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

Synopsis

• Usage:
B = killCycles(A)
• Inputs:
• 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:

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 .