It seems that implementation of polynomials in sympy and symengine could be closely parallel.
There should be three kinds of polynomials: (standard) polynomials, Laurent polynomials, and Puiseux polynomials, thus adding a "fourth dimension" to the classification in the wiki (https://github.com/sympy/symengine/wiki/En-route-to-Polynomial). They can also be used for representing (truncated) series of respective types.