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arXiv · 0904.0178

Algebraic osculation and factorization of sparse polynomials

Martin Weimann
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Abstract

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 the complex plane and D an effective divisor supported on the boundary of X. Our main result gives explicit conditions equivalent to that a given Cartier divisor on D extends to X. These osculation criterions are expressed with residues. We derive from this result a toric Hensel lifting which permits to compute the absolute factorization of a bivariate polynomial by taking in account the geometry of its Newton polytope. In particular, we reduce the number of possible recombinations when compared to the Galligo-Rupprecht algorithm.

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Martin Weimann. 2009-04-14. Algebraic osculation and factorization of sparse polynomials. https://arxiv.org/abs/0904.0178

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