Joachim von zur Gathen, Fachbereich 17 Mathematik-Informatik,Universität Paderborn Paderborn, Germany.

Subresultants revisited

Starting in the late 1960s, Collins and Brown & Traub invented polynomial remainder sequences (PRS) in order to apply the Euclidean algorithm to integer polynomials. Subresultants play a major role in this theory. We compare the various notions of subresultants, give a general and precise definition of PRS, and clean up some loose ends:

prove a 1971 conjecture of Brown that all results in the subresultant PRS are integer polynomials,
show an exponential lower bound on the pseudo PRS.

Lastly, we show how Kronecker had, already in the 1870s, discovered many of the fundamental properties of Euclid's algorithm for polynomials.