A zero-test for series defined in terms of solutions to partial differential equations
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Abstract

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 .

Keywords: zero-test, power series, partial differential equation, differential algebra

A.M.S. subject classification: 68W30, 35-04, 12H05, 40-04, 13P10

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