---------------------------
-- In Macaulay2:
-- U is the ideal $\mathcal R'$ representing the relative marked functor of Example 7.8  

T=QQ[c_1..c_(20)]

U=ideal(-c_(6)*c_(8)^2*c_(9) + c_(1)*c_(6)*c_(7) + c_(5)*c_(8)*c_(9) - c_(1)*c_(4) - c_(3)*c_(9), 
-c_(6)*c_(8)^2*c_(10) + c_(2)*c_(6)*c_(7) + c_(1)*c_(6)*c_(8) + c_(5)*c_(8)*c_(10) - c_(2)*c_(4) - c_(1)*c_(5) - c_(3)*c_(10), 
-c_(6)*c_(8)^2*c_(11) + c_(3)*c_(6)*c_(7) + c_(2)*c_(6)*c_(8) + c_(5)*c_(8)*c_(11) - c_(3)*c_(4) - c_(2)*c_(5) - c_(3)*c_(11), 
-c_(6)*c_(8)^2*c_(12) + c_(3)*c_(6)*c_(8) + c_(5)*c_(8)*c_(12) - c_(3)*c_(5) - c_(3)*c_(12), 
-c_(6)*c_(8)^2*c_(13) + c_(4)*c_(6)*c_(7) + c_(5)*c_(8)*c_(13) - c_(4)^2 - c_(1)*c_(6) - c_(3)*c_(13), 
-c_(6)*c_(8)^2*c_(14) + c_(5)*c_(6)*c_(7) + c_(4)*c_(6)*c_(8) + c_(5)*c_(8)*c_(14) - 2*c_(4)*c_(5) - c_(2)*c_(6) - c_(3)*c_(14), 
-c_(6)*c_(8)^2*c_(15) + c_(5)*c_(6)*c_(8) + c_(5)*c_(8)*c_(15) - c_(5)^2 - c_(3)*c_(6) - c_(3)*c_(15), 
-c_(6)*c_(8)^2*c_(16) + c_(6)^2*c_(7) + c_(5)*c_(8)*c_(16) - 2*c_(4)*c_(6) - c_(3)*c_(16), 
-c_(6)*c_(8)^2*c_(17) + c_(6)^2*c_(8) + c_(5)*c_(8)*c_(17) - 2*c_(5)*c_(6) - c_(3)*c_(17), 
-c_(6)*c_(8)^2*c_(18) + c_(5)*c_(8)*c_(18) - c_(6)^2 - c_(3)*c_(18), 
-c_(6)*c_(8)^2*c_(19) + c_(6)*c_(7)^2 + c_(5)*c_(8)*c_(19) - c_(4)*c_(7) - c_(3)*c_(19) + c_(1), 
-c_(6)*c_(8)^2*c_(20) + 2*c_(6)*c_(7)*c_(8) + c_(5)*c_(8)*c_(20) - c_(5)*c_(7) - c_(4)*c_(8) - c_(3)*c_(20) + c_(2), 
-c_(8)^3*c_(9)*c_(18)*c_(20) + 3*c_(7)*c_(8)^2*c_(9)*c_(18) + c_(8)^2*c_(9)*c_(17)*c_(20) - c_(8)^2*c_(9)*c_(16) - 2*c_(7)*c_(8)*c_(9)*c_(17) - c_(1)*c_(7)^2*c_(18) - c_(8)*c_(9)*c_(15)*c_(20) + c_(8)*c_(9)*c_(14) + c_(7)*c_(9)*c_(15) + c_(1)*c_(7)*c_(16) + c_(9)*c_(12)*c_(20) - c_(9)*c_(11) - c_(1)*c_(13), 
-c_(8)^3*c_(10)*c_(18)*c_(20) + c_(8)^3*c_(9)*c_(18) + 3*c_(7)*c_(8)^2*c_(10)*c_(18) + c_(8)^2*c_(10)*c_(17)*c_(20) - c_(8)^2*c_(10)*c_(16) - c_(8)^2*c_(9)*c_(17) - 2*c_(7)*c_(8)*c_(10)*c_(17) - c_(2)*c_(7)^2*c_(18) - 2*c_(1)*c_(7)*c_(8)*c_(18) - c_(8)*c_(10)*c_(15)*c_(20) + c_(8)*c_(10)*c_(14) + c_(8)*c_(9)*c_(15) + c_(7)*c_(10)*c_(15) + c_(2)*c_(7)*c_(16) + c_(1)*c_(8)*c_(16) + c_(1)*c_(7)*c_(17) + c_(10)*c_(12)*c_(20) - c_(10)*c_(11) - c_(9)*c_(12) - c_(2)*c_(13) - c_(1)*c_(14), 
