-------------------------------- -- polynomials of Equation 7 -- -------------------------------- restart -- n number of cameras n=2 load "computerVision.m2" World=worldProductRing2Points(n); Image=imageProductRing2Points(n); A=genericCameras(2,3); B = (A_0 | matrix{{u_(1,0),0},{u_(1,1),0},{u_(1,2),0}}) || (A_1 | matrix{{0,u_(2,0)},{0,u_(2,1)},{0,u_(2,2)}}); C = (A_0 | matrix{{v_(1,0),0},{v_(1,1),0},{v_(1,2),0}}) || (A_1 | matrix{{0,v_(2,0)},{0,v_(2,1)},{0,v_(2,2)}}); Q = (X_0*Y_3-Y_0*X_3)^2 + (X_1*Y_3-Y_1*X_3)^2 + (X_2*Y_3-Y_2*X_3)^2 - X_3^2*Y_3^2; T = makeQuadrilinear(Q); octics={}; for i from 1 to 6 do( for j from i to 6 do( for k from 1 to 6 do( for l from k to 6 do( octics = append(octics,contractQuadrilinear(T,{cramer(i,B),cramer(j,B),cramer(k,C),cramer(l,C)})); ); ); ); ) --polynomials span a real vector space of dimension 126 numColumns mingens ideal octics