Compute Solve traits from types as args

[lgoettgens]

My motivation for this is to be able to set a concrete type in the @attr Any call in https://github.com/oscar-system/Oscar.jl/pull/4915/files#diff-88ef12a4e6f091b2cc3dd521d7c8be444dab854cb7aef78f6837778a274315ffR489 (something along the lines of @attr solve_context_type(base_ring_type(M))).

I also copied over the two fallbacks (for ::Any and for ::DataType) over from all of the similar functions like base_ring_type and then removed some obsolete methods.

@joschmitt does this change make sense to you?

[codecov]

Codecov Report

Attention: Patch coverage is 83.33333% with 4 lines in your changes missing coverage. Please review.

Project coverage is 88.36%. Comparing base (cd318ff) to head (4d0126d).

Files with missing lines	Patch %	Lines
src/Solve.jl	83.33%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2101      +/-   ##
==========================================
- Coverage   88.36%   88.36%   -0.01%     
==========================================
  Files         126      126              
  Lines       31656    31660       +4     
==========================================
+ Hits        27974    27975       +1     
- Misses       3682     3685       +3     

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[joschmitt]

I think the idea was that the "best" matrix normal form does not only depend on the type. For example, a zzModRing might be a field in which case the flint RREF (or LU?) should be better than the Howell form. That being said, we never seemed to have followed through with this idea.

@thofma what do you think?

[thofma]

Yes, the idea was to combine it with something like is_known(F, :is_field) and to use RREF in this case (make it a runtime thing). We might have to untangle this somehow, but I don't know how yet. Having one type for all solve contexts (with some flag) won't work, since it needs to be extensible.

[lgoettgens]

Yes, the idea was to combine it with something like is_known(F, :is_field) and to use RREF in this case (make it a runtime thing). We might have to untangle this somehow, but I don't know how yet. Having one type for all solve contexts (with some flag) won't work, since it needs to be extensible.

Hmm, I don't really see how to do that without making inference of all of solving impossible. But I am open to any ideas you might have on the matter