English
Another variant of the linear-derivative expansion with additional terms.
Русский
Другой вариант разложения по линейной производной с дополнительными членами.
LaTeX
$$$$f(x+h) = f(x) + f.linearDeriv x(h) + \sum_s f((s).piecewise(h,x)).$$$$
Lean4
/-- When `ι` is finite, multilinear maps on `R^ι` with values in `M₂` are in bijection with `M₂`,
as such a multilinear map is completely determined by its value on the constant vector made of ones.
We register this bijection as a linear equivalence in `MultilinearMap.piRingEquiv`. -/
protected def piRingEquiv [Fintype ι] : M₂ ≃ₗ[R] MultilinearMap R (fun _ : ι => R) M₂
where
toFun z := MultilinearMap.mkPiRing R ι z
invFun f := f fun _ => 1
map_add' z
z' := by
ext
simp
map_smul' c
z := by
ext
simp
left_inv z := by simp
right_inv f := f.mkPiRing_apply_one_eq_self
