Skip to Main content Skip to Navigation
Journal articles

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.
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download

https://hal-normandie-univ.archives-ouvertes.fr/hal-02137318
Contributor : Martin Weimann <>
Submitted on : Wednesday, May 22, 2019 - 9:45:04 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM

File

Osculation.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

53

Files downloads

121