"Source: Text/Geometry/CrvCon.text";
"Line: 1330";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvCon.text, line: 1330
// Example: H130E12 ()
print "Example: H130E12";
ei := GetEchoInput();
SetEchoInput(true);
k := FiniteField(101);
P2<x,y,z> := ProjectiveSpace(k, 2);
f := x^7 + 3*x^3*y^2*z^2 + 5*y^4*z^3;
C := Curve(P2, f);
Genus(C);
assert $1 eq 0;
p := C![2,33,1];
p;
IsNonsingular(C, p);
assert $1;
P1<u,v> := ProjectiveSpace(k, 1);
phi := Parametrization(C, Place(p), Curve(P1));
phi;
Image(phi);
DefiningIdeal(Image(phi)) eq DefiningIdeal(C);
assert $1;
phi(P1![1, 0]);
SetEchoInput(ei);
