An Implementation of Exact Mixed Volume Computation

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

Abstract

Mixed volumes of lattice polytopes play a central role in numerical and tropical algebraic geometry. We present an implementation of a new algorithm for their computation based on tropical homotopy continuation, which is a combinatorial procedure using ideas from numerical algebraic geometry. While the mathematical aspects of the algorithm are presented elsewhere, here we mainly address technical details of the implementation, in particular how it was made fast and reliable. The implementation is distributed as part of the library gfanlib.

Original languageEnglish
Title of host publicationMathematical Software - 5th International Conference, ICMS 2016, Proceedings
EditorsGert-Martin Greuel, Thorsten Koch, Peter Paule, Andrew Sommese
Number of pages8
Volume 9725
PublisherSpringer
Publication date2016
Pages198-205
ISBN (Print)978-3-319-42431-6
ISBN (Electronic)978-3-319-42432-3
DOIs
Publication statusPublished - 2016
Externally publishedYes
EventInternational Congress on Mathematical Software - ZIB, Berlin, Germany
Duration: 11 Jul 201614 Jul 2016
Conference number: 5
http://icms2016.zib.de/

Conference

ConferenceInternational Congress on Mathematical Software
Number5
LocationZIB
Country/TerritoryGermany
CityBerlin
Period11/07/201614/07/2016
Internet address
SeriesLecture Notes in Computer Science (LNCS)
ISSN0302-9743

Keywords

  • Mixed volumes
  • Numerical algebraic geometry
  • Tropical geometry

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