Add Embedding and Projection for direct sums of rings

[cdwensley]

These small additions were originally in PR #6618 but, as advised, have been moved to a separate PR.
Having added Embedding and Projection for direct sums of algebras, it seemed sensible to provide the same for rings since DirectSum sets up an info record with empty info.embeddings and info.projections.

The first method for DirectSumOp in ringsc.gi initialises info.first as [1], but the second method (which gets called in the example used here) uses [0]. (That was why [0] was used in the methods for algebras.) To fix this inconsistency, the first method has been changed to [0]. Whether this method is used anywhere, and whether some test now fails, remains to be seen!

[codecov]

Codecov Report

❌ Patch coverage is 93.33333% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.65%. Comparing base (678f3a8) to head (7531248).
⚠️ Report is 45 commits behind head on master.

Files with missing lines	Patch %	Lines
lib/ringsc.gi	93.18%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6702      +/-   ##
==========================================
+ Coverage   79.36%   79.65%   +0.28%     
==========================================
  Files         683      684       +1     
  Lines      295286   295641     +355     
  Branches     8646     8655       +9     
==========================================
+ Hits       234366   235485    +1119     
+ Misses      59106    58329     -777     
- Partials     1814     1827      +13     

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[fingolfin]

Thanks for splitting this off. The inline comments have the details on the code; two general points here.

Tests. This PR has no test file, only the two manual examples, and both use whole small rings, where everything works. Please add tst/testinstall/ring-dsum.tst (or a similar name) which also covers a sum of subrings, a sum of three rings, and a check like ForAll( R, x -> ( x ^ Embedding( D, i ) ) ^ Projection( D, i ) = x ). As in #6618, let Test( file, rec( rewriteToFile := file ) ) write the expected output, so that the line breaks are right.

Your question about first. Changing the generic method from [1] to [0] breaks nothing: no code in GAP itself, and none in the packages I have installed, reads DirectSumInfo or its first component, and all checks here pass. Making the two methods agree is good. It does not make the new methods work for such sums, though; see the inline comment on the Embedding method.

AI disclosure: I used Claude Code (Opus 5.5) to review this PR. It built the branch, ran the examples quoted in the comments, and drafted the comments.

[cdwensley]

Note: the direct sum of three rings A,B,C gives info.rings = [A,B,C] and not [(A(+)B),C] as with algebras.

[fingolfin]

This is looking pretty good now. We could merge it, but perhaps you'd be inclined to add the subring test (I made a "change suggestion" you could apply with a click). Also some other very minor nits (not important)

[cdwensley]

The extended test file runs well for me. Sorry about the "#A's - should have noticed that. All looks good now.