TbGAL: A Tensor-Based Library for Geometric Algebra

Abstract

Geometric algebra is a powerful mathematical framework that allows us to use geometric entities (encoded by blades) and orthogonal transformations (encoded by versors) as primitives and operate on them directly. In this work, we present a high-level C++ library for geometric algebra. By manipulating blades and versors decomposed as vectors under a tensor structure, our library achieves high performance even in high-dimensional spaces ($$\bigwedge \mathbb {R}^{n}$$ with $$n > 256$$) assuming (p, q, r) metric signatures with $$r = 0$$. Additionally, to keep the simplicity of use of our library, the implementation is ready to be used both as a C++ pure library and as a back-end to a Python environment. Such flexibility allows easy manipulation accordingly to the user’s experience, without impact on the performance.