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.

与纤维塔相关的较高的Leray-Serre光谱序列表示经典的纤维化Leray-Serre光谱序列。在这项工作中，我们提出了利用有效同源性技术来计算较高Leray-Serre光谱序列的算法，该算法可以执行涉及与代数拓扑中的感兴趣对象相关联的无限类型链复合体的计算。为了开发作为计算机代数系统Kenzo的新模块实现的程序，我们在一个简单的框架中翻译了较高Leray-Serre光谱序列的原始构造，并研究了其一些基本特性。