More powerful simplification of exception lists?

[fingolfin]

Consider this example

julia> T = genchartab("SL3.n1");

julia> h = T[2] * T[2];

julia> scalar_product(T[8], h)
0
With exceptions:
  q*n1 ∈ (q^2 + q + 1)ℤ
  n1 ∈ (q^2 + q + 1)ℤ
  q*n1 + n1 ∈ (q^2 + q + 1)ℤ

Note how the list of exceptions could be simplified because $q$ resp. $q+1$ both are coprime with $q^2 + q + 1$ for any value of $q$. And that could even be determined using (tweaked) polynomial gcd, i.e. I think there is a chance of automating this kind of simplification: just factor the left side; then kill any factors which are provably coprime to the "modulus".

Actually it's not simply computing a gcd, it is a bit more: if we start with e.g. gcd(q, q^2+q+2), what I'd really want is to simplify this to gcd(q,2). At that point we arrive at a case distinction: the gcd is 1 if $q$ is odd, and it is $2$ if $q$ is even.

(Issue based on this discussion)