allow vertical slopes in slope field plots

[kcrisman]

plot_slope_field(x/y, (x,-2,2), (y,-2,2)).show(aspect_ratio=1)

currently won't show the vertical slopes at y=0, x nonzero, but there is no mathematical reason it shouldn't, so this should be fixed.

Component: graphics

Issue created by migration from https://trac.sagemath.org/ticket/5553

[jasongrout]

comment:1

plot_vector_field is already fixed. See #5259.

[jasongrout]

comment:2

That said, it'd be great to fix plot_slope_field to detect when you have a vertical slope and have it change things accordingly. I think this should be easy: just see what vectors have finite X, infinite Y, and set them to be zero X, one Y.

[kcrisman]

comment:3

I see, I thought that there was also a question of allowing infinite vectors, which I thought was weird. I didn't realize it didn't return a plot at all before!

Yes, so I will change the summary and description of this to fixing plot_slope_field. The problem is that it will be a sort of messy hack, unless it's dealt with in the plot_vector_field code using a keyword (I attempted to start this), but then you are trying to catch something that looks like (1/inf,inf/inf=NaN), which is a little tricky. But doing it in plot_slope_field means you might as well just do all the stuff in plot_vector_field there, since you'll have to catch individual vectors anyway - which is annoying, since it seems redundant.