On 02/14/2010 07:44 PM, Dana Ernst wrote:
Apparently, I'm not afraid to ask silly questions...
First, if someone can tell how to find out the answers by myself to some of the
kinds of questions I'm asking, please let me know.
For these questions, I think sage-support is a great place to find the
answers.
3. I'm trying to do plot some implicit functions. For example:
implicit_plot(x^3+y^3-2*x*y,(x,-3,3,),(y,-3,3))
(a) Why is the aspect ratio off?
The aspect ratio, by default, approximates the golden ratio, like a lot
of plotting programs. Maybe for implicit_plotting, it should default to
aspect_ratio=1. In fact, it should default to that for a lot of
plots---someone should look at this issue across all of plotting when
there is time. There is a trac ticket out there for doing "sensible"
aspect ratios for different kinds of plots.
(b) Is there a way to automatically display the axes?
use axes=True
implicit_plot(x^3+y^3-2*x*y,(x,-3,3,),(y,-3,3),axes=True)
(c) Can I color implicit plots?
Yes, using the not-very-intuitive cmap argument. The problem is that we
just pass things on to contour plot (i.e., plot the contour f==0), where
cmap makes sense, but it's not very intuitive for implicit_plot.
implicit_plot(x^3+y^3-2*x*y,(x,-3,3,),(y,-3,3),axes=True,cmap=['red'])
Can you open a trac ticket to wrap this in a color='red' argument for
implicit_plot?
(d) Is there a way to automatically display asymptotes (with dotted or dashed
lines)? (My example has one.)
hmmm...this is more difficult for implicit plots. I don't think code is
written for it, especially in your case where the asymptote is neither
vertical or horizontal. You can, of course, draw a dotted line
yourself. Maybe you could make a student project out of writing code to
automatically calculating the asymptote, and this could be added to Sage
for implicit plots?
4. When to use f.somecommand() is still mysterious to me. It seems that some
times, but not always, you can use somecommand(f). For example, take
f=(x+1)^2
Then both integral(f,x) and f.integral(x) work. However, f.is_zero() works,
but is_zero(f) does not. Can someone help me understand this (without having
to learn Python; I'll do that later)?
Certain functions are defined to work like function(f). These are in
sage/misc/functional.py, for example. Most functions use the .method()
syntax, though, to avoid cluttering the global namespace. Somewhere,
somewhen, somebody (William?) wrote code once that would take something
like is_zero(f) and automatically try to call f.is_zero() if the
is_zero() top-level function wasn't defined. I don't know how to turn
that on, though.
Thanks,
Jason
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