# please contact quan@cs.ust.hk for any question related to # this Maple procedure solving projective reconstruction # from 6 points in 3 images. solvecubic := proc(image1,image2,image3) local eqcubicx, x,y,z,t, a1,b1,c1, a2,b2,c2, a3,b3,c3, u1,v1,w1, u2,v2,w2, u3,v3,w3, A1,B1,C1,D1,E1, A2,B2,C2,D2,E2, A3,B3,C3,D3,E3; a1 := image1[1][1]; b1 := image1[1][2]; c1 := image1[1][3]; u1 := image1[2][1]; v1 := image1[2][2]; w1 := image1[2][3]; a2 := image2[1][1]; b2 := image2[1][2]; c2 := image2[1][3]; u2 := image2[2][1]; v2 := image2[2][2]; w2 := image2[2][3]; a3 := image3[1][1]; b3 := image3[1][2]; c3 := image3[1][3]; u3 := image3[2][1]; v3 := image3[2][2]; w3 := image3[2][3]; A1 := a1*(v1-w1); B1 := b1*(w1-u1); C1 := c1*(u1-v1); D1 := w1*(a1-b1); E1 := v1*(c1-a1); A2 := a2*(v2-w2); B2 := b2*(w2-u2); C2 := c2*(u2-v2); D2 := w2*(a2-b2); E2 := v2*(c2-a2); A3 := a3*(v3-w3); B3 := b3*(w3-u3); C3 := c3*(u3-v3); D3 := w3*(a3-b3); E3 := v3*(c3-a3); t := 1.0; eqcubicx := (-2*D1*B3*E1*A3*D2*E2-B3*E1^2*D3*D2*A2+E3*D1*E1*B3*D2*A2-2*E3*A1^2*D3*D2*E2+C1* E3*D1*A3*D2*E2-C1*E3*E1*A3*D2^2+B3*A1*E3*D1*D2*E2-C3*D1*A1*D3*E2^2-E3*C3*D1^2* A2*E2-E3*B1*E1*A3*D2^2-B1*E1*D3^2*A2*E2-C1*E3^2*D1*D2*A2-A1*E3^2*D1*D2*C2+D1*E3 *D3*B1*A2*E2+2*E3*A1*D1*A3*D2*E2+E3^2*D1^2*A2^2-2*E1*D1*A3^2*D2*E2+E3*D1*C1*D3* A2*E2+2*E1*D3*D1*A3*A2*E2+E1*D3*D1*A3*E2*B2+E1*D3*D1*A3*E2*C2+C1*D3*E1*A3*D2*E2 +D3*A1*E1*B3*D2*E2-2*E3*D1^2*A3*A2*E2-E3*D1^2*A3*E2*B2-E3*D1^2*A3*E2*C2-2*A1*E3 *E1*A3*D2^2-2*E3*D1*E1*D3*A2*C2-2*E3*D1*E1*D3*A2*B2+C3*D1^2*A3*E2^2-E3*D1^2*B3* A2*E2-C3*E1^2*D3*D2*A2+E3*B1*E1*D3*D2*A2+E3^2*D1^2*A2*C2-A1*E3^2*D1*D2*B2+B1*E3 *D1*A3*D2*E2+2*A1*D3*E1*A3*D2*E2-2*A1*E3^2*D1*D2*A2+E1*D3*B1*A3*D2*E2+D3*A1*E3* D1*E2*B2+2*D3*A1*E3*D1*A2*E2-2*E3*A1*B1*D3*D2*E2+A1*E3^2*B1*D2^2+D3*A1*E3*D1*E2 *C2+C3*A1*E3*D1*D2*E2-B1*D3*D1*A3*E2^2-D3*E1^2*A3*D2*B2-2*D3*E1^2*A3*D2*A2+E1^2 *D3^2*A2*B2+E1^2*D3^2*A2*C2-D3*E1^2*A3*D2*C2-E1*A1*D3^2*E2*C2-E1*A1*D3^2*E2*B2- 2*E1*A1*D3^2*A2*E2+B3*A3*D1^2*E2^2+B3*E1^2*A3*D2^2+C3*E1*E3*D1*D2*A2-C1*E1*D3^2 *A2*E2+C1*A1*D3^2*E2^2+A1*B1*D3^2*E2^2-C1*D3*D1*A3*E2^2+C3*E1^2*A3*D2^2-2*A1*D3 *D1*A3*E2^2-2*E3*D1*E1*D3*A2^2+E3^2*D1^2*A2*B2-C3*E1*E3*A1*D2^2+E3*A1*E1*D3*D2* B2+E3*A1*E1*D3*D2*C2-E3*A1*E1*B3*D2^2+2*E3*A1*E1*D3*D2*A2+C3*D1*E1*D3*A2*E2+B3* D1*E1*D3*A2*E2+E3*D1*E1*A3*D2*C2+E3*D1*E1*A3*D2*B2+2*E3*D1*E1*A3*D2*A2-2*E3*C1* A1*D3*D2*E2+E1^2*A3^2*D2^2+C1*E3^2*A1*D2^2-D1*E3^2*B1*D2*A2+C3*A1*E1*D3*D2*E2-2 *D1*C3*E1*A3*D2*E2-D3*A1*B3*D1*E2^2+E1^2*D3^2*A2^2+E3*C1*E1*D3*D2*A2+D1^2*A3^2* E2^2+A1^2*D3^2*E2^2+E3^2*A1^2*D2^2)*x^3+(A3*D1*A1*B3*E2*B2+2*E3*B1*E1*B3*D2*A2- 2*A1*B3*B1*A3*D2*E2+C3*D1*B1*D3*A2*E2+2*C3*D1*C1*D3*A2*E2+E1*C3*C1*A3*D2*A2-A3* D1*A1*B3*D2*E2+C1*E3*D1*A3*E2*B2-E3*B1*D1*B3*A2*E2+E3*C1*E1*B3*D2*A2-2*A1*D3*D1 *A3*E2*C2+A1*B3*E1*A3*D2*B2-D1*B3*E1*A3*E2*B2-D1*B3*E1*A3*D2*A2-2*D1*B3*E1*A3* D2*C2-2*D3*A1*E1*B3*A2*E2-D3*A1*E1*B3*E2*B2-E3*B1*A1*B3*D2*E2+D3*A1*E1*B3*D2*C2 -C1*E3*C3*D1*D2*A2-2*D1*B3*E1*A3*A2*B2+D3*A1*E1*B3*A2*C2+C1*B3*D1*A3*A2*E2-2*D3 *A1*E1*B3*E2*C2+E3*B1*C1*A3*D2*E2+E3*A1*C1*A3*D2*B2+D1*B3*E1*A3*E2*C2+E1*D3*D1* A3*C2*B2-2*D1*B3*E1*A3*A2*C2+E3*B1*A1*B3*D2*A2+D3*A1*E1*B3*A2*B2+E1*D3*B1*A3*A2 *B2+E1*D3*B1*A3*A2*E2+2*E1*D3*B1*A3*E2*B2+E3*A1*D1*A3*D2*C2-2*E3*D1*C1*D3*A2*B2 -E3*D1*C1*D3*A2*C2+E1*D3*D1*A3*A2*C2-E1*D3*D1*A3*A2*B2+D3*A1*C3*B1*A2*E2-2*D3* A1*C3*B1*D2*E2+E1*C3*E3*B1*D2*A2-E3*C1^2*A3*D2*A2-A1*D3*E1*A3*E2*C2-A1*D3*E1*A3 *D2*B2+D1*E3*D3*B1*A2*C2+B3*A1*E3*D1*A2*E2+B3*A1*E3*D1*A2*B2-C3*A1^2*D3*E2*C2- B1*E3*D1*A3*E2*B2+B1*E3*D1*A3*A2*B2+2*E1*D3*B1*A3*D2*A2+B3*A1*E3*D1*E2*C2+E3*B1 *C1*D3*D2*A2-2*D1*E3*C3*B1*D2*A2+2*B3*A1*E3*D1*E2*B2+B3*A1*E3*D1*A2*C2-2*C1*D3* B1*A3*A2*E2+B3*A1*E3*D1*D2*C2-2*A1*B3*C1*A3*D2*E2+A1*D3*E1*A3*E2*B2+C1*E1*D3^2* A2^2-2*A1*C3*C1*A3*D2*E2-2*A1*D3*E1*A3*C2*B2-A1*D3*E1*A3*B2^2-C3*E1*E3*A1*D2*A2 -2*C3*E1*E3*A1*D2*B2+A1*D3*E1*A3*D2*C2-E3*D1*E1*B3*A2*B2+C1*D3*B1*A3*D2*E2+D3* B1*A1*B3*A2*E2+A3*B1*E1*B3*D2*A2+A1*D3*C1*A3*E2^2+2*C1*E3*D1*A3*D2*C2+2*C1*E3* D1*A3*A2*E2-A1*D3*B1*A3*D2*E2-C1*D3*C3*A1*D2*E2+D3*A1*E3*D1*A2*C2-2*E3*A1*D1*A3 *C2*B2-C3*D1*E1*D3*A2*C2-C3*D1*A1*D3*E2*C2+C3*E1*E3*D1*A2^2-D1*C3*C1*A3*D2*E2+ C3*B1*E1*D3*D2*A2+B1*E3*D1*A3*D2*C2-B1*E3*D1*A3*D2*A2+E3*A1*E1*B3*D2*A2-E3*A1* E1*B3*D2*B2-2*E3*A1*C1*B3*D2*E2+E3*A1*E1*B3*D2*C2+E3*A1*C1*B3*D2*A2-2*B1*E3*D1* A3*E2*C2-2*C3*D1*E1*D3*A2*B2-D1*C3*E1*A3*D2*C2+A1*D3*B1*A3*E2*C2-C1*D3*D1*A3*E2 *C2-2*C3*A1*B3*D1*A2*E2+B1*C3*E1*A3*D2*A2-2*B1*C3*E1*A3*D2*E2-2*A1*E3*E1*A3*D2* B2-2*C1*E3*E1*A3*D2*B2+C1*D3*D1*A3*A2*E2+C1*D3*D1*A3*E2*B2+A3*D1*A1*B3*E2*C2+C3 *A1*E1*D3*D2*A2-2*B1*E3*D1*A3*A2*E2+B1*E3*D1*A3*A2*C2+2*A1*E3*E1*A3*D2*C2+C1^2* A3^2*D2*E2-2*C1*B3*D1*A3*D2*E2-D3*A1*E1*B3*D2*A2-B1*D3*D1*A3*A2*E2-2*D1*C3*E1* A3*A2*B2-C3^2*D1^2*A2*E2-2*B1*D3*D1*A3*E2*C2-2*D1*C3*E1*A3*A2*C2+C3*A1*E1*D3*E2 *B2+2*C3*A1*E1*D3*A2*E2+2*C3*A1*E1*D3*D2*C2+C3*A1*E1*D3*D2*B2+D1*C3*E1*A3*D2*A2 +D1*C3*E1*A3*D2*B2+E3*C1*C3*A1*D2*A2+E3*D1*E1*A3*C2*B2+E3*D1*E1*A3*A2*B2-E3*D1* E1*A3*A2*C2-E3*A1*C1*A3*D2*E2+E3*A1*C1*A3*D2*C2+C3*A1*E1*D3*A2*C2-2*C3*A1*A3*B1 *D2*E2-E3*A1*B1*D3*E2*B2+E3*A1*B1*D3*A2*E2+B3*D1*A3*B1*A2*E2+E3*A1*B1*D3*E2*C2- 2*C3*A1*E3*D1*D2*B2+E3*A1*E1*D3*C2*B2+E3*A1*E1*D3*A2*B2-E3*A1*E1*D3*A2*C2-2*D1* C3*E1*A3*E2*B2-D1*C3*E1*A3*A2*E2+D3*E1^2*A3*A2*C2+C3*A1*E3*D1*E2*B2+D3*A1*E3*D1 *C2*B2-2*E3*A1*B1*D3*D2*C2+E3*A1*C3*B1*D2*E2+C3*A1*E3*D1*A2*B2-D3*A1*E3*D1*A2* B2-2*E3*A1*B1*D3*A2*B2-2*E3*A1*B1*D3*A2*C2-E3*A1*B1*D3*D2*A2+E3*A1*A3*B1*D2*E2+ E3*A1*C3*B1*D2*A2-C3*A1*E3*D1*D2*C2-C3*A1*E3*D1*A2*E2-2*C3*A1*E3*D1*D2*A2+C3*E1 *E3*D1*A2*B2+E3*A1*A3*B1*D2*B2+E3*A1*A3*B1*D2*C2+D3*A1*E3*D1*C2^2+A1*D3*C1*A3* E2*C2+A1*D3*C1*A3*D2*E2-E3*B1*D1*B3*A2^2+A1*B3*E1*A3*D2*E2+C3*D1*A1*D3*A2*E2-C3 *D1^2*A3*A2*E2+A1*B3*E1*A3*D2*C2+A1*D3*C1*A3*E2*B2+C3*D1*A1*D3*E2*B2+2*A1*D3*D1 *A3*E2*B2-2*E3*B1*E1*D3*A2*C2-E3*B1*E1*D3*A2*B2-C3*E1^2*D3*A2^2+C3*D1*E1*B3*A2* 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*B1*A3*D2*C2+A1*D3*B1*A3*B2*C2+2*C3*E1*A1*B3*D2*C2-C3*E1*A1*B3*B2*D2+2*C1*D3*B1 *A3*E2*B2-E3*C1*A1*D3*B2*C2-E1*A3*C1*B3*D2*C2+E3*C1*A1*D3*B2^2-2*E1*C3^2*A1*B2* D2-E1*C3^2*A1*A2*B2-E3*A1*C1*B3*A2*B2-E3*A1*C1*B3*D2*C2-E3*B1^2*A3*C2*E2+E3*B1^ 2*A3*A2*C2-E3*A1*C1*B3*A2*E2+E3*B1^2*A3*D2*C2+E3*A1*E1*B3*B2*C2-E3*A1*E1*B3*A2* C2+2*C3*B1*C1*D3*A2*E2-E3*A1*C1*B3*B2*D2-B1*C3*E1*A3*A2*B2+2*D3*B1*A1*B3*C2*E2+ 2*B3*E1*C1*D3*A2*C2-2*E3*A1*C1*B3*A2*C2-2*E3*A1*C1*B3*E2*B2-B1*C3*E1*A3*A2*E2- B1*C3*E1*A3*B2*D2-B1*C3*E1*A3*D2*C2-2*B1*C3*E1*A3*E2*B2-2*B1*C3*E1*A3*A2*C2-A1* C1*B3^2*D2*A2+D1*C3^2*A1*E2*B2+E3*C1^2*D3*A2*B2+D1*C3^2*A1*A2*B2+A1*B1*D3^2*C2^ 