"Source: Text/Geometry/Scheme.text";
"Line: 7309";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 7309
// Example: H122E57 ()
print "Example: H122E57";
ei := GetEchoInput();
SetEchoInput(true);
P<x,y,z> := ProjectiveSpace(RationalField(),2);
f := x^5+x^2*y^3+y^2*z^3+x^2*z^3-y*z^4-z^5;
C := Curve(P,f);
Genus(C);
assert $1 eq 5;
SetVerbose("IsoToSub",1);
SetVerbose("EmbCrv",1);
C1, mp := EmbedPlaneCurveInP3(C);
P1 := AmbientSpace(C1);
AssignNames(~P1,["a","b","c","d"]);
C1;
Dimension(C1);
assert $1 eq 1;
ArithmeticGenus(C1);
assert $1 eq 5;
IsNonsingular(C1);
assert $1;
SetEchoInput(ei);
