Let G be a semidirect product of finitely generated abelian groups. We provide a 

method for constructing an explicit contraction (special homotopy equivalence) from 

the reduced bar construction of the group ring of G, B(ZZ[G]), to a much smaller DGA- 

module hG. Such a contraction is called a homological model for G and is used as 

the input datum in the methods described in  for calculating a generating set for 

representative 2-cocycles and n-cocycles over G, respectively. These computations have 

led to the finding of new cocyclic Hadamard matrices .