Martin Weimann

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We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton poly-tope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm of Lecerf, with now a polynomial complexity in the volume of the Newton polytope. We adopt a geometrical point of(More)
— We extend the usual projective Abel-Radon transform to the larger context of a smooth complete toric variety X. We define and study toric E-concavity attached to a split vector bundle on X. Then we obtain a multidimensional residual representation of the toric Abel-transform and we prove a toric version of the classical Abel-inverse theorem. Résumé. —(More)
We relate factorization of bivariate polynomials to singularities of projective plane curves. We prove that adjoint polynomials of a polynomial F ∈ k[x, y] with coefficients in a field k permit to recombinations of the factors of F (0, y) induced by both the absolute and rational factorizations of F , and so without using Hensel lifting. We show in such a(More)
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