Home Online Manual
Back: matrix related functions
Forward: module declarations
FastBack: matrix
FastForward: number
Up: Data types
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

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 $R$ is the basering, and $M$ is a submodule of $R^n$

generated by vectors $v_1, \ldots, v_k$, then $v_1, \ldots, v_k$

may be considered as the generators of relations of $R^n/M$ between the canonical generators gen(1),...,gen(n). Hence any finitely generated $R$-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 $\times$k for $R^n/M$, i.e., the columns of A are the vectors $v_1, \ldots, v_k$ which generate M (cf. Representation of mathematical objects).

4.12.1 module declarations  
4.12.2 module expressions  
4.12.3 module operations  
4.12.4 module related functions