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{SECT 0 {SECT 0 {PARA 216 "" 0 "" {TEXT 213 106 "We load the Hamilton
ians from the general Hamiltonian evolutions including the purely time
-dependent terms" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart:
\n" }{MPLTEXT 1 0 21 "with(LinearAlgebra):\n" }{MPLTEXT 1 0 28 "with(D
ifferentialGeometry):\n" }{MPLTEXT 1 0 13 "with(Tools):\n" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 15 "t10:=-t20-t30:\n" }{MPLTEXT 1 0 55 "P1:=u
napply( (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+(t
11+t31)*t22+t32*(t11+t21))*lambda-t10*t12-t20*t22-t30*t32+t21*t11 +t31
*t11+t21*t31,lambda);\n" }{MPLTEXT 1 0 118 "P3:=unapply(t12*t22*t32*la
mbda^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 1 "\n" }{MPLTEXT 1 0 52 "F22:=unapply(0,tt11, tt21, tt31,
 tt12, tt22, tt32);\n" }{MPLTEXT 1 0 52 "F11:=unapply(0,tt11, tt21, tt
31, 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-tt32)),tt1
1, 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)/(tt12-tt32)
^2),tt11, tt21, tt31, tt12, tt22, tt32 );\n" }{MPLTEXT 1 0 111 "F32:=u
napply(h*tt21*tt31/2*((ln(tt12-tt22)-ln(tt22-tt32))/(tt12-tt32)^2),tt1
1, 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 1 "\n" }{MPLTEXT 1 0 1 "\n" }{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*t30+(-t31-t21)*t11-t21*t31)*p+q*(q^2*t12*t22*t32+((t22*t
31+t32*t21)*t12+t22*t32*t11)*q+(t22*t30+t32*t20+t21*t31)*t12+((-t20-t3
0)*t32+t11*t31)*t22+t32*t11*t21))/((t12-t32)*(t12-t22)) \n" }{MPLTEXT 
1 0 89 "+(((t20+t30)*t12+t31*t11-t20*t32-t30*t32)*t21-t11*t20*(-t32+t2
2))/((-t22+t12)*(t12-t32))\n" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 28 "F1
1(t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 ",q,p
);\n" }{MPLTEXT 1 0 1 "\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*(t
21+t31)+t22*(t11+t31)+t32*(t11+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)*t2
2+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-t12*t30+t30*t32)*t21+t11*t20*(-t32+t22))/((-
t22+t12)*(-t32+t22))\n" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 1 0 28 "F21(t11,
t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 ",q,p);\n" 
}{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 357 "Hame31:=unapply((-p^3+(t11+t21
+t31+(t12+t22+t32)*q)*p^2+(((-t12-t22)*t32-t12*t22)*q^2+((-t21-t11)*t3
2+(-t31-t21)*t12-t22*(t11+t31))*q+(-h+t30)*t32+(-t30+h-t20)*t12+t22*t2
0+(-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)*t22+t2
1*t31)*t12+t22*t11*t31))/((t22-t32)*(t12-t32))\n" }{MPLTEXT 1 0 89 "+(
((-t20-t30)*t32+t31*t11+t12*t20+t12*t30)*t21-t11*t20*(-t32+t22))/((t12
-t32)*(-t32+t22))" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "+" }{MPLTEXT 
1 0 28 "F31(t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 
1 0 7 ",q,p);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1771 "Hame12:=unap
ply(((t32*t22*(t21+t31-2*t11)*q^3+(-(t22+t32)*(t21+t31-2*t11)*p+(-h*t3
2+t31*(t21+t31-2*t11))*t22+t32*t21*(t21+t31-2*t11))*q^2+((t21+t31-2*t1
1)*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+t20)*t21+t31*t20)*t32+t31*t21*(t21+t3
1-2*t11))*q-(p*h+(-2*t30-2*t20)*t11+(t21+t31)*(t30-h+t20))*p)*t12^2+(-
((-t11+t31)*t22-t32*(t11-t21))*t32*t22*q^3+(((-t11+t31)*t22^2-t32^2*(t
11-t21))*p+(h*t32-t31*(-t11+t31))*t22^2+(2*((1/2)*h*t32+(t11-t21)*(-t1
1+t31)))*t32*t22+t21*t32^2*(t11-t21))*q^2+(((-t11+t21)*t22+t32*(-t11+t
31))*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+t31*(t11-t21)*(-2*t11+t31))*t22+(2*((
(1/2)*t11*t20+(1/2)*(h-t20)*t21)*t32+(-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)*t21-(-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+t31)*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*t2
1*t31)*t32)*t22+(-t11^2+t21^2)*t32^2)*p+(((-t20-t30)*t11+(t30-h+t20)*t
31)*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))*t2
2+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)*t11+(1/2)*t22*t31)*(((-t20-t30)*t12-t
31*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,t3
2)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 7 ",q,p);\n" }{MPLTEXT 1 0 1 "
\n" }{MPLTEXT 1 0 1759 "Hame22:=unapply( ((t12*t32*(t11-2*t21+t31)*q^3
+(-(t12+t32)*(t11-2*t21+t31)*p+(-h*t12+t11*(t11-2*t21+t31))*t32+t12*t3
1*(t11-2*t21+t31))*q^2+((t11-2*t21+t31)*p^2+(h*t32+h*t12-(t11+t31)*(t1
1-2*t21+t31))*p+((2*t30-2*h+2*t20)*t21+(-t30+h-t20)*t31-t11*(t20+t30))
*t32+(-2*t21*t30+(-h+t30)*t31+t30*t11)*t12+t11*t31*(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*(-t21+t31))*p+(h*t12-t11*
(t11-t21))*t32^2-2*t12*(-(1/2)*h*t12+(t11-t21)*(-t21+t31))*t32-t31*(-t
21+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-t12*((-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*t31))*p)*t22+t12*((t32*(
t11-t21)+t12*(-t21+t31))*p+(-h*t12-t21*(t11-t21))*t32-t12*t21*(-t21+t3
1))*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+t3
1^2))*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*t2
1*(-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)*t2
1+t11*t31))*t32+t12*((t30-h+t20)*t12+(t11+t31)*t21+t11*t31)*(-t21+t31)
)*p)/(2*(t22-t32)^2*(t12-t22)^2)\n" }{MPLTEXT 1 0 139 "-((-t31*t11-(t2
0+t30)*(t12-t32))*t21+t11*t20*(-t32+t22))*((t12-2*t22+t32)*t21+(t11+t3
1)*t22-t11*t32-t12*t31)/(2*(-t32+t22)^2*(-t22+t12)^2)\n" }{MPLTEXT 1 
0 29 "+F22(t11,t21,t31,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 7 ",q,p);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1977 "Hame32:=unappl
y(  ((-(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+t21-2*t31)*p^2+(h*t22+
h*t12+(2*(t31-(1/2)*t11-(1/2)*t21))*(t11+t21))*p+((2*t30-2*h+2*t20)*t3
1+(-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-t3
0*(t11+t21)))*t32^2+(t12*((-t11+t31)*t22+t12*(-t21+t31))*t22*q^3+(((t1
1-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+(((t2
1-t31)*t22-t12*(-t11+t31))*p^2+(-h*t22^2+(-2*h*t12+2*t31*(-t21+t31))*t
22-h*t12^2+2*t31*(-t11+t31)*t12)*p+((-t30+h-t20)*t31+t11*(t20+t30))*t2
2^2+(((-3*t30+3*h)*t31+(-h+t20+2*t30)*t21+(-t20+t30)*t11)*t12-(2*(-t21
+t31))*(-(1/2)*t11+t31)*t11)*t22-2*t12*((-(1/2)*t31*t20-(1/2)*(h-t20)*
t21)*t12+(-t11+t31)*t21*(t31-(1/2)*t21)))*q+(2*((t31-(1/2)*t11-(1/2)*t
21)*p^2+((1/2)*h*t22+(1/2)*h*t12-(t31-(1/2)*t11-(1/2)*t21)*(t11+t21+t3
1))*p+((-(1/2)*h-t20+(1/2)*t30)*t31+t21*((1/2)*t20-(1/2)*h)-(1/2)*(-t2
0+t30)*t11)*t22+((t20+3*t30*(1/2)-3*h*(1/2))*t31+(-t30+(1/2)*h-(1/2)*t
20)*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*t1
2-t31*(-t11+t31))*t22-t12*t31*(-t21+t31))*q^2+((t12+t22)*((-t11+t31)*t
22+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+t
11*t31*(-t11+t31))*t22^2+((-t21*t30+(-h+t30)*t31)*t12+t31*((t11+t21)*t
31-2*t11*t21))*t12*t22+t31*t12^2*t21*(-t21+t31))*q-(((-t11+t31)*t22+t1
2*(-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+t2
0)*t12+(t11+t21)*t31+t11*t21)*(-t21+t31))*p)/(2*(t22-t32)^2*(t12-t32)^
2)\n" }{MPLTEXT 1 0 149 "+(((t20+t30)*t32-t31*t11-(t20+t30)*t12)*t21+t
11*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 29 "+F32(t11,t21,t3
1,t12,t22,t32)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 6 ",q,p);" }
