NiceGeneratorsAn (Odd and Even): Improve documentation, rename variables, restructure code, add tests

[TWiedemann]

The same changes as in #369 but for NiceGeneratorsAnOdd.

In addition, the random search for cycles of lengths 2, 3, and n in NiceGeneratorsAnOdd and NiceGeneratorsSn is moved to a new function RECOG.FindCycles.

Issue #381 is not resolved by this PR, but it is slightly related.

Update 19.02.2026: Added the same changes for NiceGeneratorsAnEven and updated RECOG.FindCycles to also accept n-1.

[codecov]

Codecov Report

❌ Patch coverage is 98.27586% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 72.67%. Comparing base (1d173f8) to head (5d49fbf).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
gap/perm/giant.gi	98.27%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #382      +/-   ##
==========================================
+ Coverage   69.19%   72.67%   +3.48%     
==========================================
  Files          43       43              
  Lines       18403    18400       -3     
==========================================
+ Hits        12734    13373     +639     
+ Misses       5669     5027     -642     

Files with missing lines	Coverage Δ
gap/perm/giant.gi	74.33% <98.27%> (+18.75%)	⬆️

... and 6 files with indirect coverage changes

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[fingolfin]

If you write "does not resolve XYZ" then GitHub still parses this as "resolves XYZ" and will thus close that issue if this PR is merged.

You need to rephrase it, e.g. "does no resolve issue XYZ" or "XYZ is not resolved by this" or so.

[fingolfin]

Thanks, looks pretty good! Some minor nitpicks

[TWiedemann]

If you write "does not resolve XYZ" then GitHub still parses this as "resolves XYZ" and will thus close that issue if this PR is merged.

You need to rephrase it, e.g. "does no resolve issue XYZ" or "XYZ is not resolved by this" or so.

Done.

I commited your suggestions. Some checks fail which are apparently related to #362.

[TWiedemann]

I changed the test "PSL(2,23)" in ri.possibleNearlySimple as discussed. The CI check still fails, but I cannot reproduce this failure locally. Instead, I get an error in another line, but only on the first run of the test:

gap> Test("MoreNaming.tst");
########> Diff in MoreNaming.tst:941
# Input is:
ri := RecogniseClassical(maxes_cgo_plus_8_5[1]);;
# Expected output:
# But found:
#I  Have 38644 points.
########
false
gap> Test("MoreNaming.tst");
true
gap> Test("MoreNaming.tst");
true
gap> Test("MoreNaming.tst");
true
gap> Test("MoreNaming.tst");
true
gap> Test("MoreNaming.tst");
true

[TWiedemann]

Added the same changes for NiceGeneratorsAnEven and updated RECOG.FindCycles to also accept n-1.

The CI checks now succeed (without any of my doing). Locally, Test("MoreNaming.tst"); still produces the same error as before:

gap> Test("MoreNaming.tst");
########> Diff in MoreNaming.tst:941
# Input is:
ri := RecogniseClassical(maxes_cgo_plus_8_5[1]);;
# Expected output:
# But found:
#I  Have 38644 points.
########
false                               
gap> Test("MoreNaming.tst");
true                                
gap> Test("MoreNaming.tst");
true 

I think we can merge this now, but I am not sure about the error above that appears only locally on my machine.