# getGenerators -- Returns a list of cycles whose images generate HH(A) as an algebra

## Synopsis

• Usage:
cycleList = getGenerators(A)
• Inputs:
• Optional inputs:
• DegreeLimit => ..., default value -1, Option to specify the degree to stop finding generators of HH(DGAlgebra)
• StartDegree => ..., default value 1, Option to specify the degree to start finding generators of HH(DGAlgebra)
• Verbosity => ..., default value 0, Option to specify the maximum degree to look for generators when computing the deviations
• Outputs:
• cycleList, a list,

## Description

This version of the function should only be used if all algebra generators of A are in odd homological degree, provided in the EndDegree option.

 i1 : R = ZZ/101[a,b,c]/ideal{a^3,b^3,c^3,a^2*b^2*c^2} o1 = R o1 : QuotientRing i2 : A = koszulComplexDGA(R) o2 = {Ring => R } Underlying algebra => R[T ..T ] 1 3 Differential => {a, b, c} o2 : DGAlgebra i3 : netList getGenerators(A) +------------+ | 2 | o3 = |a T | | 1 | +------------+ | 2 | |b T | | 2 | +------------+ | 2 | |c T | | 3 | +------------+ | 2 2 | |a*b c T | | 1 | +------------+ | 2 2 | |a*b c T T | | 1 2 | +------------+ | 2 2 | |a b*c T T | | 1 2 | +------------+ | 2 2 | |a*b c T T | | 1 3 | +------------+ | 2 2 | |a*b c T T T | | 1 2 3| +------------+ | 2 2 | |a b*c T T T | | 1 2 3| +------------+ | 2 2 | |a b c*T T T | | 1 2 3| +------------+

## Ways to use getGenerators :

• "getGenerators(DGAlgebra)"

## For the programmer

The object getGenerators is .