2016/06/17 by Nathan Bliss, Bliss, Nathan, Jan Verschelde +1
Computer Science · #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Polynomial and algebraic computation #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.1606.05563
openalex publication_date 2016/06/17 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
A polyhedral method to solve a system of polynomial equations exploits its\nsparse structure via the Newton polytopes of the polynomials. We propose a\nhybrid symbolic-numeric method to compute a Puiseux series expansion for every\nspace curve that is a solution of a polynomial system. The focus of this paper\nconcerns the difficult case when the leading powers of the Puiseux series of\nthe space curve are contained in the relative interior of a higher dimensional\ncone of the tropical prevariety. We show that this difficult case does not\noccur for polynomials with generic coefficients. To resolve this case, we\npropose to apply polyhedral end games to recover tropisms hidden in the\ntropical prevariety.\n