English
The nth monomial is the R-linear map sending the base R to the coefficient at n and all other indices to 0.
Русский
Н-м мономом является R-линейное отображение, отправляющее образец в коэффициент при индексе n, а все остальные индексы в 0.
LaTeX
$$$\\operatorname{monomial}(n) = \\operatorname{LinearMap.single} \\, R \\, (\\lambda _ \\mapsto R) \\, n$$$
Lean4
/-- The `n`th monomial as multivariate formal power series:
it is defined as the `R`-linear map from `R` to the semiring
of multivariate formal power series associating to each `a`
the map sending `n : σ →₀ ℕ` to the value `a`
and sending all other `x : σ →₀ ℕ` different from `n` to `0`. -/
def monomial (n : σ →₀ ℕ) : R →ₗ[R] MvPowerSeries σ R :=
letI := Classical.decEq σ
LinearMap.single R (fun _ ↦ R) n
