Split more methods for MatrixElem into seperate ones for MatElem and MatRingElem

[JohnAAbbott]

Removed is_square(::MatRingElem to see what breaks.

[fingolfin]

One of the first breakages is in function Base.inv(M::MatrixElem{T}) where {T <: FieldElement} -> time to untangle MatrixElem some more.

[JohnAAbbott]

I'm puzzled about the state of this PR: there seem to be many modifications which I certainly did not make.

[codecov]

Codecov Report

❌ Patch coverage is 65.00000% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.11%. Comparing base (9be424a) to head (2afdbf5).
⚠️ Report is 27 commits behind head on master.

Files with missing lines	Patch %	Lines
src/MatRing.jl	44.00%	14 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2325      +/-   ##
==========================================
- Coverage   88.15%   88.11%   -0.04%     
==========================================
  Files         126      128       +2     
  Lines       32093    32879     +786     
==========================================
+ Hits        28290    28972     +682     
- Misses       3803     3907     +104     

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[JohnAAbbott]

QUESTION
Of those functions which I split into two, several are not called with MatRingElem arguments in the tests. Which ones do we want to be able to apply directly to a MatRingElem value?
The functions changed are:

• inv, pseudo_inv, is_invertible, is_invertible_with_inverse
• charpoly, is_nilpotent
• is_symmetric
• tr, hessenberg, hessenberg!, is_hessenberg

The first two groups probably make sense; I am less convinced about the last two groups.

I did also introduce a (buggy?) version of charpoly_hessenberg! for MatRingElem, but since I do not know what it should do, it is likely incorrect. Does anyone know if it is really useful to have charpoly_hessenberg! operate on MatRingElem?

[lgoettgens]

If I see correctly, this line is the only breaking part of the PR. Thus, IMO, it would make sense to split this PR into two as the rest of it can be merged right now

[fingolfin]

@JohnAAbbott let's work on this together this afternoon, maybe factor out the non-breaking parts and merge them right away?

[JohnAAbbott]

I have reinstated the definition of is_square, so this PR should no longer trigger the "breaking change" alarm!

[lgoettgens]

I think in previous similar PRs these split off methods for MatRingElem were always put in the file src/MatRing.jl. Could you please do the same for the changes in this PR?

[JohnAAbbott]

Moved

[lgoettgens]

Thanks!