rootof ???

[parisse]

The 50g has a much less general system to handle algebraic extension, it handles square roots only. rootof is the general method to handle exactly roots of irreducible polynomials. For example
l:=csolve(x^3-x^2+x+1); normal(l[1]*l[2]+l[3]*l[1]+l[3]*l[2]);
There is a mechanism to detect some rootofs and rewrite them in a simpler way, that's always the case for real square roots. Perhaps it can be improved to rewrite this one in a more common way. But it's just writing, (1+i)*sqrt(2)/2 is not simpler for further exact computations that the rootof returned and if you need a numeric approximation, approx works on rootof.