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Complexes : Index
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- ComplexMap
-- perform arithmetic operations on complex maps
arithmetic with complex maps
-- perform arithmetic operations on complex maps
augmentationMap
-- map from a free resolution to a module regarded as a complex
augmentationMap(Complex)
-- map from a free resolution to a module regarded as a complex
Base
-- make a chain complex
Basic invariants and properties
-- information about accessing basic features
betti(Complex)
-- display of degrees in a complex
Boundary
-- a random map of chain complexes
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,InfiniteNumber)
-- 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
canonicalTruncation(ComplexMap,InfiniteNumber,InfiniteNumber)
-- reducing the number of non-zero terms of a complex
canonicalTruncation(ComplexMap,InfiniteNumber,ZZ)
-- reducing the number of non-zero terms of a complex
canonicalTruncation(ComplexMap,Nothing,ZZ)
-- reducing the number of non-zero terms of a complex
canonicalTruncation(ComplexMap,Sequence)
-- reducing the number of non-zero terms of a complex
canonicalTruncation(ComplexMap,ZZ,InfiniteNumber)
-- reducing the number of non-zero terms of a complex
canonicalTruncation(ComplexMap,ZZ,Nothing)
-- reducing the number of non-zero terms of a complex
canonicalTruncation(ComplexMap,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 ** ComplexMap
-- the map of complexes between tensor complexes
Complex ** Matrix
-- create the tensor product of a complex and a map of modules
Complex ** Module
-- tensor product of complexes
Complex ** Ring
-- tensor a complex along a ring map
Complex ** RingMap
-- tensor a complex along a ring map
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(...,Base=>...)
-- make a chain complex
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(ComplexMap)
-- make a complex by specifying the differential
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 * Number
-- perform arithmetic operations on complex maps
ComplexMap * RingElement
-- perform arithmetic operations on complex maps
ComplexMap ** Complex
-- the map of complexes between tensor complexes
ComplexMap ** ComplexMap
-- the map of complexes between tensor complexes
ComplexMap ** Module
-- the map of complexes between tensor complexes
ComplexMap ** Ring
-- tensor a map of complexes along a ring map
ComplexMap ** RingMap
-- tensor a map of complexes along a ring map
ComplexMap + ComplexMap
-- perform arithmetic operations on complex maps
ComplexMap + Number
-- perform arithmetic operations on complex maps
ComplexMap + RingElement
-- perform arithmetic operations on complex maps
ComplexMap ++ ComplexMap
-- direct sum of complex maps
ComplexMap - ComplexMap
-- perform arithmetic operations on complex maps
ComplexMap - Number
-- perform arithmetic operations on complex maps
ComplexMap - RingElement
-- perform arithmetic operations on complex maps
ComplexMap // ComplexMap
-- lift a map of chain complexes along a quasi-isomorphism
ComplexMap == ComplexMap
-- whether two complex maps are equal
ComplexMap == ZZ
-- whether two complex maps are equal
ComplexMap ^ Array
-- the composition with the canonical inclusion or projection map
ComplexMap ^ ZZ
-- the n-fold composition
ComplexMap _ Array
-- the composition with the canonical inclusion or projection map
ComplexMap _ ZZ
-- access individual matrices in a complex map
ComplexMap | ComplexMap
-- join or concatenate maps horizontally
ComplexMap || ComplexMap
-- join or concatenate maps vertically
ComplexMap Array
-- shift a complex or complex map
components(Complex)
-- list the components of a direct sum
components(ComplexMap)
-- list the components of a direct sum
Concentration
-- optional argument used to specify the concentration
concentration
-- indices on which a complex may be non-zero
concentration(Complex)
-- indices on which a complex may be non-zero
concentration(ComplexMap)
-- indices on which a complex map may be non-zero
cone(ComplexMap)
-- make the mapping cone of a morphism of chain complexes
connectingExtMap
-- makes the connecting maps in Ext
connectingExtMap(...,Concentration=>...)
-- makes the connecting maps in Ext
connectingExtMap(Matrix,Matrix,Module)
-- makes the connecting maps in Ext
connectingExtMap(Module,Matrix,Matrix)
-- makes the connecting maps in Ext
connectingMap
-- construct the connecting homomorphism on homology
connectingMap(...,Concentration=>...)
