ACM Communications in Computer Algebra, Vol. 45, No. 3, Issue 177, September 2011 Defect Polytopes and Counter-Examples With polymake Michael Joswig TU Darmstadt Andreas Pa enholz TU Darmstadt Abstract It is demonstrated how the software system polymake can be used for computations in toric geometry. More precisely, counter-examples to conjectures related to A-determinants and defect polytopes are constructed. Introduction polymake is a software system for computations in geometric combinatorics and related areas. The project was initiated in 1995 by Gawrilow and the rst author [5], and has continuously been expanded since. Recently, two important additions to the system have been accomplished [7]: 1. polymake now comes with an interactive shell similar to most computer algebra systems. 2. polymake has been extended to allow computations speci c to the class of lattice polytopes, i.e., convex polytopes with integral vertex coordinates, and their relation to combinatorial commutative algebra, toric geometry, and integer programming. The latest release 2.9.9 of polymake was published on November 9, 2010 and can be obtained from http: //www.polymake.org. polymake s functionality is organized in various applications. Currently there are graph, matroid, polytope, tropical, and topaz (short for topology applications zoo). Each application centers around objects,
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Defect polytopes and counter-examples with polymake
Joswig, Michael; Paffenholz, Andreas
Follow ACM Communications in Computer Algebra
, Volume 45 (3/4)
Association for Computing Machinery – Jan 23, 2012
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