-- -*- M2-comint -*- hash: 14906663521325452850

i1 : Q = QQ[x_1,x_2,y_1,y_2,z]

o1 = Q

o1 : PolynomialRing

i2 : I = ideal (x_1*x_2^2,y_1*y_2^2,z^3,x_1*x_2*y_1*y_2,y_2^2*z^2,x_2^2*z^2,x_1*y_1*z,x_2^2*y_2^2*z)

               2     2   3             2 2   2 2          2 2
o2 = ideal (x x , y y , z , x x y y , y z , x z , x y z, x y z)
             1 2   1 2       1 2 1 2   2     2     1 1    2 2

o2 : Ideal of Q

i3 : R = Q/I

o3 = R

o3 : QuotientRing

i4 : KR = koszulComplexDGA R

o4 = {Ring => R                          }
      Underlying algebra => R[T ..T ]
                               1   5
      Differential => {x , x , y , y , z}
                        1   2   1   2

o4 : DGAlgebra

i5 : z1 = z^2*T_5

      2
o5 = z T
        5

o5 : R[T ..T ]
        1   5

i6 : z2 = y_2^2*T_3

      2
o6 = y T
      2 3

o6 : R[T ..T ]
        1   5

i7 : z3 = x_2^2*T_1

      2
o7 = x T
      2 1

o7 : R[T ..T ]
        1   5

i8 : {diff(KR,z1),diff(KR,z1),diff(KR,z1)}

o8 = {0, 0, 0}

o8 : List

i9 : (lifted12,lift12) = getBoundaryPreimage(KR,z1*z2)

o9 = (true, 0)

o9 : Sequence

i10 : (lifted23,lift23) = getBoundaryPreimage(KR,z2*z3)

                2
o10 = (true, x y T T T  - x x y T T T )
              2 2 1 2 3    1 2 2 2 3 4

o10 : Sequence

i11 : diff(KR,lift23) == z2*z3

o11 = true

i12 : 
