approximate imaginary-quadratic class numbers using analytic class number formula #40907
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
|
Documentation preview for this PR (built with commit 8bf00ec; changes) is ready! 🎉 |
yyyyx4
force-pushed
the
public/approximate_class_numbers
branch
from
c0a616a to
5430772
Compare
user202729
reviewed
Sep 29, 2025
user202729
reviewed
Sep 29, 2025
user202729
reviewed
Sep 29, 2025
user202729
reviewed
Sep 29, 2025
…ing class numbers of negative fundamental discriminants
Co-authored-by: user202729 <25191436+user202729@users.noreply.github.com>
yyyyx4
force-pushed
the
public/approximate_class_numbers
branch
from
814eab3 to
bd5bba8
Compare
user202729
reviewed
Oct 8, 2025
Contributor
|
I wonder if some convergence acceleration technique can improve this. But doesn't matter that much. |
Member
Author
|
Yeah, I'm also not convinced if this is the best way of doing this... But I suppose the implementation can always be switched out for something else later if the need arises. For the moment, it seems to do what it promises, and is therefore better than nothing? 🙂 |
vbraun
pushed a commit
to vbraun/sage
that referenced
this pull request
Oct 11, 2025
sagemathgh-40907: approximate imaginary-quadratic class numbers using analytic class number formula This patch adds a simple function to *approximate* class numbers of imaginary-quadratic fields using the analytic class number formula. This approximation is accurate to a relative error factor of $<2$ even with comparatively low precision, making it useful in the context of class- group computations. An obvious next step would be to generalize it to non-fundamental and/or positive discriminants. This is left for future work. URL: sagemath#40907 Reported by: Lorenz Panny Reviewer(s): Lorenz Panny, user202729
vbraun
pushed a commit
to vbraun/sage
that referenced
this pull request
Oct 12, 2025
sagemathgh-40907: approximate imaginary-quadratic class numbers using analytic class number formula This patch adds a simple function to *approximate* class numbers of imaginary-quadratic fields using the analytic class number formula. This approximation is accurate to a relative error factor of $<2$ even with comparatively low precision, making it useful in the context of class- group computations. An obvious next step would be to generalize it to non-fundamental and/or positive discriminants. This is left for future work. URL: sagemath#40907 Reported by: Lorenz Panny Reviewer(s): Lorenz Panny, user202729
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
3 participants
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.
This patch adds a simple function to approximate class numbers of imaginary-quadratic fields using the analytic class number formula. This approximation is accurate to a relative error factor of$<2$ even with comparatively low precision, making it useful in the context of class-group computations.
An obvious next step would be to generalize it to non-fundamental and/or positive discriminants. This is left for future work.