-c_(8)^3*c_(11)*c_(18)*c_(20) + c_(8)^3*c_(10)*c_(18) + 3*c_(7)*c_(8)^2*c_(11)*c_(18) + c_(8)^2*c_(11)*c_(17)*c_(20) - c_(8)^2*c_(11)*c_(16) - c_(8)^2*c_(10)*c_(17) - 2*c_(7)*c_(8)*c_(11)*c_(17) - c_(3)*c_(7)^2*c_(18) - 2*c_(2)*c_(7)*c_(8)*c_(18) - c_(1)*c_(8)^2*c_(18) - c_(8)*c_(11)*c_(15)*c_(20) + c_(8)*c_(11)*c_(14) + c_(8)*c_(10)*c_(15) + c_(7)*c_(11)*c_(15) + c_(3)*c_(7)*c_(16) + c_(2)*c_(8)*c_(16) + c_(2)*c_(7)*c_(17) + c_(1)*c_(8)*c_(17) + c_(11)*c_(12)*c_(20) - c_(11)^2 - c_(10)*c_(12) - c_(3)*c_(13) - c_(2)*c_(14) - c_(1)*c_(15), 
-c_(8)^3*c_(12)*c_(18)*c_(20) + c_(8)^3*c_(11)*c_(18) + 3*c_(7)*c_(8)^2*c_(12)*c_(18) + c_(8)^2*c_(12)*c_(17)*c_(20) - c_(8)^2*c_(12)*c_(16) - c_(8)^2*c_(11)*c_(17) - 2*c_(7)*c_(8)*c_(12)*c_(17) - 2*c_(3)*c_(7)*c_(8)*c_(18) - c_(2)*c_(8)^2*c_(18) - c_(8)*c_(12)*c_(15)*c_(20) + c_(8)*c_(12)*c_(14) + c_(8)*c_(11)*c_(15) + c_(7)*c_(12)*c_(15) + c_(3)*c_(8)*c_(16) + c_(3)*c_(7)*c_(17) + c_(2)*c_(8)*c_(17) + c_(12)^2*c_(20) - 2*c_(11)*c_(12) - c_(3)*c_(14) - c_(2)*c_(15), 
-c_(8)^3*c_(13)*c_(18)*c_(20) + 3*c_(7)*c_(8)^2*c_(13)*c_(18) + c_(8)^2*c_(13)*c_(17)*c_(20) - c_(8)^2*c_(13)*c_(16) - 2*c_(7)*c_(8)*c_(13)*c_(17) - c_(4)*c_(7)^2*c_(18) - c_(8)*c_(13)*c_(15)*c_(20) + c_(8)*c_(13)*c_(14) + c_(7)*c_(13)*c_(15) + c_(4)*c_(7)*c_(16) + c_(1)*c_(7)*c_(18) + c_(12)*c_(13)*c_(20) - c_(4)*c_(13) - c_(11)*c_(13) - c_(1)*c_(16), 
-c_(8)^3*c_(14)*c_(18)*c_(20) + c_(8)^3*c_(13)*c_(18) + 3*c_(7)*c_(8)^2*c_(14)*c_(18) + c_(8)^2*c_(14)*c_(17)*c_(20) - c_(8)^2*c_(14)*c_(16) - c_(8)^2*c_(13)*c_(17) - 2*c_(7)*c_(8)*c_(14)*c_(17) - c_(5)*c_(7)^2*c_(18) - 2*c_(4)*c_(7)*c_(8)*c_(18) - c_(8)*c_(14)*c_(15)*c_(20) + c_(8)*c_(14)^2 + c_(8)*c_(13)*c_(15) + c_(7)*c_(14)*c_(15) + c_(5)*c_(7)*c_(16) + c_(4)*c_(8)*c_(16) + c_(4)*c_(7)*c_(17) + c_(2)*c_(7)*c_(18) + c_(1)*c_(8)*c_(18) + c_(12)*c_(14)*c_(20) - c_(5)*c_(13) - c_(12)*c_(13) - c_(4)*c_(14) - c_(11)*c_(14) - c_(2)*c_(16) - c_(1)*c_(17), 
