Implementing geometric algebra products with binary trees

DOI10.1007/s00006-014-0447-3zbMath1311.68147OpenAlexW2008609482MaRDI QIDQ742367

Laurent Fuchs, Laurent Théry

Publication date: 18 September 2014

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

Full work available at URL: https://doi.org/10.1007/s00006-014-0447-3

zbMATH Keywords

binary treegeometric algebraGrassmann-Cayley algebraformal proofCoq

Mathematics Subject Classification ID

Clifford algebras, spinors (15A66) Quadratic spaces; Clifford algebras (11E88)

Related Items (max. 100)

Formalizing geometric algebra in Lean ⋮ An extended implementation framework for geometric algebra operations on systems of coordinate frames of arbitrary signature ⋮ Formalizing basic quaternionic analysis ⋮ Computational aspects of geometric algebra products of two homogeneous multivectors ⋮ A geometric algebra implementation using binary tree ⋮ Garamon: a geometric algebra library generator ⋮ A low-memory time-efficient implementation of outermorphisms for higher-dimensional geometric algebras ⋮ Formalization of geometric algebra in HOL Light

Uses Software

• CLIFFORD
• CLUCalc
• Coq
• Gaalop
• Isabelle
• SymPy
• ML
• Why3
• Mizar
• Gaigen
• GluCat
• HOL
• HOL Light
• WhyML
• GAviewer
• GABLE
• Versor
• Clados
• GAlgebra
• GMac

Cites Work

• Solving some quadratic Diophantine equations with Clifford algebra
• Factorization of Lipschitzian elements
• Interactive 3D space group visualization with CLUCalc and the Clifford geometric algebra description of space groups.
• Interactive theorem proving and program development. Coq'Art: the calculus of inductive constructions. Foreword by Gérard Huet and Christine Paulin-Mohring.
• Foundations of geometric algebra computing.
• Multivector differential calculus
• Boosted surfaces: synthesis of meshes using point pair generators as curvature operators in the 3D conformal model
• Isabelle. A generic theorem prover
• Automated short proof generation for projective geometric theorems with Cayley and bracket algebras. I: Incidence geometry.
• Efficient Algorithms for Factorization and Join of Blades
• A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projective Geometry
• Certified Computer Algebra on Top of an Interactive Theorem Prover
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Implementing geometric algebra products with binary trees