TY - GEN

T1 - Lower bounds for zero-dimensional projections

AU - Brownawell, W. Dale

AU - Yap, Chee K.

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Chow forms

KW - Exact geometric computation

KW - Exact numerical algorithms

KW - Nullstellensatz

KW - Transcendence theory

KW - Zero bounds

UR - http://www.scopus.com/inward/record.url?scp=77950401754&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950401754&partnerID=8YFLogxK

U2 - 10.1145/1576702.1576716

DO - 10.1145/1576702.1576716

M3 - Conference contribution

AN - SCOPUS:77950401754

SN - 9781605586090

T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

SP - 79

EP - 85

BT - ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation

T2 - 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009

Y2 - 28 July 2009 through 31 July 2009

ER -