fact: Fixpoint eval_poly (e : seq F) pf := if pf is c :: q then eval_poly e q * 'X + (eval e c)%:P else 0.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype choice ssrnat seq) mathcomp(fintype generic_quotient bigop ssralg poly) mathcomp(polydiv matrix mxpoly countalg ring_quotient)