On Nov 15, 2007 1:45 AM, Dan Drake <[EMAIL PROTECTED]> wrote:
>
> I discovered Sage recently and am very excited about it. In grad school,
> I came to be very good with Mathematica, and am now doing a postdoc
> where I only have access to (an old copy of) Maple. I like the idea of
> having my mathematical software being only a 'wget' away, and even more
> I like the idea of being able to see how it works and change it as I see
> fit.
>
> But I'm having difficulty even defining a relatively simple function and
> finding a floating-point approximation. I want to do
>
> f := x -> integrate(exp(t^2), t=0..x); (Maple)
> evalf(f(2));
>
> f[x_] := Integrate[Exp[t^2], {t, 0, x}] (Mathematica)
> N[f[2]]
>
> in Sage. I know Python, and Sage is built with Python, so I tried
>
> sage: def f(x): integrate(exp(t^2), t, 0, x)
>
> which complains that "global name 't' is not defined" when I try to
> evaluate it. I don't want a global variable, just a local one to do the
> integration!
You can define that function and compute the integral in Sage as
follows:
sage: assume(x > 0)
sage: f(x,t) = integrate(exp(t^2), t, 0, x)
sage: f
(x, t) |--> -sqrt(pi)*I*erf(I*x)/2
sage: a = f(x,0)
sage: a
-sqrt(pi)*I*erf(I*x)/2
The assume is needed above because of how Maxima works (you'll be
non-interactively
asked for it if you don't give it).
Unfortunately, Sage does not have an implementation of computing
a numerical approximation of erf(a) when a is not real, as PARI only
provides this function in case a is real, and maxima also seems to
only provide it in that case. Thus you can't actually numerically evaluate
the result at some point.
You are the second person to request numerical evaluation of erf... at a
complex argument this week (Paul Zimmerman requested the same
thing a few days ago). So I hope one of the Sage developers looks into
this. I've made it:
http://trac.sagemath.org/sage_trac/ticket/1173
I also made
http://trac.sagemath.org/sage_trac/ticket/1174
which is related.
> What's the right way to go about all this? Like I said, I'm very excited
> about Sage, but this is not such an auspicious start.
Calculus is actually not at all the main focus of Sage or Sage development
yet, unfortunately, though the calculus package is very powerful. It's
something we introduced pretty recently into Sage, but it will still take
some time to get every reasonable thing implemented, which very much
is our goal. We need more people-power though, at least for the calculus
part of Sage (where there are currently very few developers compared
to other parts of Sage).
-- William
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