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Developing GA-FuL: A Generic Wide-Purpose Library for Computing with Geometric Algebra

Author

Listed:
  • Ahmad Hosny Eid

    (Department of Electrical Engineering, Faculty of Engineering, Port Said University, Port Fouad 42523, Egypt)

  • Francisco G. Montoya

    (Department of Engineering, University of Almería, 04120 Almeria, Spain)

Abstract

The Geometric Algebra Fulcrum Library (GA-FuL) version 1.0 is introduced in this paper as a comprehensive computational library for geometric algebra (GA) and Clifford algebra (CA), in addition to other classical algebras. As a sophisticated software system, GA-FuL is useful for practical applications requiring numerical or symbolic prototyping, optimized code generation, and geometric visualization. A comprehensive overview of the GA-FuL design is provided, including its core design intentions, data-driven programming characteristics, and extensible layered design. The library is capable of representing and manipulating sparse multivectors of any dimension, scalar kind, or metric signature, including conformal and projective geometric algebras. Several practical and illustrative use cases of the library are provided to highlight its potential for mathematical, scientific, and engineering applications. The metaprogramming code optimization capabilities of GA-FuL are found to be unique among other software systems. This allows for the automated production of highly efficient code, based on powerful geometric modeling formulations provided by geometric algebra.

Suggested Citation

  • Ahmad Hosny Eid & Francisco G. Montoya, 2024. "Developing GA-FuL: A Generic Wide-Purpose Library for Computing with Geometric Algebra," Mathematics, MDPI, vol. 12(14), pages 1-33, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2272-:d:1439330
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    References listed on IDEAS

    as
    1. Francisco G. Montoya & Raúl Baños & Alfredo Alcayde & Francisco M. Arrabal-Campos & Javier Roldán-Pérez, 2022. "Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
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