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Considering a multivariate polynomial ideal over a given field as a vector space, we investigate for such an ideal a particular linear basis, a so-called staggered linear basis, which contains a GrÃ¶bner basis as well. In this paper, we present a simple and efficient algorithm to compute a staggered linear basis. The new framework is equipped with some novel criteria (including both Buchberger's criteria) to detect superfluous reductions. The proposed algorithm has been implemented in Maple, and we provide an illustrative example to show how it works. Finally, the efficiency of this algorithm compared to the existing methods is discussed via a set of benchmark polynomials.
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