Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Lopsided approximation of amoebas


Authors: Jens Forsgård, Laura Felicia Matusevich, Nathan Mehlhop and Timo de Wolff
Journal: Math. Comp. 88 (2019), 485-500
MSC (2010): Primary 13P15, 14Q20, 14T05; Secondary 90C59, 90C90
DOI: https://doi.org/10.1090/mcom/3323
Published electronically: April 18, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The amoeba of a Laurent polynomial is the image of the corresponding hypersurface under the coordinatewise log absolute value map. In this article, we demonstrate that a theoretical amoeba approximation method due to Purbhoo can be used efficiently in practice. To do this, we resolve the main bottleneck in Purbhoo's method by exploiting relations between cyclic resultants. We use the same approach to give an approximation of the Log preimage of the amoeba of a Laurent polynomial using semi-algebraic sets. We also provide a SINGULAR/SAGE implementation of these algorithms, which shows a significant speedup when our specialized cyclic resultant computation is used, versus a general purpose resultant algorithm.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 13P15, 14Q20, 14T05, 90C59, 90C90

Retrieve articles in all journals with MSC (2010): 13P15, 14Q20, 14T05, 90C59, 90C90


Additional Information

Jens Forsgård
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: jensf@math.tamu.edu

Laura Felicia Matusevich
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: laura@math.tamu.edu

Nathan Mehlhop
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: mehl144@tamu.edu

Timo de Wolff
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Address at time of publication: Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
Email: dewolff@math.tamu.edu

DOI: https://doi.org/10.1090/mcom/3323
Keywords: Amoeba, amoeba computation, cyclic resultant, lopsided amoeba, resultant, Sage, SINGULAR
Received by editor(s): April 28, 2017
Received by editor(s) in revised form: August 10, 2017
Published electronically: April 18, 2018
Additional Notes: The second author was partially supported by NSF Grant DMS 1500832.
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society