-- construct the connecting homomorphism on homology
connectingMap(ComplexMap,ComplexMap)
-- construct the connecting homomorphism on homology
connectingTorMap
-- makes the connecting maps in Tor
connectingTorMap(...,Concentration=>...)
-- makes the connecting maps in Tor
connectingTorMap(Matrix,Matrix,Module)
-- makes the connecting maps in Tor
connectingTorMap(Module,Matrix,Matrix)
-- makes the connecting maps in Tor
Cycle
-- a random map of chain complexes
cylinder
-- make the mapping cylinder of a morphism of chain complexes
cylinder(ComplexMap)
-- make the mapping cylinder of a morphism of chain complexes
Default strategy for free resolutions of homogeneous modules
-- algorithm for computing free resolutions exploiting the Schreyer frame
degree(ComplexMap)
-- get the degree of a map of chain complexes
differential of a chain complex
-- get the maps between the terms in a complex
directSum(Complex)
-- direct sum of complexes
directSum(ComplexMap)
-- direct sum of complex maps
dual(Complex)
-- make the dual of a complex
dual(ComplexMap)
-- the dual of a map of complexes
extend(Complex,Complex,Matrix)
-- extend a map of modules to a map of chain complexes
extend(Complex,Complex,Matrix,Sequence)
-- extend a map of modules to a map of chain complexes
freeResolution
-- compute a free resolution of a module or ideal
freeResolution(..., Strategy => 0)
-- algorithm for computing free resolutions exploiting the Schreyer frame
freeResolution(..., Strategy => 1)
-- algorithm for computing free resolutions exploiting the Schreyer frame
freeResolution(..., Strategy => 2)
-- algorithm for computing free resolutions step by step
freeResolution(..., Strategy => 3)
-- algorithm for computing free resolutions step by step aided by Hilbert functions
freeResolution(..., Strategy => Engine)
-- algorithm for computing a free resolution
freeResolution(..., Strategy => Homogenization)
-- algorithm for computing free resolutions by first homogenizing
freeResolution(..., Strategy => Nonminimal)
-- algorithm for computing nonminimal free resolutions
freeResolution(..., Strategy => OverField)
-- algorithm for computing free resolutions over a field
freeResolution(..., Strategy => OverZZ)
-- algorithm for computing free resolutions of ZZ-modules
freeResolution(..., Strategy => Syzygies)
-- algorithm for computing free resolutions step by step using syzygies
freeResolution(...,DegreeLimit=>...)
-- optional arguments for freeResolution
freeResolution(...,HardDegreeLimit=>...)
-- optional arguments for freeResolution
freeResolution(...,LengthLimit=>...)
-- optional arguments for freeResolution
freeResolution(...,PairLimit=>...)
-- optional arguments for freeResolution
freeResolution(...,ParallelizeByDegree=>...)
-- optional arguments for freeResolution
freeResolution(...,SortStrategy=>...)
-- optional arguments for freeResolution
freeResolution(...,StopBeforeComputation=>...)
-- optional arguments for freeResolution
freeResolution(...,Strategy=>...)
-- overview of the different algorithms for computing free resolutions
freeResolution(...,SyzygyLimit=>...)
