On Nov 15, 2007, at 3:52 AM, David Joyner wrote:
> On Nov 15, 2007 2:49 AM, William Stein <[EMAIL PROTECTED]> wrote:
>>
>> On Nov 15, 2007 1:45 AM, Dan Drake <[EMAIL PROTECTED]> wrote:
>> Unfortunately, Sage does not have an implementation of computing
>> a numerical approximation of erf(a) when a is not real, as PARI only
>
> In that case, what is going on here?
>
> sage: w = var("w")
> sage: f = lambda w: exp((w+sqrt(-1))^2)
> sage: f(w)
> e^(w + I)^2
> sage: f(w).nintegral(w,0,2)[0]
> -4.4746871004750179
> sage: f = lambda w: real(exp((w+sqrt(-1))^2))
> sage: f(w).nintegral(w,0,2)[0]
> -4.4746871004750179
> sage: f = lambda w: imag(exp((w+sqrt(-1))^2))
> sage: f(w).nintegral(w,0,2)[0]
> -1.2224121101763701
I believe nintegral evaluates f itself at several points to
approximate the integral, whereas erf is only needed when one
evaluates the integral symbolically and then tries to evaluate at a
point.
- Robert
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