Opened 4 years ago

Closed 4 years ago

#23986 closed enhancement (fixed)

compute class numbers of non-maximal orders in quadratic imaginary fields

Reported by: tscholl2 Owned by:
Priority: minor Milestone: sage-8.1
Component: number fields Keywords: class number, non-maximal order, quadratic imaginary field
Cc: Merged in:
Authors: Travis Scholl Reviewers: Jeroen Demeyer, David Roe
Report Upstream: N/A Work issues:
Branch: ed1fcb1 (Commits, GitHub, GitLab) Commit: ed1fcb1930d7a613b5a6bc00fef7ee314deaff82
Dependencies: Stopgaps:

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Description (last modified by tscholl2)

Implement class number computation for non-maximal orders in quadratic fields.

Change History (8)

comment:1 Changed 4 years ago by git

  • Commit set to eae1a79f2b343eb40b08cdb0f44fd4a1640fa5ef

Branch pushed to git repo; I updated commit sha1. New commits:

eae1a79initial commit

comment:2 Changed 4 years ago by git

  • Commit changed from eae1a79f2b343eb40b08cdb0f44fd4a1640fa5ef to 6d40258ae238edb6b806d66d5be25f7eb88e01eb

Branch pushed to git repo; I updated commit sha1. New commits:

6d40258add Cox to master bibliography, fix reference in docstring

comment:3 Changed 4 years ago by tscholl2

  • Status changed from new to needs_review

I successfully tested a few orders using the following magma code:

K<a> := QuadraticField(-23);
O := sub< MaximalOrder(K) | 240 >;
print PicardNumber(O);
// 288

K<a> := QuadraticField(-3);
O := sub< MaximalOrder(K) | 6 >;
print PicardNumber(O);
// 3

comment:4 Changed 4 years ago by jdemeyer

  • Status changed from needs_review to needs_work

PARI/GP actually computes class numbers for all quadratic orders. So I would rather implement this as simply a call to pari.qfbclassno(D).

comment:5 Changed 4 years ago by git

  • Commit changed from 6d40258ae238edb6b806d66d5be25f7eb88e01eb to ed1fcb1930d7a613b5a6bc00fef7ee314deaff82

Branch pushed to git repo; I updated commit sha1. New commits:

ed1fcb1use pari to compute class number

comment:6 Changed 4 years ago by tscholl2

  • Description modified (diff)
  • Status changed from needs_work to needs_review

I replaced the formula with a call to pari.qfbclassno (thanks for pointing that function out!). I added some examples for real and imaginary non-maximal quadratic orders, and changed the error message accordingly.

comment:7 Changed 4 years ago by roed

  • Reviewers set to Jeroen Demeyer, David Roe
  • Status changed from needs_review to positive_review

Looks good to me.

comment:8 Changed 4 years ago by vbraun

  • Branch changed from u/tscholl2/class_number_nonmaximal_order to ed1fcb1930d7a613b5a6bc00fef7ee314deaff82
  • Resolution set to fixed
  • Status changed from positive_review to closed
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