TY - GEN A1 - Pfeifle, Julian A1 - Rambau, Jörg T1 - Computing Triangulations Using Oriented Matroids N2 - Oriented matroids are combinatorial structures that encode the combinatorics of point configurations. The set of all triangulations of a point configuration depends only on its oriented matroid. We survey the most important ingredients necessary to exploit oriented matroids as a data structure for computing all triangulations of a point configuration, and report on experience with an implementation of these concepts in the software package TOPCOM. Next, we briefly overview the construction and an application of the secondary polytope of a point configuration, and calculate some examples illustrating how our tools were integrated into the {\sc polymake} framework. T3 - ZIB-Report - 02-02 KW - triangulation KW - oriented matroid KW - software KW - chirotope KW - circuit KW - cocircuit KW - symmetry KW - regular KW - secondary polytope KW - hypergeometric function Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6692 ER -