"Source: Text/Ring/FldCyc.text";
"Line: 384";
"Date: Tue Jun  7 22:27:14 2016";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldCyc.text, line: 384
// Example: H38E2 ()
print "Example: H38E2";
ei := GetEchoInput();
SetEchoInput(true);
R<x> := PolynomialRing(RationalField());
W := { R | };
l := 13;
L<z> := CyclotomicField(l);
M := Divisors(l-1);
g := PrimitiveRoot(l);
for m in M do
   d := (l-1) div m;
   g_d := g^d;
   w := &+[z^g_d^i : i in [0..m-1] ];
   Include(~W, MinimalPolynomial(w));
end for;
W := { R | MinimalPolynomial(&+[z^(g^((l-1) div m))^i : i in [0..m-1] ]) :
       m in M };
W;
SetEchoInput(ei);
