"Source: Text/Ring/RngLoc.text";
"Line: 423";
"Date: Fri Sep 26 14:29:19 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngLoc.text, line: 423
// Example: H49E2 ()
print "Example: H49E2";
ei := GetEchoInput();
SetEchoInput(true);
R<x> := PolynomialRing(Integers());
R1 := pAdicRing(2, 20);
R2 := ext<R1 | 5>;
R2;
DefiningPolynomial(R2);
R3 := ext<R1 | 5 : Cyclotomic>;
R3;
DefiningPolynomial(R3);
R3.1^(2^5-1);
assert $1 eq 1;
P1<x> := PolynomialRing(R1);
f1 := x^3 + 3*x + 1;
IsInertial(f1);
assert $1;
R4 := ext<R1 | f1>;
R4;
P2<y> := PolynomialRing(R2);
f2 := y^3 + 3*y + 1;
IsInertial(f2);
assert $1;
ext<R2 | f2>;
SetEchoInput(ei);
