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"with(DifferentialGeometry):\n" }{MPLTEXT 1 0 13 "with(Tools):\n" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 58 "R1:=unapply((-s10-s20)/(xi-X1)-s 11-s21+(-s12-s22)*xi,xi);\n" }{MPLTEXT 1 0 106 "R2:=unapply(sX10*(-s10 -s20-sX10)/(xi-X1)^2+s10*s22+s11*s21+s12*s20+(s11*s22+s12*s21)*xi+s12* s22*xi^2,xi);\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 21 "sX20:=-s10-s20 -sX10;\n" }{MPLTEXT 1 0 140 "KOldCoordinates :=unapply( (1/2)*(sX10+s2 0)*(sX10+s10)*ln((s12-s22)/2)+(1/2)*X1*((X1*s12+2*s11)*s10+s20*(X1*s22 +2*s21)),s11,s21,s12,s22,X1);" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 406 "Hams11 := (-Q^4*s12*s22+(2*X1*s12*s22+(-s12-s22 )*P-s11*s22-s12*s21)*Q^3+(-X1^2*s12*s22+((2*s12+2*s22)*P+2*s11*s22+2*s 12*s21)*X1-P^2+(-s11-s21)*P+(-s20-h)*s12+(h-s10)*s22-s11*s21)*Q^2+(((- s12-s22)*P-s12*s21-s11*s22)*X1^2+(2*P^2+(2*s11+2*s21)*P+(2*s20+2*h)*s1 2+(-h+2*s10)*s22+2*s11*s21)*X1+P*(sX10+sX20))*Q+((-s20-h)*s12-P^2+(-s1 1-s21)*P-s10*s22-s11*s21)*X1^2-P*(sX10+sX20)*X1-sX10*sX20)/((Q-X1)*(-s 12+s22))\n" }{MPLTEXT 1 0 2 "+\n" }{MPLTEXT 1 0 70 "U11(s11,s21,s12,s2 2,X1) +diff(KOldCoordinates(s11,s21,s12,s22,X1),s11)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 388 "Hams21 := (Q^4*s12*s22+( -2*X1*s12*s22+(s12+s22)*P+s11*s22+s12*s21)*Q^3+(X1^2*s12*s22+((-2*s12- 2*s22)*P-2*s11*s22-2*s12*s21)*X1+P^2+(s21+s11)*P+s10*s22+s11*s21+s12*s 20)*Q^2+(((s12+s22)*P+s11*s22+s12*s21)*X1^2+(-2*P^2+(-2*s11-2*s21)*P+( -h-2*s20)*s12-2*s10*s22-2*s11*s21)*X1-P*(sX10+sX20))*Q+((s20+h)*s12+P^ 2+(s21+s11)*P+s10*s22+s11*s21)*X1^2+P*(sX10+sX20)*X1+sX10*sX20)/((Q-X1 )*(-s12+s22))\n" }{MPLTEXT 1 0 2 "+\n" }{MPLTEXT 1 0 70 "U21(s11,s21,s 12,s22,X1) +diff(KOldCoordinates(s11,s21,s12,s22,X1),s21)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1090 "Hams12 := (-(s12* s22*Q^2+((s21+P)*s12+s22*(P+s11))*Q+(s20+h)*s12+s10*s22+(P+s11)*(s21+P ))*(-s12+s22)*X1^3+(2*s22*s12*(-s12+s22)*Q^3+((-2*P-2*s21)*s12^2-3*s22 *(-s21+s11)*s12+2*s22^2*(P+s11))*Q^2+((-2*s20-2*h)*s12^2+((2*h-2*s10+2 *s20)*s22-(2*(P+3*s11*(1/2)-(1/2)*s21))*(s21+P))*s12+(2*(s10*s22+(P+s1 1)*(P-(1/2)*s11+3*s21*(1/2))))*s22)*Q+((sX10+sX20-h)*P-(-s21+s11)*(s20 +h))*s12+((-sX10-sX20+h)*P-s10*(-s21+s11))*s22-(-s21+s11)*(s21+P)*(P+s 11))*X1^2+(-s22*s12*(-s12+s22)*Q^4+((s21+P)*s12^2+3*s22*(-s21+s11)*s12 -s22^2*(P+s11))*Q^3+((s20+h)*s12^2+((s10-s20)*s22+(s21+P)*(P+3*s11-2*s 21))*s12-s22*((h+s10)*s22+(P+s11)*(P-2*s11+3*s21)))*Q^2+(((-sX10-sX20+ 2*h)*P+(2*s20+2*h)*s11-s21*(h+2*s20))*s12+((sX10+sX20-2*h)*P+(-h+2*s10 )*s11-2*s21*s10)*s22+(2*(-s21+s11))*(s21+P)*(P+s11))*Q+sX10*sX20*s12-s X10*sX20*s22-P*(-s21+s11)*(sX10+sX20))*X1-s22*(-s21+s11)*s12*Q^4+((-s2 2*h-(-s21+s11)*(s21+P))*s12-(-s22*h+(-s21+s11)*(P+s11))*s22)*Q^3+((-h* P+(-s20-h)*s11+s20*s21)*s12+(h*P+(h-s10)*s11+s21*s10)*s22-(-s21+s11)*( s21+P)*(P+s11))*Q^2+P*(-s21+s11)*(sX10+sX20)*Q-sX10*sX20*(-s21+s11))/( 2*(-s12+s22)^2*(Q-X1))\n" }{MPLTEXT 1 0 2 "+\n" }{MPLTEXT 1 0 70 "U12( s11,s21,s12,s22,X1) +diff(KOldCoordinates(s11,s21,s12,s22,X1),s12)" } {MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1091 "Hams22 : = ((s12*s22*Q^2+((s21+P)*s12+s22*(P+s11))*Q+(s20+h)*s12+s10*s22+(P+s11 )*(s21+P))*(-s12+s22)*X1^3+(-2*s22*s12*(-s12+s22)*Q^3+((2*s21+2*P)*s12 ^2+3*s22*(-s21+s11)*s12-2*s22^2*(P+s11))*Q^2+((2*s20+2*h)*s12^2+((-2*h +2*s10-2*s20)*s22+(2*(P+3*s11*(1/2)-(1/2)*s21))*(s21+P))*s12-(2*(s10*s 