Differential geometric algebra foundations using Grassmann.jl

Greetings, recently I have been working on a paper along with various packages in the Julia language to try to figure out the best foundations to unify differential geometry with geometric algebra.

This work is still in progress and not complete yet, but I’d like to open it up for discussion with enthusiasts.

This was also recently presented at JuliaCon 2019:

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Specifically, I intend on discussing the foundational aspects of differential geometry and geometric algebra. In my paper, I have a few new conventions for notation and definitions that may be slightly different from what other experienced users of GA know.

While Grassmann.jl has a fairly complete implementation, the implementation of Leibniz.jl is still a prototype and I haven’t had time to make it full featured yet. I’d like to open the discussion about this approach to the foundations already. Please let me know if there is some aspect you would like to discuss about how I am setting up mathematical foundations.


Hi Chakravala,
It appears the link to Leibniz.jl in this post is misspelled, it generates a 404 error.


Differential geometric algebra JuliaCon 2019 paper has been finalized and documentation updated:


YouTube DropBox BiVector

v0.3.3 has been tagged https://github.com/chakravala/Grassmann.jl

Since it is halloween tonight, try out the new skeleton, betti, and χ methods for Morse theory.


Documentation website https://grassmann.crucialflow.com has now been created for v0.4.0 release:

Docs Stable Docs Dev Gitter BiVector

New features include vastly improved performance for low dimensional algebras (for ℝ^5 and less) and vastly improved performance of exp function for various special cases, +(many other improvements).


New overview video for differential geometric algebra

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