Search Results - "Éric Schost"

An m-adic algorithm for bivariate Gröbner bases by Schost, Éric, St-Pierre, Catherine

“…Let A be a domain, with m⊆A a maximal ideal, and let F⊆A[x,y] be any finite generating set of an ideal with finitely many roots (in an algebraic closure of the…”
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Newton iteration for lexicographic Gröbner bases in two variables by Schost, Éric, St-Pierre, Catherine

“…We present an m-adic Newton iteration with quadratic convergence for lexicographic Gröbner basis of zero dimensional ideals in two variables. We rely on a…”
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Bit complexity for computing one point in each connected component of a smooth real algebraic set by Elliott, Jesse, Giesbrecht, Mark, Schost, Éric

“…We analyze the bit complexity of an algorithm for the computation of at least one point in each connected component of a smooth real algebraic set. This work…”
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On the evaluation of some sparse polynomials by Dorian Nogneng, Éric Schost

“…for various choices of coefficients p_i. First, we take p_i=p^i, for some fixed p; in this case, we address the question of fast evaluation at a given point in…”
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Drinfeld modules with complex multiplication, Hasse invariants and factoring polynomials over finite fields by Doliskani, Javad, Narayanan, Anand Kumar, Schost, Éric

“…We present a novel randomized algorithm to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex…”
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Genus 2 point counting over prime fields by Gaudry, Pierrick, Schost, Éric

“…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…”
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Computing roadmaps in unbounded smooth real algebraic sets I: Connectivity results by Prébet, Rémi, Safey El Din, Mohab, Schost, Éric

“…Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g…”
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Subquadratic-Time Algorithms for Normal Bases by Giesbrecht, Mark, Jamshidpey, Armin, Schost, Éric

“…For any finite Galois field extension K/F, with Galois group G = Gal (K/F), there exists an element α ∈ K whose orbit G · α forms an F-basis of K. Such an α is…”
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A softly optimal Monte Carlo algorithm for solving bivariate polynomial systems over the integers by Mehrabi, Esmaeil, Schost, Éric

“…We give an algorithm for the symbolic solution of polynomial systems in Z[X,Y]. Following previous work with Lebreton, we use a combination of lifting and…”
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Computing minimal interpolation bases by Jeannerod, Claude-Pierre, Neiger, Vincent, Schost, Éric, Villard, Gilles

“…We consider the problem of computing univariate polynomial matrices over a field that represent minimal solution bases for a general interpolation problem,…”
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A Quadratically Convergent Algorithm for Structured Low-Rank Approximation by Schost, Éric, Spaenlehauer, Pierre-Jean

“…Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix M…”
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Homotopy techniques for solving sparse column support determinantal polynomial systems by Labahn, George, Safey El Din, Mohab, Schost, Éric, Vu, Thi Xuan

“…Let K be a field of characteristic zero with K¯ its algebraic closure. Given a sequence of polynomials g=(g1,…,gs)∈K[x1,…,xn]s and a polynomial matrix…”
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Taking roots over high extensions of finite fields by DOLISKANI, JAVAD, SCHOST, ÉRIC

“…We present a new algorithm for computing m \mathbb{F}_q, with p any positive integer. In the particular case m=2 O(\mathsf {M}(n)\log (p) + \mathsf {C}(n)\log…”
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Computing critical points for invariant algebraic systems by Faugère, Jean-Charles, Labahn, George, Safey El Din, Mohab, Schost, Éric, Vu, Thi Xuan

“…Let K be a field and (f1,…,fs,ϕ) be multivariate polynomials in K[x1,…,xn] (with s<n) each invariant under the action of Sn, the group of permutations of…”
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On the complexity of computing with zero-dimensional triangular sets by Poteaux, Adrien, Schost, Éric

“…We study the complexity of some fundamental operations for triangular sets in dimension zero. Using Las Vegas algorithms, we prove that one can perform such…”
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Solving determinantal systems using homotopy techniques by Hauenstein, Jon D., Safey El Din, Mohab, Schost, Éric, Vu, Thi Xuan

“…Let K be a field of characteristic zero and let K‾ be an algebraic closure of K. Consider a sequence of polynomials G=(g1,…,gs) in K[X1,…,Xn] with s<n, a…”
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On semiring complexity of Schur polynomials by Fomin, Sergey, Grigoriev, Dima, Nogneng, Dorian, Schost, Éric

“…Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring…”
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A simple and fast online power series multiplication and its analysis by Lebreton, Romain, Schost, Éric

“…This paper focuses on online (or relaxed) algorithms for the multiplication of power series over a field and their complexity analysis. We propose a new online…”
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Interpolation of polynomials given by straight-line programs by Garg, Sanchit, Schost, Éric

“…We give an algorithm for the interpolation of a polynomial A given by a straight-line program. Its complexity is polynomial in τ , log ( d ) , L , n , where τ…”
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Modular Composition Modulo Triangular Sets and Applications by Poteaux, Adrien, Schost, Éric

“…We generalize Kedlaya and Umans’ modular composition algorithm to the multivariate case. As a main application, we give fast algorithms for many operations…”
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