Lower bounds for zero-dimensional projections

W. Dale Brownawell, Chee K. Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let I be an ideal generated by polynomials P1, . . . , P m ∈ ℤ[X1, . . . , Xn], and β be an isolated prime component of I. If the projection of Zero(β) ⊆ ℂn onto the first coordinate is a finite set, and ζ = (ζ1, . . . , ζn) ∈ Zero(β) where ζ1 ≠ 0, then we prove a lower bound on |ζ1| in terms of n,m and the maximum degree D and maximum height H of the polynomials.

Original languageEnglish (US)
Title of host publicationISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation
Pages79-85
Number of pages7
DOIs
StatePublished - 2009
Event2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of
Duration: Jul 28 2009Jul 31 2009

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Other

Other2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
CountryKorea, Republic of
CitySeoul
Period7/28/097/31/09

Keywords

  • Chow forms
  • Exact geometric computation
  • Exact numerical algorithms
  • Nullstellensatz
  • Transcendence theory
  • Zero bounds

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Brownawell, W. D., & Yap, C. K. (2009). Lower bounds for zero-dimensional projections. In ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation (pp. 79-85). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/1576702.1576716