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StatePolytope :: statePolytope(ZZ,Ideal)

statePolytope(ZZ,Ideal) -- computes the mth state polytope of an ideal

Synopsis

Description

See Sturmfels's book Groebner bases and convex polytopes, page 14 for the definition of Statem(I). (The difference between this and State(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 : statePolytope(3,I)   
This is the Gfan program for computing Groebner fans and tropical varieties.
Use the command "gfan list" to view all subcommands.
The command "gfan" is deprecate for computing all Groebner bases of an ideal.
Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end.
LP algorithm being used: "cddgmp".
polymake: used package cdd
  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

polymake: used package ppl
  The Parma Polyhedra Library (PPL): A C++ library for convex polyhedra
  and other numerical abstractions.
  http://www.cs.unipr.it/ppl/

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


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

o3 : List