Theorems · Theorem · field theory
Polynomial.nextCoeff_map_eq
∀ {R : Type u} {S : Type v} [inst : Ring R] [IsSimpleRing R] [inst_2 : Semiring S] [Nontrivial S] (p : Polynomial R)
(f : R →+* S), (Polynomial.map f p).nextCoeff = f p.nextCoeff- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.mapstatement · cited by 806
- RingHom.injectiveproof · cited by 187
- Polynomial.nextCoeffstatement · cited by 46
- IsSimpleRingstatement and proof · cited by 39
- Polynomial.nextCoeff_mapproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- PowerBasis.trace_gen_eq_sum_rootsproof · cited by 2
- Algebra.normalizedTrace_algebraMap_of_liftsproof · cited by 1