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GAP error on image(action_homomorphism(block_system)) #4756

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@lgoettgens

Description

@lgoettgens

Describe the bug
Unexpected GAP error, see below

To Reproduce
All smaller examples that I tried didn't run into this issue.
This was run on the branch of #4753, as otherwise one encounters #4752 before this issue.

julia> cube = permutation_group(48, [gen_up, gen_left, gen_front, gen_right, gen_back, gen_down])
Permutation group of degree 48

julia> gen_up    = @perm 48 ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19);

julia> gen_left  = @perm 48 ( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35);

julia> gen_front = @perm 48 (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11);

julia> gen_right = @perm 48 (25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24);

julia> gen_back  = @perm 48 (33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27);

julia> gen_down  = @perm 48 (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40);

julia> cube = permutation_group(48, [gen_up, gen_left, gen_front, gen_right, gen_back, gen_down])
Permutation group of degree 48

julia> orbs = orbits(cube)
2-element Vector{Oscar.GSetByElements{PermGroup, Int64}}:
 G-set of cube with seeds [1, 3, 17, 14, 8, 38, 9, 41, 19, 48, 22, 6, 30, 33, 43, 11, 46, 40, 24, 27, 25, 35, 16, 32]
 G-set of cube with seeds [2, 5, 12, 7, 36, 10, 47, 4, 28, 45, 34, 13, 29, 44, 20, 42, 26, 21, 37, 15, 31, 18, 23, 39]

julia> bl = blocks(orbs[1])
G-set of
  permutation group of degree 48
  with seeds [[1, 9, 35], [3, 33, 27], [17, 6, 11], [14, 46, 40], [8, 19, 25], [38, 48, 32], [41, 22, 16], [30, 43, 24]]

julia> h = action_homomorphism(bl)
Group homomorphism
  from permutation group of degree 48
  to Sym(8)

julia> image(h)
ERROR: Error thrown by GAP: Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `LargestMovedPoint' on 1 arguments at /home/lgoe/.julia/artifacts/8db0b2a1c30ae8f18d09d8f93b7cb5b1b359722d/share/gap/lib/methsel2.g:250 called from
<function "HANDLE_METHOD_NOT_FOUND">( <arguments> )
 called from read-eval loop at *defin*:0

Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] ThrowObserver(depth::Int32)
    @ GAP ~/.julia/packages/GAP/bMh5a/src/GAP.jl:101
  [3] _call_gap_func
    @ ~/.julia/packages/GAP/bMh5a/src/ccalls.jl:343 [inlined]
  [4] (::GapObj)(a1::GapObj)
    @ GAP ~/.julia/packages/GAP/bMh5a/src/ccalls.jl:320
  [5] LargestMovedPoint(x::GapObj)
    @ Oscar.GAPWrap ~/code/julia/Oscar.jl/src/GAP/wrappers.jl:282
  [6] _oscar_subgroup(obj::GapObj, G::PermGroup)
    @ Oscar ~/code/julia/Oscar.jl/src/Groups/types.jl:456
  [7] _as_subgroup_bare
    @ ~/code/julia/Oscar.jl/src/Groups/sub.jl:8 [inlined]
  [8] _as_subgroup
    @ ~/code/julia/Oscar.jl/src/Groups/sub.jl:12 [inlined]
  [9] image(f::GAPGroupHomomorphism{PermGroup, PermGroup})
    @ Oscar ~/code/julia/Oscar.jl/src/Groups/homomorphisms.jl:345
 [10] top-level scope
    @ REPL[192]:1

Expected behavior
Return me a subgroup of Sym(8), as one would expect when calling image on a group hom with that codomain.

System (please complete the following information):

julia> Oscar.versioninfo(full=true)
OSCAR version 1.4.0-DEV - #lg/orbit-caching, 3076dc6532 -- 2025-03-21 15:38:07 +0100
  combining:
    AbstractAlgebra.jl   v0.44.10
    GAP.jl               v0.13.1
    Hecke.jl             v0.35.15
    Nemo.jl              v0.49.3
    Polymake.jl          v0.11.28
    Singular.jl          v0.25.2
  building on:
    FLINT_jll                  v300.200.100+0
    GAP_jll                    v400.1400.3+0
    GAP_lib_jll                v400.1400.4+0
    Singular_jll               v404.100.104+0
    libpolymake_julia_jll      v0.13.2+0
    libsingular_julia_jll      v0.47.2+0
    polymake_jll               v400.1300.3+0
    polymake_oscarnumber_jll   v0.3.5+0
See `]st -m` for a full list of dependencies.

Julia Version 1.11.4
Commit 8561cc3d68d (2025-03-10 11:36 UTC)
Build Info:
  Official https://julialang.org/ release

Additional context

This is now indeed due to @mjrodgers recent changes to the G-Sets (as the setup didn't even work before that). I have no idea if it is an issue with the new code, or deep inside of GAP, or dunno.

cc @mjrodgers @fingolfin @ThomasBreuer

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