Number of common roots and resultant of two tropical univariate polynomials

2016/08/08 by Hoon Hong, Hong, Hoon, J. Rafael Sendra +1
Computer Science · Mathematics · #12K10 #15A15 #15A80 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1608.02394

openalex publication_date 2016/08/08 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28

Abstract

It is well known that for two univariate polynomials over complex number field the number of their common roots is equal to the order of their resultant. In this paper, we show that this fundamental relationship still holds for the tropical polynomials under suitable adaptation of the notion of order, if the roots are simple and non-zero.

Citations

• Tropical Geometry and its applications

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