International audienceWe 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 ...
The evaluation of several polynomial forms is considered. New algorithms for the evaluation of a pol...
International audienceWe present algorithmic, complexity and implementation results for the problem ...
International audienceLet A, B ∈ K[X, Y ] be two bivariate polynomials over an effective field K, an...
International audienceWe address the problem of computing a linear separating form of a system of tw...
International audienceWe address the problem of solving systems of bivariate polynomials with intege...
International audienceWe address the problem of solving systems of bivariate polynomials with intege...
Given two coprime polynomials $P$ and $Q$ in $\Z[x,y]$ of degree bounded by $d$ and bitsize bounded ...
Given two coprime polynomials $P$ and $Q$ in $\Z[x,y]$ of degree bounded by $d$ and bitsize bounded ...
International audienceGiven two coprime polynomials $P$ and $Q$ in $\Z[x,y]$ of degree bounded by $...
International audienceWe address the problem of solving systems of two bivariate polynomials of tota...
International audienceWe bound the Boolean complexity of computing isolating hyperboxes for all comp...
Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we pr...
International audienceWe bound the Boolean complexity of computing isolating hyperboxes for all comp...
AbstractThis paper is concerned with exact real solving of well-constrained, bivariate polynomial sy...
Special Issue of the Journal of Symbolic Computation on Milestones in Computer Algebra (MICA 2016)In...
The evaluation of several polynomial forms is considered. New algorithms for the evaluation of a pol...
International audienceWe present algorithmic, complexity and implementation results for the problem ...
International audienceLet A, B ∈ K[X, Y ] be two bivariate polynomials over an effective field K, an...
International audienceWe address the problem of computing a linear separating form of a system of tw...
International audienceWe address the problem of solving systems of bivariate polynomials with intege...
International audienceWe address the problem of solving systems of bivariate polynomials with intege...
Given two coprime polynomials $P$ and $Q$ in $\Z[x,y]$ of degree bounded by $d$ and bitsize bounded ...
Given two coprime polynomials $P$ and $Q$ in $\Z[x,y]$ of degree bounded by $d$ and bitsize bounded ...
International audienceGiven two coprime polynomials $P$ and $Q$ in $\Z[x,y]$ of degree bounded by $...
International audienceWe address the problem of solving systems of two bivariate polynomials of tota...
International audienceWe bound the Boolean complexity of computing isolating hyperboxes for all comp...
Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we pr...
International audienceWe bound the Boolean complexity of computing isolating hyperboxes for all comp...
AbstractThis paper is concerned with exact real solving of well-constrained, bivariate polynomial sy...
Special Issue of the Journal of Symbolic Computation on Milestones in Computer Algebra (MICA 2016)In...
The evaluation of several polynomial forms is considered. New algorithms for the evaluation of a pol...
International audienceWe present algorithmic, complexity and implementation results for the problem ...
International audienceLet A, B ∈ K[X, Y ] be two bivariate polynomials over an effective field K, an...