Expand the completeness checker with more number field, Dirichlet, and local field cases - #7167
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Expand the completeness checker with more number field, Dirichlet, and local field cases#7167roed-math wants to merge 2 commits into
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Add several new provable-completeness cases to lmfdb/utils/completeness.py, each with a message and a test using the example query from issue LMFDB#7017: - Number fields: a degree-2 field unramified outside S has |disc| dividing 8*prod_{odd p in S} p (factor 8 only if 2 in S), so it is complete when that product is within the degree-2 discriminant bound (new NFBound.clear_S_disc). - Number fields: a CM field is totally imaginary, constraining the signature to [0, n/2] (n even), which e.g. reduces degree 2 + CM to the class-number bound. - Number fields: for imaginary quadratic fields r_1 = 0, so the narrow class number/group equals the ordinary one. - Dirichlet characters: a primitive character has conductor equal to its modulus, so a conductor bound bounds the modulus. - p-adic fields: discriminant exponent c = 0 means unramified (e = 1), giving n = f via MulFiller (new UnramifiedFiller). All additions are gated on specific query keys and use string reasons, leaving clear_S/display_reason/to_rset untouched. Verified with the flask test client on the issue's example queries (before: no message; after: completeness flash) and via lmfdb/tests/test_utils.py::test_complete (new complete and not-complete cases), which passes against devmirror; pyflakes clean. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Closes #7017.
This adds several new provable-completeness cases to
lmfdb/utils/completeness.py, each drawn from the list in the issue and shipped with its example query as a test.For number fields: a degree-2 field unramified outside a set S has absolute discriminant dividing
8 * prod_{odd p in S} p(the factor of 8 only when 2 is in S), so the search is complete when that bound is within the degree-2 discriminant completeness bound; a CM field is totally imaginary, which constrains the signature (reducing e.g. degree 2 + CM to the existing class-number bound); and for imaginary quadratic fields the narrow class number equals the ordinary class number.For Dirichlet characters, a primitive character has conductor equal to its modulus, so a conductor bound bounds the modulus.
For p-adic fields, discriminant exponent
c = 0means the field is unramified (e = 1), givingn = f.All additions are gated on specific query keys and use string reasons, leaving
clear_S/display_reason/to_rsetuntouched. Verified with the flask test client on the issue's example queries and via new complete/not-complete assertions intest_complete(passing against devmirror); pyflakes clean.Note this touches the same file as the congruence-support PR (#7139) and will want a light merge if that one lands first.
Ported from roed-math#31, where the full write-up and comment history live.
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