Computing spectral sequences

In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in particular it allows the user to calculate homology and homotopy groups of complicated spaces. The new programs presented here entirely compute Serre and EilenbergMoore spectral sequences, in particular the E p,q and d r p,q for arbitrary r. They also determine when E p,q = E ∞ p,q and describe the filtration of the target homology groups Hp+q by the E ∞ p,q’s.