On Ubuntu 14.04 LTS Opteron, (a SageMathCloud node), I get numerical
noise failures, as alluded to above:

sage -t --long --warn-long 57.7
src/sage/rings/polynomial/polynomial_element.pyx  # 2 doctests failed
sage -t --long --warn-long 57.7 src/sage/rings/real_double.pyx  # 2
doctests failed
sage -t --long --warn-long 57.7 src/sage/modular/modform/numerical.py
# 2 doctests failed

In particular,

sage -t --long --warn-long 57.7 src/sage/rings/polynomial/polynomial_element.pyx
**********************************************************************
File "src/sage/rings/polynomial/polynomial_element.pyx", line 3059, in
sage.rings.polynomial.polynomial_element.Polynomial.factor
Failed example:
    f.factor()  # abs tol 1e-6
Expected:
    (x - 0.9999894993080326) * (x^2 - 2.0000105006919666*x + 1.0000105008022333)
Got:
    (x - 1.0000065719436413) * (x^2 - 1.9999934280563585*x + 0.9999934280995487)
Tolerance exceeded in 3 of 4:
    - 0.9999894993080326 vs - 1.0000065719436413, tolerance 2e-05 > 1e-06
    - 2.0000105006919666 vs - 1.9999934280563585, tolerance 2e-05 > 1e-06
    + 1.0000105008022333 vs + 0.9999934280995487, tolerance 2e-05 > 1e-06
**********************************************************************
File "src/sage/rings/polynomial/polynomial_element.pyx", line 3066, in
sage.rings.polynomial.polynomial_element.Polynomial.factor
Failed example:
    f.roots()  # abs tol 1e-6
Expected:
    [(0.9999894993080326, 1)]
Got:
    [(1.0000065719436413, 1)]
Tolerance exceeded in 1 of 2:
    0.9999894993080326 vs 1.0000065719436413, tolerance 2e-05 > 1e-06
**********************************************************************
1 item had failures:
   2 of 147 in sage.rings.polynomial.polynomial_element.Polynomial.factor
    [1644 tests, 2 failures, 17.03 s]


sage -t --long --warn-long 57.7 src/sage/rings/real_double.pyx
**********************************************************************
File "src/sage/rings/real_double.pyx", line 587, in
sage.rings.real_double.RealDoubleField_class._factor_univariate_polynomial
Failed example:
    f.roots(ring=CDF)  # abs tol 1e-6
Expected:
    [(0.9999894993080326, 1), (1.0000052503459833 -
9.09398093719616e-06*I, 1), (1.0000052503459833 +
9.09398093719616e-06*I, 1)]
Got:
    [(1.0000065719436413, 1),
     (0.9999967140281792 - 5.691454546815028e-06*I, 1),
     (0.9999967140281792 + 5.691454546815028e-06*I, 1)]
Tolerance exceeded in 5 of 8:
    0.9999894993080326 vs 1.0000065719436413, tolerance 2e-05 > 1e-06
    1.0000052503459833 vs 0.9999967140281792, tolerance 9e-06 > 1e-06
    - 9.09398093719616e-06 vs - 5.691454546815028e-06, tolerance 3e-06 > 1e-06
    1.0000052503459833 vs 0.9999967140281792, tolerance 9e-06 > 1e-06
    + 9.09398093719616e-06 vs + 5.691454546815028e-06, tolerance 3e-06 > 1e-06
**********************************************************************
File "src/sage/rings/real_double.pyx", line 592, in
sage.rings.real_double.RealDoubleField_class._factor_univariate_polynomial
Failed example:
    f.factor()  # abs tol 1e-6
Expected:
    (x - 0.9999894993080326) * (x^2 - 2.0000105006919666*x + 1.0000105008022333)
Got:
    (x - 1.0000065719436413) * (x^2 - 1.9999934280563585*x + 0.9999934280995487)
Tolerance exceeded in 3 of 4:
    - 0.9999894993080326 vs - 1.0000065719436413, tolerance 2e-05 > 1e-06
    - 2.0000105006919666 vs - 1.9999934280563585, tolerance 2e-05 > 1e-06
    + 1.0000105008022333 vs + 0.9999934280995487, tolerance 2e-05 > 1e-06
**********************************************************************
1 item had failures:


