Calculating Cyclotomic Polynomials

Andrew Arnold, Mathematics, SFU

Wednesday October 3rd, 3:30pm in K9509.


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.