Title: Irreducibility and gcd algorithms for sparse polynomials
Speaker: Michael Filaseta (University of South Carolina)
Abstract: Let f (x) be a polynomial with integer coefficients. Let n be the degree
of f , let r be its number of terms and let H be its height (the largest absolute
value of a coefficient). A sparse polynomial is one in which r is small compared
to n (a more precise definition will not be necessary). Our main objective is to
describe algorithms that run fast with r and H being fixed. Known algorithms,
such as the L3 algorithm for factoring and the Euclidean algorithm for gcd’s, run
in time that are polynomial in n. We describe algorithms that run in time that are
polynomial in log n. The results are from recent joint work with Andrew Granville
and Andrzej Schinzel. As time permits, we will discuss some practical aspects of
the above theoretical results.