Theorems · Definition · commutative algebra
MvPolynomial.esymm
(σ : Type u_5) → (R : Type u_6) → [inst : CommSemiring R] → [Fintype σ] → ℕ → MvPolynomial σ R
The nth elementary symmetric MvPolynomial σ R.
It is the sum over all the degree n squarefree monomials in MvPolynomial σ R.
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Finset.prodproof · cited by 2,356
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.Xproof · cited by 552
- Finset.powersetCardproof · cited by 60
Cited by33
Results whose statement or proof uses this declaration.
- MvPolynomial.esymmAlgHomproof · cited by 11
- MvPolynomial.esymmAlgHom_applystatement and proof · cited by 3
- MvPolynomial.esymm_zerostatement · cited by 3
- MvPolynomial.supDegree_esymmAlgHomMonomialproof · cited by 2
- MvPolynomial.monic_esymmstatement and proof · cited by 2
- MvPolynomial.rename_esymmstatement · cited by 2
- MvPolynomial.rename_esymmAlgHomproof · cited by 2
- MvPolynomial.esymmAlgHomMonomial_addproof · cited by 2
- MvPolynomial.esymmAlgHomMonomial_single_onestatement and proof · cited by 2
- MvPolynomial.esymmAlgHom_zeroproof · cited by 2
- MvPolynomial.esymmPartproof · cited by 2
- MvPolynomial.esymm_eq_multiset_esymmstatement · cited by 2