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International Conference on Mathematical Aspects of Computer and Information Sciences

MACIS 2015: Mathematical Aspects of Computer and Information Sciences pp 358–361Cite as

A New Bound for the Existence of Differential Field Extensions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

Abstract

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.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York, NY, 10016, USA

    Richard Gustavson

  2. Department of Mathematics and Statistics, McMaster University, Hamilton Hall, 1280 Main Street West, Hamilton, ON, L8S 4K1, Canada

    Omar León Sánchez

Authors
  1. Richard Gustavson
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  2. Omar León Sánchez
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Corresponding author

Correspondence to Richard Gustavson .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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© 2016 Springer International Publishing Switzerland

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Gustavson, R., Sánchez, O.L. (2016). A New Bound for the Existence of Differential Field Extensions. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_30

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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