isHomogeneous(DGAlgebra) -- Determine if the DGAlgebra respects the gradings of the ring it is defined over.

i1 : R = ZZ/101[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : A = freeDGAlgebra(R,{{1},{1},{1},{3}})

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

o2 : DGAlgebra

i3 : setDiff(A,{x,y,z,x*T_(1,2)*T_(1,3)-y*T_(1,1)*T_(1,3)+z*T_(1,1)*T_(1,2)})

o3 = {Ring => R                                                      }
      Underlying algebra => R[T   ..T   , T   ]
                               1,1   1,3   3,1
      Differential => {x, y, z, z*T   T    - y*T   T    + x*T   T   }
                                   1,1 1,2      1,1 1,3      1,2 1,3

o3 : DGAlgebra

i4 : isHomogeneous A

o4 = false

i5 : B = freeDGAlgebra(R,{{1,1},{1,1},{1,1},{3,3}})

o5 = {Ring => R                                }
      Underlying algebra => R[T   ..T   , T   ]
                               1,1   1,3   3,1
      Differential => null

o5 : DGAlgebra

i6 : setDiff(B,{x,y,z,x*T_(1,2)*T_(1,3)-y*T_(1,1)*T_(1,3)+z*T_(1,1)*T_(1,2)})

o6 = {Ring => R                                                      }
      Underlying algebra => R[T   ..T   , T   ]
                               1,1   1,3   3,1
      Differential => {x, y, z, z*T   T    - y*T   T    + x*T   T   }
                                   1,1 1,2      1,1 1,3      1,2 1,3

o6 : DGAlgebra

i7 : isHomogeneous B

o7 = true