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Computing tropical varieties. (English) Zbl 1121.14051
Summary: The tropical variety of a \(d\)-dimensional prime ideal in a polynomial ring with complex coefficients is a pure \(d\)-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 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.

MSC:
14Q99 Computational aspects in algebraic geometry
14P99 Real algebraic and real-analytic geometry
68W30 Symbolic computation and algebraic computation
Software:
cdd; Gfan; gmp
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References:
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