hyper_rationals

Exact, rational-valued hypercomplex numbers -- reals, complex numbers, quaternions, octonions, and beyond -- built via the Cayley-Dickson construction, implemented in the hyprat package.

from hyprat import Hy

z = Hy('5/2', '-16/5')          # a rational complex number
str(z)                          # '(5/2-16/5j)'

q = Hy(Hy(1, 2), Hy(3, 4))      # a rational quaternion: 1 + 2i + 3j + 4k
i = Hy(Hy(0, 1), Hy(0, 0))
j = Hy(Hy(0, 0), Hy(1, 0))
i * j                           # -> Hy(Hy('0','0'), Hy('0','1'))   (== k)

The single immutable Hy class represents every rank:

rank 0  ->  a plain fractions.Fraction        (a "real")
rank 1  ->  Hy(real, imag)                    (a "complex" number)
rank 2  ->  Hy(h1, h2), h1/h2 rank 1          (a "quaternion")
rank 3  ->  Hy(h3, h4), h3/h4 rank 2          (an "octonion")
rank n  ->  Hy(x, y),   x/y  rank (n-1)

+ - * /, conjugation, norms, and inverses all follow the standard recursive Cayley-Dickson formulas, using exact fractions.Fraction arithmetic throughout -- no floating-point rounding.

Full documentation, including the API reference, is on Read the Docs.

Installation

pip install git+https://github.com/alreich/hyper_rationals.git

Or, for local development:

git clone https://github.com/alreich/hyper_rationals.git
cd hyper_rationals
pip install -e .[dev]

Running the tests

pytest

(or python -m unittest discover -s tests)

Building the docs locally

pip install -e .[docs]
sphinx-build -b html docs/source docs/_build/html

Project layout

hyper_rationals/
+-- src/hyprat/          the hyprat package  (import as `from hyprat import Hy`)
+-- tests/                unit tests (unittest, run via pytest or unittest)
+-- docs/source/          Sphinx documentation source
+-- .github/workflows/    CI (tests + docs build)
+-- pyproject.toml        packaging / metadata
+-- .readthedocs.yaml     Read the Docs build config

License

MIT -- see LICENSE.