Implement methods like sqrt for pure scalar multivectors

[karlwessel]

I'm trying to implement sqrt for pure scalar multivectors (so for Basis{V, 0, 0}, MValue{V, 0, v, T} and SValue{V, 0, v, T}), but I have a hard time to find the right syntax for the methods type declaration. It is easy for Basis:

sqrt(t::Basis{B, 0, 0x0000000000000000}) where {B} = 1

But I'm not sure how to define the type of MValue and SValue for scalar basis v. I can get v into the scope and write

julia> basis"2"
(⟨++⟩, v, v₁, v₂, v₁₂)

julia> sqrt(x::SValue{B, 0, v, T}) where {B, T} = sqrt(x.v)
sqrt (generic function with 23 methods)

julia> sqrt(13*v)
3.605551275463989

but that seems ugly and does not make sure that v matches the scalar basis for any B.
I guess I have to use the function indexbasis but I'm not sure about its syntax.

So this is more like a question than an actual issue (except maybe a documentation issue).

Btw: What is the difference between SValue and MValue?

PS: I hope that its clear, but I'm saying it anyway: I really like this package, thanks for all the work you are putting into it.

[chakravala]

This is how to define sqrt for grade 0 values (and indexbasis would not be used for that):

Base.sqrt(x::SValue{V,0}) where V = sqrt(value(x))*basis(x)

The difference between MValue and SValue is that M stands for mutable and S for static.

[karlwessel]

Ah, right, since grade 0 already defines the scalar base vector I don't have to check for that! Thanks!

[chakravala]

More generally, you can define this method for Basis,SValue,MValue simultaneously with TensorTerm

Base.sqrt(x::T) where T<:TensorTerm{V,0} where V = sqrt(value(x))*basis(x)

since TensorTerm has Basis,SValue,MValue as a subtypes

julia> subtypes(TensorTerm{ℝ^2,0})
3-element Array{Any,1}:
 Basis{⟨++⟩,0,B} where B           
 MValue{⟨++⟩,0,B,T} where T where B
 SValue{⟨++⟩,0,B,T} where T where B