Analytical-Numerical Implementation of Polyvector Algebra in Julia

Abstract: Geometric algebra is based on the works by Grassmann and Clifford. Its main objects of research are polyvectors (p-vectors) and multivectors. Polyvectors, together with the exterior product, implement the Grassmann algebra, while multivectors with the geometric product implement the Clifford algebra. Multivector algebra generalizes many operations and objects of analytic geometry and differential geometry (e.g., vector and mixed products, normal vectors and binormals, etc.) to the multidimensional case, as well as provides their geometric interpretation. Complex numbers and quaternions are isomorphic to multivectors of a special kind. This paper applies certain ideas of geometric algebra to solve problems that occur in computer geometry. For this purpose, the Grassmann.jl package for Julia is used. © 2022, Pleiades Publishing, Ltd.