Remember this old problem?
2008/1/21 Jordi Guti?rrez Hermoso <jordigh at gmail.com>:
> If my calculations are correct, the roots of x^6 + 3*x^5 + 6*x^4 +
> 3*x^3 + 9*x +9 should all be expressible by radicals. In fact, they
> are all polynomials in terms of 2^(1/3) and a cube root of unity.
>
> How can I make Maxima tell me what the roots actually are?
Turns out that it's easy with the factor command to solve it the way I want:
expand(map(rhs,solve(factor(factor(x^6+3*x^5+6*x^4+3*x^3+9*x+9,alpha^3
-2),zeta^2+zeta+1),x)));
Now, I just want to massage the solution. Making Maxima give me the
output the way I want it is never easy. :-/
Basically, I want Maxima to apply the equation zeta^2 = -zeta -1
wherever it can, so that I can get roots in this form:
alpha + zeta
alpha + zeta^2
alpha*zeta + zeta;
alpha*zeta + zeta^2;
alpha*zeta^2 + zeta;
alpha*zeta^2 + zeta^2;
Is this possible?
Thanks,
- Jordi G. H.