sage -t --long --warn-long 57.7 src/sage/modular/modform/numerical.py
**********************************************************************
File "src/sage/modular/modform/numerical.py", line 463, in
sage.modular.modform.numerical.NumericalEigenforms.systems_of_eigenvalues
Failed example:
    numerical_eigenforms(61).systems_of_eigenvalues(10)  # rel tol 5e-14
Expected:
    [
    [-1.4811943040920152, 0.8060634335253695, 3.1563251746586642,
0.6751308705666477],
    [-1.0, -2.0000000000000027, -3.000000000000003, 1.0000000000000044],
    [0.3111078174659775, 2.903211925911551, -2.525427560843529,
-3.214319743377552],
    [2.170086486626034, -1.7092753594369208, -1.63089761381512,
-0.46081112718908984],
    [3.0, 4.0, 6.0, 8.0]
    ]
Got:
    [
    [-1.4811943040920155, 0.8060634335253688, 3.1563251746586602,
0.675130870566645],
    [-0.9999999999999977, -2.0000000000000004, -3.0000000000000058,
0.9999999999999948],
    [0.3111078174659795, 2.9032119259115508, -2.525427560843526,
-3.2143197433775454],
    [2.1700864866260234, -1.7092753594369228, -1.6308976138151452,
-0.46081112718911454],
    [3.0, 4.0, 6.0, 8.0]
    ]
Tolerance exceeded in 1 of 20:
    -0.46081112718908984 vs -0.46081112718911454, tolerance 5e-14 > 5e-14
**********************************************************************
File "src/sage/modular/modform/numerical.py", line 490, in
sage.modular.modform.numerical.NumericalEigenforms.systems_of_abs
Failed example:
    numerical_eigenforms(61).systems_of_abs(10)  # rel tol 5e-14
Expected:
    [
    [0.3111078174659775, 2.903211925911551, 2.525427560843529,
3.214319743377552],
    [1.0, 2.0000000000000027, 3.000000000000003, 1.0000000000000044],
    [1.4811943040920152, 0.8060634335253695, 3.1563251746586642,
0.6751308705666477],
    [2.170086486626034, 1.7092753594369208, 1.63089761381512,
0.46081112718908984],
    [3.0, 4.0, 6.0, 8.0]
    ]
Got:
    [
    [0.3111078174659795, 2.9032119259115508, 2.525427560843526,
3.2143197433775454],
    [0.9999999999999977, 2.0000000000000004, 3.0000000000000058,
0.9999999999999948],
    [1.4811943040920155, 0.8060634335253688, 3.1563251746586602,
0.675130870566645],
    [2.1700864866260234, 1.7092753594369228, 1.6308976138151452,
0.46081112718911454],
    [3.0, 4.0, 6.0, 8.0]
    ]
Tolerance exceeded in 1 of 20:
    0.46081112718908984 vs 0.46081112718911454, tolerance 5e-14 > 5e-14
**********************************************************************
2 items had failures:



---

Also, all those by default "warning slow doctests" things in the log
(on doing "make ptestlong") are annoying...

