An ascending filtration of a bounded (homological, lower index, or degree *-1*) chain complex *C : …→C _{i} →C_{i - 1} →…* is an ordered family of chain subcomplexes

Alternatively, a descending filtration of a bounded (cohomological, or upper index, or degree *1*) chain complex *C : …→C ^{i} →C^{i + 1} →…* is an ordered family of subchain complexes

The type `FilteredComplex` is a data type for working with bounded filtrations of bounded chain complexes.

By assumption all filtered complexes arise from bounded filtrations of bounded chain complexes. Filtrations on degree *-1* chain complexes are ascending. Filtrations on degree *1* chain complexes are descending.

- ChainComplex ** FilteredComplex -- filtered tensor product of complexes
- FilteredComplex ** ChainComplex, see ChainComplex ** FilteredComplex -- filtered tensor product of complexes
- filteredComplex(ChainComplex) -- obtain a filtered complex from a chain complex
- filteredComplex(Ideal,ChainComplex,ZZ) -- I-adic filtrations of chain complexes
- filteredComplex(List) -- obtain a filtered complex from a list of chain complex maps or a nested list of simplicial complexes
- filteredComplex(SpectralSequence) -- obtain the filtered complex associated to the spectral sequence
- Hom(ChainComplex,FilteredComplex), see Hom(FilteredComplex,ChainComplex) -- the filtered Hom complex
- Hom(FilteredComplex,ChainComplex) -- the filtered Hom complex

- associatedGradedHomologyObject(ZZ,ZZ,FilteredComplex), see associatedGradedHomologyObject -- compute the associated graded homology object
- chainComplex(FilteredComplex) -- the ambient chain complex of a filtered complex
- FilteredComplex ^ InfiniteNumber, see FilteredComplex ^ ZZ -- the filtered pieces
- FilteredComplex ^ ZZ -- the filtered pieces
- FilteredComplex _ InfiniteNumber, see FilteredComplex _ ZZ -- the filtered pieces
- FilteredComplex _ ZZ -- the filtered pieces
- filteredHomologyObject(ZZ,ZZ,FilteredComplex) -- compute the filtered homology object
- inducedMap(FilteredComplex,ZZ) -- the i th inclusion map in a filtered complex
- max(FilteredComplex) -- maximum spot where the given filtered complex has a module.
- min(FilteredComplex) -- minimum spot where the given filtered complex has a module.
- net(FilteredComplex)
- spectralSequence(FilteredComplex) -- construct a spectral sequence from a filtered complex
- spectralSequencePage(FilteredComplex,ZZ) -- construct a spectral sequence page from a filtered complex
- spectralSequencePageMap(FilteredComplex,ZZ), see spectralSequencePageMap -- compute the maps on a spectral sequence page
- spots(FilteredComplex) -- which spots does the given filtered complex has a module.
- support(FilteredComplex)

The object FilteredComplex is a type, with ancestor classes HashTable < Thing.