
R, (k2_0,k3_0,k4_0,k5_0,k6_0,k7_0,s3_0,u1_0,x1_0,x1_1,x1_2,x1_3,x1_4,x1_5,x2_0,x2_1,x2_2,x2_3,x2_4,x2_5,x2_6,x3_0,x3_1,x3_2,x3_3,x3_4,x3_5,x3_6,x4_0,x4_1,x4_2,x4_3,x4_4,x4_5) = polynomial_ring(QQ, ["k2_0","k3_0","k4_0","k5_0","k6_0","k7_0","s3_0","u1_0","x1_0","x1_1","x1_2","x1_3","x1_4","x1_5","x2_0","x2_1","x2_2","x2_3","x2_4","x2_5","x2_6","x3_0","x3_1","x3_2","x3_3","x3_4","x3_5","x3_6","x4_0","x4_1","x4_2","x4_3","x4_4","x4_5"], internal_ordering=:degrevlex)

sys = [
-867346174667989*x2_0 + 7120995548571787//18014398509481984,
k3_0*x2_0 + k6_0*x2_0 + k7_0*x2_0 - k5_0*x4_0 - 919994479098052*x1_0 + x2_1,
-s3_0*x3_0 + 5228925772313931//9007199254740992,
-k2_0*x1_0 - k3_0*x2_0 + k4_0*x3_0 + x3_1,
-867346174667989*x2_1 - 3184469477838311//18014398509481984,
k3_0*x2_1 + k6_0*x2_1 + k7_0*x2_1 - k5_0*x4_1 - 919994479098052*x1_1 + x2_2,
k2_0*x1_0 - u1_0 + 919994479098052*x1_0 + x1_1,
-k6_0*x2_0 + k5_0*x4_0 + x4_1,
-s3_0*x3_1 + 2017522455155303//36028797018963968,
-k2_0*x1_1 - k3_0*x2_1 + k4_0*x3_1 + x3_2,
-867346174667989*x2_2 + 7366969532790441//36028797018963968,
k3_0*x2_2 + k6_0*x2_2 + k7_0*x2_2 - k5_0*x4_2 - 919994479098052*x1_2 + x2_3,
-k6_0*x2_1 + k5_0*x4_1 + x4_2,
k2_0*x1_1 + 919994479098052*x1_1 + x1_2,
-s3_0*x3_2 - 6041217546414069//144115188075855872,
-k2_0*x1_2 - k3_0*x2_2 + k4_0*x3_2 + x3_3,
-867346174667989*x2_3 - 570107236120179//2251799813685248,
k3_0*x2_3 + k6_0*x2_3 + k7_0*x2_3 - k5_0*x4_3 - 919994479098052*x1_3 + x2_4,
k2_0*x1_2 + 919994479098052*x1_2 + x1_3,
-k6_0*x2_2 + k5_0*x4_2 + x4_3,
-s3_0*x3_3 + 8731056957180405//144115188075855872,
-k2_0*x1_3 - k3_0*x2_3 + k4_0*x3_3 + x3_4,
-867346174667989*x2_4 + 5710790171394371//18014398509481984,
k3_0*x2_4 + k6_0*x2_4 + k7_0*x2_4 - k5_0*x4_4 - 919994479098052*x1_4 + x2_5,
-k6_0*x2_3 + k5_0*x4_3 + x4_4,
k2_0*x1_3 + 919994479098052*x1_3 + x1_4,
-s3_0*x3_4 - 6119231669288753//72057594037927936,
-k2_0*x1_4 - k3_0*x2_4 + k4_0*x3_4 + x3_5,
-867346174667989*x2_5 - 7163234492731695//18014398509481984,
k3_0*x2_5 + k6_0*x2_5 + k7_0*x2_5 - k5_0*x4_5 - 919994479098052*x1_5 + x2_6,
k2_0*x1_4 + 919994479098052*x1_4 + x1_5,
-k6_0*x2_4 + k5_0*x4_4 + x4_5,
-s3_0*x3_5 + 8045059723501055//72057594037927936,
-k2_0*x1_5 - k3_0*x2_5 + k4_0*x3_5 + x3_6,
]

