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: 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)
```

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!

Those are NOT asymptotes. They are connecting the top of the randomly selected points super-close to the asymptotes, and so they look like asymptotes. What the answer does is show how to have those not connected.

Thanks for your comment. It does raise some questions, at least for this novice. How does the answer 'show how to have these not connected'? And how would you plot the graph with 'real' aymptotes (I understand that they would look the same as the connecting lines). I mean, I get that you could just draw vertical lines at multiples of pi/2, but is there an option that has plot(tan(x)...) draw the asymptotes? Thanks for any help.

See http://www.sagemath.org/doc/reference/plotting/sage/plot/plot.html#sage.plot.plot.plot and in particular "detect_poles - (Default: False) If set to True poles are detected. If set to show vertical asymptotes are drawn."

As I said to tmonteil (elsewhere on this page), that's what the document says, but it's not what the sage does. When you enter: sage: plot(tan(x), x, -pi, pi, detect_poles=show) you just get the graph of y = tan(x), without asymptotes. I thought perhaps this was because I was trying out cloud.sagemath, but then I tried the line in my downloaded version of sage (Sage Version 5.8, Release Date: 2013-03-15) and got the same result. And it's true if you enlarge the graph thus: sage: p = plot(tan(x), x, -pi, pi, detect_poles=show) sage: (p).show(xmin=-pi, xmax=pi, ymin=-10, ymax=10) I don't think the docs describe this behavior of plot() correctly. If you agree I think I'll send a little note to the people who maintain the docs. I appreciate your patience and interest.

I'll put my comments in an answer at this point.