"Source: Text/Geometry/CrvCon.text";
"Line: 1015";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvCon.text, line: 1015
// Example: H130E9 ()
print "Example: H130E9";
ei := GetEchoInput();
SetEchoInput(true);
SetSeed(19);
P2<x,y,z> := ProjectiveSpace(RationalField(), 2);
f := 9220*x^2 + 97821*x*y + 498122*y^2 + 8007887*y*z - 3773857*z^2;
C := Conic(P2, f);
HasRationalPoint(C);
p := RationalPoint(C);
p;
p := C! [157010/741 , -19213/741 , 1];
IsReduced(p);
assert $1;
q := Random(C : Reduce := true);
q;
IsReduced(q);
assert $1;
q := Random(C : Bound := 10^5);
q;
IsReduced(q);
assert not $1;
Reduction(q);
IsReduced($1);
assert $1;
phi := Parametrization(C);
P1<u,v> := Domain(phi);
q0 := P1![0, 1];  q1 := P1![1, 1];  q2 := P1![1, 0];
phi(q0);
phi(q1);
phi(q2);
C1, psi := ReducedLegendreModel(C);
psi(phi(q0));
p0 := Reduction($1);
p0;
IsReduced(p0);
assert $1;
p0 @@ psi;
SetEchoInput(ei);
