Commit 2025-07-04 09:20 789b5d30
View on Github →feat(WithZero): exp : ℤ → ℤᵐ⁰
, log : ℤᵐ⁰ → ℤ
(#24977)
In valuation theory, valuations have codomain {0} ∪ {e ^ n | n : ℤ}
, which we can formalise as
ℤₘ₀ := WithZero (Multiplicative ℤ)
. It is important to be able to talk about the maps
n ↦ e ^ n
and e ^ n ↦ n
. We define these as exp : ℤ → ℤₘ₀
and log : ℤₘ₀ → ℤ
with junk
value log 0 = 0
. Junkless versions are defined as expEquiv : ℤ ≃ ℤₘ₀ˣ
and logEquiv : ℤₘ₀ˣ ≃ ℤ
.