Computational Algebra Seminar

Let K = Q(a1,a2,...,am) be a number field with m>0 field extensions. Let f1 and f2 be polynomials in K[x1,x2,...,xn] and let g = GCD(f1,f2) be the greatest common divisor of f1 and f2. In this talk I will outline an algorithm for computing g, present my Magma implementation of this algorithm and compare my code with the built-in Gcd operation in Magma.

The reason for my interest in this problem is because I believe it is the one of the most important and difficult computational problems in a general purpose computer algebra system to get right; my timings will give some indication as to why this is the case but I will seek to give general reasons to justify this.

I would like also to present for dicussion three problems that I encountered when writing the Magma code and possible solutions that Allan, Claus and I have ``mulled over'' for more general discussion.