22+(P+s11)*(P-(1/2)*s11+3*s21*(1/2))))*s22)*Q+((-sX10-sX20+h)*P+(-s21+ s11)*(s20+h))*s12+((sX10+sX20-h)*P+s10*(-s21+s11))*s22+(-s21+s11)*(s21 +P)*(P+s11))*X1^2+(s22*s12*(-s12+s22)*Q^4+((-s21-P)*s12^2-3*s22*(-s21+ s11)*s12+s22^2*(P+s11))*Q^3+((-2*h-s20)*s12^2+((2*h-s10+s20)*s22-(s21+ P)*(P+3*s11-2*s21))*s12+s22*(s10*s22+(P+s11)*(P-2*s11+3*s21)))*Q^2+((( sX10+sX20-2*h)*P+(-2*s20-2*h)*s11+s21*(h+2*s20))*s12+((-sX10-sX20+2*h) *P+(h-2*s10)*s11+2*s21*s10)*s22-(2*(-s21+s11))*(s21+P)*(P+s11))*Q-sX10 *sX20*s12+sX10*sX20*s22+P*(-s21+s11)*(sX10+sX20))*X1+s22*(-s21+s11)*s1 2*Q^4+(s12^2*h+(-s22*h+(-s21+s11)*(s21+P))*s12+s22*(-s21+s11)*(P+s11)) *Q^3+((h*P+(s20+h)*s11-s20*s21)*s12+(-h*P+(-h+s10)*s11-s21*s10)*s22+(- s21+s11)*(s21+P)*(P+s11))*Q^2-P*(-s21+s11)*(sX10+sX20)*Q+sX10*sX20*(-s 21+s11))/(2*(-s12+s22)^2*(Q-X1))\n" }{MPLTEXT 1 0 2 "+\n" }{MPLTEXT 1 0 70 "U22(s11,s21,s12,s22,X1) +diff(KOldCoordinates(s11,s21,s12,s22,X1 ),s22)" }{MPLTEXT 1 0 2 ":\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 384 " HamX1 := (Q^4*s12*s22+(-2*X1*s12*s22+(s12+s22)*P+s11*s22+s12*s21)*Q^3+ (X1^2*s12*s22+((-2*s12-2*s22)*P-2*s11*s22-2*s12*s21)*X1+(s20+h)*s12+P^ 2+(s21+s11)*P+s10*s22+s11*s21)*Q^2+(((s12+s22)*P+s11*s22+s12*s21)*X1^2 +(-2*P^2+(-2*s11-2*s21)*P+(-2*s20-2*h)*s12-2*s10*s22-2*s11*s21)*X1-(sX 10+sX20-h)*P)*Q+((s20+h)*s12+P^2+(s21+s11)*P+s10*s22+s11*s21)*X1^2+(sX 10+sX20-h)*P*X1+sX10*sX20)/(Q-X1)\n" }{MPLTEXT 1 0 2 "+\n" }{MPLTEXT 1 0 69 "UX1(s11,s21,s12,s22,X1) +diff(KOldCoordinates(s11,s21,s12,s22, X1),X1)" }{MPLTEXT 1 0 1 ":" }{MPLTEXT 1 0 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#R1G6\"f*6#I#xiGF$F$6$I)operatorGF$I&arrowGF$F$,**&,&I$ s10GF$!\"\"I$s20GF$F/\"\"\",&9$F1I#X1GF$F/F/F1I$s11GF$F/I$s21GF$F/*&,& I$s12GF$F/I$s22GF$F/F1F3F1F1F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I #R2G6\"f*6#I#xiGF$F$6$I)operatorGF$I&arrowGF$F$,.*(I%sX10GF$\"\"\",(I$ s10GF$!\"\"I$s20GF$F1F-F1F.,&9$F.I#X1GF$F1!\"#F.*&F0F.I$s22GF$F.F.*&I$ s11GF$F.I$s21GF$F.F.*&I$s12GF$F.F2F.F.*&,&*&F:F.F8F.F.*&F=F.F;F.F.F.F4 F.F.*(F=F.F8F.F4\"\"#F.F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%sX20 G6\",(I$s10GF$!\"\"I$s20GF$F'I%sX10GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0KOldCoordinatesG6\"f*6'I$s11GF$I$s21GF$I$s12GF$I$s22GF$I#X1GF$F $6$I)operatorGF$I&arrowGF$F$,&*(,&I%sX10GF$\"\"\"I$s20GF$F3F3,&F2F3I$s 10GF$F3F3-I#lnG6$%*protectedGI(_syslibGF$6#,&9&#F3\"\"#9'#!\"\"F@F3F?* &9(F3,&*&,&*&FEF3F>F3F39$F@F3F6F3F3*&F4F3,&*&FEF3FAF3F39%F@F3F3F3F?F$F $F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 214 39 "We load the purely time-d ependent terms" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "U11 := u napply( ((X1*s22+s21)*s10+(X1*s12+s11)*s20)/(s12-s22) +s22*X1/(s12-s 22)*h,s11,s21,s12,s22,X1);\n" }{MPLTEXT 1 0 83 "U21 := unapply(-((X1*s 22+s21)*s10+(X1*s12+s11)*s20)/(s12-s22) -s12*X1/(s12-s22)*h" } {MPLTEXT 1 0 20 ",s11,s21,s12,s22,X1)" }{MPLTEXT 1 0 2 ";\n" }{MPLTEXT 1 0 94 "U12 := unapply( (X1*(s12-s22)-s11+s21)*((s10*s22+s12*s20)*X1+ s21*s10+s11*s20)/(2*(s12-s22)^2)\n" }{MPLTEXT 1 0 59 "+(-s22^2*X1+(X1* s12-s11)*s22+s12*s21)*X1/(2*(s12-s22)^2)*h\n" }{MPLTEXT 1 0 22 ",s11,s 21,s12,s22,X1);\n" }{MPLTEXT 1 0 94 "U22 := unapply(-(X1*(s12-s22)-s11 +s21)*((s10*s22+s12*s20)*X1+s21*s10+s11*s20)/(2*(s12-s22)^2)\n" } {MPLTEXT 1 0 59 "-h*(X1*s12^2+(-X1*s22+s21)*s12-s11*s22)*X1/(2*(s12-s2 2)^2)\n" }{MPLTEXT 1 0 22 ",s11,s21,s12,s22,X1);\n" }{MPLTEXT 1 0 49 " UX1 := unapply( (X1*s22+s21)*s10+(X1*s12+s11)*s20" }{MPLTEXT 1 0 21 ", s11,s21,s12,s22,X1);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$U11G6\"f*6'I$s11GF$I$s21GF$I$s12GF$I$s22GF$I#X1GF$F$6$I)operato rGF$I&arrowGF$F$,&*&,&*&,&*&9(\"\"\"9'F6F69%F6F6I$s10GF$F6F6*&,&*&F5F6 9&F6F69$F6F6I$s20GF$F6F6F6,&F=F6F7!