HIGH-QUALITY COMPUTING OF POLYNOMIAL PROBLEMS BY RISA ASIR/

This paper deals with polynomial problem solving by computer algebra t echnologies as an approach to high-quality computing. It focuses on Gr obner basis techniques and illustrates the effectiveness of algebraic approaches for solving multi-variate polynomial equations as observed by the authors. The basics of Grobner bases are explained. Then, the a uthors' improvements for computing Grobner bases are presented. The re sults of such improvements are examined on a computer algebra system, called Risa/Asir, which the authors have developed. The performance of Risa/Asir with several benchmarks is compared with that of other syst ems.