(D1) CSM$USERS:[WHEREMAN]S_KAR3.OUT;1 (C2) BATCH("s_kar3.dat")$ (C3) parameters:[s1,s2,w1,w2,a1,a2]; (D3) [S1, S2, W1, W2, A1, A2] (C4) sublisteqs:[e1]; (D4) [E1] (C5) info_given:true; (D5) TRUE (C6) highest_derivatives:all; (D6) ALL (C7) warnings:true; (D7) TRUE (C8) subst_deriv_of_vi:true; (D8) TRUE (C9) p:4; (D9) 4 (C10) q:3; (D10) 3 (C11) m:3; (D11) 3 (C12) depends([eta1,eta2,eta3,phi1],[x[1],x[2],x[3],x[4],u[1],u[2]]); (D12) [ETA1(X , X , X , X , U , U ), ETA2(X , X , X , X , U , U ), 1 2 3 4 1 2 1 2 3 4 1 2 ETA3(X , X , X , X , U , U ), PHI1(X , X , X , X , U , U )] 1 2 3 4 1 2 1 2 3 4 1 2 (C13) depends([phi2,phi3],[x[1],x[2],x[3],x[4],u[1],u[2],u[3]]); (D13) [PHI2(X , X , X , X , U , U , U ), PHI3(X , X , X , X , U , U , U )] 1 2 3 4 1 2 3 1 2 3 4 1 2 3 (C14) depends(eta4,x[4]); (D14) [ETA4(X )] 4 (C15) e1:u[1,[0,0,0,1]]+w1*u[1,[0,0,1,0]]+1/2*(s1*(2*u[1,[1,0,0,0]]*u[2,[1,0,0,0]]+ 2*u[1,[0,1,0,0]]*u[2,[0,1,0,0]]+u[1]*u[2,[2,0,0,0]]+u[1]*u[2,[0,2,0,0]])+ s2*(2*u[1,[0,0,1,0]]*u[2,[0,0,1,0]]+u[1]*u[2,[0,0,2,0]])); (D15) U W1 + ((U U 1, [0, 0, 1, 0] 1 2, [0, 0, 2, 0] + 2 U U ) S2 1, [0, 0, 1, 0] 2, [0, 0, 1, 0] + (U U + 2 U U 1 2, [2, 0, 0, 0] 1, [1, 0, 0, 0] 2, [1, 0, 0, 0] + U U + 2 U U ) S1)/2 1 2, [0, 2, 0, 0] 1, [0, 1, 0, 0] 2, [0, 1, 0, 0] + U 1, [0, 0, 0, 1] (C16) e2:u[2,[0,0,0,1]]+w1*u[2,[0,0,1,0]]-1/2*(s1*(u[1,[2,0,0,0]]/u[1]+ u[1,[0,2,0,0]]/u[1]-u[2,[1,0,0,0]]^2-u[2,[0,1,0,0]]^2)+ s2*(u[1,[0,0,2,0]]/u[1]-u[2,[0,0,1,0]]^2))+a1*u[3]; U 1, [0, 0, 2, 0] 2 (D16) U W1 - ((---------------- - U ) S2 2, [0, 0, 1, 0] U 2, [0, 0, 1, 0] 1 U U 2 2 1, [2, 0, 0, 0] 1, [0, 2, 0, 0] + (- U - U + ---------------- + ----------------) 2, [1, 0, 0, 0] 2, [0, 1, 0, 0] U U 1 1 S1)/2 + U A1 + U 3 2, [0, 0, 0, 1] (C17) e3:u[3,[0,0,0,2]]-w2^2*(u[3,[2,0,0,0]]+u[3,[0,2,0,0]]+u[3,[0,0,2,0]])- 2*a2*u[1]*(u[1,[2,0,0,0]]+u[1,[0,2,0,0]]+u[1,[0,0,2,0]])- 2*a2*(u[1,[1,0,0,0]]^2+u[1,[0,1,0,0]]^2+u[1,[0,0,1,0]]^2); 2 (D17) - (U + U + U ) W2 3, [2, 0, 0, 0] 3, [0, 2, 0, 0] 3, [0, 0, 2, 0] - 2 U (U + U + U ) A2 1 1, [2, 0, 0, 0] 1, [0, 2, 0, 0] 1, [0, 0, 2, 0] 2 2 2 - 2 (U + U + U ) A2 1, [1, 0, 0, 0] 1, [0, 1, 0, 0] 1, [0, 0, 1, 0] + U 3, [0, 0, 0, 