Can sage determine if a cone is gorenstein?

asked 2016-09-04 17:36:58 -0600

done_with_fish gravatar image

Let M and N be dual lattices of rank d. A d-dimensional rational finite polyhedral cone C is called a Gorenstein cone if it is generated by finitely many lattice points which are contained in an affine hyperplane ${x in M_RR : <x,n>=1}$ for some n in N.

Does sage have the capibility to determine if a given cone is Gorenstein?

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Normaliz might be useful here. It's an optional package of sage and if you have it installed you can use it:

sage: import PyNormaliz
sage: C = PyNormaliz.NmzCone("cone", [[0, 0, 1, -1], [0, 1, -1, 0], [1, -1, 0, 0]])  # homogenous input
sage: PyNormaliz.NmzResult(C, "IsGorenstein")

I'm not sure, whether or not the definition in normaliz agrees with your definition.

Jonathan Kliem gravatar imageJonathan Kliem ( 2020-04-23 16:30:25 -0600 )edit