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TitleComputing tropical varieties
Author(s) T. Bogart, Anders N. Jensen, D. Speyer, Bernd Sturmfels, Rekha R. Thomas
TypeArticle in Journal
AbstractThe 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.
KeywordsTropical geometry, Tropical variety, Tropical basis, Gröbner fan, Bergman fan
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717106000642
LanguageEnglish
JournalJournal of Symbolic Computation
Volume42
Number12
Pages54 - 73
Year2007
NoteEffective Methods in Algebraic Geometry (MEGA 2005)
Edition0
Translation No
Refereed No
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