Computing Tropical Varieties

D. Speyer; Anders Nedergaard Jensen; T. Bogart; B. Sturmfels; R. Thomas

Computing Tropical Varieties

D. Speyer
, Anders Nedergaard Jensen
, T. Bogart
, B. Sturmfels
, R. Thomas

Publikation: Working paper/Preprint › Working paper › Forskning

Abstract

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.

Originalsprog	Engelsk
Antal sider	21
Status	Udgivet - 2005

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T1 - Computing Tropical Varieties

AU - Speyer, D.

AU - Jensen, Anders Nedergaard

AU - Bogart, T.

AU - Sturmfels, B.

AU - Thomas, R.

PY - 2005

Y1 - 2005

N2 - 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.

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M3 - Working paper

BT - Computing Tropical Varieties

ER -

Computing Tropical Varieties

Abstract

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