\"\"FAF6**F7F6F5F6F@FAI\"hGF$F6F6F$ F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$U21G6\"f*6'I$s11GF$I$s21GF$I$ s12GF$I$s22GF$I#X1GF$F$6$I)operatorGF$I&arrowGF$F$,&*&,&*&,&*&9(\"\"\" 9'F6F69%F6F6I$s10GF$F6F6*&,&*&F5F69&F6F69$F6F6I$s20GF$F6F6F6,&F=F6F7! \"\"FAFA**F=F6F5F6F@FAI\"hGF$F6FAF$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$U12G6\"f*6'I$s11GF$I$s21GF$I$s12GF$I$s22GF$I#X1GF$F$6$I)operato rGF$I&arrowGF$F$,&*(,(*&9(\"\"\",&9&F49'!\"\"F4F49$F89%F4F4,(*&,&*&I$s 10GF$F4F7F4F4*&F6F4I$s20GF$F4F4F4F3F4F4*&F:F4F?F4F4*&F9F4FAF4F4F4F5!\" ##F4\"\"#**,(*&F7FFF3F4F8*&,&*&F3F4F6F4F4F9F8F4F7F4F4*&F6F4F:F4F4F4F3F 4F5FDI\"hGF$F4FEF$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$U22G6\"f*6' I$s11GF$I$s21GF$I$s12GF$I$s22GF$I#X1GF$F$6$I)operatorGF$I&arrowGF$F$,& *(,(*&9(\"\"\",&9&F49'!\"\"F4F49$F89%F4F4,(*&,&*&I$s10GF$F4F7F4F4*&F6F 4I$s20GF$F4F4F4F3F4F4*&F:F4F?F4F4*&F9F4FAF4F4F4F5!\"##F8\"\"#**I\"hGF$ F4,(*&F3F4F6FFF4*&,&*&F3F4F7F4F8F:F4F4F6F4F4*&F9F4F7F4F8F4F3F4F5FDFEF$ F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$UX1G6\"f*6'I$s11GF$I$s21GF$I$ s12GF$I$s22GF$I#X1GF$F$6$I)operatorGF$I&arrowGF$F$,&*&,&*&9(\"\"\"9'F4 F49%F4F4I$s10GF$F4F4*&,&*&F3F49&F4F49$F4F4I$s20GF$F4F4F$F$F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "HamtdX1checkQcheckPbis := ( " }{MPLTEXT 1 0 6 "checkQ" }{MPLTEXT 1 0 107 "-tdX1)*checkP^2+h*checkP -checkQ^3+tdX1*checkQ^2-(-h+s10-s20)*checkQ-(s10+s20+2*sX10)^2/(-4*tdX 1+4*checkQ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I7HamtdX1checkQcheckPb isG6\",.*&,&I'checkQGF$\"\"\"I%tdX1GF$!\"\"F)I'checkPGF$\"\"#F)*&I\"hG F$F)F,F)F)*$F(\"\"$F+*&F*F)F(F-F)*&,(F/F+I$s10GF$F)I$s20GF$F+F)F(F)F+* &,(F5F)F6F)I%sX10GF$F-F-,&F*!\"%F(\"\"%F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Sinfty2function:=s12+s22;\n" }{MPLTEXT 1 0 26 "Sin fty1function:=s11+s21;\n" }{MPLTEXT 1 0 35 "S2function:=sqrt(s12-s22)/ sqrt(2);\n" }{MPLTEXT 1 0 45 "S1function:=(s11-s21)/sqrt(2)/sqrt(s12-s 22);\n" }{MPLTEXT 1 0 40 "tdX1function:=X1*S2function+S1function;\n" } {MPLTEXT 1 0 67 "solve( \{s12+s22=Sinfty2,s11+s21=Sinfty1, S2=sqrt(s12 -s22)/sqrt(2),\n" }{MPLTEXT 1 0 36 "S1=(s11-s21)/sqrt(2)/sqrt(s12-s22) ,\n" }{MPLTEXT 1 0 55 "tdX1=X1*S2function+S1function\},\{s12,s22,s11,s 21,X1\}); \n" }{MPLTEXT 1 0 67 "X1function := unapply( -(S1-tdX1)/S2 , Sinfty1,Sinfty2,S1,S2,tdX1);\n" }{MPLTEXT 1 0 73 "s11function:= unappl y( S2*S1+(1/2)*Sinfty1, Sinfty1,Sinfty2,S1,S2,tdX1);\n" }{MPLTEXT 1 0 72 "s12function:= unapply( S2^2+(1/2)*Sinfty2, Sinfty1,Sinfty2,S1,S2,t dX1);\n" }{MPLTEXT 1 0 74 "s21function:= unapply( -S2*S1+(1/2)*Sinfty1 , Sinfty1,Sinfty2,S1,S2,tdX1);\n" }{MPLTEXT 1 0 74 "s22function:= unap ply( -S2^2+(1/2)*Sinfty2, Sinfty1,Sinfty2,S1,S2,tdX1 );\n" }{MPLTEXT 1 0 90 "simplify(X1function(Sinfty1function,Sinfty2function,S1function ,S2function,tdX1function));\n" }{MPLTEXT 1 0 91 "simplify(s11function( Sinfty1function,Sinfty2function,S1function,S2function,tdX1function)); \n" }{MPLTEXT 1 0 91 "simplify(s12function(Sinfty1function,Sinfty2func tion,S1function,S2function,tdX1function));\n" }{MPLTEXT 1 0 91 "simpli fy(s21function(Sinfty1function,Sinfty2function,S1function,S2function,t