Skip to main content
SpringerLink
Log in

Construction of Classes of Irreducible Bivariate Polynomials

  • Conference paper
Computer Algebra in Scientific Computing (CASC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8136))

Included in the following conference series:

Abstract

We describe a method for constructing classes of bivariate polynomials which are irreducible over algebraically closed fields of characteristic zero. The constructions make use of some factorization conditions and apply to classes of polynomials that includes the generalized difference polynomials.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angermüller, G.: A generalization of Ehrenfeucht’s irreducibility criterion. J. Number Theory 36, 80–84 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ayad, M.: Sur les polynômes f(X,Y) tels que K[f] est intégralement fermé dans K[X,Y]. Acta Arith. 105, 9–28 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bhatia, S., Khanduja, S.K.: Difference polynomials and their generalizations. Mathematika 48, 293–299 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bishnoi, A., Khanduja, S.K., Sudesh, K.: Some extensions and applications of the Eisenstein irreducibility criterion. Developments in Mathematics 18, 189–197 (2010)

    Article  Google Scholar 

  5. Cohen, S.D., Movahhedi, A., Salinier, A.: Factorization over local fields and the irreducibility of generalized difference polynomials. Mathematika 47, 173–196 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Panaitopol, L., Ştefănescu, D.: On the generalized difference polynomials. Pacific J. Math. 143, 341–348 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Rubel, L.A., Schinzel, A., Tverberg, H.: On difference polynomials and hereditary irreducible polynomials. J. Number Theory 12, 230–235 (1980)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Bucharest, Romania

    Doru Ştefănescu

Authors
  1. Doru Ştefănescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

  4. Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Ştefănescu, D. (2013). Construction of Classes of Irreducible Bivariate Polynomials. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02297-0_32

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02296-3

  • Online ISBN: 978-3-319-02297-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation