On computation of Boolean involutive bases

BIBasis, a package for reduce and Macaulay2 computer algebra systems to compute Boolean involutive and Gröbner bases

“…The involutive algorithm most frequently executes operations on base objects (monomials and polynomi als) [8]; consequently, these operations take the most processor time. The package BIBasis for the REDUCE system (like other implementations of the involutive algorithm considered in this study) uses a sparse dis tributive representation for both monomials and poly nomials.…”

“…In recent years, two versions of a Boolean involu tive algorithm using the Janet and Pommaret divisions have been developed [6][7][8], implemented, and used for computing Boolean Gröbner bases. The practice of C++ implementations of these versions shows that the Pommaret division based algorithm is more advanta geous; unlike the involutive algorithm in a ring of polynomials with rational coefficients, where the Janet division is more preferable, and the use of the Pommaret division may lead to an infinite basis.…”