chakravala / chakravala/Grassmann.jl
Differential forms, chain rule, and automatic differentiation with mixedbasis
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- Julia
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Description
Hi @chakravala,
In your JuliaCon paper, I noticed the statement "Mixed-symmetry algebra with `Leibniz.jl` and `Grassmann.jl`, having the geometric algebraic product chain rule, yields automatic differ- entiation and...", and I found a related simple example in the `README.md` file, section `"Differential forms and Leibniz tangent algebra"`.
Would you mind providing one or two concrete examples on symbolic differentiation using `Grassmann.jl`? For example, with respect to a rotor/versor, or a bivector.
I'm thinking that the key part is about a proper setup of a `@mixedbasis tangent ...`. Am I right?
I'm reading Chapter 8 of the book "Geometric Algebra for Computer Science", but there are just a few examples of basic functions. I would like to apply vector/multivector differentiation on some more functions, and verify my results.
I'm trying to differentiate a function like `\sum_i weight_i || V Bivector_0 /V \wedge v_i ||^2` with respect to the versor `V`.
Thank you!
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