Opened 10 years ago

Closed 8 years ago

# Period method for quadratic irrationals

Reported by: Owned by: benjaminfjones davidloeffler minor sage-duplicate/invalid/wontfix number fields continued fraction, arithmetic kcrisman Benjamin Jones, Vincent Delecroix N/A #14567

### Description

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

### comment:1 Changed 10 years ago by kcrisman

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?

### comment:2 follow-up: ↓ 3 Changed 10 years ago by 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.

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

### comment:3 in reply to: ↑ 2 Changed 10 years ago by kcrisman

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.

### comment:4 Changed 8 years ago by vdelecroix

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

### comment:5 Changed 8 years ago by benjaminfjones

Agreed. Nice work on #14567.

### comment:6 Changed 8 years ago by kcrisman

• Authors Benjamin Jones, Seth Dutter deleted
• Milestone changed from sage-5.10 to sage-pending
• Reviewers set to Benjamin Jones, Vincent Delecrois
• Status changed from new to needs_review

### comment:7 Changed 8 years ago by kcrisman

• Dependencies set to #14567
• Reviewers changed from Benjamin Jones, Vincent Delecrois to Benjamin Jones, Vincent Delecroix
• Status changed from needs_review to positive_review

To release manager: when #14567 is merged, this should become sage-duplicate.

### comment:8 Changed 8 years ago by jdemeyer

• Milestone changed from sage-pending to sage-duplicate/invalid/wontfix

### comment:9 Changed 8 years ago by jdemeyer

• Resolution set to duplicate
• Status changed from positive_review to closed
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