invFun — Mathlib

English

The bare function invFun : A[X] → A ⊗R R[X] is defined by evaluating p at includeLeft and at 1 ⊗ X.

Русский

Бессекундная функция invFun : A[X] → A ⊗R R[X] задаётся как ε-образование полинома p по includeLeft и 1 ⊗ X.

LaTeX

$$invFun_R A(p) = p.eval₂(includeLeft, (1 : A) ⊗ X)$$

Lean4

/-- (Implementation detail.)

The bare function `A[X] → A ⊗[R] R[X]`.
(We don't need to show that it's an algebra map, thankfully --- just that it's an inverse.)
-/
def invFun (p : A[X]) : A ⊗[R] R[X] :=
  p.eval₂ (includeLeft : A →ₐ[R] A ⊗[R] R[X]) ((1 : A) ⊗ₜ[R] (X : R[X]))

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