Theorems · Theorem · commutative algebra
Multiset.esymm_neg
∀ {R : Type u_1} [inst : CommRing R] (s : Multiset R) (k : ℕ), (Multiset.map Neg.neg s).esymm k = (-1) ^ k * s.esymm k- Defined in
- Mathlib.RingTheory.Polynomial.Vieta
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement and proof · cited by 876
- Multiset.prodproof · cited by 528
- Multiset.sumproof · cited by 388
- Multiset.cardproof · cited by 375
- Multiset.map_congrproof · cited by 232
- Multiset.map_mapproof · cited by 151
- neg_one_mulproof · cited by 61
- Multiset.prod_replicateproof · cited by 40
- Multiset.map_id'proof · cited by 35
- Multiset.powersetCardproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.prod_X_sub_C_coeffproof · cited by 2
- Multiset.prod_X_sub_X_eq_sum_esymmproof · cited by 0