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BIBasis :: BIBasis

BIBasis -- Involutive Pommaret basis in a Boolean ring


BIBasis is the package which implements the methods for constructing the reduced Pommaret and Gröbner bases in a Boolean ring for a given polynomial Ideal.

Some references:

  • V. P. Gerdt and M. V. Zinin, Involutive Method for Computing Gröbner Bases over F2. Programming and Computer Software, Vol. 34, No. 4, 2008, 191-203.
  • V.P.Gerdt and M.V.Zinin. A Pommaret Division Algorithm for Computing Gröbner Bases in Boolean Rings. Proceedings of ISSAC 2008, ACM Press, 2008, pp.95--102.
  • Vladimir Gerdt, Mikhail Zinin and Yuri Blinkov. On computation of Boolean involutive bases. Programming and Computer Software, Vol. 36, No. 2, 2010, 117-123.



This documentation describes version 0.6.3 of BIBasis.

Source code

The source code from which this documentation is derived is in the file BIBasis.m2.


  • Functions and commands
    • biBasis -- constructs a reduced Boolean Gröbner basis for the given Ideal, if the second argument is true (default), and reduced Boolean Pommaret basis otherwise.
  • Symbols
    • toGroebner (missing documentation)