Theorems · Theorem · field theory
Polynomial.roots_prod_X_sub_C
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (s : Finset R),
(∏ a ∈ s, (Polynomial.X - Polynomial.C a)).roots = s.val- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- Finset.prodstatement · cited by 2,356
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Finset.valstatement and proof · cited by 438
- Polynomial.rootsstatement · cited by 264
Cited by2
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.isRoot_cyclotomicproof · cited by 4
- Polynomial.roots_of_cyclotomicproof · cited by 0