For almost 20 years the CoCoA project has been conducting research into computational commutative algebra, developing new algorithms and offering implementations in the interactive program "CoCoA." Recently we took the decision to rebuild the software from scratch with the specific aim of making excellent implementations available to all researchers. The implementations will be accessible in three distinct ways: as a standalone interactive system, as a networked service (via an OpenMath-like communications channel), as a C++ library, called CoCoALib (free and open in the sense of the GPL). CoCoALib, being the core of the project, is also its most evolved part, and is the part that we shall look at most closely.