Use quadclassunit instead of qfbclassno when proof=True for class number computation #41320
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
PARI documentation warns that qfbclassno may return incorrect results for large discriminants when the class group has many cyclic factors. This change ensures: - proof=True (default): uses quadclassunit for reliable results (assuming GRH) - proof=False: uses qfbclassno for speed (user explicitly opts out of proof) Modified files: - src/sage/rings/number_field/order.py: quadratic_order_class_number() - src/sage/quadratic_forms/bqf_class_group.py: BQFClassGroup.order() - src/sage/rings/integer.pyx: Integer.class_number()
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Summary
This PR fixes a correctness issue where Sage used PARI's
qfbclassno()by default to compute class numbers of quadratic orders. PARI's documentation explicitly warns thatqfbclassno()"may give incorrect results when the class group has many cyclic factors."Changes
proof=True(default): usequadclassunit()for reliable results (assuming GRH)proof=False: useqfbclassno()for speed (user explicitly opts out)Files Modified
src/sage/rings/number_field/order.py-quadratic_order_class_number()src/sage/quadratic_forms/bqf_class_group.py-BQFClassGroup.order()andcardinality()src/sage/rings/integer.pyx-Integer.class_number()References
qfbclassno: states results may be incorrect for large discriminantsquadclassunit: recommended for proven results (assuming GRH)