2014/05/19 by Yacine Bouzidi, Sylvain Lazard, Bouzidi, Yacine +7
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Formal Methods in Verification #Numerical Methods and Algorithms #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.CG #cs.SC
paper · pdf · doi:10.48550/arxiv.1405.4740
ISSAC - 39th International Symposium on Symbolic and Algebraic Computation (2014)
arxiv created 2014/05/19 · openalex publication_date 2014/05/19 · arxiv updated 2014/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the problem of computing a linear separating form of a system of two bivariate polynomials with integer coefficients, that is a linear combination of the variables that takes different values when evaluated at the distinct solutions of the system. The computation of such linear forms is at the core of most algorithms that solve algebraic systems by computing rational parameterizations of the solutions and this is the bottleneck of these algorithms in terms of worst-case bit complexity. We present for this problem a new algorithm of worst-case bit complexity \sOB(d7+d6τ) where d and τ denote respectively the maximum degree and bitsize of the input (and where \sO refers to the complexity where polylogarithmic factors are omitted and OB refers to the bit complexity). This algorithm simplifies and decreases by a factor d the worst-case bit complexity presented for this problem by Bouzidi et al. \citebouzidiJSC2014a. This algorithm also yields, for this problem, a probabilistic Las-Vegas algorithm of expected bit complexity \sOB(d5+d4τ).