"Source: Text/RepThy/GalRep.text";
"Line: 1869";
"Date: Fri Sep 26 12:10:12 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/RepThy/GalRep.text, line: 1869
// Example: H58E49 ()
print "Example: H58E49";
ei := GetEchoInput();
SetEchoInput(true);
K:=pAdicField(3,20);
R<x>:=PolynomialRing(K);
list:=GaloisRepresentations(x^5-3);
list;
[Minimize(A): A in list];
forall{A: A in list | A eq Minimize(A)};
F:=ext<K|4>;                    // Take F = degree 4 unr. ext. of K, and
B:=PermutationCharacter(F,K);   // any B with BaseField(B)=K, Field(B)=F
list[2];
Minimize(list[2]: To:=B);
Minimize(list[2]);
SetEchoInput(ei);
