Theorems · Definition · field theory
Polynomial.nthRoots
{R : Type u} → [inst : CommRing R] → [IsDomain R] → ℕ → R → Multiset RnthRoots n a noncomputably returns the solutions to x ^ n = a.
- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.rootsproof · cited by 264
Cited by22
Results whose statement or proof uses this declaration.
- primitiveRootsproof · cited by 57
- Polynomial.nthRootsFinsetproof · cited by 23
- Polynomial.mem_nthRootsstatement · cited by 9
- Polynomial.nthRoots_zerostatement · cited by 5
- IsPrimitiveRoot.nthRoots_eqstatement and proof · cited by 3
- IsPrimitiveRoot.nthRoots_one_nodupstatement · cited by 3
- IsPrimitiveRoot.card_nthRoots_onestatement · cited by 3
- Polynomial.card_nthRootsstatement and proof · cited by 3
- rootsOfUnityEquivNthRootsstatement and proof · cited by 3
- card_rootsOfUnityproof · cited by 2
- IsCyclotomicExtension.finite_of_singletonproof · cited by 2
- IsPrimitiveRoot.card_nthRootsstatement and proof · cited by 2