Tries for Polynomials

A deep dive into representing multivariate polynomials as tries in Haskell. Starting from McIlroy's power series paper, the post builds up from list-based polynomials to a trie-based representation that naturally encodes Horner's rule for efficient evaluation. It covers multivariate extensions, lens-based division, monomial orderings (grlex, grevlex), breadth-first monomial enumeration, and efficient leading-monomial extraction using priority search queues (OrdPSQ). The post also touches on noncommutative Gröbner bases via Buchberger's algorithm and discusses the tradeoffs of the trie representation for computer algebra.