Hello (about factoring into explicit algebraic numbers)

>
> Your problem cannot be solved in general form mathematically,
> and so you should not expect that some program would solve it.
>

Yes, of course. But in terms of what a user might expect... Maxima in
general has a "best effort" philosophy -- integrate and solve and for that
matter basic simplification do whatever they can -- which is far short of
what is theoretically possible.

Maxima could perfectly well factor all quartics etc. irreducible over the
integers. But the reason it shouldn't is pragmatic -- it is usually not
useful to have big messes of factorization.

I think the helpful and educational answer to queries like this is a simple
little Maxima function that uses Solve to find roots and constructs the
polynomial. The user should quickly realize that the results are usually
uninteresting. Another useful variant would factorize into *real* factors
(as requested by a previous user). Then there's the floating case, where
realroots/allroots are the right way to proceed (though of course the
numerical result may be numerically unstable).

-s