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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 M is a submodule of Rn,

R

the basering, generated by vectors v1,,vk, then v1,,vk may be considered as the generators of relations of Rn∕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×k for Rn/M, i.e., the columns of A are the vectors v1,,vk which generate M (cf. Representation of mathematical objects).


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            User manual for Singular version 2-0-4, October 2002, generated by texinfo.