2] (C18) v1:u[1,[0,0,0,1]]; (D18) U 1, [0, 0, 0, 1] (C19) v2:u[2,[0,0,0,1]]; (D19) U 2, [0, 0, 0, 1] (C20) v3:u[3,[0,0,0,2]]; (D20) U 3, [0, 0, 0, 2] (C22) SYMMETRY(1,0,0)$ /*********************************************************/ /* WELCOME TO THE MACSYMA PROGRAM FOR THE */ /* CALCULATION OF THE SYMMETRY GROUP */ /* IN BATCH MODE */ /* WRITTEN BY B. CHAMPAGNE AND W. HEREMAN */ /* Project Supervision: P. WINTERNITZ */ /* Version 2.0 released on May 29, 1995 */ /* Copyright 1991 */ /*********************************************************/ You are using only the equation : [E1] of the given system consisting of 3 equations in total. *** Number of determining equations before simplifications: 130 . *** 2 WARNING ! We eliminated the factor: U S2 1 2 dPHI2 which was the coefficient of U ----- S2 1 dU 3 WARNING ! We eliminated the factor: S2 dETA3 which was the coefficient of - ----- S2 dU 2 2 WARNING ! We eliminated the factor: U 1 2 dETA1 dETA3 which was the coefficient of - 2 U (----- S2 + ----- S1) 1 dX dX 3 1 WARNING ! We eliminated the factor: U S2 1 2 d PHI2 dPHI1 which was the coefficient of U (U ------ + -----) S2 1 1 2 dU dU 2 2 WARNING ! We eliminated the factor: U 1 dETA2 dETA3 which was the coefficient of - 2 U (----- S2 + ----- S1) 1 dX dX 3 2 WARNING ! We eliminated the factor: U S1 1 2 d PHI2 dPHI1 which was the coefficient of U (U ------ + -----) S1 1 1 2 dU dU 2 2 2 WARNING ! We eliminated the factor: U S1 1 2 dETA2 dETA1 which was the coefficient of - 2 U (----- + -----) S1 1 dX dX 1 2 WARNING ! We eliminated the factor: S1 2 dPHI2 dPHI1 which was the coefficient of (U ----- + -----) S1 1 dU dU 1 2 List of parameters that were factored out and cancelled: 2 2 2 [S1, U S1, U S1, U , U S2, U , S2, U S2] 1 1 1 1 1 1 *** Number of determining equations after simplifications: 26 . *** *** These determining equations are stored in: LODE. *** (C23) SAVE("lodekarpmanrun3.lsp",LODE); (D23) [lodekarpmanrun3.lsp, LODE] (C24) PRINTEQN(LODE); dPHI2 Equation 1 : ----- = 0 dU 3 dETA3 Equation 2 : ----- = 0 dU 1 dETA2 Equation 3 : ----- = 0 dU 1 dETA1 Equation 4 : ----- = 0 dU 1 dETA3 Equation 5 : ----- = 0 dU 2 dETA2 Equation 6 : ----- = 0 dU 2 