Theorems · Theorem · field theory
Polynomial.aeval_algEquiv
∀ {R : Type u} {A : Type z} {B : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A ≃ₐ[R] B) (x : A),
Polynomial.aeval (f x) = (↑f).comp (Polynomial.aeval x)- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement · cited by 5,681
- AlgHomstatement · cited by 3,236
- AlgEquivstatement and proof · cited by 1,681
- Polynomial.aevalstatement · cited by 615
- AlgHom.compstatement · cited by 501
- AlgEquiv.toAlgHomstatement and proof · cited by 273
- Polynomial.aeval_algHomproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- PowerBasis.equivOfRoot_mapproof · cited by 1