This repository accompanies the article:

Unified Slice Regularity on Clifford Algebras: A Geometric and Operator-Theoretic Framework
by Mirco A. Mannucci
📄 Read the article here ←

CliffordLab is a lightweight laboratory for experimenting with unified slice regularity on real Clifford algebras ( \mathrm{Cl}(p,q) ).

It supports:

• Minimal pure-Python Clifford algebra engine (no deps)
• Unified slice utilities for ( J^2 = \pm 1 ) (elliptic & hyperbolic)
• Numerical Cauchy-type reconstruction
• Symbolic CR checks (via SymPy)
• Optional backend using pygae/clifford

CliffordLab/
├── README.md                # This file
├── LICENSE                  # MIT License
├── logo.svg                  # Project logo
├── pyproject.toml            # Package metadata (to be added)
├── requirements.txt          # Minimal dependencies
├── requirements-dev.txt      # Dev/test dependencies
├── src/
│   └── cliffordlab/
│       ├── __init__.py
│       ├── core.py           # Pure-Python GA & slice tools
│       ├── sym.py            # Symbolic (SymPy) helpers
│       ├── pygae.py          # pygae/clifford backend
├── examples/
│   └── CliffordLab_Tutorial.ipynb  # Jupyter tutorial
├── tests/
│   └── test_cr_conditions.py  # Unit tests for CR conditions
└── .github/
    └── workflows/
        └── ci.yml            # GitHub Actions CI pipeline

git clone https://github.com/Mircus/CliffordLab.git
cd CliffordLab

python3 -m venv .venv
source .venv/bin/activate

Minimal (pure-Python):

pip install -e .

With SymPy and pygae/clifford:

pip install -e .[sym,pygae]

Run the documented notebook:

jupyter notebook examples/CliffordLab_Tutorial.ipynb

Or run the basic demo script:

python -m cliffordlab.core

• Pure-Python GA core — portable, zero dependencies.
• Unified slice regularity — works for (J^2 = -1) (elliptic) and (J^2 = +1) (hyperbolic).
• Cauchy-type formula — numerically reconstruct (f(z_0)) from boundary data.
• Symbolic verification — exact CR checks with SymPy.
• pygae/clifford integration — optional high-performance backend.

Run tests:

pytest

Run lint:

ruff check src

CliffordLab incorporates ideas from the theory of slice regularity in quaternionic and Clifford analysis, and extensions to unified slice regularity for mixed signature algebras.