Volume 18, Number 2, Summer 2010
RESULTANTS FOR SYSTEMS OF
MULTIVARIATE POLYNOMIALS
CHRISTOPHER S. WITHERS AND SARALEES NADARAJAH
Abstract. The relation between the coefficients of n + 1
polynomials equations in n variables can be expressed as R =
det M = 0, where the elements of M are the coefficients of the
polynomials and zeros. We call R the resultant of the system.
The form for M when n = 1 is wellknown. Here, we
illustrate with a number of examples with n ≤ 4 how R may be
found. It is useful for solving a systems of n + 1 polynomials in
n + 1 unknowns and for developing an eigen theory for nonlinear
systems.
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