-- optional arguments for freeResolution
freeResolution(Ideal)
-- compute a free resolution of a module or ideal
freeResolution(Matrix)
-- compute the induced map between free resolutions
freeResolution(Module)
-- compute a free resolution of a module or ideal
freeResolution(MonomialIdeal)
-- 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 ComplexMap
-- induced map on homology or cohomology
HH^ZZ Complex
-- homology or cohomology module of a complex
HH^ZZ ComplexMap
-- induced map on homology or cohomology
HH_ZZ Complex
-- homology or cohomology module of a complex
HH_ZZ ComplexMap
-- induced map on homology or cohomology
Hom(Complex,Complex)
-- the complex of homomorphisms between two complexes
Hom(Complex,ComplexMap)
-- the map of complexes between Hom complexes
Hom(Complex,Matrix)
-- the map of complexes between Hom complexes
Hom(Complex,Module)
-- the complex of homomorphisms between two complexes
Hom(Complex,Ring)
-- the complex of homomorphisms between two complexes
Hom(ComplexMap,Complex)
-- the map of complexes between Hom complexes
Hom(ComplexMap,ComplexMap)
-- the map of complexes between Hom complexes
Hom(ComplexMap,Matrix)
-- the map of complexes between Hom complexes
Hom(ComplexMap,Module)
-- the map of complexes between Hom complexes
Hom(ComplexMap,Ring)
-- the map of complexes between Hom complexes
Hom(Matrix,Complex)
-- the map of complexes between Hom complexes
Hom(Matrix,ComplexMap)
-- the map of complexes between Hom complexes
Hom(Module,Complex)
-- the complex of homomorphisms between two complexes
Hom(Module,ComplexMap)
-- the map of complexes between Hom complexes
Hom(Ring,Complex)
-- the complex of homomorphisms between two complexes
Hom(Ring,ComplexMap)
-- the map of complexes between Hom complexes
Homogenization
-- algorithm for computing free resolutions by first homogenizing
homomorphism'(ComplexMap)
-- get the element of Hom from a map of complexes
homomorphism(ComplexMap)
-- get the homomorphism from an element of Hom
homomorphism(ZZ,Matrix,Complex)
-- get the homomorphism from an element of Hom
homotopyMap
-- lift a map of chain complexes along a quasi-isomorphism
homotopyMap(ComplexMap)
-- lift a map of chain complexes along a quasi-isomorphism
horseshoeResolution
-- make the horseshoe resolution
horseshoeResolution(...,LengthLimit=>...)
-- make the horseshoe resolution
horseshoeResolution(Complex)
-- make the horseshoe resolution
horseshoeResolution(Matrix,Matrix)
-- make the horseshoe resolution
id _ Complex
-- the identity map of a chain complex
image(ComplexMap)
-- make the image of a map of complexes
inducedMap(Complex,Complex)
-- make the map of complexes induced at each term by the identity map
InternalDegree
-- a random map of chain complexes
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
isHomogeneous(ComplexMap)
-- whether a map of complexes is homogeneous
isNullHomotopic
-- whether a map of complexes is null-homotopic
isNullHomotopic(ComplexMap)
-- whether a map of complexes is null-homotopic
isNullHomotopyOf
-- whether the first map of chain complexes is a null homotopy for the second
isNullHomotopyOf(ComplexMap,ComplexMap)
-- whether the first map of chain complexes is a null homotopy for the second
isQuasiIsomorphism
-- whether a map of complexes is a quasi-isomorphism
isQuasiIsomorphism(...,Concentration=>...)
-- whether a map of complexes is a quasi-isomorphism
isQuasiIsomorphism(ComplexMap)
-- whether a map of complexes is a quasi-isomorphism
isShortExactSequence
-- whether a chain complex is a short exact sequence
isShortExactSequence(Complex)
-- whether a chain complex is a short exact sequence
isShortExactSequence(ComplexMap,ComplexMap)
-- whether a pair of complex maps forms a short exact sequence
isShortExactSequence(Matrix,Matrix)
-- whether a pair of matrices forms a short exact sequence
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
koszulComplex
-- makes the Koszul complex
koszulComplex(List)
-- makes the Koszul complex
koszulComplex(List,Concentration=>...)
-- makes the Koszul complex
koszulComplex(Matrix)
-- makes the Koszul complex
koszulComplex(Matrix,Concentration=>...)
-- makes the Koszul complex
length(Complex)
-- length of a complex
liftMapAlongQuasiIsomorphism
-- lift a map of chain complexes along a quasi-isomorphism
liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap)
-- lift a map of chain complexes along a quasi-isomorphism
longExactSequence
-- make the long exact sequence in homology
longExactSequence(ComplexMap,ComplexMap)
-- make the long exact sequence in homology
longExactSequence(ComplexMap,ComplexMap,Concentration=>...)
