> I agree with Simon, although finding a nice expression like sqrt(2)+3^(1/3)
> can be very costly deppending on how the algebraic number was constructed.

Yepyep. As Simon said we cannot always express algebraic numbers in
such a nice way, though..... Well, if you want to build such an object
*in Sage* then you must describe your value somehow, and it is also
stored internally somewhere.. And I wonder how, and whether we can
base the representation on this internal version of the value :-)

> Anyways we could have such an expression for the cases where it is evident
> from the number construction.

+1

> Related to that, i think the current 17? digits are way too much for a
> visually nice representation. I would prefear to see 1.4142... than
> 1.414213562373095?  inside an expression.

+1. It would also lessen the odds of having people believe that it is
stored as a float (with possibly many, but finitely many, digits)

Nathann

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