Sharedsupport / 2016-01-19-141325-galois-group.sagewsOpen in CoCalc
Examples for support purposes...
x = polygen(QQ,'x')
f = x^4 + 3*x^2 + 1
G = f.galois_group()
G

Transitive group number 2 of degree 4
G.gens()

[(1,2)(3,4), (1,4)(2,3)]
G.order()

4
show(f.roots(ring=SR))

[($\displaystyle -\sqrt{\frac{1}{2} \, \sqrt{5} - \frac{3}{2}}$, $\displaystyle 1$), ($\displaystyle \sqrt{\frac{1}{2} \, \sqrt{5} - \frac{3}{2}}$, $\displaystyle 1$), ($\displaystyle -\sqrt{-\frac{1}{2} \, \sqrt{5} - \frac{3}{2}}$, $\displaystyle 1$), ($\displaystyle \sqrt{-\frac{1}{2} \, \sqrt{5} - \frac{3}{2}}$, $\displaystyle 1$)]