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Massive Geometric Algebra: Visions for C++ Implementations of Geometric Algebra to Scale into the Big Data Era

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Abstract

Geometric algebra (GA) is a promising approach to address interoperability bottlenecks that are particularly prominent in the big data era. Similar to how GA unites and simplifies otherwise distinct mathematical branches it may also help to unite software via common interfaces between otherwise distinct applications. The promising potential of GA would be best exhibited by the ability of seamless integration into existing, complex applications. To achieve this vision various constraints have to be considered. Particularly having C++ in focus, we discuss the “wish list” that an optimal C++ implementation should provide. We find that to cover the various constraints an hybrid approach benefiting from multiple programming paradigms, ranging from generic to object-oriented programming, will be needed. C++ is a very suitable platform providing all these capabilities and promising approaches like Generative Programming and Active Libraries provide technology highly desirable for universally promoting GA to an extensive range of application domains.

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Acknowledgements

This work was completed in partial support by NSF Award #1251095 BIGDATA: Small: DCM: Collaborative Research: An efficient, versatile, scalable, and portable storage system for scientific data containers.

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  1. AHM Software GmbH, Feldstrasse 1b, 6020, Innsbruck, Austria

    Werner Benger & Wolfgang Dobler

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  1. Werner Benger
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Correspondence to Werner Benger.

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Benger, W., Dobler, W. Massive Geometric Algebra: Visions for C++ Implementations of Geometric Algebra to Scale into the Big Data Era. Adv. Appl. Clifford Algebras 27, 2153–2174 (2017). https://doi.org/10.1007/s00006-017-0780-4

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