{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#P1G6\"f*6#I'lam
bdaGF$F$6$I)operatorGF$I&arrowGF$F$,**&,(I$t12GF$\"\"\"I$t22GF$F/I$t32
GF$F/F/9$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$\"\"\"I$t22GF$F0F0*&F/F0I$t32GF$F0F0*&F1F0F3F0F0F09$\"\"#F
0*&,(*&,&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$" }}{PARA 11 "" 1 
"" {XPPMATH 20 ">I#P3G6\"f*6#I'lambdaGF$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$F.F.F.F1\"\"#F.*&,.*(,&I$t20
GF$!\"\"I$t30GF$FAF.F/F.F0F.F.*(F0F.F6F.F8F.F.*(F/F.F6F.F:F.F.*(F-F.F0
F.F@F.F.*(F-F.F8F.F:F.F.*(F-F.F/F.FBF.F.F.F1F.F.F$F$F$" }}{PARA 11 "" 
1 "" {XPPMATH 20 ">I$F22G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%
tt22GF$I%tt32GF$F$6$I)operatorGF$I&arrowGF$F$\"\"!F$F$F$" }}{PARA 11 "
" 1 "" {XPPMATH 20 ">I$F11G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$
I%tt22GF$I%tt32GF$F$6$I)operatorGF$I&arrowGF$F$\"\"!F$F$F$" }}{PARA 11
 "" 1 "" {XPPMATH 20 ">I$F31G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12G
F$I%tt22GF$I%tt32GF$F$6$I)operatorGF$I&arrowGF$F$,$*(I\"hGF$\"\"\"9%F3
,(*$,&9(F39)!\"\"F:F:*&-I#lnG6$%*protectedGI(_syslibGF$6#F7F3,&9'F3F9F
:F:F:*&-F=6#,&FCF3F8F:F3FBF:F3F3#F3\"\"#F$F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I$F12G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%tt22G
F$I%tt32GF$F$6$I)operatorGF$I&arrowGF$F$,$**I\"hGF$\"\"\"9%F39&F3,&*&-
I#lnG6$%*protectedGI(_syslibGF$6#,&9(F39)!\"\"F3,&9'F3F@FA!\"#F3*&-F96
#,&FCF3F?FAF3FBFDFAF3#F3\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">
I$F32G6\"f*6(I%tt11GF$I%tt21GF$I%tt31GF$I%tt12GF$I%tt22GF$I%tt32GF$F$6
$I)operatorGF$I&arrowGF$F$,$*,I\"hGF$\"\"\"9%F39&F3,&-I#lnG6$%*protect
edGI(_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%tt
21GF$I%tt31GF$I%tt12GF$I%tt22GF$I%tt32GF$F$6$I)operatorGF$I&arrowGF$F$
,$*(I\"hGF$\"\"\"9&F3,(*$,&9(F39)!\"\"F:F3*&-I#lnG6$%*protectedGI(_sys
libGF$6#,&9'F3F8F:F3,&FCF3F9F:F:F3*&-F=6#F7F3FDF:F:F3#F3\"\"#F$F$F$" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame11G6\"f*6$I\"qGF$I\"pGF$F$6$I)op
eratorGF$I&arrowGF$F$,&*(,**$9%\"\"$!\"\"*&,**&,(I$t12GF$\"\"\"I$t22GF
$F8I$t32GF$F8F89$F8F8I$t11GF$F8I$t21GF$F8I$t31GF$F8F8F0\"\"#F8*&,0*&,&
*&,&F9F2F:F2F8F7F8F8*&F9F8F:F8F2F8F;F?F8*&,(*&,&F>F2F=F2F8F7F8F8*&,&F<
F2F>F2F8F9F8F8*&F:F8,&F<F8F=F8F8F2F8F;F8F8*&,&I$t20GF$F2I$t30GF$F2F8F7
F8F8*&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,&F7F8F:F2F2,&F7F8F9F2F2F8*(,&
*&,**&,&FQF8FRF8F8F7F8F8FboF8*&F:F8FQF8F2FTF2F8F=F8F8*(F<F8FQF8,&F:F2F
9F8F8F2F8FdoF2FeoF2F8F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame21
G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$,(*(,**$9%\"\"$\"\"
\"*&,**&,(I$t12GF$!\"\"I$t22GF$F8I$t32GF$F8F29$F2F2I$t31GF$F8I$t11GF$F
8I$t21GF$F8F2F0\"\"#F2*&,0*&,&*&,&F7F2F:F2F2F9F2F2*&F7F2F:F2F2F2F;F?F2
*&,(*&,&F>F2F<F2F2F7F2F2*&,&F=F2F<F2F2F9F2F2*&F:F2,&F=F2F>F2F2F2F2F;F2
F2*&,&I\"hGF$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*&,(*&F7F2F
UF2F2*&,(FUF8FQF2FRF8F2F:F2F2*&F<F2F=F2F2F2F9F2F2*&,&*&,&FQF8FRF2F2F:F
2F2FXF2F2F7F2F2*(F:F2F=F2F>F2F2F2F8F2,&F:F8F9F2F8,&F7F2F9F8F8F2*(,&*&,
**&,&F7F8F:F2F2FRF2F2FboF8F_oF8FVF2F2F>F2F2*(F=F2FRF2FhoF2F2F2FhoF8Fio
F8F2*(FQF2F<F2,(*$FhoF8F2*&-I#lnG6$%*protectedGI(_syslibGF$6#FioF2,&F7
F2F:F8F8F2*&-Ffp6#FhoF2F[qF8F8F2#F2F?F$F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I'Hame31G6\"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$F8F8F0\"\"#F8*&,0*&,&*&,&F7F2F9F2F8F:F8
F8*&F7F8F9F8F2F8F;F?F8*&,(*&,&F=F2F<F2F8F:F8F8*&,&F>F2F=F2F8F7F8F8*&,&
F<F8F>F8F8F9F8F2F8F;F8F8*&,&I\"hGF$F2I$t30GF$F8F8F:F8F8*&,(FRF2FQF8I$t
20GF$F2F8F7F8F8*&FUF8F9F8F8*&FLF8F<F8F8*&F=F8F>F8F2F8F0F8F8*&F;F8,,**F
;F?F7F8F9F8F:F8F8*&,&*&,&*&F<F8F9F8F8*&F7F8F=F8F8F8F:F8F8*(F7F8F9F8F>F
8F8F8F;F8F8*&,(*&F7F8FUF8F8*&FTF8F9F8F8*&F=F8F<F8F8F8F:F8F8*&,&*&FPF8F
9F8F8FXF8F8F7F8F8*(F9F8F<F8F>F8F8F8F8F8,&F:F2F9F8F2,&F7F8F:F2F2F8*(,&*
&,**&,&FUF2FRF2F8F:F8F8*&F>F8F<F8F8F_oF8*&F7F8FRF8F8F8F=F8F8*(F<F8FUF8
FfoF8F2F8FfoF2FgoF2F8*(FQF8F=F8,(*$FfoF2F2*&-I#lnG6$%*protectedGI(_sys
libGF$6#FfoF8FgoF2F2*&-Ffp6#,&F7F8F9F2F8FgoF2F8F8#F8F?F$F$F$" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I'Hame12G6\"f*6$I\"qGF$I\"pGF$F$6$I)operatorG
F$I&arrowGF$F$,(*(,,*&,***I$t32GF$\"\"\"I$t22GF$F3,(I$t21GF$F3I$t31GF$
F3I$t11GF$!\"#F39$\"\"$F3*&,(*(,&F4F3F2F3F3F5F39%F3!\"\"*&,&*&I\"hGF$F
3F2F3FA*&F7F3F5F3F3F3F4F3F3*(F2F3F6F3F5F3F3F3F:\"\"#F3*&,,*&F5F3F@FHF3
*&,(*&FEF3F4F3F3FDF3*&,&F6F3F7F3F3F5F3FAF3F@F3F3*&,(*&I$t30GF$F3F8F3F9
*&F6F3FTF3F3*&,&FEFAFTF3F3F7F3F3F3F4F3F3*&,(*&F8F3I$t20GF$F3F9*&,&FEFA
FenF3F3F6F3F3*&F7F3FenF3F3F3F2F3F3*(F7F3F6F3F5F3F3F3F:F3F3*&,(*&F@F3FE
F3F3*&,&FTF9FenF9F3F8F3F3*&FPF3,(FTF3FEFAFenF3F3F3F3F@F3FAF3I$t12GF$FH
F3*&,***,&*&,&F8FAF7F3F3F4F3F3*&F2F3,&F8F3F6FAF3FAF3F2F3F4F3F:F;FA*&,*
*&,&*&FgoF3F4FHF3*&F2FHFioF3FAF3F@F3F3*&,&FDF3*&F7F3FgoF3FAF3F4FHF3*(,
&FD#F3FH*&FioF3FgoF3F3F3F2F3F4F3FH*(F6F3F2FHFioF3F3F3F:FHF3*&,,*&,&*&,
&F8FAF6F3F3F4F3F3*&F2F3FgoF3F3F3F@FHF3*&,**&FEF3F4FHFA*&,&FDF9*&F8F3Fi
oF3FHF3F4F3F3*&FEF3F2FHFA*(F8F3FgoF3F2F3F9F3F@F3F3*&,&FSF3FVFAF3F4FHF3
*&,&*&,(*&,&FenF;FTF;F3F8F3F3*&,(FEF3FenFAFTF9F3F6F3F3*&,(FEFAFenFHFTF
3F3F7F3FAF3F2F3F3*(F7F3FioF3,&F8F9F7F3F3F3F3F4F3F3*&,&*&,&FZFep*&,&FEF
3FenFAF3F6F3FepF3F2F3F3*(FgoF3F6F3,&F6#FAFHF8F3F3F3F3F2F3FHF3F:F3F3*&F
@F3,,FKF3*&,(FNFAFDFA*&,(F8F3F6F3F7F3F3F5F3FAF3F@F3F3*&,(*&,&FenF;FTF3
F3F8F3F3FirF3FarFAF3F4F3F3*&,(*&F8F3,&FenF3FTF;F3F3F_rF3FVFAF3F2F3F3*&
F5F3,&*&F8F3FPF3F3*&F6F3F7F3F3F3F3F3FAF3FaoF3F3**F2F3,(*&FeoF3F@F3F3*&
,&FDFA*&F8F3FgoF3FAF3F4F3F3*(F2F3F8F3FioF3F3F3F4F3F:FHF3*&,,*(FeoF3F?F
3F@FHFA*&,(*&,(FDF3*$F8FHFA*$F7FHF3F3F4FHF3*&,&FeqF3*&,&F^uF9F_tFHF3F2
F3F3F3F4F3F3*&,&F^uFA*$F6FHF3F3F2FHF3F3F@F3F3*&,&*&,&*&,&FenFAFTFAF3F8
F3F3*&F`oF3F7F3F3F3F2F3F3*(F8F3F7F3FgoF3FAF3F4FHF3*(F2F3,&*&,&*&F8F3,&
FenF3FTF3F3F3*&F`oF3F6F3FAF3F2F3F3*&,&F^tF3F_tF9F3F8F3FAF3F4F3FA**F2FH
F8F3F6F3FioF3F3F3F:F3F3*&F@F3,,*&FeoF3F@FHF3*&,&*&,&FDFA*&FgoF3FcsF3FA
F3F4F3F3*(F2F3FioF3FcsF3F3F3F@F3F3*(FenF3FgoF3F4FHFA*&,&*&,(FcvF3FirF3
FVFAF3F2F3F3*&FgoF3F]tF3F3F3F4F3F3*(F2F3,(*&,&F7FAF6FAF3F8F3F3*&FTF3F2
F3F3F_tFAF3FioF3F3F3F3F3,&FaoF3F2FAF9,&FaoF3F4FAF9Fep**,**&,&FaoF]sF2F
epF3F6F3F3*&,&F8F3F7F]sF3FaoF3F3*&,&F4F]sF2F]sF3F8F3F3*&F4F3F7F3FepF3,
&*&,(*&F\\vF3FaoF3F3*&F7F3F8F3FA*&FdvF3F2F3F3F3F6F3F3*(F8F3FenF3,&F2FA
F4F3F3F3F3F]xF9F^xF9F3**FEF3F6F3F7F3,&*&-I#lnG6$%*protectedGI(_syslibG
F$6#F_yF3F]xF9F3*&-Fdy6#F^xF3F]xF9FAF3FepF$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$t11GF$F3I$t21GF$!\"#I$t31GF
$F3F39$\"\"$F3*&,(*(,&F2F3F4F3F3F5F39%F3!\"\"*&,&*&I\"hGF$F3F2F3FA*&F6
F3F5F3F3F3F4F3F3*(F2F3F9F3F5F3F3F3F:\"\"#F3*&,,*&F5F3F@FHF3*&,(*&FEF3F
4F3F3FDF3*&,&F6F3F9F3F3F5F3FAF3F@F3F3*&,(*&,(I$t30GF$FHFEF8I$t20GF$FHF
3F7F3F3*&,(FUFAFEF3FVFAF3F9F3F3*&F6F3,&FVF3FUF3F3FAF3F4F3F3*&,(*&F7F3F
UF3F8*&,&FEFAFUF3F3F9F3F3*&FUF3F6F3F3F3F2F3F3*(F6F3F9F3F5F3F3F3F:F3F3*
&,(*&F@F3FEF3F3*&,&FEF8FVFHF3F7F3F3*&FVF3FPF3FAF3F@F3FAF3I$t22GF$FHF3*
&,***F2F3F4F3,&*&F4F3,&F6F3F7FAF3F3*&F2F3,&F7FAF9F3F3F3F3F:F;FA*&,**&,
&*&F4FHFhoF3F3*&F2FHFjoF3F3F3F@F3F3*&,&FDF3*&F6F3FhoF3FAF3F4FHF3*(F2F3
