Results, Remarks, Conclusions
It is astonishing simple to implement complex mathematical structures in an object oriented environment "from scratch".
You are invited to experiment, contribute, or share experiences. The package com.perisic.ring is available and documented at http://ring.perisic.com.
Caveat: There are drawbacks: performance, decisions on how to organise classes, implementing specialised algorithms (primality testing, factoring, …)