adjoinVariables -- Adjoins variables to make the specified cycles boundaries.

i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3-d^4}

o1 = R

o1 : QuotientRing

i2 : A = koszulComplexDGA(R)

o2 = {Ring => R                      }
      Underlying algebra => R[T ..T ]
                               1   4
      Differential => {a, b, c, d}

o2 : DGAlgebra

i3 : A.diff

o3 = map (R[T ..T ], R[T ..T ], {a, b, c, d, a, b, c, d})
             1   4      1   4

o3 : RingMap R[T ..T ] <-- R[T ..T ]
                1   4         1   4

i4 : prune homology(1,A)

o4 = cokernel | d c b a 0 0 0 0 0 0 0 0 |
              | 0 0 0 0 d c b a 0 0 0 0 |
              | 0 0 0 0 0 0 0 0 d c b a |

                            3
o4 : R-module, quotient of R

i5 : B = adjoinVariables(A,{a^2*T_1})

o5 = {Ring => R                         }
      Underlying algebra => R[T ..T ]
                               1   5
                                    2
      Differential => {a, b, c, d, a T }
                                      1

o5 : DGAlgebra

i6 : B.diff

                                              2
o6 = map (R[T ..T ], R[T ..T ], {a, b, c, d, a T , a, b, c, d})
             1   5      1   5                   1

o6 : RingMap R[T ..T ] <-- R[T ..T ]
                1   5         1   5

i7 : prune homology(1,B)

o7 = cokernel | d c b a 0 0 0 0 |
              | 0 0 0 0 d c b a |

                            2
o7 : R-module, quotient of R