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Computing tropical bitangents to smooth quartic curves in polymake

2021/12/08 by Alheydis Geiger, Geiger, Alheydis, Marta Panizzut +1
Agricultural and Biological Sciences · Computer Science · #14T15 #14T20 #52B55 #Advanced Data Storage Technologies #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Plant responses to water stress #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2112.04447

openalex publication_date 2021/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we introduce the recently developed polymake extension TropicalQuarticCurves and its associated database entry in polyDB dealing with smooth tropical quartic curves. We report on algorithms implemented to analyze tropical bitangents and their lifting conditions over real closed valued fields. The new functions and data were used by the authors to provide a tropical proof of Plücker and Zeuthen's count of real bitangents to smooth quartic curves.

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