Computing the Elementary Symmetric Polynomials of the Multiplier Spectra of z^2 + c
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This project investigates a family of polynomials that occur in the field of arithmetic dynamics. These polynomials correspond to quadratic rational maps and are difficult to compute in general. We focused on the subfamily of maps z² + c. Our goal was to create and implement an algorithm to compute the corresponding polynomials and to use the resulting data to hypothesize about patterns in their general forms.