#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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Description changed by mmasdeu:
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.
>
> This is a
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.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11380#comment:2>
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