lower bounds for zero-dimensional projections
Let I be an ideal generated by polynomials P 1, ... P m, ? Z [ X 1 ,..., X n ], and ? be an isolated prime component of I . If the projection of Z ERO (?)? C n onto the first coordinate is a finite set, and =( 1 ,..., n ) ?Z ERO (?) where  1 0, then we prove a lower bound on || in terms of n, m and the maximum degree D and maximum height H of the polynomials.
nullstellensatz exact geometric computation exact numerical algorithms chow forms zero bounds transcendence theory