Opened 4 years ago
Closed 4 years ago
#23986 closed enhancement (fixed)
compute class numbers of nonmaximal orders in quadratic imaginary fields
Reported by:  tscholl2  Owned by:  

Priority:  minor  Milestone:  sage8.1 
Component:  number fields  Keywords:  class number, nonmaximal 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: 
Description (last modified by )
Implement class number computation for nonmaximal orders in quadratic fields.
Change History (8)
comment:1 Changed 4 years ago by
 Commit set to eae1a79f2b343eb40b08cdb0f44fd4a1640fa5ef
comment:2 Changed 4 years ago by
 Commit changed from eae1a79f2b343eb40b08cdb0f44fd4a1640fa5ef to 6d40258ae238edb6b806d66d5be25f7eb88e01eb
Branch pushed to git repo; I updated commit sha1. New commits:
6d40258  add Cox to master bibliography, fix reference in docstring

comment:3 Changed 4 years ago by
 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
 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
 Commit changed from 6d40258ae238edb6b806d66d5be25f7eb88e01eb to ed1fcb1930d7a613b5a6bc00fef7ee314deaff82
Branch pushed to git repo; I updated commit sha1. New commits:
ed1fcb1  use pari to compute class number

comment:6 Changed 4 years ago by
 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 nonmaximal quadratic orders, and changed the error message accordingly.
comment:7 Changed 4 years ago by
 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
 Branch changed from u/tscholl2/class_number_nonmaximal_order to ed1fcb1930d7a613b5a6bc00fef7ee314deaff82
 Resolution set to fixed
 Status changed from positive_review to closed
Branch pushed to git repo; I updated commit sha1. New commits:
initial commit