(D1) CSM$USERS:[WHEREMAN]S_KAR5.OUT;2 (C2) BATCH("s_kar5.dat")$ (C3) parameters:[s1,s2,w1,w2,a1,a2]; (D3) [S1, S2, W1, W2, A1, A2] (C4) sublisteqs:[all]; (D4) [ALL] (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,x[2]); (D12) [ETA1(X )] 2 (C13) depends(eta2,x[1]); (D13) [ETA2(X )] 1 (C14) depends(f4,[x[1],x[2],x[3],x[4]]); (D14) [F4(X , X , X , X )] 1 2 3 4 (C15) depends(f2,x[4]); (D15) [F2(X )] 4 (C16) depends(phi1,u[1]); (D16) [PHI1(U )] 1 (C17) depends(phi2,x[4]); (D17) [PHI2(X )] 4 (C18) depends(phi3,[x[1],x[2],x[3],x[4],u[3]]); (D18) [PHI3(X , X , X , X , U )] 1 2 3 4 3 (C19) eta1 : k1*x[2]+k2; (D19) K2 + X K1 2 (C20) eta2 : -k1*x[1]+k3; (D20) K3 - X K1 1 (C21) eta3 : k4; (D21) K4 (C22) eta4 : k5; (D22) K5 (C23) phi1 : k6*u[1]; (D23) U K6 1 (C24) phi2 : f2; (D24) F2 (C25) phi3 : 2*k6*u[3]+f4; (D25) 2 U K6 + F4 3 (C26) 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]])); (D26) 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] (C27) 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 (D27) 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] (C28) 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 (D28) - (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] (C29) v1:u[1,[0,0,0,1]]; (D29) U 1, [0, 0, 0, 1] (C30) v2:u[2,[0,0,0,1]]; (D30) U 2, [0, 0, 0, 1] (C31) v3:u[3,[0,0,0,2]]; (D31) U 3, [0, 0, 0, 2] (C33) 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 the 3 equations of the system. *** Number of determining equations before simplifications: 2 . *** *** Number of determining equations after simplifications: 2 . *** *** These determining equations are stored in: LODE. *** (C34) PRINTEQN(LODE); Equation 1 : dF2 2 U A1 K6 + A1 F4 + --- = 0 3 dX 4 Equation 2 : 2 2 2 2 d F4 2 d F4 2 d F4 2 d F4 ---- W2 + ---- W2 + ---- W2 - ---- = 0 2 2 2 2 dX dX dX dX 3 2 1 4 (D34) DONE (C35) CLOSEFILE();