Theorems · Theorem · field theory
Polynomial.roots_expand_image_iterateFrobenius
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {p n : ℕ} [inst_2 : ExpChar R p] {f : Polynomial R}
[PerfectRing R p] [inst_4 : DecidableEq R],
Finset.image (⇑(iterateFrobenius R p n)) ((Polynomial.expand R (p ^ n)) f).roots.toFinset = f.roots.toFinset- Defined in
- Mathlib.FieldTheory.Perfect
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Multisetproof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- LT.lt.ne'proof · cited by 1,417
- Finset.imagestatement · cited by 910
- ExpCharstatement and proof · cited by 276
- Polynomial.rootsstatement and proof · cited by 264
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