Lower bounds for zero-dimensional projections

W. Dale Brownawell, Chee 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

Other

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

Fingerprint

Zero-dimensional
Projection
Lower bound
Polynomial
Zero
Maximum Degree
Finite Set

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

Lower bounds for zero-dimensional projections. / Brownawell, W. Dale; Yap, Chee.

ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation. 2009. p. 79-85.

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

Brownawell, WD & Yap, C 2009, Lower bounds for zero-dimensional projections. in ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation. pp. 79-85, 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009, Seoul, Korea, Republic of, 7/28/09. https://doi.org/10.1145/1576702.1576716
Brownawell WD, Yap C. Lower bounds for zero-dimensional projections. In ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation. 2009. p. 79-85 https://doi.org/10.1145/1576702.1576716
Brownawell, W. Dale ; Yap, Chee. / Lower bounds for zero-dimensional projections. ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation. 2009. pp. 79-85
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