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Consider an effective differential ring of computable power series in for some field and assume that we have an effective zero-test for elements in . Consider a system of algebraic partial differential equations with . If is the unique solution to this system of equations with suitable initial conditions, then we obtain a new effective differential ring of computable power series when adjoining to . Under a mild additional hypothesis, we will describe a zero-test for elements in .

**Occasions:** ANR Gecko meeting, Sophia Antibes, November
20, 2007

**Documents:** slideshow, TeXmacs
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