1. A bound for orders in differential Nullstellensatz
- Author
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Agnes Szanto, Oleg Golubitsky, M. V. Kondratieva, and Alexey Ovchinnikov
- Subjects
Discrete mathematics ,Pure mathematics ,Polynomial ,Conjecture ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,12H05, 13N10, 13P10 ,010102 general mathematics ,Combinatorial proof ,Elimination theory ,010103 numerical & computational mathematics ,Algebraic geometry ,Mathematics - Commutative Algebra ,Commutative Algebra (math.AC) ,01 natural sciences ,Mathematics - Algebraic Geometry ,FOS: Mathematics ,0101 mathematics ,Algebraic number ,Affine variety ,Algebraic Geometry (math.AG) ,Differential (mathematics) ,Mathematics - Abstract
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., Comment: 25 pages; improved bound; simplified main argument; more detailed proofs
- Published
- 2009
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