,&FD#FAFH*&FhoF3FjoF3F3F3F4F3F8*(F9F3FjoF3F2FHFAF3F:FHF3*&,,*&,&*&FjoF
3F4F3F3*&F2F3FhoF3F3F3F@FHF3*&,(*&FEF3F4FHFA*&,&FDF8*&F7F3FjoF3F8F3F4F
3F3*&F2F3,&FDF3*&F7F3FhoF3FHF3FAF3F@F3F3*&,&*&FXF3F7F3F3FYF3F3F4FHF3*&
,&*&,(*&,&FEF;FV!\"$F3F7F3F3*&,(FEFAFVFHFUF3F3F9F3F3*&,&FVFAFUF3F3F6F3
FAF3F2F3F3*(F6F3,&F7F8F6F3F3FjoF3FAF3F4F3F3*&F2F3,&*&,&FgnFAFhnF3F3F2F
3F3*(F9F3FhoF3,&F9F3F7F8F3F3F3FAF3F:F3F3*&,,FKF3*&,(FNFAFDFA*&,(F6F3F7
F3F9F3F3F5F3FAF3F@F3F3*&,(*&,(FUFHFEF3FVFAF3F7F3F3*&,&FEF3FUFAF3F9F3F3
FdrFAF3F4F3F3*&,(*&,(FUF8FEF;FVFarF3F7F3F3FbrF3FYF3F3F2F3F3*&F5F3,&*&F
PF3F7F3F3*&F9F3F6F3F3F3F3F3F@F3FAF3FboF3F3**F2F3,(*&FfoF3F@F3F3*&,&FDF
AFgqFAF3F4F3F3*(F2F3F7F3FjoF3FAF3F4F3F:FHF3*&,,*(F?F3FfoF3F@FHFA*&,(*&
,(FDF3*$F6FHF3*$F7FHFAF3F4FHF3*&,&*&FEF3F2FHF3*&,&*&F6F3F9F3FHF`uF8F3F
2F3F3F3F4F3F3*&F2FH,&F`uFA*$F9FHF3F3F3F3F@F3F3*&,&*&,&*&,&FEFAFVF3F3F7
F3F3*&F6F3FVF3FAF3F2F3F3*(F6F3F7F3FhoF3FAF3F4FHF3*(F2F3,(*&,&*&,&FEF3F
VFAF3F7F3F3*&F9F3FVF3F3F3F2F3F3*&,&F6FAF9FAF3F7FHF3*(F6F3F7F3F9F3FHF3F
4F3FA**F9F3F2FHF7F3FjoF3FAF3F:F3F3*&,,*&FfoF3F@FHF3*&,&*&,&FDFA*&FhoF3
FcsF3FAF3F4F3F3*(F2F3FjoF3FcsF3FAF3F@F3F3*(FUF3FhoF3F4FHFA*&,&*&,(FfvF
3FhsF3FYF3F3F2F3F3*&FhoF3F_tF3F3F3F4F3F3*(F2F3,(*&,(FUF3FEFAFVF3F3F2F3
F3F`tF3FatF3F3FjoF3F3F3F@F3F3F3,&F4FAFboF3F8,&F2F3FboFAF8#F3FH**,&*&,&
FatFA*&FZF3,&F2F3F4FAF3FAF3F7F3F3*(F6F3FVF3F`xF3F3F3,**&,(F2F3FboF8F4F
3F3F7F3F3*&FPF3FboF3F3*&F4F3F6F3FA*&F2F3F9F3FAF3F`xF8FaxF8FfpF$F$F$" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">I'Hame32G6\"f*6$I\"qGF$I\"pGF$F$6$I)op
eratorGF$I&arrowGF$F$,(*(,,*&,***,(I$t31GF$\"\"\"I$t11GF$#!\"\"\"\"#I$
t21GF$F6F4I$t12GF$F4I$t22GF$F49$\"\"$!\"#*&,(*(F2F4,&F:F4F;F4F49%F4F8*
&,&*&I\"hGF$F4F:F4F7*&F2F4F5F4F>F4F;F4F4*(F2F4F:F4F9F4F>F4F<F8F4*&,,*&
,(F5F4F9F4F3F>F4FCF8F4*&,(*&FGF4F;F4F4FFF4*&F2F4,&F5F4F9F4F4F8F4FCF4F4
*&,(*&,(I$t30GF$F8FGF>I$t20GF$F8F4F3F4F4*&,(FWF7FGF4FXF7F4F9F4F4*&F5F4
,&FXF4FWF4F4F7F4F;F4F4*&,(*&F3F4FXF4F>*&,&FGF7FXF4F4F9F4F4*&F5F4FXF4F4
F4F:F4F4*(F9F4F2F4F5F4F>F4F<F4F4*&FCF4,(*&FCF4FGF4F4*&,&FWF8FGF>F4F3F4
F4*&FWF4FRF4F7F4F7F4I$t32GF$F8F4*&,***F:F4,&*&,&F5F7F3F4F4F;F4F4*&F:F4
,&F9F7F3F4F4F4F4F;F4F<F=F4*&,**&,&*&,&F5F4F3F7F4F;F8F4*&F:F8F\\pF4F7F4
FCF4F4*&,&FFF4*&F5F4FjoF4F4F4F;F8F4*(F:F4,&FFF6*&F\\pF4FjoF4F4F4F;F4F>
*(F9F4F:F8F\\pF4F4F4F<F8F4*&,,*&,&*&,&F9F4F3F7F4F;F4F4*&F:F4FjoF4F7F4F
CF8F4*&,**&FGF4F;F8F7*&,&FFF>*&F3F4F\\pF4F8F4F;F4F4*&FGF4F:F8F7*(F3F4F
joF4F:F4F8F4FCF4F4*&,&*&FZF4F3F4F4FenF4F4F;F8F4*&,&*&,(*&,&FW!\"$FGF=F
4F3F4F4*&,(FGF7FXF4FWF8F4F9F4F4*&,&FXF7FWF4F4F5F4F4F4F:F4F4*(F\\pF4,&F
5F6F3F4F4F5F4F>F4F;F4F4*&F:F4,&*&,&FinF6*&,&FGF4FXF7F4F9F4F6F4F:F4F4*(
FjoF4F9F4,&F3F4F9F6F4F4F4F>F4F<F4F4*&,,*&F2F4FCF8F4*&,(FP#F4F8FFFgs*&F
2F4,(F5F4F9F4F3F4F4F7F4FCF4F4*&,(*&,(FGF6FXF7FWFgsF4F3F4F4*&F9F4,&FXFg
sFGF6F4F4FfrF6F4F;F4F4*&,(*&,(FXF4FW#F=F8FG#FcrF8F4F3F4F4*&,(FWF7FGFgs
FXF6F4F9F4F4FenF6F4F:F4F4*&F2F4,&*&FRF4F3F4F4*&F9F4F5F4F4F4F4F4FCF4F8F
4FdoF4F4**F:F4F;F4,(*&FhoF4FCF4F4*&,&FFF4*&F3F4FjoF4F7F4F;F4F4*(F:F4F3
F4F\\pF4F7F4F<F8F7*&,,*(FBF4FhoF4FCF8F4*&,(*&,(FFF4*$F5F8F4*$F3F8F7F4F
;F8F4*&,&FhqF4*&,&*&F5F4F9F4F8F[vF>F4F:F4F4F4F;F4F4*&,&*$F9F8F4F[vF7F4
F:F8F4F4FCF4F4*&,&*&,&*&,&FGF7FWF4F4F3F4F4*&FWF4F5F4F7F4F:F4F4*(F5F4F3
F4FjoF4F4F4F;F8F4*(,&*&,&*&F9F4FWF4F7FhvF4F4F:F4F4*&F3F4,&FjtF4F[uF>F4
F4F4F:F4F;F4F4**F3F4F:F8F9F4F\\pF4F4F4F<F4F4*&,,*&FhoF4FCF8F4*&,&*&,&F
FF4*&FjoF4FisF4F7F4F;F4F4*(F:F4F\\pF4FisF4F7F4FCF4F4*(FXF4FjoF4F;F8F7*
&,&*&,(FhvF4FjnF4FenF7F4F:F4F4*&FjoF4FitF4F4F4F;F4F4*(F:F4,(*&,(FWF4FG
F7FXF4F4F:F4F4FjtF4F[uF4F4F\\pF4F4F4FCF4F7F4,&FdoF7F;F4F>,&F:F4FdoF7F>
Fgs**,&*&,(*&FfnF4FdoF4F4*&F3F4F5F4F7*&FfnF4F:F4F7F4F9F4F4*(F5F4FXF4Fg
xF4F4F4,**&FhxF4F9F4F4*&,&F5F7F3F8F4FdoF4F4*&,&F:F7F;F7F4F3F4F4*&F;F4F
5F4F4F4FgxF>FhxF>Fgs*,FGF4F9F4F3F4,&-I#lnG6$%*protectedGI(_syslibGF$6#
,&F:F4F;F7F4-F[z6#FgxF7F4FhxF>FgsF$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 110 "Hame11bis:=unapply(1/((t12-t32)*(t12-t22))*(-p^3+ P1
(q)*p^2-P2(q)*p+P3(q)) +t11*t21*t31/((t12-t22)*(t12-t32))\n" }{MPLTEXT
 1 0 67 "-t11*t20*(t22-t32)/((t12-t22)*(t12-t32))  -t10*t21/(t12-t22),
q,p):\n" }{MPLTEXT 1 0 95 "t11*t21*t31/((t12-t22)*(t12-t32))-t11*t20*(
t22-t32)/((t12-t22)*(t12-t32))  -t10*t21/(t12-t22);\n" }{MPLTEXT 1 0 
50 "series(simplify(Hame11(q,p)-Hame11bis(q,p)),t21);\n" }{MPLTEXT 1 
0 106 "Hame21bis:=unapply(-1/((t22-t32)*(t12-t22))*(-p^3+ P1(q)*p^2-P2
(q)*p+P3(q)) +(p-q*t32)*h/(t32-t22), q,p):\n" }{MPLTEXT 1 0 78 "series
(simplify(Hame21(q,p)-(Hame21bis(q,p)-t11*t21*t31/((t12-t22)*(t22-t32)
)\n" }{MPLTEXT 1 0 96 "+t11*t20/(t12-t22)+t10*(t12-t32)*t21/((t22-t32)
*(t12-t22))+F21(t11,t21,t31,t12,t22,t32))),t21);\n" }{MPLTEXT 1 0 35 "
-t11*t21*t31/((t12-t22)*(t22-t32))\n" }{MPLTEXT 1 0 89 "+t11*t20/(t12-
t22)+t10*(t12-t32)*t21/((t22-t32)*(t12-t22))+F21(t11,t21,t31,t12,t22,t
32);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 106 "Hame31bis:=unapply((1/
((t22-t32)*(t12-t32))*(-p^3+ P1(q)*p^2-P2(q)*p+P3(q)) -(p-q*t22)*h/(t3
2-t22)),q,p):\n" }{MPLTEXT 1 0 154 "series(simplify(Hame31(q,p)-(Hame3
1bis(q,p)+t11*t21*t31/((t22-t32)*(t12-t32))-t11*t20/(t12-t32)-t10*t21/
(t22-t32)   +F31(t11,t21,t31,t12,t22,t32))),t31);\n" }{MPLTEXT 1 0 
102 "t11*t21*t31/((t22-t32)*(t12-t32))-t11*t20/(t12-t32)-t10*t21/(t22-
t32)   +F31(t11,t21,t31,t12,t22,t32);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "
" 1 "" {XPPMATH 20 ",(*,I$t11G6\"\"\"\"I$t21GF%F&I$t31GF%F&,&I$t12GF%F
&I$t32GF%!\"\"F,,&F*F&I$t22GF%F,F,F&*,F$F&I$t20GF%F&,&F+F,F.F&F&F)F,F-
F,F,*(,&F0F,I$t30GF%F,F&F'F&F-F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",**,I$t11G6\"\"\"\"I$t21GF%F&I$t31GF%F&,&I$t32GF%!\"\"I$t
22GF%F&F+,&I$t12GF%F&F,F+F+F+*(F$F&I$t20GF%F&F-F+F&*,,&F0F+I$t30GF%F+F
&,&F.F&F*F+F&F'F&F)F+F-F+F&*(I\"hGF%F&F(F&,(*$F)F+F&*&-I#lnG6$%*protec
tedGI(_syslibGF%6#F-F&F4F+F&*&-F;6#F)F&F4F+F+F&#F&\"\"#" }}{PARA 11 ""
 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**,I$t11G6
\"\"\"\"I$t21GF%F&I$t31GF%F&,&I$t32GF%!\"\"I$t22GF%F&F+,&I$t12GF%F&F*F
+F+F&*(F$F&I$t20GF%F&F-F+F+*(,&F0F+I$t30GF%F+F&F'F&F)F+F+*(I\"hGF%F&F'
F&,(*$F)F+F+*&-I#lnG6$%*protectedGI(_syslibGF%6#F)F&F-F+F+*&-F:6#,&F.F
&F,F+F&F-F+F&F&#F&\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "
Hama1:=unapply( simplify(" }{MPLTEXT 1 0 35 "2*(t12-t32)*(t12-t22)*Ham
e12(q,p)+(" }{MPLTEXT 1 0 75 "t12*(3*t11-t21-t31)-(t12+t22+t32)*t11+ t
22*t31+t32*t21)*Hame11(q,p)),q,p):\n" }{MPLTEXT 1 0 62 "Hama1bis:=unap
ply( h*( (t22+t32)*q*p-p^2+(t21+t31)*p -t32*t22*" }{MPLTEXT 1 0 32 "q^
2 -(t22*t31+t32*t21)*q),q,p):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 
25 "Hama2:=unapply( simplify(" }{MPLTEXT 1 0 21 "2*(t22-t12)*(t22-t32)
" }{MPLTEXT 1 0 14 "*Hame22(q,p)+(" }{MPLTEXT 1 0 22 "t22*(3*t21-t11-t
31)- (" }{MPLTEXT 1 0 32 "t12+t22+t32)*t21+t12*t31+t32*t11" }{MPLTEXT 
1 0 21 ")*Hame21(q,p)),q,p):\n" }{MPLTEXT 1 0 19 "Hama2bis:=unapply( "
 }{MPLTEXT 1 0 73 "h*( (t12+t32)*q*p-p^2+(t11+t31)*p -t32*t12*q^2 -(t1
2*t31+t32*t11)*q),q,p)" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 25 "Hama3:=unapply( simplify(" }{MPLTEXT 1 0 21 "2*(t32-t
12)*(t32-t22)" }{MPLTEXT 1 0 14 "*Hame32(q,p)+(" }{MPLTEXT 1 0 54 "t32
