(D1) CSM$USERS:[WHEREMAN]S_KAR2.OUT;1 (C2) BATCH("s_kar2.dat")$ (C3) parameters:[w1,w2,s1,s2,a1,a2]; (D3) [W1, W2, S1, S2, A1, A2] (C4) sublisteqs:[e2,e3]; (D4) [E2, E3] (C5) info_given:true; (D5) TRUE (C6) highest_derivatives:1; (D6) 1 (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,phi2,phi3],[x[1],x[2],x[3],x[4],u[1],u[2],u[3]]); (D12) [ETA1(X , X , X , X , U , U , U ), ETA2(X , X , X , X , U , U , U ), 1 2 3 4 1 2 3 1 2 3 4 1 2 3 ETA3(X , X , X , X , U , U , U ), PHI1(X , X , X , X , U , U , U ), 1 2 3 4 1 2 3 1 2 3 4 1 2 3 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 (C13) depends(eta4,x[4]); (D13) [ETA4(X )] 4 (C14) 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]])); (D14) 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] (C15) 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 (D15) 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] (C16) 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 (D16) - (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] (C17) v1:u[1,[0,0,0,1]]; (D17) U 1, [0, 0, 0, 1] (C18) v2:u[2,[0,0,0,1]]; (D18) U 2, [0, 0, 0, 1] (C19) v3:u[3,[0,0,0,2]]; (D19) U 3, [0, 0, 0, 2] (C21) 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 */ /*********************************************************/ Using only the information from terms involving the highest derivatives, i.e. : [U , U , U , 2, [0, 0, 4, 0] 1, [0, 0, 4, 0] 2, [2, 0, 2, 0] U , U , U , U , 2, [0, 2, 2, 0] 1, [2, 0, 2, 0] 1, [0, 2, 2, 0] 2, [4, 0, 0, 0] U , U , U , U , 2, [2, 2, 0, 0] 2, [0, 4, 0, 0] 1, [4, 0, 0, 0] 1, [2, 2, 0, 0] U ] 1, [0, 4, 0, 0] in the search for determining equations. You are using only the 2 equations : [E2, E3] of the given system consisting of 3 equations in total. *** Number of determining equations before simplifications: 4 . *** WARNING ! We eliminated the factor: U S2 1 dETA3 which was the coefficient of U ----- S2 1 dU 3 List of parameters that were factored out and cancelled: [U S2] 1 *** Number of determining equations after simplifications: 4 . *** *** These determining equations are stored in: LODE. *** (C22) PRINTEQN(LODE); dETA3 Equation 1 : ----- = 0 dU 3 dETA2 Equation 2 : ----- = 0 dU 3 dETA1 Equation 3 : ----- = 0 dU 3 dPHI1 Equation 4 : ----- = 0 dU 3 (D22) DONE (C23) CLOSEFILE();