Bit-size estimates for triangular sets in positive dimension

2010/08/20 by Xavier Dahan, Dahan, Xavier, Abdulilah Kadri +3 · 2 citations
Computer Science · #FOS: Computer and information sciences #Symbolic Computation (cs.SC) #cs.SC

paper · pdf · doi:10.48550/arxiv.1008.3459

37 pages

arxiv created 2010/08/20 · arxiv updated 2010/11/24

Abstract

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 inter- polation 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.

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