#11380: Computing continued fractions on real quadratic fields
-------------------------------------+-------------------------------------
Reporter: mmasdeu | Owner: was
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.4
Component: number theory | Resolution:
Keywords: norm-euclidean, | Merged in:
two-stage euclidean, continued | Reviewers:
fraction | Work issues: Documentation needed
Authors: Xevi Guitart, | Commit:
Marc Masdeu | ee8aeb6f358a12a73d3fc5681ee4667db68dbd7c
Report Upstream: N/A | Stopgaps:
Branch: u/chapoton/11380 |
Dependencies: |
-------------------------------------+-------------------------------------
Description changed by chapoton:
Old description:
> We have implemented some routines that allow for the computation of
> continued fractions in real quadratic number fields of class number one.
> This uses 2-stage division chains as defined in G.E.Cooke,"A weakening of
> the euclidean property for integral domains and applications to algebraic
> number theory".
>
> The algorithm finds a set of "hyperbolic regions" as described in the
> above article, large enough so that it covers a fundamental domain. These
> regions are used to construct 2-stage division chains and therefore
> obtain continued fractions with elements of the ring of integers of the
> number field.
>
> More information can be found in the preprint posted in the Math Arxiv:
> http://arxiv.org/abs/1106.0856
>
> Apply trac_11380_quadratic_cont_frac.patch
New description:
We have implemented some routines that allow for the computation of
continued fractions in real quadratic number fields of class number one.
This uses 2-stage division chains as defined in G.E.Cooke,"A weakening of
the euclidean property for integral domains and applications to algebraic
number theory".
The algorithm finds a set of "hyperbolic regions" as described in the
above article, large enough so that it covers a fundamental domain. These
regions are used to construct 2-stage division chains and therefore obtain
continued fractions with elements of the ring of integers of the number
field.
More information can be found in the preprint posted in the Math Arxiv:
http://arxiv.org/abs/1106.0856
--
--
Ticket URL: <http://trac.sagemath.org/ticket/11380#comment:22>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
