An approach to the zero recognition problem by Buchberger algorithm

✍ Scribed by Nobuki Takayama

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 698 KB
• Volume: 14
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1016/0747-7171(92)90039-7

✦ Synopsis

The class of "holonomic function" is considered . We present a quasi-algorithm that recognizes whether a holonomic function is zero or not . The algorithm consists of procedures which obtain differential operators that annihilate sums, products, and definite integrals with, respect to parameters of holonomic functions . A Weyl algebra-analog of Buchberger's algorithm is used. A "holonomic" approach to the zero recognition algorithm was initiated by D . Zeilberger (1990) who realized it by Sylvester's dyalitic elimination. Our algorithm uses Buchberger's algorithm to improve Zeilberger's algorithm .