-- make the long exact sequence in homology
Making chain complexes
-- information about the basic constructors
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,List)
-- make a map of chain complexes
map(Complex,Complex,ZZ)
-- make the zero map or identity between chain complexes
Matrix ** Complex
-- create the tensor product of a complex and a map of modules
max(Complex)
-- indices on which a complex may be non-zero
min(Complex)
-- indices on which a complex may be non-zero
minimalPresentation(Complex)
-- minimal presentation of all terms in a complex
minimalPresentation(ComplexMap)
-- 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
-- a quasi-isomorphic complex whose terms have minimal rank
Module ** Complex
-- tensor product of complexes
Module ** ComplexMap
-- the map of complexes between tensor complexes
naiveTruncation
-- drops all terms of a complex outside a given interval
naiveTruncation(Complex,InfiniteNumber,InfiniteNumber)
-- 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
naiveTruncation(ComplexMap,InfiniteNumber,InfiniteNumber)
-- drops all terms in the source of a complex outside a given interval
naiveTruncation(ComplexMap,InfiniteNumber,ZZ)
-- drops all terms in the source of a complex outside a given interval
naiveTruncation(ComplexMap,Nothing,ZZ)
-- drops all terms in the source of a complex outside a given interval
naiveTruncation(ComplexMap,Sequence)
-- drops all terms in the source of a complex outside a given interval
naiveTruncation(ComplexMap,Sequence,Sequence)
-- drops all terms in the source of a complex outside a given interval
naiveTruncation(ComplexMap,ZZ,InfiniteNumber)
-- drops all terms in the source of a complex outside a given interval
naiveTruncation(ComplexMap,ZZ,Nothing)
-- drops all terms in the source of a complex outside a given interval
naiveTruncation(ComplexMap,ZZ,ZZ)
-- drops all terms in the source of a complex outside a given interval
Nonminimal
-- algorithm for computing nonminimal free resolutions
nullHomotopy
-- a map which is a candidate for being a null homotopy
nullHomotopy(ComplexMap)
-- a map which is a candidate for being a null homotopy
Number * ComplexMap
-- perform arithmetic operations on complex maps
Number + ComplexMap
-- perform arithmetic operations on complex maps
Number - ComplexMap
-- perform arithmetic operations on complex maps
OverField
-- algorithm for computing free resolutions over a field
OverZZ
-- algorithm for computing free resolutions of ZZ-modules
part(List,Complex)
-- extract a graded component of a complex
part(List,ComplexMap)
-- extract a graded component of a map of complexes
part(ZZ,Complex)
-- extract a graded component of a complex
part(ZZ,ComplexMap)
-- extract a graded component of a map of complexes
poincare(Complex)
-- assemble degrees of a chain complex into a polynomial
poincareN(Complex)
-- assemble degrees of a chain complex into a polynomial
prune(Complex)
-- minimal presentation of all terms in a complex
prune(ComplexMap)
-- minimal presentation of all terms in a complex
quotient(ComplexMap,ComplexMap)
-- lift a map of chain complexes along a quasi-isomorphism
randomComplexMap
-- a random map of chain complexes
randomComplexMap(...,Boundary=>...)
-- a random map of chain complexes
randomComplexMap(...,Cycle=>...)
-- a random map of chain complexes
randomComplexMap(...,Degree=>...)
-- a random map of chain complexes
randomComplexMap(...,InternalDegree=>...)
-- a random map of chain complexes
randomComplexMap(Complex,Complex)
-- a random map of chain complexes
regularity(Complex)
-- compute the Castelnuovo-Mumford regularity
resolution(Complex)
-- minimal free resolution of a complex
resolutionMap
-- map from a free resolution to the given complex
resolutionMap(...,DegreeLimit=>...)
-- map from a free resolution to the given complex
resolutionMap(...,HardDegreeLimit=>...)
-- map from a free resolution to the given complex
resolutionMap(...,LengthLimit=>...)
-- map from a free resolution to the given complex
resolutionMap(...,PairLimit=>...)
-- map from a free resolution to the given complex
resolutionMap(...,SortStrategy=>...)
-- map from a free resolution to the given complex
resolutionMap(...,StopBeforeComputation=>...)
-- map from a free resolution to the given complex
resolutionMap(...,Strategy=>...)
-- map from a free resolution to the given complex
resolutionMap(...,SyzygyLimit=>...)
