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2.3 module

Modules are left submodules of a free module over the basering with basis gen(1), gen(2), ... . They are represented by lists of vectors (vector data type is the same as in SINGULAR) which generate the submodule. Like vectors they can only be defined or accessed with respect to a basering.

If $M$ is a submodule of $R^n$( $R$ is the basering) 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 PLURAL 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.

2.3.1 module declarations  
2.3.2 module expressions  
2.3.3 module operations  
2.3.4 module related functions  


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            User manual for Singular version 2-1-99, August 2004, generated by texi2html.