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
of self what to do.  limit requires "x=x0" as second argument, and not "x==x0"
as would be natural for an equation.  The syntax for lambda is completely
different to usual function definition - no parens for example.  sage just eats
all cpu time when I call contour_plot with an equation as self by mistake.  In
general, it seems that functions are "dangerous", i.e., do little to no type
checking, but it's not at all clear when a method does the same thing as the
function, and when it is available at all (eg. contour_plot is not a method,
while plot is.)  A general rule would be extremely helpful here.

Sorry for the rant.

"William Stein" <[EMAIL PROTECTED]> writes:
> Is this what you want?
> 
> sage: (sin(x)^(1/3)).taylor(x,0,10)
> x^(1/3) - x^(7/3)/18 - x^(13/3)/3240 - 53*x^(19/3)/1224720 -
> 191*x^(25/3)/62985600

Oh, I didn't realize that taylor does Puiseux.  Can I coerce this to an object
of PowerSeriesRing, or something similar, so that I can play with it?  In other
words: is there a Ring of Puiseux series in Sage?

More questions:

Is there a way to obtain a power series solution to a differential equation?

Is there a way to solve an ODE?

(ideally, without resorting to maxima or fricas syntax...)

Many thanks,

Martin


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