Unify eigenvalue interface

[joschmitt]

This is one half of my proposal to unify the eigenvalue interface throughout OSCAR (oscar-system/Oscar.jl#2017). The other half is thofma/Hecke.jl#1344 .

The changes are:

• Consistently use the name eigvals and introduce the alias eigenvalues (in consistency with LinearAlgebra).
• If a field is supplied in which the eigenvalues are supposed to be computed, this comes first in the signature (in consistency with e.g. factor(ZZ, QQ(2))). I assume this change constitutes a breaking change.
• The return type is a dictionary with key-value-pairs the eigenvalue and its multiplicity (in consistency with other things returning multiplicities like factor, but not consistent with eigvals from LinearAlgebra). Another breaking change.

This is what seems to me to be "the most consistent" right now. I don't insist on any of these changes and I am happy to change things back/differently.

EDIT: This list is not up to date anymore. See oscar-system/Oscar.jl#2017 (comment) for what was decided.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (3572e5d) 84.07% compared to head (322234b) 84.10%.
Report is 3 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1611      +/-   ##
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+ Coverage   84.07%   84.10%   +0.03%     
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  Files          93       93              
  Lines       36769    36826      +57     
==========================================
+ Hits        30915    30974      +59     
+ Misses       5854     5852       -2     

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[lgoettgens]

Thanks for taking care of this. Two comments:

1. The generic implementation should move from Hecke to AA.
2. I think that eigenvalues fits more our general naming scheme than eigvalues. There is already a list in AA of things that we aliased from LinearAlgebra to our own names, so that would be no contradicting point to naming it eigenvalues

[joschmitt]

eigenvalues would also go better with eigenspaces in Hecke. (Although it doesn't really matter as long as both options exist.) Other opinions?

[lgoettgens]

What does this function even do? I am asking as we didn't talk about it today.

[joschmitt]

According to the doc string, it computes eigenvalues, but the function only works if the matrix has only "simple eigenvalues" (I assume simple = multiplicity 1).

[joschmitt]

I didn't find a better place to put this. In Aliases.jl it is too late.

[lgoettgens]

This looks good now, and just waits for the next time we do a breaking release.