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Fix IsFlagTransitiveGeometry for rank >= 4 - #59

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mh/fix-flag-transitivity
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The Buekenhout-Hermand criterion must hold for every set of types J with |J| >= 3, but only the suffixes {k..n} were checked. For rank 4 this skipped {1,2,3}, {1,2,4} and {1,3,4}, so some coset incidence systems with several orbits on flags were reported as flag-transitive.

Check all such J, with the minimal type of J as the distinguished one.

Fixes #57

Assisted-by: Claude Code (Opus 5.5)

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 53.75%. Comparing base (b5c0d01) to head (93fc1a5).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files
@@            Coverage Diff             @@
##           master      #59      +/-   ##
==========================================
+ Coverage   53.55%   53.75%   +0.20%     
==========================================
  Files          34       34              
  Lines       17059    17066       +7     
==========================================
+ Hits         9136     9174      +38     
+ Misses       7923     7892      -31     

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The Buekenhout-Hermand criterion must hold for every set of types J
with |J| >= 3, but only the suffixes {k..n} were checked. For rank 4
this skipped {1,2,3}, {1,2,4} and {1,3,4}, so some coset incidence
systems with several orbits on flags were reported as flag-transitive.

Check all such J, with the minimal type of J as the distinguished one.

Fixes #57

Assisted-by: Claude Code (Opus 5.5)
@fingolfin
fingolfin force-pushed the mh/fix-flag-transitivity branch from d3264da to 465300d Compare October 1, 2026 23:53
GAP does not document which point of FactorCosetAction corresponds to
the subgroup itself. Build the action from an explicit transversal and
look the trivial coset up instead.

Also add a flag-transitive rank-4 case to the regression test, so a
method that always answers false would fail it.

Assisted-by: Claude Code (Fable 5.1)

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Error in Flag Transitivity

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