F*F+F6F+F+F+F$F,F+**,&F6F+F:F
)F+F2F+,&I#T2GF&F+I#T4GF&!\"$F+F0F+F;F+F0#F)F-F2FH,(F*F-F%FGF(FGF'!\"%
" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "pdsolve
(\{\n" }{MPLTEXT 1 0 34 "diff(G(T1,T2,T3,T4,T5,tau),tau) = " }{MPLTEXT
 1 0 32 "Termdtaufunction(T1,T2,T3,T4,T5)" }{MPLTEXT 1 0 2 ",\n" }
{MPLTEXT 1 0 32 "diff(G(T1,T2,T3,T4,T5,tau),T1)= " }{MPLTEXT 1 0 31 "T
ermdT1function(T1,T2,T3,T4,T5)" }{MPLTEXT 1 0 2 ",\n" }{MPLTEXT 1 0 
21 "diff(G(T1,T2,T3,T4,T5" }{MPLTEXT 1 0 4 ",tau" }{MPLTEXT 1 0 7 "),T
2)= " }{MPLTEXT 1 0 31 "TermdT2function(T1,T2,T3,T4,T5)" }{MPLTEXT 1 
0 2 ",\n" }{MPLTEXT 1 0 21 "diff(G(T1,T2,T3,T4,T5" }{MPLTEXT 1 0 4 ",t
au" }{MPLTEXT 1 0 7 "),T3)= " }{MPLTEXT 1 0 31 "TermdT3function(T1,T2,
T3,T4,T5)" }{MPLTEXT 1 0 2 ",\n" }{MPLTEXT 1 0 21 "diff(G(T1,T2,T3,T4,
T5" }{MPLTEXT 1 0 4 ",tau" }{MPLTEXT 1 0 7 "),T4)= " }{MPLTEXT 1 0 31 
"TermdT4function(T1,T2,T3,T4,T5)" }{MPLTEXT 1 0 2 ",\n" }{MPLTEXT 1 0 
21 "diff(G(T1,T2,T3,T4,T5" }{MPLTEXT 1 0 4 ",tau" }{MPLTEXT 1 0 7 "),T
5)= " }{MPLTEXT 1 0 31 "TermdT5function(T1,T2,T3,T4,T5)" }{MPLTEXT 1 
0 1 "\}" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 3 ",\{G" }{MPLTEXT 1 0 23 
"(T1,T2,T3,T4,T5,tau)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "<#/-I\"GG6
\"6(I#T1G6\"I#T2G6\"I#T3G6\"I#T4G6\"I#T5G6\"I$tauG6\"*(,&I#T5G6\"!\"\"
I#T3G6\"\"\"\"#!\"\"\"\"#,&*.I$tauG6\"\"\"\",(I#T3G6\"!\"\"I#T5G6\"!\"
#I#T1G6\"\"\"\"#\"\"\"\"\"#,&I$t20G6\"\"\"\"I$t30G6\"!\"\"\"\"\",&I#T5
G6\"!\"\"I#T3G6\"\"\"\"\"\"\",&I#T2G6\"\"\"\"I#T4G6\"!\"$\"\"\",(I#T3G
6\"!\"#I#T5G6\"!\"\"I#T1G6\"\"\"\"#\"\"\"\"\"#\"\"\"*&,&I#T5G6\"!\"\"I
#T3G6\"\"\"\"#\"\"\"\"\"#,.**I$t30G6\"\"\"\",(I#T1G6\"\"\"\"I#T3G6\"#!
\"$\"\"#I#T5G6\"#!\"$\"\"#\"\"#,&I$t20G6\"\"\"\"I$t30G6\"\"\"\"\"\"\"-
I#lnG6$%*protectedGI(_syslibG6\"6#,(I#T3G6\"\"\"\"I#T5G6\"\"\"#I#T1G6
\"!\"\"\"\"\"!\"\"**,(I#T1G6\"\"\"\"I#T3G6\"#!\"$\"\"#I#T5G6\"#!\"$\"
\"#\"\"#,&I$t20G6\"\"\"\"I$t30G6\"\"\"\"\"\"\"I$t20G6\"\"\"\"-I#lnG6$%
*protectedGI(_syslibG6\"6#,(I#T3G6\"\"\"#I#T5G6\"\"\"\"I#T1G6\"!\"\"\"
\"\"!\"\"**I$t30G6\"\"\"\",(I#T1G6\"\"\"\"I#T3G6\"#!\"$\"\"#I#T5G6\"#!
