### Abstract

Let I be an ideal generated by polynomials P_{1}, . . . , P _{m} ∈ ℤ[X_{1}, . . . , X_{n}], and β be an isolated prime component of I. If the projection of Zero(β) ⊆ ℂ^{n} onto the first coordinate is a finite set, and ζ = (ζ_{1}, . . . , ζ_{n}) ∈ Zero(β) where ζ_{1} ≠ 0, then we prove a lower bound on |ζ_{1}| in terms of n,m and the maximum degree D and maximum height H of the polynomials.

Original language | English (US) |
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Title of host publication | ISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation |

Pages | 79-85 |

Number of pages | 7 |

DOIs | |

State | Published - 2009 |

Event | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of Duration: Jul 28 2009 → Jul 31 2009 |

### Other

Other | 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 7/28/09 → 7/31/09 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Lower bounds for zero-dimensional projections

AU - Brownawell, W. Dale

AU - Yap, Chee

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

SP - 79

EP - 85

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

ER -