// eco12 dense with modest coefficients
debug_infolevel:=1;
vars := [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12]:;
sys := [
x1*x12*x2 + x1*x12 + x10*x11*x12 + x10*x12*x9 + x12*x2*x3 + x12*x3*x4 + x12* x4*x5 + x12*x5*x6 + x12*x6*x7 + x12*x7*x8 + x12*x8*x9 - 1,
x1*x12*x3 + x10*x12*x8 + x11*x12*x9 + x12*x2*x4 + x12*x2 + x12*x3*x5 + x12* x4*x6 + x12*x5*x7 + x12*x6*x8 + x12*x7*x9 - 2,
x1*x12*x4 + x10*x12*x7 + x11*x12*x8 + x12*x2*x5 + x12*x3*x6 + x12*x3 + x12* x4*x7 + x12*x5*x8 + x12*x6*x9 - 3,
x1*x12*x5 + x10*x12*x6 + x11*x12*x7 + x12*x2*x6 + x12*x3*x7 + x12*x4*x8 + x12*x4 + x12*x5*x9 - 4,
x1*x12*x6 + x10*x12*x5 + x11*x12*x6 + x12*x2*x7 + x12*x3*x8 + x12*x4*x9 + x12*x5 - 5,
x1*x12*x7 + x10*x12*x4 + x11*x12*x5 + x12*x2*x8 + x12*x3*x9 + x12*x6 - 6,
x1*x12*x8 + x10*x12*x3 + x11*x12*x4 + x12*x2*x9 + x12*x7 - 7,
x1*x12*x9 + x10*x12*x2 + x11*x12*x3 + x12*x8 - 8,
x1*x10*x12 + x11*x12*x2 + x12*x9 - 9,
x1*x11*x12 + x10*x12 - 10,
x11*x12 - 11,
x1 + x10 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + 1
]:;
proba_epsilon:=1e-7;
time(H:=gbasis(sys,vars,rur));
size(eval(H,1));
write("Heco12",H);
// check
debug_infolevel:=0;
l:=subst(sys,vars,H[4..size(H)-1]/H[3]):;
map(l,x->rem(numer(x),H[2],H[1]));
time(R:=realroot(eval(H[2],1)));
write("Reco12",R);
size(R); 
