Grassmann.jl VS TensorOperations.jl

Here's how to do it with Grassmann.jl

Surprise announcement: the next version of Grassmann.jl has a new algebra type SimplexComplex{V,B,T} (yes, that's right SimplexComplex) which is a wrapper for Julia's native Base.Complex{T} type. This allows you to work with the performance of the base language complex numbers while retaining the Grassmann algebra interface and additional products. The new type is not limited to only regular complex numbers, it supports the creation of a SimplexComplex using any basis element B by simply taking the sum of a scalar with that basis element. ```Julia julia> using Grassmann

I still have never been able to post my paper about my Grassmann.jl geometric algebra foundations research on arxiv.

https://github.com/chakravala/Grassmann.jl

Seems like a useless overrated website.

I was able to post my article on my own website instead.

Arxiv is really a useless website.

This article is really about geometric algebra, check out my geometric algebra software https://github.com/chakravala/Grassmann.jl

https://github.com/chakravala/Grassmann.jl

In the future, geometric algebra will likely be part of everything we do, but it is still very unknown as of now.

I heart your Grassman gradient vector field representations: https://github.com/chakravala/Grassmann.jl. They, heh heh, point the way toward representing aspects of physics and math that should be used far more frequently than they are now. They display the quirks that you could never apprehend looking at an equation. Your representations could eviscerate the representations of data base on paper-like metaphors.

Sadly our leaders, the John Baez and Scott Aronson and people like that, prefer to think in Euler notation and WordPress posts. As Kurt Vonnegut said: So it goes.

The world of representation of difficult concepts using interactive 3D and elegant code is still in its infancy. You are not yet at the ground floor of the construction of a future elegant structure. You - and a few others - are in at the second basement.

Fortunately, the only way out is to look up!

Sometimes broadcasting feels like magic to me. It just works more often than not even when I am confused with the dimensions. If you do a lot of Tensor stuff it's also worth checking out Einstein notation (https://github.com/Jutho/TensorOperations.jl)

There are some libraries and macros for Einstein notation and related ideas, like TensorOperations.jl in Julia, einsum in numpy which someone already mentioned, and some small-scale/research languages like Diderot and Egison. In the mainstream, I guess languages generally use for loops or list comprehensions and try to recover vectorisation from that after the fact, but don’t guarantee it. Those that do make guarantees tend to use combinators that are matrixwise/function-level. I admit I pretty much categorically prefer the latter so I’m not as aware of the state of this as I’d like to be able to help.