comparison with quadratic number field elements

[mwhansen]

sage: I^2
-1
sage: bool(I^2 < 0)
True
sage: bool(I^2 > 0)
True

Apply:

• attachment: trac_7160-doctest.take2.patch

Depends on #13213

CC: @videlec

Component: number fields

Keywords: sd35

Author: Vincent Delecroix

Reviewer: Burcin Erocal

Merged: sage-5.11.beta0

Issue created by migration from https://trac.sagemath.org/ticket/7160

[mwhansen]

comment:2

This is basically the same as #6132.

[JohnCremona]

comment:3

I think this is confusing: you have an ordering of elements of a real or imaginary quadratic field which is based on some kind of lexicographic ordering on the representation of the elements rather than anything mathematical. Presumably this is so lists, etc, can be sorted in a pythonic way. But I find this bizarre:

sage: K.<i> = QuadraticField(-1)
sage: i>0
True

and this raises a strange error:

sage: K.<a> = NumberField(x^2+x-10)
sage: a < -a
---------------------------------------------------------------------------
SystemError                               Traceback (most recent call last)

/home/john/.sage/temp/ubuntu/790/_home_john__sage_init_sage_0.py in <module>()

SystemError: error return without exception set
sage: Type(K)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)

/home/john/.sage/temp/ubuntu/790/_home_john__sage_init_sage_0.py in <module>()

NameError: name 'Type' is not defined
sage: type(K)
<class 'sage.rings.number_field.number_field.NumberField_quadratic'>

[kcrisman]

comment:4

Apparently related to #6132 and #10064, see this sage-devel discussion.

[mwhansen]

comment:5

I've put up a new patch which is minimally invasive and fixes the issue.

[kcrisman]

comment:6

Does this result in any interesting speed regressions when doing things with I?