Theorems · Theorem · field theory
Polynomial.coeff_prod_of_natDegree_le
∀ {R : Type u} {ι : Type w} (s : Finset ι) [inst : CommSemiring R] (f : ι → Polynomial R) (n : ℕ),
(∀ p ∈ s, (f p).natDegree ≤ n) → (∏ i ∈ s, f i).coeff (s.card * n) = ∏ i ∈ s, (f i).coeff n- Defined in
- Mathlib.Algebra.Polynomial.BigOperators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- Semiringproof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Multisetproof · cited by 2,627
- Finset.prodstatement and proof · cited by 2,356
- Finset.cardstatement and proof · cited by 2,327
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
- Multiset.cardproof · cited by 375
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.coeff_det_X_add_C_cardproof · cited by 1