Add hypercomplex data type based on Cayley-Dickson construction

[sritchie]

We currently have real, complex, and Quaternions as of sicmutils/sicmutils#461. It would be lovely to "complete" the story here by implementing a Hypercomplex type wrapping a vector of length 2^n.

Here is one Clojure implementation of this idea: https://github.com/ogeagla/clj-hypercomplex/blob/master/src/hypercomplex/core.clj

I think ours should stick to a flat vector for the data type instead of the nested map in the implementation above.

In theory we could macro-generate the complex and quaternion specialized types from functions here... maybe that is a good idea, as an exercise, as least :)

Bicomplex etc

There are lots of new weird types we get if we use real, split-complex or dual numbers as entries in these formulations.

• Bicomplex numbers are complex numbers with complex entries
• Biquaternions have complex entries
• Split-biquaternions use split-complex coefficients
• Dual quaternions use dual number entries

This is interesting as a story about fleshing out an abstraction.

References:

• https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction
• More notes on hyperbolic / split-complex numbers https://www.reddit.com/r/math/comments/7g82yv/splitcomplex_numbers/