IMO, as what I've suggested in this comment, #206 (comment).
template <typename Domain, typename Poly,
typename Evals = typename Domain::Evals, typename F>
Evals CoeffToExtendedPart(const Domain* domain, const Poly& poly, const F& zeta,
this kind of code would be more correct to be written as below.
template <typename Domain>
typename Domain::Evals CoeffToExtendedPart(const Domain* domain, const typename Domain::Poly& poly, const typename Domain::Field& zeta,