"Source: Text/Ring/RngLoc.text";
"Line: 3462";
"Date: Fri Sep 26 14:29:19 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngLoc.text, line: 3462
// Example: H49E23 ()
print "Example: H49E23";
ei := GetEchoInput();
SetEchoInput(true);
P<y> := PolynomialRing(Integers());
L<b> := ext<ext<pAdicRing(5, 20) | 2> |  y^2 + 5*y + 5>;
R<x> := PolynomialRing(L);
f := (x - 1)^3*(x - b)^2*(x - b^2 + b - 1);
SuggestedPrecision(f);
Factorization(f);
f := (x + 2)^3*(x + b)*(x + 3)^4;
f;
SuggestedPrecision(f);
Precision(L);
P<y> := PolynomialRing(Integers());
R<b> := ext<ext<pAdicRing(3, 20) | 2> |  y^2 + 3*y + 3>;
P<x> := PolynomialRing(R);
f := x^12 + 100*x^11 + 4050*x^10 + 83700*x^9 + 888975*x^8 + 3645000*x^7 - 
10570500*x^6 - 107163000*x^5 + 100875375*x^4 + 1131772500*x^3 - 
329614375*x^2 + 1328602500*x + 332150625;
SuggestedPrecision(f);
Factorization(f);
R<b> := ext<ext<pAdicRing(3, 25) | 2> |  y^2 + 3*y + 3>;
P<x> := PolynomialRing(R);
f := x^12 + 100*x^11 + 4050*x^10 + 83700*x^9 + 888975*x^8 + 3645000*x^7 -
10570500*x^6 - 107163000*x^5 + 100875375*x^4 + 1131772500*x^3 -
329614375*x^2 + 1328602500*x + 332150625;
Factorization(f);
SetEchoInput(ei);
