This paper provides some technical results on the reduction of polynomials to canonical forms. The main new concept introduced is the D-base, which Pan claims is the first type of base that is defined by a reduction over an arbitrary polynomial ideal domain. Pan gives an algorithm for D-base construction as well as a necessary and sufficient condition for testing for D-bases.

In general D-bases do not possess unique irreducible elements. The paper defines B-bases, a different form of base which does not have this limitation, and B-reductions. B-bases and B-reductions are generalizations of Gröbner bases and their reductions, which are well known in symbolic mathematical computing for their ability to support computations on multivariate polynomials. The author shows that an entity G is a B-basis if and only if G is a D-basis, and that G is a G-reduced basis if and only if G is a D-reduced B-basis.

Pan makes some conjectures (such as that D-base coincide with B-bases in a polynomial ring over a principal ideal domain, and that B-reduced bases exist and coincide with D-reduced bases for each ideal in the same ring) which could increase the interest of D-bases for specialists in symbolic computing if they were proved true.