Singular Manual: module (plural)

> | ### 7.2.3 module (plural) Modules are left submodules of a free module over the basering with basis `gen(1)`, `gen(2)`, ..., `gen(n)` for some natural number `n`. They are represented by lists of vectors, which generate the left submodule. Like vectors, they can only be defined or accessed with respect to a basering. If is a left submodule of (where is the basering) generated by vectors , then these generators 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 PLURAL by its module of relations. This is the so-called Coker-representation. The assignments `module M=v1,...,vk; matrix A=M;` create the presentation matrix of size ,with the columns of A being the vectors which generate .
> 7.2.3.1 module declarations (plural) |  |
> 7.2.3.2 module expressions (plural) |  |
> 7.2.3.3 module operations (plural) |  |
> 7.2.3.4 module related functions (plural) |  |

User manual for Singular version 4-1-1p4, 2018, generated by texi2html.