Computational aspects of geometric algebra products of two homogeneous multivectors

DOI10.1007/s00006-022-01249-5zbMath1505.15020arXiv2002.11313OpenAlexW4308948208MaRDI QIDQ2680610

Vincent Nozick, Stéphane Breuils, Sugimoto, Akihiro

Publication date: 4 January 2023

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.11313

zbMATH Keywords

computational complexityClifford algebrageometric algebraarithmetic operations

Mathematics Subject Classification ID

Clifford algebras, spinors (15A66) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)

Uses Software

• BIGEBRA
• CLIFFORD
• GluCat
• OpenCLLink
• cmulNUM
• cmulRS
• cmulW
• cmulWpar
• GAviewer
• GitHub
• ganja.js
• TbGAL
• GATL

Cites Work

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• Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple
• On parallelizing the Clifford algebra product for \texttt{CLIFFORD}
• Implementing geometric algebra products with binary trees
• Geometric algebra enhanced precompiler for C++, OpenCL and Mathematica's OpenCLLink
• Geometric algebra with applications in engineering
• Quadric conformal geometric algebra of \({\mathbb {R}}^{9,6}\)
• A geometric algebra implementation using binary tree
• A generalized FFT for Clifford algebras
• Calculating the rotor between conformal objects
• TbGAL: a tensor-based library for geometric algebra
• Garamon: a geometric algebra library generator
• \(R(4, 4)\) as a computational framework for 3-dimensional computer graphics
• Understanding Geometric Algebra

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