C == D
C == 0
Two complexes are equal if the corresponding objects and corresponding maps at each index are equal.
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Both the maps and the objects must be equal.
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A complex is equal to zero if all the objects and maps are zero. This could require computation to determine if something that is superficially not zero is in fact zero.
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Testing for equality is not the same testing for isomorphism. In particular, different presentations of a complex need not be equal.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Complexes/ChainComplexDoc.m2:805:0.