(D1) CSM$USERS:[WHEREMAN]S_KAR4.OUT;1 (C2) BATCH("s_kar4.dat")$ (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,eta2,eta3,f1,f2],[x[1],x[2],x[3],x[4]]); (D12) [ETA1(X , X , X , X ), ETA2(X , X , X , X ), ETA3(X , X , X , X ), 1 2 3 4 1 2 3 4 1 2 3 4 F1(X , X , X , X ), F2(X , X , X , X )] 1 2 3 4 1 2 3 4 (C13) depends(eta4,x[4]); (D13) [ETA4(X )] 4 (C14) depends(phi1,[x[1],x[2],x[3],x[4],u[1]]); (D14) [PHI1(X , X , X , X , U )] 1 2 3 4 1 (C15) depends(phi2,[x[1],x[2],x[3],x[4],u[2]]); (D15) [PHI2(X , X , X , X , U )] 1 2 3 4 2 (C16) depends(phi3,[x[1],x[2],x[3],x[4],u[1],u[2],u[3]]); (D16) [PHI3(X , X , X , X , U , U , U )] 1 2 3 4 1 2 3 (C17) phi1 : f1*u[1]; (D17) U F1 1 (C18) phi2 : (2*diff(eta1,x[1])-diff(eta4,x[4]))*u[2]+f2; dETA1 dETA4 (D18) F2 + U (2 ----- - -----) 2 dX dX 1 4 (C19) gradef(eta3,x[1],-(s2/s1)*diff(eta1,x[3])); (D19) ETA3 (C20) gradef(eta3,x[2],-(s2/s1)*diff(eta2,x[3])); (D20) ETA3 (C21) gradef(eta2,x[1],-diff(eta1,x[2])); (D21) ETA2 (C22) gradef(eta3,x[3],diff(eta1,x[1])); (D22) ETA3 (C23) gradef(eta2,x[2],diff(eta1,x[1])); (D23) ETA2 (C24) 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]])); (D24) 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] (C25) 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 (D25) 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] (C26) 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 (D26) - (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] (C27) v1:u[1,[0,0,0,1]]; (D27) U 1, [0, 0, 0, 1] (C28) v2:u[2,[0,0,0,1]]; (D28) U 2, [0, 0, 0, 1] (C29) v3:u[3,[0,0,0,2]]; (D29) U 3, [0, 0, 0, 2] (C31) 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: 249 . *** 2 2 WARNING ! We eliminated the factor: U S1 S2 1 2 dPHI3 2 which was the coefficient of - U ----- S1 S2 1 dU 2 3 2 WARNING ! We eliminated the factor: U S1 S2 1 3 dPHI3 2 which was the coefficient of 4 U ----- S1 S2 1 dU 1 2 WARNING ! We eliminated the factor: U S1 1 2 2 d PHI3 which was the coefficient of 4 U ------ S1 1 2 dU 3 WARNING ! We eliminated the factor: S2 2 dF1 d ETA2 which was the coefficient of - (2 --- + -------) S2 dX dX dX 3 2 3 WARNING ! We eliminated the factor: S1 dETA4 dETA1 which was the coefficient of - 2 (----- - 2 -----) S1 dX dX 4 1 2 2 WARNING ! We eliminated the factor: U W2 1 2 dETA2 2 which was the coefficient of - 8 U ----- (S2 - S1) W2 1 dX 3 2 2 WARNING ! We eliminated the factor: U S1 W2 1 2 dETA4 dETA1 2 which was the coefficient of - 8 U (----- - -----) S1 W2 1 dX dX 4 1 3 WARNING ! We eliminated the factor: U A2 1 3 dETA2 which was the coefficient of - 16 U A2 ----- (S2 - S1) 1 dX 3 2 WARNING ! We eliminated the factor: U A2 1 2 dETA1 which was the coefficient of - 16 U A2 ----- (S2 - S1) 1 dX 3 3 WARNING ! We eliminated the factor: U A2 S1 1 2 3 dF1 d ETA2 which was the coefficient of - 8 U A2 (4 --- - ------) S1 1 dX 2 2 dX 3 WARNING ! We eliminated the factor: U S2 1 2 2 dF1 d ETA2 d ETA1 which was the coefficient of U (2 --- + ------- + 4 -------) S2 1 dX dX dX dX dX 3 2 3 1 3 WARNING ! We eliminated the factor: U 1 2 2 d ETA2 dF1 d ETA1 which was the coefficient of - U (------ S2 - 2 --- S1 - 4 ------- S1) 1 2 dX dX dX dX 2 1 2 3 2 WARNING ! We eliminated the factor: U A2 S1 1 2 dPHI3 dETA4 dETA1 which was the coefficient of 8 U A2 (----- - 