(ALGFORMINPUT)
setinvars x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13;
x8,
-x2^2-2*x1*x3+x4*x5+x8*x10,
x4^2-x3*x5-x2*x6-x1*x7+x8*x9,
x4*x7+x8^2-x3*x9-x2*x10-x1*x11+x12*x13,
x4*x6+x8*x11+x12^2-x3*x13,
-x1*x4+x5^2-x3*x6-x2*x7+x9*x10,
x1*x3-x4*x5-2*x6*x7+x9^2,
x1*x2+x5*x7-x5*x8-x4*x9+x8*x9-x7*x10-x6*x11+x13^2,
x1^2+x5*x6+x9*x11-x5*x12-x4*x13+x12*x13,
x5*x6-x2*x8-x1*x9+x10^2-x3*x11,
x2*x3+x4*x6-x6*x8-x5*x9-x4*x10+x9*x10-x7*x11,
x2^2+x6*x7-x9^2-x8*x10-x11^2,
x1*x2+x6^2+x10*x11-x10*x12-x9*x13,
x5*x7+x10*x11-x3*x12-x2*x13,
x3^2+x4*x7+x9*x11-x7*x12-x6*x13,
x2*x3+x7^2+x8*x11-x11*x12-x10*x13;
%x1*x3+x6*x7+x11^2;
