Handle $mod operator in completeness checks

[Copilot]

Searches for "multiple of" conductor/level crash with ValueError: Unsupported key $mod in completeness checking. The to_rset() function converts query operators to RealSets but lacks support for psycodict's $mod operator.

Changes

• lmfdb/utils/completeness.py: Added $mod operator handling in to_rset(). Since $mod represents unbounded arithmetic progressions, treat as full real line, causing completeness checks to correctly return False.

• lmfdb/tests/test_utils.py: Added unit tests for $mod operator and integration tests with elliptic curve/modular form queries.

Technical Notes

psycodict uses {'$mod': [remainder, divisor]} format (opposite of MongoDB). Example: {'$mod': [0, 7]} matches multiples of 7 (where value % 7 == 0).

# Before: ValueError when processing this query
query = {'conductor': {'$mod': [0, 7]}}

# After: Returns unbounded RealSet → completeness check returns False
rset = to_rset(query)  # Returns (-∞, +∞)

Affected searches:

• /EllipticCurve/Q/?conductor_type=multiple&conductor=7
• /ModularForm/GL2/Q/holomorphic/?level_type=multiple&level=23

Original prompt

---

This section details on the original issue you should resolve

<issue_title>Error searching for ECQ multiple of conductor</issue_title>
<issue_description>Searching for "multiple of" in the conductor field (e.g. take 7) in
https://www.lmfdb.org/EllipticCurve/Q/?search_type=
gives an error:
https://www.lmfdb.org/EllipticCurve/Q/?conductor_type=multiple&conductor=7

</issue_description>

Comments on the Issue (you are @copilot in this section)

@jenpaulhus This issue comes during the check for completeness of the particular search.

The feature on the ECQ pages requires $mod and that's where the error is coming from in utils/completeness.py

Traceback (most recent call last):
  File "/scratch/sage/sage-10.3/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/flask/app.py", line 2091, in __call__
    return self.wsgi_app(environ, start_response)
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/app.py", line 42, in __call__
    return self.app(environ, start_response)
  File "/scratch/sage/sage-10.3/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/flask/app.py", line 2076, in wsgi_app
    response = self.handle_exception(e)
  File "/scratch/sage/sage-10.3/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/flask/app.py", line 2073, in wsgi_app
    response = self.full_dispatch_request()
  File "/scratch/sage/sage-10.3/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/flask/app.py", line 1519, in full_dispatch_request
    rv = self.handle_user_exception(e)
  File "/scratch/sage/sage-10.3/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/flask/app.py", line 1517, in full_dispatch_request
    rv = self.dispatch_request()
  File "/scratch/sage/sage-10.3/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/flask/app.py", line 1503, in dispatch_request
    return self.ensure_sync(self.view_functions[rule.endpoint])(**req.view_args)
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/elliptic_curves/elliptic_curve.py", line 93, in rational_elliptic_curves
    return elliptic_curve_search(info)
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/utils/search_wrapper.py", line 274, in __call__
    complete, msg, caveat = results_complete(table.search_table, query, table._db, info.get("search_array"))
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/utils/completeness.py", line 49, in results_complete
    return lookup[table].check(query, db, search_array)
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/utils/completeness.py", line 678, in check
    if test(db, [query[col] for col in cols]):
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/utils/completeness.py", line 703, in __call__
    return all(self.cls(D).is_subset(B) for D, B in zip(Ds, self.bounds))
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/utils/completeness.py", line 703, in <genexpr>
    return all(self.cls(D).is_subset(B) for D, B in zip(Ds, self.bounds))
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/utils/completeness.py", line 438, in __init__
    self.rset = integer_normalize(to_rset(x))
  File "/scratch/home/jenpaulhus/lmfdb/lmfdb/utils/completeness.py", line 159, in to_rset
    raise ValueError(f"Unsupported key {k}")
ValueError: Unsupported key $mod
```</body></comment_new>
<comment_new><author>@jenpaulhus</author><body>
Someone also just reported this on the bugreport so I'm adding the production issue label.</body></comment_new>
<comment_new><author>@edgarcosta</author><body>
Another one:

Exception on /ModularForm/GL2/Q/holomorphic/ [GET]
Traceback (most recent call last):
File "/home/sage/sage-10.5/local/var/lib/sage/venv-python3.12/lib/python3.12/site-packages/flask/app.py", line 1511, in wsgi_app
response = self.full_dispatch_request()
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/sage/sage-10.5/local/var/lib/sage/venv-python3.12/lib/python3.12/site-packages/flask/app.py", line 919, in full_dispatch_request
rv = self.handle_user_exception(e)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/sage/sage-10.5/local/var/lib/sage/venv-python3.12/lib/python3.12/site-packages/flask/app.py", line 917, in full_dispatch_request
rv = self.dispatch_request()
^^^^^^^^^^^^^^^^^^^^^^^
File "/home/sage/sage-10.5/local/var/lib/sage/venv-python3.12/lib/python3.12/site-packages/flask/app.py", line 902, in dispatch_request
return self.ensure_sync(self.view_functions[rule.endpoint])(**view_args) # type: ignore[no-any-return]
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/lmfdb/lmfdb-git-web/lmfdb/classical_modular_forms/main.py", line 172, in index
return newform_search(info)
^^^^^^^^^^^^^^^^^^^^
File "/home/lmfdb/lmfdb-git-web/lmfdb/utils/search_wrapper.py", line 274, in call
complete, msg, caveat = result...

• Fixes Error searching for ECQ multiple of conductor #6822

---

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[jenpaulhus]

What's the status of this PR? There's now yet another bugreport about someone trying to search with $mod and an error coming up.

[roed314]

I'm not thrilled with this solution, which is why I didn't initially approve it. Then I got distracted. Here's an example of the kind of output that I think may end up biting us in the future:

mod_query = {'$mod': [0, 7]}
rset = to_rset(mod_query)
self.assertEqual(str(rset), "(-oo, +oo)")
        
# Test that IntegerSet can be created from $mod query without error
iset = IntegerSet(mod_query)
self.assertEqual(str(iset.rset), "(-oo, +oo)")
        
bounded = IntegerSet([1, 500000])
self.assertEqual(bounded.is_subset(iset), True)

I'll try to think of a different way to solve this issue.

[roed314]

I'm closing this in favor of #6879, with more discussion on #6822 for solving the underlying problem.