- Conjugate operator — as in complex conjugate.
- Sample generator — 0 argument function that returns a random value from algebra.
- Zero — Additive identity
- Zero predicate — test a value for being zero.
- One — Multiplicative identity
- Addition operator Note that "+" is an argument!
- Subtraction operator
- Multiplication operator
- Multiplicative inverse

The function `testAlg` takes an algebra and tests for familiar field like properties.
Successive algebras deteriorate by losing properties.