4.12 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
is the basering, and
is a submodule of
generated by vectors
, then
may be considered as the generators of relations of
between the
canonical generators gen(1) ,...,gen(n) . Hence any finitely
generated
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
k for
, i.e., the
columns of A are the vectors
which generate M (cf.
Representation of mathematical objects).
