Tropical bases by regular projections

Hept, Kerstin; Theobald, Thorsten

doi:10.1090/S0002-9939-09-09843-8

Tropical bases by regular projections
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by Kerstin Hept and Thorsten Theobald

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

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

Published electronically: February 18, 2009

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Abstract:

We consider the tropical variety $\mathcal {T}(I)$ of a prime ideal $I$ generated by the polynomials $f_1, \ldots , f_r$ and revisit the regular projection technique introduced by Bieri and Groves from a computational point of view. In particular, we show that $I$ has a short tropical basis of cardinality at most $r+ \textrm {codim} I+1$ at the price of increased degrees, and we provide a computational description of these bases.

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