proposition: Lemma msym_coeff (p : {mpoly R[n]}) (m : 'X_{1..n}) (s : 'S_n) : p \is symmetric -> p@_(m#s) = p@_m.
proof: Proof. move/issymP=> /(_ s^-1)%g {1}<-; rewrite mcoeff_sym. by congr (_@__); apply/mnmP=> i /=; rewrite !mnmE permKV. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finfun bigop finset binomial) mathcomp(order fingroup perm ssralg zmodp poly ssrint) mathcomp(matrix vector) mathcomp(bigenough) ssrcomplements freeg