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The degree of a tropical basis


Authors: Michael Joswig and Benjamin Schröter
Journal: Proc. Amer. Math. Soc. 146 (2018), 961-970
MSC (2010): Primary 13P10, 14T05
DOI: https://doi.org/10.1090/proc/13787
Published electronically: October 5, 2017
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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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Michael Joswig
Affiliation: Institut für Mathematik, TU Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
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

DOI: https://doi.org/10.1090/proc/13787
Keywords: Universal Gr\"obner bases, $f$-vectors of tropical varieties
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
Article copyright: © Copyright 2017 American Mathematical Society

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