Tropical bases by regular projections
Kerstin Hept, Thorsten Theobald · Proceedings of the American Mathematical Society · 2009
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.