sqrt() for QQbar and AA should have a parameter "all"

[JohnCremona]

This is inconsistent with other versions of sqrt():

sage: QQbar(2).sqrt()
1.414213562373095?
sage: QQbar(2).sqrt(all=True)

In addition, there should be a parameter "extend" to handle this:

sage: AA(2).sqrt()
1.414213562373095?
sage: AA(-2).sqrt()
1.414213562373095?*I

In the second example, we should not return a root in QQbar unless extend=True.

CC: @robertwb @loefflerd @JohnCremona

Component: algebra

Author: John Cremona, Barinder Banwait

Reviewer: Robert Bradshaw, David Loeffler

Merged: sage-4.4.4.alpha1

Issue created by migration from https://trac.sagemath.org/ticket/8802

[sagetrac-barinder]

Attachment: trac_8802-sqrt-qqbar.patch.gz

Add all and extend parameters to sqrt for QQbar and AA

[sagetrac-barinder]

comment:2

Patch based on 4.4.2 and works fine on 4.4.3. The two problems identified by cremona have been resolved:

sage: QQbar(2).sqrt()
1.414213562373095?
sage: QQbar(2).sqrt(all=True)
[1.414213562373095?, -1.414213562373095?]

The following command

sage: AA(-2).sqrt(extend=False)

returns an error, like it should.

[robertwb]

comment:4

Mostly looks good. Some minor comments:

• There's a lot of redundancy between the AA and QQbar cases, perhaps it could be consolidated (this isn't that big of a deal though)
• You normalize the root order in the all=True case, which I think is good, but the same normalization would probably be worth doing for the all=False case too (I'd be happy if it might negate twice to simplify the logic, as that will be relatively cheap).

[sagetrac-barinder]

Attachment: trac_8802-sqrt-qqbar-v2.patch.gz

As before, but addresses the ordering issue raised by robertwb

[JohnCremona]

Attachment: trac_8802-sqrt-qqbar-v3.patch.gz

Fixed docstring format issues and simplified: applies to 4.4.4.alpha0

[JohnCremona]

comment:7

Version 3 of the patch (jointly written by Barinder and John) simplifies the code more and fixes docstring issues. We removed the sign normalisation code, since the pow function already delivers a normalised result.

[loefflerd]

Author: John Cremona, Barinder Banwait

[loefflerd]

Reviewer: Robert Bradshaw, David Loeffler

[robertwb]

comment:9

Looks good to me too.

[mwhansen]

Merged: sage-4.4.4.alpha1