"Source: Text/Ring/RngLoc.text";
"Line: 5738";
"Date: Fri Sep 26 14:29:19 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngLoc.text, line: 5738
// Example: H49E37 ()
print "Example: H49E37";
ei := GetEchoInput();
SetEchoInput(true);
Qp := pAdicField(17 : Exact);
P<x> := PolynomialRing(Qp : Exact);
f := (x - 14)*(x - Qp.1)*(x - Qp.1 - 1);
NewtonPolygon(f);
HasRoot(f);
Roots(f);
Factorization(f);
IsIrreducible(f);
IsHenselLiftable(f, Qp!14);
IsHenselLiftable(f, Qp!10);
RamificationResidualPolynomials(x^3 + 3*17*x^2 + 2*17^2*x + 5*17);
SetEchoInput(ei);
