Macaulay2 » Documentation
Packages » MatrixFactorizations :: Index

MatrixFactorizations : Index

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

- ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
adjoinRoot -- Adjoin a root of unity to the underlying object input
adjoinRoot(ZZ,Ring,RingElement) -- Adjoin a root of unity to the underlying object input
adjoinRoot(ZZ,Ring,Symbol) -- Adjoin a root of unity to the underlying object input
adjoinRoot(ZZdFactorization,RingElement) -- Adjoin a root of unity to the underlying object input
adjoinRoot(ZZdFactorization,Symbol) -- Adjoin a root of unity to the underlying object input
adjoinRoot(ZZdFactorizationMap,RingElement) -- Adjoin a root of unity to the underlying object input
adjoinRoot(ZZdFactorizationMap,Symbol) -- Adjoin a root of unity to the underlying object input
adjointFactorization -- Constructs matrix factorization of a determinant of a matrix
adjointFactorization(Matrix) -- Constructs matrix factorization of a determinant of a matrix
arithmetic with ZZ/d-graded factorization maps -- perform arithmetic operations on ZZ/d-graded factorization maps
Basic invariants and properties -- information about accessing basic features
branchedToMF -- Converts a maximal Cohen-Macaulay module over a d-fold branched cover into a d-fold factorization
branchedToMF(Matrix) -- Converts a maximal Cohen-Macaulay module over a d-fold branched cover into a d-fold factorization
branchedToMF(Matrix,Ring) -- Converts a maximal Cohen-Macaulay module over a d-fold branched cover into a d-fold factorization
branchedToMF(Module) -- Converts a maximal Cohen-Macaulay module over a d-fold branched cover into a d-fold factorization
branchedToMF(Module,Ring) -- Converts a maximal Cohen-Macaulay module over a d-fold branched cover into a d-fold factorization
coimage(ZZdFactorizationMap) -- make the coimage of a map of ZZ/d-graded factorizations
cokernel(ZZdFactorizationMap) -- make the cokernel of a map of ZZ/d-graded factorizations
collapseMF -- Converts a d-fold factorization into a (d-1)-fold factorization by composing the kth differential with the (k+1)th differential
collapseMF(ZZdFactorization,ZZ) -- Converts a d-fold factorization into a (d-1)-fold factorization by composing the kth differential with the (k+1)th differential
Complex ** ZZdFactorization -- tensor product of ZZ/d-graded factorizations
Complex ** ZZdFactorizationMap -- the map of ZZ/d-graded factorizations between tensor factorizations, obtained by first folding the relevant complex map
ComplexMap ** ZZdFactorizationMap -- the map of ZZ/d-graded factorizations between tensor factorizations, obtained by first folding the relevant complex map
components(ZZdFactorization) -- list the components of a direct sum
components(ZZdFactorizationMap) -- list the components of a direct sum
cone(ZZdFactorizationMap) -- make the mapping cone of a morphism of ZZ/d-graded factorizations
degree(ZZdFactorizationMap) -- get the degree of a map of ZZ/d-graded factorizations
differential of a ZZ/d-graded factorization -- get the maps between the terms in a ZZ/d-graded factorization
directSum(ZZdFactorization) -- direct sum of ZZ/d-graded factorizations
directSum(ZZdFactorizationMap) -- direct sum of ZZ/d-graded factorization maps
dual(ZZdFactorization) -- make the dual of a ZZ/d-graded factorization
dual(ZZdFactorization,RingElement) -- make the dual of a ZZ/d-graded factorization
dual(ZZdFactorization,Symbol) -- make the dual of a ZZ/d-graded factorization
dual(ZZdFactorizationMap) -- the dual of a map of ZZ/d-graded factorizations
dual(ZZdFactorizationMap,RingElement) -- the dual of a map of ZZ/d-graded factorizations
dual(ZZdFactorizationMap,Symbol) -- the dual of a map of ZZ/d-graded factorizations
euler(ZZdFactorization) -- Calculates the Euler characteristic of a ZZdFactorization
eulerMF -- Construct a Koszul matrix factorization with respect to the Jacobian ideal
