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