2 F1 - 2 ----- + 2 -----) S1 1 dU dX dX 3 4 1 List of parameters that were factored out and cancelled: 2 3 2 3 2 2 2 2 2 [U A2 S1, U , U S2, U A2 S1, U A2, U A2, U S1 W2 , U W2 , S1, S2, U S1, 1 1 1 1 1 1 1 1 1 3 2 2 2 U S1 S2 , U S1 S2 ] 1 1 *** Number of determining equations after simplifications: 30 . *** *** These determining equations are stored in: LODE. *** (C32) SAVE("lodekarpmanrun4.lsp",LODE); (D32) [lodekarpmanrun4.lsp, LODE] (C33) PRINTEQN(LODE); dPHI3 Equation 1 : ----- = 0 dU 2 dPHI3 Equation 2 : ----- = 0 dU 1 2 d PHI3 Equation 3 : ------ = 0 2 dU 3 dETA3 Equation 4 : ----- = 0 dX 4 dETA2 Equation 5 : ----- = 0 dX 4 dETA1 Equation 6 : ----- = 0 dX 4 Equation 7 : 2 dF1 d ETA2 2 --- + ------- = 0 dX dX dX 3 2 3 Equation 8 : dETA4 dETA1 ----- - 2 ----- = 0 dX dX 4 1 Equation 9 : 2 d ETA2 dF1 ------ S2 - 2 --- S1 = 0 2 dX dX 2 3 Equation 10 : dETA2 ----- (S2 - S1) = 0 dX 3 Equation 11 : dETA1 ----- (S2 - S1) = 0 dX 3 Equation 12 : dETA4 dETA1 ----- - ----- = 0 dX dX 4 1 Equation 13 : 2 2 d PHI3 d ETA4 2 ------- - ------ = 0 dU dX 2 3 4 dX 4 Equation 14 : 2 2 d PHI3 d ETA2 2 ------- - ------ = 0 dX dU 2 2 3 dX 3 Equation 15 : 2 dF1 d ETA2 4 --- - ------ = 0 dX 2 2 dX 3 Equation 16 : 2 2 dF1 d ETA2 d ETA1 2 --- + ------- + 4 ------- = 0 dX dX dX dX dX 3 2 3 1 3 Equation 17 : 2 2 d ETA2 dF1 d ETA1 ------ S2 - 2 --- S1 - 4 ------- S1 = 0 2 dX dX dX dX 2 1 2 3 Equation 18 : 2 dETA2 dF2 d ETA1 ----- W1 - --- S1 - 2 U ------- S1 = 0 dX dX 2 dX dX 3 2 1 2 Equation 19 : 2 dETA1 dF2 d ETA1 ----- W1 - --- S1 - 2 U ------ S1 = 0 dX dX 2 2 3 1 dX 1 Equation 20 : 2 2 2 d ETA1 dF1 d ETA1 d ETA1 ------ S2 - 2 --- S1 + ------ S1 - 3 ------ S1 = 0 2 dX 2 2 dX 1 dX dX 3 2 1 Equation 21 : 2 dETA4 dETA1 dF2 d ETA1 ----- W1 - ----- W1 + --- S2 + 2 U ------- S2 = 0 dX dX dX 2 dX dX 4 1 3 1 3 Equation 22 : 2 2 2 d ETA1 dF1 d ETA1 d ETA1 ------ S2 - 2 --- S1 + ------ S1 + ------ S1 = 0 2 dX 2 2 dX 1 dX dX 3 2 1 Equation 23 : 2 2 2 2 d ETA2 d ETA1 d PHI3 d ETA1 ------- S2 + ------- S2 + 2 ------- S1 - ------- S1 = 0 dX dX dX dX dU dX dX dX 2 3 1 3 3 3 1 3 Equation 24 : 2 2 2 2 d PHI3 d ETA1 d ETA1 d ETA1 2 ------- - ------ - ------ - ------ = 0 dX dU 2 2 2 1 3 dX dX dX 3 2 1 Equation 25 : dPHI3 dETA4 dETA1 ----- - 2 F1 - 2 ----- + 2 ----- = 0 dU dX dX 3 4 1 Equation 26 : 2 2 2 dF1 d ETA1 d ETA1 d ETA1 4 --- - ------ - ------ - ------ = 0 dX 2 2 2 1 dX dX dX 3 2 1 Equation 27 : 2 2 2 d ETA2 d ETA1 dF1 d ETA1 ------- S2 + ------- S2 + 4 --- S1 - ------- S1 = 0 dX dX dX dX dX dX dX 2 3 1 3 3 1 3 Equation 28 : 2 2 2 2 2 2 d PHI3 2 d PHI3 2 d PHI3 2 d PHI3 2 d F1 2 d F1 ------ W2 + ------ W2 + ------ W2 - ------ + 2 U A2 ---- + 2 U A2 ---- 2 2 2 2 1 2 1 2 dX dX dX dX dX dX 3 2 1 4 3 2 2 2 d F1 + 2 U A2 ---- = 0 1 2 dX 1 Equation 29 : 2 3 2 2 3 dF1 d F2 d ETA1 d F2 d F2 d ETA1 2 --- W1 + ---- S2 + 2 U ------- S2 + ---- S1 + ---- S1 + 2 U ------ S1 dX 2 2 2 2 2 2 3 3 dX dX dX dX dX dX 3 1 3 2 1 1 3 d ETA1 dF1 + 2 U ------- S1 + 2 --- = 0 2 2 dX dX dX 4 1 2 Equation 30 : 2 2 2 2 dF2 d ETA1 d F1 d F1 d F1 dF2 2 --- W1 + 4 U ------- W1 - ---- S2 - ---- S1 - ---- S1 + 2 A1 PHI3 + 2 --- dX 2 dX dX 2 2 2 dX 3 1 3 dX dX dX 4 3 2 1 2 d ETA4 dETA4 dETA1 - 2 U ------ + 4 U A1 ----- - 4 U A1 ----- = 0 2 2 3 dX 3 dX dX 4 1 4 (D33) DONE (C34) CLOSEFILE();