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<head><title>statePolytope(ZZ,Ideal) -- computes the mth state polytope of an ideal</title>
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<div><h1>statePolytope(ZZ,Ideal) -- computes the mth state polytope of an ideal</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>statePolytope(m,I)</tt></div>
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<li><span>Function: <a href="_state__Polytope.html" title="computes state polytopes of ideals">statePolytope</a></span></li>
<li><div class="single">Inputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, specifies to compute the mth state polytope</span></li>
<li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, the ideal</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, the list of vertices of the state polytope</span></li>
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<div class="single"><h2>Description</h2>
<div>See Sturmfels's book <i>Groebner bases and convex polytopes</i>, page 14 for the definition of <i>State</i><sub>m</sub>(I). (The difference between this and <i>State</i>(I) is that for all sufficiently large m, <i>State</i><sub>m</sub>(I) does not distinguish between initial ideals which have the same saturation with regard to the irrelevant ideal, whereas in <i>State</i>(I), these are separated.) <table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = ideal(a*c-b^2,a*d-b*c,b*d-c^2);
o2 : Ideal of R</pre>
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<tr><td><pre>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,
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3}, {6, 12, 3, 9}, {4, 14, 5, 7}, {3, 14, 8, 5}}
o3 : List</pre>
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