# Galois group command for Magma online calculator?

I need to test if a family of 7th deg and 13 deg equations are solvable. I’m new to Magma, so my apologies, but what would I type in,

http://magma.maths.usyd.edu.au/calc/

to determine the Galois group of $x^5+5x-12=0$ (for example)?

#### Solutions Collecting From Web of "Galois group command for Magma online calculator?"

> P< x >:=PolynomialAlgebra(Rationals());

> f:=x^5+5*x-12;

> G:=GaloisGroup(f);

> print G;

Symmetric group G acting on a set of cardinality 5
Order = 120 = 2^3 * 3 * 5

Although the permutation group on [1..Degree($f$)] is permutationally isomorphic to the Galois group, the bijection with the set of roots of your separable irreducible polynomial $f$ is not determined. For more details see the Magma handbook.

GaloisGroup(FldFin, FldFin) is available. Make an extension of F_7 using your polynomial then call GaloisGroup.

GaloisGroup is also available for polynomials over char p function fields. Coerce your polynomial to be over a function field over F_7 and compute the GaloisGroup of that polynomial.