Ticket #12861 (closed enhancement: fixed)
maximal_order of quaternion algebras should be more general
|Reported by:||daniels||Owned by:||daniels|
|Report Upstream:||N/A||Reviewers:||Aly Deines|
|Authors:||Daniel Smertnig||Merged in:||sage-5.3.beta1|
Description (last modified by daniels) (diff)
Currently Sage can only compute maximal orders in quaternion algebras over QQ having prime discriminant.
Algorithms exist to do this for arbitrary discriminants over arbitrary number fields, and should probably be implemented at least over QQ (for general number fields we don't have the necessary basics to deal with pseudo-bases of quaternion orders implemented at the moment).
The attached patch implements the algorithm from J. Voight, "Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms" over QQ. (Needs to be applied after the patch from #12860)