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

## 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 , T , T ] 1 2 3 4 Differential => {a, b, c, d} isHomogeneous => false o2 : DGAlgebra``` ```i3 : A.diff o3 = map(R[T , T , T , T ],R[T , T , T , T ],{a, b, c, d, a, b, c, d}) 1 2 3 4 1 2 3 4 o3 : RingMap R[T , T , T , T ] <--- R[T , T , T , T ] 1 2 3 4 1 2 3 4``` ```i4 : B = killCycles(A) o4 = {Ring => R } Underlying algebra => R[T , T , T , T , T , T , T ] 1 2 3 4 5 6 7 2 2 2 3 Differential => {a, b, c, d, a T , b T , - c T + d T } 1 2 3 4 isHomogeneous => false o4 : DGAlgebra``` ```i5 : B.diff 2 2 2 3 o5 = map(R[T , T , T , T , T , T , T ],R[T , T , T , T , T , T , T ],{a, b, c, d, a T , b T , - c T + d T , a, b, c, d}) 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 o5 : RingMap R[T , T , T , T , T , T , T ] <--- R[T , T , T , T , T , T , T ] 1 2 3 4 5 6 7 1 2 3 4 5 6 7```

## Ways to use killCycles :

• killCycles(DGAlgebra)