Martin Weimann
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View article: Improvements of convex-dense factorization of bivariate polynomials
Improvements of convex-dense factorization of bivariate polynomials Open
We develop a new algorithm for factoring a bivariate polynomial $F\in \mathbb{K}[x,y]$ which takes fully advantage of the geometry of the Newton polygon of $F$. Under a non degeneracy hypothesis, the complexity is $\tilde{\mathcal{O}}(Vr_0…
View article: Fast computation of integral bases
Fast computation of integral bases Open
We obtain new complexity bounds for computing a triangular integral basis of a number field or a function field. We reach for function fields a softly linear cost with respect to the size of the output when the residual characteristic is z…
View article: Polynomial factorization over henselian fields
Polynomial factorization over henselian fields Open
Given a valued field $(K,v)$ and an irreducible polynomial $g\in K[x]$, we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaquié and Herrera-Olalla-Mahboub-Spivakovsky, leading (under certain conditions) to an algorithm to find the fact…
View article: Local polynomial factorisation:improving the Montes algorithm
Local polynomial factorisation:improving the Montes algorithm Open
We improve significantly the Nart-Montes algorithm for factoring polynomials over a complete discrete valuation ring A. Our first contribution is to extend the Hensel lemma in the context of generalised Newton polygons, from which we deriv…
View article: Evaluating Nanobiomaterial induced DNA strand breaks using the alkaline Comet Assay
Evaluating Nanobiomaterial induced DNA strand breaks using the alkaline Comet Assay Open
Due to their unique chemical and physical properties, nanobiomaterials (NBM’s) are extensively studied for applications in medicine and drug delivery. Despite these exciting properties, their small sizes also make them susceptible to toxic…
View article: A quasi-linear irreducibility test in K[[x]][y]
A quasi-linear irreducibility test in K[[x]][y] Open
We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the discriminant valuation, assuming the input polynomial F square-free and K a perfect field of characteristic zero or greater than d…
View article: Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]
Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y] Open
We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the valuation of the discriminant, assuming the input polynomial F square-free and K a perfect field of characteristic zero or greater…
View article: Plane curves with minimal discriminant
Plane curves with minimal discriminant Open
We give lower bounds for the degree of the discriminant with respect to $y$ of squarefree polynomials $f\in \mathbb {K}[x,y]$ over an algebraically closed field of characteristic zero. Depending on the invariants involved in the lower boun…
View article: Plane curves with minimal discriminant
Plane curves with minimal discriminant Open
We give lower bounds for the degree of the discriminant with respect to y of separable polynomials f in K[x,y] over an algebraically closed field of characteristic zero. Depending on the invariants involved in the lower bound, we give a ge…