方程组求解（或无解证明）

mathe

18棵树18行方程2: solve([+1-1*Q_X*R_Y,+1*F_Y+1*H_Y*Q_X+1*M_X*Q_Y-1*N_X*Q_Y-1*R_Y+1*N_X*R_Y-2*Q_X*R_Y,+1*G_X-1*H_Y*Q_X-1*M_X*Q_Y+1*N_X*Q_Y-1*F_Y*R_X+3*R_Y-2*G_X*R_Y-1*N_X*R_Y+2*Q_X*R_Y-1*R_X*R_Y,+1*F_Y*G_X-1*F_Y*R_X-1*G_X*R_Y,+1*H_Y-1*H_Y*Q_X-1*M_X*Q_Y+1*N_X*Q_Y-1*R_Y+1*Q_X*R_Y,+1*G_X*H_Y+1*N_X*P_Y-1*H_Y*Q_X-1*M_X*Q_Y+1*N_X*Q_Y-1*F_Y*R_X-1*R_Y-1*G_X*R_Y+2*Q_X*R_Y,+1*I_X-1*I_X*P_Y-1*H_Y*Q_X-1*M_X*Q_Y+1*N_X*Q_Y+1*R_Y-1*N_X*R_Y+1*Q_X*R_Y,+1*F_Y*I_X-1*I_X*P_Y-1*H_Y*Q_X-1*M_X*Q_Y+1*N_X*Q_Y+1*R_Y+1*I_X*R_Y-1*N_X*R_Y+1*Q_X*R_Y-1*R_X*R_Y,+1*I_Y+1*H_Y*Q_X+1*M_X*Q_Y-1*N_X*Q_Y-1*R_Y-1*I_X*R_Y+1*N_X*R_Y-2*Q_X*R_Y+1*R_X*R_Y,+1*F_Y*M_X-1*M_X*P_Y+1*H_Y*Q_X+1*M_X*Q_Y-1*N_X*Q_Y+1*N_X*R_Y-2*Q_X*R_Y,+1*I_Y*M_X-1*I_X*R_Y,+1*N_X-1*N_X*P_Y+1*R_Y-1*N_X*R_Y,+1*F_Y*N_X-1*N_X*P_Y+1*H_Y*Q_X+1*M_X*Q_Y-1*N_X*Q_Y+1*R_Y-2*Q_X*R_Y,+1*I_Y*N_X-1*I_X*P_Y-1*H_Y*Q_X-1*M_X*Q_Y+1*N_X*Q_Y+1*R_Y-1*N_X*R_Y+1*Q_X*R_Y,+1*P_Y+1*R_Y-1*R_X*R_Y,+1*G_X*P_Y-1*H_Y*Q_X-1*M_X*Q_Y+1*N_X*Q_Y-1*F_Y*R_X+2*R_Y-1*G_X*R_Y-1*N_X*R_Y+3*Q_X*R_Y-1*R_X*R_Y,+1*Q_X-1*P_Y*Q_X+1*M_X*Q_Y+1*R_Y-2*Q_X*R_Y,+1*F_Y*Q_X+1*H_Y*Q_X-1*P_Y*Q_X+2*M_X*Q_Y-1*N_X*Q_Y-1*R_Y+1*N_X*R_Y-4*Q_X*R_Y+1*R_X*R_Y,+1*Q_Y-1*M_X*Q_Y-1*R_Y+1*Q_X*R_Y,+1*R_X-1*P_Y*R_X+1*R_Y-1*Q_X*R_Y,+1*D_Y+1*F_Y-1*P_Y,+1+1*K_Y-1*P_Y-1*R_Y,+1*H_X-1*N_X,-1+1*C_Y,-1+1*P_X,-1+1*C_X,+1*N_Y-1*R_Y,+1*M_Y-1*R_Y,+1*B_X-1*N_X,-1+1*B_Y],[F_Y,G_X,H_Y,I_X,I_Y,M_X,N_X,P_Y,Q_X,Q_Y,R_X,R_Y,D_Y,K_Y,H_X,C_Y,P_X,C_X,N_Y,M_Y,B_X,B_Y]);

