"Source: Text/Geometry/Crv.text";
"Line: 7043";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Crv.text, line: 7043
// Example: H124E42 ()
print "Example: H124E42";
ei := GetEchoInput();
SetEchoInput(true);
P5<x,y,z,s,t,u> := ProjectiveSpace(Rationals(),5);
C := Curve(P5,[
-y*z+x*s-y*s+z*t-4*s*t+t^2+2*s*u-3*t*u+2*u^2,
-z^2+s^2+x*t+2*z*t-2*t^2-4*s*u-2*t*u+4*u^2,
-z*s-s^2+z*t+t^2+x*u-2*s*u-7*t*u+6*u^2,
-z*s+s^2+y*t+2*s*t-t^2-2*s*u+t*u,
-s^2+s*t+y*u-s*u-t*u+u^2,
-s*t+t^2+z*u-s*u-3*t*u+2*u^2,
x^3-3*x^2*y+7*x*y^2+3*y^3+x*y*z-y*z^2+9*z^3+3*y^2*s-3*y*z*s-7*z^2*s-7*y*s^2+
17*z*s^2-86*s^3-4*z*s*t-16*s^2*t-185*z*t^2+807*s*t^2-406*t^3+17*s^2*u-
666*s*t*u+1391*t^2*u+228*s*u^2-1378*t*u^2+393*u^3,
x^2*z-2*x*y*z+5*y^2*z+y*z^2+3*z^3+8*y^2*s+y*z*s-7*z^2*s+3*y*s^2+17*z*s^2-
47*s^3+6*z^2*t+9*z*s*t+s^2*t+32*z*t^2+11*s*t^2-103*t^3-51*s^2*u-171*s*t*u+
433*t^2*u+89*s*u^2-577*t*u^2+246*u^3,
x*z^2-y*z^2-z^3+4*y*z*s+z^2*s+8*y*s^2-3*z*s^2-5*s^3+7*z^2*t-3*z*s*t+17*s^2*t+
8*z*t^2-2*s*t^2+62*t^3-41*s^2*u-34*s*t*u-28*t^2*u+14*s*u^2-127*t*u^2+92*u^3
]);
// C a genus 6 canonical curve of gonality 3
mp3 := CliffordIndexOne(C);
mp3;
defs := DefiningPolynomials(mp3);
D1 := Scheme(C,defs[1]);
D2 := Scheme(C,defs[2]);
D12 := Scheme(C,defs);
Degree(D1); Degree(D2);
Dimension(D12); Degree(D12);
SetEchoInput(ei);
