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.