Construction of Janet Bases II. Polynomial Bases

In this paper we give a detailed description of an algorithm for computation of polynomial Janet bases and present its implementation in C, C++ and Reduce. This algorithm extends to polynomial ideals the algorithm for computation of monomial Janet bases presented in the first part of our paper and improves the specialization to Janet division of the general algorithm for computation of involutive polynomial bases. The computational efficiency of our codes is compared with that of computer algebra system Singular which provides one of the best implementations of the Buchberger algorithm for computation of Gröbner bases.