Thanks for the replies (and the great work!).  Some followup below:

> Nope, none of these are fixed by the new changes.  I tried Maple and
> it did the same thing -- I don't know what Mathematica does.  You can
> do these as a workaround:
>

Interesting that Maple does it.  Anyone know about Mma?  Mac's Grapher
definitely IS smart about this, rather elegantly so.

> sage: plot(tan,-20,20).show(ymin=-5, ymax=5)
> sage: plot((x-1)/(x+2),-4,4).show(ymin=-10, ymax=10)
>

Of course, these plots still have the Intermediate Value Property on
the entire real line.

> I don't know the best way to be "smart" about fixing this such as how
> much of the asymptote to include, etc.

Yeah, I was thinking about this, because what you would really want to
do is have an algorithm which would automatically check if the 'bend'
was too great compared to the rest of the function and then NOT plot
the line connecting those points.  But would that slow plotting down
too much (since you'd have to compare *all* the bends to each other,
not just to max_bend like in adaptive refinement, as I understand
it)?  Not to mention trying to decide what "too great compared" means.

Speaking of asymptotes, any ideas on 
http://trac.sagemath.org/sage_trac/ticket/3907
?  I would be glad to try it, but don't understand enough of how
infinity and _tasteful_ticks work in Sage.

> > 1) It would be useful for those involved to put a summary of the
> > plotting improvements/changes in internals on a wiki page, once the
> > whole overhaul is complete.
>
> I'll do this in the next day or two.

Thanks.

>
> > 2) Specifically, will the old syntax plot(sin,-5,5) continue to be
> > valid under the new plot(sin,(-5,5)) syntax, or will it be completely
> > deprecated?  Despite the logic of the new syntax, the old one is
> > REALLY convenient and intuitive, and it would be a shame to have to
> > change all those old worksheets...
>
> plot(sin, -5, 5) still works.
>

Very good!  Any ideas on why plot(2*sin, -5, 5) doesn't (see
http://trac.sagemath.org/sage_trac/ticket/3906)?  Again, I'd be glad
to help if I understood anything of the symbolics.

- kcrisman
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