Theorems · Theorem · field theory

Polynomial.map_aeval_eq_aeval_map

∀ {R : Type u} [inst : CommSemiring R] {S : Type u_3} {T : Type u_4} {U : Type u_5} [inst_1 : Semiring S]
  [inst_2 : CommSemiring T] [inst_3 : Semiring U] [inst_4 : Algebra R S] [inst_5 : Algebra T U] {φ : R →+* T}
  {ψ : S →+* U},
  (algebraMap T U).comp φ = ψ.comp (algebraMap R S) →
    ∀ (p : Polynomial R) (a : S), ψ ((Polynomial.aeval a) p) = (Polynomial.aeval (ψ a)) (Polynomial.map φ p)

Defined in

Mathlib.Algebra.Polynomial.AlgebraMap

Cited by

14 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringCommSemiringSemiringAlgebraAlgebra