How to Recognize Zero

✍ Scribed by DANIEL RICHARDSON

• Book ID: 102976518
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 516 KB
• Volume: 24
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1997.0157

✦ Synopsis

An elementary point is a point in complex n space, which is an isolated, nonsingular solution of n equations in n variables, each equation being either of the form p = 0, where p is a polynomial in Q[x 1 , . . . , xn], or of the form x je x i = 0. An elementary number is the polynomial image of an elementary point. In this article a semi algorithm is given to decide whether or not a given elementary number is zero. It is proved that this semi algorithm is an algorithm, i.e. that it always terminates, unless it is given a problem containing a counterexample to Schanuel's conjecture.