Unimodularity of a subdivision

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EnisKaya
Posts: 7
Joined: 27 Jan 2025, 16:03

Unimodularity of a subdivision

Postby EnisKaya » 24 Apr 2025, 12:49

The following code creates the curve in Example 3.1.8.(3) in the book Introduction to Tropical Geometry by Maclagan-Strumfels:

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$mons = [[0,3,0],[0,2,1],[0,1,2],[0,0,3],[1,2,0,],[1,1,1],[1,0,2],[2,1,0],[2,0,1],[3,0,0]]; $vals = [3,1,1,3,1,0,1,1,1,3]; $C = new Hypersurface<Min>(MONOMIALS=>$mons, COEFFICIENTS=>$vals); $C -> VISUAL;
(check the first curve in the second row of Figure 3.1.2). Moreover, the following code gives its dual subdivision:

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$ds = $C -> dual_subdivision(); $ds -> VISUAL;
This subdivision looks highly unimodular to me, but it's not according to polymake; the code

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print $ds -> UNIMODULAR;
returns false. Am I doing something stupid again? :|

blorenz
Developer
Posts: 149
Joined: 10 Jan 2011, 17:21

Re: Unimodularity of a subdivision

Postby blorenz » 05 May 2025, 07:29

Unfortunately, our unimodularity check currently requires a full dimensional subdivision and will return false if it is low-dimensional. We are working on fixing this for the next polymake release.


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