Groebner Bases for Everyone with CoCoA-5 and CoCoALib

TL;DR

This paper surveys the developments in Groebner bases and demonstrates their implementation in CoCoA, a user-friendly computational algebra system designed for studying commutative algebra and Groebner bases.

Contribution

It provides an overview of CoCoA's evolution, highlighting its flexible design and the integration of Groebner bases functionalities across various levels of use.

Findings

CoCoA offers comprehensive Groebner bases tools for all user levels.

The software has been completely rewritten for improved performance and usability.

Open source CoCoALib enables external contributions and advanced implementations.

Abstract

We present a survey on the developments related to Groebner bases, 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 Groebner bases. Always maintaining this "friendly" tradition, the project has grown and evolved, and the software has been completely rewritten. CoCoA offers Groebner 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.