From the beginning of David Hestenes rediscovery of geometric algebra in the 1960s, outermorphisms have been a cornerstone in the mathematical development of GA. Many important mathematical formulations in GA can be expressed as outermorphisms such as versor products, linear projection operators, and mapping between related coordinate frames. Over the last two decades, GA-based mathematical models and software implementations have been developed in many fields of science and engineering. As such, efficient implementations of outermorphisms are of significant importance within this context. This work attempts to shed some light on the problem of optimizing software implementations of outermorphisms for practical prototyping applications using geometric algebra. The approach we propose here for implementing outermorphisms requires orders of magnitude less memory compared to other common approaches, while being comparable in time performance, especially for high-dimensional geometric algebras.

中文翻译：

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高维几何代数的超同构的低内存时间高效实现

从1960年代David Hestenes重新发现几何代数开始，外同构一直是GA数学发展的基石。GA中许多重要的数学公式都可以表示为外态，例如versor乘积，线性投影算子以及相关坐标系之间的映射。在过去的二十年中，已经在许多科学和工程领域开发了基于GA的数学模型和软件实现。因此，在这种情况下，有效实现外态性非常重要。这项工作试图阐明使用几何代数为实际原型应用优化外态的软件实现的问题。