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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The degree of a tropical basis
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by Michael Joswig and Benjamin Schröter PDF
Proc. Amer. Math. Soc. 146 (2018), 961-970 Request permission

Abstract:

We give an explicit upper bound for the degree of a tropical basis of a homogeneous polynomial ideal. As an application $f$-vectors of tropical varieties are discussed. Various examples illustrate differences between Gröbner and tropical bases.
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Additional Information
  • Michael Joswig
  • Affiliation: Institut für Mathematik, TU Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
  • ORCID: 0000-0002-4974-9659
  • Email: joswig@math.tu-berlin.de
  • Benjamin Schröter
  • Affiliation: Institut für Mathematik, TU Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
  • Email: schroeter@math.tu-berlin.de
  • Received by editor(s): December 1, 2015
  • Received by editor(s) in revised form: April 19, 2017
  • Published electronically: October 5, 2017
  • Additional Notes: Research by the authors was carried out in the framework of Matheon supported by Einstein Foundation Berlin. Further support by Deutsche Forschungsgemeinschaft (SFB-TRR 109: “Discretization in Geometry and Dynamics” and SFB-TRR 195: “Symbolic Tools in Mathematics and their Application”) is gratefully acknowledged
  • Communicated by: Irena Peeva
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 961-970
  • MSC (2010): Primary 13P10, 14T05
  • DOI: https://doi.org/10.1090/proc/13787
  • MathSciNet review: 3750210