dX1function));\n" }{MPLTEXT 1 0 91 "simplify(s22function(Sinfty1functi on,Sinfty2function,S1function,S2function,tdX1function));\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 94 "PartialtdX1function:=simplify(diff(s11fun ction(Sinfty1,Sinfty2,S1,S2,tdX1),tdX1))*Partials11+\n" }{MPLTEXT 1 0 72 "simplify(diff(s21function(Sinfty1,Sinfty2,S1,S2,tdX1),tdX1))*Parti als21\n" }{MPLTEXT 1 0 73 "+simplify(diff(s12function(Sinfty1,Sinfty2, S1,S2,tdX1),tdX1))*Partials12\n" }{MPLTEXT 1 0 73 "+simplify(diff(s22f unction(Sinfty1,Sinfty2,S1,S2,tdX1),tdX1))*Partials22\n" }{MPLTEXT 1 0 71 "+simplify(diff(X1function(Sinfty1,Sinfty2,S1,S2,tdX1),tdX1))*Par tialX1;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0Sinfty2functionG6\",&I$s12 GF$\"\"\"I$s22GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I0Sinfty1functio nG6\",&I$s21GF$\"\"\"I$s11GF$F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+S2 functionG6\",$*&,&I$s12GF$\"\"\"I$s22GF$!\"\"#F)\"\"#F-F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+S1functionG6\",$*(,&I$s21GF$!\"\"I$s11GF$\" \"\"F+\"\"##F+F,,&I$s12GF$F+I$s22GF$F)#F)F,F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I-tdX1functionG6\",&*(I#X1GF$\"\"\",&I$s12GF$F(I$s22GF$! \"\"#F(\"\"#F.F-F-*(,&I$s21GF$F,I$s11GF$F(F(F.F-F)#F,F.F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "<'/I#X1G6\",$*&I#S2GF%!\"\",&I#S1GF%\"\"\"I%tdX1G F%F)F,F)/I$s11GF%,&*&F+F,F(F,F,I(Sinfty1GF%#F,\"\"#/I$s12GF%,&*$F(F4F, I(Sinfty2GF%F3/I$s21GF%,&F1F)F2F3/I$s22GF%,&F8F)F9F3" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I+X1functionG6\"f*6'I(Sinfty1GF$I(Sinfty2GF$I#S1GF$I# S2GF$I%tdX1GF$F$6$I)operatorGF$I&arrowGF$F$,$*&9'!\"\",&9&\"\"\"9(F2F5 F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,s11functionG6\"f*6'I(Sinf ty1GF$I(Sinfty2GF$I#S1GF$I#S2GF$I%tdX1GF$F$6$I)operatorGF$I&arrowGF$F$ ,&*&9&\"\"\"9'F2F29$#F2\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I ,s12functionG6\"f*6'I(Sinfty1GF$I(Sinfty2GF$I#S1GF$I#S2GF$I%tdX1GF$F$6 $I)operatorGF$I&arrowGF$F$,&*$9'\"\"#\"\"\"9%#F3F2F$F$F$" }}{PARA 11 " " 1 "" {XPPMATH 20 ">I,s21functionG6\"f*6'I(Sinfty1GF$I(Sinfty2GF$I#S1 GF$I#S2GF$I%tdX1GF$F$6$I)operatorGF$I&arrowGF$F$,&*&9&\"\"\"9'F2!\"\"9 $#F2\"\"#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I,s22functionG6\"f*6 'I(Sinfty1GF$I(Sinfty2GF$I#S1GF$I#S2GF$I%tdX1GF$F$6$I)operatorGF$I&arr owGF$F$,&*$9'\"\"#!\"\"9%#\"\"\"F2F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "I#X1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$s11G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$s12G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$s21G6 \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I$s22G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I4PartialtdX1functionG6\"*&I#S2GF$!\"\"I*PartialX1GF$\" \"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "checkQfunction:=S2* Q+S1;\n" }{MPLTEXT 1 0 35 "checkPfunction=1/S2*(P-1/2*R1(Q));\n" } {MPLTEXT 1 0 23 "SolQ:=-(S1-checkQ)/S2;\n" }{MPLTEXT 1 0 43 "SolP:=che ckP*S2+(1/2)*R1(-(S1-checkQ)/S2);\n" }{MPLTEXT 1 0 31 "simplify(checkQ -(S2*SolQ+S1));\n" }{MPLTEXT 1 0 44 "simplify(checkP-(1/S2*(SolP-1/2*R 1(SolQ))));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 19 "checkSolQ:=unapply (" }{MPLTEXT 1 0 30 "S2function*Q+S1function,Q,P);\n" }{MPLTEXT 1 0 19 "checkSolP:=unapply(" }{MPLTEXT 1 0 26 "1/S2function*(P-1/2*R1(Q))" }{MPLTEXT 1 0 6 ",Q,P);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I/checkQfun ctionG6\",&*&I\"QGF$\"\"\"I#S2GF$F(F(I#S1GF$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "/I/checkPfunctionG6\"*&I#S2GF$!