"Source: Text/Ring/FldFunG.text";
"Line: 2014";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 2014
// Example: H46E16 ()
print "Example: H46E16";
ei := GetEchoInput();
SetEchoInput(true);
F<t> := FunctionField(GF(5));
P<x> := PolynomialRing(F);
f := x^3-2*t;
GaloisSplittingField(f);
K, R, G := $1;
K:Maximal;
[x^3 : x in R];
GaloisSplittingField(f:Name := "K");
(K where K := $1):Maximal;
G, r, S := GaloisGroup(f);
GaloisSplittingField(f:Galois := <G, r, S>, 
    Chain := CompositionSeries(G), Name := "K", AllAuto);
(K where K := $1):Maximal;
f := x^6 - t^14*x^4 - t^19*x^2 - t^52;
G, r, S := GaloisGroup(f); G;
TransitiveGroupIdentification(G);
TransitiveGroupDescription(G);
time K, R := GaloisSplittingField(f:Name := "K");
K:Maximal;
SetEchoInput(ei);
