Algebraic osculation and factorization of sparse polynomials
| dc.creator | Weimann, Martin | |
| dc.date | 2009-04-01 | |
| dc.date | 2009-04-14 | |
| dc.date.accessioned | 2026-07-07T13:03:14Z | |
| dc.date.available | 2026-07-07T13:03:14Z | |
| dc.description | 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. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0904.0178 | |
| dc.identifier | http://arxiv.org/abs/0904.0178 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226724 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14Q05 | |
| dc.title | Algebraic osculation and factorization of sparse polynomials | |
| dc.type | text |