Using of a table method of simplification of polynomial equation systems

Abstract

The solution of polynomial equation systems is a problem frequently encountered by researchers in solving equations in specific derivatives, algebraic geometry and in optimization tasks. There exist various realizations of the Gröbner basis building method, but their serious disadvantage is the high complexity of calculations. Therefore, the algorithms currently employed for symbol-aided solutions are effective only for lower order polynomial equations systems. The article offers a method based on tables individually corresponding to a polynomial which makes it possible to forgo the solution of the problem of dividing the matrix into parts in distributing the calculations on the systems enabling the parallel execution of the program. The tables corresponding to individual polynomials of the initial system or the basis can be distributed among the processors without decomposition.