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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 well-known. 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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