eulerMF(RingElement) -- Construct a Koszul matrix factorization with respect to the Jacobian ideal
Fold -- Convert any complex or complex map into a ZZ/d-graded factorization (or map) for a fixed integer d
Fold(Complex,ZZ) -- Convert any complex or complex map into a ZZ/d-graded factorization (or map) for a fixed integer d
Fold(ComplexMap,ZZ) -- Convert any complex or complex map into a ZZ/d-graded factorization (or map) for a fixed integer d
fullCollapse -- Converts a d-fold factorization into a 2-fold factorization
fullCollapse(ZZdFactorization,ZZ,ZZ) -- Converts a d-fold factorization into a 2-fold factorization
gradedModule(ZZdFactorization) -- a new ZZ/d-graded factorization in which the differential is zero
HH ZZdFactorization -- homology of a ZZ/d-graded factorization
HH ZZdFactorizationMap -- induced map on homology or cohomology
HH^ZZ ZZdFactorizationMap -- induced map on homology or cohomology
HH_ZZ ZZdFactorization -- homology or cohomology module of a ZZ/d-graded factorization
HH_ZZ ZZdFactorizationMap -- induced map on homology or cohomology
HH_ZZ(ZZ,ZZdFactorization) -- homology or cohomology module of a ZZ/d-graded factorization
higherHomotopyFactorization -- Constructs the matrix factorization associated with a system of higher homotopies
higherHomotopyFactorization(List,Complex) -- Constructs the matrix factorization associated with a system of higher homotopies
higherHomotopyFactorization(RingElement,Complex) -- Constructs the matrix factorization associated with a system of higher homotopies
Hom(Complex,ZZdFactorization) -- the ZZ/d-graded homomorphism factorization formed by folding the complex, then taking the ZZ/d-graded Hom factorization
Hom(Complex,ZZdFactorization,RingElement) -- the ZZ/d-graded homomorphism factorization formed by folding the complex, then taking the ZZ/d-graded Hom factorization
Hom(Complex,ZZdFactorization,Symbol) -- the ZZ/d-graded homomorphism factorization formed by folding the complex, then taking the ZZ/d-graded Hom factorization
Hom(ComplexMap,ZZdFactorizationMap) -- the map of factorizations between Hom factorizations formed by first folding the relevant complex map
Hom(ComplexMap,ZZdFactorizationMap,RingElement) -- the map of factorizations between Hom factorizations formed by first folding the relevant complex map
Hom(ComplexMap,ZZdFactorizationMap,Symbol) -- the map of factorizations between Hom factorizations formed by first folding the relevant complex map
Hom(Matrix,ZZdFactorization) -- the map of factorizations between Hom complexes
Hom(Matrix,ZZdFactorizationMap) -- the map of factorizations between Hom complexes
Hom(Module,ZZdFactorization) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(Module,ZZdFactorizationMap) -- the map of factorizations between Hom complexes
Hom(Ring,ZZdFactorization) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(Ring,ZZdFactorizationMap) -- the map of factorizations between Hom complexes
Hom(ZZdFactorization,Complex) -- the ZZ/d-graded homomorphism factorization formed by folding the complex, then taking the ZZ/d-graded Hom factorization
Hom(ZZdFactorization,Complex,RingElement) -- the ZZ/d-graded homomorphism factorization formed by folding the complex, then taking the ZZ/d-graded Hom factorization
Hom(ZZdFactorization,Complex,Symbol) -- the ZZ/d-graded homomorphism factorization formed by folding the complex, then taking the ZZ/d-graded Hom factorization
Hom(ZZdFactorization,Matrix) -- the map of factorizations between Hom complexes
Hom(ZZdFactorization,Matrix,RingElement) -- the map of factorizations between Hom complexes
Hom(ZZdFactorization,Matrix,Symbol) -- the map of factorizations between Hom complexes
Hom(ZZdFactorization,Module) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(ZZdFactorization,Module,RingElement) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(ZZdFactorization,Module,Symbol) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(ZZdFactorization,Ring) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(ZZdFactorization,ZZdFactorization) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(ZZdFactorization,ZZdFactorization,RingElement) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(ZZdFactorization,ZZdFactorization,Symbol) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
Hom(ZZdFactorization,ZZdFactorizationMap) -- the map of factorizations between Hom complexes
Hom(ZZdFactorization,ZZdFactorizationMap,RingElement) -- the map of factorizations between Hom complexes
Hom(ZZdFactorization,ZZdFactorizationMap,Symbol) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,ComplexMap) -- the map of factorizations between Hom factorizations formed by first folding the relevant complex map
Hom(ZZdFactorizationMap,ComplexMap,RingElement) -- the map of factorizations between Hom factorizations formed by first folding the relevant complex map
Hom(ZZdFactorizationMap,ComplexMap,Symbol) -- the map of factorizations between Hom factorizations formed by first folding the relevant complex map
Hom(ZZdFactorizationMap,Matrix) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Matrix,RingElement) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Matrix,Symbol) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Module) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Module,RingElement) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Module,Symbol) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Ring) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Ring,RingElement) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,Ring,Symbol) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,ZZdFactorization) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,ZZdFactorization,RingElement) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,ZZdFactorization,Symbol) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,ZZdFactorizationMap) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,ZZdFactorizationMap,RingElement) -- the map of factorizations between Hom complexes
Hom(ZZdFactorizationMap,ZZdFactorizationMap,Symbol) -- the map of factorizations between Hom complexes
homomorphism'(ZZdFactorizationMap) -- get the element of Hom from a map of factorizations
homomorphism(ZZ,Matrix,ZZdFactorization) -- get the homomorphism from an element of Hom
homomorphism(ZZdFactorizationMap) -- get the homomorphism from an element of Hom
id _ ZZdFactorization -- the identity map of a ZZ/d-graded factorization
image(ZZdFactorizationMap) -- make the image of a map of ZZ/d-graded factorizations
inducedMap(ZZdFactorization,ZZdFactorization) -- make the map of ZZ/d-graded factorizations induced at each term by the identity map
injectiveCover -- Constructs the injective hull of a d-fold matrix factorization
injectiveCover(ZZdFactorization) -- Constructs the injective hull of a d-fold matrix factorization
isCommutative(ZZdFactorizationMap) -- whether a ZZ/d-graded factorization map commutes with the differentials
isdFactorization -- Checks if the differentials of a factorization compose to a scalar multiple of the identity
isdFactorization(ZZdFactorization) -- Checks if the differentials of a factorization compose to a scalar multiple of the identity
isFactorizationMorphism -- whether a ZZdFactorizationMap is a morphism of factorizations
isFactorizationMorphism(ZZdFactorizationMap) -- whether a ZZdFactorizationMap is a morphism of factorizations
isFree -- whether a ZZ/d-graded factorization consists of free modules
isFree(ZZdFactorization) -- whether a ZZ/d-graded factorization consists of free modules
isHomogeneous(ZZdFactorizationMap) -- whether a map of ZZ/d-graded factorizations is homogeneous
isNullHomotopic(ZZdFactorizationMap) -- whether a map of ZZ/d-graded factorizations is null-homotopic
