Integer and polynomial GCD calculations: useful properties, Euclidean techniques,Resultants and the Sylvester matrix, non-Euclidean modular GCD by large/many small primes.

An algorithm for determining a Gröbner basis for a collection of polynomials.

A Gröbner basis for a system of polynomials preserves the common roots whilst being simpler relative to an ordering.

Discussion of canonical forms for polynomials- single variable dense and sparse representations; orderings for multivariate polynomials.