Gröbner basis computation in Risa/Asir (Computer Algebra --Theory and its Applications)

Abstract

The first implementation of Grabner basis computation in Risa/Asir started in 1993. The Shimoyama-Yokoyama algorithm for primary decomposition of ideals was implemented by using it in 1996. In 2003 a completely new package for Grabner basis computation was developed. By using this new package we implemented a new primary decomposition algorithm that does not produce any redundant primary component in 2011. We want many people to use new functions, but unfortunately not a few people still use old ones. Recently we replaced the functions for bignum computation with GMP [9]. As a result we could greatly improve the efficiency of Groebner basis computation over the rationals. In this article we show the current status of Risa/Asir to make the new features known by as many people as possible.