-- map from a free resolution to the given complex
resolutionMap(Complex)
-- map from a free resolution to the given complex
Ring ** Complex
-- tensor a complex along a ring map
Ring ** ComplexMap
-- tensor a map of complexes along a ring map
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
-- perform arithmetic operations on complex maps
RingElement + ComplexMap
-- perform arithmetic operations on complex maps
RingElement - ComplexMap
-- perform arithmetic operations on complex maps
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
Strategies for free resolutions
-- overview of the different algorithms for computing free resolutions
Strategy for free resolutions of homogeneous modules aided by Hilbert functions
-- algorithm for computing free resolutions step by step aided by Hilbert functions
Strategy for free resolutions of homogeneous modules via successive syzygies
-- algorithm for computing free resolutions step by step
Strategy for free resolutions over a field
-- algorithm for computing free resolutions over a field
Strategy for free resolutions over the integers
-- algorithm for computing free resolutions of ZZ-modules
Strategy for free resolutions via homogenization
-- algorithm for computing free resolutions by first homogenizing
Strategy for free resolutions via Schreyer-Lascala
-- algorithm for computing free resolutions exploiting the Schreyer frame
Strategy for free resolutions via syzygies
-- algorithm for computing free resolutions step by step using syzygies
Strategy for nonminimal free resolutions
-- algorithm for computing nonminimal free resolutions
sum(Complex)
-- make the direct sum of all terms
sum(ComplexMap)
-- make the direct sum of all terms
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(Complex,RingMap)
-- tensor a complex along a ring map
tensor(ComplexMap,ComplexMap)
-- the map of complexes between tensor complexes
tensor(ComplexMap,RingMap)
-- tensor a map of complexes along a ring map
tensor(RingMap,Complex)
-- tensor a complex along a ring map
tensor(RingMap,ComplexMap)
-- tensor a map of complexes along a ring map
tensorAssociativity(Complex,Complex,Complex)
-- make the canonical isomorphism arising from associativity
tensorCommutativity
-- make the canonical isomorphism arising from commutativity
tensorCommutativity(Complex,Complex)
-- make the canonical isomorphism arising from commutativity
tensorCommutativity(Module,Module)
-- make the canonical isomorphism arising from commutativity
Tor_ZZ(Matrix,Module)
-- make the induced map on Tor modules
Tor_ZZ(Module,Matrix)
-- make the induced map on Tor modules
torSymmetry
-- makes the canonical isomorphism realizing the symmetry of Tor
torSymmetry(ZZ,Module,Module)
-- makes the canonical isomorphism realizing the symmetry of Tor
Towards computing in the derived category
truncate(List,Complex)
-- truncation of a complex at a specified degree or set of degrees
truncate(List,ComplexMap)
-- truncation of a complex map at a specified degree or set of degrees
truncate(ZZ,Complex)
-- truncation of a complex at a specified degree or set of degrees
truncate(ZZ,ComplexMap)
-- truncation of a complex map at a specified degree or set of degrees
UseTarget
-- gets the natural map arising from various constructions
Working with Ext
-- information about functorial properties
Working with Tor
-- information about functorial properties
yonedaExtension
-- creates a chain complex representing an extension of modules
yonedaExtension'
-- identifies the element of Ext corresponding to an extension
yonedaExtension'(...,MinimalGenerators=>...)
-- identifies the element of Ext corresponding to an extension
yonedaExtension'(Complex)
-- identifies the element of Ext corresponding to an extension
yonedaExtension(Matrix)
-- creates a chain complex representing an extension of modules
yonedaMap
-- creates a chain complex map representing an extension of modules
yonedaMap'
-- identifies the element of Ext corresponding to a map of free resolutions
yonedaMap'(...,MinimalGenerators=>...)
-- identifies the element of Ext corresponding to a map of free resolutions
yonedaMap'(ComplexMap)
-- identifies the element of Ext corresponding to a map of free resolutions
yonedaMap(...,LengthLimit=>...)
-- creates a chain complex map representing an extension of modules
yonedaMap(Matrix)
-- creates a chain complex map representing an extension of modules
yonedaProduct
-- make the product of two elements in Ext modules
yonedaProduct(Matrix,Matrix)
-- make the product of two elements in Ext modules
yonedaProduct(Module,Module)
-- make the product map between Ext modules
ZZ == Complex
-- whether two complexes are equal
ZZ == ComplexMap
-- whether two complex maps are equal