"Source: Text/Ring/RngLoc.text";
"Line: 1187";
"Date: Fri Sep 26 14:29:19 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngLoc.text, line: 1187
// Example: H49E6 ()
print "Example: H49E6";
ei := GetEchoInput();
SetEchoInput(true);
Zp := pAdicRing(5, 20);
I<a> := UnramifiedExtension(Zp, 3);
R<x> := PolynomialRing(I);
L<b> := ext<I | x^3 + 5*a*x^2 + 5>;
Prime(L);
assert $1 eq 5;
InertiaDegree(L);
assert $1 eq 1;
InertiaDegree(L, Zp);
assert $1 eq 3;
Degree(L);
assert $1 eq 3;
Degree(L, Zp);
assert $1 eq 9;
DefiningPolynomial(L);
P<y> := PolynomialRing(Zp);
DefiningPolynomial(I);
BaseRing(L);
PrimeRing(L);
PrimeRing(I);
ResidueClassField(L);
ResidueClassField(I);
UniformizingElement(L);
Precision(L);
assert $1 eq 60;
Precision(I);
assert $1 eq 20;
R<a> := ext<pAdicRing(2) | 2>;
DefiningPolynomial(R);
Precision(R);
SetEchoInput(ei);
