Efficient Alternative Method for Computing Multivariate Resultant Formation

Surajo Sulaiman (Department of Mathematics, Faculty of Science, Northwest University Kano 700221, Kano)
Noraini Aris (Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor,)
Shamsatun Nahar Ahmad (Department of Computer and Mathematical Sciences, Universiti Teknologi Mara Segamat, Jalan Universiti Off Km. 12 Jalan Muar, 85000 Segamat, Johor Darul Ta'zim)

Journal of Mathematical and Fundamental Sciences
Vol. 51 No. 1 (2019)

In elimination theory, the matrix method of computing resultant remains the most popular due to its less computational complexity compared to Groebner basis and set characteristics approaches. However, for a matrix method to be effective, the size and the nature of elements of the matrix play an important role, since 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 proposed construction consists of four blocks, one of the blocks uses an entry formula of computing a Dixon matrix, while, two of the blocks use a mapping from the Jouanolou's method and the last block consists of only zero elements. The new formulation is computed without intermediate cancelling terms which reduces the complexity of the construction and enhances its effectiveness.