bobo.sagews

var('x')

x

f=x^3+3*x-1
f

x^3 + 3*x - 1

r=f.roots()
r
pretty_print(r)

[(-1/2*(1/2*sqrt(5) + 1/2)^(1/3)*(I*sqrt(3) + 1) + 1/2*(-I*sqrt(3) + 1)/(1/2*sqrt(5) + 1/2)^(1/3), 1), (-1/2*(1/2*sqrt(5) + 1/2)^(1/3)*(-I*sqrt(3) + 1) + 1/2*(I*sqrt(3) + 1)/(1/2*sqrt(5) + 1/2)^(1/3), 1), ((1/2*sqrt(5) + 1/2)^(1/3) - 1/(1/2*sqrt(5) + 1/2)^(1/3), 1)]

[($\displaystyle -\frac{1}{2} \, {\left(\frac{1}{2} \, \sqrt{5} + \frac{1}{2}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{-i \, \sqrt{3} + 1}{2 \, {\left(\frac{1}{2} \, \sqrt{5} + \frac{1}{2}\right)}^{\frac{1}{3}}}$, $\displaystyle 1$), ($\displaystyle -\frac{1}{2} \, {\left(\frac{1}{2} \, \sqrt{5} + \frac{1}{2}\right)}^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + \frac{i \, \sqrt{3} + 1}{2 \, {\left(\frac{1}{2} \, \sqrt{5} + \frac{1}{2}\right)}^{\frac{1}{3}}}$, $\displaystyle 1$), ($\displaystyle {\left(\frac{1}{2} \, \sqrt{5} + \frac{1}{2}\right)}^{\frac{1}{3}} - \frac{1}{{\left(\frac{1}{2} \, \sqrt{5} + \frac{1}{2}\right)}^{\frac{1}{3}}}$, $\displaystyle 1$)]