How do I simply express a canonical basis for G4 using Symbolics.jl

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I am fumbling my way through learning basic Geometric Algebra. I want to bootstrap my understanding of using Symbolics.jl at the same time. I have some dumb questions about the mathematics, and usage of the Symbolics package.

If anyone knows a more appropriate forum - please advise…

I’m using MacDonald’s A survey of geometric algebra and geometric calculus as one starting point. I’m aware of Grassman.jl - but I don’t want to drown.

I’d like to be able to generate variables to represent the canonical basis vectors as shown in the table. First step - just properly declared Symbolics variables, looking like nice math. I want to enjoy the result :slight_smile:

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  1. I suppose I would really like an expression that would generate a zero-based array of length 5, containing the basis of vectors of order 0…4. as per the table.
  2. What is the formal name for this kind of sub-setting? I can’t look it up without the name.
  3. I’d like subscripts to work so that G4[1,1] gives e0
  4. What LaTeX expressions should I use to get nice R and G for Reals and Geometrics in Pluto?
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Someone could definitely make this. No one has though.

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I was worried I was asking a silly question :slight_smile:
How hard would it be to do? Is there anything like this I can look at to learn how to do it?