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Symbolic and User-friendly Geometric Algebra Routines ( SUGAR ) for Computations in Matlab

Symbolic and user-friendly geometric algebra routines (SUGAR) for computations in Matlab
Authors: Velasco García, Manel; Zaplana Agut, Isiah; Dòria Cerezo, Arnau; Martí Colom, Pau;

Symbolic and User-friendly Geometric Algebra Routines ( SUGAR ) for Computations in Matlab

Abstract

Geometric Algebra (GA) provides a unified, compact mathematical framework for geometric computing, simplifying relations typically handled with more complex tools like matrix multiplication. In fields like robotics, GA replaces conventional coordinate-based approaches with the multiplication of special elements called rotors, offering greater efficiency. Despite its advantages, GA’s complexity and the lack of symbolic tools hinder its broader adoption among applied mathematicians and engineers. To address this, this article introduces Symbolic and User-friendly Geometric Algebra Routines (SUGAR), an open source Matlab toolbox. SUGAR streamlines GA usage in Matlab through a collection of user-friendly functions that support both numeric and symbolic computations, even in high-dimensional algebras. Designed for applied mathematics and engineering, it enables intuitive manipulation of geometric elements and transformations in two- and three-dimensional projective and conformal GAs, consistent with established computational methods. Moreover, SUGAR manages multivector functions such as exponential, logarithmic, sinusoidal, and cosine operations, enhancing its applicability in domains like robotics, control systems, and power electronics. Finally, this article also presents three validation examples across these fields, showcasing SUGAR’s practical utility in solving real-world engineering and applied mathematics problems.

Country
Spain
Keywords

FOS: Computer and information sciences, G.4, High-dimensional systems, engineering, Systems and Control (eess.SY), geometric algebra, Symbolic computations, symbolic computations, Electrical Engineering and Systems Science - Systems and Control, high-dimensional systems, Geometric algebra, Computer Science - Robotics, Engineering, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional, FOS: Electrical engineering, electronic engineering, information engineering, Computer Science - Mathematical Software, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica, Mathematical Software (cs.MS), Robotics (cs.RO), Numerical analysis, Matlab

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green