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# killCycles -- Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.

- Usage:
    `B = killCycles(A)`
- Inputs:
  - A, an instance of the type DGAlgebra,
- Optional inputs:
  - EndDegree => ..., default value -1, Option to specify the degree to stop looking for cycles
  - StartDegree => ..., default value 1, Option to specify the degree to start looking for cycles
- Outputs:
  - B, an instance of the type DGAlgebra,

## Description

    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 : B = killCycles(A)

    o4 = {Ring => R                                              }
          Underlying algebra => R[T ..T ]
                                   1   7
                                        2     2       2      3
          Differential => {a, b, c, d, a T , b T , - c T  + d T }
                                          1     2       3      4

    o4 : DGAlgebra

    i5 : B.diff

                                                  2     2       2      3
    o5 = map (R[T ..T ], R[T ..T ], {a, b, c, d, a T , b T , - c T  + d T , a, b, c, d})
                 1   7      1   7                   1     2       3      4

    o5 : RingMap R[T ..T ] <-- R[T ..T ]
                    1   7         1   7

## Ways to use killCycles:

- `killCycles(DGAlgebra)`

## For the programmer

The object killCycles is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/DGAlgebras.m2:2128:0.