Singular

D.16.2.7 gorensteinIndex

Syntax:

Polymake::gorensteinIndex( polytope p )

Assume:

p is Gorenstein, i.e. n*p+v is reflexive for some dilatation n and translation v.

Type:

int

Purpose:

returns a factor n such that n*p+v is reflexive for some translation v.

Note:

you can check whether p is Gorenstein by Polymake::isGorenstein(p); the translation v can be computed via Polymake::gorensteinVector(p).

Example:

LIB"polymake.lib"; ==> Welcome to polymake ==> Copyright (c) 1997-2012 ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt) ==> http://www.polymake.org intmat M[4][3]=1,1,0, 1,0,1, 1,0,0, 1,1,1; polytope p = polytopeViaPoints(M); Polymake::gorensteinIndex(p); ==> 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 ==> ==> polymake: used package lrslib ==> Implementation of the reverse search algorithm of Avis and Fukuda. ==> Copyright by David Avis. ==> http://cgm.cs.mcgill.ca/~avis/lrs.html ==> ==> 2 intmat N[3][3]=1,2,0, 1,0,2, 1,-2,-2; polytope q = polytopeViaPoints(N); Polymake::gorensteinIndex(q); ==> ? gorensteinIndex: input polytope not gorenstein ==> ? error occurred in or before ./examples/gorensteinIndex.sing line 7: \ ` Polymake::gorensteinIndex(q);`