another suggestion about octonions: since we're unifying i j in C and H, i think it's nicer to have k as "the one spanning octonions from quaternions" (exactly what cayley-dickson construction did), despite there's convention from quaternions that "ij=k". this way we could have i, j, ij, k, ik, jk, (ij)k as e1~e7. furthermore, it's ok to use ÿ as ij digraph that also avoids the necessity of parenthesis in (ij)k. then they become i, j, ÿ, k, ik, jk, ÿk.
bug report: entering 1/94906266, the denominator from this on, C, H jump out mysteriously...
and suggestion continued: for split complex (i'd rather call them hyperbolic), i think it's better to use "i'"=1 since it's completely different from i. also j'^2=ÿ'^2=1. and there's split quaternion using i' j or i j' together.... and (completely) hyperbolic quaternion i' j' ÿ' and so on... imo it's generally better this way.