"Source: Text/Geometry/Toric.text";
"Line: 254";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Toric.text, line: 254
// Example: H129E4 ()
print "Example: H129E4";
ei := GetEchoInput();
SetEchoInput(true);
P:=PolytopeSmoothFanoDim3(15);
P;
X<x,y,u,z,v>:=ToricVariety(Rationals(),SpanningFan(P));
X;
IsNonsingular(X);
assert $1;
IsFano(X);
assert $1;
K:=CanonicalDivisor(X);
phi:=WeilToClassLatticesMap(X);
fano_idx:=GCD(Eltseq(phi(Weil(-K))));
fano_idx;
assert $1 eq 2;
half_K:=phi(Weil(-K)) / 2;
A:=Divisor(X,half_K @@ phi);
A;
IsCartier(A);
assert $1;
IsAmple(A);
assert $1;
bool:=AreLinearlyEquivalent(-K, 2 * A);
bool;
assert $1;
Degree(-K);
assert $1 eq 56;
HilbertCoefficients(-K,5);
SetEchoInput(ei);
