-- -*- M2-comint -*- {* hash: -340869498 *}

i1 : R = QQ[a..d];

i2 : I = ideal(a*c-b^2,a*d-b*c,b*d-c^2);

o2 : Ideal of R

i3 : statePolytope(3,I)   
LP algorithm being used: "cddgmp".
polymake: used package cddlib
 Implementation of the double description method of Motzkin et al.
 Copyright by Komei Fukuda.
 http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html

VERTICES
1 9 6 6 9
1 9 3 12 6
1 7 5 14 4
1 5 8 14 3
1 3 12 12 3
1 6 12 3 9
1 4 14 5 7
1 3 14 8 5


o3 = {{9, 6, 6, 9}, {9, 3, 12, 6}, {7, 5, 14, 4}, {5, 8, 14, 3}, {3, 12, 12,
     ------------------------------------------------------------------------
     3}, {6, 12, 3, 9}, {4, 14, 5, 7}, {3, 14, 8, 5}}

o3 : List

i4 :