Theorems · Theorem · field theory
Polynomial.nthRootsFinset_zero
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (a : R), Polynomial.nthRootsFinset 0 a = ∅- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 134 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.
- 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.nthRootsFinsetstatement · cited by 23
- Polynomial.nthRoots_zeroproof · cited by 5
- Polynomial.nthRootsFinset_defproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRootsproof · cited by 2
- Polynomial.map_mem_nthRootsFinsetproof · cited by 1
- Polynomial.ne_zero_of_mem_nthRootsFinsetproof · cited by 0
- Polynomial.mul_mem_nthRootsFinsetproof · cited by 0