implement round for number field elements with real embedding

[videlec]

Real embedded element has a floor and ceil but no round (= nearest integer)

sage: a = QuadraticField(2).gen()
sage: a.floor()
1
sage: a.ceil()
2
sage: a.round()
Traceback (most recent call last):
...
AttributeError: 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic' object has no attribute 'round'

Depends on #22095

CC: @mkoeppe @seblabbe

Component: number fields

Keywords: days79

Author: Vincent Delecroix

Branch/Commit: 720f040

Reviewer: Jean-Philippe Labbé, Sébastien Labbé

Issue created by migration from https://trac.sagemath.org/ticket/21935

[videlec]

New commits:

720f040

21935: implement round for nf element

[videlec]

Branch: u/vdelecroix/21935

[videlec]

Commit: 720f040

[jplab]

comment:2

Hi Vincent,

This looks good to me. All test passed on Sage7.5.b3. Up to the reaction of the bot, you can set it to positive review.

JP

[jplab]

Author: Vincent Delecroix

[jplab]

Reviewer: Jean-Philippe Labbé

[videlec]

comment:3

patchbot is happy ;-)

[vbraun]

comment:4

On OSX

5772sage -t --long src/sage/rings/number_field/number_field_element_quadratic.pyx
5773**********************************************************************
5774File "src/sage/rings/number_field/number_field_element_quadratic.pyx", line 1997, in sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic.round
5775Failed example:
5776    for _ in range(100):
5777       a = QQ.random_element(1000,20)
5778       b = QQ.random_element(1000,20)
5779       assert round(a) == round(K2(a)), a
5780       assert round(a) == round(K3(a)), a
5781       assert round(a) == round(K5(a)), a
5782       assert round(a+b*sqrt(2.)) == round(a+b*sqrt2), (a, b)
5783       assert round(a+b*sqrt(3.)) == round(a+b*sqrt3), (a, b)
5784       assert round(a+b*sqrt(5.)) == round(a+b*sqrt5), (a, b)
5785Exception raised:
5786    Traceback (most recent call last):
5787      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 498, in _run
5788        self.compile_and_execute(example, compiler, test.globs)
5789      File "/Users/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 861, in compile_and_execute
5790        exec(compiled, globs)
5791      File "<doctest sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic.round[8]>", line 5, in <module>
5792        assert round(a) == round(K3(a)), a
5793    AssertionError: 9/11
5794**********************************************************************
57951 item had failures:
5796   1 of  10 in sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic.round
5797    [472 tests, 1 failure, 21.51 s]

[seblabbe]

comment:6

I can reproduce the doctest failure.

But I can not reproduce the problem on the command line:

sage: a = 9/11
sage: round(a)
1
sage: round(K3(a))
1

[seblabbe]

comment:7

With

diff --git a/src/sage/rings/number_field/number_field_element_quadratic.pyx b/src/sage/rings/number_field/number_field_element_quadratic.pyx
index 83f5495..fad31df 100644
--- a/src/sage/rings/number_field/number_field_element_quadratic.pyx
+++ b/src/sage/rings/number_field/number_field_element_quadratic.pyx
@@ -2054,7 +2054,8 @@ cdef class NumberFieldElement_quadratic(NumberFieldElement_absolute):
             ....:    a = QQ.random_element(1000,20)
             ....:    b = QQ.random_element(1000,20)
             ....:    assert round(a) == round(K2(a)), a
-            ....:    assert round(a) == round(K3(a)), a
+            ....:    if not round(a) == round(K3(a)): 
+            ....:        print "left={}, right={}, a={}".format(round(a), round(K3(a)), a)
             ....:    assert round(a) == round(K5(a)), a
             ....:    assert round(a+b*sqrt(2.)) == round(a+b*sqrt2), (a, b)
             ....:    assert round(a+b*sqrt(3.)) == round(a+b*sqrt3), (a, b)

I get:

$ sage -tp src/sage/rings/number_field/number_field_element_quadratic.pyx
Running doctests with ID 2016-12-23-15-11-57-2aaeb3bd.
Git branch: 21935
Using --optional=4ti2,atlas,ccache,latte_int,meataxe,mpir,pandoc_attributes,pandocfilters,python2,rst2ipynb,sage
Doctesting 1 file using 4 threads.
sage -t --warn-long 40.9 src/sage/rings/number_field/number_field_element_quadratic.pyx
**********************************************************************
File "src/sage/rings/number_field/number_field_element_quadratic.pyx", line 2053, in sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic.round
Failed example:
    for _ in range(100):
       a = QQ.random_element(1000,20)
       b = QQ.random_element(1000,20)
       assert round(a) == round(K2(a)), a
       if not round(a) == round(K3(a)): 
           print "left={}, right={}, a={}".format(round(a), round(K3(a)), a)
       assert round(a) == round(K5(a)), a
       assert round(a+b*sqrt(2.)) == round(a+b*sqrt2), (a, b)
       assert round(a+b*sqrt(3.)) == round(a+b*sqrt3), (a, b)
       assert round(a+b*sqrt(5.)) == round(a+b*sqrt5), (a, b)
Expected nothing
Got:
    left=1, right=0, a=9/11
    left=0, right=1, a=1/13
**********************************************************************
1 item had failures:
   1 of  10 in sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic.round
    [485 tests, 1 failure, 7.31 s]
----------------------------------------------------------------------
sage -t --warn-long 40.9 src/sage/rings/number_field/number_field_element_quadratic.pyx  # 1 doctest failed
----------------------------------------------------------------------

[videlec]

comment:8

Can someone can give me ssh access to an OSX computer? This really needs to be fixed!!

[seblabbe]

comment:9

Replying to @videlec:

Can someone can give me ssh access to an OSX computer? This really needs to be fixed!!

I was using my desktop at work when I reproduced the error earlier today which runs Ubuntu.

Don't you get the same error on your machine?

[videlec]

comment:10

Indeed, I am able to reproduce it and has nothing to do with the current branch

Failed example:
    K3(9/11) - 0
Expected:
    9/11
Got:
    -1/2*sqrt3 + 9/11

[videlec]

comment:11

Even better ;-)

Failed example:
    K3.zero()
Expected:
    0
Got:
    1/2*sqrt3

[videlec]

comment:12

#22095

[videlec]

comment:13

test passes for me when #22095 applied.

[videlec]

Dependencies: #22095

[seblabbe]

Changed reviewer from Jean-Philippe Labbé to Jean-Philippe Labbé, Sébastien Labbé

[seblabbe]

comment:14

I do not have access anymore to my Ubuntu machine to test the problem I had earlier.

All tests passed on my OSX. Positive review.

[vbraun]

Changed branch from u/vdelecroix/21935 to 720f040