Tropical bases by regular projections

Authors:
Kerstin Hept and Thorsten Theobald

Journal:
Proc. Amer. Math. Soc. **137** (2009), 2233-2241

MSC (2000):
Primary 13P10, 14Q99

DOI:
https://doi.org/10.1090/S0002-9939-09-09843-8

Published electronically:
February 18, 2009

MathSciNet review:
2495256

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the tropical variety of a prime ideal generated by the polynomials and revisit the regular projection technique introduced by Bieri and Groves from a computational point of view. In particular, we show that has a short tropical basis of cardinality at most at the price of increased degrees, and we provide a computational description of these bases.

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Additional Information

**Kerstin Hept**

Affiliation:
FB 12 – Institut für Mathematik, J.W. Goethe-Universität, Postfach 111932, D-60054 Frankfurt am Main, Germany

Email:
hept@math.uni-frankfurt.de

**Thorsten Theobald**

Affiliation:
FB 12 – Institut für Mathematik, J.W. Goethe-Universität, Postfach 111932, D-60054 Frankfurt am Main, Germany

Email:
theobald@math.uni-frankfurt.de

DOI:
https://doi.org/10.1090/S0002-9939-09-09843-8

Keywords:
Tropical geometry,
tropical variety,
tropical basis,
Bieri-Groves Theorem.

Received by editor(s):
September 21, 2007

Received by editor(s) in revised form:
September 29, 2008

Published electronically:
February 18, 2009

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2009
American Mathematical Society