Polynomial equation solving by lifting procedures for ramified fibers
- 作者：Bompadre ; A. ; Matera ; G. ; Wachenchauzer ; R. ; Waissbein ; A.
- 关键词：Efficient polynomial equation solving ; Ramified fibers of dominant mappings ; Puiseux expansions of space curves ; Newton&ndash ; Hensel lifting
- 刊名：Theoretical Computer Science
- 出版年：2004
- 期刊代码：114_03043975
- 类别：cp
- 出版时间：May 6, 2004
- 卷：315
- 期：2-3
- 页码：335-369
- 文件大小：489 K
摘要
Let be given a parametric polynomial equation system which represents a generically unramified family of zero-dimensional algebraic varieties. We exhibit an efficient algorithm which computes a complete description of the solution set of an arbitrary parameter instance from a complete description of the infinitesimal structure of a particular ramified parameter instance of our family. This generalizes in the case of space curves previous methods of Heintz et al. and Schost, which require the given parameter instance to be unramified. We illustrate our method solving particular polynomial equation systems by deformation techniques.