  The higher Leray-Serre spectral sequence associated with a tower of
fibrations represents a generalization of the classical Leray-Serre spectral
sequence of a fibration. In this work, we present algorithms to compute higher
Leray-Serre spectral sequences leveraging the effective homology technique,
which allows to perform computations involving chain complexes of infinite type
associated with interesting objects in algebraic topology. In order to develop
the programs, implemented as a new module for the Computer Algebra system
Kenzo, we translated the original construction of the higher Leray-Serre
spectral sequence in a simplicial framework and studied some of its fundamental
properties.
