Towards knots

[fieker]

When run, the following will produce a nice Gap problem:

using Oscar
Oscar.example("H2.jl")
A = abelian_group(PermGroup, [2,2])
B = [sub(A, [A[1]])[1], sub(A, [A[2]])[1]]
Main.H2_G_QmodZ_mod.H2_G_QmodZ_kern_restriction(A, B)

namely:

julia> Main.H2_G_QmodZ_mod.H2_G_QmodZ_kern_restriction(A, B)
ERROR: AssertionError: GAP.Globals.HasIsWholeFamily(G.X) && GAPWrap.IsWholeFamily(G.X)
Stacktrace:
 [1] quo(G::FPGroup, elements::Vector{FPGroupElem})
   @ Oscar ~/.julia/dev/Oscar/src/Groups/sub.jl:333

using the "/" in Gap directly can compute the quotient...
@fingolfin , @ThomasBreuer ?

[fieker]

a slightly differetn versio produced:

julia> Main.H2_G_QmodZ_mod.H2_G_QmodZ_kern_restriction(G, [x[1] for x = U])
ERROR: Not a known type of group
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] _get_type(G::GAP_jll.GapObj)
   @ Oscar ~/.julia/dev/Oscar/src/Groups/types.jl:395
 [3] quo(G::FPGroup, N::FPGroup)
   @ Oscar ~/.julia/dev/Oscar/src/Groups/sub.jl:408

I think this was obtained by doing quo(k, sub(k, ...)[1]), ie. explicitly using sub first

[fieker]

when playing, one should not try this:

julia> [describe(Main.H2_G_QmodZ_mod.H2_G_QmodZ(transitive_group(8, i))) for i=1:22]
ERROR: Error thrown by GAP: Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `RelatorsOfFpGroup' on 1 arguments at /home/fieker/.julia/artifacts/70f7ea74308ce9d94343b89b97f71ce69490cf51/share/gap/lib/methsel2.g:249 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/dev/GAP/src/GAP.jl:88
  [3] _call_gap_func(func::GAP_jll.GapObj, a1::GAP_jll.GapObj)
    @ GAP ~/.julia/dev/GAP/src/ccalls.jl:258
  [4] call_gap_func_nokw
    @ ~/.julia/dev/GAP/src/ccalls.jl:224 [inlined]
  [5] GapObj
    @ ~/.julia/dev/GAP/src/ccalls.jl:235 [inlined]
  [6] RelatorsOfFpGroup
    @ ~/.julia/dev/Oscar/src/GAP/wrappers.jl:371 [inlined]
  [7] relators(G::FPGroup)
    @ Oscar ~/.julia/dev/Oscar/src/Groups/GAPGroups.jl:1475
  [8] describe(G::FPGroup)
    @ Oscar ~/.julia/dev/Oscar/src/Groups/GAPGroups.jl:1849
  [9] (::var"#65#66")(i::Int64)

[fieker]

(this is from i==1, the group is trivial (order() returns 1, but describe is unhappy)

[ThomasBreuer]

The current situation with quotient groups of finitely presented groups in GAP is as follows.
If G is a full free group or a full finitely presented group (i.e., not a subgroup of this full group) then one can form the quotient of G by the normal closure of a given set of elements of G.
For subgroups of such full groups, GAP either issues an error or returns some object. In the case of subgroups of free groups, a returned object is corrupted, that is why I had added the assertion on the Oscar side. (See also gap-system/gap/issues/4897 for a change that improves this situation.)
In the current example, the subgroup of an f.p. group shall be factored by an empty list, and apparently GAP has some applicable method for that; however, I fear that this is a bug in GAP because this is a method for semigroups. In any case, the object returned by GAP is not a group in the sense of GAP, in particular it cannot be turned into an Oscar group, hence the Not a known type of group error on the Oscar side.

[fingolfin]

Is the file examples/GaloisLattice.jl removed intentionally?

Should we merge this PR now?

[fieker]

On Thu, Jan 19, 2023 at 02:42:45PM -0800, Max Horn wrote: Is the file `examples/GaloisLattice.jl` removed intentionally?

Yes

Should we merge this PR now?

probably _ I haven't looked at it in a while

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[thofma]

This now needs a rebase

[fieker]

too much git-fu required. I am happy to remove this PR as the change is a one-liner in examples...

[fingolfin]

On current master, I get this (no error, and w/o the patch in this PR):

julia> Oscar.example("H2.jl")
Main.H2_G_QmodZ_mod

julia> A = abelian_group(PermGroup, [2,2])
Group([ (1,2), (3,4) ])

julia> B = [sub(A, [A[1]])[1], sub(A, [A[2]])[1]]
2-element Vector{PermGroup}:
 Group([ (1,2) ])
 Group([ (3,4) ])

julia> Main.H2_G_QmodZ_mod.H2_G_QmodZ_kern_restriction(A, B)
(Group([ <identity ...>, (F2*F1)^2, <identity ...> ]), Group homomorphism from
Group([ <identity ...>, (F2*F1)^2, <identity ...> ])
to
Group([ <identity ...>, (F2*F1)^2, <identity ...> ]))

Note that this returns a tuple, while the version in this patch just returns the group from the first tuple entry.

Anyway, I think this means this PR is not needed?

[fieker]

On Mon, Jan 30, 2023 at 02:56:44AM -0800, Max Horn wrote: On current master, I get this (no error, and w/o the patch in this PR): ``` julia> Oscar.example("H2.jl") Main.H2_G_QmodZ_mod julia> A = abelian_group(PermGroup, [2,2]) Group([ (1,2), (3,4) ]) julia> B = [sub(A, [A[1]])[1], sub(A, [A[2]])[1]] 2-element Vector{PermGroup}: Group([ (1,2) ]) Group([ (3,4) ]) julia> Main.H2_G_QmodZ_mod.H2_G_QmodZ_kern_restriction(A, B) (Group([ <identity ...>, (F2*F1)^2, <identity ...> ]), Group homomorphism from Group([ <identity ...>, (F2*F1)^2, <identity ...> ]) to Group([ <identity ...>, (F2*F1)^2, <identity ...> ])) ``` Note that this returns a tuple, while the version in this patch just returns the group from the first tuple entry. Anyway, I think this means this PR is not needed?

Quite likely - I shall remove it

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[ThomasBreuer]

The reported problem with quo had been solved with pull request #1837. As I had said above, using GAP's \/ directly yields a result on the GAP side that cannot be used by Oscar.
Thus it was the right solution to close this pull request without merging it.