threads:=2;
debug_infolevel:=1;
kat10:=[x1 + 2*x2 + 2*x3 + 2*x4 + 2*x5 + 2*x6 + 2*x7 + 2*x8 + 2*x9 + 2*x10 - 1, x1^2 + 2*x2^2 + 2*x3^2 + 2*x4^2 + 2*x5^2 + 2*x6^2 + 2*x7^2 + 2*x8^2 + 2*x9^2 + 2*x10^2 - x1, 2*x1*x2 + 2*x2*x3 + 2*x3*x4 + 2*x4*x5 + 2*x5*x6 + 2*x6*x7 + 2*x7*x8 + 2*x8*x9 + 2*x9*x10 - x2, x2^2 + 2*x1*x3 + 2*x2*x4 + 2*x3*x5 + 2*x4*x6 + 2*x5*x7 + 2*x6*x8 + 2*x7*x9 + 2*x8*x10 - x3, 2*x2*x3 + 2*x1*x4 + 2*x2*x5 + 2*x3*x6 + 2*x4*x7 + 2*x5*x8 + 2*x6*x9 + 2*x7*x10 - x4, x3^2 + 2*x2*x4 + 2*x1*x5 + 2*x2*x6 + 2*x3*x7 + 2*x4*x8 + 2*x5*x9 + 2*x6*x10 - x5, 2*x3*x4 + 2*x2*x5 + 2*x1*x6 + 2*x2*x7 + 2*x3*x8 + 2*x4*x9 + 2*x5*x10 - x6, x4^2 + 2*x3*x5 + 2*x2*x6 + 2*x1*x7 + 2*x2*x8 + 2*x3*x9 + 2*x4*x10 - x7, 2*x4*x5 + 2*x3*x6 + 2*x2*x7 + 2*x1*x8 + 2*x2*x9 + 2*x3*x10 - x8, x5^2 + 2*x4*x6 + 2*x3*x7 + 2*x2*x8 + 2*x1*x9 + 2*x2*x10 - x9];
proba_epsilon:=1e-7;
time(H:=gbasis(kat10 ,[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10],rur));
write("Hkat10",H);
time(R:=realroot(eval(H[2],1)));
write("Rkat10",R);
size(R);