"Source: Text/Ring/FldAb.text";
"Line: 1809";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldAb.text, line: 1809
// Example: H41E9 ()
print "Example: H41E9";
ei := GetEchoInput();
SetEchoInput(true);
k := CyclotomicField(5);
kt := ext<k|>;   
K := NumberField(kt.1^20 - k.1*kt.1^10 +k.1^2);
A := AbelianExtension(K);
A;
Conductor(A);
m_0, m_inf := $1;
A := AbelianExtension(K : Conductor := [* m_0, m_inf *]);
IsLocalNorm(A, BaseRing(A)!2);
assert not $1;
IsLocalNorm(A, BaseRing(A)!5);
assert $1;
Knot(A);                                       
NormEquation(A, BaseRing(A)!5);
_, s := $1;
Norm(s[1]);
assert $1 eq 5;
SetEchoInput(ei);
