A Bound for Orders in Differential Nullstellensatz

Details A Bound for Orders in Differential Nullstellensatz A Bound for Orders in Differential Nullstellensatz

2008-03-03

arxiv.org/abs/0803.0160v2

Mathematics

Commutative Algebra

25 pages; improved bound; simplified main argument; more detailed proofs

Scientific paper

10.1016/j.jalgebra.2009.05.032

We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed by A. Seidenberg but no complete solution was given. Our result is a complement to the corresponding result in algebraic geometry, which gives a bound on degrees of polynomial coefficients in effective Nullstellensatz.

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