2-E3*C3*B1^2*A2^2+C1*D3*D1*A3*B2*C2+D3*B1*A1*B3*A2*C2-D3*B1*C1*B3*A2*E2-D3*B1* C1*B3*A2^2-D1*C3^2*A1*B2*D2+B3*A3*D1^2*C2^2-C1*E3^2*B1*A2^2+E1*C3^2*B1*A2^2+E1* A3^2*B1*B2*C2-C1*D3*D1*A3*A2*B2+B1*C3*C1*A3*A2*E2+C1*A3^2*D1*B2*C2+E3*C1^2*B3* A2^2+A1*B1*D3^2*A2*C2-C3^2*A1^2*B2*D2-B1*A3^2*D1*B2*C2-B1*A3^2*D1*C2^2-C3*E1*C1 *B3*A2^2-D1^2*A3^2*B2*C2+C1^2*D3^2*A2*B2-2*B1*E3*D1*A3*C2^2-C1^2*A3^2*B2*D2-C1* E3*E1*A3*A2*B2+C1*E1*A3^2*E2*B2+2*B3*A1*C1*D3*A2*C2-B3*A1*C1*D3*E2*B2-C3*E1*C1* D3*A2*B2+C1*A3^2*D1*B2*D2+2*B3*A1*C1*D3*C2*E2+A1*C1*B3^2*A2*E2-C1*E3*E1*A3*B2^2 -C1*D3^2*B1*A2*C2+B3*A1*C1*D3*D2*C2+A1*C1*B3^2*E2^2+2*C3*D1*C1*B3*A2*E2+C3*D1* C1*B3*A2^2-E3*D1*C1*B3*A2*C2+C3*D1*C1*B3*D2*A2+C1*B1*A3^2*E2*B2-E3*D1*C1*B3*A2* B2+C3*B1^2*D3*A2*E2-B3*A1*C1*D3*D2*A2+A1*C1*B3^2*D2*E2+B3*A1*C1*D3*A2*B2+C3*D1* A3*B1*A2*B2-C3*D1*A3*B1*E2*B2-D3*B1*E1*B3*A2*C2+B3*D1*C1*D3*A2*C2-D1*C3*C1*A3* A2*B2-C1*B1*A3^2*C2*E2+2*B3*E1*C1*D3*A2*B2-D1*C3*C1*A3*E2*B2+D1*C3*C1*A3*B2*D2- C3*D1^2*B3*A2*C2-C3*D1^2*B3*A2^2-C3*D1*E1*B3*A2*B2-B1*C3*C1*A3*D2^2-C1*D3*C3*A1 *A2*B2-C1*D3*C3*A1*E2*B2-E3*B1*C1*D3*A2*B2+C1*D3*C3*A1*B2*D2-C3*D1*E1*B3*A2*C2+ D1*E1*B3^2*A2*C2+E3*B1*E1*A3*B2*C2-E3*B1*E1*A3*A2*C2-C1*B1*A3^2*B2*D2+C1*B1*A3^ 2*D2*C2+B3*D1*C1*D3*A2^2-C3*B1*E1*D3*A2*B2+E3*A1^2*B3*C2*E2+E3*A1^2*B3*B2*C2-D3 *A1*B3*D1*A2*C2-A1*C3*D1*A3*B2*D2+C3*A1*E1*D3*B2^2-C1*B3*B1*A3*E2^2-A1*C3*D1*A3 *B2*C2-A1*C3*D1*A3*B2^2+D3*C1^2*A3*A2*B2+D3*C1^2*A3*E2*B2-C3*B1*E1*D3*A2*C2+B3* A1^2*D3*E2*C2+C3*A1^2*D3*E2*B2-C3*B3*A1^2*C2*E2+E3*C3*A1^2*D2*B2-C3*B3*A1^2*B2* D2+C3*B3*A1^2*D2*C2+2*C3*D1*A3*B1*A2*C2-C3*B3*A1^2*D2^2+C3*D1*A3*B1*D2*C2+D1*E3 *C3*B1*A2^2+C3*B3*A1^2*E2*B2+2*A1*B3*B1*A3*C2*E2-E3*C1*C3*B1*D2*A2+C3*D1*B1*D3* A2*C2+E3*B1*C1*B3*A2^2+C1*E1*A3^2*D2*B2+2*C3*D1*A3*B1*C2*E2-C3*D1*A3*B1*D2*A2- C1*D3*E1*A3*B2*C2-C3*D1*A3*B1*A2*E2+C1*A3^2*D1*E2*B2-C1*E3*D1*A3*A2*B2-2*E1*D1* A3^2*C2*B2-2*E3*A1^2*D3*C2*B2+E1*A3^2*B1*D2*C2+B1*A3^2*D1*E2*C2-2*C3*B3*A1^2*D2 *E2)*t^2*x+(-C1^2*B3^2*A2^2-C3^2*A1^2*B2^2-A3^2*B1^2*C2^2-C1^2*A3^2*B2^2-B3^2* A1^2*C2^2-C3*B1*C1*D3*B2*A2+2*C3*A1*B3*D1*B2*C2+E1*C3*C1*A3*B2^2+A3*B1*E1*B3*C2 ^2-E1*C3^2*A1*B2^2-C3*B1*E1*B3*A2*C2-E3*A1*C3*B1*B2*C2+B3*C1^2*A3*B2*E2-C3^2*B1 ^2*A2^2-D3*A1*C3*B1*B2*C2-C1*B3*C3*A1*B2*D2+D1*C3*C1*A3*B2^2-C3*D1*C1*B3*B2*A2+ 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*A3*B2*C2+2*A1*C3*C1*A3*B2^2+2*C1*D3*B1*A3*B2*C2-2*C3*B1*A1*B3*A2*C2-C3^2*B1^2* A2*E2-C1^2*B3^2*A2*E2+B3*C1^2*D3*B2*A2-C3*B1*D1*B3*A2*C2-E3*C1^2*A3*B2^2-C1*B3* D1*A3*B2*C2+E3*C1^2*B3*B2*A2+E3*B1*A1*B3*C2^2+E1*C3^2*B1*B2*A2+E3*C3*B1^2*A2*C2 +E1*C1*B3^2*A2*C2-D3*B1^2*A3*C2^2-C1^2*B3^2*A2*D2)*t^3; #==================y eqcubicy := (-E3*A1*C1*A3*B2*C2-C1^2*A3^2*B2*E2-A1^2*C3^2*B2*E2+E3*C1^2*A3*B2*A2+A1*B1*C3^2 *E2*A2+B3*A1^2*C3*E2*C2-E1*A3*A1*C3*B2*C2-E1*C3^2*B1*A2^2-A3*C1*E1*B3*A2*C2+A3* E1*A1*B3*C2^2-A3*B1*A1*C3*E2*C2+2*E1*A3*B1*C3*A2*C2-E3*A1^2*B3*C2^2-A1*C3*C1*B3 *E2*A2-E3*C1*A1*C3*B2*A2-A3*C1*A1*B3*E2*C2+2*E3*C1*A1*B3*A2*C2+A3*B3*C1^2*E2*A2 -E3*A1*C3*B1*A2*C2-E1*C3*A3*C1*B2*A2+2*A1*C3*C1*A3*B2*E2+E3*C1*B1*C3*A2^2+E3*A1 ^2*C3*B2*C2+C1*B1*A3^2*E2*C2+E1*C3*C1*B3*A2^2-E3*B1*C1*A3*A2*C2+A1*E3*B1*A3*C2^ 2+A1*E1*C3^2*B2*A2-A3*C1*B1*C3*E2*A2+E1*A3^2*C1*B2*C2-E1*C3*A1*B3*A2*C2-E1*A3^2 *B1*C2^2-E3*C1^2*B3*A2^2)*t^3+(E3*A1*C1*A3*B2*C2+C1^2*A3^2*B2*E2+A1^2*C3^2*B2* 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*A3*A1*C3*B2*D2+B3*A1^2*C3*E2*B2-E1*A3*E3*C1*B2*A2-E1*A3*E3*C1*B2^2-D1*A3^2*B1* E2*C2+2*C1*D1*A3^2*E2*B2+A3*B1^2*C3*E2*A2-E3*A1*E1*B3*C2*A2+E1*A3*E3*B1*B2*C2- E3*B1*C1*D3*A2^2-E3*B1*C1*A3*C2*D2+C3*E1^2*A3*B2^2+D1*A3*C3*B1*E2*A2-D1*A3*C3* B1*E2*C2+E3*A1*C1*A3*B2^2+E1*B3*A3*B1*E2*C2+E3*C1*A1*D3*B2*A2-E3*C1*A1*D3*B2*C2 -B3*A1^2*C3*D2*E2-E1*B3*A3*B1*C2*A2+E3*B1*C1*A3*E2*B2-E3*C1*D1*C3*B2*A2-A1*E3* E1*C3*B2*A2+E1*D3*C1*A3*B2*A2+2*E1*D3*C1*A3*B2*C2-B3*A1^2*C3*E2^2+D1*B1*C3^2*E2 *A2+2*E1*A3*A1*E3*B2*C2+E3*A1*D3*B1*C2*A2+E3*A1*D3*B1*C2^2-A1*E3*B1*A3*B2*C2-A3 *B1*C1*B3*E2*A2-2*A1*E3*B1*A3*C2*D2-A1*E3*B1*A3*E2*C2-2*E3*D1*A3*C1*B2*A2-E3*D1 *A3*C1*B2*C2-C1*E3^2*B1*A2^2+E3*A1*C1*A3*B2*D2-E3*A1*C1*A3*E2*B2+C1*A1*E3^2*B2^ 2-A1^2*B3^2*E2*C2-A1*B1*C3^2*E2*A2-B3*A1^2*C3*E2*C2+E1*A3*A1*C3*B2*C2+E1*C3^2* B1*A2^2+A3*C1*E1*B3*A2*C2-A3*E1*A1*B3*C2^2+A3*B1*A1*C3*E2*C2-2*E1*A3*B1*C3*A2* C2+E3*A1^2*B3*C2^2+A1*C3*C1*B3*E2*A2+E3*C1*A1*C3*B2*A2+A3*C1*A1*B3*E2*C2-A3^2* B1^2*E2*C2-A3^2*E1^2*B2*C2+2*E1*C3*A1*B3*E2*A2-E1*D3*A1*C3*B2*C2-2*D1*A1*C3^2* E2*B2+E1*A3*D1*C3*B2*A2-E1*A3*D1*C3*B2*C2-A1*D3*C1*B3*E2*C2-E1*A3^2*D1*B2*C2-A3 *C1*E1*B3*E2*A2+E3*A1^2*B3*B2*C2-D1*E3*B1*C3*A2^2-D1*E3*B1*C3*C2*A2-A3*C1*B1*C3 *D2*E2-D3*C1*B1*C3*E2*A2+D1*A3*E3*B1*C2^2+E3*C1^2*A3*B2*D2-A3*B1*C1*B3*E2^2-C1* E3^2*B1*B2*A2-2*A3*E1*A1*B3*C2*D2+A1*B1*C3^2*D2*E2-2*E3*B1*E1*B3*C2*A2+C1*A1*E3 ^2*B2*A2-A3*C1*E1*B3*C2*D2+2*E1*A3*B1*C3*C2*D2-E1*C3*D1*B3*C2*A2+D1*C3*A1*B3*E2 *A2+2*D1*C3*A1*B3*E2*C2-E1*C3*D3*C1*B2*A2-D3*A1^2*B3*E2*C2-E1*C3*A3*C1*B2*D2+E3 ^2*B1^2*C2*A2+E1^2*B3^2*C2*A2-A1^2*E3^2*B2*C2+2*D1*C3*C1*A3*E2*B2-E1*C1*B3^2*E2 *A2+E1*C3*A1*B3*D2*A2+2*E3*C1*B1*C3*D2*A2-E3*B1*C1*D3*C2*A2-2*E1*D3*A1*C3*B2*A2 -E1*C3*A1*B3*B2*A2-E1*C3*A1*B3*C2*D2+E1*C3*A1*B3*E2*B2-E1*A3^2*C1*B2^2-E1*A3^2* C1*B2*D2+E1*A3^2*C1*E2*B2+2*E1*A3^2*B1*C2*D2+E1*A3^2*B1*E2*C2+E1*A3^2*B1*B2*C2- 2*E3*C1^2*B3*D2*A2+E1*B3*B1*C3*A2^2-2*E3*C1*A1*B3*A2*C2-A3*B3*C1^2*E2*A2+E3*A1* 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*D2+D3*C1*B1*C3*E2*D2-E1*C3*A1*B3*D2^2-E1*A3^2*D1*B2*D2-2*A1*D3*D1*C3*E2*B2+E3* C1^2*B3*D2^2+2*D3*B1*D1*B3*E2*A2+2*D3*B1*D1*B3*E2*C2+E1*C3*D1*B3*D2*A2+E1*A3*D1 *B3*C2*D2+D1*C3*A1*B3*E2*D2+E1*C3*D3*C1*B2*D2-D3*A1^2*B3*E2*D2+A1^2*D3^2*E2*B2+ D1^2*C3^2*E2*B2-E3*C1*B1*C3*D2^2-E1*A1*D3^2*B2*C2+E3*D1^2*B3*A2^2+2*E3*D1^2*B3* C2*A2+E3*D1^2*B3*C2^2+A1*E3*D1*A3*B2*D2-A3*D1^2*B3*C2*E2-2*E1*D3*C3*B1*D2*A2-D1 *E3*B1*D3*A2^2-2*D1*E3*B1*D3*C2*A2-D1*E3*B1*D3*C2^2-E3*A1*C3*B1*D2^2+E1*D3*A3* D1*B2*C2)*y^3; #=====================z eqcubicz := (-E1^2*C3^2*D2^2-D1^2*E3^2*C2^2-D1^2*C3^2*E2^2+B1*A3*E1*C3*D2*E2-2*B1*E3*A3*E1* C2*D2-A1*E3^2*C1*D2*A2-A1*E3^2*C1*D2*B2+2*D3*A1*B1*C3*E2^2-2*E3*A1*B3*E1*C2*D2- D3*B1*A3*C1*E2^2-2*A1*E3*A3*E1*C2*D2-D1*E1*A3^2*C2*E2-2*B1*D3*E1*C3*E2*A2-B1*E3 ^2*C1*D2*B2+A1*B3*E3*C1*D2*E2+E1*B3*E3*C1*D2*A2+B3*D1*E1*C3*E2*A2-2*E3*B1*B3*E1 *C2*D2+D1*E3*B3*E1*C2*A2+D1*E3*B3*E1*C2*B2+D1*E3*B1*C3*E2*B2+D1*E3*A1*C3*E2*A2+ D1*E3*A1*C3*E2*B2-2*B1*D3*E1*C3*E2*B2-2*C3*A1*D3*E1*E2*A2+D1*A3*E1*C3*E2*A2-D1* B3*A1*C3*E2^2+E3*B1*B3*C1*D2*E2-B1*E3^2*C1*D2*A2-A3*C3*E1^2*D2*A2-A3*C3*E1^2*D2 *B2-D1*B1*E3^2*C2*A2+D3*E1^2*C3*A2^2+2*D3*E1^2*C3*A2*B2+D3*E1^2*C3*B2^2+D3*E1* B3*C1*E2*A2+D3*E1*B3*C1*E2*B2-D1*A3*B1*C3*E2^2+D1*C1*A3^2*E2^2-D1*B3^2*E1*C2*E2 +D1*A3*E1*C3*E2*B2-2*C3*A1*D3*E1*E2*B2-2*B3*D1*A3*E1*C2*E2-2*C3*A1*B1*E3*D2*E2- D1*E3*E1*C3*A2^2-D3*A1*C1*A3*E2^2-2*D1*E3*E1*C3*A2*B2-D1*E3*E1*C3*B2^2+2*A1*B1* E3^2*C2*D2+D3*B1*D1*C3*E2^2+D1*B3^2*C1*E2^2+A1*E3*A3*C1*D2*E2+B3*A1*E1*C3*D2*E2 +2*B3*A3*E1^2*C2*D2-E3*B1^2*C3*D2*E2-D3*B1*B3*C1*E2^2-C3*E1*A3*C1*D2*E2+2*C1*E3 *C3*E1*D2*A2+2*C1*E3*C3*E1*B2*D2+2*C1*E3*C3*E1*D2^2-D3*B3*C1^2*E2^2-D1*A1*C3^2* E2^2+A3*E3*C1^2*D2*E2-B1*E3^2*C1*D2^2+B1*E3^2*C1*C2*D2-D1*B1*C3^2*E2^2-E3*C1*A3 *E1*C2*D2-A1*D3^2*C1*E2^2+C1*D3^2*E1*A2*E2+C1*D3^2*E1*B2*E2+2*C1*D3^2*E1*C2*E2+ D1*C3*A3*C1*E2^2-D1*E3*D3*C1*A2*E2-D1*E3*D3*C1*B2*E2-2*D1*E3*D3*C1*C2*E2+E3*B3* C1^2*D2*E2+2*D1*E3*A1*C3*C2*E2+D3*E3*C1^2*A2*E2+D3*E3*C1^2*B2*E2+2*D3*E3*C1^2* D2*E2-C3*E1*D3*C1*A2*E2-C3*E1*D3*C1*B2*E2-2*C3*E1*D3*C1*D2*E2+A1*E3*D3*E1*C2^2- A1*E3*D3*E1*C2*D2+2*C3*D1*D3*C1*E2^2+B3*D1^2*E3*C2*E2+E3*C1*A3*E1*D2^2-D1*E3*E1 *C3*D2*A2-D1*E3*E1*C3*C2*A2-D1*E3*E1*C3*B2*D2-D1*E3*E1*C3*C2*B2-2*D1*E3*E1*C3* C2*D2+B1*D3^2*E1*C2*E2+2*D1*A3*E1*C3*D2*E2-D1*A3*E1*C3*C2*E2+A1*E1*C3^2*D2*E2- B3*D1*D3*E1*C2*E2-D1*E3*D3*A1*C2*E2+A3*D1^2*E3*C2*E2+A3*C3*E1^2*C2*D2-B1*D3^2* C1*E2^2-D3*A3*C1^2*E2^2+D3*E1^2*C3*D2*A2+D3*E1^2*C3*C2*A2-D3*E1*B3*C1*D2*E2+2* D3*E1*B3*C1*C2*E2+E1*B3*E3*C1*D2^2-E1*B3*E3*C1*C2*D2+E3*D1*A3*E1*C2^2-E3*D1*A3* E1*C2*D2-B3*D3*E1^2*C2*A2+A1*E3*D1*A3*C2*E2-D3*B1^2*E3*C2*E2+A1*E3*D3*E1*C2*A2+ A1*E3*D3*E1*C2*B2-D3*E3*A1^2*C2*E2+D3*C1*A1*C3*E2^2-E1*A3*D3*C1*D2*E2+2*E1*A3* D3*C1*C2*E2-B3*D3*E1^2*C2^2+B3*D3*E1^2*C2*D2+B1*E3*E1*C3*D2^2-B1*E3*E1*C3*C2*D2 +D3*E1^2*C3*C2*B2+2*D3*E1^2*C3*C2*D2+D3*B1*E3*C1*E2*A2+D3*B1*E3*C1*E2*B2-A3*D3* E1^2*C2*A2-A3*D3*E1^2*C2*B2+D1*E3^2*C1*B2^2-2*E1*B3*A3*C1*D2*E2-2*D1*B3*E3*C1* E2*A2-D3^2*C1^2*E2^2-B3*D3*E1^2*C2*B2-D1*A3*A1*C3*E2^2+B1*D3*E1*A3*C2*E2+D1*E3^ 2*C1*A2^2-D3^2*E1^2*C2^2-2*D1*A3*E3*C1*E2*B2-2*C1*E3*D3*E1*A2*B2-C1*E3*D3*E1*B2 ^2+D1*B3*B1*E3*C2*E2-C1*E3*D3*E1*A2^2+E1^2*A3^2*C2*D2-E3*A1^2*C3*D2*E2+B3^2*E1^ 2*C2*D2+B1^2*E3^2*C2*D2+B3*E1*B1*C3*D2*E2-B3*C3*E1^2*D2*A2-B3*C3*E1^2*D2*B2+D3* E1*B1*E3*C2*A2+D3*E1*B1*E3*C2*B2+2*D1*B3*A3*C1*E2^2+D1*E3*B1*C3*E2*A2+B3*D1*E1* C3*E2*B2+E3*A1*E1*C3*D2*A2+D3*A1*B3*E1*C2*E2+D1*E3*B3*A1*C2*E2-B3*D1*B1*C3*E2^2 +A1^2*E3^2*C2*D2+E3*D1*A3*E1*C2*A2+E3*D1*A3*E1*C2*B2+E1*B3*E3*C1*D2*B2-D1*B1*E3 ^2*C2*B2-D1*E3^2*A1*C2*A2-D1*E3^2*A1*C2*B2+E3*A1*E1*C3*D2*B2+B1*E3*E1*C3*D2*A2+ D3*A1*A3*E1*C2*E2+B1*E3*E1*C3*D2*B2-2*D3*A1*B1*E3*C2*E2+B1*E3*A3*C1*D2*E2-E1*B3 ^2*C1*D2*E2+A1*C3*E1*A3*D2*E2-E1*C1*A3^2*D2*E2+D3*A1^2*C3*E2^2-E3^2*C1^2*D2^2- B1*D3*E1*C3*D2*E2-B1*D3*E1*C3*C2*E2-C3*A1*D3*E1*D2*E2-C3*A1*D3*E1*C2*E2-C3*E1* 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A1*B1*C3*C2*A2-2*D3*A1*B1*C3*A2*E2+A3*D1^2*C3*A2*B2+E1*A3*D3*C1*B2^2-D1*A3*D3* C1*A2*B2+D1*A3*D3*C1*C2*B2-2*D1*E3*B3*A1*C2*A2-D1*E3*B3*A1*C2*B2+2*B3*D1*B1*C3* A2*E2-D1^2*A3^2*C2*B2-A3^2*C1^2*D2*B2+D1^2*C3^2*A2*B2+D3^2*C1^2*A2*B2-E3*A1^2* C3*D2*B2-2*A3*E1*B3*A1*C2*D2-B3*A1^2*C3*E2*D2-B3*A1^2*C3*D2^2+B3*A1^2*C3*C2*D2+ D3*A1*D1*C3*C2*B2-A1^2*C3^2*D2*B2-D3^2*A1^2*C2*B2-B3*E1*B1*C3*D2*A2-D3*B1*B3*E1 *C2*A2+2*D3*A1*B3*C1*C2*A2-D3*B3*C1^2*D2*A2+D3*A1*C1*E3*A2*B2+D1*A3*B1*C3*A2*E2 -D1*A3*B1*C3*D2*A2-D1*A3*B1*C3*E2*B2+A1*B3^2*C1*E2*D2+D1*E3*A1*C3*A2*B2+D1*E3* A1*C3*B2^2-B3*D1*B1*A3*C2*E2+D3*A1*B1*A3*C2^2+D3*A1*B1*A3*C2*E2-D3*A1*B1*A3*C2* D2-B3*D1*E1*C3*A2^2-B3*D1*E1*C3*A2*B2-2*B1*A3*A1*E3*C2*D2+D3*A1*B3*E1*C2*A2+2* D3*A1*B3*E1*C2*B2+2*D1*A3*D3*A1*C2*B2+D1*B3*D3*C1*A2^2+D1*B3*D3*C1*C2*A2-D1*B1* A3^2*C2*B2+D3*B1*B3*A1*C2*A2+D3*B1^2*C3*A2^2-2*D3*A1*B1*C3*A2*B2+D3*B1*A3*C1*A2 *B2-D3*B1^2*A3*C2*A2+D1*A3*B1*C3*A2*B2-A1*B3^2*C1*D2*A2+B3*D1*B1*A3*C2*A2+D3*A1 *B1*A3*C2*B2-2*D1*B3*A3*C1*A2*B2-B3*D1*B1*C3*A2^2+B3^2*A1^2*C2*D2-B3*A1^2*C3*D2 *B2+D3*A1*B3*C1*A2*B2-A3*B1^2*C3*D2*A2-2*A3*B1*B3*A1*C2*D2)*t^2*z+(D3*B1*B3*C1* A2^2+D1*A3*A1*C3*B2^2-A1*B3*B1*C3*D2*A2-A3*B1*A1*C3*D2*B2+D3*A1*C1*A3*B2^2-D1* B3^2*C1*A2^2-D1*C1*A3^2*B2^2+B1*A3^2*C1*D2*B2+D3*B3*A1^2*C2*B2-B3*A1*A3*C1*D2* B2-D1*B3*A1*C3*A2*B2+D1*B3^2*A1*C2*A2-D1*A3*B3*A1*C2*B2-B1^2*A3^2*C2*D2-D3*A1^2 *C3*B2^2-B1*A3*B3*C1*D2*A2+D1*B1*A3^2*C2*B2-D3*B1*B3*A1*C2*A2-D3*B1^2*C3*A2^2+2 *D3*A1*B1*C3*A2*B2-D3*B1*A3*C1*A2*B2+D3*B1^2*A3*C2*A2-D1*A3*B1*C3*A2*B2+A1*B3^2 *C1*D2*A2-B3*D1*B1*A3*C2*A2-D3*A1*B1*A3*C2*B2+2*D1*B3*A3*C1*A2*B2+B3*D1*B1*C3* A2^2-B3^2*A1^2*C2*D2+B3*A1^2*C3*D2*B2-D3*A1*B3*C1*A2*B2+A3*B1^2*C3*D2*A2+2*A3* B1*B3*A1*C2*D2)*t^3; #=========solve them lprint(fsolve(eqcubicx,x,complex)); lprint(fsolve(eqcubicy,y,complex)); lprint(fsolve(eqcubicz,z,complex)); end;