On Sun, Sep 28, 2014 at 9:47 AM, John Cremona <[email protected]> wrote:
> I am getting a doctest failure in src/doc/en/bordeaux_2008/elliptic_curves.rst
> and I wonder if others can confirm or deny.  You should have
>
> sage: C = CremonaDatabase()
> sage: C[37]
> {'allcurves': {'a1': [[0, 0, 1, -1, 0], 1, 1],
>   'b1': [[0, 1, 1, -23, -50], 0, 3],
>   'b2': [[0, 1, 1, -1873, -31833], 0, 1],
>   'b3': [[0, 1, 1, -3, 1], 0, 3]}}
>
> but with 6.4.beta4 + the optional larger database_cremona_ellcurve
> installed I get something different because C[37] now has many more
> fields and displays different ones first.  It would be sensible to
> replace the doctest as is with
>
> sage: C[37]['allcurves']
> {'a1': [[0, 0, 1, -1, 0], 1, 1],
>  'b1': [[0, 1, 1, -23, -50], 0, 3],
>  'b2': [[0, 1, 1, -1873, -31833], 0, 1],
>  'b3': [[0, 1, 1, -3, 1], 0, 3]}
>
> I think this will have been caused by the new doctest output
> formatting recently merged.
>
> John
>
>
> On 28 September 2014 13:46, Volker Braun <[email protected]> wrote:
>> This is some more fallout from #16858. Jeroen, do you already have a
>> followup ticket for numerical noise?
>>
>>
>>
>> On Saturday, September 27, 2014 9:51:46 PM UTC+1, Justin C. Walker wrote:
>>>
>>>
>>> On Sep 27, 2014, at 07:51 , Volker Braun wrote:
>>>
>>> > As usual, get the updated "develop" git branch. Alternatively,
>>> > self-contained source tarball is here:
>>> >
>>> > http://boxen.math.washington.edu/home/release/sage-6.4.beta4.tar.gz
>>>
>>> Built from the tarball on two OS X systems (10.6.8/Dual 6-core Xeons;
>>> 10.9.5/Quad-core Core i7).  Build completed successfully on each.
>>>
>>> On 10.9.5, the tests ('pteestlong') completed w/o problems.
>>> On 10.6.8, there was one glitch,
>>>   sage -t --long --warn-long 84.6
>>> src/sage/rings/polynomial/polynomial_element.pyx
>>>   # 3 doctests failed
>>>
>>> The failures are repeatable.
>>>
>>> viz:
>>>
>>> File "src/sage/rings/polynomial/polynomial_element.pyx", line 5345, in
>>> sage.ring
>>> s.polynomial.polynomial_element.Polynomial.roots
>>> Failed example:
>>>     ((x^3 -1)).roots()
>>> Expected:
>>>     [(0.9999999999999998, 1)]
>>> Got:
>>>     [(1.0000000000000002, 1)]
>>> **********************************************************************
>>> File "src/sage/rings/polynomial/polynomial_element.pyx", line 5347, in
>>> sage.ring
>>> s.polynomial.polynomial_element.Polynomial.roots
>>> Failed example:
>>>     ((x^3 -1)).roots(multiplicities=False)
>>> Expected:
>>>     [0.9999999999999998]
>>> Got:
>>>     [1.0000000000000002]
>>> **********************************************************************
>>> File "src/sage/rings/polynomial/polynomial_element.pyx", line 5453, in
>>> sage.ring
>>> s.polynomial.polynomial_element.Polynomial.roots
>>> Failed example:
>>>     for (fld_in, fld_out) in flds:
>>>         x = polygen(fld_in)
>>>         f = x^3 - fld_in(2)
>>>         x2 = polygen(fld_out)
>>>         f2 = x2^3 - fld_out(2)
>>>         for algo in (None, 'pari', 'numpy'):
>>>             rts = f.roots(ring=fld_out, multiplicities=False)
>>>             if fld_in == fld_out and algo is None:
>>>                 print fld_in, rts
>>>             for rt in rts:
>>>                 assert(abs(f2(rt)) <= 1e-10)
>>>                 assert(rt.parent() == fld_out)
>>> Expected:
>>>     Real Field with 53 bits of precision [1.25992104989487]
>>>     Real Double Field [1.2599210498948734]
>>>     Real Field with 100 bits of precision [1.2599210498948731647672106073]
>>>     Complex Field with 53 bits of precision [1.25992104989487,
>>> -0.62996052494743
>>> ... - 1.09112363597172*I, -0.62996052494743... + 1.09112363597172*I]
>>>     Complex Double Field [1.259921049894873, -0.6299605249474364 -
>>> 1.09112363597
>>> 17214*I, -0.6299605249474365 + 1.0911236359717214*I]
>>>     Complex Field with 100 bits of precision
>>> [1.2599210498948731647672106073, -0
>>> .62996052494743658238360530364 - 1.0911236359717214035600726142*I,
>>> -0.6299605249
>>> 4743658238360530364 + 1.0911236359717214035600726142*I]
>>> Got:
>>>     Real Field with 53 bits of precision [1.25992104989487]
>>>     Real Double Field [1.259921049894873]
>>>     Real Field with 100 bits of precision [1.2599210498948731647672106073]
>>>     Complex Field with 53 bits of precision [1.25992104989487,
>>> -0.62996052494743
>>> 7 - 1.09112363597172*I, -0.629960524947437 + 1.09112363597172*I]
>>>     Complex Double Field [1.2599210498948727, -0.6299605249474364 -
>>> 1.0911236359
>>> 717214*I, -0.6299605249474362 + 1.0911236359717211*I]
>>>     Complex Field with 100 bits of precision
>>> [1.2599210498948731647672106073, -0
>>> .62996052494743658238360530364 - 1.0911236359717214035600726142*I,
>>> -0.6299605249
>>> 4743658238360530364 + 1.0911236359717214035600726142*I]
>>> **********************************************************************
>>>
>>> Justin
>>>
>>> --
>>> Justin C. Walker, Curmudgeon at Large
>>> Institute for the Absorption of Federal Funds
>>> -----------
>>> Like the ski resort full of girls hunting for husbands
>>> and husbands hunting for girls, the situation is not
>>> as symmetrical as it might seem.
>>>   - Alan MacKay
>>> --
>>>
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>
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-- 
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
[email protected]

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