[math-fun] Chebyshev/Dickson representation of polynomials

The really cool Chebfun computer algebra system represents polynomials in a Chebyshev basis instead of a "monomial" (power) basis: www.chebfun.org Among other things, there are "fast" algorithms for computing products of polys in a Chebyshev basis. The recent discussions of "permutation polynomials" led to finding that some of these polynomials are *Dickson* polynomials -- i.e., Chebyshev polynomials! Soooo, inspired by Chebfun, perhaps polynomials over finite fields should also be represented by Chebyshev/Dickson polynomials. Such a representation inverts the discussion, because we are now representing (at least in some cases) non-permutation polynomials in terms of permutation polynomials. Perhaps someone has already done this?