"Source: Text/Ring/FldFunG.text";
"Line: 1862";
"Date: Thu Jun 16 15:04:46 2022";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Ring/FldFunG.text, line: 1862
// Example: H45E15 ()
print "Example: H45E15";
ei := GetEchoInput();
SetEchoInput(true);
Qt<t> := FunctionField(Rationals());
Qtx<x> := PolynomialRing(Qt);
f := x^9 - 3*x^7 + (-6*t - 6)*x^6 + 3*x^5 + (12*t - 6)*x^4 + 
(12*t^2 - 84*t + 11)*x^3 + (-6*t - 6)*x^2 + (-12*t^2 + 12*t + 24)*x - 
8*t^3 - 24*t^2 - 24*t - 6;
time GeometricGaloisGroup(f);
f := x^6 + t^6 - 1; 
HilbertIrreducibilityCurves(f);
SetEchoInput(ei);