-c_(8)^3*c_(15)*c_(18)*c_(20) + c_(8)^3*c_(14)*c_(18) + 3*c_(7)*c_(8)^2*c_(15)*c_(18) + c_(8)^2*c_(15)*c_(17)*c_(20) - c_(8)^2*c_(15)*c_(16) - c_(8)^2*c_(14)*c_(17) - 2*c_(7)*c_(8)*c_(15)*c_(17) - 2*c_(5)*c_(7)*c_(8)*c_(18) - c_(4)*c_(8)^2*c_(18) - c_(8)*c_(15)^2*c_(20) + 2*c_(8)*c_(14)*c_(15) + c_(7)*c_(15)^2 + c_(5)*c_(8)*c_(16) + c_(5)*c_(7)*c_(17) + c_(4)*c_(8)*c_(17) + c_(3)*c_(7)*c_(18) + c_(2)*c_(8)*c_(18) + c_(12)*c_(15)*c_(20) - c_(5)*c_(14) - c_(12)*c_(14) - c_(4)*c_(15) - c_(11)*c_(15) - c_(3)*c_(16) - c_(2)*c_(17), 
-c_(8)^3*c_(16)*c_(18)*c_(20) + 3*c_(7)*c_(8)^2*c_(16)*c_(18) + c_(8)^2*c_(16)*c_(17)*c_(20) - c_(8)^2*c_(16)^2 - 2*c_(7)*c_(8)*c_(16)*c_(17) - c_(6)*c_(7)^2*c_(18) - c_(8)*c_(15)*c_(16)*c_(20) + c_(6)*c_(7)*c_(16) + c_(8)*c_(14)*c_(16) + c_(7)*c_(15)*c_(16) + c_(4)*c_(7)*c_(18) + c_(12)*c_(16)*c_(20) - c_(6)*c_(13) - c_(4)*c_(16) - c_(11)*c_(16) - c_(1)*c_(18), 
-c_(8)^3*c_(17)*c_(18)*c_(20) + c_(8)^3*c_(16)*c_(18) + 3*c_(7)*c_(8)^2*c_(17)*c_(18) + c_(8)^2*c_(17)^2*c_(20) - 2*c_(8)^2*c_(16)*c_(17) - 2*c_(7)*c_(8)*c_(17)^2 - 2*c_(6)*c_(7)*c_(8)*c_(18) - c_(8)*c_(15)*c_(17)*c_(20) + c_(6)*c_(8)*c_(16) + c_(8)*c_(15)*c_(16) + c_(6)*c_(7)*c_(17) + c_(8)*c_(14)*c_(17) + c_(7)*c_(15)*c_(17) + c_(5)*c_(7)*c_(18) + c_(4)*c_(8)*c_(18) + c_(12)*c_(17)*c_(20) - c_(6)*c_(14) - c_(5)*c_(16) - c_(12)*c_(16) - c_(4)*c_(17) - c_(11)*c_(17) - c_(2)*c_(18), 
-c_(8)^3*c_(18)^2*c_(20) + 3*c_(7)*c_(8)^2*c_(18)^2 + c_(8)^2*c_(17)*c_(18)*c_(20) - c_(8)^2*c_(16)*c_(18) - 2*c_(7)*c_(8)*c_(17)*c_(18) - c_(8)*c_(15)*c_(18)*c_(20) + c_(6)*c_(7)*c_(18) + c_(8)*c_(14)*c_(18) + c_(7)*c_(15)*c_(18) + c_(12)*c_(18)*c_(20) - c_(6)*c_(16) - c_(4)*c_(18) - c_(11)*c_(18), 
