This function computes the element in the homology algebra of a cycle in a DGAlgebra. In order to do this, the homologyAlgebra is retrieved (or computed, if it hasn't been already).
i1 : Q = QQ[x,y,z] o1 = Q o1 : PolynomialRing |
i2 : I = ideal (x^3,y^3,z^3)
3 3 3
o2 = ideal (x , y , z )
o2 : Ideal of Q
|
i3 : R = Q/I o3 = R o3 : QuotientRing |
i4 : KR = koszulComplexDGA R
o4 = {Ring => R }
Underlying algebra => R[T ..T ]
1 3
Differential => {x, y, z}
o4 : DGAlgebra
|
i5 : z1 = x^2*T_1
2
o5 = x T
1
o5 : R[T ..T ]
1 3
|
i6 : z2 = y^2*T_2
2
o6 = y T
2
o6 : R[T ..T ]
1 3
|
i7 : H = HH(KR) Finding easy relations : -- used 0.0406202 seconds o7 = H o7 : PolynomialRing, 3 skew commutative variables |
i8 : homologyClass(KR,z1*z2)
o8 = X X
1 2
o8 : H
|
The object homologyClass is a method function.