Bit-size estimates for triangular sets in positive dimension

Xavier Dahan, Abdulilah Kadri, Eric Schost

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)109-135
Number of pages27
JournalJournal of Complexity
Volume28
Issue number1
DOIs
Publication statusPublished - 2012 Feb

Keywords

  • Bit size
  • Chow form
  • Height function
  • Regular chain
  • Triangular set

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

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