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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