Generic constructor fails for Signature "-+"

[chakravala]

Generic constructor fails for Signature "-+"

[chakravala]

You are mistaken, the geometric product works for all the algebras

julia> using Grassmann

julia> @basis S"-+"
(⟨-+⟩, v, v₁, v₂, v₁₂)

julia> v1*v2
v₁₂

julia> @basis S"-++"
(⟨-++⟩, v, v₁, v₂, v₃, v₁₂, v₁₃, v₂₃, v₁₂₃)

julia> v1*v2
v₁₂

that version of the constructor relies on V"..." which defers to either D"..." or S"..." and for the input value of -+ and -++ the V"..." constructor selects D"..."

Look closely at the error you posted ⟨-,++⟩ is the vector space, which is what you get with

julia> D"-++"
⟨-,++⟩

julia> S"-++"
⟨-++⟩

This is merely an issue with the default generic constructor of DirectSum and has nothing to do with Grassmann package. In an ambiguity, a specific constructor must be used.

[karlwessel]

Ah, I see! Is there some documentation on the difference between the D"-++" and the S"-++" constructor?

[chakravala]

No, it's not documented yet and there are going to be more variations coming into existence.

D is for DiagonalForm and S for Signature type.. however more types are coming

Therefore, it's still an open problem. However, the constructor issue is not my primary concern right now, although I have been aware of it already. This package is still going to change a lot before I take another look at the generic constructor issue.

[karlwessel]

Alright, knowing that I just have to explicitly use S"-+" instead of V"-+" works for me.

Thanks for the quick clarification!