Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Grigoriev, Dima; Podolskii, Vladimir V. License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-49286


Tropical Effective Primary and Dual Nullstellens"atze



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

  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 =		{},
  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
Seminar: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue date: 2015
Date of publication: 26.02.2015

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