A poly algorithm for computing resultants - Bartolome, Jose Ronello Tamayo (2003)
It is well known that resultant computations are very important in computer algebra systems because of their contribution as essential tools to many applications. The resultant of two polynomials is a form in the coefficients of the same polynomials whose vanishing is a necessary and sufficient condition for these two polynomials to have common zeros. Several methods exist for computing the resultant of two multivariate polynomials with integer coefficients which includes Bezout's method and Collins' modular method. However, no method exists for automatically choosing which resultant algorithm would give the best performance with respect to actual computing time. This study describes a polyalgorithm for computing the resultant of two multivariate polynomials, that chooses the better method given a specified pair of polynomial inputs by inspecting the properties of the polynomials. These properties are the degree, the number of variables, the integer coefficient lenghts, and the sparsity. Results revealed that the polyalgorithm is consistent enough in choosing the faster method.