also hard code the reduction table, but check it in the tests...

This makes sure that the coefficients and polynomial match such
that either there's enough coefficients, or the polynomial is..

also use 0 as a coeff, the original paper uses 0.

for powerseries, my docs were correct, but the implementation
wrong...  partly because I used zip which works on mismatched
lengths..

the last two are scarily short.