\"\",,I\"PGF$\"\"\"*&,&I$s 10GF$F'I$s20GF$F'F*,&I\"QGF$F*I#X1GF$F'F'#F'\"\"#I$s11GF$#F*F3I$s21GF$ F5*&,&I$s12GF$F'I$s22GF$F'F*F0F*F2F*" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I%SolQG6\",$*&,&I#S1GF$\"\"\"I'checkQGF$!\"\"F)I#S2GF$F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%SolPG6\",,*&I'checkPGF$\"\"\"I#S2GF$F(F(*&, &I$s10GF$!\"\"I$s20GF$F-F(,&*&,&I#S1GF$F(I'checkQGF$F-F(F)F-F-I#X1GF$F -F-#F(\"\"#I$s11GF$#F-F6I$s21GF$F8*(,&I$s12GF$F-I$s22GF$F-F(F1F(F)F-F8 " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I*checkSolQG6\"f*6$I\"QGF$ I\"PGF$F$6$I)operatorGF$I&arrowGF$F$,&*(9$\"\"\",&I$s12GF$F/I$s22GF$! \"\"#F/\"\"#F5F4F4*(,&I$s21GF$F3I$s11GF$F/F/F5F4F0#F3F5F4F$F$F$" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I*checkSolPG6\"f*6$I\"QGF$I\"PGF$F$6$I) operatorGF$I&arrowGF$F$*(,&I$s12GF$\"\"\"I$s22GF$!\"\"#F1\"\"#F3#F/F3, ,9%F/*&,&I$s10GF$F1I$s20GF$F1F/,&9$F/I#X1GF$F1F1F2I$s11GF$F4I$s21GF$F4 *&,&F.F1F0F1F/F " 0 "" {MPLTEXT 1 0 40 "HamtdX1checkQcheckPbisfunction:=unapply(" }{MPLTEXT 1 0 40 "Hamt dX1checkQcheckPbis ,checkQ,checkP):\n" }{MPLTEXT 1 0 41 "HamtdX1checkQ checkPbisfunction2:=unapply(" }{MPLTEXT 1 0 31 "HamtdX1checkQcheckPbis function(" }{MPLTEXT 1 0 15 "checkSolQ(Q,P)," }{MPLTEXT 1 0 23 "checkS olP(Q,P)),tdX1):\n" }{MPLTEXT 1 0 32 "HamtdX1OldCoordinates:=simplify( " }{MPLTEXT 1 0 47 "HamtdX1checkQcheckPbisfunction2(tdX1function));" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I6HamtdX1OldCoordin atesG6\"**\"\"##\"\"\"F&,2**,&I\"QGF$F(I#X1GF$!\"\"F(,,*(F,F(F+F(I$s22 GF$F(F(*&I\"PGF$F(F+F(F(*&I$s21GF$F(F+F(F(I\"hGF$F(I$s20GF$F(F(F,F(I$s 12GF$F(F(**F+F(F,F(,(F2F(*&I$s11GF$F(F+F(F(I$s10GF$F(F(F1F(F(*&F+F&F3F &F(*(F+F(,,F;F(F4F(F6F(F=F(F7F(F(F3F(F(*(F+F(,(F4F(F6F(F7F(F(F " 0 "" {MPLTEXT 1 0 44 "DGsetup([s11,s21,s12,s22,X1,Q,P],B, verbose);" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "IOThe~fo llowing~coordinates~have~been~protected:G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7)I$s11G%*protectedGI$s21GF$I$s12GF$I$s22GF$I#X1GF$I\"QGF $I\"PGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "IgnThe~following~vector~fiel ds~have~been~defined~and~protected:G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6&-I%mrowG F$6/-F,6%-I#miGF$6%Q$_DGF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'- I#moGF$6-Q0⁡F'/F8Q'normalF'/%&fenceGQ&falseF'/%*separato rGFB/%)stretchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'ac centGFB/%'lspaceGQ&0.0emF'/%'rspaceGFQ-F#6$-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'-F 16%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^o F`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\"2F'F>F>F^pFapF^oF`qF>F^pFapF>F^pFa pF>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\"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$-F,6#-F# 6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Faq6$Q\"5F'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\"6F'F>F>F^pFapF^oF`qF>F^pFapF>F^pFapF >F^pFapF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F# 6&-F,6#-Faq6$Q\"7F'F>F>F^pFapF^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~and~protected:G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I(mfencedG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6&-I%mrowGF$6 /-F,6%-I#miGF$6%Q$_DGF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#m oGF$6-Q0⁡F'/F8Q'normalF'/%&fenceGQ&falseF'/%*separatorGF B/%)stretchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accen tGFB/%'lspaceGQ&0.0emF'/%'rspaceGFQ-F#6$-F,6#-F#6&-F,6%-F#6&-F,6'-I#ms GF$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 $Q\"2F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6 #-F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"3F'F>F>F[pF^pF ^oFgoF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#-F#6&-F,6%FfnF^o- F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"4F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[p F^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-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$Q \"6F'F>F>F[pF^pF^oFgoF>F[pF^pF>F[pF^pF>F[pF^pF>F^o-F,6%F0F:-F#6$-F,6#- F#6&-F,6%FfnF^o-F#6&-F,6#-F#6&-F,6%-F#6&-F,6#-Fho6$Q\"7F'F>F>F[pF^pF^o FgoF>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 0 110 " dcheckQ:=(simplify(diff(checkSolQ(Q,P),s11)))*(DGform(s11))+(simplify( diff(checkSolQ(Q,P),s21)))*(DGform(s21))" }{MPLTEXT 1 0 246 "+(simplif y(diff(checkSolQ(Q,P),s12)))*(DGform(s12))+(simplify(diff(checkSolQ(Q, P),s22)))*(DGform(s22))+(simplify(diff(checkSolQ(Q,P),X1)))*(DGform(X1 ))+(simplify(diff(checkSolQ(Q,P),Q)))*(DGform(Q))+(simplify(diff(check SolQ(Q,P),P)))*(DGform(P));" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 110 "dcheckP:=(simplify(diff(checkSolP(Q,P),s11)))*(DGf orm(s11))+(simplify(diff(checkSolP(Q,P),s21)))*(DGform(s21))" } {MPLTEXT 1 0 246 "+(simplify(diff(checkSolP(Q,P),s12)))*(DGform(s12))+ (simplify(diff(checkSolP(Q,P),s22)))*(DGform(s22))+(simplify(diff(chec kSolP(Q,P),X1)))*(DGform(X1))+(simplify(diff(checkSolP(Q,P),Q)))*(DGfo rm(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>/%)bevel ledGQ&falseF'-I#moGF$6-Q1⁢F'F4/%&fenceGFC/%*separatorGF C/%)stretchyGFC/%*symmetricGFC/%(largeopGFC/%.movablelimitsGFC/%'accen tGFC/%'lspaceGQ&0.0emF'/%'rspaceGFX-F.6(-F#6%-I&msqrtGF$6#F7FD-F#6%-I# miGF$6%Q$_DGF'/%'italicGQ%trueF'/F5Q'italicF'-FE6-Q0⁡F'F 4FHFJFLFNFPFRFTFVFY-I(mfencedGF$6$-F#6#-F[p6&-F#6%-F[p6&-F#6'-I#msGF$6 #Q%formF'-FE6-Q\",F'F4FH/FKFdoFLFNFPFRFTFV/FZQ,0.3333333emF'-F_o6%Q\"B F'FboFeoF[qF0F4/%%openGQ\"[F'/%&closeGQ\"]F'F[q-F[p6&-F#6#-F[p6&-F#6%- F[p6&-F#6#F0F4FdqFgqF[qF0F4FdqFgqF4FdqFgqF4FdqFgqF4-F#6#-Fjn6#-F#6%-F_ o6%Q$s12F'FboFeo-FE6-Q(−F'F4FHFJFLFNFPFRFT/FWQ,0.2222222emF'/FZF cs-F_o6%Q$s22F'FboFeoF:F/%)bevelledGQ&falseF'-I#moGF$6-Q1⁢F'F4/%&fenceGF C/%*separatorGFC/%)stretchyGFC/%*symmetricGFC/%(largeopGFC/%.movableli mitsGFC/%'accentGFC/%'lspaceGQ&0.0emF'/%'rspaceGFX-F.6(-F#6%-I&msqrtGF $6#F7FD-F#6%-I#miGF$6%Q$_DGF'/%'italicGQ%trueF'/F5Q'italicF'-FE6-Q0&Ap plyFunction;F'F4FHFJFLFNFPFRFTFVFY-I(mfencedGF$6$-F#6#-F[p6&-F#6%-F[p6 &-F#6'-I#msGF$6#Q%formF'-FE6-Q\",F'F4FH/FKFdoFLFNFPFRFTFV/FZQ,0.333333 3emF'-F_o6%Q\"BF'FboFeoF[qF0F4/%%openGQ\"[F'/%&closeGQ\"]F'F[q-F[p6&-F #6#-F[p6&-F#6%-F[p6&-F#6#F0F4FdqFgqF[qF0F4FdqFgqF4FdqFgqF4FdqFgqF4-F#6 #-Fjn6#-F#6%-F_o6%Q$s12F'FboFeo-FE6-Q(−F'F4FHFJFLFNFPFRFT/FWQ,0. 