Groebner Bases for Everyone with CoCoA-5 and CoCoALib

We present a survey on the developments related to GBases, and show explicit examples in cocoa. The CoCoA project dates back to 1987: its aim was to create a ``mathematician''-friendly computational laboratory for studying Commutative Algebra, most especially Gr"obner bases. Always maintaining this ``friendly'' tradition, the project has grown and evolved, and the software has been completely rewritten. cocoa offers Gr"obner bases for all levels of interest: from the basic, explicit call in the interactive system CoCoA-5, to problem-specific optimized implementations, to the computer--computer communication with the open source C++ software library, CoCoALib, or the prototype OpenMath-based server. The openness and clean design of CoCoALib and CoCoA-5 are intended to offer different levels of usage, and to encourage external contributions.