reₗ — Mathlib

English

re acts as a linear map from QuadraticAlgebra to the base ring, i.e., it is a linear functional given by the real part.

Русский

re выступает как линейный отображение из QuadraticAlgebra в базовое кольцо.

LaTeX

$$$\mathrm{re}_\ell : \text{QuadraticAlgebra}(R,a,b) \to R$ is linear with toFun = re$$

Lean4

/-- `QuadraticAlgebra.re` as a `LinearMap` -/
@[simps]
def reₗ : QuadraticAlgebra R a b →ₗ[R] R where
  toFun := re
  map_add' _ _ := rfl
  map_smul' _ _ := rfl

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