BRiAl is the successor to PolyBoRi.

The core of PolyBoRi is a C++ library, which provides high-level data
types for Boolean polynomials and monomials, exponent vectors, as well
as for the underlying polynomial rings and subsets of the powerset of
the Boolean variables. As a unique approach, binary decision diagrams
are used as internal storage type for polynomial structures. On top of
this C++-library we provide a Python interface. This allows parsing of
complex polynomial systems, as well as sophisticated and extendable
strategies for Groebner base computation. PolyBoRi features a powerful
reference implementation for Groebner basis computation.