isZero(DGModule) -- Does the DG object have no natural generators?

i1 : R = ZZ/101[x]

o1 = R

o1 : PolynomialRing

i2 : A = koszulComplexDGA R

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

o2 : DGAlgebra

i3 : M0 = freeDGModule(A, {})

o3 = {Base ring => R             }
      DG algebra => R[T   ]
                       1,1
      Natural module => 0
      Generator degrees => {}
      Differentials on gens => {}

o3 : DGModule

i4 : isZero M0

o4 = true

i5 : M = freeDGModule(A, {0})

o5 = {Base ring => R               }
      DG algebra => R[T   ]
                       1,1
                                 1
      Natural module => (R[T   ])
                            1,1
      Generator degrees => {{0, 0}}
      Differentials on gens => {0}

o5 : DGModule

i6 : not isZero M

o6 = true

i7 : Anat = A.natural

o7 = Anat

o7 : PolynomialRing, 1 skew commutative variable(s)

i8 : Z = dgSubmodule(M, map(M.natural, (Anat)^0, 0))

o8 = DGSubmodule of ambient DGModule
     Degrees  => {}
     natural  => 0
     inclusion => 0

o8 : DGSubmodule

i9 : isZero Z

o9 = true

i10 : Full = dgSubmodule(M, id_(M.natural))

o10 = DGSubmodule of ambient DGModule
      Degrees  => {{0, 0}}
                      1
      natural  => Anat
      inclusion => | 1 |

o10 : DGSubmodule

i11 : Q = M / Full

o11 = DGQuotientModule Q = M / S
      Q.natural = cokernel | 1 |
      Degrees   = {{0, 0}}

o11 : DGQuotientModule

i12 : isZero Q

o12 = true