SpectralSequences : Index
- A spectral sequence which fails to degenerate quickly
- associatedGradedHomologyObject -- compute the associated graded homology object
- associatedGradedHomologyObject(ZZ,ZZ,FilteredComplex) -- compute the associated graded homology object
- Balancing Tor
- basis(List,SpectralSequencePage) -- generators of a particular degree
- basis(ZZ,SpectralSequencePage) -- generators of a particular degree
- ChainComplex ** FilteredComplex -- filtered tensor product of complexes
- chainComplex(FilteredComplex) -- the ambient chain complex of a filtered complex
- chainComplex(SpectralSequence) -- the underlying chain complex of a Spectral Sequence
- Computing the Serre Spectral Sequence associated to a Hopf Fibration
- connectingMorphism -- use spectral sequences to compute connecting morphisms
- connectingMorphism(ChainComplexMap,ZZ) -- use spectral sequences to compute connecting morphisms
- degree(Page)
- describe(Page) -- real description
- describe(PageMap) -- real description
- describe(SpectralSequence) -- real description
- describe(SpectralSequencePage) -- real description
- describe(SpectralSequencePageMap) -- real description
- Edge homomorphisms
- edgeComplex -- the edge homomorphisms
- edgeComplex(SpectralSequence) -- the edge homomorphisms
- Example 1 -- Easy example of a filtered simpilcial complex
- Example 2 -- Easy example of a filtered simplicial complex
- Example 3 -- Easy example of a filtered simplical complex
- Examples of change of rings Spectral Sequences
- Examples of filtered complexes and spectral sequences -- How to use this package
- expression(SpectralSequence)
- Filtered complexes and simplicial complexes
- filtered complexes and spectral sequences from simplicial complexes
- FilteredComplex -- the type of all filtered complexes
- filteredComplex -- make a filtered complex
- FilteredComplex ** ChainComplex -- filtered tensor product of complexes
- FilteredComplex ^ InfiniteNumber -- the filtered pieces
- FilteredComplex ^ ZZ -- the filtered pieces
- FilteredComplex _ InfiniteNumber -- the filtered pieces
- FilteredComplex _ ZZ -- the filtered pieces
- filteredComplex(..., ReducedHomology => ...)
- filteredComplex(..., Shift => ...)
- 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
- filteredHomologyObject -- compute the filtered homology object
- filteredHomologyObject(ZZ,ZZ,FilteredComplex) -- compute the filtered homology object
- Filtrations and homomorphism complexes
- Filtrations and tensor product complexes
- hilbertPolynomial(SpectralSequencePage) -- the Hilbert polynomial of a spectral sequence page
- Hom(ChainComplex,FilteredComplex) -- the filtered Hom complex
- Hom(FilteredComplex,ChainComplex) -- the filtered Hom complex
- homologyIsomorphism -- compute the homology isomorphism
- homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ) -- the homology isomorphism
- How to make filtered complexes from chain complex maps
- I-adic filtrations of chain complexes and their spectral sequences
- Identifying anti-podal points of the two sphere
- 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.
- minimalPresentation(SpectralSequence) -- a minimal presentation of a spectral sequence
- minimalPresentation(SpectralSequencePage) -- a minimal presentation of a spectral sequence page
- net(FilteredComplex)
- net(Page)
- net(PageMap)
- net(SpectralSequence)
- net(SpectralSequencePage)
- netPage -- display a small portion of a given Spectral Sequence page
- netPage(Page,List,List) -- display a small portion of a given Spectral Sequence page
- new Page
- Page -- the type of all pages
- page
- Page _ List
- page(..., Prune => ...)
- page(List,List,Page)
- page(SpectralSequencePage)
- PageMap -- the type of all page maps
- pageMap
- PageMap _ List
- prune(SpectralSequence) -- a minimal presentation of a spectral sequence
- prune(SpectralSequencePage) -- a minimal presentation of a spectral sequence page
- pruningMaps -- compute the pruning maps on a spectral sequence page
- pruningMaps(SpectralSequencePage) -- compute the pruning maps on a spectral sequence page
- ReducedHomology -- name for an optional argument
- ring(Page)
- Seeing Cancellations
- Shift -- name for an optional argument
- sourcePruningMap
- Spectral sequences and connecting morphisms
- Spectral sequences and hypercohomology calculations
- Spectral sequences and non-Koszul syzygies
- SpectralSequence -- the type of all spectral sequences
- spectralSequence -- construct a spectral sequence
- SpectralSequence ^ InfiniteNumber -- the infinity page of a spectral sequence
- SpectralSequence ^ ZZ -- the kth page of a spectral sequence
- SpectralSequence _ InfiniteNumber -- the infinity page of a spectral sequence
- SpectralSequence _ ZZ -- the kth page of a spectral sequence
- spectralSequence(..., Prune => ...)
- spectralSequence(FilteredComplex) -- construct a spectral sequence from a filtered complex
- SpectralSequencePage -- the type of all spectral sequence pages
- spectralSequencePage -- construct a spectral sequence page from a filtered complex
- SpectralSequencePage ^ List -- the module in the i,j position on the page
- SpectralSequencePage _ List -- the module in the i,j position on the page
- spectralSequencePage(..., Prune => ...)
- spectralSequencePage(FilteredComplex,ZZ) -- construct a spectral sequence page from a filtered complex
- SpectralSequencePageMap -- the type of all spectral sequence page maps
- spectralSequencePageMap -- compute the maps on a spectral sequence page
- SpectralSequencePageMap ^ List -- the p,q th map on of a spectral sequence page
- SpectralSequencePageMap _ List -- The p,q th map on of a spectral sequence page
- spectralSequencePageMap(..., Prune => ...)
- spectralSequencePageMap(FilteredComplex,ZZ) -- compute the maps on a spectral sequence page
- SpectralSequences -- a package for working with filtered complexes and spectral sequences
- spots -- which spots does the given page has a module.
- spots(ChainComplex) -- which spots does the given chain complex has a module.
- spots(FilteredComplex) -- which spots does the given filtered complex has a module.
- spots(Page) -- which spots does the given page has a module.
- spots(PageMap)
- support(ChainComplex) -- nonzero parts of a chain complex
- support(FilteredComplex)
- support(Page) -- which non-zero modules appear in the given page.
- support(PageMap)
- support(SpectralSequencePage)
- targetPruningMap
- tensor(RingMap,ChainComplex) -- tensor product of a chain complex by a ring map
- The fibration of the Klein Bottle over the sphere with fibers the sphere
- The trivial fibration over the sphere with fibers the sphere
- truncate(ChainComplex,ZZ) -- compute the hard truncation of a chain complex