In this paper, we present an algorithm for construction of minimal involutive polynomial bases which are Gröbner bases of the special form. The most general involutive algorithms are based on the concept of involutive monomial division which leads to partition of variables into multiplicative...

In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a monomial set. Such a division provides for each monomial...

In the neighbourhood of irregular singularities the formal power series solutions of complex analytic ordinary differential equations are generally divergent. The resummation theory developed by J. Ecalle and J.P. Ramis enables us to sum these series by multisummation effective algorithms. In...

An involution approach to solving systems of polynomial equations is proposed. A notion of involutive polynomial system is introduced and an algorithm for its construction is presented. The relation between involutive systems and Gröbner bases is clarified, and some advantages of the involution...