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Most explicit transcendental functions which occur in computer algebra are analytic functions. Usually, they can be explicitly written as expressions in solutions of algebraic differential equations with specified initial conditions. Testing whether such a function is identically zero can be decomposed in two subproblems: the constant problem (usually very difficult) and the zero-test problem for power series expansions (assuming an oracle for the constant problem). We will present an overview of the state for these problems, while concentrating mostly on the second one.

**Occasions:** Zero 2007, workshop, July 19, Seoul

**Documents:** slideshow, TeXmacs
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