isNullHomotopyOf(ZZdFactorizationMap,ZZdFactorizationMap) -- whether the first map of ZZ/d-graded factorizations is a null homotopy for the second
isQuasiIsomorphism(ZZdFactorizationMap) -- whether a map of ZZ/d-graded factorizations is a quasi-isomorphism
isShortExactSequence(ZZdFactorizationMap,ZZdFactorizationMap) -- whether a pair of ZZ/d-graded factorization maps forms a short exact sequence
isWellDefined(ZZdFactorization) -- whether a ZZ/d-graded factorization is well-defined
isWellDefined(ZZdFactorizationMap) -- whether a map of ZZ/d-graded factorizations is well-defined
isZZdComplex -- Checks if the differentials of a factorization compose to 0
isZZdComplex(ZZdFactorization) -- Checks if the differentials of a factorization compose to 0
kernel(ZZdFactorizationMap) -- make the kernel of a map of ZZ/d-graded factorizations
koszulMF -- Construct a Koszul matrix factorization from an ideal and a polynomial
koszulMF(Ideal,RingElement) -- Construct a Koszul matrix factorization from an ideal and a polynomial
koszulMF(List,RingElement) -- Construct a Koszul matrix factorization from an ideal and a polynomial
koszulMF(RingElement) -- Construct a Koszul matrix factorization from an ideal and a polynomial
linearMF -- Constructs a Koszul d-fold factorization of a homogeneous element of degree d
linearMF(RingElement) -- Constructs a Koszul d-fold factorization of a homogeneous element of degree d
linearMF(RingElement,RingElement) -- Constructs a Koszul d-fold factorization of a homogeneous element of degree d
linearMF(RingElement,Symbol) -- Constructs a Koszul d-fold factorization of a homogeneous element of degree d
Making maps between factorizations -- information about the basic constructors
Making maps between ZZ/d-graded factorizations -- information about the basic constructors
Making ZZdFactorizations -- Information about the basic constructors
map(ZZdFactorization,ZZdFactorization,HashTable) -- make a map of ZZ/d-graded factorizations
map(ZZdFactorization,ZZdFactorization,ZZ) -- make the zero map or identity between ZZ/d-graded factorizations
map(ZZdFactorization,ZZdFactorization,ZZdFactorizationMap) -- make a new map of ZZ/d-graded factorizations from an existing one (for inducing maps)
Matrix ** ZZdFactorization -- create the tensor product of a ZZ/d-graded factorization and a map of modules
MatrixFactorizations -- A package for creating and computing objects in the category of ZZ/d-graded factorizations, such as matrix factorizations
minimalPresentation(ZZdFactorization) -- minimal presentation of all terms in a ZZ/d-graded factorization
minimalPresentation(ZZdFactorizationMap) -- minimal presentation of all terms in a ZZ/d-graded factorization
Module ** ZZdFactorization -- tensor product of ZZ/d-graded factorizations
Module ** ZZdFactorizationMap -- the map of ZZ/d-graded factorizations between tensor factorizations
monomialMF -- Construct a trivial d-fold factorization of a monomial
monomialMF(RingElement) -- Construct a trivial d-fold factorization of a monomial
mooreMF -- Constructs the matrix factorization of the Moore matrix and its adjoint
mooreMF(ZZ) -- Constructs the matrix factorization of the Moore matrix and its adjoint
nullHomotopy(ZZdFactorizationMap) -- a map which is a candidate for being a null homotopy
Number * ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
Number + ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
Number - ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
period -- the period of a ZZ/d-graded factorization or map
period(ZZdFactorization) -- the period of a ZZ/d-graded factorization or map
period(ZZdFactorizationMap) -- the period of a ZZ/d-graded factorization or map
potential -- Outputs the polynomial $f$ such that the dth power of the differentials is equal to $ f \cdot \text{id}$
