@Preben Alsholm  Thanks. It seems to me that, since we end up with a (circular) list of points, it would be easy to see if any three or more in a row are collinear and, if so, knock out the middle ones.

@Alejandro Jakubi Thanks. I got some good answers here. My point was that I, the user, did not choose the symbol. The system did.

Here is a chunk of the actual help from PolynomialTools[MinimalPolynomial] (Maple13, maybe I should update) and what happens if I try to type the second line rather than just paste it from the help:

So yes, I can avoid this, I just wondered what the solution was, now I know.