On the computation of A∞-maps

Starting from a chain contraction (a special chain homotopy equivalence) connecting a differential graded algebra A with a differential graded module M, the so-called homological perturbation technique "tensor trick" [8] provides a family of maps, {m(i)} i >= 1, describing an A(infinity)-algebra structure on M derived from the one of algebra on A. In this paper, taking advantage of some annihilation properties of the component morphisms of the chain contraction, we obtain a simplified version of the existing formulas of the mentioned A(infinity)-maps, reducing the computational cost of computing m. from O(n!(2)) to O(n!).