"David Joyner" <[EMAIL PROTECTED]> writes:
> On Mon, Oct 27, 2008 at 1:59 PM, Martin Rubey <[EMAIL PROTECTED]> wrote:
> >
> > Dear William,
> >
> > thanks for your quick answer, even though it doesn't make me too happy. I'm
> > having a hard time here, I must admit. So far I thought that sage would do
> > most things out of the box, and it's only inconsistent (eg., arguments to
> > plot,
> > plot3d and integrate vary wildly. There are several functions plot, plot3d,
> > contour_plot, parametric_plot, etc. and not only one that decides on the
> > type
>
>
> I don't see the problem in having more than one function name for plotting.
Well, the problem is namespace pollution. Already now, if I hit tab after x, I
get roughly 100 possible completions. In a strongly typed environment, this is
unnecessary. I do not see any benefit in having more than one name to do one
thing. Of course, if the argument types are the same you will probably need to
have several functions.
> Actually I think I agree with you about one (easily fixed) problem, since the
> various plot functions might be hard to find. It would be nice for all
> plotting functions to start with plot (eg, plot_parametric could be an alias
> for parametric_plot), so the variations can be found by tab completion.
Oh no, more namespace pollution :-)
> > Is there a way to obtain a power series solution to a differential equation?
>
> David Harvey implemented something for 1st order linear DEs of the form
> y'=ay+b:
>
> sage: R.<t> = PowerSeriesRing(QQ, default_prec=10)
> sage: a = 2 - 3*t + 4*t^2 + O(t^10)
> sage: b = 3 - 4*t^2 + O(t^7)
> sage: a.solve_linear_de(prec=5, b=b, f0=3/5)
> 3/5 + 21/5*t + 33/10*t^2 - 38/15*t^3 + 11/24*t^4 + O(t^5)
> > Is there a way to solve an ODE?
> >
> > (ideally, without resorting to maxima or fricas syntax...)
>
> Yes, in the 1st or 2nd order linear cases, but the methods call Maxima:
>
> sage: x = var('x')
> sage: y = function('y', x)
> sage: desolve(diff(y,x) + y - 1, y)
> e^(-x)*(e^x + c)
> sage: f = desolve(diff(y,x) + y - 1, y, ics=[10,2]); f
> e^(-x)*(e^x + e^10)
> sage: plot(f)
>
> See calculus/desolvers for more details/examples. Hats off to
> Robert Bradshaw for this.
Ah, great. That's exactly what I was looking for (except, why is it called
desolve and not solve, so I can find it...?) And why is it a function?
Martin
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