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Implement mapping symmetric polynomial to Laurent polynomial

How can you implement transforming a symmetric polynomial into a Laurent polynomial by mapping some variables to the inverses of others? In other words, given, say, a polynomial in $x_0,y_0,x_1,y_1$, how can we output this polynomial under the map sending $y_i$ to $x_i^{-1}$? I'm specifically looking to apply this to Hall-Littlewood polynomials if that helps.