HH_ZZ DGAlgebra -- Computes the homology of a DG algebra as a module

• Function: homology

• Usage:

  H = homology(n,A)

• Inputs:
  • n, an integer,
  • A, an instance of the type DGAlgebra,
• Outputs:
  • H, a module, The nth homology of A.

i1 : R = ZZ/32003[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : A = koszulComplexDGA(R)

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,3
      Differential => {x, y, z}

o2 : DGAlgebra

i3 : apply(numgens R+1, i -> numgens prune homology(i,A))

o3 = {1, 0, 0, 0}

o3 : List