34 citations · 45 across the 3 of their papers we have counts for
3 papers
math.AG2013★ 2 cited
Unconstraint global polynomial optimization via Gradient Ideal
Marta Abril Bucero, Bernard Mourrain, Philippe Trebuchet
In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming tha…
cs.SC2008★ 34 cited
Stable normal forms for polynomial system solving
Bernard Mourrain, Philippe Trébuchet
This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal . The criterion used in the computation involves specific commutation polynomia…
cs.SC2006★ 9 cited
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry
Mohab Safey El Din, Philippe Trebuchet
Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebr…