1946	 Computing Polynomial Resultants Bezout s Determinant vs. Collins Reduced P.R.S. Algorithm	 Algorithms for computing the resultant of two polynomials in several variables a key repetitive step of computation in solving systems of polynomial equations by elimination are studied. Determining the best algorithm for computer implementation depends upon the extent to which extraneous factors are introduced the extent of propagation of errors caused by truncation of real coefficients memory requirements and computing speed. Preliminary considerations narrow the choice of the best algorithm to Bezout s determinant and Collins reduced polynomial remainder sequence p.r.s. algorithm. Detailed tests performed on sample problems conclusively show that Bezout s determinant is superior in all respects except for univariate polynomials in which case Collins reduced p.r.s. algorithm is somewhat faster. In particular Bezout s determinant proves to be strikingly superior in numerical accuracy displaying excellent stability with regard to round-off errors. Results of tests are reported in detail. resultant algorithm g.c.d. algorithm polynomial resultant elimination Bezout s determinant Sylvester s determinant reduced p.r.s. algorithm Euclidean algorithm multivariate polynomial equations
