Complexes : Index
-
augmentationMap (missing documentation)
-
Base -- make a chain complex
-
Basic invariants and properties -- information about accessing basic features
-
betti(Complex) -- display of degrees in a complex
-
Boundary (missing documentation)
-
canonicalMap -- gets the natural map arising from various constructions
-
canonicalMap(..., UseTarget => ...) -- gets the natural map arising from various constructions
-
canonicalMap(Complex,Complex) -- gets the natural map arising from various constructions
-
canonicalTruncation -- reducing the number of non-zero terms of a complex
-
canonicalTruncation(Complex,InfiniteNumber,ZZ) -- reducing the number of non-zero terms of a complex
-
canonicalTruncation(Complex,Nothing,ZZ) -- reducing the number of non-zero terms of a complex
-
canonicalTruncation(Complex,Sequence) -- reducing the number of non-zero terms of a complex
-
canonicalTruncation(Complex,ZZ,InfiniteNumber) -- reducing the number of non-zero terms of a complex
-
canonicalTruncation(Complex,ZZ,Nothing) -- reducing the number of non-zero terms of a complex
-
canonicalTruncation(Complex,ZZ,ZZ) -- reducing the number of non-zero terms of a complex
-
chainComplex(Complex) -- translate between data types for chain complexes
-
chainComplex(ComplexMap) -- translate between data types for chain complexes
-
coimage(ComplexMap) -- make the coimage of a map of complexes
-
cokernel(ComplexMap) -- make the cokernel of a map of complexes
-
Complex -- the class of all chain complexes
-
complex -- make a chain complex
-
Complex ** Complex -- tensor product of complexes
-
Complex ** Module -- tensor product of complexes
-
Complex ++ Complex -- direct sum of complexes
-
Complex == Complex -- whether two complexes are equal
-
Complex == ZZ -- whether two complexes are equal
-
Complex ^ Array -- the canonical inclusion or projection map of a direct sum
-
Complex ^ ZZ -- access individual object in a complex
-
Complex _ Array -- the canonical inclusion or projection map of a direct sum
-
Complex _ ZZ -- access individual object in a complex
-
Complex Array -- shift a complex or complex map
-
complex(ChainComplex) -- translate between data types for chain complexes
-
complex(ChainComplexMap) -- translate between data types for chain complex maps
-
complex(Complex) -- make a complex by reindexing the terms of the complex
-
complex(HashTable) -- make a chain complex
-
complex(Ideal) -- make a chain complex of length zero
-
complex(List) -- make a chain complex
-
complex(Module) -- make a chain complex of length zero
-
complex(Ring) -- make a chain complex of length zero
-
Complexes -- development package for beta testing new version of chain complexes
-
ComplexMap -- the class of all maps between chain complexes
-
ComplexMap * ComplexMap -- composition of homomorphisms of complexes
-
ComplexMap == ComplexMap -- whether two complex maps are equal
-
ComplexMap == ZZ -- whether two complex maps are equal
-
ComplexMap Array -- shift a complex or complex map
-
components(Complex) -- list the components of a direct sum
-
Concentration (missing documentation)
-
concentration -- indices on which a complex may be non-zero
-
concentration(Complex) -- indices on which a complex may be non-zero
-
cone(ComplexMap) -- make the mapping cone of a morphism of chain complexes
-
connectingMap (missing documentation)
-
Cycle (missing documentation)
-
cylinder -- make the mapping cylinder of a morphism of chain complexes
-
cylinder(ComplexMap) -- make the mapping cylinder of a morphism of chain complexes
-
differential of a chain complex -- get the maps between the terms in a complex
-
directSum(Complex) -- direct sum of complexes
-
dual(Complex) -- make the dual of a complex
-
freeResolution -- compute a free resolution of a module or ideal
-
freeResolution(Ideal) -- compute a free resolution of a module or ideal
-
freeResolution(Module) -- compute a free resolution of a module or ideal
-
gradedModule(Complex) -- a new complex in which the differential is zero
-
HH Complex -- homology of a complex
-
HH^ZZ Complex -- homology or cohomology module of a complex
-
HH_ZZ Complex -- homology or cohomology module of a complex
-
Hom(Complex,Complex) -- the complex of homomorphisms between two complexes
-
Hom(Complex,Module) -- the complex of homomorphisms between two complexes
-
Hom(Module,Complex) -- the complex of homomorphisms between two complexes
-
homotopic (missing documentation)
-
homotopy (missing documentation)
-
HomWithComponents (missing documentation)
-
horseshoeResolution (missing documentation)
-
id _ Complex -- the identity map of a chain complex
-
image(ComplexMap) -- make the image of a map of complexes
-
