square root with all=True should not return ValueError but empty list

[mstreng]

With Sage 4.4.4 and no relevant patches, I got the following:

sage: FiniteField(3)(2).sqrt(all = True)
[]

sage: 2.sqrt(extend = False, all = True)
ValueError: square root of 2 not an integer

sage: FiniteField(next_prime(2^100))(2).sqrt(extend = False, all = True)
ValueError: self must be a square

sage: _.<a>=FiniteField(9)
sage: a.sqrt(extend = False, all = True)
ValueError: must be a perfect square.

At sage days 23 we agreed that square root with all=True should not raise an error. If no square roots exist, then it should return an empty list.

Right now, it returns an empty list for elements of small prime finite fields, but raises an error for integers, elements of large prime finite fields, and elements of non-prime finite fields.

apply

• attachment: 9466.patch

CC: @koffie @sagetrac-ruckers

Component: algebra

Keywords: sd23 sd51 sqrt all

Author: Marco Streng, Sonseeahray Rucker

Reviewer: Alejandro Argaez, Angelos Koutsianas

Merged: sage-5.12.beta3

Issue created by migration from https://trac.sagemath.org/ticket/9466

[sagetrac-ruckers]

Fixes the code: sage: 2.sqrt(extend = False, all = True)

[sagetrac-ruckers]

Attachment: my1.patch.gz

Attachment: my2.patch.gz

Fixes the code: sage: FiniteField(next_prime(2^100))(2).sqrt(extend = False, all = True)

[sagetrac-ruckers]

comment:3

I was not able to fix this code.

sage: _.=FiniteField(9)

sage: a.sqrt(extend = False, all = True)

ValueError: must be a perfect square.

[mstreng]

comment:4

Thanks! That bug has been around for too long :)

Why were you not able to fix the FiniteField(9) case?

Unfortunately, the patches need some more work, for the following three reasons.

• With my2.patch:

  sage: Zmod(7)(3).sqrt(extend=True)
  sqrt3
  sage: Zmod(7)(3).sqrt(all=True, extend=True)
  []
  

  The second one should either output [sqrt3, -sqrt3] or raise NotImplementedError, but never an empty list.

• Patches must have your name and email address in them. This is done by putting your email address and name in your .hgrc file as specified here

• Add an example of the new functionality to the documentation:

  • This helps the user understand what the function does.
  • Through the doctesting framework, this prevents other people from accidentally breaking your added functionality.
  • This is required for your patch to be able to get a positive review. In fact, the manual says that you should also mention the ticket number square root with all=True should not return ValueError but empty list #9466 with your example.

If you have any questions, let me know!

[mstreng]

Attachment: 9466.2.patch.gz

[mstreng]

Attachment: 9466.3.patch.gz

[mstreng]

Changed keywords from none to sd23 sd51 sqrt all

[mstreng]

comment:5

Attachment: 9466.patch.gz

Does anyone know who user "ruckers" is? (s)he should be added to the list of authors

apply 9466.patch

[mstreng]

Author: Marco Streng

[mstreng]

comment:6

please review!

[mstreng]

Changed author from Marco Streng to Marco Streng and the person with trac account ruckers

[sagetrac-akoutsianas]

Reviewer: Alejandro Argaez, Angelos Koutsianas

[sagetrac-akoutsianas]

comment:7

The patch passed all the tests for sage 5.11 version.

[jdemeyer]

Merged: sage-5.12.beta3

[kcrisman]

Changed author from Marco Streng and the person with trac account ruckers to Marco Streng, Sonseeahray Rucker