Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering

We present an efficient algorithm for the transformation of a Gröbner basis of a zero-dimensional ideal with respect to any given ordering into a Gröbner basis with respect to any other ordering. This algorithm is polynomial in the degree of the ideal. In particular the lexicographical Gröbner basis can be obtained by applying this algorithm after a total degree Gröbner basis computation: it is usually much faster to compute the basis this way than with a direct application of Buchbergerʹs algorithm.