mathe

方程3: solve([+1+1*A_Y*O_X+1/2*R_Y-1/2*M_X*R_Y,+1*A_Y-1*A_Y*N_X+1*N_X*R_Y,+1*A_Y*I_X-1*A_Y*O_X-1/2*R_Y+1/2*M_X*R_Y,+1*A_Y*M_X-1*A_Y*N_X-1/2*R_Y-1/2*M_X*R_Y+1*N_X*R_Y,+1*N_X+1*A_Y*O_X-1/2*N_X*Q_Y+1/2*R_Y-1/2*M_X*R_Y+3/2*N_X*R_Y,+1*N_Y-1*N_X*R_Y,+1*P_Y-2*R_Y+1*M_X*R_Y-1*P_Y*R_Y+3/2*Q_Y*R_Y+1/2*R_Y*R_Y,+1*A_Y*P_Y+1/2*A_Y*Q_Y+2*R_Y-1/2*A_Y*R_Y-1*M_X*R_Y+1*P_Y*R_Y-3/2*Q_Y*R_Y-1/2*R_Y*R_Y,+1*I_X*P_Y+1/2*M_X*Q_Y-3/2*R_Y+1*I_X*R_Y+1*M_X*R_Y-1*P_Y*R_Y+3/2*Q_Y*R_Y+1/2*R_Y*R_Y,+1*N_X*P_Y-1/2*N_X*Q_Y-1/2*R_Y+1/2*M_X*R_Y-1/2*N_X*R_Y,+1*O_X*P_Y+2*R_Y-2*M_X*R_Y+1*O_X*R_Y+2*P_Y*R_Y-1*Q_Y*R_Y-1*R_Y*R_Y,+1*P_Y*P_Y-1*R_Y+1*M_X*R_Y-1/2*P_Y*R_Y+1/2*Q_Y*R_Y,+1*Q_Y-1*M_X*R_Y,+1*I_X*Q_Y+1*M_X*Q_Y+1*I_X*R_Y-1*M_X*R_Y,+1*O_X*Q_Y+3*R_Y-3*M_X*R_Y+1*O_X*R_Y+4*P_Y*R_Y-2*Q_Y*R_Y-2*R_Y*R_Y,+1*P_Y*Q_Y-2*R_Y+2*M_X*R_Y-2*P_Y*R_Y+2*Q_Y*R_Y+1*R_Y*R_Y,+1*Q_Y*Q_Y-2*P_Y*R_Y+1*R_Y*R_Y,-1+1*P_X+1*P_Y+1/2*Q_Y-1/2*R_Y,+1*O_Y-1/2*Q_Y+1/2*R_Y,+1*K_Y-1*P_Y+1/2*Q_Y-1/2*R_Y,-1+1*J_X+1*P_Y+1/2*Q_Y-1/2*R_Y,+1*C_Y-1*P_Y-1/2*Q_Y+1/2*R_Y,-1+1*R_X,-1+1*F_X,+1*F_Y-1/2*Q_Y+1/2*R_Y,-1+1*C_X+1*P_Y+1/2*Q_Y-1/2*R_Y,+1*M_Y-1*Q_Y,+1*J_Y-1*Q_Y,+1*E_Y-1/2*Q_Y+1/2*R_Y,-1+1*Q_X+1*Q_Y],[A_Y,I_X,M_X,N_X,N_Y,O_X,P_Y,Q_Y,R_Y,P_X,O_Y,K_Y,J_X,C_Y,R_X,F_X,F_Y,C_X,M_Y,J_Y,E_Y,Q_X]);

