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