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GAP Symplectic Group Construction does not see Zmod(N) is finite #36441

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GiacomoPope opened this issue Oct 10, 2023 · 2 comments · May be fixed by #39858
Open
2 tasks done

GAP Symplectic Group Construction does not see Zmod(N) is finite #36441

GiacomoPope opened this issue Oct 10, 2023 · 2 comments · May be fixed by #39858
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c: group theory t: bug

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@GiacomoPope
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Steps To Reproduce

GAP does not allow custom invariant forms for finite groups. An implementation error is raised when an invariant form for GF(p) is used:

sage: I = Matrix(Zmod(11),4,4,[0,0,1,0,0,0,0,1,-1,0,0,0,0,-1,0,0])
sage: G = Sp(4, GF(11), invariant_form=I)
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
Cell In [15], line 1
----> 1 G = Sp(Integer(4), GF(Integer(11)), invariant_form=I)

File ~/sage/sage-10.0/src/sage/groups/matrix_gps/symplectic.py:150, in Sp(n, R, var, invariant_form)
    148 if invariant_form is not None:
    149     if isinstance(ring, FiniteField):
--> 150         raise NotImplementedError("invariant_form for finite groups is fixed by GAP")
    152     invariant_form = normalize_args_invariant_form(ring, degree, invariant_form)
    153     if not invariant_form.is_alternating():

NotImplementedError: invariant_form for finite groups is fixed by GAP

If instead someone uses Zmod(11), then this error is avoided but the invariant form is not set:

sage: I = Matrix(Zmod(11),4,4,[0,0,1,0,0,0,0,1,-1,0,0,0,0,-1,0,0])
sage: G = Sp(4, Zmod(11), invariant_form=I)
sage: G.invariant_form()
[ 0  0  0  1]
[ 0  0  1  0]
[ 0 10  0  0]
[10  0  0  0]
sage: G
Symplectic Group of degree 4 over Ring of integers modulo 11 with respect to alternating bilinear form
[ 0  0  1  0]
[ 0  0  0  1]
[10  0  0  0]
[ 0 10  0  0]

Expected Behavior

G = Sp(4, Zmod(11), invariant_form=I)

Should raise an error

Actual Behavior

It silently fails.

    if invariant_form is not None:
        if isinstance(ring, FiniteField):
            raise NotImplementedError("invariant_form for finite groups is fixed by GAP")

My thought is that this check should be ring.is_finite() -- I am happy to change this, but wanted some advice on what's best here.

Additional Information

No response

Environment

- **OS**: Mac OS
- **Sage Version**: 10.0

Checklist

  • I have searched the existing issues for a bug report that matches the one I want to file, without success.
  • I have read the documentation and troubleshoot guide
@EigenVector22
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EigenVector22 commented Apr 3, 2025 •
edited
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@mkoeppe hello, should i go ahead and raise the PR and make the proposed changes?
Thanks,

@GiacomoPope
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If you have a fix, make a PR and then tag this issue.

EigenVector22 added a commit to EigenVector22/sage that referenced this issue Apr 3, 2025
@EigenVector22
Use ring.is_finite() for Sp invariant_form check
8f402e9 
Fixes sagemath#36441
The check for whether a custom invariant_form could be used with
Sp(n, R) incorrectly used `isinstance(ring, FiniteField)`. Due to this
it failed to detect finite rings like Zmod(p) (p prime), leading to
the invariant_form being silently ignored by GAP instead of raising
the expected NotImplementedError.

Changed the check to `ring.is_finite()`, which fixes the described
limitation.

Added Doctests.
@EigenVector22 EigenVector22 linked a pull request Apr 3, 2025 that will close this issue
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Use ring.is_finite() for Sp invariant_form check EigenVector22/sage
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@mkoeppe @GiacomoPope @EigenVector22