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CoCoA.4 Logo.png
Initial release 1987; 31 years ago (1987)
Stable release
5.2.4 / 9 August 2018; 2 months ago (2018-08-09)[1]
Preview release
5.2.6 / October 2018; 0 months ago (2018-10)
Written in C++
Type Computer algebra system
License GNU GPL
Initial release 27 April 2007; 11 years ago (2007-04-27)
Stable release
0.99600 / 9 August 2018; 2 months ago (2018-08-09)
Preview release
0.99610 / October 2018; 0 months ago (2018-10)
Written in C++
Type Library
License GNU GPL

CoCoA (Computations in Commutative Algebra)[2] is a free computer algebra system developed by the University of Genova, Italy, used to compute with numbers and polynomials. The CoCoA Library (CoCoALib[3]) is available under GNU General Public License. CoCoA has been ported to many operating systems including Macintosh on PPC and x86, Linux on x86, x86-64 & PPC, Solaris on SPARC and Windows on x86. CoCoA is mainly used by researchers (see citations at[4] and[5]), but can be useful even for "simple" computations.

CoCoA's features include:

It is able to perform simple and sophisticated operations on multivariate polynomials and on various data related to them (ideals, modules, matrices, rational functions). For example, it can readily compute Gröbner basis, syzygies and minimal free resolution, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincaré series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA and the flexibility of its use are further enhanced by the dedicated high-level programming language.

Its mathematical core, CoCoALib, has been designed as an open source C++ library, focussing on ease of use and flexibility.

CoCoALib is based on GNU Multi-Precision Library.

CoCoALib is used by ApCoCoA[6] and NmzIntegrate[7]

See also[edit]


  1. ^ "CoCoA 5 Release Notes".
  2. ^ "CoCoA website".
  3. ^ "CoCoALib home page".
  4. ^ "CoCoA in swMath".
  5. ^ "CoCoA in GoogleScholar".
  6. ^ "ApCoCoA website".
  7. ^ "Normaliz website".

External links[edit]