Theorems · Theorem · field theory
Polynomial.roots_expand_map_frobenius
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {p : ℕ} [inst_2 : ExpChar R p] {f : Polynomial R}
[PerfectRing R p], Multiset.map (⇑(frobenius R p)) ((Polynomial.expand R p) f).roots = p • f.roots- Defined in
- Mathlib.FieldTheory.Perfect
- Cited by
- 1 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.
Cites21
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
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Multiset.mapstatement and proof · cited by 876
- RingEquiv.symmproof · cited by 567
- ExpCharstatement and proof · cited by 276
- Polynomial.rootsstatement and proof · cited by 264
- Multiset.map_congrproof · cited by 232
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.roots_expand_image_frobeniusproof · cited by 0