68 citations · 110 across the 8 of their papers we have counts for
8 papers
Fast interpolation of sparse multivariate polynomials
Joris van der Hoeven, Grégoire Lecerf
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbi…
A proof of the Brill-Noether method from scratch
Elena Berardini, Alain Couvreur, Grégoire Lecerf
In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being…
Modular SIMD arithmetic in Mathemagix
Joris van der Hoeven, Grégoire Lecerf, Guillaume Quintin
Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes. Although recent microprocessors typically offer a wide range of…
Faster polynomial multiplication over finite fields
David Harvey, Joris van der Hoeven, Grégoire Lecerf
Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n)…
Even faster integer multiplication
David Harvey, Joris van der Hoeven, Grégoire Lecerf
We give a new proof of Fürer's bound for the cost of multiplying n-bit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coeffici…
Degeneracy loci and polynomial equation solving
Bernd Bank, Marc Giusti, Joos Heintz +3
Let V be a smooth equidimensional quasi-affine variety of dimension r over the complex numbers and let be a -matrix of coordinate functions of , where $s…