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- Mohab Safey El Din, Éric Schost
- ISSAC
- 2003

Let f<inf>1</inf>, ldots, f<inf>s</inf> be polynomials in <b>Q</b>[X<inf>1</inf>, ..., X<inf>n</inf>] that generate a radical ideal and let V be their complex zero-set. Suppose that V is smooth and… (More)

- Éric Schost
- Applicable Algebra in Engineering, Communication…
- 2003

Abstract Given a polynomial system of n equations in n unknowns that depends on some parameters, we define the notion of parametric geometric resolution as a means to represent some generic solutions… (More)

- Xavier Dahan, Éric Schost
- ISSAC
- 2004

We study the triangular representation of zero-dimensional varieties defined over the rational field (resp. a rational function field). We prove polynomial bounds in terms of intrinsic quantities for… (More)

- Sanchit Garg, Éric Schost
- Theor. Comput. Sci.
- 2009

We give an algorithm for the interpolation of a polynomial A given by a straight-line program. Its complexity is polynomial in @t,log(d),L,n, where @t is an input bound on the number of terms in A, d… (More)

- Xavier Dahan, Marc Moreno Maza, Éric Schost, Wenyuan Wu, Yuzhen Xie
- ISSAC
- 2005

We present lifting techniques for triangular decompositions of zero-dimensional varieties, that extend the range of the previous methods. We discuss complexity aspects, and report on a preliminary… (More)

- Pierrick Gaudry, Éric Schost
- J. Symb. Comput.
- 2012

For counting points of Jacobians of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof's genus 1 algorithm. We propose various practical… (More)

- Xin Li, Marc Moreno Maza, Éric Schost
- J. Symb. Comput.
- 2009

We study arithmetic operations for triangular families of polynomials, concentrating on multiplication in dimension zero. By a suitable extension of fast univariate Euclidean division, we obtain… (More)

- Alin Bostan, Éric Schost
- J. Complexity
- 2005

We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric… (More)

- Alin Bostan, Grégoire Lecerf, Éric Schost
- ISSAC
- 2003

The transposition principle, also called Tellegen's principle, is a set of transformation rules for linear programs. Yet, though well known, it is not used systematically, and few practical… (More)

- Pierrick Gaudry, Éric Schost
- ANTS
- 2004

We present an algorithm based on the birthday paradox, which is a low-memory parallel counterpart to the algorithm of Matsuo, Chao and Tsujii. This algorithm computes the group order of the Jacobian… (More)