tfga 0.1.9

Clifford and Geometric Algebra with TensorFlow

TFGA - TensorFlow Geometric Algebra

GitHub | Docs | Benchmarks

Python package for Geometric / Clifford Algebra with TensorFlow 2.

This project is a work in progress. Its API may change and the examples aren't polished yet. Pull requests and suggestions either by opening an issue or by sending me an email are welcome.

Installation

Install using pip: pip install tfga

Requirements:

• Python 3
• tensorflow 2
• numpy

Basic usage

from tfga import GeometricAlgebra

# Create an algebra with 3 basis vectors given their metric.
# Used to create MultiVector instances.
ga = GeometricAlgebra(metric=[1, 1, 1])

# 1 e_0 + 1 e_1 + 1 e_2
ordinary_vector = ga.ones(batch_shape=[], kind="vector")

# 5 + 5 e_01 + 5 e_02 + 5 e_12
quaternion = ga.fill(batch_shape=[], fill_value=5.0, kind="even")

# 5 + 1 e_0 + 1 e_1 + 1 e_2 + 5 e_01 + 5 e_02 + 5 e_12
multivector = ordinary_vector + quaternion

# Inner product e_0 | 1 e_0 + 1 e_1 + 1 e_2 = 1
print(ga.basis_mvs[0] | ordinary_vector)

# Exterior product e_0 ^ e_1 = e_01
print(ga.basis_mvs[0] ^ ga.basis_mvs[1])

# Grade reversal ~(5 + 5 e_01 + 5 e_02 + 5 e_12)
# = 5 + 5 e_10 + 5 e_20 + 5 e_21
# = 5 - 5 e_01 - 5 e_02 - 5 e_12
print(~quaternion)

# tf.Tensor 5
print(quaternion.scalar)

# tf.Tensor -5 (ie. reversed sign of e_01 component)
print(quaternion.tensor("10"))

# MultiVector with only e_01: 5 e_01
print(quaternion["10"])

Notebooks

Generic examples

Quantum Electrodynamics using Geometric Algebra

Projective Geometric Algebra