I have assumed that you know what a GCD (Greatest Common Divisor)
is. See for example the treatment in the beginning chapter of
Cox et al.'s book `Ideals, Varieties, and Algorithms' if you
need a reference, or look in Geddes et. al. `Algorithms for
Computer Algebra.' In brief, a greatest common divisor of two
polynomials **p** and **q** is a polynomial **d** of maximal degree
such that **d | p** and **d | q**. Such a polynomial always exists
and can be computed by the Euclidean Algorithm. In Geddes et. al.
you learn that the naively implemented Euclidean algorithm is
far too expensive for even moderate problems, and that efficiency
in such a computation is greatly to be desired, and that it is
possible.

I suppose this actually deserves some treatment in detail, and I will get back to this if I have time; for now we will just take Maple's (very efficient) gcd routine for granted.

Wed Feb 28 18:25:56 EST 1996