isValidDGAlgebra -- Structural invariant check for a DG algebra

• Usage:

  b = isValidDGAlgebra A

• Inputs:
  • A, an instance of the type DGAlgebra,
• Outputs:
  • b, a Boolean value, true when A has all required keys of the expected types (ring, natural algebra, degree list, differential list, cache table).

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 : isValidDGAlgebra A

o3 = true