Given two coprime polynomials P and Q in Z [x, y] of degree bounded by d and bitsize
bounded by τ, we address the problem of solving the system {P, Q}. We are interested in …

Given two coprime polynomials $ P $ and $ Q $ in $\Z [x, y] $ of degree bounded by $ d $
and bitsize bounded by $\tau $, we address the problem of solving the system $\{P, Q\} …

We address the problem of solving systems of two bivariate polynomials of total degree at
most d with integer coefficients of maximum bitsize τ We suppose known a linear separating …

We address the problem of solving systems of bivariate polynomials with integer coefficients.
We first present an algorithm for computing a separating linear form of such systems, that is …

This paper is devoted to the {\it resolution} of zero-dimensional systems in $ K [X_1,\ldots
X_n] $, where $ K $ is a field of characteristic zero (or strictly positive under some …

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 …

We present an algorithm for computing a separating linear form of a system of bivariate
polynomials with integer coefficients, that is a linear combination of the variables that takes …

On the complexity of solving bivariate systems Page 1 On the Complexity of Solving Bivariate
Systems: The Case of Non-singular Solutions Romain Lebreton LIRMM, UMR 5506 CNRS …

Given a set of multivariate polynomials $\{f\sb1,\..., f\sb {k}\}\subset {\rm l\! k}\lbrack x\sb1,\...,
x\sb {n}\rbrack, $ consider the algebraic set $ V=\{x\in {\bf K}\sp {n}\vert f\sb1 (x)=\...= f\sb …

This paper presents a lecture on existing algorithms for solving polynomial systems with
their complexity analysis from our experiments on the subject. It is based on our studies of …