exp — Mathlib

English

The exponential map on algebras is defined by exp(a) = sum_{i=0}^{nilpotencyClass(a)-1} (i!)^{-1} a^i.

Русский

Экспоненциальная карта на алгебрах задана как exp(a) = сумма_{i=0}^{nilpotencyClass(a)-1} (i!)^{-1} a^i.

LaTeX

$$exp(a) = \sum_{i=0}^{\mathrm{nilpotencyClass}(a)-1} (i!)^{-1} \cdot a^{i}$$

Lean4

/-- The exponential map on algebras, defined in analogy with the usual exponential series.
It provides meaningful (non-junk) values for nilpotent elements. -/
noncomputable def exp (a : A) : A :=
  ∑ i ∈ range (nilpotencyClass a), (i.factorial : ℚ)⁻¹ • (a ^ i)

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