-c_(8)^3*c_(18)*c_(19)*c_(20) + 3*c_(7)*c_(8)^2*c_(18)*c_(19) + c_(8)^2*c_(17)*c_(19)*c_(20) - c_(7)^3*c_(18) - c_(8)^2*c_(16)*c_(19) - 2*c_(7)*c_(8)*c_(17)*c_(19) - c_(8)*c_(15)*c_(19)*c_(20) + c_(7)^2*c_(16) + c_(8)*c_(14)*c_(19) + c_(7)*c_(15)*c_(19) + c_(12)*c_(19)*c_(20) - c_(7)*c_(13) - c_(11)*c_(19) + c_(9), 
-c_(8)^3*c_(18)*c_(20)^2 + c_(8)^3*c_(18)*c_(19) + 3*c_(7)*c_(8)^2*c_(18)*c_(20) + c_(8)^2*c_(17)*c_(20)^2 - 3*c_(7)^2*c_(8)*c_(18) - c_(8)^2*c_(17)*c_(19) - c_(8)^2*c_(16)*c_(20) - 2*c_(7)*c_(8)*c_(17)*c_(20) - c_(8)*c_(15)*c_(20)^2 + 2*c_(7)*c_(8)*c_(16) + c_(7)^2*c_(17) + c_(8)*c_(15)*c_(19) + c_(8)*c_(14)*c_(20) + c_(7)*c_(15)*c_(20) + c_(12)*c_(20)^2 - c_(8)*c_(13) - c_(7)*c_(14) - c_(12)*c_(19) - c_(11)*c_(20) + c_(10), 
c_(8)^3*c_(12)*c_(18) - c_(8)^2*c_(12)*c_(17) - c_(3)*c_(8)^2*c_(18) + c_(8)*c_(12)*c_(15) + c_(3)*c_(8)*c_(17) - c_(12)^2 - c_(3)*c_(15), 
c_(8)^3*c_(15)*c_(18) - c_(8)^2*c_(15)*c_(17) - c_(5)*c_(8)^2*c_(18) + c_(8)*c_(15)^2 + c_(5)*c_(8)*c_(17) + c_(3)*c_(8)*c_(18) - c_(5)*c_(15) - c_(12)*c_(15) - c_(3)*c_(17), 
c_(8)^3*c_(17)*c_(18) - c_(8)^2*c_(17)^2 - c_(6)*c_(8)^2*c_(18) + c_(6)*c_(8)*c_(17) + c_(8)*c_(15)*c_(17) + c_(5)*c_(8)*c_(18) - c_(6)*c_(15) - c_(5)*c_(17) - c_(12)*c_(17) - c_(3)*c_(18), 
c_(8)^3*c_(18)^2 - c_(8)^2*c_(17)*c_(18) + c_(6)*c_(8)*c_(18) + c_(8)*c_(15)*c_(18) - c_(6)*c_(17) - c_(5)*c_(18) - c_(12)*c_(18), 
-c_(6)*c_(18), 
c_(7)*c_(9) - c_(1)*c_(19), 
c_(8)*c_(9) + c_(7)*c_(10) - c_(2)*c_(19) - c_(1)*c_(20), 
c_(8)*c_(10) + c_(7)*c_(11) - c_(3)*c_(19) - c_(2)*c_(20) - c_(1), 
c_(8)*c_(11) + c_(7)*c_(12) - c_(3)*c_(20) - c_(2), 
c_(8)*c_(12) - c_(3), 
c_(7)*c_(13) - c_(4)*c_(19) + c_(9), 
c_(8)*c_(13) + c_(7)*c_(14) - c_(5)*c_(19) - c_(4)*c_(20) + c_(10), 
c_(8)*c_(14) + c_(7)*c_(15) - c_(5)*c_(20) - c_(4) + c_(11), 
c_(8)*c_(15) - c_(5) + c_(12), 
c_(7)*c_(16) - c_(6)*c_(19) + c_(13), 
c_(8)*c_(16) + c_(7)*c_(17) - c_(6)*c_(20) + c_(14), 
c_(8)*c_(17) - c_(6) + c_(15), 
c_(7)*c_(18) + c_(16), 
c_(8)*c_(18) + c_(17), 
c_(18), 
