"Source: Text/Ring/Newton.text";
"Line: 525";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Newton.text, line: 525
// Example: H56E4 ()
print "Example: H56E4";
ei := GetEchoInput();
SetEchoInput(true);
P<y> := PuiseuxSeriesRing(Rationals());
R<x> := PolynomialRing(P);
f := 3*x^4 + (5*y^3 + 4*y^(1/4))*x^3 + (7*y^2 + 1/2*y^(1/3))*x^2 + 6*x + y^(
4/5);
N := NewtonPolygon(f);
N6 := NewtonPolygon({<1, 4>, <1, 6>, <2, 4>, <3, 1>, <6, 1>, <5, 2>, <4, 5>,
<4, 7>, <6, 6>, <7, 7>, <2, 7>, <5, 9>, <8, 4>, <8, 6>, <8, 8>, <7, 9>});
AN := AllFaces(N);
AN;
A6 := AllFaces(N6);
A6;
AllVertices(N);
AllVertices(N6);
EndVertices(AN[1]);
EndVertices(AN[4]);
EndVertices(A6[1]);
EndVertices(A6[5]);
EndVertices(A6[9]);
FacesContaining(N, <1, 0>);
FacesContaining(N6, <1, 0>);
FacesContaining(N6, <4, 1>);
FacesContaining(N, <4, 1>); 
FacesContaining(N6, <3, 1>);
SetEchoInput(ei);
