
R, (Ki_0,k1_0,k2_0,k4_0,k5_0,k6_0,x1_0,x1_1,x1_2,x1_3,x1_4,x2_0,x2_1,x2_2,x2_3,x2_4,x3_0,x3_1,x3_2,x3_3,x3_4,x3_5) = polynomial_ring(QQ, ["Ki_0","k1_0","k2_0","k4_0","k5_0","k6_0","x1_0","x1_1","x1_2","x1_3","x1_4","x2_0","x2_1","x2_2","x2_3","x2_4","x3_0","x3_1","x3_2","x3_3","x3_4","x3_5"], internal_ordering=:degrevlex)

sys = [
-x1_0 + 1716268278212207//18014398509481984,
Ki_0^10*k2_0*x1_0 + k2_0*x1_0*x3_0^10 - Ki_0^10*k1_0 + Ki_0^10*x1_1 + x1_1*x3_0^10,
-x3_0 + 5596177093787589//2251799813685248,
-k5_0*x2_0 + k6_0*x3_0 + x3_1,
-x1_1 - 5427922070074225//576460752303423488,
Ki_0^10*k2_0*x1_1 + k2_0*x1_1*x3_0^10 + 10*k2_0*x1_0*x3_0^9*x3_1 + Ki_0^10*x1_2 + x1_2*x3_0^10 + 10*x1_1*x3_0^9*x3_1,
-x3_1 - 6588473772201205//576460752303423488,
-k5_0*x2_1 + k6_0*x3_1 + x3_2,
k4_0*x2_0 - 3869549432583*x1_0 + x2_1,
-x1_2 + 8731863118467557//9223372036854775808,
Ki_0^10*k2_0*x1_2 + k2_0*x1_2*x3_0^10 + 20*k2_0*x1_1*x3_0^9*x3_1 + 90*k2_0*x1_0*x3_0^8*x3_1^2 + 10*k2_0*x1_0*x3_0^9*x3_2 + Ki_0^10*x1_3 + x1_3*x3_0^10 + 20*x1_2*x3_0^9*x3_1 + 90*x1_1*x3_0^8*x3_1^2 + 10*x1_1*x3_0^9*x3_2,
-x3_2 + 327438017945479//4503599627370496,
-k5_0*x2_2 + k6_0*x3_2 + x3_3,
k4_0*x2_1 - 3869549432583*x1_1 + x2_2,
-x1_3 - 2341962518309147//18446744073709551616,
Ki_0^10*k2_0*x1_3 + k2_0*x1_3*x3_0^10 + 30*k2_0*x1_2*x3_0^9*x3_1 + 270*k2_0*x1_1*x3_0^8*x3_1^2 + 720*k2_0*x1_0*x3_0^7*x3_1^3 + 30*k2_0*x1_1*x3_0^9*x3_2 + 270*k2_0*x1_0*x3_0^8*x3_1*x3_2 + 10*k2_0*x1_0*x3_0^9*x3_3 + Ki_0^10*x1_4 + x1_4*x3_0^10 + 30*x1_3*x3_0^9*x3_1 + 270*x1_2*x3_0^8*x3_1^2 + 720*x1_1*x3_0^7*x3_1^3 + 30*x1_2*x3_0^9*x3_2 + 270*x1_1*x3_0^8*x3_1*x3_2 + 10*x1_1*x3_0^9*x3_3,
-x3_3 - 6872225295903555//288230376151711744,
-k5_0*x2_3 + k6_0*x3_3 + x3_4,
k4_0*x2_2 - 3869549432583*x1_2 + x2_3,
-x3_4 + 5751021917252629//1152921504606846976,
-k5_0*x2_4 + k6_0*x3_4 + x3_5,
k4_0*x2_3 - 3869549432583*x1_3 + x2_4,
]

