Calculating Cyclotomic Polynomials
Andrew Arnold, Mathematics, SFU
Abstract: This talk will detail two methods of computing cyclotomic polynomials. The first method computes cyclotomic polynomials recursively through a series of polynomial divisions. We've recently implemented a new, surprisingly fast algorithm which calculates cyclotomic polynomials as a product of sparse power series. We will also show some results we've obtained on the height and length of cyclotomic polynomials. In particular, we have found a number of cyclotomic polynomials with very large height, as well as the cyclotomic polynomial of smallest order whose height exceeds its order squared.