CoCoA-4.7.5

First released in 1988, CoCoA is a freely available special-purpose system for doing Computations in Commutative Algebra. It belongs to an elite group of highly specialized systems (like "Macaulay2" and "Singular") having as their main forte the capability to calculate Groebner bases. This means that CoCoA is optimized for working with multivariate polynomials, their ideals and modules, and operations on these objects. Other special strengths of CoCoA include polynomial factorization, exact linear algebra, Hilbert functions, zero-dimensional schemes, and toric ideals. About 10 years ago, a new initiative began: namely, to rebuild the whole software in C++ without the inherent limitations of the original. The new software comprises three main components: a C++ library (CoCoALib), an algebra computation server (CoCoAServer), and an interactive system (CoCoA-5). Of these components CoCoALib is the heart; it embodies all the ``mathematical knowledge'' and it is the most evolved part. All the new code is free and open source software (released under GPL). CoCoA-4.7.5, the last release of the "4" series, in addition to it C kernel functionalities, offers a preview of the CoCoA-5 future capabilities through the communication with the CoCoAServer. It includes contributions by foreign researchers for computing Mayer-Vietoris trees (Eduardo Saenz de Cabezon, Spain) and with monomial ideals (Bjarke Roune, Denmark)