Basic invariants and properties -- information about accessing basic features

Predicates for complexes and complex maps

• isWellDefined(Complex) -- whether a complex is well-defined
• isExact(Complex) -- whether a complex is exact
• isHomogeneous(Complex) -- whether a complex is homogeneous
• isFree(Complex) -- whether a complex consists of free modules
• isShortExactSequence(Complex) -- whether a chain complex is a short exact sequence
• isWellDefined(ComplexMap) -- whether a map of chain complexes is well-defined
• isCommutative(ComplexMap) -- whether a complex map commutes with the differentials
• isComplexMorphism(ComplexMap) -- whether a complex map is a morphism of complexes
• isQuasiIsomorphism(ComplexMap) -- whether a map of complexes is a quasi-isomorphism
• isShortExactSequence(ComplexMap,ComplexMap) -- whether a pair of complex maps forms a short exact sequence
• isNullHomotopic(ComplexMap) -- whether a map of complexes is null-homotopic
• isNullHomotopyOf(ComplexMap,ComplexMap) -- whether the first map of chain complexes is a null homotopy for the second

Other invariants for complexes

• ring(Complex) -- access the ring of a complex or a complex map
• concentration(Complex) -- indices on which a complex may be non-zero
• max(Complex) -- indices on which a complex may be non-zero
• min(Complex) -- indices on which a complex may be non-zero
• length(Complex) -- length of a complex
• regularity(Complex) -- compute the Castelnuovo-Mumford regularity
• betti(Complex) -- display of degrees in a complex
• poincare(Complex) -- assemble degrees of a chain complex into a polynomial
• poincareN(Complex) -- assemble degrees of a chain complex into a polynomial
• components(Complex) -- list the components of a direct sum

Other invariants for complex maps

• source(ComplexMap) -- get the source of a map of chain complexes
• target(ComplexMap) -- get the target of a map of chain complexes
• degree(ComplexMap) -- get the degree of a map of chain complexes
• ring(ComplexMap) -- access the ring of a complex or a complex map
• concentration(ComplexMap) -- indices on which a complex map may be non-zero
• isHomogeneous(ComplexMap) -- whether a map of complexes is homogeneous
• components(ComplexMap) -- list the components of a direct sum