2222222emF'/FZFcs-F_o6%Q$s22F'FboFeoF:F " 0 "" {MPLTEXT 1 0 56 "dcheckQwedgedcheckP:=simplify((dcheckQ)&wedge(dcheckP)):" }}} {EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 18 "dtdX1:=simplify( \n" } {MPLTEXT 1 0 16 " (simplify(diff(" }{MPLTEXT 1 0 12 "tdX1function" } {MPLTEXT 1 0 22 ",s11)))*(DGform(s11))\n" }{MPLTEXT 1 0 16 "+(simplify (diff(" }{MPLTEXT 1 0 12 "tdX1function" }{MPLTEXT 1 0 22 ",s21)))*(DGf orm(s21))\n" }{MPLTEXT 1 0 16 "+(simplify(diff(" }{MPLTEXT 1 0 12 "tdX 1function" }{MPLTEXT 1 0 22 ",s12)))*(DGform(s12))\n" }{MPLTEXT 1 0 16 "+(simplify(diff(" }{MPLTEXT 1 0 12 "tdX1function" }{MPLTEXT 1 0 22 ",s22)))*(DGform(s22))\n" }{MPLTEXT 1 0 16 "+(simplify(diff(" } {MPLTEXT 1 0 12 "tdX1function" }{MPLTEXT 1 0 20 ",X1)))*(DGform(X1))\n " }{MPLTEXT 1 0 3 ");\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "d" } {MPLTEXT 1 0 21 "HamtdX1OldCoordinates" }{MPLTEXT 1 0 13 ":=simplify( \+ \n" }{MPLTEXT 1 0 16 " (simplify(diff(" }{MPLTEXT 1 0 21 "HamtdX1OldCo ordinates" }{MPLTEXT 1 0 22 ",s11)))*(DGform(s11))\n" }{MPLTEXT 1 0 16 "+(simplify(diff(" }{MPLTEXT 1 0 21 "HamtdX1OldCoordinates" } {MPLTEXT 1 0 22 ",s21)))*(DGform(s21))\n" }{MPLTEXT 1 0 16 "+(simplify (diff(" }{MPLTEXT 1 0 21 "HamtdX1OldCoordinates" }{MPLTEXT 1 0 22 ",s1 2)))*(DGform(s12))\n" }{MPLTEXT 1 0 16 "+(simplify(diff(" }{MPLTEXT 1 0 21 "HamtdX1OldCoordinates" }{MPLTEXT 1 0 22 ",s22)))*(DGform(s22))\n " }{MPLTEXT 1 0 16 "+(simplify(diff(" }{MPLTEXT 1 0 21 "HamtdX1OldCoor dinates" }{MPLTEXT 1 0 20 ",X1)))*(DGform(X1))\n" }{MPLTEXT 1 0 16 "+( simplify(diff(" }{MPLTEXT 1 0 21 "HamtdX1OldCoordinates" }{MPLTEXT 1 0 18 ",Q)))*(DGform(Q))\n" }{MPLTEXT 1 0 16 "+(simplify(diff(" } {MPLTEXT 1 0 21 "HamtdX1OldCoordinates" }{MPLTEXT 1 0 22 ",P)))*(DGfor m(P)) ):\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 33 "dtdX1dwedgedHamtdX 1:= simplify((d" }{MPLTEXT 1 0 4 "tdX1" }{MPLTEXT 1 0 8 ")&wedge(" } {MPLTEXT 1 0 22 "dHamtdX1OldCoordinates" }{MPLTEXT 1 0 3 ")):" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I%mrowG6#/I+modulen ameG6\"I,TypesettingGI(_syslibGF'6$-I#moGF$6-Q*&uminus0;F'/%,mathvaria ntGQ'normalF'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4/%*symmetr icGF4/%(largeopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ,0.2222222 emF'/%'rspaceGFC-F#6%-I&mfracGF$6(-I#mnGF$6$Q\"1F'F/-FL6$Q\"2F'F//%.li nethicknessGFN/%+denomalignGQ'centerF'/%)numalignGFV/%)bevelledGF4-F,6 -Q1⁢F'F/F2F5F7F9F;F=F?/FBQ&0.0emF'/FEFin-FI6(-F#6%-I&ms qrtGF$6#FOFen-I(mfencedGF$6$-F#6'-F#6%-Fco6$-F#6*F+-F#6%FHFen-F#6%-I#m iGF$6%Q$s12F'/%'italicGQ%trueF'/F0Q'italicF'Fen-Fbp6%Q#X1F'FepFhp-F,6- Q\"+F'F/F2F5F7F9F;F=F?FAFD-F#6%FHFen-F#6%-Fbp6%Q$s22F'FepFhpFenFjpF]q- F#6%FHFen-F#6#-Fbp6%Q$s11F'FepFhp-F,6-Q(−F'F/F2F5F7F9F;F=F?FAFD- F#6%FHFen-F#6#-Fbp6%Q$s21F'FepFhpF/Fen-F#6%-Fbp6%Q$_DGF'FepFhp-F,6-Q0& ApplyFunction;F'F/F2F5F7F9F;F=F?FhnFjn-Fco6$-F#6#-Fco6&-F#6%-Fco6&-F#6 '-I#msGF$6#Q%formF'-F,6-Q\",F'F/F2/F6FgpF7F9F;F=F?Fhn/FEQ,0.3333333emF '-Fbp6%Q\"BF'FepFhpF`tFKF//%%openGQ\"[F'/%&closeGQ\"]F'F`t-Fco6&-F#6#- Fco6&-F#6%-Fco6&-F#6#-FL6$Q\"3F'F/F/FitF\\uF`tFKF/FitF\\uF/FitF\\uF/Fi tF\\uF/F]q-F#6%-Fco6$-F#6)F]pF^rF`qF^rFgqF]qFarF/Fen-F#6%FjrF]s-Fco6$- F#6#-Fco6&-F#6%FhsF`t-Fco6&-F#6#-Fco6&-F#6%-Fco6&-F#6#-FL6$Q\"4F'F/F/F itF\\uF`tFKF/FitF\\uF/FitF\\uF/FitF\\uF/F]q-F#6%-Fco6$-F#6'-F#6%-Fco6$ -F#6&F+FapF]qFdqF/Fen-F#6%FjrF]s-Fco6$-F#6#-Fco6&-F#6%FhsF`t-Fco6&-F#6 #-Fco6&-F#6%-Fco6&-F#6#-FL6$Q\"5F'F/F/FitF\\uF`tFKF/FitF\\uF/FitF\\uF/ FitF\\uF/F]q-F#6%FjrF]s-Fco6$-F#6#-Fco6&-F#6%FhsF`t-Fco6&-F#6#-Fco6&-F #6%-Fco6&-F#FaoF/FitF\\uF`tFKF/FitF\\uF/FitF\\uF/FitF\\uF/F^r-F#6%FjrF ]s-Fco6$-F#6#-Fco6&-F#6%FhsF`t-Fco6&-F#6#-Fco6&-F#6%-Fco6&-F#6#FKF/Fit F\\uF`tFKF/FitF\\uF/FitF\\uF/FitF\\uF/F/Fen-Fco6$-F#6%FapF^rFdqF/F/-F# 6#-I%msupGF$6%F]]l-F#6%F[v-F,6-Q\"/F'F/F2F5/F8FgpF9F;F=F?