mathe

方程5: solve([+1-1*P_Y*Q_X-2*P_Y*Q_Y+2*Q_Y*Q_Y+1*R_Y-1*P_Y*R_Y+1*Q_Y*R_Y,+1*J_X-1*P_Y*Q_X-2*P_Y*Q_Y+2*Q_Y*Q_Y+1*J_X*R_Y,+1*J_Y-1*J_X*Q_Y+1*R_Y-1*J_X*R_Y-1*P_Y*R_Y+1*Q_Y*R_Y,+1*N_X-2*P_Y*Q_X-3*P_Y*Q_Y+3*Q_Y*Q_Y+2*R_Y+1*N_X*R_Y-2*P_Y*R_Y+2*Q_Y*R_Y,+1*N_Y-1*N_X*Q_Y-1*N_X*R_Y,+1*O_X-1*O_X*Q_Y+1*R_Y-1*P_Y*R_Y+1*Q_Y*R_Y,+1*J_Y*O_X-1*P_Y*Q_X-2*P_Y*Q_Y+2*Q_Y*Q_Y+1*J_X*R_Y,+1*P_X-1*P_X*R_Y+1*Q_X*R_Y,+1*P_Y-1*P_Y*Q_X-1*P_Y*Q_Y+1*Q_Y*Q_Y,+1*J_X*P_Y-1*J_X*Q_Y+1*R_Y-1*J_X*R_Y-1*P_Y*R_Y+1*Q_Y*R_Y,+1*J_Y*P_Y-1*P_Y*Q_X+1*J_X*Q_Y-1*J_Y*Q_Y-1*P_Y*Q_Y+1*Q_Y*Q_Y-1*R_Y+1*J_X*R_Y+1*P_Y*R_Y-1*Q_Y*R_Y,+1*N_X*P_Y+1*N_Y*P_Y-2*P_Y*Q_X-1*N_X*Q_Y-1*N_Y*Q_Y-2*P_Y*Q_Y+2*Q_Y*Q_Y+2*R_Y-2*P_Y*R_Y+2*Q_Y*R_Y,+1*O_X*P_Y-1*O_X*Q_Y+1*R_Y-1*P_Y*R_Y-1*Q_X*R_Y+1*Q_Y*R_Y,+1*Q_X-1*P_Y*Q_X-1*P_Y*Q_Y+1*Q_Y*Q_Y+1*Q_X*R_Y,+1*N_Y*Q_X+1*P_Y*Q_X-1*N_X*Q_Y+2*P_Y*Q_Y-2*Q_Y*Q_Y-1*R_Y-1*N_X*R_Y+1*P_Y*R_Y-1*Q_Y*R_Y,+1*Q_Y-1*R_Y+1*P_Y*R_Y-1*Q_Y*R_Y,+1*P_X*Q_Y+1*P_Y*Q_Y-1*Q_Y*Q_Y-1*R_Y-1*P_X*R_Y+1*P_Y*R_Y+1*Q_X*R_Y-1*Q_Y*R_Y,+1*Q_X*Q_Y-1*R_Y+1*P_Y*R_Y+1*Q_X*R_Y-1*Q_Y*R_Y,-1+1*M_X+1*P_Y-1*Q_Y,+1*K_Y-1*Q_Y-1*R_Y,-1+1*C_Y+1*Q_Y,+1*I_X-1*Q_X,-1+1*F_X,-1+1*R_X,+1+1*B_Y-1*Q_Y,-1+1*O_Y,+1*F_Y-1*P_Y,+1*M_Y-1*P_Y,+1*D_X-1*Q_X,-1+1*D_Y],[J_X,J_Y,N_X,N_Y,O_X,P_X,P_Y,Q_X,Q_Y,R_Y,M_X,K_Y,C_Y,I_X,F_X,R_X,B_Y,O_Y,F_Y,M_Y,D_X,D_Y]);

