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Bareiss'algorithm computes the determinant of a matrix. It eliminates in an optimal way the coordinates of its column vectors by fraction-free triangularisation. The subresultant algorithm also calculates the resultant and the greatest common divisor of two polynomials by eliminating optimally their coefficients. In this article, we relate these two algorithms in a single mathematical concept. Intrinsic aspects of this relation are emphasized, thus most of the calculations is avoided as they are long and complicated. Finally, we give a variation of the subresultant algorithm which makes the computation of the chain of the subresultant polynomials more economical (see section 6.2 page 23).

Algorithme de Bareiss, algorithme des sous-résultants