Theorems · Theorem · field theory
Polynomial.roots_prod
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] {ι : Type u_1} (f : ι → Polynomial R) (s : Finset ι),
s.prod f ≠ 0 → (s.prod f).roots = s.val.bind fun i => (f i).roots- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Finsetstatement and proof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- Finset.prodstatement · cited by 2,356
- IsDomainstatement and proof · cited by 2,196
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
- Finset.valstatement · cited by 438
- Polynomial.rootsstatement and proof · cited by 264
- Multiset.Nodupproof · cited by 148
- Multiset.bindstatement and proof · cited by 59
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.IsSymmetric.roots_charpoly_eq_eigenvaluesproof · cited by 4
- Matrix.IsHermitian.roots_charpoly_eq_eigenvaluesproof · cited by 4
- Polynomial.roots_prod_X_sub_Cproof · cited by 2
- Polynomial.rootSet_prodproof · cited by 1