Remove is_square(::MatRingElem); to apply to MatRingElem work with underlying matrix

[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 63.63636% with 16 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.03%. Comparing base (9be424a) to head (7456380).
⚠️ Report is 9 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Matrix.jl	63.63%	16 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2325      +/-   ##
==========================================
- Coverage   88.15%   88.03%   -0.12%     
==========================================
  Files         126      126              
  Lines       32093    32139      +46     
==========================================
+ Hits        28290    28295       +5     
- Misses       3803     3844      +41     

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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