*(3*t31-t11-t21)- (t12+t22+t32)*t31+t12*t21+t22*t11" }{MPLTEXT 1 0 21 
")*Hame31(q,p)),q,p):\n" }{MPLTEXT 1 0 19 "Hama3bis:=unapply( " }
{MPLTEXT 1 0 68 "h*( (t12+t22)*q*p-p^2+(t11+t21)*p -t22*t12*q^2 -(t12*
t21+t22*t11)*q)" }{MPLTEXT 1 0 8 ",q,p):\n\n" }}}{EXCHG {PARA 0 "> " 0
 "" {MPLTEXT 1 0 36 "Hamv1:=unapply(simplify(Hame11(q,p)+" }{MPLTEXT 
1 0 12 "Hame21(q,p)+" }{MPLTEXT 1 0 12 "Hame31(q,p))" }{MPLTEXT 1 0 8 
" ,q,p):\n" }{MPLTEXT 1 0 53 "Termv1:=h/2*( (t31-t21)/(t22-t32)   +(ln
(t12-t22)-ln(" }{MPLTEXT 1 0 3 "t22" }{MPLTEXT 1 0 29 "-t32))*(t21+t31
)/(t12-t32));\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 27 "Hamv1(q
,p)- (-h*q+Termv1));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 68 "Hamv2:=unapply(simplify(Hame12(q,p)+Hame22(q,p)+Hame3
2(q,p)) ,q,p):\n" }{MPLTEXT 1 0 43 "simplify(series(Hamv2(q,p)+h*q^2/2
, q=0));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 80 "Hamu1:=unapply(simp
lify(t12*Hame11(q,p)+t22*Hame21(q,p)+t32*Hame31(q,p)) ,q,p):\n" }
{MPLTEXT 1 0 15 "Termu1:=h/2*( (" }{MPLTEXT 1 0 8 "t22*t31-" }{MPLTEXT
 1 0 35 "t21*t32)/(t22-t32)+(ln(t12-t22)-ln(" }{MPLTEXT 1 0 3 "t22" }
{MPLTEXT 1 0 39 "-t32))*(t21*t32+t22*t31)/(t12-t32)   );" }{MPLTEXT 1 
0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 27 "Hamu1(q,p)- (-h
*p+Termu1));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 
30 "Hamu2:=unapply(simplify(2*t12*" }{MPLTEXT 1 0 12 "Hame12(q,p)+" }
{MPLTEXT 1 0 6 "2*t22*" }{MPLTEXT 1 0 12 "Hame22(q,p)+" }{MPLTEXT 1 0 
6 "2*t32*" }{MPLTEXT 1 0 12 "Hame32(q,p)+" }{MPLTEXT 1 0 56 "t11*Hame1
1(q,p)+t21*Hame21(q,p)+t31*Hame31(q,p)) ,q,p):\n" }{MPLTEXT 1 0 40 "si
mplify(series(Hamu2(q,p)+h*p*q, p=0));" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I'Termv1G6\",$*&I\"hGF$\"\"\",&*&,&I$t21GF$!\"\"I$t31GF$F(F(,&I$t32
GF$F-I$t22GF$F(F-F(*(,&-I#lnG6$%*protectedGI(_syslibGF$6#,&I$t12GF$F(F
1F-F(-F56#F/F-F(,&F,F(F.F(F(,&F;F(F0F-F-F(F(#F(\"\"#" }}{PARA 11 "" 1 
"" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 ">I'Termu1G6\",$*&I\"hGF$\"\"\",&*&,&*&I$t21GF$
F(I$t32GF$F(!\"\"*&I$t22GF$F(I$t31GF$F(F(F(,&F.F/F1F(F/F(*(,&-I#lnG6$%
*protectedGI(_syslibGF$6#,&I$t12GF$F(F1F/F(-F76#F3F/F(,&F,F(F0F(F(,&F=
F(F.F/F/F(F(#F(\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 43 
"We load the change of times and coordinates" }}}{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,t3
2);\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 0 132 "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 0 238 "solve(\{TT1(t11,t21,t31,t12,t22,t32)=T
1,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,taufunctio
n(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(T
T1(t11function,t21function,t31function,t12function,t22function,t32func
tion));\n" }{MPLTEXT 1 0 88 "simplify(TT2(t11function,t21function,t31f
unction,t12function,t22function,t32function));\n" }{MPLTEXT 1 0 88 "si
mplify(TT3(t11function,t21function,t31function,t12function,t22function
,t32function));\n" }{MPLTEXT 1 0 88 "simplify(TT4(t11function,t21funct
ion,t31function,t12function,t22function,t32function));\n" }{MPLTEXT 1 
0 88 "simplify(TT5(t11function,t21function,t31function,t12function,t22
function,t32function));\n" }{MPLTEXT 1 0 96 "simplify(taufunction(t11f
unction,t21function,t31function,t12function,t22function,t32function));
\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 250 "partialtaufunction:=unappl
y( diff(t11function,tau)*partialt11 + diff(t21function,tau)*partialt21
+diff(t31function,tau)*partialt31+diff(t12function,tau)*partialt12+dif
f(t22function,tau)*partialt22+diff(t32function,tau)*partialt32,T1,T2,T
3,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
),taufunction(t11,t21,t31,t12,t22,t32)   ):\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 65 "Coefft21:=factor(residue(partialtau/partialt21^2,part
ialt21=0));\n" }{MPLTEXT 1 0 65 "Coefft31:=factor(residue(partialtau/p
artialt31^2,partialt31=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 29 "Ltaup:=-diff(Hamtau(q,p),q):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 79 "checkSolq:=unapply( \+
sqrt((t12-t32)/((t22-t12)*(t32-t22)))*(-p+t22*q+t21),q,p);\n" }
{MPLTEXT 1 0 78 "checkSolp:=unapply( sqrt((t32-t22)/((t12-t32)*(t22-t1
2)))*(p-t12*q-t11),q,p);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 66 "SOL
L:=solve(\{checkSolq(q,p)=checkq,checkSolp(q,p)=checkp\},\{q,p\}):\n" 
}{MPLTEXT 1 0 30 "Solp:=simplify(rhs(SOLL[1])):\n" }{MPLTEXT 1 0 31 "S
olq:=simplify(rhs(SOLL[2])): \n" }{MPLTEXT 1 0 39 "simplify(checkSolq(
Solq,Solp)-checkq);\n" }{MPLTEXT 1 0 39 "simplify(checkSolp(Solq,Solp)
-checkp);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 171 "LtaucheckSolq:=un
apply( simplify( diff(checkSolq(q,p),q)*Ltauq+diff(checkSolq(q,p),p)*L
taup+Coefft21*h*diff(checkSolq(q,p),t21)+Coefft31*h*diff(checkSolq(q,p
),t31)),q,p):\n" }{MPLTEXT 1 0 170 "LtaucheckSolp:=unapply(simplify( d
iff(checkSolp(q,p),q)*Ltauq+diff(checkSolp(q,p),p)*Ltaup+Coefft21*h*di
ff(checkSolp(q,p),t21)+Coefft31*h*diff(checkSolp(q,p),t31)),q,p):\n" }
{MPLTEXT 1 0 90 "LtaucheckSolq2:=unapply(simplify(LtaucheckSolq(Solq,S
olp)),t11, t21, t31, t12, t22, t32):\n" }{MPLTEXT 1 0 90 "LtaucheckSol
p2:=unapply(simplify(LtaucheckSolp(Solq,Solp)),t11, t21, t31, t12, t22
, t32):\n" }{MPLTEXT 1 0 115 "Ltaucheckq:=simplify(LtaucheckSolq2(t11f
unction,t21function ,t31function ,t12function ,t22function ,t32functio
n)):\n" }{MPLTEXT 1 0 115 "Ltaucheckp:=simplify(LtaucheckSolp2(t11func
tion,t21function ,t31function ,t12function ,t22function ,t32function))
:\n" }{MPLTEXT 1 0 150 "HamtaucheckCoordinates:=unapply(simplify(int(L
taucheckq,checkp)-int(simplify(diff(int(Ltaucheckq,checkp),checkq)+Lta
ucheckp),checkq)),checkq,checkp);\n" }{MPLTEXT 1 0 73 "simplify(Ltauch
eckq-diff(HamtaucheckCoordinates(checkq,checkp),checkp));\n" }{MPLTEXT
 1 0 72 "simplify(Ltaucheckp+diff(HamtaucheckCoordinates(checkq,checkp
),checkq));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 53 "solve(taufunction(
t11,t21,t31,t12,t22,t32)=tau,t31):\n" }{MPLTEXT 1 0 99 "t31function:=-
(tau*sqrt((t22-t12)*(t12-t32)*(t32-t22))-t12*t21+t22*t11-t32*t11+t32*t
21)/(t12-t22):\n" }{MPLTEXT 1 0 55 "simplify(taufunction(t11,t21,t31fu
nction,t12,t22,t32));" }}{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$I&arro
wGF$F$,(9'\"\"\"9(F29)F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$TT2
G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operator
GF$I&arrowGF$F$,(9$\"\"\"9%F29&F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 
20 ">I$TT3G6\"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$
TT4G6\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)opera
torGF$I&arrowGF$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,taufunctionG6
\"f*6(I$t11GF$I$t21GF$I$t31GF$I$t12GF$I$t22GF$I$t32GF$F$6$I)operatorGF
$I&arrowGF$F$*&,(*&,&9%\"\"\"9&!\"\"F59'F5F5*&,&9$F7F6F5F59(F5F5*&9)F5
,&F;F5F4F7F5F5F5*(,&F<F5F8F7F5,&F8F5F>F7F5,&F>F5F<F7F5#F7\"\"#F$F$F$" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "<(/I$t11G6\"I#T4GF%/I$t12GF%,(I#T3GF%!
\"\"I#T5GF%F+I#T1GF%\"\"\"/I$t21GF%*&,.*&I$tauGF%F.*(,(F*!\"#F,F+F-F.F
.,&F,F+F*F.F.,(F*F+F,F7F-F.F.#F.\"\"#F.*&F-F.I#T2GF%F.F.*&F-F.F&F.F+*&
F*F.F=F.F7*&F,F.F=F.F+*&F*F.F&F.\"\"$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$t32GF%F," }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I,t11functionG6\"I#T4GF$" }}{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$F)F),&F.F/F,F)F),(F,F/F.F-F0F)
F)#F)\"\"#F)*&F0F)I#T2GF$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,t31functi
onG6\",$*&,.*&I$tauGF$\"\"\"*(,(I#T3GF$!\"#I#T5GF$!\"\"I#T1GF$F*F*,&F/
F0F-F*F*,(F-F0F/F.F1F*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#T2G6\"" }}
{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$tauG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Coefft21
G6\"*&*(,&I$t12GF$\"\"\"I$t22GF$!\"\"F),&I$t32GF$F+F*F)F),&F(F)F-F+F)#
F)\"\"#,(F(F0F*F+F-F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I)Coefft31G6
\",$*&*(,&I$t12GF$\"\"\"I$t22GF$!\"\"F*,&I$t32GF$F,F+F*F*,&F)F*F.F,F*#
F*\"\"#,(F)F1F+F,F.F,F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*checkSol
qG6\"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$t21GF$F0F0F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*checkSolpG6
\"f*6$I\"qGF$I\"pGF$F$6$I)operatorGF$I&arrowGF$F$*&*(,&I$t32GF$\"\"\"I
$t22GF$!\"\"F0,&I$t12GF$F0F/F2F2,&F1F0F4F2F2#F0\"\"#,(*&9$F0F4F0F29%F0
I$t11GF$F2F0F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I7Hamtauc
heckCoordinatesG6\"f*6$I'checkqGF$I'checkpGF$F$6$I)operatorGF$I&arrowG
F$F$*,*(,(I#T3GF$!\"#I#T5GF$!\"\"I#T1GF$\"\"\"F4,&F1F2F/F4F4,(F/F2F1F0
F3F4F4#F4\"\"#,&*,9$F4F6F4F.F4,**$9%F8F4I\"hGF$F4I$t20GF$F2I$t30GF$F2F
4*(F5F4F6F2F.F2F7F2*&,&*(F-F7F;F4I$tauGF$F4F4***(F6F4F.F2F5F2F7F.F4F5F
4,&*$F;F8F2F@F4F4F4F4F>F4F4F4F.F2F5F2F6F2F$F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 
"" 1 "" {XPPMATH 20 "I$tauG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 263 297 "We compute the Ham
iltonian in direction t11, t21, t31 in terms of \\check\{q\} and \\che
ck\{p\}. Since the shift is time-dependent, we need to use the evoluti
ons and the shift and integrate them. In particular, we cannot just si
mply replace (q,p) by their expressions in terms of (\\check\{q\}, \\c
heck\{p\})." }{TEXT 263 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
28 "Le11q:=diff(Hame11(q,p),p):\n" }{MPLTEXT 1 0 19 "Le11p:=-diff(Hame
11" }{MPLTEXT 1 0 5 "(q,p)" }{MPLTEXT 1 0 5 ",q):\n" }{MPLTEXT 1 0 28 
"Le21q:=diff(Hame21(q,p),p):\n" }{MPLTEXT 1 0 29 "Le21p:=-diff(Hame21(
q,p),q):\n" }{MPLTEXT 1 0 28 "Le31q:=diff(Hame31(q,p),p):\n" }{MPLTEXT
 1 0 28 "Le31p:=-diff(Hame31(q,p),q):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 64 "Le11checkSolq:=unapply( simplify( h*diff(checkSolq(q,
p),t12)*0+ " }{MPLTEXT 1 0 211 "h*diff(checkSolq(q,p),t22)*0+h*diff(ch
eckSolq(q,p),t32)*0+h*diff(checkSolq(q,p),t11)*1+h*diff(checkSolq(q,p)
,t21)*0+h*diff(checkSolq(q,p),t31)*0+diff(checkSolq(q,p),q)*Le11q+diff
(checkSolq(q,p),p)*Le11p), q,p):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 274 "Le11checkSolp:=unapply( simplify( h*diff(checkSolp(q,p),t12)*0+
 h*diff(checkSolp(q,p),t22)*0+h*diff(checkSolp(q,p),t32)*0+h*diff(chec
kSolp(q,p),t11)*1+h*diff(checkSolp(q,p),t21)*0+h*diff(checkSolp(q,p),t
31)*0+diff(checkSolp(q,p),q)*Le11q+diff(checkSolp(q,p),p)*Le11p),q,p):
\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 48 "Le11checkq:=simplify(Le11ch
eckSolq(Solq,Solp)):\n" }{MPLTEXT 1 0 45 "Le11checkp:=simplify(Le11che
ckSolp(Solq,Solp)" }{MPLTEXT 1 0 2 "):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT
 1 0 1 "\n" }{MPLTEXT 1 0 31 "Hame11check:=unapply(simplify( " }
{MPLTEXT 1 0 28 "int(Le11checkq,checkp) -int(" }{MPLTEXT 1 0 54 "Le11c
heckp+diff(int(Le11checkq,checkp),checkq),checkq)" }{MPLTEXT 1 0 4 " )
  " }{MPLTEXT 1 0 15 ",checkq,checkp)" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 62 "simplify(Le11checkq-diff(Hame11check(chec
kq,checkp),checkp));\n" }{MPLTEXT 1 0 60 "simplify(Le11checkp+diff(Ham
e11check(checkq,checkp),checkq))" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 0 
"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,Hame11checkG6\"f*6$I'checkqGF$I'
checkpGF$F$6$I)operatorGF$I&arrowGF$F$*(,&*,9$\"\"\",&I$t12GF$F0I$t32G
F$!\"\"F0,&F2F0I$t22GF$F4F0,**$9%\"\"#F0I\"hGF$F0I$t20GF$F4I$t30GF$F4F
0*(,&F3F4F6F0F0F1F4F5F4#F0F:F0*&,&**F?F0,&*$F/F:F0F<F4F0F5F0*(F1F0F5F4
F?F4F@F0*&F/F0,(*&F2F0,&I$t21GF$F4I$t31GF$F0F0F0*&F6F0,&I$t11GF$F0FLF4
F0F0*&F3F0,&FOF0FKF4F0F4F0F0F0F9F0F0F0F1F4F5F4F$F$F$" }}{PARA 11 "" 1 
"" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 275 "Le21checkSolq:=unapply( sim
plify( h*diff(checkSolq(q,p),t12)*0+ h*diff(checkSolq(q,p),t22)*0+h*di
ff(checkSolq(q,p),t32)*0+h*diff(checkSolq(q,p),t11)*0+h*diff(checkSolq
(q,p),t21)*1+h*diff(checkSolq(q,p),t31)*0+diff(checkSolq(q,p),q)*Le21q
+diff(checkSolq(q,p),p)*Le21p), q,p):\n" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 274 "Le21checkSolp:=unapply( simplify( h*diff(checkSolp(q
,p),t12)*0+ h*diff(checkSolp(q,p),t22)*0+h*diff(checkSolp(q,p),t32)*0+
h*diff(checkSolp(q,p),t11)*0+h*diff(checkSolp(q,p),t21)*1+h*diff(check
Solp(q,p),t31)*0+diff(checkSolp(q,p),q)*Le21q+diff(checkSolp(q,p),p)*L
e21p),q,p):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 48 "Le21checkq:=simp
lify(Le21checkSolq(Solq,Solp)):\n" }{MPLTEXT 1 0 48 "Le21checkp:=simpl
ify(Le21checkSolp(Solq,Solp)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 
133 "Hame21check:=unapply(simplify( int(Le21checkq,checkp) -int(Le21ch
eckp+diff(int(Le21checkq,checkp),checkq),checkq) )  ,checkq,checkp);" 
}{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 62 "simplify(Le21checkq-diff(Hame21
check(checkq,checkp),checkp));\n" }{MPLTEXT 1 0 62 "simplify(Le21check
p+diff(Hame21check(checkq,checkp),checkq));\n" }{MPLTEXT 1 0 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I,Hame21checkG6\"f*6$I'checkqGF$I'check
pGF$F$6$I)operatorGF$I&arrowGF$F$*(,&*,9$\"\"\",&I$t12GF$F0I$t32GF$!\"
\"F0,&F2F0I$t22GF$F4F0,**$9%\"\"#F0I\"hGF$F0I$t20GF$F4I$t30GF$F4F0*(,&
F3F4F6F0F0F1F4F5F4#F0F:F4*&,&**F?F0,&*$F/F:F0F<F4F0F5F0*(F1F0F5F4F?F4F
@F0*&F/F0,(*&F2F0,&I$t21GF$F4I$t31GF$F0F0F0*&F6F0,&I$t11GF$F0FLF4F0F0*
&F3F0,&FOF0FKF4F0F4F0F0F0F9F0F4F0F?F4F5F4F$F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 275 "Le31checkSolq:=unapply( simplify( \+
h*diff(checkSolq(q,p),t12)*0+ h*diff(checkSolq(q,p),t22)*0+h*diff(chec
kSolq(q,p),t32)*0+h*diff(checkSolq(q,p),t11)*0+h*diff(checkSolq(q,p),t
21)*0+h*diff(checkSolq(q,p),t31)*1+diff(checkSolq(q,p),q)*Le31q+diff(c
heckSolq(q,p),p)*Le31p), q,p):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 
274 "Le31checkSolp:=unapply( simplify( h*diff(checkSolp(q,p),t12)*0+ h
*diff(checkSolp(q,p),t22)*0+h*diff(checkSolp(q,p),t32)*0+h*diff(checkS
olp(q,p),t11)*0+h*diff(checkSolp(q,p),t21)*0+h*diff(checkSolp(q,p),t31
)*1+diff(checkSolp(q,p),q)*Le31q+diff(checkSolp(q,p),p)*Le31p),q,p):\n
" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 48 "Le31checkq:=simplify(Le31chec
kSolq(Solq,Solp)):\n" }{MPLTEXT 1 0 48 "Le31checkp:=simplify(Le31check
Solp(Solq,Solp)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 133 "Hame31che
ck:=unapply(simplify( int(Le31checkq,checkp) -int(Le31checkp+diff(int(
Le31checkq,checkp),checkq),checkq) )  ,checkq,checkp);" }{MPLTEXT 1 0 
1 "\n" }{MPLTEXT 1 0 62 "simplify(Le31checkq-diff(Hame31check(checkq,c
heckp),checkp));\n" }{MPLTEXT 1 0 61 "simplify(Le31checkp+diff(Hame31c
heck(checkq,checkp),checkq));" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ">I,Hame31checkG6\"f*6$I'checkqGF$I'checkpGF$F$6$I)operato
rGF$I&arrowGF$F$*(,&*,9$\"\"\",&I$t12GF$F0I$t32GF$!\"\"F0,&F2F0I$t22GF
$F4F0,**$9%\"\"#F0I\"hGF$F0I$t20GF$F4I$t30GF$F4F0*(,&F3F4F6F0F0F1F4F5F
4#F0F:F0*&,&**F?F0,&*$F/F:F0F<F4F0F5F0*(F1F0F5F4F?F4F@F0*&F/F0,(*&F2F0
,&I$t21GF$F4I$t31GF$F0F0F0*&F6F0,&I$t11GF$F0FLF4F0F0*&F3F0,&FOF0FKF4F0
F4F0F0F0F9F0F0F0F?F4F1F4F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!"
 }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "Hame11checkinter:=unapply(" }{MPLTEXT 1 0 11 "Hame11c
heck" }{MPLTEXT 1 0 1 "(" }{MPLTEXT 1 0 21 "checkq,checkp),t31):\n" }
{MPLTEXT 1 0 25 "simplify(series(simplify(" }{MPLTEXT 1 0 41 "Hame11ch
eckinter(t31function)),checkp)):\n" }{MPLTEXT 1 0 24 "Hame11checkbis:=
unapply(" }{MPLTEXT 1 0 55 "simplify(Hame11checkinter(t31function)),ch
eckq,checkp);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 155 "Hame11checkter:
=unapply((checkq*checkp^2+(checkq^2-checkq*tau-t20)*checkp +(-t30+h-t2
0)*checkq)*sqrt(t32-t22)/(sqrt(t22-t12)*sqrt(t12-t32)),checkq,checkp);
" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 30 "H
ame11checkbis(checkq,checkp)-" }{MPLTEXT 1 0 14 "Hame11checkter" }
{MPLTEXT 1 0 24 "(checkq,checkp),symbolic" }{MPLTEXT 1 0 2 ");" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I/Hame11checkbisG6\"f*6$I'checkqGF$I'ch
eckpGF$F$6$I)operatorGF$I&arrowGF$F$*(,&*,9$\"\"\",&I$t12GF$F0I$t32GF$
!\"\"F0,&F2F0I$t22GF$F4F0,**$9%\"\"#F0I\"hGF$F0I$t20GF$F4I$t30GF$F4F0*
(,&F3F4F6F0F0F1F4F5F4#F0F:F0*&,&**F?F0,&*$F/F:F4F<F0F0F5F0*(F1F0F5F4F?
