"Source: Text/Ring/Newton.text";
"Line: 1067";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Newton.text, line: 1067
// Example: H56E6 ()
print "Example: H56E6";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PuiseuxSeriesRing(Rationals());
R<y> := PolynomialRing(P);
f := y^3 + 2*x^-1*y^2 + 1*x^-2*y + 2*x;
c := PuiseuxExpansion(f, 0);
A<a> := Parent(c[1]);
N<n> := CoefficientRing(A);
Q<q> := PolynomialRing(A);
c;
[ExpandToPrecision(f, c[i], 10) : i in [1 .. #c]];
c := PuiseuxExpansion(f, 10);
A<a> := Parent(c[1]);
N<n> := CoefficientRing(A);
c;
time c := PuiseuxExpansion(f, 100);
time c := PuiseuxExpansion(f, 10);
A<a> := Parent(c[1]);
N<n> := CoefficientRing(A);
time ExpandToPrecision(f, c[1], 100);
SetEchoInput(ei);