mathe

方程8: solve([+1+1*Q_Y+1*Q_Y*Q_Y-3*Q_X*R_X-3*Q_Y*R_X-3*R_Y-3*O_Y*R_Y,+1*O_Y+1/2*Q_Y+1/2*O_Y*Q_Y-1/2*Q_Y*Q_Y,+1*O_Y*O_Y-3/2*Q_Y-1/2*O_Y*Q_Y-1/2*Q_Y*Q_Y+3*Q_X*R_X+3*Q_Y*R_X+3*R_Y+3*O_Y*R_Y,+1*P_X-1*O_Y*P_X-1*P_Y*Q_X+1/2*Q_Y-1/2*O_Y*Q_Y+1/2*Q_Y*Q_Y-1*Q_X*R_X-1*Q_Y*R_X-1*R_Y-1*O_Y*R_Y,+1*P_Y+1*P_Y*Q_X+1/2*Q_Y+1/2*O_Y*Q_Y+1/2*Q_Y*Q_Y-2*Q_X*R_X-2*Q_Y*R_X-2*R_Y-2*O_Y*R_Y,+1*O_Y*P_Y+2*P_Y*Q_X+1*P_Y*Q_Y-1*Q_X*R_X-1*Q_Y*R_X-1*R_Y-1*O_Y*R_Y,+1*Q_X+3/2*Q_Y+1/2*O_Y*Q_Y+1/2*Q_Y*Q_Y-2*Q_X*R_X-2*Q_Y*R_X-2*R_Y-2*O_Y*R_Y,+1*O_Y*Q_X-1/2*Q_Y+1/2*O_Y*Q_Y-1/2*Q_Y*Q_Y+1*Q_X*R_X+1*Q_Y*R_X+1*R_Y+1*O_Y*R_Y,+1*P_X*Q_X-1*P_Y*Q_X+1*P_X*Q_Y,+1*Q_X*Q_X+1/2*Q_Y+1/2*O_Y*Q_Y-1/2*Q_Y*Q_Y+1*Q_X*R_X+1*Q_Y*R_X+1*R_Y+1*O_Y*R_Y,+1*Q_X*Q_Y+1*Q_Y*Q_Y-2*Q_X*R_X-2*Q_Y*R_X-2*R_Y-2*O_Y*R_Y,+1*I_Y-1*O_Y,-1+1*J_X+1*Q_X+1*Q_Y,-1+1*A_X-1*O_Y,+1+1*H_X+1*O_Y-2*Q_X-1*Q_Y,+1*M_Y-1*Q_X-1*Q_Y,-1+1*L_Y-1*O_Y+1*Q_X,+1*J_Y-1*Q_X-1*Q_Y,-1+1*O_X,+1+1*G_Y,+1*M_X-1*Q_X,+1*L_X-1*Q_X,-1+1*C_X,+1*B_Y-1*Q_X-1*Q_Y,-1+1*H_Y-1*O_Y+1*Q_X,-1+1*C_Y-1*O_Y+1*Q_X],[O_Y,P_X,P_Y,Q_X,Q_Y,R_X,R_Y,I_Y,J_X,A_X,H_X,M_Y,L_Y,J_Y,O_X,G_Y,M_X,L_X,C_X,B_Y,H_Y,C_Y]);

