Allow complex functions in implicit_plot

[sagetrac-ajdunlap]

Currently implicit_plot does not allow you to plot the zero sets of complex functions. It would be nice if one could do this. (This was mentioned in an email thread last year but I haven't found any other work on it.)

Depends on #32234
Depends on #8450

CC: @orlitzky

Component: graphics

Keywords: fast_callable

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/16899

[sagetrac-ajdunlap]

comment:1

I think this would be solved by switching contour_plot to use fast_callable instead of fast_float, as was done for plot in #15030.

[sagetrac-ajdunlap]

Changed keywords from none to fast_callable

[mkoeppe]

Dependencies: #32234

[orlitzky]

comment:4

This is probably fixed by #8450, but bugs in contour_plot are getting in the way (#21042).

[orlitzky]

comment:5

The following modification of the email example z - |z| works after #8450:

sage: x,y = SR.var('x,y')                                                       
sage: z = x + I*y                                                               
sage: f = (z - abs(z)).real()                                                   
sage: implicit_plot(f + 0.2, (0,1), (0,1))

First, you have to take the real part of the answer, since the plotting functions are expecting a real result. But then to avoid the issue in #21042, we have to perturb the whole thing (by 0.2, in my example).

If we are willing to accept the need to add real() onto the example, then I think we can consider this fixed by #8450, and deal with the contour_plot() zero issue on its own ticket.

[orlitzky]

Changed dependencies from #32234 to #32234, #8450