Abstract:
Given the coefficients of a polynomial in one variable it is easy to compute an upper bound R > 0 for the absolute value of the roots of the polynomial. Consequently, there is an algorithm that takes as input the coefficients of a polynomial and outputs R > 0 such that, if the polynomial has an integer root, the polynomial has an integer root with absolute value less than R.
The talk focuses on the search for a generalization of this algorithm to handle polynomials in multiple variables. Along the way, Gödel’s second incompleteness theorem and Hilbert’s tenth problem will make an appearance.