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A polynomial approach for the calculation of the reflectance, the transmittance, and the ellipsometric parameters of a stratified isotropic planar structure is presented. We show that these parameters can be written in a very simple and compact form using the so-called elementary symmetric functions that are extensively used in the mathematical theory of polynomials. This approach is applied to quarter-wave Bragg reflectors. The numerical results reveal an exact match with the well known matrix formalism.