11 citations · 38 across the 15 of their papers we have counts for
6 papers · 1 filter
Bivariate trinomials over finite fields
Martin Avendano, Jorge Martin-Morales
We study the number of points in the family of plane curves defined by a trinomial \[ \mathcal{C}(α,β)= \{(x,y)\in\mathbb{F}_q^2\,:\,αx^{a_{11}}y^{a_{12}}+βx^{a_{21}}y^{a_{22}}=x^{…
Faster p-adic Feasibility for Certain Multivariate Sparse Polynomials
Martín Avendaño, Ashraf Ibrahim, J. Maurice Rojas +1
We present algorithms revealing new families of polynomials allowing sub-exponential detection of p-adic rational roots, relative to the sparse encoding. For instance, we show that…
Sharp bounds for the number of roots of univariate fewnomials
Martin Avendano, Teresa Krick
Let K be a field and t>=0. Denote by Bm(t,K) the maximum number of non-zero roots in K, counted with multiplicities, of a non-zero polynomial in K[x] with at most t+1 monomial term…
Near NP-Completeness for Detecting p-adic Rational Roots in One Variable
Martin Avendano, Ashraf Ibrahim, J. Maurice Rojas +1
We show that deciding whether a sparse univariate polynomial has a p-adic rational root can be done in NP for most inputs. We also prove a polynomial-time upper bound for trinomial…
Factoring bivariate sparse (lacunary) polynomials
Martin Avendano, Teresa Krick, Martin Sombra
We present a deterministic algorithm for computing all irreducible factors of degree of a given bivariate polynomial over an algebraic number field and th…
Newton-Hensel Interpolation Lifting
Martin Avendaño, Teresa Krick, Ariel Pacetti
The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in from information modulo…