Fix RingGeneralMappingByImages for non-SCRing

[fingolfin]

A filter was computed but not used. The filter that was used instead always implied IsSCRingGeneralMappingByImagesDefaultRep which is too broad. As a result, inappropriate methods were applied to some ring homomorphisms.

Also add an example for using RingByStructureConstants.

---

Motivated by a report by Stefan Witzel on the GAP Forum. He wanted to do this:

R := ZmodnZ(9);
S := ZmodnZ(3);
RingHomomorphismByImages(R,S,[One(R)],[One(S)]);

# or:
RingHomomorphismByImages(S,S,[One(S)],[One(S)]);

# or:
RingHomomorphismByImages(Integers,Integers,[1],[1]);

but in all cases got errors of the form

Error, Record Element: '<rec>.moduli' must have an assigned value

This PR does not include a test case, because the example still error, but now with a "no method found" error:

gap> RingHomomorphismByImages(Integers,Integers,[1],[1]);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `GeneratorsOfNearAdditiveGroup' on 1 arguments
*[1] GeneratorsOfAdditiveGroup( elms )
   @ /Users/mhorn/Projekte/GAP/gap/lib/mapphomo.gi:717
 [2] PreImagesSet( map, Range( map ) )
   @ /Users/mhorn/Projekte/GAP/gap/lib/mapping.gi:1154
 [3] PreImagesRange( map )
   @ /Users/mhorn/Projekte/GAP/gap/lib/mapping.gi:574
 [4] IsMapping( hom )
   @ /Users/mhorn/Projekte/GAP/gap/lib/ringhom.gi:86
<function "RingHomomorphismByImages">( <arguments> )
 called from read-eval loop at *stdin*:3
type 'quit;' to quit to outer loop
brk>

While one can solve that one by doing SetGeneratorsOfAdditiveGroup(Integers, [1]);, one just runs into the next "method not found". Similar for the finite rings R, S, where one gets a little bit farther, but not much.

So in the end, this is simply a missing feature, which is not great, but at least explicable.

A workaround can be to use rings created via RingByStructureConstants, for those more functionality exists:

gap> T:= EmptySCTable( 1, 0 );;
gap> SetEntrySCTable( T, 1, 1, [ 1, 1 ] );
gap> R:=RingByStructureConstants([9], T);
<ring with 1 generator>
gap> S:=RingByStructureConstants([3], T);
<ring with 1 generator>
gap> hom := RingHomomorphismByImages(R,S,[One(R)],[One(S)]);
[ r.1 ] -> [ r.1 ]
gap> AsSet(Kernel(hom));
[ 0*r.1, 3*r.1, 6*r.1 ]

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 78.89%. Comparing base (e94091c) to head (14624a0).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6418      +/-   ##
==========================================
- Coverage   78.89%   78.89%   -0.01%     
==========================================
  Files         685      685              
  Lines      293554   293551       -3     
  Branches     8672     8672              
==========================================
- Hits       231592   231586       -6     
  Misses      60156    60156              
- Partials     1806     1809       +3     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.