doctest fix for: cot(float) returns complex

[paulmasson]

sage: cot(float(.1))
(9.966644423259224+0j)

This causes a plot of cot() on the real axis to fail. Sample output:

sage: set_verbose(1)
sage: plot(cot(x),(x,.1,.5),plot_points=5)
verbose 1 (3743: plot.py, generate_plot_points) can't convert complex to float
Unable to compute f(0.1) (time = 1.604825)
verbose 1 (3743: plot.py, generate_plot_points) can't convert complex to float
Unable to compute f(0.199629500548) (time = 1.615858)
verbose 1 (3743: plot.py, generate_plot_points) can't convert complex to float
Unable to compute f(0.263010079144) (time = 1.616164)
verbose 1 (3743: plot.py, generate_plot_points) can't convert complex to float
Unable to compute f(0.373209060982) (time = 1.616497)
verbose 1 (3743: plot.py, generate_plot_points) can't convert complex to float
Unable to compute f(0.5) (time = 1.616673)
verbose 0 (3743: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 5 points.
verbose 0 (3743: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'
Launched png viewer for Graphics object consisting of 0 graphics primitives

There is no problem plotting 1/tan().

Component: symbolics

Author: Ralf Stephan

Branch/Commit: c0ef7a5

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/21365

[rwst]

comment:2

real(cot(x)) works too.

[rwst]

comment:3

When inserting a print at this line:
https://github.com/pynac/pynac/blob/master/ginac/inifcns_trig.cpp#L777
in order to print what is returned there I get:

9.96664442325922
verbose 1 (3743: plot.py, generate_plot_points) can't convert complex to float
Unable to compute f(0.1) (time = 0.176)
...

which is exactly cot(0.1) and does not look complex. So Pynac does not seem the direct cause of it.

[paulmasson]

comment:4

I downloaded older binaries to determine the version in which this error first occurs. The cotangent plots just fine in 7.1 and fails in 7.2.

Sage 7.2.rc1 included Pynac 0.6.5, which is precisely the last time the cotangent function was modified in Pynac. That is unlikely to be a coincidence.

This is not a graphics issue. The plotting method returning the error hasn't been modified in years. And this is not the first time in my experience a change in Pynac has had consequences for plotting (#20818).

[tscrim]

comment:5

The issue is when you pass a floating point, not a sage.rings.real_mpfr.RealLiteral:

sage: cot(float(0.5))
(1.8304877217124513+0j)

in contrast with:

sage: type(sin(float(1.1)))
<type 'float'>

Thus the bug is likely coming from that the internal plot functions use python/machine floating points as they are Python (i.e., not run through the Sage preparser).

[tscrim]

comment:6

Tracing slightly further, the python math (which is the first place the code checks) does not have a cot function. Looking into it more now.

[tscrim]

comment:7

Okay, I'm not quite sure what happens. It seems to fall into the generic Function.__call__, but I'm just tracing through the logical output at this point.

[paulmasson]

Description changed:

--- 
+++ 
@@ -1,4 +1,10 @@
-Sample output:
+
+```
+sage: cot(float(.1))
+(9.966644423259224+0j)
+```
+
+This causes a plot of cot() on the real axis to fail. Sample output:
 
 ```
 sage: set_verbose(1)
@@ -18,13 +24,4 @@
 Launched png viewer for Graphics object consisting of 0 graphics primitives
 ```
 
-This is peculiar because the individual points look fine:
-
-```
-sage: cot(.5)
-1.83048772171245
-sage: type(cot(.5))
-<type 'sage.rings.real_mpfr.RealNumber'>
-```
-
-Some type of coercion error somewhere? There is no problem plotting 1/tan().
+There is no problem plotting 1/tan().