-c_(8)^5*c_(9)*c_(20)^3 + 2*c_(8)^5*c_(9)*c_(19)*c_(20) + 5*c_(7)*c_(8)^4*c_(9)*c_(20)^2 - 5*c_(7)*c_(8)^4*c_(9)*c_(19) - 10*c_(7)^2*c_(8)^3*c_(9)*c_(20) + 10*c_(7)^3*c_(8)^2*c_(9) - c_(1)*c_(7)^4, 
-c_(8)^5*c_(10)*c_(20)^3 + 2*c_(8)^5*c_(10)*c_(19)*c_(20) + c_(8)^5*c_(9)*c_(20)^2 + 5*c_(7)*c_(8)^4*c_(10)*c_(20)^2 - c_(8)^5*c_(9)*c_(19) - 5*c_(7)*c_(8)^4*c_(10)*c_(19) - 5*c_(7)*c_(8)^4*c_(9)*c_(20) - 10*c_(7)^2*c_(8)^3*c_(10)*c_(20) + 10*c_(7)^2*c_(8)^3*c_(9) + 10*c_(7)^3*c_(8)^2*c_(10) - c_(2)*c_(7)^4 - 4*c_(1)*c_(7)^3*c_(8), 
-c_(8)^5*c_(11)*c_(20)^3 + 2*c_(8)^5*c_(11)*c_(19)*c_(20) + c_(8)^5*c_(10)*c_(20)^2 + 5*c_(7)*c_(8)^4*c_(11)*c_(20)^2 - c_(8)^5*c_(10)*c_(19) - 5*c_(7)*c_(8)^4*c_(11)*c_(19) - c_(8)^5*c_(9)*c_(20) - 5*c_(7)*c_(8)^4*c_(10)*c_(20) - 10*c_(7)^2*c_(8)^3*c_(11)*c_(20) + 5*c_(7)*c_(8)^4*c_(9) + 10*c_(7)^2*c_(8)^3*c_(10) + 10*c_(7)^3*c_(8)^2*c_(11) - c_(3)*c_(7)^4 - 4*c_(2)*c_(7)^3*c_(8) - 6*c_(1)*c_(7)^2*c_(8)^2, 
-c_(8)^5*c_(12)*c_(20)^3 + 2*c_(8)^5*c_(12)*c_(19)*c_(20) + c_(8)^5*c_(11)*c_(20)^2 + 5*c_(7)*c_(8)^4*c_(12)*c_(20)^2 - c_(8)^5*c_(11)*c_(19) - 5*c_(7)*c_(8)^4*c_(12)*c_(19) - c_(8)^5*c_(10)*c_(20) - 5*c_(7)*c_(8)^4*c_(11)*c_(20) - 10*c_(7)^2*c_(8)^3*c_(12)*c_(20) + c_(8)^5*c_(9) + 5*c_(7)*c_(8)^4*c_(10) + 10*c_(7)^2*c_(8)^3*c_(11) + 10*c_(7)^3*c_(8)^2*c_(12) - 4*c_(3)*c_(7)^3*c_(8) - 6*c_(2)*c_(7)^2*c_(8)^2 - 4*c_(1)*c_(7)*c_(8)^3, 
-c_(8)^5*c_(13)*c_(20)^3 + 2*c_(8)^5*c_(13)*c_(19)*c_(20) + 5*c_(7)*c_(8)^4*c_(13)*c_(20)^2 - 5*c_(7)*c_(8)^4*c_(13)*c_(19) - 10*c_(7)^2*c_(8)^3*c_(13)*c_(20) + 10*c_(7)^3*c_(8)^2*c_(13) - c_(4)*c_(7)^4 + c_(1)*c_(7)^3, 
-c_(8)^5*c_(14)*c_(20)^3 + 2*c_(8)^5*c_(14)*c_(19)*c_(20) + c_(8)^5*c_(13)*c_(20)^2 + 5*c_(7)*c_(8)^4*c_(14)*c_(20)^2 - c_(8)^5*c_(13)*c_(19) - 5*c_(7)*c_(8)^4*c_(14)*c_(19) - 5*c_(7)*c_(8)^4*c_(13)*c_(20) - 10*c_(7)^2*c_(8)^3*c_(14)*c_(20) + 10*c_(7)^2*c_(8)^3*c_(13) + 10*c_(7)^3*c_(8)^2*c_(14) - c_(5)*c_(7)^4 - 4*c_(4)*c_(7)^3*c_(8) + c_(2)*c_(7)^3 + 3*c_(1)*c_(7)^2*c_(8), 
