Bit-size estimates for triangular sets in positive dimension

We give bit-size estimates for the coefficients appearing in triangular sets describing positive-dimensional algebraic sets defined over Q. 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 results by the first and 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.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Xavier Dahan, Abdulilah Kadri, Éric Schost
• Keywords: Algebraic Sets, Bit-size Estimates, CORR 2010, Education, Positive-dimensional Algebraic Sets