SpectralSequencePage -- the type of all spectral sequence pages

Description

A (homological, or lower index) spectral sequence page consists of:

1. A fixed integer r ≥0, the page number;

2. A sequence of modules {E^r_p,q} for p,q ∈ℤ;

3. A collection of homomorphisms {d^r_p,q: E^r_p,q →E^r_p-r,q+r-1} for p,q ∈ℤ, r ≥0 such that d^r_p,q d^r_p+r,q-r+1 = 0 ;

4. A collection of isomorphisms E^r+1_p,q →ker d^r_p,q / image d^r_p+r,q-r+1.

Alternatively a (cohomological, or upper index) spectral sequence page consists of:

1’. A fixed integer r ≥0, the page number;

2’. A sequence of modules {E_r^p,q} for p,q ∈ℤ;

3’. A collection of homomorphisms {d_r^p,q: E_r^p,q →E_r^p+r,q-r+1} for p,q ∈ℤ, r ≥0 such that d_r^p,q d_r^p-r,q+r-1 = 0 ;

4’. A collection of isomorphisms E_r+1^p,q →ker d_r^p,q / image d_r^p-r,q+r-1.

The type SpectralSequencePage is a data type for working with spectral sequences and spectral sequence pages.

The isomorphisms 4 and 4’ are not explicitly part of the data type, although they can be obtained by using the command homologyIsomorphism.

minimalPresentation(SpectralSequencePage) -- a minimal presentation of a spectral sequence page
prune(SpectralSequencePage), see minimalPresentation(SpectralSequencePage) -- a minimal presentation of a spectral sequence page
spectralSequencePage(FilteredComplex,ZZ) -- construct a spectral sequence page from a filtered complex

basis(List,SpectralSequencePage) -- generators of a particular degree
basis(ZZ,SpectralSequencePage), see basis(List,SpectralSequencePage) -- generators of a particular degree
describe(SpectralSequencePage) -- real description
hilbertPolynomial(SpectralSequencePage) -- the Hilbert polynomial of a spectral sequence page
net(SpectralSequencePage)
page(SpectralSequencePage)
pruningMaps(SpectralSequencePage) -- compute the pruning maps on a spectral sequence page
SpectralSequencePage ^ List -- the module in the i,j position on the page
SpectralSequencePage _ List -- the module in the i,j position on the page
support(SpectralSequencePage)