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

doi:10.1007/978-3-662-44199-2_29

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 proceeding › Conference 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 language	English (US)
Title of host publication	Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings
Publisher	Springer Verlag
Pages	175-182
Number of pages	8
ISBN (Print)	9783662441985
DOIs	https://doi.org/10.1007/978-3-662-44199-2_29
State	Published - Jan 1 2014
Event	4th International Congress on Mathematical Software, ICMS 2014 - Seoul, Korea, Republic of Duration: Aug 5 2014 → Aug 9 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8592 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	4th International Congress on Mathematical Software, ICMS 2014
Country	Korea, Republic of
City	Seoul
Period	8/5/14 → 8/9/14

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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

Brake, Daniel A. ; Bates, Daniel J. ; Hao, Wenrui ; Hauenstein, Jonathan D. ; Sommese, Andrew J. ; Wampler, Charlesw. / Bertini-real : Software for one- and two-dimensional real algebraic sets. Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings. Springer Verlag, 2014. pp. 175-182 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Brake, DA, Bates, DJ, Hao, W, Hauenstein, JD, Sommese, AJ & Wampler, C 2014, Bertini-real: Software for one- and two-dimensional real algebraic sets. in Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8592 LNCS, Springer Verlag, pp. 175-182, 4th International Congress on Mathematical Software, ICMS 2014, Seoul, Korea, Republic of, 8/5/14. https://doi.org/10.1007/978-3-662-44199-2_29

Bertini-real : Software for one- and two-dimensional real algebraic sets. / Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charlesw.

Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings. Springer Verlag, 2014. p. 175-182 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8592 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

Access to Document

10.1007/978-3-662-44199-2_29