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Simple Differential Field Extensions and Effective Bounds

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

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

Abstract

We establish several variations on Kolchin’s differential primitive element theorem, and conjecture a generalization of Pogudin’s primitive element theorem. These results are then applied to improve the bounds for the effective Differential Lüroth theorem.

J. Freitag—Thanks Dave Marker, Omar León Sanchez, and Gabriela Jeronimo for useful conversations related to this work. JF was partially supported by NSF MSPRF 1204510.

W. Li—Partially supported by a National Key Basic Research Project of China (2011CB302400) and by grants from NSFC (60821002, 11301519) and thanks the University of California, Berkeley for providing a good research environment during her appointment as a Visiting Scholar.

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Author information

Authors and Affiliations

  1. UCLA Mathematics Department, Box 951555, Los Angeles, CA, 90095-1555, USA

    James Freitag

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55 Zhongguancun East Road, Beijing, 100190, China

    Wei Li

Authors
  1. James Freitag
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  2. Wei Li
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Correspondence to James Freitag .

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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Freitag, J., Li, W. (2016). Simple Differential Field Extensions and Effective Bounds. 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_29

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

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