 LIB "polymake.lib";
ring r=0,(x,y,z),dp;
matrix M[4][1]=1,x,y,z;
poly f=y3+x2+xy+2xz+yz+z2+1;
// the Newton polytope of f is
list gf=groebnerFanP(f);
// the exponent vectors of f are ordered as follows
gf[4];
// the first cone of the groebner fan has the inequalities
gf[1][1][1];
// as a string they look like
gf[1][1][2];
// and it has the extreme rays
print(gf[1][1][3]);
// the linearity space is spanned by
print(gf[2]);
// the vertices of the Newton polytope are:
gf[3][1];
// its dimension is
gf[3][2];
// np[3] contains information how the vertices are connected to each other,
// e.g. the 1st vertex is connected to the 2nd, 3rd and 4th vertex
gf[3][3][1];
