4.14 module
Modules are submodules of a free module over the basering with basis
gen(1) , gen(2) , ... .
They are represented by lists of vectors which generate the submodule.
Like vectors they
can only be defined or accessed with respect to a basering.
If
53#53 is the basering, and
13#13 is a submodule of
90#90
generated by vectors
91#91, then
91#91
may be considered as the generators of relations of
92#92 between the
canonical generators gen(1) ,...,gen(n) . Hence any finitely
generated
53#53-module can be represented in SINGULAR by its module
of relations. The assignments module M=v1,...,vk; matrix A=M; create
the presentation matrix of size n
93#93k for
92#92, i.e., the
columns of A are the vectors
91#91 which generate M (cf.
Representation of mathematical objects).
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