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

Synopsis

Usage:

cycleList = getGenerators(A)
Inputs:
- A, an instance of the type DGAlgebra,
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 a method function with options.