truncateGenerators -- Restrict a DG algebra to its generators of hom-degree strictly above a bound

• Usage:

  B = truncateGenerators(A, n)

• Inputs:
  • A, an instance of the type DGAlgebra,
  • n, an integer, A hom-degree bound; generators of hom-degree <= n are dropped.
• Optional inputs:
  • InitializeDegreeZeroHomology => a Boolean value, default value true, Default true.
  • InitializeComplex => a Boolean value, default value false, Default false.
• Outputs:
  • B, an instance of the type DGAlgebra, The sub-DG algebra of A generated by the DG generators whose first-hom-degree component is strictly greater than n.

i1 : R = QQ[x, y] / ideal(x^2, y^2)

o1 = R

o1 : QuotientRing

i2 : A = koszulComplexDGA R

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o2 : DGAlgebra

i3 : B = truncateGenerators(A, 0)

o3 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o3 : DGAlgebra

i4 : numgens B.natural

o4 = 2