>
> Maxima does solve 2,3,4-degree polynomials (and their functional
> compositions using polydecomp, try x^6+2*x^4-x^3+x^2-x-1) using radicals
> -- in the Solve command. Although *some* polynomials of higher degree
> (e.g. x^5+20*x+32) can be solved in radicals, Maxima does not support
> that.
maxima's solve command can be extended to some high-order polinomials,
such as sum(a[i]*((lambda^(n-1)*x^i+x^(n+i),i,0,n)=0, which requires
lisp hacking.
factoring with respect to roots is called 'splitting' in certain CASes.
--
Andrei Zorine