CoCoA » CoCoALib

To create a module hom from M1 to M2 we must specify where each generator of M1 maps to. These could be specified as a list of ModuleElem or as a matrix.

We must also check the self-consistency of the proposed map: I think it is enough to verify that each syzygy of the given gens of M1 maps to zero in M2.

Actually applying the map seems to require representing the element to be mapped as a linear combination of the generators -- this could be expensive, no?

Note that some homs may not be induced by a hom from a containing FreeModule. Consider the submodule generated by (x,0) which maps this generator into (1,0) -- in some sense the hom "divides by x".