Theorems · Definition · field theory
Polynomial.nthRootsFinset
ℕ → {R : Type u_1} → R → [inst : CommRing R] → [IsDomain R] → Finset RThe multiset nthRoots ↑n a as a Finset. Previously nthRootsFinset n was defined to be
nthRoots n (1 : R) as a Finset. That situation can be recovered by setting a to be (1 : R)
- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 13,712
- IsDomainstatement and proof · cited by 2,196
- Multiset.toFinsetproof · cited by 230
- Polynomial.nthRootsproof · cited by 19
Cited by23
Results whose statement or proof uses this declaration.
- Polynomial.mem_nthRootsFinsetstatement · cited by 6
- Polynomial.nthRootsFinset_zerostatement · cited by 4
- Polynomial.nthRootsFinset.congr_simpstatement and proof · cited by 2
- IsPrimitiveRoot.nthRootsFinset_pairwise_associated_sub_one_sub_of_primestatement and proof · cited by 2
- IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRootsstatement · cited by 2
- Polynomial.nthRootsFinset_defstatement · cited by 2
- mem_nthRootsFinset_iff_of_primestatement · cited by 1
- Polynomial.X_pow_sub_one_eq_prodstatement · cited by 1
- Polynomial.map_mem_nthRootsFinsetstatement and proof · cited by 1
- Polynomial.map_mem_nthRootsFinset_onestatement and proof · cited by 1
- isPrimitiveRoot_of_mem_nthRootsFinsetstatement and proof · cited by 1
- IsPrimitiveRoot.card_nthRootsFinsetstatement · cited by 1