R = QQ[ -- Parameters for the Segre variety z, a1, b1, c1, a2, b2, c2, -- Relevant Moebius coordinates, S stands for "sum" q11S, q12S, q21S, q22S, q1S1, q1S2, q2S1, q2S2, qS11, qS12, qS21, qS22, q1SS, q2SS, qS1S, qS2S, qSS1, qSS2, qSSS, MonomialOrder => Eliminate 7 ]; -- Parametrization of the relevant Moebius coordinates as in Section 3. I = ideal( q11S - z*a1*b1*(1-c1-c2), q12S - z*a1*b2*(1-c1-c2), q21S - z*a2*b1*(1-c1-c2), q22S - z*a2*b2*(1-c1-c2), q1S1 - z*a1*(1-b1-b2)*c1, q1S2 - z*a1*(1-b1-b2)*c2, q2S1 - z*a2*(1-b1-b2)*c1, q2S2 - z*a2*(1-b1-b2)*c2, qS11 - z*(1-a1-a2)*b1*c1, qS12 - z*(1-a1-a2)*b1*c2, qS21 - z*(1-a1-a2)*b2*c1, qS22 - z*(1-a1-a2)*b2*c2, q1SS - z*a1*(1-b1-b2)*(1-c1-c2), q2SS - z*a2*(1-b1-b2)*(1-c1-c2), qS1S - z*(1-a1-a2)*b1*(1-c1-c2), qS2S - z*(1-a1-a2)*b2*(1-c1-c2), qSS1 - z*(1-a1-a2)*(1-b1-b2)*c1, qSS2 - z*(1-a1-a2)*(1-b1-b2)*c2, qSSS - z*(1-a1-a2)*(1-b1-b2)*(1-c1-c2) ); -- Implicitize M = eliminate({z, a1, b1, c1, a2, b2, c2}, I); << betti mingens M << endl << endl; << betti res M << endl << endl; exit();