#14567: Refactor continued fractions
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Reporter: vdelecroix |
Owner: vdelecroix
Type: enhancement |
Status: needs_review
Priority: major |
Milestone: sage-5.10
Component: number theory |
Resolution:
Keywords: continued fractions, numerical approximation | Work
issues:
Report Upstream: N/A |
Reviewers:
Authors: vdelecroix | Merged
in:
Dependencies: #13213, #13957, #14563, #14568 |
Stopgaps:
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Changes (by vdelecroix):
* status: new => needs_review
Old description:
> Continued fractions (in sage.rings.contfrac) do not do what we expect:
> * it only deals with rational numbers
> * there is no dedicated method for numerical approximations (which is
> one of the first aim of continued fractions)
> * there is no bridge with words (sage.combinat.words)
> * there is no bridge with quadratic numbers (see also #11345)
>
> Moreover, categories are not properly initialized nor used.
>
> The patch proposed here improves the current version by addressing the
> four issues above.
New description:
Continued fractions (in sage.rings.contfrac) do not do what we expect:
0. categories are not properly initialized nor used.
1. it only deals with rational numbers
2. there is no dedicated method for numerical approximations (which is
one of the first aim of continued fractions)
4. there is no bridge with quadratic numbers (see also #11345)
3. there is no bridge with words (sage.combinat.words)
The patch proposed here develop some general design for dealing with
continued fractions and solves the issues 0, 1 and 4 (and I hope 2); see
the discussion below.
{{{
sage: K.<sqrt2> = QuadraticField(2)
sage: cff = (sqrt2/3 + 1/4).continued_fraction(); cff
[0; 1, (2, 1, 1, 2, 3, 2, 1, 1, 2, 5, 1, 1, 14, 1, 1, 5)*]
sage: cff.value()
1/3*sqrt2 + 1/4
}}}
In particular we solve the question in #11345.
--
Comment:
The ticket is not yet finished but the review may start (all test pass on
my computer... waiting for patchbot). Here are some questions I am not
sure how to deal about.
* How to cleanly implement numerical approximations of continued
fractions (see the current (stupid) implementation of `_mpfr_` in
sage.rings.continued_fraction_element`) ?
* What method name do we choose for conversion to continued fractions ?
(ZZ has `_integer_`, QQ has `_rational_` and RR has `_mpfr_`, ...). For
now it is simply `continued_fraction` as the user may prefer
`my_number.continued_fraction()` to `CFF(my_number)`.
* The link with words is not yet done and perhaps should be delayed to
another ticket as the patch is yet 2500 lines long.
* some of the stuff about continued fractions in `sage.rings.arith`
should move to `sage.rings.continued_fraction_field` (I think I do prefer
`sage.rings.continued_fractions` to
`sage.rings.continued_fraction_field`...).
* I did not check what are the Pari's fonctionnalities that may be used
here
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14567#comment:2>
Sage <http://www.sagemath.org>
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