All elementary functions from a single operator

Primitive operator: eml(x, y) = e^x − ln(y)

1. Core building blocks

From eml and 1, we recover exponential and logarithm, then arithmetic kernels.

E(x) = eml(x, 1), L(x) = ln(x), S(a, b) = eml(ln(a), e^b)

A(a, b) = a + b, G(a, b) = a − b, M(x, y) = xy, D(x, y) = x/y

Use the explorer to inspect one construct at a time and see domain restrictions.

exp / log

E(x) = eml(x, 1); L(x) = eml(1, eml(eml(1, x), 1))

Valid on ℝ with x > 0 for L(x).

Domain: ℝ Shortcut: ← / → to change operation

In ℂ we fix a branch of Log. Principal branch gives i = e^iπ/2 and π = −i Log(−1).

sin(x) = (e^ix − e^−ix) / 2i, cos(x) = (e^ix + e^−ix) / 2

Different branches can flip signs or shift by odd multiples of π.

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