F4F@F0*(*(F5F0F?F0F1F0F@I$tauGF$F0F/F0F0F0F9F0F4F0F1F4F5F4F$F$F$" }}
{PARA 11 "" 1 "" {XPPMATH 20 ">I/Hame11checkterG6\"f*6$I'checkqGF$I'ch
eckpGF$F$6$I)operatorGF$I&arrowGF$F$**,(*&9$\"\"\"9%\"\"#F0*&,(*$F/F2F
0*&F/F0I$tauGF$F0!\"\"I$t20GF$F8F0F1F0F0*&,(I$t30GF$F8I\"hGF$F0F9F8F0F
/F0F0F0,&I$t32GF$F0I$t22GF$F8#F0F2,&F@F0I$t12GF$F8#F8F2,&FCF0F?F8FDF$F
$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 59 "Hame21checkinter:=unapply(Hame21check(checkq,checkp
),t31):\n" }{MPLTEXT 1 0 7 "factor(" }{MPLTEXT 1 0 76 "simplify(series
(simplify(Hame21checkinter(t31function)),checkp),symbolic)):\n" }
{MPLTEXT 1 0 79 "Hame21checkbis:=unapply(simplify(Hame21checkinter(t31
function)),checkq,checkp);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 247 "Ha
me21checkter := unapply(-(-t30+h-t20)*checkq*sqrt(t12-t32)/(sqrt(t12-t
22)*sqrt(-t32+t22))+(-checkq^2+checkq*tau+t20)*sqrt(t12-t32)*checkp/(s
qrt(-t32+t22)*sqrt(t12-t22))-checkq*sqrt(t12-t32)*checkp^2/(sqrt(t12-t
22)*sqrt(-t32+t22)),checkq,checkp);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 79 "simplify(Hame21checkbis(checkq,checkp)-Hame21checkter(checkq,che
ckp),symbolic);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
/Hame21checkbisG6\"f*6$I'checkqGF$I'checkpGF$F$6$I)operatorGF$I&arrowG
F$F$*(,&*,9$\"\"\",&I$t12GF$F0I$t32GF$!\"\"F0,&F2F0I$t22GF$F4F0,**$9%
\"\"#F0I\"hGF$F0I$t20GF$F4I$t30GF$F4F0*(,&F3F4F6F0F0F1F4F5F4#F0F:F4*&,
&**F?F0,&*$F/F:F4F<F0F0F5F0*(F1F0F5F4F?F4F@F0*(*(F5F0F?F0F1F0F@I$tauGF
$F0F/F0F0F0F9F0F0F0F5F4F?F4F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I/
Hame21checkterG6\"f*6$I'checkqGF$I'checkpGF$F$6$I)operatorGF$I&arrowGF
$F$,(*,,(I$t30GF$!\"\"I\"hGF$\"\"\"I$t20GF$F0F29$F2,&I$t12GF$F2I$t32GF
$F0#F2\"\"#,&F6F2I$t22GF$F0#F0F9,&F7F0F;F2F<F0*,,(*$F4F9F0*&F4F2I$tauG
F$F2F2F3F2F2F5F89%F2F:F<F=F<F2*,F4F2F5F8FCF9F:F<F=F<F0F$F$F$" }}{PARA 
11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 59 "Hame31checkinter:=unapply(Hame31check(checkq,checkp),t31):\n" }
{MPLTEXT 1 0 75 "simplify(series(simplify(Hame31checkinter(t31function
)),checkp),symbolic):\n" }{MPLTEXT 1 0 79 "Hame31checkbis:=unapply(sim
plify(Hame31checkinter(t31function)),checkq,checkp);" }{MPLTEXT 1 0 1 
"\n" }{MPLTEXT 1 0 244 "Hame31checkter:=unapply(checkq*(-t30+h-t20)*sq
rt(t12-t22)/(sqrt(t12-t32)*sqrt(-t32+t22))-sqrt(t12-t22)*(-checkq^2+ch
eckq*tau+t20)*checkp/(sqrt(t12-t32)*sqrt(-t32+t22))+checkq*sqrt(t12-t2
2)*checkp^2/(sqrt(t12-t32)*sqrt(-t32+t22)),checkq,checkp);" }{MPLTEXT 
1 0 1 "\n" }{MPLTEXT 1 0 79 "simplify(Hame31checkbis(checkq,checkp)-Ha
me31checkter(checkq,checkp),symbolic);" }}{PARA 11 "" 1 "" {XPPMATH 20
 ">I/Hame31checkbisG6\"f*6$I'checkqGF$I'checkpGF$F$6$I)operatorGF$I&ar
rowGF$F$*(,&*,9$\"\"\",&I$t12GF$F0I$t32GF$!\"\"F0,&F2F0I$t22GF$F4F0,**
$9%\"\"#F0I\"hGF$F0I$t20GF$F4I$t30GF$F4F0*(,&F3F4F6F0F0F1F4F5F4#F0F:F0
*&,&**F?F0,&*$F/F:F4F<F0F0F5F0*(F1F0F5F4F?F4F@F0*(*(F5F0F?F0F1F0F@I$ta
uGF$F0F/F0F0F0F9F0F4F0F?F4F1F4F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "
>I/Hame31checkterG6\"f*6$I'checkqGF$I'checkpGF$F$6$I)operatorGF$I&arro
wGF$F$,(*,9$\"\"\",(I$t30GF$!\"\"I\"hGF$F/I$t20GF$F2F/,&I$t12GF$F/I$t3
2GF$F2#F2\"\"#,&F6F/I$t22GF$F2#F/F9,&F7F2F;F/F8F/*,F:F<,(*$F.F9F2*&F.F
/I$tauGF$F/F/F4F/F/9%F/F5F8F=F8F2*,F.F/F:F<FCF9F5F8F=F8F/F$F$F$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
262 61 "We may now obtain the Hamiltonian evolution relatively to tau"
 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Hamtaucheck:=unapply( si
mplify( Coefft21*" }{MPLTEXT 1 0 30 "Hame21checkbis(checkq,checkp)+" }
{MPLTEXT 1 0 9 "Coefft31*" }{MPLTEXT 1 0 30 "Hame31checkbis(checkq,che
ckp))" }{MPLTEXT 1 0 17 ", checkq,checkp);" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 59 "Hamtaucheckbis:=unapply( -(checkq*checkp^2+checkp*che
ckq^2-" }{MPLTEXT 1 0 3 "tau" }{MPLTEXT 1 0 16 "*checkq*checkp -" }
{MPLTEXT 1 0 4 "t20*" }{MPLTEXT 1 0 16 "checkp +checkq*(" }{MPLTEXT 1 
0 25 "t10+h)) ,checkq,checkp);\n" }{MPLTEXT 1 0 36 "simplify(Hamtauche
ck(checkq,checkp)-" }{MPLTEXT 1 0 41 "Hamtaucheckbis(checkq,checkp),sy
mbolic);\n" }{MPLTEXT 1 0 55 "hdcheckqdtau:=diff(Hamtaucheck(checkq,ch
eckp),checkp):\n" }{MPLTEXT 1 0 56 "hdcheckpdtau:=-diff(Hamtaucheck(ch
eckq,checkp),checkq):\n" }{MPLTEXT 1 0 90 "HamtaucheckOldCoordinatesfu
nction:=unapply(Hamtaucheck(checkq,checkp),checkq,checkp,tau):\n" }
{MPLTEXT 1 0 139 "HamtaucheckOldCoordinates:=simplify(HamtaucheckOldCo
ordinatesfunction(checkSolq(q,p),checkSolp(q,p),taufunction(t11,t21,t3
1,t12,t22,t32))):" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,HamtaucheckG6\"f
*6$I'checkqGF$I'checkpGF$F$6$I)operatorGF$I&arrowGF$F$,$*,,&*,9$\"\"\"
,&I$t12GF$F1I$t32GF$!\"\"F1,&F3F1I$t22GF$F5F1,**$9%\"\"#F1I\"hGF$F1I$t
20GF$F5I$t30GF$F5F1*(,&F4F5F7F1F1F2F5F6F5#F1F;F1*&,&**F@F1,&*$F0F;F5F=
F1F1F6F1*(F2F1F6F5F@F5FAF1*(*(F6F1F@F1F2F1FAI$tauGF$F1F0F1F1F1F:F1F5F1
FIFAF6F5F@F5F2F5F5F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I/Hamtauche
ckbisG6\"f*6$I'checkqGF$I'checkpGF$F$6$I)operatorGF$I&arrowGF$F$,,*&9$
\"\"\"9%\"\"#!\"\"*&F0F/F.F1F2*(F0F/F.F/I$tauGF$F/F/*&F0F/I$t20GF$F/F/
*&,(I$t30GF$F2I\"hGF$F/F7F2F/F.F/F2F$F$F$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 0 {PARA 217 "" 0 "" {TEXT 213 119 "We now need to compute the sy
mplectic two form Omega using the differential geometry package to com
pute wedge products." }{TEXT 213 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "DGsetup([t12,t22,t32,t11,t21,t31,q,p],B,verbose);" }
{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "IOThe~following~coor
dinates~have~been~protected:G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7*I$
t12G%*protectedGI$t22GF$I$t32GF$I$t11GF$I$t21GF$I$t31GF$I\"qGF$I\"pGF$
" }}{PARA 11 "" 1 "" {XPPMATH 20 "IgnThe~following~vector~fields~have~
been~defined~and~protected:G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mf
encedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6&-I%mrowGF$61-F,6%
-I#miGF$6%Q$_DGF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-
Q0&ApplyFunction;F'/F8Q'normalF'/%&fenceGQ&falseF'/%*separatorGFB/%)st
retchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/%
'lspaceGQ&0.0emF'/%'rspaceGFQ-F#6$-F,6#-F#6&-F,6%-F#6&-F,6'-I#msGF$6#Q
'vectorF'-F;6-Q\",F'F>F@/FDF6FEFGFIFKFMFO/FSQ,0.3333333emF'-F16%Q\"BF'
F4F7F^o-F#6&-F,6#-F16%Q!F'F4F7F>/%%openGQ\"[F'/%&closeGQ\"]F'F>F^pFapF
^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-I#mnGF$6$Q\"1F'F>F>F^pFapF^oF`qF>F^pF
apF>F^pFapF>F^pFapF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F
#6&-F,6%-F#6&-F,6#-Faq6$Q\"2F'F>F>F^pFapF^oF`qF>F^pFapF>F^pFapF>F^pFap
F>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#
-Faq6$Q\"3F'F>F>F^pFapF^oF`qF>F^pFapF>F^pFapF>F^pFapF>F^o-F,6%F0F:-F#6
$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Faq6$Q\"4F'F>F>F^
pFapF^oF`qF>F^pFapF>F^pFapF>F^pFapF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%Ff
nF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Faq6$Q\"5F'F>F>F^pFapF^oF`qF>F^pFap
F>F^pFapF>F^pFapF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6
&-F,6%-F#6&-F,6#-Faq6$Q\"6F'F>F>F^pFapF^oF`qF>F^pFapF>F^pFapF>F^pFapF>
F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-F
aq6$Q\"7F'F>F>F^pFapF^oF`qF>F^pFapF>F^pFapF>F^pFapF>F^o-F,6%F0F:-F#6$-
F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Faq6$Q\"8F'F>F>F^pF
apF^oF`qF>F^pFapF>F^pFapF>F^pFapF>F>F^pFap" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "I^oThe~following~differential~1-forms~have~been~defined~a
nd~protected:G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+mod
ulenameG6\"I,TypesettingGI(_syslibGF'6&-I%mrowGF$61-F,6%-I#miGF$6%Q$_D
GF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q0&ApplyFuncti
on;F'/F8Q'normalF'/%&fenceGQ&falseF'/%*separatorGFB/%)stretchyGFB/%*sy
mmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/%'lspaceGQ&0.0e
mF'/%'rspaceGFQ-F#6$-F,6#-F#6&-F,6%-F#6&-F,6'-I#msGF$6#Q%formF'-F;6-Q
