Computing Tropical Curves via Homotopy Continuation

Anders Nedergaard Jensen; Anton Leykin; Josephine Yu

doi:10.1080/10586458.2015.1037407

Computing Tropical Curves via Homotopy Continuation

Anders Nedergaard Jensen, Anton Leykin, Josephine Yu^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

3 Citations (Scopus)

Abstract

Exploiting a connection between amoebas and tropical curves, we devise a method for computing tropical curves using numerical algebraic geometry and give an implementation. As an application, we use this technique to compute Newton polygons of A-polynomials of knots.

Original language	English
Journal	Experimental Mathematics
Volume	25
Issue	1
Pages (from-to)	83-93
Number of pages	11
ISSN	1058-6458
DOIs	https://doi.org/10.1080/10586458.2015.1037407
Publication status	Published - 2016

Keywords

tropical curves
homotopy continuation
numerical algebraic geometry
tropical geometry
SPARSE POLYNOMIAL SYSTEMS
ALGORITHM

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10.1080/10586458.2015.1037407

https://arxiv.org/pdf/1408.3105.pdf

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title = "Computing Tropical Curves via Homotopy Continuation",

abstract = "Exploiting a connection between amoebas and tropical curves, we devise a method for computing tropical curves using numerical algebraic geometry and give an implementation. As an application, we use this technique to compute Newton polygons of A-polynomials of knots.",

keywords = "tropical curves, homotopy continuation, numerical algebraic geometry, tropical geometry, SPARSE POLYNOMIAL SYSTEMS, ALGORITHM",

author = "Jensen, {Anders Nedergaard} and Anton Leykin and Josephine Yu",

year = "2016",

doi = "10.1080/10586458.2015.1037407",

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T1 - Computing Tropical Curves via Homotopy Continuation

AU - Jensen, Anders Nedergaard

AU - Leykin, Anton

AU - Yu, Josephine

PY - 2016

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N2 - Exploiting a connection between amoebas and tropical curves, we devise a method for computing tropical curves using numerical algebraic geometry and give an implementation. As an application, we use this technique to compute Newton polygons of A-polynomials of knots.

AB - Exploiting a connection between amoebas and tropical curves, we devise a method for computing tropical curves using numerical algebraic geometry and give an implementation. As an application, we use this technique to compute Newton polygons of A-polynomials of knots.

KW - tropical curves

KW - homotopy continuation

KW - numerical algebraic geometry

KW - tropical geometry

KW - SPARSE POLYNOMIAL SYSTEMS

KW - ALGORITHM

U2 - 10.1080/10586458.2015.1037407

DO - 10.1080/10586458.2015.1037407

M3 - Journal article

SN - 1058-6458

VL - 25

SP - 83

EP - 93

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 1

ER -

Computing Tropical Curves via Homotopy Continuation

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Keywords

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