\"$\"\"#\"\"#I$t20G6\"\"\"\"-I#lnG6$%*protectedGI(_syslibG6\"6#,&I#T5G
6\"!\"\"I#T3G6\"\"\"\"\"\"\"\"\"\"*(,(I#T3G6\"!\"#I#T5G6\"!\"\"I#T1G6
\"\"\"\"\"\"\",**&I$tauG6\"\"\"#I#T3G6\"\"\"\"#!\"&\"\"%*&I$tauG6\"\"
\"#I#T5G6\"\"\"\"#!\"(\"\"%*&I$tauG6\"\"\"#I#T1G6\"\"\"\"\"\"\"*$,&I#T
2G6\"\"\"\"I#T4G6\"!\"$\"\"##!\"\"\"\"%\"\"\"I$t20G6\"\"\"\"!\"\"*&,,*
&I#T3G6\"\"\"#I$tauG6\"\"\"##!\"\"\"\"#*&,(*&I$tauG6\"\"\"#I#T5G6\"\"
\"\"#\"\"\"\"\"%*&I$tauG6\"\"\"#I#T1G6\"\"\"\"#\"\"\"\"\"%*$,&I#T2G6\"
\"\"\"I#T4G6\"!\"$\"\"##!\"\"\"\"%\"\"\"I#T3G6\"\"\"\"\"\"\"*&I$tauG6
\"\"\"#I#T5G6\"\"\"##\"\"\"\"\"%*&,&*&I$tauG6\"\"\"#I#T1G6\"\"\"\"#!\"
\"\"\"%*$,&I#T2G6\"\"\"\"I#T4G6\"!\"$\"\"##!\"\"\"\"#\"\"\"I#T5G6\"\"
\"\"\"\"\"*&I#T1G6\"\"\"\",&I#T2G6\"\"\"\"I#T4G6\"!\"$\"\"##\"\"\"\"\"
%\"\"\"I$t30G6\"\"\"\"\"\"\"*&I$_C1G6\"\"\"\",(I#T1G6\"\"\"\"I#T3G6\"#
!\"$\"\"#I#T5G6\"#!\"$\"\"#\"\"#\"\"#\"\"\"\"\"#\"\"\",(I#T1G6\"\"\"#I
#T3G6\"!\"$I#T5G6\"!\"$!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 563 "GSol :=unapply( (ta
u*sqrt(-T3-2*T5+T1)*(t20-t30)*(-T5+T3)*(T2-3*T4)*sqrt(-2*T3-T5+T1)+(2*
(-(T1-3*T3*(1/2)-3*T5*(1/2))^2*t30*(t20+t30)*ln(T3+2*T5-T1)-(T1-3*T3*(
1/2)-3*T5*(1/2))^2*t20*(t20+t30)*ln(2*T3+T5-T1)+(T1-3*T3*(1/2)-3*T5*(1
/2))^2*t30*t20*ln(-T5+T3)-(-2*T3-T5+T1)*(-5*tau^2*T3*(1/4)-7*tau^2*T5*
(1/4)+tau^2*T1-(1/4)*(T2-3*T4)^2)*t20+(-(1/2)*T3^2*tau^2+((1/4)*tau^2*
T5+(1/4)*tau^2*T1-(1/4)*(T2-3*T4)^2)*T3+(1/4)*T5^2*tau^2+(-(1/4)*tau^2
*T1-(1/2)*(T2-3*T4)^2)*T5+(1/4)*T1*(T2-3*T4)^2)*t30))*sqrt(-T5+T3))/(s
qrt(-T5+T3)*(2*T1-3*T3-3*T5)^2) ,T1,T2,T3,T4,T5,tau);\n" }{MPLTEXT 1 
0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 36 "diff(GSol(T1,T2
,T3,T4,T5,tau),tau) -" }{MPLTEXT 1 0 32 "Termdtaufunction(T1,T2,T3,T4,
T5)" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 
35 "diff(GSol(T1,T2,T3,T4,T5,tau),T1) -" }{MPLTEXT 1 0 31 "TermdT1func
tion(T1,T2,T3,T4,T5)" }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 44 "simplif
y(diff(GSol(T1,T2,T3,T4,T5,tau),T2) -" }{MPLTEXT 1 0 5 "Termd" }
{MPLTEXT 1 0 2 "T2" }{MPLTEXT 1 0 24 "function(T1,T2,T3,T4,T5)" }
{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 44 "simplify(diff(GSol(T1,T2,T3,T4
,T5,tau),T3) -" }{MPLTEXT 1 0 31 "TermdT3function(T1,T2,T3,T4,T5)" }
{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 44 "simplify(diff(GSol(T1,T2,T3,T4
