"Source: Text/Ring/Newton.text";
"Line: 1716";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Newton.text, line: 1716
// Example: H56E10 ()
print "Example: H56E10";
ei := GetEchoInput();
SetEchoInput(true);
SetVerbose("Newton", 1);
P<x> := PuiseuxSeriesRing(Rationals());
R<y> := PolynomialRing(P);
f := y^3 + 2*x^-1*y^2 + 1*x^-2*y + 2*x;
Roots(f);
f := f^2;
Roots(f);
f := y^3 + 2*x^-1*y^2 + 1*x^-2*y + 2*x;
f +:= O(x^20)*(y^3 + y^2 + y + 1);
f;
Roots(f, 10);
f := f^2;
f;
Roots(f, 10);
f := (y - x^(1/4))*(y - x^(1/3));                                            
Roots(f);
SetEchoInput(ei);
