#11380: Computing continued fractions on real quadratic fields
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Reporter: mmasdeu | Owner: was
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-4.7.1
Component: number theory | Keywords: norm-euclidean, two-stage
euclidean, continued fraction
Work_issues: | Upstream: N/A
Reviewer: | Author: Xevi Guitart and Marc Masdeu
Merged: | Dependencies:
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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
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
Apply trac_11380_quadratic_cont_frac.patch
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Comment(by chapoton):
for the bot:
Apply trac_11380_quadratic_cont_frac.patch
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11380#comment:11>
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