# Accession Number:

## ADA453878

# Title:

## Effective Bezout Identities in Q[z1,...,Zn]

# Descriptive Note:

## Journal article

# Corporate Author:

## MARYLAND UNIV COLLEGE PARK DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 1987-01-01

# Pagination or Media Count:

## 72.0

# Abstract:

If psub 1..... , Psub mare n-variate polynomials with integral coefficients and no common zeros in Cexp n, Brownawell has shown in 1986 that there exist qsub 1 ...., qsub m polynomials with integral coefficients and nu is an element of Z such that psub 1 qsub 1 ... psub m qsub m nu, and max deg qsub j max deg psub j exp n. On the other hand if h logarithm of the largest coefficient of all the psub j, and hsub 1 is the corresponding quantity for the qsub j, then there is no sharp estimate of hsub 1 in terms of h and max deg psub j. In this paper we show that when the variety of common zeros at infinity of the psub j is discrete then essentially we have hsub 1 Dexp cnh for an absolute constant c. If there were an algorithm to compute the qsub j in Dexp cn time one would obtain exactly the above estimate. Current algorithms require about Dexp n squared operations.

# Descriptors:

# Subject Categories:

- Numerical Mathematics