On Friday 17 April 2009, Stavros Macrakis wrote:
> In this cubic, all three roots are real, but cannot be expressed with
> real radicals, even in principle. See
> http://en.wikipedia.org/wiki/Casus_irreducibilis . They *can* be
> expressed as real expressions involving trigonometric functions, which
> is what rectform does for you.
>
> That said, I wonder why you want the roots expressed as symbolic
> expressions. I suppose there must be some application where
> (8*cos(atan(sqrt(2101)/(69*sqrt(3)))/3)-sqrt(3))/sqrt(3) is more
> useful than 3.584428340330492, but usually the latter is what you
> really want, in which case why not calculate it directly using
> realroots or allroots (which, unlike solve, work for *all*
> polynomials, not just those which reduce to the quartic case or
> simpler by factorization or polynomial decomposition).
I still use Maxima 5.15.0,
and I cannot find poly_discriminant in the html documentation
poly_discriminant is nice to detect the casus irreducibilis
Andre