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How to recognize zero? (English) Zbl 0917.11062
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 \(\mathbb{Q}[x_1, \dots, x_n]\), or of the form \(x_j-e^{x_i}=0\). An elementary number is the polynomial image of an elementary point. The scope of this paper is to present a semi-algorithm 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.

11U05 Decidability (number-theoretic aspects)
11J91 Transcendence theory of other special functions
11Y16 Number-theoretic algorithms; complexity
68W30 Symbolic computation and algebraic computation
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