"Source: Text/Ring/Newton.text";
"Line: 1234";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Newton.text, line: 1234
// Example: H56E8 ()
print "Example: H56E8";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PuiseuxSeriesRing(FiniteField(5, 3));
R<y> := PolynomialRing(P);
f := (1+x)*y^4 - x^(-1/3)*y^2 + y + x^(1/2);
time c := PuiseuxExpansion(f, 5); 
c;
PuiseuxExponents(c[1]);
PuiseuxExponents(c[3]);
P<x> := PuiseuxSeriesRing(FiniteField(5, 3));
R<y> := PolynomialRing(P);
f := ((y^2 - x^3)^2 - y*x^6)^2 - y*x^15;
c := PuiseuxExpansion(f, 0);
A<a> := Parent(c[1]);
N<n> := CoefficientRing(A);
Q<q> := PolynomialRing(A);
c;
PuiseuxExponentsCommon(c[1], c[1]);
PuiseuxExponentsCommon(c[1], c[2]);
PuiseuxExponentsCommon(c[1], c[3]);
PuiseuxExponentsCommon(c[1], c[8]);
SetEchoInput(ei);
