Computing Tropical Varieties
arXiv:math/0507563 · doi:10.1016/j.jsc.2006.02.004
Abstract
The tropical variety of a -dimensional prime ideal in a polynomial ring with complex coefficients is a pure -dimensional polyhedral fan. This fan is shown to be connected in codimension one. We present algorithmic tools for computing the tropical variety, and we discuss our implementation of these tools in the Gröbner fan software \texttt{Gfan}. Every ideal is shown to have a finite tropical basis, and a sharp lower bound is given for the size of a tropical basis for an ideal of linear forms.
22 pages, 2 figures
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Cited by in corpus (52)
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