Theorems · Theorem · commutative algebra

Multiset.prod_X_sub_X_eq_sum_esymm

∀ {R : Type u_1} [inst : CommRing R] (s : Multiset R),
  (Multiset.map (fun t => Polynomial.X - Polynomial.C t) s).prod =
    ∑ j ∈ Finset.range (s.card + 1), (-1) ^ j * (Polynomial.C (s.esymm j) * Polynomial.X ^ (s.card - j))

Defined in

Mathlib.RingTheory.Polynomial.Vieta

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRing