Computational algorithms for algebraic operations on multidimensional polynomials

Abstract

Algebraic operations on m-D (m-dimensional) polynomials (m≥ 2) are considered. In particular the addition, multiplication and division of such polynomials are described by means of algorithms in appropriate computational form. The special case of division of a multidimensional polynomial by a polynomial of lower order in each variable is examined, and, apart from the corresponding algorithm, necessary and sufficient conditions for the existence of the quotient and a remainder polynomial of lower order than the divisor are introduced. These conditions can be formulated by inspection of the coefficients of the dividend and divisor polynomials.