Lopsided approximation of amoebas
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- by Jens Forsgård, Laura Felicia Matusevich, Nathan Mehlhop and Timo de Wolff HTML | PDF
- Math. Comp. 88 (2019), 485-500 Request permission
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
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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
- MR Author ID: 632562
- 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
- MR Author ID: 1019872
- Email: dewolff@math.tamu.edu
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 485-500
- MSC (2010): Primary 13P15, 14Q20, 14T05; Secondary 90C59, 90C90
- DOI: https://doi.org/10.1090/mcom/3323
- MathSciNet review: 3854068