-- I define the ideal I defining Grass(2, 4) as the general theory -- gives it. I find the generators with Maple which is easier to program. -- The ideal I is not a radical ideal and to find the radical I use (guess what?) -- radical I -- Note that dim I gives you the dimension of the conical set in A^6 -- corresponding to the closed set in P^5. You should substract one -- to get a correct result. R = QQ[a14, a23, a12, a13, a24, a34] I = ideal( a14^2*a23-a14*a13*a24+a34*a12*a14, -a13*a14*a23+a13^2*a24-a34*a12*a13, -a13*a12*a24+a14*a12*a23+a34*a12^2, a24*a14*a23-a13*a24^2+a34*a12*a24, -a14*a23^2+a23*a13*a24-a34*a12*a23, -a13*a12*a24+a14*a12*a23+a34*a12^2, -a24*a13*a34+a34*a14*a23+a12*a34^2, -a14*a23^2+a23*a13*a24-a34*a12*a23, a13*a14*a23-a13^2*a24+a34*a12*a13, -a24*a13*a34+a34*a14*a23+a12*a34^2, -a24*a14*a23+a13*a24^2-a34*a12*a24, a14^2*a23-a14*a13*a24+a34*a12*a14); radical I I == radical I dim I