As shown at the end of this post, I recently ported pga3d.cpp (the bivector.net C++ reference implementation of projective geometric algebra) to Julia because bivector.net does not currently offer a Julia reference implementation. Before I offer my proposed Julia reference implementation of projecti…

If I were able to edit the title of this post, I would change it to “A fast and pretty reference implementation of projective geometric algebra”, adding the word “reference” to indicate it demonstrates functionality. However, there clearly is an interest in the people who were kind enough to review …

[image] g2g: Instead, Vector{Float32} is the data type for all the multivectors. Changing the dimension of the space (e.g., 2D, 3D, 4D, 5D) changes the length of the Vector{Float32} and changes some of the overloaded operators but does not change any of the geometric algebra equations General…

You might have seen some GA in Julia on Github? Perhaps GitHub - chakravala/Grassmann.jl: ⟨Leibniz-Grassmann-Clifford⟩ differential geometric algebra / multivector simplicial complex ?

I did look at a few Julia geometric algebra packages but my primary interest is in applications and I didn’t see a lot of geometric algebra applications that used a Julia geometric algebra package. In contrast, Steven De Keninck has an impressive collection of geometric algebra applications at https…

[image] stevengj: you almost always want to use StaticArrays.jl for performance reasons I don’t know yet if I’ll encounter an application that requires a lot of multivectors. The projective geometric algebra applications I’ve seen so far are very short. One could reasonably argue that the pr…

[image] g2g: Base.:*(a::Vector{Float32},b::Vector{Float32}) This is type-piracy. I will let you read the docs on why it is considered poor practice

[image] oxinabox: This is type-piracy. Thanks for the feedback. Is that operator overloading still considered poor practice even when the non-overloaded operation is not allowed? For example, a * b does not compile but a .* b does.

This case, where you define a method such that it used to be an error and now it does something sensible, is considered a less bad form of piracy; vs change changing the behavior of something that currently works to make it work differently (i.e. monkey patching a special case). I sometimes call th…

[image] oxinabox: I sometimes call this case, misdemeanor type piracy Expecting some sort of warning or error message, I successfully ran the following code in the same Julia REPL session that successfully ran pga.jl, the proposed projective geometric algebra implementation. # base_conflict.…

Imagine if there were a norm that packages could overload Base.:*(a::Vector{Float32},b::Vector{Float32}) whenever they wanted. So you had PkgA: *(a::V, b::V) = "a string" and PkgB: *(a::V, b::V) = 1 Then if you did using PkgA function foo(a::V, b::V) a * b end using PkgB foo() Using PkgB wou…

[image] g2g: When I repeatedly alternate between running each of them, they both appear to run with their own unique overload of the * operator, as if the operator overload in Base is not a shared resource. That’s weird. That is not what i would expect to happen at all.

A fast reference implementation of a pretty projective geometric algebra

General Usage

pdeffebach December 9, 2022, 9:00pm 13

OP did *(a::V, b::V) not import Base; Base.*(a::V, b::V), which is why they are seeing the results they are.

I guess this isn’t type piracy per-se, but it does make code not very readable.

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A fast reference implementation of a pretty projective geometric algebra

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