Zero-tests for differentially algebraic functions
Joris Van Der Hoeven
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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.