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SpectralSequences -- a package for working with filtered complexes and spectral sequences


Spectral sequences, although notoriously technical, are very useful in applications---especially when they degenerate quickly. By contrast, little is known about their general structure when they fail to degenerate quickly. Even in cases when the terms in the spectral sequences are well understood, the maps remain mysterious. One of the motivations behind this package is to shed light on spectral sequences through examples. Its purpose is to allow for effective calculations of particular kinds of spectral sequences. As one general situation, which illustrates some capabilities of this package, let k be a computable field, S a k-algebra of finite type, C a bounded chain complex of finitely generated S-modules, and FC a bounded ascending filtration of C. This package is capable of computing, under these assumptions, the spectral sequence---especially the differentials on each page---determined by FC.

Constructors used in this package

Other examples which illustrate this package

More easy topological examples



This documentation describes version 1.0 of SpectralSequences.

Source code

The source code from which this documentation is derived is in the file SpectralSequences.m2.


For the programmer

The object SpectralSequences is a package.