Bertini-real: Software for one- and two-dimensional real algebraic sets

Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, Charlesw Wampler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations

Abstract

Bertini-real is a command line program for numerically decomposing the real portion of a one- or two-dimensional complex irreducible algebraic set in any reasonable number of variables. Using numerical homotopy continuation to solve a series of polynomial systems via regeneration from a witness set, a set of real vertices is computed, along with connection information and associated homotopy functions. The challenge of embedded singular curves is overcome using isosingular deflation. This decomposition captures the topological information and can be used for further computation and refinement.

Original languageEnglish (US)
Title of host publicationMathematical Software, ICMS 2014 - 4th International Congress, Proceedings
PublisherSpringer Verlag
Pages175-182
Number of pages8
ISBN (Print)9783662441985
DOIs
StatePublished - Jan 1 2014
Event4th International Congress on Mathematical Software, ICMS 2014 - Seoul, Korea, Republic of
Duration: Aug 5 2014Aug 9 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8592 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th International Congress on Mathematical Software, ICMS 2014
CountryKorea, Republic of
CitySeoul
Period8/5/148/9/14

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Brake, D. A., Bates, D. J., Hao, W., Hauenstein, J. D., Sommese, A. J., & Wampler, C. (2014). Bertini-real: Software for one- and two-dimensional real algebraic sets. In Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings (pp. 175-182). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8592 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-662-44199-2_29