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# Basic invariants and properties -- information about accessing basic features

## Predicates for factorizations and factorization maps

- isWellDefined(ZZdFactorization) -- whether a ZZ/d-graded factorization is well-defined
- isFree(ZZdFactorization) -- whether a ZZ/d-graded factorization consists of free modules
- isWellDefined(ZZdFactorizationMap) -- whether a map of ZZ/d-graded factorizations is well-defined
- isCommutative(ZZdFactorizationMap) -- whether a ZZ/d-graded factorization map commutes with the differentials
- 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

## Other invariants for ZZdFactorizations

- ring(ZZdFactorization) -- access the ring of a ZZ/d-graded factorization or a factorization map
- period(ZZdFactorization) -- the period of a ZZ/d-graded factorization or map
- components(ZZdFactorization) -- list the components of a direct sum

## Other invariants for 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
- degree(ZZdFactorizationMap) -- get the degree of a map of ZZ/d-graded factorizations
- ring(ZZdFactorizationMap) -- access the ring of a ZZ/d-graded factorization or a factorization map
- components(ZZdFactorizationMap) -- list the components of a direct sum

## See also

- Making ZZdFactorizations -- Information about the basic constructors
- Making maps between factorizations -- information about the basic constructors
- Preprogrammed examples and operations -- Information about the basic constructors

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MatrixFactorizations/MatrixFactorizationsDOC.m2:219:0.