A Variant of Gerdts Algorithm for Computing Involutive Bases
In, the fist author presented an efficient algorithm for computing involutive (and reduced Gr̈obner) bases. In this paper, we consider a modiﬁcation of the 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 and implemented in Maple too. In doing so, we have taken care to provide uniform implementation details for the both algorithms.