Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4608947 | Journal of Complexity | 2012 | 27 Pages |
Abstract
We give bit-size estimates for the coefficients appearing in triangular sets describing positive-dimensional algebraic sets defined over QQ. These estimates are worst case upper bounds; they depend only on the degree and height of the underlying algebraic sets. We illustrate the use of these results in the context of a modular algorithm.This extends the results by the first and the last author, which were confined to the case of dimension 0. Our strategy is to get back to dimension 0 by evaluation and interpolation techniques. Even though the main tool (height theory) remains the same, new difficulties arise to control the growth of the coefficients during the interpolation process.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xavier Dahan, Abdulilah Kadri, Éric Schost,