Theorems · Theorem · field theory
Polynomial.roots_X_pow_char_pow_sub_C
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {p n : ℕ} [inst_2 : ExpChar R p] [inst_3 : PerfectRing R p]
{y : R}, (Polynomial.X ^ p ^ n - Polynomial.C y).roots = p ^ n • {(iterateFrobeniusEquiv R p n).symm y}- Defined in
- Mathlib.FieldTheory.Perfect
- Cited by
- 2 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.
Cites22
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
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- RingEquivstatement · cited by 1,147
- Multiset.mapproof · cited by 876
- RingEquiv.symmstatement and proof · cited by 567
- map_subproof · cited by 565
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.roots_X_pow_char_pow_sub_C_powproof · cited by 1
- Polynomial.roots_X_pow_char_sub_Cproof · cited by 0