Efficient Alternative Method for Computing Multivariate Resultant Formulation

In elimination theory, the matrix method of computing the resultant remains the most popular method due to its lower computational complexity compared to Groebner-based and set characteristics approaches. However, for the matrix method to be effective, the size and nature of the elements of the matrix play an important role. If the resultant is not an exact resultant it has to be extracted from the determinant of the corresponding resultant matrix. In this paper, a new resultant matrix is proposed. The hybrid construction consists of four blocks, one of which uses an entry formula for computing a Dixon matrix, while two of the blocks use a mapping from Jouanolou's method, and the final block consists of zero elements only. The new formulation is computed without intermediate cancelling terms, which reduces the complexity of the construction and enhances its effectiveness.