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Computing triangulations using oriented matroids. (English) Zbl 1027.52015
Joswig, Michael (ed.) et al., Algebra, geometry, and software systems. Berlin: Springer. 49-75 (2003).
Oriented matroids are a suitable interface between calculations in coordinates and computations in combinatorial geometry.
This paper surveys a selection of efficient combinatorial methods to compute triangulations of a point configuration, which depend only on its oriented matroids.
The authors present 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. Finally, they calculate some examples illustrating how these tools (the construction of the secondary polytope of a point configuration) were integrated into the POLYMAKE framework.
For the entire collection see [Zbl 1008.00013].

MSC:
52C40 Oriented matroids in discrete geometry
05B35 Combinatorial aspects of matroids and geometric lattices
Software:
polymake; TOPCOM
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