"Source: Text/Ring/FldFunG.text";
"Line: 1742";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 1742
// Example: H46E13 ()
print "Example: H46E13";
ei := GetEchoInput();
SetEchoInput(true);
k<t>:= FunctionField(Rationals());
R<x>:= PolynomialRing(k);
f:= x^15 + (-1875*t^2 - 125)*x^3 + (4500*t^2 + 300)*x^2 + 
    (-3600*t^2 - 240)*x + 960*t^2+ 64;
G, r, S:= GaloisGroup(f);
TransitiveGroupDescription(G);
A := Universe(r);
AssignNames(~A,  ["t"]);
A;
r[1];
S;
TransitiveGroupIdentification(G);
SetEchoInput(ei);
