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- Bruno Grenet, Pascal Koiran, Natacha Portier, Yann Strozecki
- FSTTCS
- 2011
Polynomial identity testing and arithmetic circuit lower bounds are two central questions in algebraic complexity theory. It is an intriguing fact that these questions are actually related. One of… (More)
- Bruno Grenet
- 2012
The Permanent versus Determinant problem is the following: Given an n × n matrix X of indeterminates over a field of characteristic different from two, find the smallest matrix M whose coefficients… (More)
- Bruno Grenet, Joris van der Hoeven, Grégoire Lecerf
- ISSAC
- 2015
Consider a finite field Fq whose multiplicative group has smooth cardinality. We study the problem of computing all roots of a polynomial that splits over Fq, which was one of the bottlenecks for… (More)
- Bruno Grenet, Pascal Koiran, Natacha Portier
- MFCS
- 2010
The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable… (More)
We present an algorithm which computes the multilinear factors of bivariate lacunary polynomials. It is based on a new Gap theorem which allows to test whether… (More)
We present a deterministic polynomial-time algorithm which computes the multilinear factors of multivariate lacunary polynomials over number fields. It is based on a new Gap theorem which allows to… (More)
- Bruno Grenet, Pascal Koiran, Natacha Portier
- J. Complexity
- 2013
The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable… (More)
- Bruno Grenet, Joris van der Hoeven, Grégoire Lecerf
- Applicable Algebra in Engineering, Communication…
- 2015
We design new deterministic algorithms, based on Graeffe transforms, to compute all the roots of a polynomial which splits over a finite field $$\mathbb {F}_q$$Fq. Our algorithms were designed to be… (More)
- Bruno Grenet, Erich Kaltofen, Pascal Koiran, Natacha Portier
- ArXiv
- 2011
We deploy algebraic complexity theoretic techniques to construct symmetric determinantal representations of formulas and weakly skew circuits. Our representations produce matrices of much smaller… (More)
- Bruno Grenet
- ISSAC
- 2014
We present a new algorithm for the computation of the irreducible factors of degree at most d, with multiplicity, of multivariate lacunary polynomials over fields of characteristic zero. The… (More)