Theorems · Theorem · field theory

Polynomial.map_sub_roots_sprod_eq_prod_map_eval

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] (s : Multiset R) (g : Polynomial R),
  g.Monic →
    g.Splits →
      (Multiset.map (fun ij => ij.1 - ij.2) (g.roots ×ˢ s)).prod =
        (-1) ^ (s.card * g.roots.card) * (Multiset.map (fun x => Polynomial.eval x g) s).prod

Defined in

Mathlib.Algebra.Polynomial.Splits

Cited by

1 results in Mathlib

Foundations

Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomain