Towards computing in the derived category

freeResolution(Complex) -- minimal free resolution of a complex
resolutionMap(Complex) -- map from a free resolution to the given complex
isShortExactSequence(ComplexMap,ComplexMap) -- whether a pair of complex maps forms a short exact sequence
isQuasiIsomorphism(ComplexMap) -- whether a map of complexes is a quasi-isomorphism
liftMapAlongQuasiIsomorphism(ComplexMap,ComplexMap) -- lift a map of chain complexes along a quasi-isomorphism
connectingMap(ComplexMap,ComplexMap) -- construct the connecting homomorphism on homology
longExactSequence(ComplexMap,ComplexMap) -- make the long exact sequence in homology
horseshoeResolution(Complex) -- make the horseshoe resolution

See also