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4.10 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 a submodule of
,
the basering, 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
R
/M,
i.e., the columns of A are the vectors
which generate M (cf. Representation of mathematical objects).
4.10.1 module declarations 4.10.2 module expressions 4.10.3 module operations 4.10.4 module related functions