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Your problem is that you are putting something in for detect_poles that is not 'show'.

Compare the following.

sage: plot(tan(x), x, -pi, pi, detect_poles=True) 
sage: plot(tan(x), x, -pi, pi, detect_poles=show) 
sage:

The first two are equivalent, because show is an actual function, hence Python evaluates it as a True boolean:

sage: bool(show)
True

But of course that will give the same behavior. You need the quotes in the last one to make the asymptotes appear. That is why the word is given as "show" and not show in the documentation.

That said, this will still be a not-so-helpful graph unless you use additional keywords.

sage: plot(tan(x), x, -pi, pi, detect_poles='show', ymin=-50,ymax=50)

image description

This is also the type of example given in the documentation:

sage: plot(gamma, (-3, 4), detect_poles = 'show').show(ymin = -5, ymax = 5)

Hope this helps!

Your problem is that you are putting something in for detect_poles that is not 'show'.

Compare the following.

sage: plot(tan(x), x, -pi, pi, detect_poles=True) 
sage: plot(tan(x), x, -pi, pi, detect_poles=show) 
sage:
sage: plot(tan(x), x, -pi, pi, detect_poles='show')

The first two are equivalent, because show is an actual function, hence Python evaluates it as a True boolean:

sage: bool(show)
True

But of course that will give the same behavior. You need the quotes in the last one to make the asymptotes appear. That is why the word is given as "show" and not show in the documentation.

That said, this will still be a not-so-helpful graph unless you use additional keywords.

sage: plot(tan(x), x, -pi, pi, detect_poles='show', ymin=-50,ymax=50)

image description

This is also the type of example given in the documentation:

sage: plot(gamma, (-3, 4), detect_poles = 'show').show(ymin = -5, ymax = 5)

Hope this helps!