-c_(8)^5*c_(15)*c_(20)^3 + 2*c_(8)^5*c_(15)*c_(19)*c_(20) + c_(8)^5*c_(14)*c_(20)^2 + 5*c_(7)*c_(8)^4*c_(15)*c_(20)^2 - c_(8)^5*c_(14)*c_(19) - 5*c_(7)*c_(8)^4*c_(15)*c_(19) - c_(8)^5*c_(13)*c_(20) - 5*c_(7)*c_(8)^4*c_(14)*c_(20) - 10*c_(7)^2*c_(8)^3*c_(15)*c_(20) + 5*c_(7)*c_(8)^4*c_(13) + 10*c_(7)^2*c_(8)^3*c_(14) + 10*c_(7)^3*c_(8)^2*c_(15) - 4*c_(5)*c_(7)^3*c_(8) - 6*c_(4)*c_(7)^2*c_(8)^2 + c_(3)*c_(7)^3 + 3*c_(2)*c_(7)^2*c_(8) + 3*c_(1)*c_(7)*c_(8)^2, 
-c_(8)^5*c_(16)*c_(20)^3 + 2*c_(8)^5*c_(16)*c_(19)*c_(20) + 5*c_(7)*c_(8)^4*c_(16)*c_(20)^2 - 5*c_(7)*c_(8)^4*c_(16)*c_(19) - 10*c_(7)^2*c_(8)^3*c_(16)*c_(20) + 10*c_(7)^3*c_(8)^2*c_(16) - c_(6)*c_(7)^4 + c_(4)*c_(7)^3 - c_(1)*c_(7)^2, 
-c_(8)^5*c_(17)*c_(20)^3 + 2*c_(8)^5*c_(17)*c_(19)*c_(20) + c_(8)^5*c_(16)*c_(20)^2 + 5*c_(7)*c_(8)^4*c_(17)*c_(20)^2 - c_(8)^5*c_(16)*c_(19) - 5*c_(7)*c_(8)^4*c_(17)*c_(19) - 5*c_(7)*c_(8)^4*c_(16)*c_(20) - 10*c_(7)^2*c_(8)^3*c_(17)*c_(20) + 10*c_(7)^2*c_(8)^3*c_(16) + 10*c_(7)^3*c_(8)^2*c_(17) - 4*c_(6)*c_(7)^3*c_(8) + c_(5)*c_(7)^3 + 3*c_(4)*c_(7)^2*c_(8) - c_(2)*c_(7)^2 - 2*c_(1)*c_(7)*c_(8), 
-c_(8)^5*c_(18)*c_(20)^3 + 2*c_(8)^5*c_(18)*c_(19)*c_(20) + 5*c_(7)*c_(8)^4*c_(18)*c_(20)^2 - 5*c_(7)*c_(8)^4*c_(18)*c_(19) - 10*c_(7)^2*c_(8)^3*c_(18)*c_(20) + 10*c_(7)^3*c_(8)^2*c_(18) + c_(6)*c_(7)^3 - c_(4)*c_(7)^2 + c_(1)*c_(7), 
-c_(8)^5*c_(19)*c_(20)^3 + 2*c_(8)^5*c_(19)^2*c_(20) + 5*c_(7)*c_(8)^4*c_(19)*c_(20)^2 - 5*c_(7)*c_(8)^4*c_(19)^2 - 10*c_(7)^2*c_(8)^3*c_(19)*c_(20) + 10*c_(7)^3*c_(8)^2*c_(19) - c_(7)^5, 
-c_(8)^5*c_(20)^4 + 3*c_(8)^5*c_(19)*c_(20)^2 + 5*c_(7)*c_(8)^4*c_(20)^3 - c_(8)^5*c_(19)^2 - 10*c_(7)*c_(8)^4*c_(19)*c_(20) - 10*c_(7)^2*c_(8)^3*c_(20)^2 + 10*c_(7)^2*c_(8)^3*c_(19) + 10*c_(7)^3*c_(8)^2*c_(20) - 5*c_(7)^4*c_(8), 
c_(8)^5*c_(12)*c_(20)^2 - c_(8)^5*c_(12)*c_(19) - c_(8)^5*c_(11)*c_(20) - 5*c_(7)*c_(8)^4*c_(12)*c_(20) + c_(8)^5*c_(10) + 5*c_(7)*c_(8)^4*c_(11) + 10*c_(7)^2*c_(8)^3*c_(12) - 6*c_(3)*c_(7)^2*c_(8)^2 - 4*c_(2)*c_(7)*c_(8)^3 - c_(1)*c_(8)^4, 
