derivative' — Mathlib

English

There is a canonical linear map A → Derivation R R[X] A that sends each a ∈ A to a derivation on R[X] with value a on X.

Русский

Существует каноническое линейное отображение A → Derivation R R[X] A, отправляющее каждый a ∈ A в производку на R[X], которая принимает значение a на X.

LaTeX

$$$mkDerivation : A \to_{R} \mathrm{Derivation}(R, R[X], A)$$$

Lean4

/-- `Polynomial.derivative` as a derivation. -/
@[simps]
def derivative' : Derivation R R[X] R[X] where
  toFun := derivative
  map_add' _ _ := derivative_add
  map_smul' := derivative_smul
  map_one_eq_zero' := derivative_one
  leibniz' f g := by simp [mul_comm, add_comm, derivative_mul]

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