A New Bound for the Existence of Differential Field Extensions

  • Richard GustavsonEmail author
  • Omar León Sánchez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)


We prove a new upper bound for the existence of a differential field extension of a differential field \((K,\varDelta )\) that is compatible with a given field extension of K. In 2014, Pierce provided an upper bound in terms of lengths of certain antichain sequences of \({\text {I}\!\text {N}}^m\) equipped with the product order. This result has had several applications to effective methods in differential algebra such as the effective differential Nullstellensatz problem. Using a new approach involving Macaulay’s theorem on the Hilbert function, we produce an improved upper bound.


Algebraic theory of differential equations Fields with several commuting derivations Differential field extensions 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsCUNY Graduate CenterNew YorkUSA
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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