A softly optimal Monte Carlo algorithm for solving bivariate polynomial systems over the integers
| dc.contributor.author | Schost, Eric | |
| dc.contributor.author | Mehrabi, Esmaeil | |
| dc.date.accessioned | 2023-03-21T19:07:10Z | |
| dc.date.available | 2023-03-21T19:07:10Z | |
| dc.date.issued | 2016-06 | |
| dc.description.abstract | We give an algorithm for the symbolic solution of polynomial systems in Z[X,Y]. Following previous work with Lebreton, we use a combination of lifting and modular composition techniques, relying in particular on Kedlaya and Umans’ recent quasi-linear time modular composition algorithm. The main contribution in this paper is an adaptation of a deflation algorithm of Lecerf, that allows us to treat singular solutions for essentially the same cost as the regular ones. Altogether, for an input system with degree d and coefficients of bit-size h, we obtain Monte Carlo algorithms that achieve probability of success at least 1-1/2^P, with running time d^{2+e} O~(d^2+dh+dP+P^2) bit operations, for any e>0, where the O~ notation indicates that we omit polylogarithmic factors | en |
| dc.identifier.uri | https://doi.org/10.1016/j.jco.2015.11.009 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19221 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartofseries | Journal of Complexity; | |
| dc.subject | bivariate system | en |
| dc.subject | complexity | en |
| dc.subject | algorithm | en |
| dc.title | A softly optimal Monte Carlo algorithm for solving bivariate polynomial systems over the integers | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Mehrabi, E., & Schost, É. (2016). A softly optimal Monte Carlo Algorithm for solving bivariate polynomial systems over the integers. Journal of Complexity, 34, 78–128. https://doi.org/10.1016/j.jco.2015.11.009 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | David R. Cheriton School of Computer Science | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |