"Source: Text/Geometry/AlgSrf.text";
"Line: 6366";
"Date: Mon Mar 29 22:30:18 2021";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Geometry/AlgSrf.text, line: 6366
// Example: H123E39 ()
print "Example: H123E39";
ei := GetEchoInput();
SetEchoInput(true);
r4<x,y,z,w> := PolynomialRing(Rationals(),4);
surf := x^3 + (x-y+2*z)^3 + (y-w)^3 + z^3 + (x - 3*y-2*z-7*w)^3;
p_id := PentahedronIdeal(surf);
Points(Cluster(ProjectiveSpace(Rationals(),3),Basis(p_id)));
diag := x^3 + y^3 + z^3 + w^3;
p_id2 := PentahedronIdeal(diag);
Points(Cluster(ProjectiveSpace(Rationals(),3),Basis(p_id2)));
degen := x^3+y^3+z^3 + x*y*z+ w^3;
p_id3 := PentahedronIdeal(degen);
Points(Cluster(ProjectiveSpace(Rationals(),3),Basis(p_id3)));
SetEchoInput(ei);
