"Source: Text/Ring/FldNum.text";
"Line: 2491";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldNum.text, line: 2491
// Example: H36E15 ()
print "Example: H36E15";
ei := GetEchoInput();
SetEchoInput(true);
x := PolynomialRing(Integers()).1;
K := NumberField([x^2-229, x^2-2]);
NormEquation(K, 3);
F := AbsoluteField(K);
t := F!K.2;
t^2;
assert $1 eq 2;
A, _, mA := AutomorphismGroup(F);
S := sub<A | [ x : x in A | mA(x)(t) eq t]>;
N := map<F -> F | x:-> &* [ mA(y)(x) : y in S]>;
NormEquation(3, N);
f, s, base := NormEquation(3, N:Raw);
s;
z := PowerProduct(base, s[1]);
z;
N(z);
assert $1 eq 3;
SetEchoInput(ei);