potential(ZZdFactorization) -- Outputs the polynomial $f$ such that the dth power of the differentials is equal to $ f \cdot \text{id}$
Preprogrammed examples and operations -- Information about the basic constructors
projectiveCover -- Constructs the projective cover of a d-fold matrix factorization
projectiveCover(ZZdFactorization) -- Constructs the projective cover of a d-fold matrix factorization
prune(ZZdFactorization) -- minimal presentation of all terms in a ZZ/d-graded factorization
prune(ZZdFactorizationMap) -- minimal presentation of all terms in a ZZ/d-graded factorization
randomFactorizationMap -- a random map of ZZ/d-graded factorizations
randomFactorizationMap(...,Boundary=>...) -- a random map of ZZ/d-graded factorizations
randomFactorizationMap(...,Cycle=>...) -- a random map of ZZ/d-graded factorizations
randomFactorizationMap(...,Degree=>...) -- a random map of ZZ/d-graded factorizations
randomFactorizationMap(...,InternalDegree=>...) -- a random map of ZZ/d-graded factorizations
randomFactorizationMap(ZZdFactorization,ZZdFactorization) -- a random map of ZZ/d-graded factorizations
randomLinearMF -- Generates a linear d-fold factorization of a random degree d polynomial
randomLinearMF(ZZ,Ring) -- Generates a linear d-fold factorization of a random degree d polynomial
randomLinearMF(ZZ,Ring,RingElement) -- Generates a linear d-fold factorization of a random degree d polynomial
randomLinearMF(ZZ,Ring,Symbol) -- Generates a linear d-fold factorization of a random degree d polynomial
randomTailMF -- Construct a matrix factorization from a high syzygy of a random module over a hypersurface
randomTailMF(RingElement) -- Construct a matrix factorization from a high syzygy of a random module over a hypersurface
randomTailMF(RingElement,ZZ,ZZ) -- Construct a matrix factorization from a high syzygy of a random module over a hypersurface
randomTailMF(RingElement,ZZ,ZZ,ZZ) -- Construct a matrix factorization from a high syzygy of a random module over a hypersurface
Ring ** ZZdFactorization -- tensor a ZZ/d-graded factorization along a ring map
Ring ** ZZdFactorizationMap -- tensor a map of ZZ/d-graded factorizations along a ring map
ring(ZZdFactorization) -- access the ring of a ZZ/d-graded factorization or a factorization map
ring(ZZdFactorizationMap) -- access the ring of a ZZ/d-graded factorization or a factorization map
RingElement * ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
RingElement + ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
RingElement - ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
RingElement == ZZdFactorizationMap -- whether two ZZ/d-graded factorization maps are equal
RingMap ** ZZdFactorization -- tensor a ZZ/d-graded factorization along a ring map
RingMap ** ZZdFactorizationMap -- tensor a map of ZZ/d-graded factorizations along a ring map
RingMap ZZdFactorization -- apply a ring map
RingMap ZZdFactorizationMap -- apply a ring map to a map of ZZ/d-graded factorizations
rk1MCM2gen -- Construct every possible rank 1, 2-generated maximal Cohen-Macaulay module over the cubic Fermat hypersurface in 4 variables
rk1MCM2gen(List) -- Construct every possible rank 1, 2-generated maximal Cohen-Macaulay module over the cubic Fermat hypersurface in 4 variables
rk1MCM2gen(List,ZZ) -- Construct every possible rank 1, 2-generated maximal Cohen-Macaulay module over the cubic Fermat hypersurface in 4 variables
RootOfUnity -- Adjoin a root of unity to the underlying object input
rootOfUnity -- Adjoin a root of unity to the underlying object input
source(ZZdFactorizationMap) -- get the source of a map of ZZ/d-graded factorizations
suspension -- Constructs the suspension of a d-fold factorization
suspension(ZZ,ZZdFactorization) -- Constructs the suspension of a d-fold factorization
suspension(ZZdFactorization) -- Constructs the suspension of a d-fold factorization
suspension(ZZdFactorizationMap) -- Constructs the suspension of a d-fold factorization
