KNOWPIA
WELCOME TO KNOWPIA

Original author(s) | Abbott, J. and Bigatti, A. M. and Robbiano, L.^{[1]} |
---|---|

Initial release | 1987 |

Stable release | 5.3.2
/ 6 May 2020 ^{[2]} |

Preview release | 5.3.4
/ 6 November 2020 ^{[2]} |

Written in | C++ |

Operating system | Windows, Linux/Unix, macOS |

Type | Computer algebra system |

License | GNU GPL |

Website | cocoa |

Original author(s) | Abbott, J. and Bigatti, A. M.^{[1]} |
---|---|

Initial release | 27 April 2007 |

Stable release | 0.99710
/ 7 May 2020 ^{[3]} |

Preview release | 0.99712
/ 22 December 2020 ^{[3]} |

Written in | C++ |

Type | Library |

License | GNU GPL |

Website | cocoa |

**CoCoA** (**Co**mputations in **Co**mmutative **A**lgebra)^{[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:

- Very big integers and rational numbers using the GNU Multi-Precision Library
- Multivariate Polynomials
- Gröbner basis
- User interfaces: text; Emacs-based; Qt-based

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]}

Wikimedia Commons has media related to Computations in Commutative Algebra. |

- ^
^{a}^{b}"Citing CoCoA".*cocoa.dima.unige.it*. Retrieved 2021-03-30. - ^
^{a}^{b}"CoCoA 5 Release Notes".*cocoa.dima.unige.it*. Retrieved 2021-03-30. - ^
^{a}^{b}"CoCoALib".*cocoa.dima.unige.it*. Retrieved 2021-03-30. **^**"CoCoA website".**^**"CoCoALib home page".**^**"CoCoA - Mathematical software - swMATH".**^**"CoCoA in GoogleScholar".**^**"ApCoCoA website".**^**"Normaliz website". Archived from the original on 2015-12-08. Retrieved 2014-05-22.

- Official website
- ApCoCoA, an extension of CoCoA