Computing Polynomial Resultants: Bezout's Determinant vs. Collins' Reduced P. 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. CACM January, 1969 Ku, S. Y. Adler, R. J. 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 4.40 5.10 5.15 5.41 CA690103 JB February 20, 1978 12:10 PM 1024 4 1946 1051 4 1946 1098 4 1946 1214 4 1946 1380 4 1946 1388 4 1946 1393 4 1946 1396 4 1946 1396 4 1946 1485 4 1946 1487 4 1946 1549 4 1946 1570 4 1946 1878 4 1946 1931 4 1946 1946 4 1946 1946 4 1946 1946 4 1946 1946 4 1946 1946 4 1946 1946 4 1946 1946 4 1946 1946 4 1946 1957 4 1946 2167 4 1946 2168 4 1946 2723 4 1946 2857 4 1946 2857 4 1946 3112 4 1946 902 5 1946 1093 5 1946 1177 5 1946 1393 5 1946 1387 5 1946 1946 5 1946 1946 5 1946 1946 5 1946 360 5 1946 731 5 1946 878 5 1946