// debug_infolevel:=1 [80.5,45.2] [76.7, 43.25]
// 76.3s, 75.6, 71.9, 74s [79, 44.3], 70.7 [75.2, 42.4]
// 64.93s [68.7, 38.4]
// 60.2 full interreduced
// 53 [58.6, 32.]
// 52.3 [57.75,31.57]
cyclic8:=[x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8, x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7 + x1*x8 + x7*x8, x1*x2*x3 + x2*x3*x4 + x3*x4*x5 + x4*x5*x6 + x5*x6*x7 + x1*x2*x8 + x1*x7*x8 + x6*x7*x8, x1*x2*x3*x4 + x2*x3*x4*x5 + x3*x4*x5*x6 + x4*x5*x6*x7 + x1*x2*x3*x8 + x1*x2*x7*x8 + x1*x6*x7*x8 + x5*x6*x7*x8, x1*x2*x3*x4*x5 + x2*x3*x4*x5*x6 + x3*x4*x5*x6*x7 + x1*x2*x3*x4*x8 + x1*x2*x3*x7*x8 + x1*x2*x6*x7*x8 + x1*x5*x6*x7*x8 + x4*x5*x6*x7*x8, x1*x2*x3*x4*x5*x6 + x2*x3*x4*x5*x6*x7 + x1*x2*x3*x4*x5*x8 + x1*x2*x3*x4*x7*x8 + x1*x2*x3*x6*x7*x8 + x1*x2*x5*x6*x7*x8 + x1*x4*x5*x6*x7*x8 + x3*x4*x5*x6*x7*x8, x1*x2*x3*x4*x5*x6*x7 + x1*x2*x3*x4*x5*x6*x8 + x1*x2*x3*x4*x5*x7*x8 + x1*x2*x3*x4*x6*x7*x8 + x1*x2*x3*x5*x6*x7*x8 + x1*x2*x4*x5*x6*x7*x8 + x1*x3*x4*x5*x6*x7*x8 + x2*x3*x4*x5*x6*x7*x8, x1*x2*x3*x4*x5*x6*x7*x8 - 1];
threads:=1;
time(H:=gbasis(cyclic8,indets(cyclic8),revlex,irem));
write("Hcyclic8",H);
//proba_epsilon:=0;
//time(H:=gbasis(cyclic8,indets(cyclic8),revlex,irem));
//time(H:=gbasis(cyclic8,indets(cyclic8),revlex,modular_check));
