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StatePolytope :: polymakeStatePolytope(Ideal)

polymakeStatePolytope(Ideal) -- computes the state polytope of an ideal

Synopsis

Description

See Sturmfels's book Groebner bases and convex polytopes, page 14 for the definition of State(I). (The difference between this and Statem(I) is that for all sufficiently large m, Statem(I) does not distinguish between initial ideals which have the same saturation with regard to the irrelevant ideal, whereas in State(I), these are separated.)
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 : polymakeStatePolytope(I)

o3 = {{11, 7, 7, 11}, {7, 15, 3, 11}, {4, 18, 6, 8}, {3, 18, 9, 6}, {11, 3,
     ------------------------------------------------------------------------
     15, 7}, {8, 6, 18, 4}, {6, 9, 18, 3}, {3, 15, 15, 3}}

o3 : List