The algorithm for completing the standard table

摘要

The present article describes the computational scheme for numerical solving practical and theoretical problems. This scheme realizes the algorithm for completing the standard table (from top to bottom and from left to right). Among the computation features of this scheme are computer memory saving, the possibility to estimate the number of executed operations, parallelization of computations. The calculating formulae used in the scheme are given and the work of the algorithm for completing the standard table is illustrated with three numerical examples. The first example describes the simplest case when every coefficient of the group equation induces the whole finite group. The second example describes the general case. There could be some group elements among the coefficients of the group equation, which order is smaller than the finite group one. The third example shows that not all the points defining the hyperplane are the vertices of the polytope of the group equation. Note that in the applications the coefficients of the inequation, which defines the face of the polytope, are calculated with the filling of the standard table (this inequation is called the cut or the valid inequation in discrete optimization).