Symbol ^ ZZdFactorization -- get the maps between the terms in a ZZ/d-graded factorization
tailMF -- Generate a ZZdFactorization from a module over a hypersurface ring
tailMF(Ideal) -- Generate a ZZdFactorization from a module over a hypersurface ring
tailMF(Module) -- Generate a ZZdFactorization from a module over a hypersurface ring
target(ZZdFactorizationMap) -- get the target of a map of ZZ/d-graded factorizations
tensor(RingMap,ZZdFactorization) -- tensor a ZZ/d-graded factorization along a ring map
tensor(RingMap,ZZdFactorizationMap) -- tensor a map of ZZ/d-graded factorizations along a ring map
tensor(ZZdFactorization,RingMap) -- tensor a ZZ/d-graded factorization along a ring map
tensor(ZZdFactorization,ZZdFactorization) -- tensor product of ZZ/d-graded factorizations
tensor(ZZdFactorizationMap,RingMap) -- tensor a map of ZZ/d-graded factorizations along a ring map
tensor(ZZdFactorizationMap,ZZdFactorizationMap) -- the map of ZZ/d-graded factorizations between tensor factorizations
tensorAssociativity(ZZdFactorization,ZZdFactorization,ZZdFactorization) -- make the canonical isomorphism arising from associativity
tensorCommutativity(ZZdFactorization,ZZdFactorization) -- make the canonical isomorphism arising from commutativity of the tensor product operation
toBranchedCover -- Converts a d-fold matrix factorization into a maximal Cohen-Macaulay module over a d-fold branched cover of the potential
toBranchedCover(ZZdFactorization,RingElement) -- Converts a d-fold matrix factorization into a maximal Cohen-Macaulay module over a d-fold branched cover of the potential
toBranchedCover(ZZdFactorization,Symbol) -- Converts a d-fold matrix factorization into a maximal Cohen-Macaulay module over a d-fold branched cover of the potential
trivialMF -- Constructs the trivial matrix factorization of an element f
trivialMF(Module,RingElement) -- Constructs the trivial matrix factorization of an element f
trivialMF(ZZ,Module,RingElement) -- Constructs the trivial matrix factorization of an element f
trivialMF(ZZ,ZZ,Module,RingElement) -- Constructs the trivial matrix factorization of an element f
trivialMF(ZZ,ZZ,Module,ZZ) -- Constructs the trivial matrix factorization of an element f
unfold -- Converts a factorization into a complex
unfold(ZZdFactorization,List) -- Converts a factorization into a complex
unfold(ZZdFactorization,ZZ) -- Converts a factorization into a complex
unfold(ZZdFactorizationMap,List) -- Converts a factorization into a complex
unfold(ZZdFactorizationMap,ZZ) -- Converts a factorization into a complex
WellDefined (missing documentation)
zeroOutDegrees -- Converts a d-fold matrix factorization into a maximal Cohen-Macaulay module over a d-fold branched cover of the potential
zeroOutDegrees(Ring) -- Converts a d-fold matrix factorization into a maximal Cohen-Macaulay module over a d-fold branched cover of the potential
zeroOutDegrees(ZZdFactorization) -- Converts a d-fold matrix factorization into a maximal Cohen-Macaulay module over a d-fold branched cover of the potential
ZZ == ZZdFactorization -- whether two ZZ/d-graded factorizations are equal
ZZ == ZZdFactorizationMap -- whether two ZZ/d-graded factorization maps are equal
ZZdFactorization -- the class of all ZZ/d-graded factorizations
ZZdfactorization -- make a ZZ/d-graded factorization
ZZdFactorization ** Complex -- tensor product of ZZ/d-graded factorizations
ZZdFactorization ** Matrix -- create the tensor product of a ZZ/d-graded factorization and a map of modules
ZZdFactorization ** Module -- tensor product of ZZ/d-graded factorizations
ZZdFactorization ** Ring -- tensor a ZZ/d-graded factorization along a ring map
ZZdFactorization ** RingMap -- tensor a ZZ/d-graded factorization along a ring map
ZZdFactorization ** ZZdFactorization -- tensor product of ZZ/d-graded factorizations