,T5,tau),T4) -" }{MPLTEXT 1 0 31 "TermdT4function(T1,T2,T3,T4,T5)" }
{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 44 "simplify(diff(GSol(T1,T2,T3,T4
,T5,tau),T5) -" }{MPLTEXT 1 0 31 "TermdT5function(T1,T2,T3,T4,T5)" }
{MPLTEXT 1 0 3 ");\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)*sqr
t(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)
*tau^2/2/(2*T1-3*T3-3*T5)^2" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 72 "s
implify(series(simplify(GSol(T1, T2, T3, T4, T5, tau)-GSolbis),tau=0))
;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%GSolG6\"f*6(I#T1GF$I#T2GF$I#T3GF
$I#T4GF$I#T5GF$I$tauGF$F$6$I)operatorGF$I&arrowGF$F$*(,&*.9)\"\"\",(9&
!\"\"9(!\"#9$F4#F4\"\"#,&I$t20GF$F4I$t30GF$F7F4,&F8F7F6F4F4,&9%F49'!\"
$F4,(F6F9F8F7F:F4F;F4*&,,**F?F4,(F:F4F6#FDF<F8FJF<,&F>F4F?F4F4-I#lnG6$
%*protectedGI(_syslibGF$6#,(F6F4F8F<F:F7F4F7**FIF<FKF4F>F4-FM6#,(F6F<F
8F4F:F7F4F7**F?F4FIF<F>F4-FM6#F@F4F4*(FEF4,**&F3F<F6F4#!\"&\"\"%*&F3F<
F8F4#!\"(Fin*&F3F<F:F4F4*$FAF<#F7FinF4F>F4F7*&,,*&F6F<F3F<#F7F<*&,(Fjn
#F4FinF]oFfoF^oF_oF4F6F4F4*&F3F<F8F<Ffo*&,&F]oF_oF^oFcoF4F8F4F4*&F:F4F
AF<FfoF4F?F4F4F4F@F;F<F4F@Fco,(F:F<F6FDF8FDF9F$F$F$" }}{PARA 11 "" 1 "
" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 
"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I(GSolbisG6\",,*&,&I$t20GF$\"
\"\"I$t30GF$F)F),&*&F(F)-I#lnG6$%*protectedGI(_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$F)I#T4GF$!\"$F5,&*&,(F4!\"#F6F8F7
F)F)F(F)F)*&,(F4F8F6FKF7F)F)F*F)F)F),(F7F5F4FGF6FGFKFB*0FMFBFJFBFAFBFD
F),&F(F)F*F8F)I$tauGF$F)FNFKF)**,&*&,(F7\"\"%F4!\"&F6!\"(F)F(F)F)*&F*F
)FAF)F8F)FJF)FQF5FNFKF=" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "GSolOldCoordinatesfunction:=
unapply(simplify(GSol(TT1(t11, t21, t31, t12, t22, t32)," }{MPLTEXT 1 
0 34 "TT2(t11, t21, t31, t12, t22, t32)," }{MPLTEXT 1 0 34 "TT3(t11, t
21, t31, t12, t22, t32)," }{MPLTEXT 1 0 34 "TT4(t11, t21, t31, t12, t2
2, t32)," }{MPLTEXT 1 0 78 "TT5(t11, t21, t31, t12, t22, t32),taufunct
ion(t11, t21, t31, t12, t22, t32)))," }{MPLTEXT 1 0 31 "t11, t21, t31,
 t12, t22, t32):\n" }{MPLTEXT 1 0 47 "assume(tt12>tt22 and tt22>tt32 a
nd tt12>tt32):\n" }{MPLTEXT 1 0 46 "GSolOldCoordinatesfunction2:=unapp
ly(simplify(" }{MPLTEXT 1 0 27 "GSolOldCoordinatesfunction(" }{MPLTEXT
 1 0 2 " t" }{MPLTEXT 1 0 36 "t11, tt21, tt31, tt12, tt22, tt32))," }
{MPLTEXT 1 0 35 "tt11, tt21, tt31, tt12, tt22, tt32)" }{MPLTEXT 1 0 1 
":" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 20 "GSolOldCoordinates:=" }
{MPLTEXT 1 0 53 "GSolOldCoordinatesfunction2(t11,t21,t31,t12,t22,t32);
" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I3GSolOldCoordinatesG6\",$*(,,*,I$t
30GF$\"\"\",&I$t12GF$F*I$t32GF$!\"\"F*,&F-F.I$t22GF$F*F*,&I$t20GF$F*F)
F*F*-I#lnG6$%*protectedGI(_syslibGF$6#,&F,F.F-F*F*F.*,F2F*F+F*F/F*F1F*
-F46#,&F0F*F,F.F*F.*,F2F*F)F*F+F*F/F*-F46#F/F*F**&,(*(,&I$t11GF$F*I$t2
1GF$F.F*,(FEF*FFF*I$t31GF$!\"#F*F-F*F.*&F0F*,&FEF*FHF.\"\"#F**&F,F*,&F
FF*FHF.FLF.F*F2F*F**(F)F*FKFLF/F*F*F*F+F.F/F.#F*FL" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 94 "GSolOldCoordinatesbis:= 1/2*(t30*t10*ln(-t1
2+t32)  +t10*t20*ln(t22-t12)+ln(-t32+t22)*t20*t30)\n" }{MPLTEXT 1 0 1 
"-" }{MPLTEXT 1 0 43 "t10*t11^2/2/(t12-t32)-t20*t21^2/2/(t22-t32)" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 22 "+t30*t31^2/2/(t12-t32)" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "-(1/2)*(" }{MPLTEXT 1 0 3 "t12" }
{MPLTEXT 1 0 38 "-t22)*t31^2*t20/((t22-t32)*(t12-t32))\n" }{MPLTEXT 1 
0 8 "+t31*t11" }{MPLTEXT 1 0 4 "*t10" }{MPLTEXT 1 0 32 "/(t12-t32)+t20
*t31*t21/(t22-t32)" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT
 1 0 73 "simplify(series(simplify(GSolOldCoordinates-GSolOldCoordinate
sbis),t11));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I6GSolOldCoordinatesbis
G6\",4*(I$t30GF$\"\"\",&I$t20GF$!\"\"F'F+F(-I#lnG6$%*protectedGI(_sysl
ibGF$6#,&I$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 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "simpl
ify(omegaJMUdt11  -(" }{MPLTEXT 1 0 115 "1/((t12-t32)*(t22-t12))*(-p^3
+ P1(q)*p^2-P2(q)*p+P3(q))-t11*t21*t31/(t12-t32)/(t12-t22)+t10*t21/(t1
2-t22)+t11*t20*(" }{MPLTEXT 1 0 3 "t22" }{MPLTEXT 1 0 8 "-t32)/((" }
{MPLTEXT 1 0 3 "t12" }{MPLTEXT 1 0 20 "-t22)*(t12-t32))   +" }{MPLTEXT
 1 0 5 "diff(" }{MPLTEXT 1 0 26 "GSolOldCoordinatesbis,t11)" }{MPLTEXT
 1 0 9 "    )   )" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 25 "simplify(omegaJMUdt21  -(" }{MPLTEXT 1 0 
2 "1/" }{MPLTEXT 1 0 21 "((t22-t32)*(t12-t22))" }{MPLTEXT 1 0 33 "*(-p
^3+ P1(q)*p^2-P2(q)*p+P3(q))+" }{MPLTEXT 1 0 13 "t11*t21*t31/(" }
{MPLTEXT 1 0 3 "t12" }{MPLTEXT 1 0 7 "-t22)/(" }{MPLTEXT 1 0 3 "t22" }
{MPLTEXT 1 0 6 "-t32)-" }{MPLTEXT 1 0 27 "t20*t11/(t12-t22)-t21*t10*("
