Singular Manual: module

> | ## 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).
> 4.14.1 module declarations |  |
> 4.14.2 module expressions |  |
> 4.14.3 module operations |  |
> 4.14.4 module related functions |  |

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