I tried the first example below in sage. It failed , complaining that
maxima wanted to know whether x was positive, negative or 0. Hence, I
tried maxima via "sage -maxima". To my surprise, maxima computed the
limit without asking for extra information. Is the maxima that gets
called from sage put in a more inquisitive mode?
I figure this might be a symptom of a sub-optimal interaction between
sage and maxima and hence might have some interest to developers.
///////////////////////////////////////////////////////////////////////////////////
%sage
var('p x')
limit((p+1)/pi*(1-x^2/4)/((sqrt(p)+sqrt(1/p))^2-x^2),p=oo)
//complains that maxima wants extra information
////////////////////////////////////////////////////////////////////////////////////
%maxima
f(p,x):=(p+1)/pi*(1-x^2/4)/((sqrt(p)+sqrt(1/p))^2-x^2);
limit(f(p,x),p, infinity);
//works
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