ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 23 Apr 2020 23:30:25 +0200Can sage determine if a cone is gorenstein?https://ask.sagemath.org/question/34720/can-sage-determine-if-a-cone-is-gorenstein/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?Mon, 05 Sep 2016 00:36:58 +0200https://ask.sagemath.org/question/34720/can-sage-determine-if-a-cone-is-gorenstein/Comment by Jonathan Kliem for <p>Let M and N be dual lattices of rank d. A d-dimensional rational finite polyhedral cone C is called a <em>Gorenstein cone</em> 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.</p>
<p>Does sage have the capibility to determine if a given cone is Gorenstein?</p>
https://ask.sagemath.org/question/34720/can-sage-determine-if-a-cone-is-gorenstein/?comment=50974#post-id-50974Normaliz 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")
True
I'm not sure, whether or not the definition in normaliz agrees with your definition.Thu, 23 Apr 2020 23:30:25 +0200https://ask.sagemath.org/question/34720/can-sage-determine-if-a-cone-is-gorenstein/?comment=50974#post-id-50974