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
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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 -