Linear programs and convex hulls over fields of puiseux fractions

Michael Joswig; Georg Loho; Benjamin Lorenz; Benjamin Schröter

doi:10.1007/978-3-319-32859-1_37

Linear programs and convex hulls over fields of puiseux fractions

Michael Joswig^*, Georg Loho, Benjamin Lorenz, Benjamin Schröter

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

9 Citations (Scopus)

Abstract

We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful for computations in tropical geometry.

Original language	English
Title of host publication	Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers
Editors	Ilias S. Kotsireas, Siegfried M. Rump, Chee K. Yap
Publisher	Springer
Pages	429-445
Number of pages	17
ISBN (Print)	9783319328584
DOIs	https://doi.org/10.1007/978-3-319-32859-1_37
Publication status	Published - 2016
Externally published	Yes
Event	6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 - Berlin, Germany Duration: 11 Nov 2015 → 13 Nov 2015 Conference number: 6

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9582
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015
Abbreviated title	MACIS 2015
Country/Territory	Germany
City	Berlin
Period	11/11/15 → 13/11/15

Keywords

Convex hull computation over ordered fields
Linear programming over ordered fields
Puiseux series
Rational functions
Tropical convex hull computation

Access to Document

10.1007/978-3-319-32859-1_37

Cite this

Joswig, M., Loho, G., Lorenz, B., & Schröter, B. (2016). Linear programs and convex hulls over fields of puiseux fractions. In I. S. Kotsireas, S. M. Rump, & C. K. Yap (Eds.), Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers (pp. 429-445). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582). Springer. https://doi.org/10.1007/978-3-319-32859-1_37

Joswig, Michael ; Loho, Georg ; Lorenz, Benjamin et al. / Linear programs and convex hulls over fields of puiseux fractions. Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. editor / Ilias S. Kotsireas ; Siegfried M. Rump ; Chee K. Yap. Springer, 2016. pp. 429-445 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Linear programs and convex hulls over fields of puiseux fractions",

abstract = "We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful for computations in tropical geometry.",

keywords = "Convex hull computation over ordered fields, Linear programming over ordered fields, Puiseux series, Rational functions, Tropical convex hull computation",

author = "Michael Joswig and Georg Loho and Benjamin Lorenz and Benjamin Schr{\"o}ter",

year = "2016",

doi = "10.1007/978-3-319-32859-1_37",

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isbn = "9783319328584",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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editor = "Kotsireas, {Ilias S.} and Rump, {Siegfried M.} and Yap, {Chee K.}",

booktitle = "Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers",

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Joswig, M, Loho, G, Lorenz, B & Schröter, B 2016, Linear programs and convex hulls over fields of puiseux fractions. in IS Kotsireas, SM Rump & CK Yap (eds), Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9582, Springer, pp. 429-445, 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, Berlin, Germany, 11/11/15. https://doi.org/10.1007/978-3-319-32859-1_37

Linear programs and convex hulls over fields of puiseux fractions. / Joswig, Michael; Loho, Georg; Lorenz, Benjamin et al.
Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. ed. / Ilias S. Kotsireas; Siegfried M. Rump; Chee K. Yap. Springer, 2016. p. 429-445 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Linear programs and convex hulls over fields of puiseux fractions

AU - Joswig, Michael

AU - Loho, Georg

AU - Lorenz, Benjamin

AU - Schröter, Benjamin

N1 - Conference code: 6

PY - 2016

Y1 - 2016

N2 - We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful for computations in tropical geometry.

AB - We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful for computations in tropical geometry.

KW - Convex hull computation over ordered fields

KW - Linear programming over ordered fields

KW - Puiseux series

KW - Rational functions

KW - Tropical convex hull computation

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DO - 10.1007/978-3-319-32859-1_37

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SN - 9783319328584

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 429

EP - 445

BT - Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers

A2 - Kotsireas, Ilias S.

A2 - Rump, Siegfried M.

A2 - Yap, Chee K.

PB - Springer

T2 - 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015

Y2 - 11 November 2015 through 13 November 2015

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Joswig M, Loho G, Lorenz B, Schröter B. Linear programs and convex hulls over fields of puiseux fractions. In Kotsireas IS, Rump SM, Yap CK, editors, Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Springer. 2016. p. 429-445. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-32859-1_37

Linear programs and convex hulls over fields of puiseux fractions

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