 }{MPLTEXT 1 0 14 "t12-t32)/((t12" }{MPLTEXT 1 0 16 "-t22)*(t22-t32))"
 }{MPLTEXT 1 0 46 "   +diff(GSolOldCoordinatesbis,t21)    )   );\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 26 "simplify(omegaJMUdt31  -(-" }
{MPLTEXT 1 0 56 "1/((t22-t32)*(t12-t32))*(-p^3+ P1(q)*p^2-P2(q)*p+P3(q
))-" }{MPLTEXT 1 0 64 "t11*t21*t31/(t12-t32)/(t22-t32)-t30*t21/(t22-t3
2)+t20*(t22*t11+(" }{MPLTEXT 1 0 3 "t21" }{MPLTEXT 1 0 21 "-t11)*t32-t
12*t21)/((" }{MPLTEXT 1 0 3 "t22" }{MPLTEXT 1 0 16 "-t32)*(t12-t32))" 
}{MPLTEXT 1 0 45 "   +diff(GSolOldCoordinatesbis,t31)    )   );" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "
\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0
 "" {MPLTEXT 1 0 60 "simplify(omegaJMUdt12-  simplify(-residue(Hame12(
q,p)/h,h=0)" }{MPLTEXT 1 0 32 "+diff(GSolOldCoordinatesbis,t12)" }
{MPLTEXT 1 0 5 "  ));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 60 "simplify
(omegaJMUdt22-  simplify(-residue(Hame22(q,p)/h,h=0)" }{MPLTEXT 1 0 
32 "+diff(GSolOldCoordinatesbis,t22)" }{MPLTEXT 1 0 4 "));\n" }
{MPLTEXT 1 0 60 "simplify(omegaJMUdt32-  simplify(-residue(Hame32(q,p)
/h,h=0)" }{MPLTEXT 1 0 32 "+diff(GSolOldCoordinatesbis,t32)" }{MPLTEXT
 1 0 4 "));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 98 "simplify(omegaJM
Udt11-  simplify(-residue(Hame11(q,p)/h,h=0)+diff(GSolOldCoordinatesbi
s,t11)  ));\n" }{MPLTEXT 1 0 96 "simplify(omegaJMUdt21-  simplify(-res
idue(Hame21(q,p)/h,h=0)+diff(GSolOldCoordinatesbis,t21)));\n" }
{MPLTEXT 1 0 95 "simplify(omegaJMUdt31-  simplify(-residue(Hame31(q,p)
/h,h=0)+diff(GSolOldCoordinatesbis,t31)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "
\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "GSolOldCoordinates
bisfunction:=unapply(GSolOldCoordinatesbis,t11,t21,t31,t12,t22,t32,t20
,t30);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I>GSolOldCoordinatesbisfuncti
onG6\"f*6*I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$I$t20GF$I$t3
0GF$F$6$I)operatorGF$I&arrowGF$F$,4*(9+\"\"\",&9*!\"\"F4F8F5-I#lnG6$%*
protectedGI(_syslibGF$6#,&9'F89)F5F5#F5\"\"#*(F6F5F7F5-F:6#,&9(F5F@F8F
5FB*(-F:6#,&FHF5FAF8F5F7F5F4F5FB*(F6F59$FC,&F@F5FAF8F8#F8FC*(F7F59%FCF
LF8FP*(F4F59&FCFOF8FB*,,&F@F5FHF8F5FTFCF7F5FLF8FOF8FP**FTF5FNF5F6F5FOF
8F5**F7F5FTF5FRF5FLF8F5F$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 9 10 1803 1 1 1 1 }{PAGENUMBERS 0 1 
2 33 1 1 }