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

## Synopsis

• Function: isHomogeneous
• Usage:
isHom = isHomogeneous(A)
• Inputs:
• Outputs:
• isHom, , Whether or not the DGA respects the grading

## 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