What question did this study set out to answer?

The research aims to develop a method for calculating the resultants of multivariate polynomials with integer coefficients efficiently.

October 1, 1971Journal of the ACM241 citationsOpen Access

The Calculation of Multivariate Polynomial Resultants

GCGeorge E. Collins

Key Points

The research aims to develop a method for calculating the resultants of multivariate polynomials with integer coefficients efficiently.
Utilized modular homomorphisms alongside the Chinese remainder theorem.
Applied evaluation homomorphisms and interpolation techniques.
Reduced multivariate problems to univariate polynomial resultant calculations over GF(p).
Successfully demonstrated an efficient algorithm for resultant calculation.

Abstract

An efficient algorithm is presented for the exact calculation of resultants of multivariate polynomials with integer coefficients. The algorithm applies modular homomorphisms and the Chinese remainder theorem, evaluation homomorphisms and interpolation, in reducing the problem to resultant calculation for univariate polynomials over GF(p), whereupon a polynomial remainder sequence algorithm is used.

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