proposition: Lemma Cauchy_homsymp_zhomsymp m n d : [char R] =i pred0 -> Cauchy_kernel m n R d = \sum_(la : 'P_d) 'hp[la](X) * ((zcard la)%:R^-1 *: 'hp[la](Y)).
proof: Proof. move=> Hchar. rewrite /Cauchy_kernel symh_to_symp // !rmorph_sum /=; apply eq_bigr => la _. by rewrite linearZ /= -scalerAr prod_sympXY; congr (_ *: _). Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssrint rat ssralg ssrnum algC matrix vector) mathcomp(mpoly) tools partition ordtype antisym Schur_mpoly Schur_altdef sympoly homogsym permcent