Theorems · Theorem · field theory
Polynomial.nodup_roots
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] {p : Polynomial R}, p.Separable → p.roots.Nodup- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 133 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
- IsDomainstatement and proof · cited by 2,196
- Polynomial.rootsstatement · cited by 264
- Multiset.Nodupstatement · cited by 148
- Polynomial.Separablestatement and proof · cited by 117
- Multiset.nodup_iff_count_le_oneproof · cited by 8
- Polynomial.count_roots_le_oneproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.card_rootSet_eq_natDegreeproof · cited by 3
- FiniteField.roots_X_pow_card_sub_Xproof · cited by 2
- AlgHom.natCard_of_powerBasisproof · cited by 2
- ConjRootClass.nodup_aroots_minpolyproof · cited by 2
- Polynomial.Gal.galActionHom_bijective_of_prime_degreeproof · cited by 1
- Polynomial.nodup_roots_iff_of_splitsproof · cited by 1
- Algebra.norm_eq_prod_embeddings_genproof · cited by 1
- Algebra.discr_powerBasis_eq_normproof · cited by 1
- trace_eq_sum_embeddings_genproof · cited by 1
- ConjRootClass.minpoly.map_eq_prodproof · cited by 0