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in for matrix groups has hiccups #4568

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joschmitt opened this issue Feb 10, 2025 · 3 comments · May be fixed by #4640
Open

in for matrix groups has hiccups #4568

joschmitt opened this issue Feb 10, 2025 · 3 comments · May be fixed by #4640
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@ThomasBreuer
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bug Something isn't working topic: groups

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@joschmitt
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Describe the bug
Testing containment with in gives an error for matrix groups (over number fields) if the order of the group is known.

To Reproduce

julia> K, a = cyclotomic_field(12, "a")
(Cyclotomic field of order 12, a)

julia> K, a = cyclotomic_field(12, "a");

julia> G = matrix_group([K[a^2 0; 0 inv(a^2)], K[0 -1; 1 0]]);

julia> M = K[a^3 0; 0 a^-3];

julia> M in G
false

julia> order(G)
12

julia> M in G
ERROR: Error thrown by GAP: Error, ArgumentError: Element not in the group in
  GAP_jl._apply( julia_obj, args ) at /home/johannes/.julia/packages/GAP/bMh5a/pkg/JuliaInterface/gap/calls.gi:15 called from 
map!.fun( elm ) at /home/johannes/.julia/artifacts/553ff06be6f5ceb880f85c7905595c81d539bbf7/share/gap/lib/mapprep.gi:616 called from
ImagesRepresentative( nice, elm ) at /home/johannes/.julia/artifacts/553ff06be6f5ceb880f85c7905595c81d539bbf7/share/gap/lib/grpnice.gi:240 called from
<function "in by nice monomorphism">( <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:356 [inlined]
 [4] (::GapObj)(a1::GapObj, a2::GapObj)
   @ GAP ~/.julia/packages/GAP/bMh5a/src/ccalls.jl:321
 [5] IN(x::GapObj, y::GapObj)
   @ GAP.Wrappers ~/.julia/packages/GAP/bMh5a/src/wrappers.jl:25
 [6] in
   @ ~/.julia/packages/GAP/bMh5a/src/adapter.jl:364 [inlined]
 [7] lies_in(x::AbstractAlgebra.Generic.MatSpaceElem{…}, G::MatrixGroup{…}, x_gap::Nothing)
   @ Oscar ~/.julia/dev/Oscar/src/Groups/matrices/MatGrp.jl:293
 [8] in(x::AbstractAlgebra.Generic.MatSpaceElem{…}, G::MatrixGroup{…})
   @ Oscar ~/.julia/dev/Oscar/src/Groups/matrices/MatGrp.jl:296
 [9] top-level scope
   @ REPL[8]:1
Some type information was truncated. Use `show(err)` to see complete types.

System (please complete the following information):

julia> Oscar.versioninfo(full=true)
OSCAR version 1.3.0-DEV - #master, 8fc7969f37 -- 2025-02-08 18:29:40 +0000
  combining:
    AbstractAlgebra.jl   v0.44.5
    GAP.jl               v0.13.1
    Hecke.jl             v0.35.9
    Nemo.jl              v0.48.2
    Polymake.jl          v0.11.25
    Singular.jl          v0.24.1
  building on:
    FLINT_jll               v300.100.301+0
    GAP_jll                 v400.1400.3+0
    Singular_jll            v404.1.700+0
    libpolymake_julia_jll   v0.13.1+0
    libsingular_julia_jll   v0.46.1+0
    polymake_jll            v400.1300.2+0
See `]st -m` for a full list of dependencies.

Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × 12th Gen Intel(R) Core(TM) i5-1250P
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)
Environment:
  JULIA_EDITOR = vim
Official https://julialang.org/ release

Additional context
There is no issue if I revert #4525.
@joschmitt joschmitt added bug Something isn't working topic: groups labels Feb 10, 2025
@fingolfin
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Thank you for the report!

The \in method used by GAP here looks like this:

InstallMethod( \in,
    "by nice monomorphism",
    IsElmsColls,
    [ IsMultiplicativeElementWithInverse,
      IsGroup and IsHandledByNiceMonomorphism ],
    0,

function( elm, G )
    local   nice,  img;

    if HasGeneratorsOfGroup(G) and elm in GeneratorsOfGroup(G) then
      return true;
    fi;
    nice := NiceMonomorphism( G );
    img  := ImagesRepresentative( nice, elm:actioncanfail:=true );  # <-- error happens here
    return img<>fail and img in NiceObject( G )
       and PreImagesRepresentative( nice, img ) = elm;
end );

I marked the critical line: we invoke the nice monomorphism with an option that is meant to instruct it to return fail if the input is not in the target group, instead of raising an error.

My guess is that the maps introduced in PR #4525 don't respect this:

  img = function(x)
    return Gp(_reduce(matrix(x), OtoFq))
  end
...
    # map from Gap_G to Gap_Gp
    fun = x -> GapObj(img(G(preimage_matrix(risoG, x); check=false)))

I do see check=false in the second map, but it calls img which doesn't do this. If I insert check=false there, it all works, but I suspect this isn't what we want in general.

@fingolfin
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@ThomasBreuer can you have a look? PR #4525 was by you so I think you know the code best

@ThomasBreuer ThomasBreuer linked a pull request Feb 25, 2025 that will close this issue
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@ThomasBreuer
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The analysis is correct.
However, #4640 tries to solve the problem by avoiding the calls that require check=false:
For GAP, the map in question deals with matrices, embedding them into groups and then unpacking these group elements is in fact not needed.

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fix a NiceMonomorphism for GAP constructed in Oscar ThomasBreuer/Oscar.jl
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@fingolfin @ThomasBreuer @joschmitt