Octonions

extend_analytic(f, o::Octonion)

Evaluate the extension of the complex analytic function f to the octonions at o.

Given $o = s + a u$, where $s$ is the real part, $u$ is a pure unit octonion, and $a \ge 0$ is the magnitude of the imaginary part of $o$,

\[f(o) = \Re(f(z)) + \Im(f(z)) u,\]

is the extension of f to the octonions, where $z = s + a i$ is a complex analog to $o$.

See ^{[DentoniSce1973]} and ^{[ColomboSabadini2020]} for details.