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DGAlgebras :: isHomogeneous(DGAlgebra)

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

Synopsis

Description

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 ]
                               1   4
      Differential => null

o2 : DGAlgebra
i3 : setDiff(A,{x,y,z,x*T_2*T_3-y*T_1*T_3+z*T_1*T_2})

o3 = {Ring => R                                          }
      Underlying algebra => R[T ..T ]
                               1   4
      Differential => {x, y, z, z*T T  - y*T T  + x*T T }
                                   1 2      1 3      2 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 ]
                               1   4
      Differential => null

o5 : DGAlgebra
i6 : setDiff(B,{x,y,z,x*T_2*T_3-y*T_1*T_3+z*T_1*T_2})

o6 = {Ring => R                                          }
      Underlying algebra => R[T ..T ]
                               1   4
      Differential => {x, y, z, z*T T  - y*T T  + x*T T }
                                   1 2      1 3      2 3

o6 : DGAlgebra
i7 : isHomogeneous B

o7 = true