\",F'F>F@/FDF6FEFGFIFKFMFO/FSQ,0.3333333emF'-F16%Q\"BF'F4F7F^o-I#mnGF$
6$Q\"1F'F>F>/%%openGQ\"[F'/%&closeGQ\"]F'F^o-F#6&-F,6#-F#6&-F,6%-F#6&-
F,6#FgoF>F[pF^pF^oFgoF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#-
F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"2F'F>F>F[pF^pF^o
FgoF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#
6&-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"3F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[pF^
pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-
F#6&-F,6#-Fho6$Q\"4F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6
%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"
5F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#-F#
6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"6F'F>F>F[pF^pF^oFg
oF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&
-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"7F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[pF^pF
>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#
6&-F,6#-Fho6$Q\"8F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[pF^pF>F[pF^pF>F>F[pF^p"
 }}{PARA 11 "" 1 "" {XPPMATH 20 "I.frame~name:~BG6\"" }}}{EXCHG {PARA 
0 "B > " 0 "" {MPLTEXT 1 0 111 "dcheckq:=(simplify(diff(checkSolq(q,p)
,t12)))*(DGform(t12))+(simplify(diff(checkSolq(q,p),t22)))*(DGform(t22
))\n" }{MPLTEXT 1 0 299 "+(simplify(diff(checkSolq(q,p),t32)))*(DGform
(t32))+(simplify(diff(checkSolq(q,p),t11)))*(DGform(t11))+(simplify(di
ff(checkSolq(q,p),t21)))*(DGform(t21))+(simplify(diff(checkSolq(q,p),t
31)))*(DGform(t31))+(simplify(diff(checkSolq(q,p),q)))*(DGform(q))+(si
mplify(diff(checkSolq(q,p),p)))*(DGform(p));" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 111 "dcheckp:=(simplify(diff(checkSo
lp(q,p),t12)))*(DGform(t12))+(simplify(diff(checkSolp(q,p),t22)))*(DGf
orm(t22))\n" }{MPLTEXT 1 0 299 "+(simplify(diff(checkSolp(q,p),t32)))*
(DGform(t32))+(simplify(diff(checkSolp(q,p),t11)))*(DGform(t11))+(simp
lify(diff(checkSolp(q,p),t21)))*(DGform(t21))+(simplify(diff(checkSolp
(q,p),t31)))*(DGform(t31))+(simplify(diff(checkSolp(q,p),q)))*(DGform(
q))+(simplify(diff(checkSolp(q,p),p)))*(DGform(p));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6-
-F#6%-I&mfracGF$6(-I#mnGF$6$Q\"1F'/%,mathvariantGQ'normalF'-F16$Q\"2F'
F4/%.linethicknessGF3/%+denomalignGQ'centerF'/%)numalignGF>/%)bevelled
GQ&falseF'-I#moGF$6-Q1&InvisibleTimes;F'F4/%&fenceGFC/%*separatorGFC/%
)stretchyGFC/%*symmetricGFC/%(largeopGFC/%.movablelimitsGFC/%'accentGF
C/%'lspaceGQ&0.0emF'/%'rspaceGFX-F.6(-F#6%-I(mfencedGF$6$-F#6(-FE6-Q*&
uminus0;F'F4FHFJFLFNFPFRFT/FWQ,0.2222222emF'/FZFbo-F#6%-I#miGF$6%Q\"qF
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FLFNFPFRFTFaoFco-Fgo6%Q\"pF'FjoF]p-FE6-Q(&minus;F'F4FHFJFLFNFPFRFTFaoF
co-Fgo6%Q$t21F'FjoF]pF4FD-F#6%-Fgo6%Q$_DGF'FjoF]p-FE6-Q0&ApplyFunction
;F'F4FHFJFLFNFPFRFTFVFY-Fjn6$-F#6#-Fjn6&-F#6%-Fjn6&-F#6'-I#msGF$6#Q%fo
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\\uFhpF_pF4FD-Fjn6$-F#6&F^oF_uFbpF_pF4F:F<F?FAFD-I%msupGF$6%FduF7/%1su
perscriptshiftGQ\"0F'F:F<F?FAFbp-F#6%F-FD-F.6(-F#6'-Fjn6$-F#6'-F#6%-Fj
n6$-F#6)FdoFhp-F#6'F7FDFfoFDF_uFbpFepFhpF[qF4FDF\\uFbp-F#6%-Fjn6$-F#6'
-F#6%FfoFDF_uFhp-F#6%F7FDFepFbp-F#6%F7FDF[qF4FDF_pFbp-F#6%F_uFD-Fjn6$-
F#6%FepFhpF[qF4F4FD-Fjn6$FjtF4FD-F#6%F`qFcq-Fjn6$-F#6#-Fjn6&-F#6%F^rFf
r-Fjn6&-F#6#-Fjn6&-F#6%-Fjn6&-F#6#F7F4F_sFbsFfrF0F4F_sFbsF4F_sFbsF4F_s
FbsF4-F#6'FctFDF\\vFD-F]v6%FhuF7F_vF:F<F?FAFbp-F#6%F-FD-F.6(-F#6%-Fjn6
$-F#6'FdoFhpFepFbpF[qF4FD-F#6%F`qFcq-Fjn6$-F#6#-Fjn6&-F#6%F^rFfr-Fjn6&
-F#6#-Fjn6&-F#6%-Fjn6&-F#6#-F16$Q\"3F'F4F4F_sFbsFfrF0F4F_sFbsF4F_sFbsF
4F_sFbsF4-F#6%FctFDF`zF:F<F?FAFbp-F#6%FctFD-F#6%F`qFcq-Fjn6$-F#6#-Fjn6
&-F#6%F^rFfr-Fjn6&-F#6#-Fjn6&-F#6%-Fjn6&-F#6#-F16$Q\"5F'F4F4F_sFbsFfrF
0F4F_sFbsF4F_sFbsF4F_sFbsF4Fbp-F#6'FctFDF_pFD-F#6%F`qFcq-Fjn6$-F#6#-Fj
n6&-F#6%F^rFfr-Fjn6&-F#6#-Fjn6&-F#6%-Fjn6&-F#6#-F16$Q\"7F'F4F4F_sFbsFf
rF0F4F_sFbsF4F_sFbsF4F_sFbsF4Fhp-F#6%FctFD-F#6%F`qFcq-Fjn6$-F#6#-Fjn6&
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F4F_sFbsF4F_sFbsF4F_sFbsF4" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#
/I+modulenameG6\"I,TypesettingGI(_syslibGF'6.-I#moGF$6-Q*&uminus0;F'/%
,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4
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p6$Q\"2F'F//%.linethicknessGF`p/%+denomalignGQ'centerF'/%)numalignGFhp
/%)bevelledGF4Fin-F#6%-FQ6%Q\"qF'FTFWFinFfn-F,6-Q(&minus;F'F/F2F5F7F9F
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Fin-F#6%-FQ6%Q$_DGF'FTFW-F,6-Q0&ApplyFunction;F'F/F2F5F7F9F;F=F?F\\oF^
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&closeGQ\"]F'F`u-FL6&-F#6#-FL6&-F#6%-FL6&-F#6#F]pF/FiuF\\vF`uF]pF/FiuF
\\vF/FiuF\\vF/FiuF\\vF/-F#6'-I&msqrtGF$6#-FG6(-F#6#FN-F#6%-FL6$-F#6%F_
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perscriptshiftGQ\"0F'Fin-F_x6%FjwFapFaxFdpFfpFipF[qFY-F#6%F[pFin-FG6(-
F#6%-FL6$-F#6(F+-F#6%F_qFinF_rFYFiqFbqF\\rF/Fin-F#6%FjsF]t-FL6$-F#6#-F
L6&-F#6%FhtF`u-FL6&-F#6#-FL6&-F#6%-FL6&-F#6#FapF/FiuF\\vF`uF]pF/FiuF
\\vF/FiuF\\vF/FiuF\\vF/-F#6%F]wFinFdxFdpFfpFipF[qFY-F#6%F[pFin-FG6(-F#
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FL6&-F#6#-FL6&-F#6%-FL6&-F#6#-F^p6$Q\"3F'F/F/FiuF\\vF`uF]pF/FiuF\\vF/F
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L6$-F#6#-FL6&-F#6%FhtF`u-FL6&-F#6#-FL6&-F#6%-FL6&-F#6#-F^p6$Q\"4F'F/F/
FiuF\\vF`uF]pF/FiuF\\vF/FiuF\\vF/FiuF\\vF/Fbq-F#6'F]wFinF_rFin-F#6%Fjs
F]t-FL6$-F#6#-FL6&-F#6%FhtF`u-FL6&-F#6#-FL6&-F#6%-FL6&-F#6#-F^p6$Q\"7F
'F/F/FiuF\\vF`uF]pF/FiuF\\vF/FiuF\\vF/FiuF\\vF/FY-F#6%F]wFin-F#6%FjsF]
t-FL6$-F#6#-FL6&-F#6%FhtF`u-FL6&-F#6#-FL6&-F#6%-FL6&-F#6#-F^p6$Q\"8F'F
/F/FiuF\\vF`uF]pF/FiuF\\vF/FiuF\\vF/FiuF\\vF/" }}}{EXCHG {PARA 0 "B > 
" 0 "" {MPLTEXT 1 0 56 "dcheckqwedgedcheckp:=simplify((dcheckq)&wedge(
dcheckp)):" }}}{EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 89 "dtau:=simpl
ify( (simplify(diff(taufunction(t11,t21,t31,t12,t22,t32),t12)))*(DGfor
m(t12))\n" }{MPLTEXT 1 0 74 "+(simplify(diff(taufunction(t11,t21,t31,t
12,t22,t32),t22)))*(DGform(t22))\n" }{MPLTEXT 1 0 74 "+(simplify(diff(
taufunction(t11,t21,t31,t12,t22,t32),t32)))*(DGform(t32))\n" }{MPLTEXT
 1 0 74 "+(simplify(diff(taufunction(t11,t21,t31,t12,t22,t32),t11)))*(
DGform(t11))\n" }{MPLTEXT 1 0 74 "+(simplify(diff(taufunction(t11,t21,
t31,t12,t22,t32),t21)))*(DGform(t21))\n" }{MPLTEXT 1 0 76 "+(simplify(
diff(taufunction(t11,t21,t31,t12,t22,t32),t31)))*(DGform(t31)));\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 100 "dHamtaucheckOldCoordinates:=sim
plify( (simplify(diff(HamtaucheckOldCoordinates,t12)))*(DGform(t12))\n
" }{MPLTEXT 1 0 63 "+(simplify(diff(HamtaucheckOldCoordinates,t22)))*(
DGform(t22))\n" }{MPLTEXT 1 0 63 "+(simplify(diff(HamtaucheckOldCoordi
nates,t32)))*(DGform(t32))\n" }{MPLTEXT 1 0 63 "+(simplify(diff(Hamtau
checkOldCoordinates,t11)))*(DGform(t11))\n" }{MPLTEXT 1 0 63 "+(simpli
fy(diff(HamtaucheckOldCoordinates,t21)))*(DGform(t21))\n" }{MPLTEXT 1 
0 63 "+(simplify(diff(HamtaucheckOldCoordinates,t31)))*(DGform(t31))\n
" }{MPLTEXT 1 0 59 "+(simplify(diff(HamtaucheckOldCoordinates,q)))*(DG
form(q))\n" }{MPLTEXT 1 0 63 "+(simplify(diff(HamtaucheckOldCoordinate
s,p)))*(DGform(p))  ):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 71 "dtaud
wedgedHamtau:= simplify((dtau)&wedge(dHamtaucheckOldCoordinates)):" }
{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulen
ameG6\"I,TypesettingGI(_syslibGF'6%-I&mfracGF$6(-I#mnGF$6$Q\"1F'/%,mat
hvariantGQ'normalF'-F/6$Q\"2F'F2/%.linethicknessGF1/%+denomalignGQ'cen
terF'/%)numalignGF</%)bevelledGQ&falseF'-I#moGF$6-Q1&InvisibleTimes;F'
F2/%&fenceGFA/%*separatorGFA/%)stretchyGFA/%*symmetricGFA/%(largeopGFA
/%.movablelimitsGFA/%'accentGFA/%'lspaceGQ&0.0emF'/%'rspaceGFV-F,6(-F#
6#-F#6'-F#6)F5FB-I(mfencedGF$6$-F#6'-F#6%-F\\o6$-F#6'-I#miGF$6%Q$t11F'
/%'italicGQ%trueF'/F3Q'italicF'-FC6-Q(&minus;F'F2FFFHFJFLFNFPFR/FUQ,0.
