Use type traits in linear solving

[joschmitt]

So far this does not change the functionality. I open this pull request already now to discuss names and the design.

I will add the new Howell form to the system and try to clean up more of the _can_solve... methods in src/Matrix.jl (no promises on this though).

Oh, and this will break Nemo in the current state.

[codecov]

Codecov Report

Attention: Patch coverage is 98.45201% with 5 lines in your changes missing coverage. Please review.

Project coverage is 87.70%. Comparing base (abdcb76) to head (ec35a1e).
Report is 4 commits behind head on master.

Files	Patch %	Lines
src/Solve.jl	98.45%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1738      +/-   ##
==========================================
+ Coverage   87.39%   87.70%   +0.30%     
==========================================
  Files         117      117              
  Lines       29919    30160     +241     
==========================================
+ Hits        26149    26451     +302     
+ Misses       3770     3709      -61     

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[thofma]

https://github.com/Nemocas/AbstractAlgebra.jl/actions/runs/9975920868/job/27580200035?pr=1738 should be working?

[joschmitt]

https://github.com/Nemocas/AbstractAlgebra.jl/actions/runs/9975920868/job/27580200035?pr=1738 should be working?

I don't fully understand what's going on there. An Aqua test in Nemo is failing and I have the impression that it is testing Nemo against the released version of AbstractAlgebra. Then this

WARNING: could not import AbstractAlgebra.howell_form! into Nemo
ERROR: LoadError: UndefVarError: `matrix_normal_form_type` not defined

would be expected.

[lgoettgens]

Nemocas/AbstractAlgebra.jl/actions/runs/9975920868/job/27580200035?pr=1738 should be working?

I don't fully understand what's going on there. An Aqua test in Nemo is failing and I have the impression that it is testing Nemo against the released version of AbstractAlgebra. Then this

WARNING: could not import AbstractAlgebra.howell_form! into Nemo
ERROR: LoadError: UndefVarError: `matrix_normal_form_type` not defined

would be expected.

This is probably due to JuliaTesting/Aqua.jl#292