Looks great, thanks for all the help!
I'll see about messing around with complex_plot a bit to support pure zero
plots, if it amounts to something I'll get back in touch...
On Monday, June 10, 2013 11:55:28 AM UTC-5, William wrote:
>
> Try this:
>
> z,n = var('z,n')
>
> @interact
> def _(f = ((z+1)^n-abs(z^n+1)), n = (2..10), B=(2..10)):
> f = f.subs(n=n)
> show(f)
> show(complex_plot(f, (-B,B), (-B,B)))
>
> On Mon, Jun 10, 2013 at 9:42 AM, <computati...@gmail.com <javascript:>>
> wrote:
> > Okay, so the following works:
> >
> >
> > z = var('z')
> > n = 2
> > @interact
> > def _(f = ((z+1)^n-abs(z^n+1)), B=(2..10)):
> > show(complex_plot(f, (-B,B), (-B,B)))
> >
> > But the following doesn't:
> >
> >
> > z = var('z')
> >
> > @interact
> > def _(f = ((z+1)^n-abs(z^n+1)), n = (2..10), B=(2..10)):
> > show(complex_plot(f, (-B,B), (-B,B)))
> >
> > On Monday, June 10, 2013 11:33:01 AM UTC-5, William wrote:
> >>
> >> On Mon, Jun 10, 2013 at 9:24 AM, <computati...@gmail.com> wrote:
> >> > Ah, that's unfortunate. Might be a fun summer project to try to
> >> > implement,
> >> > if I knew where to start.
> >>
> >> 1. http://www.sagemath.org/development.html
> >>
> >> 2. SAGE_ROOT/devel/sage/sage/plot/complex_plot.pyx which I found by
> >> doing search_src('complex_plot')
> >>
> >> > On another note: I really like the @interact annotation. I'm messing
> >> > around
> >> > with it, because I would like to add another parameter to my plot -
> an
> >> > integer representing an index in a discrete family of functions. But
> I
> >> > keep
> >> > getting python errors about my expression not being symbolic when I
> try
> >> > to
> >> > include an integer parameter (like n = var('n'), then passing in
> n=2).
> >> > Any
> >> > tips?
> >>
> >> Just put
> >>
> >> n = 2
> >>
> >> instead? You have to post code for a more useful answer....
> >>
> >> >
> >> > On Monday, June 10, 2013 11:13:41 AM UTC-5, William wrote:
> >> >>
> >> >> On Mon, Jun 10, 2013 at 9:09 AM, <computati...@gmail.com> wrote:
> >> >> > Thanks, this is exactly what I was looking for!
> >> >> >
> >> >> > In fact, I had tried out complex_plot but I must have been using a
> >> >> > different
> >> >> > color function or something, because the roots were much less
> >> >> > apparent
> >> >> > to
> >> >> > me. Not sure why I couldn't figure this out on my own...
> >> >> >
> >> >> > I suppose I have two follow-up questions now:
> >> >> > 1. how can I improve the precision of the zero set (it seems to be
> >> >> > drawn
> >> >> > in
> >> >> > low resolution right now)
> >> >>
> >> >> Use plot_points:
> >> >>
> >> >> f(z) = z - abs(z)
> >> >> complex_plot(f, (-3,3), (-3,3), plot_points=200)
> >> >>
> >> >> > 2. what is the best way to "turn off" the other colors (draw
> >> >> > non-zeros
> >> >> > as
> >> >> > white)
> >> >>
> >> >> I don't know if this is possible or implemented at present.
> >> >>
> >> >> >
> >> >> > On Monday, June 10, 2013 10:02:12 AM UTC-5, William wrote:
> >> >> >>
> >> >> >> On Sun, Jun 9, 2013 at 3:25 PM, <computati...@gmail.com> wrote:
> >> >> >> > Suppose I have a complex function f(z) with a continuous family
> of
> >> >> >> > zeros
> >> >> >> > (e.g., f(z)=z-|z|)
> >> >> >> >
> >> >> >> > Is there a way to easily plot the set of zeros of f in sage,
> >> >> >> > regardless
> >> >> >> > of how complicated the function f is?
> >> >> >> >
> >> >> >>
> >> >> >> You might find complex_plot useful. For example, for
> >> >> >>
> >> >> >> f(z) = z - abs(z)
> >> >> >> complex_plot(f, (-3,3), (-3,3))
> >> >> >>
> >> >> >> you'll see a *black line* at the zero set of f(z).
> >> >> >>
> >> >> >> In the notebook you mind find an interact like this useful:
> >> >> >>
> >> >> >>
> >> >> >> z = var('z')
> >> >> >> @interact
> >> >> >> def _(f = z-abs(z), B=(2..10)):
> >> >> >> show(complex_plot(f, (-B,B), (-B,B)))
> >> >> >>
> >> >> >> Or just click on
> >> >> >>
> >> >> >>
> http://sagecell.sagemath.org/?q=cdcdd7e5-73b4-4c87-87e2-1be300f86674
> >> >> >>
> >> >> >> > --
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> >> >> >> >
> >> >> >>
> >> >> >>
> >> >> >>
> >> >> >> --
> >> >> >> William Stein
> >> >> >> Professor of Mathematics
> >> >> >> University of Washington
> >> >> >> http://wstein.org
> >> >> >
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> >> >>
> >> >>
> >> >> --
> >> >> William Stein
> >> >> Professor of Mathematics
> >> >> University of Washington
> >> >> http://wstein.org
> >> >
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> >> --
> >> William Stein
> >> Professor of Mathematics
> >> University of Washington
> >> http://wstein.org
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>
> --
> William Stein
> Professor of Mathematics
> University of Washington
> http://wstein.org
>
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