"Source: Text/Geometry/AlgSrf.text";
"Line: 6105";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/AlgSrf.text, line: 6105
// Example: H126E35 ()
print "Example: H126E35";
ei := GetEchoInput();
SetEchoInput(true);
q<tt> := PolynomialRing(RationalField());
p6 := tt^6 + 34*tt^4 + 180*tt^3 + 458*tt^2 + 524*tt + 212;
CoblesRadicand(p6);
assert $1 eq -676;
eqn := CubicSurfaceByHexahedralCoefficients(p6);
Max([AbsoluteValue(c) : c in Coefficients(eqn)]);
S := MinimizeReduce(DelPezzoSurface(eqn));
Equation(S);
M := PicardGaloisModule(S);
Order(Group(M));
assert $1 eq 72;
CohomologyGroup( CohomologyModule(Group(M),M), 1);
SetEchoInput(ei);
