Add vector_space_dim for matrix spaces

[emikelsons]

• Added vector_space_dim for matrix spaces and matrix rings over fields,
• Expanded the documentation for vector_space_dim slightly.

This partially has the PR oscar-system/Oscar.jl#4967 and issue oscar-system/Oscar.jl#4606 in mind.
@fingolfin

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 88.34%. Comparing base (3abc3d0) to head (19f15bd).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2109      +/-   ##
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- Coverage   88.36%   88.34%   -0.02%     
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  Files         126      126              
  Lines       31668    31676       +8     
==========================================
+ Hits        27982    27984       +2     
- Misses       3686     3692       +6     

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[fingolfin]

That doesn't fit together with the docstring which claim that this is the dimension over base_ring(F) where F is the field given as input.

But this will almost always be wrong here, as base_ring(F) != F basically always holds.

So either we don't define this here; or we have to reconsider how a user can ascertain the "base field" for a "vector space" -- say by introducing a dedicated function for this.

@thofma @fieker you have implemented algebras in Hecke; what is the convention for getting the field over which the algebra is defined? Same for e.g. field extensions I guess...

[emikelsons]

I could also rewrite the documentation, i.e., I could say that it will be over base_ring(F), when base_ring(F) applies.

[thofma]

So either we don't define this here; or we have to reconsider how a user can ascertain the "base field" for a "vector space" -- say by introducing a dedicated function for this.

I think we should not define it.

@thofma @fieker you have implemented algebras in Hecke; what is the convention for getting the field over which the algebra is defined? Same for e.g. field extensions I guess...

The infamous base_ring. (But I was thinking about changing it to base_field).