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A Low-Memory Time-Efficient Implementation of Outermorphisms for Higher-Dimensional Geometric Algebras

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Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

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.

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Notes

  1. https://enkimute.github.io/ganja.js/examples/coffeeshop.html.

  2. https://github.com/ga-explorer/GeometricAlgebraNumericsLib.

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Acknowledgements

I would like to express my gratitude to the editor and reviewers for their valuable comments and constructive remarks leading to much improvement in the article’s final version in both readability and content.

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Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, Port-Said University, Port Fuad, Egypt

    Ahmad Hosny Eid

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  1. Ahmad Hosny Eid
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Correspondence to Ahmad Hosny Eid.

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Communicated by Leo Dorst.

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Eid, A.H. A Low-Memory Time-Efficient Implementation of Outermorphisms for Higher-Dimensional Geometric Algebras. Adv. Appl. Clifford Algebras 30, 24 (2020). https://doi.org/10.1007/s00006-020-1047-z

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