wayne

我把没有实数解的情况去掉了。 放在那边主题的附件里，请老大过目

数学星空

方程1,2,3,5,8的解依次为: (1)RootOf(_Z^2+1-_Z) = a, RootOf(_Z^2+(2*a-1)*_Z-a) = b {A_X = a+b+1-b*a, D_Y = -b+b*a, H_Y = -2+a+b*a, J_Y = -a-b+b*a, L_Y = b*a, P_Y = b*a-1+a, Q_X = b, Q_Y = a, J_X = a+b-b*a, K_Y = b*a-1-b, L_X = 1-b*a, O_X = b+a, P_X = -b*a+1+b, C_X = -b*a+1+b, C_Y = 1, K_X = -b*a+1+b, D_X = a+b-b*a, B_Y = b*a-1+a, R_Y = -1, E_X = a+b-b*a, A_Y = b*a-1+a, E_Y = 1} (2)RootOf(_Z^2+_Z+1) = a {F_Y = -(1/2)*a+1/2, G_X = a+2, H_Y = -a, I_X = 1/3+(2/3)*a, I_Y = -(1/3)*a+1/3, M_X = 1/2+(1/2)*a, N_X = a, P_Y = 1/2+(1/2)*a, Q_X = 2+2*a, Q_Y = -a-1, R_X = a+1, R_Y = -(1/2)*a, D_Y = a, K_Y = -1/2, H_X = a, C_Y = 1, P_X = 1, C_X = 1, N_Y = -(1/2)*a, M_Y = -(1/2)*a, B_X = a, B_Y = 1} (3)RootOf(3*_Z^2+1) = a {[A_Y = A_Y, I_X = -1/A_Y, M_X = 1, N_X = 1, N_Y = 0, O_X = -1/A_Y, P_Y = 0, Q_Y = 0, R_Y = 0, P_X = 1, O_Y = 0, K_Y = 0, J_X = 1, C_Y = 0, R_X = 1, F_X = 1, F_Y = 0, C_X = 1, M_Y = 0, J_Y = 0, E_Y = 0, Q_X = 1], [A_Y = -1/2+(1/2)*a, I_X = 3/2+(3/2)*a, M_X = -3*a, N_X = -a, N_Y = 2/3, O_X = -1/2+(3/2)*a, P_Y = -2*a, Q_Y = 2, R_Y = 2*a, P_X = 3*a, O_Y = 1-a, K_Y = -a-1, J_X = 3*a, C_Y = -3*a+1, R_X = 1, F_X = 1, F_Y = 1-a, C_X = 3*a, M_Y = 2, J_Y = 2, E_Y = 1-a, Q_X = -1]} (5)RootOf(1+_Z+_Z^3) = a {J_X = 4/9+(2/9)*a-(1/9)*a^2, J_Y = (1/3)*a+2/3+(1/3)*a^2, N_X = -a+2+a^2, N_Y = a-a^2, O_X = 1/3-(1/3)*a-(1/3)*a^2, P_X = -1/3+(1/3)*a-(2/3)*a^2, P_Y = a^2+2, Q_X = -(1/3)*a+4/3+(2/3)*a^2, Q_Y = a, R_Y = a+1, M_X = -1-a^2+a, K_Y = 2*a+1, C_Y = 1-a, I_X = -(1/3)*a+4/3+(2/3)*a^2, F_X = 1, R_X = 1, B_Y = -1+a, O_Y = 1, F_Y = a^2+2, M_Y = a^2+2, D_X = -(1/3)*a+4/3+(2/3)*a^2, D_Y = 1} (8)RootOf(_Z^2+1-_Z) = a, RootOf(_Z^2+_Z+1) = b {[O_Y = -1+a, P_X = 2/3-(1/3)*a, P_Y = a, Q_X = 1-a, Q_Y = 2*a, R_X = R_X, R_Y = 1+a-2*R_X+a*R_X, I_Y = -1+a, J_X = -a, A_X = a, H_X = 2-a, M_Y = a+1, L_Y = 2*a-1, J_Y = a+1, O_X = 1, G_Y = -1, M_X = 1-a, L_X = 1-a, C_X = 1, B_Y = a+1, H_Y = 2*a-1, C_Y = 2*a-1], [O_Y = -b-1, P_X = -(1/3)*b+1/3, P_Y = 0, Q_X = -b, Q_Y = b, R_X = R_X, R_Y = 0, I_Y = -b-1, J_X = 1, A_X = -b, H_X = 0, M_Y = 0, L_Y = 0, J_Y = 0, O_X = 1, G_Y = -1, M_X = -b, L_X = -b, C_X = 1, B_Y = 0, H_Y = 0, C_Y = 0]}