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.

中文翻译：

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TbGAL：基于张量的几何代数库

几何代数是一个功能强大的数学框架，它使我们能够将几何实体（由叶片编码）和正交变换（由versors编码）用作图元并直接对其进行操作。在这项工作中，我们为几何代数提供了一个高级C ++库。通过操纵在张量结构下分解为矢量的叶片和叶片，即使在高维空间（\（\ bigwedge \ mathbb {R} ^ {n} \）且\（n> 256 \））下，我们的库也能实现高性能（p，  q，  r）具有\（r = 0 \）的度量签名。另外，为了使我们的库的使用简单，可以将该实现既用作C ++纯库，又用作Python环境的后端。这种灵活性允许根据用户的体验轻松进行操作，而不会影响性能。