"Source: Text/Ring/Newton.text";
"Line: 1160";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Newton.text, line: 1160
// Example: H56E7 ()
print "Example: H56E7";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PuiseuxSeriesRing(Rationals());
R<y> := PolynomialRing(P);
f := (y^2 - x^3)^2 - y*x^6;
IsPartialRoot(f, x^(3/2));
assert $1;
IsUniquePartialRoot(f, x^(3/2));
assert not $1;
c := PuiseuxExpansion(f, 0);
A<a> := Parent(c[1]);
N<n> := CoefficientRing(A);
Q<q> := PolynomialRing(A);
c;
IsUniquePartialRoot(f, x^(3/2) + 1/2*x^(9/4));
assert $1;
ExpandToPrecision(f, x^(3/2) + 1/2*x^(9/4), 10);
IsPartialRoot(f, x^(3/2) + x^2);
assert not $1;
SetEchoInput(ei);
