Jaa/is nilpotent

[JohnAAbbott]

Usefully faster implementation of is_nilpotent(::ResElem), but it is longer...

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 88.01%. Comparing base (fc77b13) to head (956abae).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1974      +/-   ##
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+ Coverage   87.98%   88.01%   +0.02%     
==========================================
  Files          98       98              
  Lines       36063    36024      -39     
==========================================
- Hits        31730    31705      -25     
+ Misses       4333     4319      -14     

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[JohnAAbbott]

The new code (or most of it) has been moved into AbstractAlgebra.

[JohnAAbbott]

Bother! This PR will work only with the revised AA (see PR 1933 there)

[JohnAAbbott]

I am wondering whether all tests related to is_nilpotent should be moved into AbstractAlgebra since the implementation now resides there. The distinction between what AbstractAlgebra handles and what Nemo handles is not entirely clear to me.
Maybe some tests need to be duplicated? If I load the package AbstractAlgebra, there is already a function to create residue_ring(ZZ,720); but if I load Nemo (or all of Oscar) as well then residue_ring(ZZ,720) calls a different function, presumably using a different interna; representation. So probably the tests should be made both in the AbstractAlgebra tests and in the Nemo tests.

[fingolfin]

To summarize what I explained earlier in my office: ideally as much of this testing as possible is done in generic "ring conformance tests" which then can be applied to all ring types we define in AA, Nemo, Hecke, Oscar, or elsewhere. In some cases one may still wish to have additional tests to e.g. cover certain corner cases or otherwise specific quirks of an implementation, these then of course should go into the respective package.

From that perspective the tests in here are not very special, and could just be dropped here.

[JohnAAbbott]

Hoping this is now fully complete. The main implementations of is_unit and is_nilpotent for quotient rings of ZZ are now in AbstractAlgebra, but we do some tests here because there are new specialized implementations of quotient rings of ZZ.