A Variant of Gerdt's Algorithm for Computing Involutive Bases

Abstract

In [Ger05], the first author presented an efficient algorithm for computing involutive (and reduced Gröbner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove correctness and termination of the modified algorithm and also correctness of the used criteria. The proposed algorithm has been implemented in Maple. We present experimental comparison, via some examples, of performance of the modified algorithm with its original form described in [Ger05] and has been implemented in Maple too. In doing so, we have taken care to provide uniform implementation details for the both algorithms.