Abstract
In order to be able to manipulate solutions of systems of differential equations, one usually constructs differential extensions of differential rings, but the effectivity of the equality test in the extension is not trivial. In the ordinary differential case, the problem has been solved (see [13] and [3]). We propose here a method in the case of extensions obtained by adjunction of formal power series defined as solutions of a system of non linear PDE's associated with a finite set of initial conditions.
Research supported by the CNRS GDR 1026 (MEDICIS), the GDR-PRC 967 (Math-Info), and the CEC ESPRIT BRA contract 6846 (POSSO).
The author would like to thank F. Ollivier for many fruitful suggestions and M.Petitot and J. A. Weil for interesting conversations during the preparation of this paper.
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Péladan-Germa, A. (1995). Testing identities of series defined by algebraic partial differential equations. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_30
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DOI: https://doi.org/10.1007/3-540-60114-7_30
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