>
> The former seems likely : Maxima's default for domain is "real" (and in
> turns out that my example runs under this assumption). In sage, immediatly
> after the horror reported above :
>
> sage: maxima("domain")
> complex
> sage: maxima("domain:real;")
> real
> sage: maxima("ratsimp(integrate(%e^-x*sinh(sqrt(x)),x,0,inf)),
> gamma_expand:super;")
> %e^(1/4)*sqrt(%pi)/2
>
> This problem happens often enough to make me wonder if integrate, limit
> and analytical friends shouldn't deserve a "maxima_domain" option, set to
> "complex" by default but settable as "real for one-shots.
>
> <PipeDream>
> Similarly, an easy shortcut such as analytical_domain (or maxima.domain ?)
> could be introduced and widely publicized...
> </PipeDream>
>
>
You can do
sage: maxima_calculus("domain:real")
real
sage: integrate(e^-x*sinh(sqrt(x)),x,0,oo)
1/4*sqrt(pi)*(erf(1) - 1)*e^(1/4) - 1/4*(sqrt(pi)*(erf(1) - 1) - sqrt(pi) +
2*e^(-1) - 2)*e^(1/4) + 1/4*sqrt(pi)*e^(1/4) - 1/2*e^(1/4) + 1/2*e^(-3/4)
sage: _.simplify_rational()
1/2*sqrt(pi)*e^(1/4)
while in a vanilla Sage session, for me
sage: integrate(e^-x*sinh(sqrt(x)),x,0,oo)
<hangs for a loooonng time>
Yes this should be much better documented. See
also http://trac.sagemath.org/ticket/14630 and I think there are some
related tickets.
Maybe it's time for someone (who knows what they are doing) to write a
"thematic tutorial" on "hard calculus problems in Sage".
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