License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2015.379
URN: urn:nbn:de:0030-drops-49286
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/4928/
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Grigoriev, Dima ; Podolskii, Vladimir V.

Tropical Effective Primary and Dual Nullstellens"atze

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Abstract

Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties and algebraic curves from the computational point of view. This makes it important to study both mathematical and computational aspects of tropical polynomials.

In this paper we prove tropical Nullstellensatz and moreover we show effective formulation of this theorem. Nullstellensatz is a next natural step in building algebraic theory of tropical polynomials and
effective version is relevant for computational aspects of this field.

BibTeX - Entry

@InProceedings{grigoriev_et_al:LIPIcs:2015:4928,
  author =	{Dima Grigoriev and Vladimir V. Podolskii},
  title =	{{Tropical Effective Primary and Dual Nullstellens"atze}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{379--391},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4928},
  URN =		{urn:nbn:de:0030-drops-49286},
  doi =		{10.4230/LIPIcs.STACS.2015.379},
  annote =	{Keywords: tropical algebra, tropical geometry, Nullstellensatz}
}

Keywords: tropical algebra, tropical geometry, Nullstellensatz
Collection: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue Date: 2015
Date of publication: 26.02.2015

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