2222222emF'/FXFcp-F#6%F+FB-F#6#-Fgo6%Q$t21F'FjoF]pF_p-F#6%F+FB-F#6#-Fg
o6%Q$t31F'FjoF]pF2FB-Fgo6%Q$t12F'FjoF]p-FC6-Q\"+F'F2FFFHFJFLFNFPFRFbpF
dp-F#6%-F\\o6$-F#6&-FC6-Q*&uminus0;F'F2FFFHFJFLFNFPFRFbpFdp-F#6%F+FB-F
#6#FfoFfqF\\qF2FB-Fgo6%Q$t22F'FjoF]pF_p-F#6%F+FB-F#6%-Fgo6%Q$t32F'FjoF
]pFB-F\\o6$-F#6%FfoF_pFipF2F2FB-I%msupGF$6%-F\\o6$-F#6&F_rF]sFfqFfrF2F
5/%1superscriptshiftGQ\"0F'FB-F#6%-Fgo6%Q$_DGF'FjoF]p-FC6-Q0&ApplyFunc
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$6#Q%formF'-FC6-Q\",F'F2FF/FIF\\pFJFLFNFPFRFT/FXQ,0.3333333emF'-Fgo6%Q
\"BF'FjoF]pFfuF.F2/%%openGQ\"[F'/%&closeGQ\"]F'Ffu-F\\o6&-F#6#-F\\o6&-
F#6%-F\\o6&-F#6#F.F2F_vFbvFfuF.F2F_vFbvF2F_vFbvF2F_vFbvF2F_p-F#6'-F\\o
6$-F#6'-F#6%-F\\o6$-F#6%FipF_pF`qF2FBFcqFfq-F#6%-F\\o6$-F#6'FfoF_p-F#6
%F5FBFipFfqF`qF2FBFfrF_pF[sF2FB-Fes6%-F\\o6$-F#6%FcqF_pF]sF2F5F[tFB-F#
6%F`tFct-F\\o6$-F#6#-F\\o6&-F#6%F^uFfu-F\\o6&-F#6#-F\\o6&-F#6%-F\\o6&-
F#6#F5F2F_vFbvFfuF.F2F_vFbvF2F_vFbvF2F_vFbvF2Ffq-F#6%-F\\o6$-F#6%FcqF_
pFfrF2FB-F\\o6$-F#6%-F#6'-F\\o6$-F#6'FgwFfq-F#6%FfrFB-F\\o6$-F#6%FfoF_
pF`qF2F_p-F#6%F]sFB-F\\o6$-F#6'FfoFfqFipF_p-F#6%F5FBF`qF2F2FBFczFB-F#6
%F`tFct-F\\o6$-F#6#-F\\o6&-F#6%F^uFfu-F\\o6&-F#6#-F\\o6&-F#6%-F\\o6&-F
#6#-F/6$Q\"3F'F2F2F_vFbvFfuF.F2F_vFbvF2F_vFbvF2F_vFbvF2F_p-F#6)F5FBFgs
FBFgxFB-F\\o6$-F#6'-F#6%FgsFB-F#6%F`tFct-F\\o6$-F#6#-F\\o6&-F#6%F^uFfu
-F\\o6&-F#6#-F\\o6&-F#6%-F\\o6&-F#6#-F/6$Q\"4F'F2F2F_vFbvFfuF.F2F_vFbv
F2F_vFbvF2F_vFbvF2Ffq-F#6%-F\\o6$-F#6&F_rFcqFfqF]sF2FB-F#6%F`tFct-F\\o
6$-F#6#-F\\o6&-F#6%F^uFfu-F\\o6&-F#6#-F\\o6&-F#6%-F\\o6&-F#6#-F/6$Q\"5
F'F2F2F_vFbvFfuF.F2F_vFbvF2F_vFbvF2F_vFbvF2Ffq-F#6%-F#6%F`tFct-F\\o6$-
F#6#-F\\o6&-F#6%F^uFfu-F\\o6&-F#6#-F\\o6&-F#6%-F\\o6&-F#6#-F/6$Q\"6F'F
2F2F_vFbvFfuF.F2F_vFbvF2F_vFbvF2F_vFbvF2FBFczF2F2-F#6)-I&msqrtGF$6#-F#
6'FczFBFgsFBFgxFBFczFBFgsFBFgxF8F:F=F?" }}}{EXCHG {PARA 0 "B > " 0 "" 
{MPLTEXT 1 0 54 "Omega2:=simplify( (h&mult(dcheckqwedgedcheckp))&minus
(" }{MPLTEXT 1 0 21 "dtaudwedgedHamtau) ):" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 393 "dHame11:=(simplify(diff(H
ame11(q,p),t12)))*(DGform(t12))+ (simplify(diff(Hame11(q,p),t22)))*(DG
form(t22))+ (simplify(diff(Hame11(q,p),t32)))*(DGform(t32))+ (simplify
(diff(Hame11(q,p),t11)))*(DGform(t11))+ (simplify(diff(Hame11(q,p),t21
)))*(DGform(t21))+ (simplify(diff(Hame11(q,p),t31)))*(DGform(t31))+ (s
implify(diff(Hame11(q,p),q)))*(DGform(q))+ (simplify(diff(Hame11(q,p),
p)))*(DGform(p)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 393 "dHame21:=
(simplify(diff(Hame21(q,p),t12)))*(DGform(t12))+ (simplify(diff(Hame21
(q,p),t22)))*(DGform(t22))+ (simplify(diff(Hame21(q,p),t32)))*(DGform(
t32))+ (simplify(diff(Hame21(q,p),t11)))*(DGform(t11))+ (simplify(diff
(Hame21(q,p),t21)))*(DGform(t21))+ (simplify(diff(Hame21(q,p),t31)))*(
DGform(t31))+ (simplify(diff(Hame21(q,p),q)))*(DGform(q))+ (simplify(d
iff(Hame21(q,p),p)))*(DGform(p)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 
0 393 "dHame31:=(simplify(diff(Hame31(q,p),t12)))*(DGform(t12))+ (simp
lify(diff(Hame31(q,p),t22)))*(DGform(t22))+ (simplify(diff(Hame31(q,p)
,t32)))*(DGform(t32))+ (simplify(diff(Hame31(q,p),t11)))*(DGform(t11))
+ (simplify(diff(Hame31(q,p),t21)))*(DGform(t21))+ (simplify(diff(Hame
31(q,p),t31)))*(DGform(t31))+ (simplify(diff(Hame31(q,p),q)))*(DGform(
q))+ (simplify(diff(Hame31(q,p),p)))*(DGform(p)):\n" }{MPLTEXT 1 0 1 "
\n" }{MPLTEXT 1 0 393 "dHame12:=(simplify(diff(Hame12(q,p),t12)))*(DGf
orm(t12))+ (simplify(diff(Hame12(q,p),t22)))*(DGform(t22))+ (simplify(
diff(Hame12(q,p),t32)))*(DGform(t32))+ (simplify(diff(Hame12(q,p),t11)
))*(DGform(t11))+ (simplify(diff(Hame12(q,p),t21)))*(DGform(t21))+ (si
mplify(diff(Hame12(q,p),t31)))*(DGform(t31))+ (simplify(diff(Hame12(q,
p),q)))*(DGform(q))+ (simplify(diff(Hame12(q,p),p)))*(DGform(p)):\n" }
{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 393 "dHame22:=(simplify(diff(Hame22(
q,p),t12)))*(DGform(t12))+ (simplify(diff(Hame22(q,p),t22)))*(DGform(t
22))+ (simplify(diff(Hame22(q,p),t32)))*(DGform(t32))+ (simplify(diff(
Hame22(q,p),t11)))*(DGform(t11))+ (simplify(diff(Hame22(q,p),t21)))*(D
Gform(t21))+ (simplify(diff(Hame22(q,p),t31)))*(DGform(t31))+ (simplif
y(diff(Hame22(q,p),q)))*(DGform(q))+ (simplify(diff(Hame22(q,p),p)))*(
DGform(p)):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 392 "dHame32:=(simpl
ify(diff(Hame32(q,p),t12)))*(DGform(t12))+ (simplify(diff(Hame32(q,p),
t22)))*(DGform(t22))+ (simplify(diff(Hame32(q,p),t32)))*(DGform(t32))+
 (simplify(diff(Hame32(q,p),t11)))*(DGform(t11))+ (simplify(diff(Hame3
2(q,p),t21)))*(DGform(t21))+ (simplify(diff(Hame32(q,p),t31)))*(DGform
(t31))+ (simplify(diff(Hame32(q,p),q)))*(DGform(q))+ (simplify(diff(Ha
me32(q,p),p)))*(DGform(p)):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "B >
 " 0 "" {MPLTEXT 1 0 37 "Omega:=(dHame12)&wedge(DGform(t12)):\n" }
{MPLTEXT 1 0 8 "Omega:=(" }{MPLTEXT 1 0 30 "(dHame22)&wedge(DGform(t22
))) " }{MPLTEXT 1 0 14 "&plus(Omega):\n" }{MPLTEXT 1 0 8 "Omega:=(" }
{MPLTEXT 1 0 30 "(dHame32)&wedge(DGform(t32))) " }{MPLTEXT 1 0 13 "&pl
us(Omega):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 8 "Omega:=(" }{MPLTEXT 
1 0 30 "(dHame11)&wedge(DGform(t11))) " }{MPLTEXT 1 0 14 "&plus(Omega)
:\n" }{MPLTEXT 1 0 8 "Omega:=(" }{MPLTEXT 1 0 30 "(dHame21)&wedge(DGfo
rm(t21))) " }{MPLTEXT 1 0 13 "&plus(Omega):" }{MPLTEXT 1 0 1 "\n" }
{MPLTEXT 1 0 8 "Omega:=(" }{MPLTEXT 1 0 30 "(dHame31)&wedge(DGform(t31
))) " }{MPLTEXT 1 0 13 "&plus(Omega):" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 
1 0 7 "Omega:=" }{MPLTEXT 1 0 37 "(h&mult(DGform(q))&wedge (DGform(p))
)" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 13 "&plus(Omega):" }{MPLTEXT 1 0 
1 "\n" }{MPLTEXT 1 0 23 "Omega:=simplify(Omega):" }}}{EXCHG {PARA 0 "B
 > " 0 "" {MPLTEXT 1 0 50 "DifferenceFundamentalForm:= (Omega)&minus(O
mega2):" }}}{EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 27 "DifferenceFund
amentalForm:=" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 27 "Differenc
eFundamentalForm):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 213 213 "Maple has
 trouble to simplify the expressions due to the presence of square roo
ts that he cannot simplify. In order to help him, we shall make some a
ssumptions on the signs so that he can simplify the expressions." }}}
{EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 25 "ExtractionCoeff:=convert("
 }{MPLTEXT 1 0 33 "DifferenceFundamentalForm,list):\n" }{MPLTEXT 1 0 
41 "ListCoefficients:=ExtractionCoeff[1][2]:\n" }{MPLTEXT 1 0 39 "Eq1:
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