Period method for quadratic irrationals

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Period method for quadratic irrationals #11345

Closed benjaminfjones closed 11 years ago

benjaminfjones commented 13 years ago

We propose implementing a period method for quadratic irrational elements of the field of continued fractions.

See the post at http://ask.sagemath.org/question/545/continued-fraction-expansion-of-quadratic for an algorithm.

Depends on #14567

CC: @kcrisman

Component: number fields

Keywords: continued fraction, arithmetic

Reviewer: Benjamin Jones, Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/11345

kcrisman commented 13 years ago

comment:1

Well, an algorithm isn't a patch :) but this is a promising start.

However, one would want to make sure there was a way to check whether this was actually a quadratic surd before using this method. I think that the poster's comment about the Maple documentation for this could provide some helpful thoughts, though I don't think we'd want to slavishly follow the syntax or anything, especially as we have the field of continued fractions to help us out.

One more random thought; is it possible to hack out the code from GAP for this in some way, so as not to reinvent the wheel?

benjaminfjones commented 13 years ago

comment:2

I intend to provide a patch, I just thought I'd get the ball rolling. Maybe I should have waited to file the ticket, though. I'll be on vacation until June 6.

I'm not familiar with the term "surd", but I guess that means an algebraic number, or maybe just an n-th root?

kcrisman commented 13 years ago

comment:3

Replying to @benjaminfjones:

I intend to provide a patch, I just thought I'd get the ball rolling. Maybe I should have waited to file the ticket, though. I'll be on vacation until June 6.

No, always file a ticket - then others know about it, and so forth. Many, many, many tickets are filed that don't have patches for a long time, but do have ideas.

I'm not familiar with the term "surd", but I guess that means an algebraic number, or maybe just an n-th root?

See here, for example. It's an old term for (quadratic) irrationals, more or less. You see it a lot in books written before about 1960, esp. number theory ones.

videlec commented 11 years ago

comment:4

Hi,

This is a long standing ticket and I guess nobody is working on it anymore. I will close it as a duplicate as soon as #14567 is finished. Any comment or contribution welcome!

Vincent

benjaminfjones commented 11 years ago

comment:5

Agreed. Nice work on #14567.