Preprogrammed examples and operations -- Information about the basic constructors

Basic constructors

• ZZdfactorization(HashTable) -- make a ZZ/d-graded factorization
• ZZdfactorization(List) -- make a ZZ/d-graded factorization
• isWellDefined(ZZdFactorization) -- whether a ZZ/d-graded factorization is well-defined
• isdFactorization(ZZdFactorization) -- Checks if the differentials of a factorization compose to a scalar multiple of the identity

Important constructors for creating ZZ/d-graded factorizations

• koszulMF(List,RingElement) -- Construct a Koszul matrix factorization from an ideal and a polynomial
• linearMF(RingElement) -- Constructs a Koszul d-fold factorization of a homogeneous element of degree d
• randomLinearMF(ZZ,Ring) -- Generates a linear d-fold factorization of a random degree d polynomial
• tailMF(Module) -- Generate a ZZdFactorization from a module over a hypersurface ring
• randomTailMF(RingElement) -- Construct a matrix factorization from a high syzygy of a random module over a hypersurface
• gradedModule(ZZdFactorization) -- a new ZZ/d-graded factorization in which the differential is zero
• HH ZZdFactorization -- homology of a ZZ/d-graded factorization

More advanced constructors

• ZZdFactorization ++ ZZdFactorization -- direct sum of ZZ/d-graded factorizations
• ZZdFactorization ** ZZdFactorization -- tensor product of ZZ/d-graded factorizations
• Hom(ZZdFactorization,ZZdFactorization) -- the ZZ/d-graded homomorphism factorization between two ZZ/d-graded factorizations
• dual(ZZdFactorization) -- make the dual of a ZZ/d-graded factorization
• RingMap ZZdFactorization -- apply a ring map
• RingMap ** ZZdFactorization -- tensor a ZZ/d-graded factorization along a ring map
• minimalPresentation(ZZdFactorization) -- minimal presentation of all terms in a ZZ/d-graded factorization

Extracting ZZ/d-graded factorization from ZZ/d-graded factorization maps

• source(ZZdFactorizationMap) -- get the source of a map of ZZ/d-graded factorizations
• target(ZZdFactorizationMap) -- get the target of a map of ZZ/d-graded factorizations
• kernel(ZZdFactorizationMap) -- make the kernel of a map of ZZ/d-graded factorizations
• cokernel(ZZdFactorizationMap) -- make the cokernel of a map of ZZ/d-graded factorizations
• image(ZZdFactorizationMap) -- make the image of a map of ZZ/d-graded factorizations
• coimage(ZZdFactorizationMap) -- make the coimage of a map of ZZ/d-graded factorizations
• cone(ZZdFactorizationMap) -- make the mapping cone of a morphism of ZZ/d-graded factorizations