Symbolic computations in the lattice space $\mathbb{R}_{c}^{n}$

The methods of cubic structure coding for an $n$-cube and a cubic $n$-neighborhood in the lattice space $\mathbb{R}_{c}^{n}$ are developed in a more general context of the language formalism. The choice of an alphabet and its relation to the above problems on cubic structures for a cubic $n$-neighborhood of radius $r$ ($r$ is integer) are considered with the aim of computer constructing of cubic structures and manifolds with prescribed properties. The mapping of subsets of the set $\mathbb{Z}$ onto the finite Hausdorff metric spaces whose points are all $k$-dimensional faces of an $n$-cube is analyzed. The efficiency of symbolic computations is discussed in the context of computer implementation. This work was supported by the Russian Foundation for Basic Research (project no. 09-07-12135-ofi_m).