Grassmann.jl

⟨Grassmann-Clifford-Hodge⟩ multilinear differential geometric algebra

The Grassmann.jl package provides tools for computations based on multi-linear algebra and spin groups using the extended geometric algebra known as Grassmann-Clifford-Hodge algebra. Algebra operations include exterior, regressive, inner, and geometric, along with the Hodge star and boundary operators. Code generation enables concise usage of the algebra syntax. 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. The design is based on TensorAlgebra{V} abstract type interoperability from AbstractTensors.jl with a $\mathbb{K}$-module type parameter $V$ from DirectSum.jl. Abstract vector space type operations happen at compile-time, resulting in a differential geometric algebra of multivector forms.

• TensorAlgebra{V} design and code generation
• • Direct sum parametric type polymorphism
  • Higher dimensions with SparseBasis and ExtendedBasis
  • Interoperability for TensorAlgebra{V}
• Grassmann elements and geometric algebra Λ(V)
• • Grassmann.jl API design overview
  • Grassmann-Hodge complement
  • Symbolic coefficients by declaring algebra
• Grassmann.jl videos
• Grassmann.jl Library
• References

This Grassmann package for the Julia language was created by github.com/chakravala for mathematics and computer algebra research with differential geometric algebras. These projects and repositories were started entirely independently and are available as free software to help spread the ideas to a wider audience. Please consider donating to show your thanks and appreciation to this project at liberapay, GitHub Sponsors, Patreon, Tidelift, Bandcamp or contribute (documentation, tests, examples) in the repositories.