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Algebra |
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Authors: Michael Reed
The Grassmann.jl package provides tools for computations based on multilinear algebra and spin groups using the extended geometric algebra known as Leibniz-Grassmann-Clifford-Hestenes algebra. Combinatorial products include exterior, regressive, inner, and geometric; along with the Hodge star, adjoint, reversal, and boundary operators. The kernelized operations are built up from composite sparse tensor products and Hodge duality, with high dimensional support for up to 62 indices using staged caching and pre-compilation. Code generation enables concise yet highly extensible definitions. DirectSum.jl multivector parametric type polymorphism is based on tangent vector spaces and conformal projective geometry. Additionally, the universal interoperability between different sub-algebras is enabled by AbstractTensors.jl, on which the type system is built.
Comments: 6 Pages. (2019)
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[v1] 2025-05-15 20:35:33
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