R = QQ[x,y,z,u,v,w,c300,c210,c120,c030,c021,c012,c003,c102,c201,c111]; I = ideal( c300*w^3-c003*u^3-c201*u*w^2+c102*u^2*w, -c021*v*w^2-c003*v^3+c012*v^2*w+c030*w^3, -c030*u^3+c300*v^3+c120*u^2*v-c210*u*v^2, -c012*v^2*w+c003*v^3-c030*w^3+c021*v*w^2, -c120*u^2*v-c300*v^3+c030*u^3+c210*u*v^2, -c300*w^3-c102*u^2*w+c201*u*w^2+c003*u^3, c012*u^2*w+c210*w^3-3*c003*v*u^2-c201*v*w^2-c111*u*w^2+2*c102*v*u*w, c102*v^2*w-c021*u*w^2+c120*w^3+2*c012*v*u*w-3*c003*v^2*u-c111*v*w^2, 2*c120*w*u*v+c201*v^3-3*c030*w*u^2-c210*w*v^2-c111*u*v^2+c021*u^2*v, -c012*u*v^2+c120*w^2*v+c102*v^3-c111*w*v^2-3*c030*w^2*u+2*c021*w*u*v, -c111*v*u^2-c120*w*u^2+c201*v^2*u+c021*u^3-3*c300*w*v^2+2*c210*w*v*u, 2*c201*w*v*u-3*c300*w^2*v-c102*v*u^2+c012*u^3+c210*w^2*u-c111*w*u^2); I = I:ideal(u); I = I:ideal(v); I = I:ideal(w); I = I:ideal(u); I = I:ideal(v); I = I:ideal(w); codim I, degree I betti mingens I toString mingens I I == I:ideal(u) I == I:ideal(v) I == I:ideal(w)