Improved algorithm for computing separating linear forms for bivariate systems - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2014

Improved algorithm for computing separating linear forms for bivariate systems

Abstract

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 $\sOB(d^7+d^6\tau)$ where $d$ and $\tau$ denote respectively the maximum degree and bitsize of the input (and where $\sO$ refers to the complexity where polylogarithmic factors are omitted and $O_B$ 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. \cite{bouzidiJSC2014a}. This algorithm also yields, for this problem, a probabilistic Las-Vegas algorithm of expected bit complexity $\sOB(d^5+d^4\tau)$.
Fichier principal
Vignette du fichier
separating_element_curve.pdf (230.22 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-00992634 , version 1 (19-05-2014)

Identifiers

Cite

Yacine Bouzidi, Sylvain Lazard, Guillaume Moroz, Marc Pouget, Fabrice Rouillier. Improved algorithm for computing separating linear forms for bivariate systems. ISSAC - 39th International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan. ⟨hal-00992634⟩
330 View
201 Download

Altmetric

Share

Gmail Facebook X LinkedIn More