#12861: maximal_order of quaternion algebras should be more general
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Reporter: daniels | Owner: daniels
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.1
Component: algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: #12860 | Stopgaps:
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Description changed by daniels:
Old description:
> 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).
>
> Note: I'm working on this and should have code for QQ available soon.
New description:
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)
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12861#comment:1>
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