Test failure in `plot/plot.py` with specific random seed

[antonio-rojas]

Only happens when testing with --long and using this specific random seed (even though the test itself is not tagged long and does not use any random data)

sage -t --long --random-seed=169929447503951982293191593843049330333 /usr/lib/python3.10/site-packages/sage/plot/plot.py
**********************************************************************
File "/usr/lib/python3.10/site-packages/sage/plot/plot.py", line 1824, in sage.plot.plot.plot
Failed example:
    plot(f, (x, -3.5, 3.5), detect_poles='show', exclude=[-3..3], ymin=-5, ymax=5)
Expected:
    Graphics object consisting of 12 graphics primitives
Got:
    Graphics object consisting of 13 graphics primitives
**********************************************************************

Component: graphics

Issue created by migration from https://trac.sagemath.org/ticket/34772

[tornaria]

Here is this happening without --long for a different seed:

sage -t --warn-long 63.8 --random-seed=282881802734238572874437030739135357256 /usr/lib/python3.11/site-packages/sage/plot/plot.py
**********************************************************************
File "/usr/lib/python3.11/site-packages/sage/plot/plot.py", line 1824, in sage.plot.plot.plot
Failed example:
    plot(f, (x, -3.5, 3.5), detect_poles='show', exclude=[-3..3], ymin=-5, ymax=5)
Expected:
    Graphics object consisting of 12 graphics primitives
Got:
    Graphics object consisting of 13 graphics primitives
**********************************************************************

In fact, this happens about 0.5% of the time:

sage: f(x) = (floor(x)+0.5) / (1-(x-0.5)^2)
sage: ls = [ len(plot(f, (x, -3.5, 3.5), detect_poles='show', exclude=[-3..3], ymin=-5, ymax=5)) for _ in range(1000) ]
sage: ls.count(12)
994
sage: ls.count(13)
6

I guess an easy fix is to replace 12 by ... but I wonder if this is the only place where this happens.

Plotting seems highly non-deterministic:

sage: [len(p) for p in plot(f, (x, -3.5, 3.5), detect_poles='show', exclude=[-3..3], ymin=-5, ymax=5)]
[19, 33, 45, 167, 2, 138, 43, 184, 2, 209, 58, 17]
sage: [len(p) for p in plot(f, (x, -3.5, 3.5), detect_poles='show', exclude=[-3..3], ymin=-5, ymax=5)]
[19, 33, 48, 128, 2, 172, 43, 211, 2, 192, 58, 16]
sage: [len(p) for p in plot(f, (x, -3.5, 3.5), detect_poles='show', exclude=[-3..3], ymin=-5, ymax=5)]
[17, 35, 47, 155, 2, 152, 39, 207, 2, 205, 59, 16]
...
sage: [len(p) for p in plot(f, (x, -3.5, 3.5), detect_poles='show', exclude=[-3..3], ymin=-5, ymax=5)]
[16, 36, 48, 160, 2, 140, 2, 41, 209, 2, 211, 56, 16]

[tornaria]

Aha, the segments of length 2 above correspond to the vertical asymptotes drawn at the poles. The difference between 12 or 13 primitives is an extra 2 drawing a vertical segment on x=0 which the axes shadow. You can see it with axes=False:

• 12 primitives

• 13 primitives

So this seems to be a bug after all, as this function doesn't have a pole at x=0.