dETA1 Equation 7 : ----- = 0 dU 2 Equation 8 : 2 dPHI2 dPHI1 U ----- + ----- = 0 1 dU dU 1 2 Equation 9 : dETA1 dETA3 ----- S2 + ----- S1 = 0 dX dX 3 1 Equation 10 : dETA2 dETA3 ----- S2 + ----- S1 = 0 dX dX 3 2 Equation 11 : 2 d PHI2 dPHI1 U ------ + ----- = 0 1 2 dU dU 2 2 Equation 12 : dETA2 dETA1 ----- + ----- = 0 dX dX 1 2 Equation 13 : 2 d PHI2 dPHI2 U ------ + 2 ----- = 0 1 2 dU dU 1 1 Equation 14 : 2 dPHI2 d PHI2 dETA4 dETA3 ----- + U ------- + ----- - 2 ----- = 0 dU 1 dU dU dX dX 2 1 2 4 3 Equation 15 : 2 dPHI2 d PHI2 dETA4 dETA2 ----- + U ------- + ----- - 2 ----- = 0 dU 1 dU dU dX dX 2 1 2 4 2 Equation 16 : 2 dPHI2 d PHI2 dETA4 dETA1 ----- + U ------- + ----- - 2 ----- = 0 dU 1 dU dU dX dX 2 1 2 4 1 Equation 17 : 2 dETA2 dPHI2 d PHI2 dETA2 ----- W1 - ----- S1 - U ------- S1 + ----- = 0 dX dX 1 dU dX dX 3 2 1 2 4 Equation 18 : 2 dETA1 dPHI2 d PHI2 dETA1 ----- W1 - ----- S1 - U ------- S1 + ----- = 0 dX dX 1 dU dX dX 3 1 1 1 4 Equation 19 : dPHI2 dPHI1 dETA4 dETA3 U ----- - U ----- + PHI1 + U ----- - 2 U ----- = 0 1 dU 1 dU 1 dX 1 dX 2 1 4 3 Equation 20 : 2 2 2 2 d PHI2 dPHI1 d ETA3 d ETA3 d ETA3 2 U ------- S2 + 2 ----- S2 - U ------ S2 - U ------ S1 - U ------ S1 = 0 1 dU dX dX 1 2 1 2 1 2 2 3 3 dX dX dX 3 2 1 Equation 21 : 2 2 2 2 d ETA2 d PHI2 dPHI1 d ETA2 d ETA2 U ------ S2 - 2 U ------- S1 - 2 ----- S1 + U ------ S1 + U ------ S1 = 0 1 2 1 dU dX dX 1 2 1 2 dX 2 2 2 dX dX 3 2 1 Equation 22 : dPHI2 dPHI1 dETA4 dETA1 U ----- - U ----- + PHI1 + U ----- - 2 U ----- = 0 1 dU 1 dU 1 dX 1 dX 2 1 4 1 Equation 23 : 2 2 2 2 d ETA1 d PHI2 dPHI1 d ETA1 d ETA1 U ------ S2 - 2 U ------- S1 - 2 ----- S1 + U ------ S1 + U ------ S1 = 0 1 2 1 dX dU dX 1 2 1 2 dX 1 2 1 dX dX 3 2 1 Equation 24 : dPHI2 dPHI1 dETA4 dETA2 U ----- - U ----- + PHI1 + U ----- - 2 U ----- = 0 1 dU 1 dU 1 dX 1 dX 2 1 4 2 Equation 25 : 2 dETA4 dETA3 dPHI2 d PHI2 dETA3 ----- W1 - ----- W1 + ----- S2 + U ------- S2 - ----- = 0 dX dX dX 1 dU dX dX 4 3 3 1 3 4 Equation 26 : 2 2 2 dPHI1 d PHI2 d PHI2 d PHI2 dPHI1 2 ----- W1 + U ------ S2 + U ------ S1 + U ------ S1 + 2 ----- dX 1 2 1 2 1 2 dX 3 dX dX dX 4 3 2 1 dPHI1 - 2 U A1 ----- = 0 3 dU 2 (D24) DONE (C25) CLOSEFILE();