I've since worked out what, I believe, is a much more elegant specification of polynomials, which I offer below for your enjoyment. One interesting aspect of these traits is the following. The trait Coefficients specifies coefficient lists. In Polynomial, there is specified an isomorphism between polynomials and coefficient lists. Then other operations on polynomials are specified in a more convenient manner than would be the case with just pure polynomials or pure coeffieient lists.
Comments are welcome.
If there is interest, I can make these available from the WWW and by ftp in a more standard fashion.