Quaternion Orders over Number Fields

[4dfe6752-6233-4f7f-8e0e-e1363b12c1b7]

Generalizes the code for quaternion orders of quaternion algebras over QQ to allow for quaternion orders of quaternion algebras over number fields.

CC: @sagetrac-schisholm @dansme

Component: algebra

Keywords: quaternion, order

Author: Aly Deines

Branch/Commit: u/aurel/13568-review @ afba274

Reviewer: Gonzalo Tornaría

Issue created by migration from https://trac.sagemath.org/ticket/13568

[4dfe6752-6233-4f7f-8e0e-e1363b12c1b7]

Attachment: Trac13569_quaternion_orders.patch.gz

[tornaria]

comment:8

Rebased the patch to sage-6.4.beta1 and moved to git

[tornaria]

Commit: 733e651

[tornaria]

Branch: u/tornaria/ticket/13568

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 733e651 to 9858d7e

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

e495dc1	Trac #13569: fix whitespace
70614dd	Trac #13569: fix usage of raise
0a3ca50	Trac #13569: remove unnecessary import
4fbac85	Trac #13569: style changes
f824306	Trac #13569: Revert basis of quaternion algebras and orders to be tuples
9858d7e	Trac #13569: document and test new argument ideal_list

[tornaria]

comment:11

I've pushed a bunch of reviewer commits, the log explains them (esp f824306).

There's still a bug, namely when the base field is QQ and a pseudo-basis is given, the current code will just ignore the ideals.

[4dfe6752-6233-4f7f-8e0e-e1363b12c1b7]

comment:12

Okay. I'll get on that.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 9858d7e to 1e8d1e2

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

1e8d1e2

Trac #13569: fix when base_field=QQ and pseudo-basis is given

[tornaria]

comment:14

I'm happy with this now. Since I made a lot of changes I'm leaving it as needs_review.

[tornaria]

Reviewer: tornaria

[4dfe6752-6233-4f7f-8e0e-e1363b12c1b7]

Changed branch from u/tornaria/ticket/13568 to u/aly.deines/ticket/13568

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 1e8d1e2 to bd9fe85

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

bd9fe85

Some cleanup.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from bd9fe85 to 9f9af0d

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

9f9af0d

Fixed the Brandt.py documentation.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

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

130d486	Removed extra generated files.
8ed696d	Delated an extra git-trac-command folder.

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 9f9af0d to 8ed696d

[mmasdeu]

Changed commit from 8ed696d to 73909fd

[mmasdeu]

Changed branch from u/aly.deines/ticket/13568 to u/mmasdeu/13568-review

[mmasdeu]

comment:20

I started reviewing it, and made some changes. Some are to make it more pythonic, some are for clarity.

I've set it to needs_work because the patch fails when using quaternion algebras not defined over number fields:

sage: A.<i,j,k> = QuaternionAlgebra(ZZ['x'].fraction_field(),-1,-1)
sage: A.quaternion_order([1,i,j,k])                                
---------------------------------------------------------------------------
UnboundLocalError                         Traceback (most recent call last)
...
UnboundLocalError: local variable 'M1' referenced before assignment

[jdemeyer]

comment:21

Just a remark: this functionality is in PARI now, so you could just try to wrap PARI.

[cd1fd1a3-1fd5-4c80-88ce-04d187901b3d]

Changed branch from u/mmasdeu/13568-review to u/aurel/13568-review

[cd1fd1a3-1fd5-4c80-88ce-04d187901b3d]

Changed commit from 73909fd to afba274

[cd1fd1a3-1fd5-4c80-88ce-04d187901b3d]

comment:23

With Marc Masdeu, we checked that this is still compiling after rebasing on develop. We intend to have a look at this ticket.

---

Last 10 new commits:

c4276e6	Fixed a merging error.
055e633	Changed to tuples.
18c5420	More fixes.
5b1046e	Some cleanup.
9c67df8	Fixed the Brandt.py documentation.
188229b	Removed extra generated files.
f668c09	Delated an extra git-trac-command folder.
b7a7864	Trac 13568: Reviewer's patch.
aa554bc	Fixed transpose mistake.
afba274	Some minor changes, initialized __basis and __pseudobasis to None.

[jdemeyer]

Changed dependencies from #13509 - Pari nfhnf to none

[jdemeyer]

Changed reviewer from tornaria to Gonzalo Tornaría