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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)

- MARTIN WEIMANN
- 2009

We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of C 2 and D an effective divisor with support ∂X = X \ C 2. Our main result gives explicit conditions equivalent to that a given Cartier divisor on the subscheme (|D|, O D) extends to X. These… (More)

- Victor C. Li, Michael Lepech, Shuxin Wang, Martin Weimann, Gregory Keoleian
- 2004

Over the last decade, enormous strides have been made in creating engineered cementitious composites (ECC) with extreme tensile ductility, on the order of several hundred times that of normal concrete or fiber reinforced concrete (FRC). Current ECC investigations include load carrying structural members in new infrastructure systems, as well as for repair… (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)

- G. Chèze, M. Elkadi, A. Galligo, M. Weimann
- ACCA
- 2009

We describe an efficient algorithm and an implementation for computing an absolute factorization of a bivariate polynomial with a given bidegree. Results of experimentation and an illustrative example are provided. This algorithm is a generalization of the previous one by Rupprecht-Galligo-Chèze which works after a generic change of coordinates. It… (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)

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