"Source: Text/Geometry/Crv.text";
"Line: 7249";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Crv.text, line: 7249
// Example: H124E43 ()
print "Example: H124E43";
ei := GetEchoInput();
SetEchoInput(true);
P4<x,y,z,t,u> := ProjectiveSpace(Rationals(),4);
C := Curve(P4,[
-x^2-x*y-y*z+z^2-x*t-y*t-z*t+t^2-x*u+y*u-t*u,
-x*y+y^2+y*z+x*t+y*t-z*t+z*u+t*u+u^2,
-x^2-x*y-y*z+z^2+x*t-y*t+t^2-x*u+y*u+z*u+t*u+u^2]);
g,mp4,F,f := Genus5GonalMap(C);
g;
assert $1 eq 4;
mp4;
F;
P3<x,y,z,t> := ProjectiveSpace(Rationals(),3);
C := Curve(P3,[ x^2*y^2-x^2*t^2-z^2*t^2+2*t^4,
   y^4-x*z^2*t-2*y^2*t^2+2*x*t^3+t^4,
   x^3-y^2*t+t^3 ]);
Genus(C);
assert $1 eq 6;
g,t,mp4,mpE := Genus6GonalMap(C);
g; t;
mp4;
mpE;
SetEchoInput(ei);
