I'm interested in coding up a small project that solves uni-variate algebraic equations (up to cubic) by simulating the actions of a human expert in solving the equation. To do this, I've drafted a set of production rules (if/then rules applied to an equation when certain conditions hold). However, I'd like to compare my rule set to perhaps other production systems in the same domain. I've been told that algebra problems are often used as the problem domain in research papers on intelligent tutors. So far I've found this paper, which is a bit dated, and only includes production rules for linear equations (on page 4). I know that more recently (in the 90s) Koedinger at CMU did some work on an intelligent tutoring system called PAT which seems related to what I'm doing; however, I haven't been able to find anything about the specific rule set used by PAT.
So the question is, does anyone know of any research papers that include a list of production rules to solve algebraic equations?