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On the separability of multivariable polynomials

A simple test for the separability of multivariable (MV) polynomials which occur in the study of MV networks and multi-dimensional digital filters, etc., is presented. The separability condition is given in terms of the coefficients of the MV polynomials and expressing the given polynomial, if separable, as a product of single-variable polynomials is a direct consequence of the test for separability.