Theorems · Theorem · field theory
Polynomial.roots_multiset_prod
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (m : Multiset (Polynomial R)),
0 ∉ m → m.prod.roots = m.bind Polynomial.roots- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Multiset.prodstatement · cited by 528
- Polynomial.rootsstatement · cited by 264
- Multiset.bindstatement · cited by 59
- Polynomial.roots_list_prodproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.roots_prodproof · cited by 4
- Polynomial.roots_multiset_prod_X_sub_Cproof · cited by 3