Homological models for semidirect products of finitely generated Abelian groups

Let 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 , , to a much smaller DGA-module . Such a contraction is called a homological model for and is used as the input datum in the methods described in Alvarez et al. (J Symb Comput 44:558-570, 2009; 2012) for calculating a generating set for representative 2-cocycles and -cocycles over , respectively. These computations have led to the finding of new cocyclic Hadamard matrices (Alvarez et al. in 2006).