The replenishment algorithm in algebras of sets (Q2058702)

In [Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Innsbruck: Univ. Innsbruck, Mathematisches Institut (Diss.) (1965; Zbl 1245.13020)] \textit{B. Buchberger} described an algorithm, known as Buchberger's algorithm, for the construction of Gröbner bases. In this paper, the authors present an analogue of this algorithm (see also the Knuth-Bendix algorithm) for the computation of standard bases in algebras of finite, numerical, and linear semialgebraic sets, as well as in the algebra of multisets. They refer to this algorithm as the replenishment algorithm and it can be used mainly to solve the membership problem in the mentioned kinds of algebras. Furthermore, they apply the replenishment algorithm to solve some algorithmic problems in the algebra of linear semialgebraic sets.