moble
commented
2 years ago Not solving the problem, but hopefully some useful info. Technically, this is documented behavior — though I agree it's surprising and undesirable.
Note that typeof(e1), etc., is UnionAll, which is not a type we want to see very often. In any case, we find the specific wedge function that gets called here, and it does indeed state that "indices must be in acending order". That function just calls the * function directly above it, which returns Nothing if the indices are not in ascending order, which is why you see what you see.
What you've done here seems like one of the most natural things you could want to do with a GA package, so it seems like room for improvement. However, also note that multiplying these basis elements by a number gives you more useful things:
julia> 1e₃ ∧ 1e₂
-1e₂₃Also note that e1, etc., are not the handiest names for these variables, since 1e1 is parsed as 10.0, 1e2 as 100.0, etc. So you'd have to say 1*e1 — but * has lower precedence than ∧, so you'd have to write this as
julia> (1*e3) ∧ (1*e2)
-1e₂₃
peeterjoot
Ran:
using Multivectors;
@generate_basis("+++", true) # generate blades for euclidean 3D-space
e1 = e₁ e2 = e₂ e3 = e₃
e1 ∧ e2 e2 ∧ e3 e3 ∧ e1 e1 ∧ e3
This produced:
julia> using Multivectors;
julia> @generate_basis("+++", true) # generate blades for euclidean 3D-space
julia> e1 = e₁ e₁
julia> e2 = e₂ e₂
julia> e3 = e₃ e₃
julia> e1 ∧ e2 e₁₂
julia> e2 ∧ e3 e₂₃
julia> e3 ∧ e1 Nothing
julia> e1 ∧ e3 e₁₃
I expected:
-e₁₃
Not 'Nothing' for e3 ∧ e1.