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Algebraic Osculation and Application to Factorization of Sparse Polynomials

Abstract : We prove a theorem on algebraic osculation and apply our result to the computer algebra problem of polynomial factorization. We consider X a smooth completion of the complex plane C^2 and D an effective divisor with support the boundary ∂X = X \ C^2. Our main result gives explicit conditions that are necessary and sufficient for a given Cartier divisor on the subscheme (|D|, O_D) to extend to X. These osculation criterions are expressed with residues. When applied to the toric setting, our result gives rise to a new algorithm for factoring sparse bivariate polynomials which takes into account the geometry of the Newton polytope.
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Submitted on : Wednesday, May 22, 2019 - 9:45:04 PM
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Martin Weimann. Algebraic Osculation and Application to Factorization of Sparse Polynomials. Foundations of Computational Mathematics, Springer Verlag, 2012, 12 (2), pp.173-201. ⟨10.1007/s10208-012-9114-z⟩. ⟨hal-02137318⟩



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