ZZdFactorization ** ZZdFactorizationMap -- the map of ZZ/d-graded factorizations between tensor factorizations
ZZdFactorization ++ ZZdFactorization -- direct sum of ZZ/d-graded factorizations
ZZdFactorization == ZZ -- whether two ZZ/d-graded factorizations are equal
ZZdFactorization == ZZdFactorization -- whether two ZZ/d-graded factorizations are equal
ZZdFactorization ^ Array -- the canonical inclusion or projection map of a direct sum
ZZdFactorization ^ ZZ -- access individual object in a ZZ/d-graded factorization
ZZdFactorization _ Array -- the canonical inclusion or projection map of a direct sum
ZZdFactorization _ ZZ -- access individual object in a ZZ/d-graded factorization
ZZdFactorization Array -- shift a ZZ/d-graded factorization or map of ZZ/d-graded factorizations
ZZdfactorization(HashTable) -- make a ZZ/d-graded factorization
ZZdfactorization(Ideal,ZZ) -- convert a module/ring/ideal into a ZZ/d-graded factorization for specified period d
ZZdfactorization(List) -- make a ZZ/d-graded factorization
ZZdfactorization(Module,ZZ) -- convert a module/ring/ideal into a ZZ/d-graded factorization for specified period d
ZZdfactorization(Ring,ZZ) -- convert a module/ring/ideal into a ZZ/d-graded factorization for specified period d
ZZdfactorization(ZZdFactorization) -- make a ZZ/d-graded factorization with shifted base; used for permuting the modules without adding signs
ZZdFactorizationMap -- the class of all maps between ZZ/d-graded factorizations
ZZdFactorizationMap * Number -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap * RingElement -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap * ZZdFactorizationMap -- composition of homomorphisms of ZZ/d-graded factorizations
ZZdFactorizationMap ** Complex -- the map of ZZ/d-graded factorizations between tensor factorizations, obtained by first folding the relevant complex map
ZZdFactorizationMap ** ComplexMap -- the map of ZZ/d-graded factorizations between tensor factorizations, obtained by first folding the relevant complex map
ZZdFactorizationMap ** Module -- the map of ZZ/d-graded factorizations between tensor factorizations
ZZdFactorizationMap ** Ring -- tensor a map of ZZ/d-graded factorizations along a ring map
ZZdFactorizationMap ** RingMap -- tensor a map of ZZ/d-graded factorizations along a ring map
ZZdFactorizationMap ** ZZdFactorization -- the map of ZZ/d-graded factorizations between tensor factorizations
ZZdFactorizationMap ** ZZdFactorizationMap -- the map of ZZ/d-graded factorizations between tensor factorizations
ZZdFactorizationMap + Number -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap + RingElement -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap + ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap ++ ZZdFactorizationMap -- direct sum of ZZ/d-graded factorization maps
ZZdFactorizationMap - Number -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap - RingElement -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap - ZZdFactorizationMap -- perform arithmetic operations on ZZ/d-graded factorization maps
ZZdFactorizationMap == RingElement -- whether two ZZ/d-graded factorization maps are equal
ZZdFactorizationMap == ZZ -- whether two ZZ/d-graded factorization maps are equal
ZZdFactorizationMap == ZZdFactorizationMap -- whether two ZZ/d-graded factorization maps are equal
ZZdFactorizationMap ^ Array -- the composition with the canonical inclusion or projection map
ZZdFactorizationMap ^ ZZ -- the n-fold composition
ZZdFactorizationMap _ Array -- the composition with the canonical inclusion or projection map
ZZdFactorizationMap _ ZZ -- access individual matrices in a ZZ/d-graded factorization map
ZZdFactorizationMap | ZZdFactorizationMap -- join or concatenate maps horizontally
ZZdFactorizationMap || ZZdFactorizationMap -- join or concatenate maps vertically
ZZdFactorizationMap Array -- shift a ZZ/d-graded factorization or map of ZZ/d-graded factorizations