/FBQ,0.166666 7emF'/FEF]^lFO/%1superscriptshiftGQ\"0F'FRFTFWFY" }}}{EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 54 "Omega2:=simplify( (h&mult(dcheckQwedgedchec kP))&minus(" }{MPLTEXT 1 0 19 "dtdX1dwedgedHamtdX1" }{MPLTEXT 1 0 4 ") ):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 10 "dHams11:=\n" }{MPLTEXT 1 0 44 "(simplify(diff(Hams11,s11)))*(DGform(s 11))+\n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams11,s21)))*(DGform(s21))+ \n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams11,s12)))*(DGform(s12))+ \n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams11,s22)))*(DGform(s22))+ \n" } {MPLTEXT 1 0 44 "(simplify(diff(Hams11,X1)))*(DGform(X1))+ \n" } {MPLTEXT 1 0 41 "(simplify(diff(Hams11,Q)))*(DGform(Q))+ \n" }{MPLTEXT 1 0 40 "(simplify(diff(Hams11,P)))*(DGform(P)):\n" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 10 "dHams21:=\n" }{MPLTEXT 1 0 44 "(simplify(diff(Ha ms21,s11)))*(DGform(s11))+\n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams21, s21)))*(DGform(s21))+ \n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams21,s12) ))*(DGform(s12))+ \n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams21,s22)))*( DGform(s22))+ \n" }{MPLTEXT 1 0 44 "(simplify(diff(Hams21,X1)))*(DGfor m(X1))+ \n" }{MPLTEXT 1 0 41 "(simplify(diff(Hams21,Q)))*(DGform(Q))+ \n" }{MPLTEXT 1 0 39 "(simplify(diff(Hams21,P)))*(DGform(P)):" } {MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 10 "dHams12:=\n " }{MPLTEXT 1 0 44 "(simplify(diff(Hams12,s11)))*(DGform(s11))+\n" } {MPLTEXT 1 0 45 "(simplify(diff(Hams12,s21)))*(DGform(s21))+ \n" } {MPLTEXT 1 0 45 "(simplify(diff(Hams12,s12)))*(DGform(s12))+ \n" } {MPLTEXT 1 0 45 "(simplify(diff(Hams12,s22)))*(DGform(s22))+ \n" } {MPLTEXT 1 0 44 "(simplify(diff(Hams12,X1)))*(DGform(X1))+ \n" } {MPLTEXT 1 0 41 "(simplify(diff(Hams12,Q)))*(DGform(Q))+ \n" }{MPLTEXT 1 0 40 "(simplify(diff(Hams12,P)))*(DGform(P)):\n" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 10 "dHams22:=\n" }{MPLTEXT 1 0 44 "(simplify(diff(Ha ms22,s11)))*(DGform(s11))+\n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams22, s21)))*(DGform(s21))+ \n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams22,s12) ))*(DGform(s12))+ \n" }{MPLTEXT 1 0 45 "(simplify(diff(Hams22,s22)))*( DGform(s22))+ \n" }{MPLTEXT 1 0 44 "(simplify(diff(Hams22,X1)))*(DGfor m(X1))+ \n" }{MPLTEXT 1 0 41 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0 8 "Omega:=(" }{MPLTEXT 1 0 29 "(dHams21)&wedge(DGform(s21)))" } {MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 14 "&plus(Omega):\n" }{MPLTEXT 1 0 8 "Omega:=(" }{MPLTEXT 1 0 29 "(dHams12)&wedge(DGform(s12)))" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 13 "&plus(Omega):" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 8 "Omega:=(" }{MPLTEXT 1 0 29 "(dHams22)&wedge(DGform(s22 )))" }{MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 14 "&plus(Omega):\n" }{MPLTEXT 1 0 8 "Omega:=(" }{MPLTEXT 1 0 27 "(dHamX1)&wedge(DGform(X1)))" } {MPLTEXT 1 0 1 " " }{MPLTEXT 1 0 13 "&plus(Omega):" }{MPLTEXT 1 0 1 " \n" }{MPLTEXT 1 0 7 "Omega:=" }{MPLTEXT 1 0 37 "(h&mult(DGform(Q))&wed ge (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(Omega2):" }}}{EXCHG {PARA 0 "B > " 0 "" {MPLTEXT 1 0 27 "DifferenceFundamentalForm:=" }{MPLTEXT 1 0 9 "simplify(" }{MPLTEXT 1 0 27 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