c_(8)^5*c_(15)*c_(20)^2 - c_(8)^5*c_(15)*c_(19) - c_(8)^5*c_(14)*c_(20) - 5*c_(7)*c_(8)^4*c_(15)*c_(20) + c_(8)^5*c_(13) + 5*c_(7)*c_(8)^4*c_(14) + 10*c_(7)^2*c_(8)^3*c_(15) - 6*c_(5)*c_(7)^2*c_(8)^2 - 4*c_(4)*c_(7)*c_(8)^3 + 3*c_(3)*c_(7)^2*c_(8) + 3*c_(2)*c_(7)*c_(8)^2 + c_(1)*c_(8)^3, 
c_(8)^5*c_(17)*c_(20)^2 - c_(8)^5*c_(17)*c_(19) - c_(8)^5*c_(16)*c_(20) - 5*c_(7)*c_(8)^4*c_(17)*c_(20) + 5*c_(7)*c_(8)^4*c_(16) + 10*c_(7)^2*c_(8)^3*c_(17) - 6*c_(6)*c_(7)^2*c_(8)^2 + 3*c_(5)*c_(7)^2*c_(8) + 3*c_(4)*c_(7)*c_(8)^2 - c_(3)*c_(7)^2 - 2*c_(2)*c_(7)*c_(8) - c_(1)*c_(8)^2, 
c_(8)^5*c_(18)*c_(20)^2 - c_(8)^5*c_(18)*c_(19) - 5*c_(7)*c_(8)^4*c_(18)*c_(20) + 10*c_(7)^2*c_(8)^3*c_(18) + 3*c_(6)*c_(7)^2*c_(8) - c_(5)*c_(7)^2 - 2*c_(4)*c_(7)*c_(8) + c_(2)*c_(7) + c_(1)*c_(8), 
-c_(8)^5*c_(12)*c_(20) + c_(8)^5*c_(11) + 5*c_(7)*c_(8)^4*c_(12) - 4*c_(3)*c_(7)*c_(8)^3 - c_(2)*c_(8)^4, 
-c_(8)^5*c_(15)*c_(20) + c_(8)^5*c_(14) + 5*c_(7)*c_(8)^4*c_(15) - 4*c_(5)*c_(7)*c_(8)^3 - c_(4)*c_(8)^4 + 3*c_(3)*c_(7)*c_(8)^2 + c_(2)*c_(8)^3, 
-c_(8)^5*c_(17)*c_(20) + c_(8)^5*c_(16) + 5*c_(7)*c_(8)^4*c_(17) - 4*c_(6)*c_(7)*c_(8)^3 + 3*c_(5)*c_(7)*c_(8)^2 + c_(4)*c_(8)^3 - 2*c_(3)*c_(7)*c_(8) - c_(2)*c_(8)^2, 
-c_(8)^5*c_(18)*c_(20) + 5*c_(7)*c_(8)^4*c_(18) + 3*c_(6)*c_(7)*c_(8)^2 - 2*c_(5)*c_(7)*c_(8) - c_(4)*c_(8)^2 + c_(3)*c_(7) + c_(2)*c_(8), 
c_(8)^5*c_(12) - c_(3)*c_(8)^4, 
c_(8)^5*c_(15) - c_(5)*c_(8)^4 + c_(3)*c_(8)^3, 
c_(8)^5*c_(17) - c_(6)*c_(8)^4 + c_(5)*c_(8)^3 - c_(3)*c_(8)^2, 
c_(8)^5*c_(18) + c_(6)*c_(8)^3 - c_(5)*c_(8)^2 + c_(3)*c_(8), 
-c_(6)*c_(7)^2 + c_(4)*c_(7) - c_(1), 
-2*c_(6)*c_(7)*c_(8) + c_(5)*c_(7) + c_(4)*c_(8) - c_(2), 
-c_(6)*c_(8)^2 + c_(5)*c_(8) - c_(3))

-- with the following commands the Krull dimension and the primary decomposition of U can be computed 

dim U

C = primaryDecomposition U

#C 

C#0

U==intersect C

-- with the following command the associated primes of U are computed

P = associatedPrimes U