[Maxima] Finding roots of sextic in radicals

Stavros Macrakis macrakis at alum.mit.edu
Tue Jan 22 09:54:28 CST 2008


On Jan 22, 2008 7:38 AM, S. Newhouse <sen1 at math.msu.edu> wrote:

> Jordi Gutiérrez Hermoso wrote:
> ...the roots of x^6 + 3*x^5 + 6*x^4 + 3*x^3 + 9*x +9 should all be
> expressible by radicals....
>


>
> Using the fact that the roots are polynomials in 2^(1/3), the following
> commands makes the list sol_list of roots.
>

Nice solution!  Maxima actually lets you do this even more simply:

    p: x^6+3*x^5+6*x^4+3*x^3+9*x+9;
    p2: factor(p,q^3-2)$
    solve(subst(q=2^(1/3),p2),x);

             -s
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