InternalDegree (missing documentation)
-
isCommutative(ComplexMap) -- whether a complex map commutes with the differentials
-
isComplexMorphism -- whether a complex map is a morphism of complexes
-
isComplexMorphism(ComplexMap) -- whether a complex map is a morphism of complexes
-
isExact -- whether a complex is exact
-
isExact(Complex) -- whether a complex is exact
-
isExact(Complex,InfiniteNumber,InfiniteNumber) -- whether a complex is exact
-
isExact(Complex,InfiniteNumber,Number) -- whether a complex is exact
-
isExact(Complex,Number,InfiniteNumber) -- whether a complex is exact
-
isExact(Complex,Number,Number) -- whether a complex is exact
-
isFree -- whether a complex consists of free modules
-
isFree(Complex) -- whether a complex consists of free modules
-
isHomogeneous(Complex) -- whether a complex is homogeneous
-
isNullHomotopic (missing documentation)
-
isNullHomotopyOf (missing documentation)
-
isQuasiIsomorphism (missing documentation)
-
isShortExactSequence (missing documentation)
-
isWellDefined(Complex) -- whether a complex is well-defined
-
isWellDefined(ComplexMap) -- whether a map of chain complexes is well-defined
-
kernel(ComplexMap) -- make the kernel of a map of complexes
-
length(Complex) -- length of a complex
-
liftMapAlongQuasiIsomorphism (missing documentation)
-
Making chain complexes -- information about the basic constructors
-
Making complexes
-
Making maps between chain complexes -- information about the basic constructors
-
map(Complex,Complex,ComplexMap) -- make a new map of chain complexes from an existing one
-
map(Complex,Complex,Function) -- make a map of chain complexes
-
map(Complex,Complex,HashTable) -- make a map of chain complexes
-
map(Complex,Complex,ZZ) -- make the zero map or identity between chain complexes
-
minimalPresentation(Complex) -- minimal presentation of all terms in a complex
-
minimize -- a quasi-isomorphic complex whose terms have minimal rank
-
minimize(Complex) -- a quasi-isomorphic complex whose terms have minimal rank
-
minimizingMap (missing documentation)
-
Module ** Complex -- tensor product of complexes
-
naiveTruncation -- drops all terms of a complex outside a given interval
-
naiveTruncation(Complex,InfiniteNumber,ZZ) -- drops all terms of a complex outside a given interval
-
naiveTruncation(Complex,Nothing,ZZ) -- drops all terms of a complex outside a given interval
-
naiveTruncation(Complex,Sequence) -- drops all terms of a complex outside a given interval
-
naiveTruncation(Complex,ZZ,InfiniteNumber) -- drops all terms of a complex outside a given interval
-
naiveTruncation(Complex,ZZ,Nothing) -- drops all terms of a complex outside a given interval
-
naiveTruncation(Complex,ZZ,ZZ) -- drops all terms of a complex outside a given interval
-
nullHomotopy (missing documentation)
-
Number * ComplexMap -- composition of homomorphisms of complexes
-
part(List,Complex) -- extract a graded component of a complex
-
part(ZZ,Complex) -- extract a graded component of a complex
-
prune(Complex) -- minimal presentation of all terms in a complex
-
randomComplexMap (missing documentation)
-
resolution(Complex) -- minimal free resolution of a complex
-
ResolutionMap (missing documentation)
-
resolutionMap -- map from a free resolution to the given complex
-
resolutionMap(Complex) -- map from a free resolution to the given complex
-
ring(Complex) -- access the ring of a complex or a complex map
-
ring(ComplexMap) -- access the ring of a complex or a complex map
-
RingElement * ComplexMap -- composition of homomorphisms of complexes
-
RingMap ** Complex -- tensor a complex along a ring map
-
RingMap ** ComplexMap -- tensor a map of complexes along a ring map
-
RingMap Complex -- apply a ring map
-
RingMap ComplexMap -- apply a ring map to a map of complexes
-
source(ComplexMap) -- get the source of a map of chain complexes
-
Symbol ^ Complex -- get the maps between the terms in a complex
-
target(ComplexMap) -- get the target of a map of chain complexes
-
tensor(Complex,Complex) -- tensor product of complexes
-
tensor(RingMap,Complex) -- tensor a complex along a ring map
-
tensor(RingMap,ComplexMap) -- tensor a map of complexes along a ring map
-
Towards computing in the derived category
-
UseTarget (missing documentation)
-
Working with Ext -- information about functorial properties
-
Working with Tor -- information about functorial properties
-
yonedaExtension (missing documentation)
-
yonedaExtension' (missing documentation)
-
yonedaMap (missing documentation)
-
yonedaMap' (missing documentation)
-
yonedaProduct (missing documentation)
-
ZZ == Complex -- whether two complexes are equal
-
ZZ == ComplexMap -- whether two complex maps are equal