CoCoA.4 Logo.png
Original author(s)Abbott, J. and Bigatti, A. M. and Robbiano, L.[1]
Initial release1987; 34 years ago (1987)
Stable release
5.3.2 / 6 May 2020; 19 months ago (2020-05-06)[2]
Preview release
5.3.4 / 6 November 2020; 13 months ago (2020-11-06)[2]
Written inC++
Operating systemWindows, Linux/Unix, macOS
TypeComputer algebra system
LicenseGNU GPL
Original author(s)Abbott, J. and Bigatti, A. M.[1]
Initial release27 April 2007; 14 years ago (2007-04-27)
Stable release
0.99710 / 7 May 2020; 19 months ago (2020-05-07)[3]
Preview release
0.99712 / 22 December 2020; 11 months ago (2020-12-22)[3]
Written inC++
LicenseGNU GPL Edit this on Wikidata

CoCoA (Computations in Commutative Algebra)[4] is a free computer algebra system developed by the University of Genova, Italy, used to compute with numbers and polynomials. The CoCoA Library (CoCoALib[5]) 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[6] and[7]), 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 resolutions, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincaré series and Hilbert functions, factorization of polynomials, and 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[8] and NmzIntegrate[9]

See also


  1. ^ a b "Citing CoCoA". Retrieved 2021-03-30.
  2. ^ a b "CoCoA 5 Release Notes". Retrieved 2021-03-30.
  3. ^ a b "CoCoALib". Retrieved 2021-03-30.
  4. ^ "CoCoA website".
  5. ^ "CoCoALib home page".
  6. ^ "CoCoA - Mathematical software - swMATH".
  7. ^ "CoCoA in GoogleScholar".
  8. ^ "ApCoCoA website".
  9. ^ "Normaliz website". Archived from the original on 2015-12-08. Retrieved 2014-05-22.

External links

  • Official website
  • ApCoCoA, an extension of CoCoA