Skip to main content
SpringerLink
Log in
Book cover

European Computer Algebra Conference

EUROCAM 1982: Computer Algebra pp 231–236Cite as

Linear algebraic approach for computing polynomial resultant

  • 6. Algorithms III
  • Conference paper
  • First Online:

  • 174 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 144))

Abstract

This paper presents a linear algebraic method for computing the re sultant of two polynomials. This method is based on the computation of a determinant of order equal to the minimum of the degrees of the two giv en polynomials. This method turns out to be preferable to other known linear algebraic methods both from a computational point of view and for a total generality respect to the class of the given polynomials. Some relationships of this method with the polynomial pseudo-remainder operation are also discussed.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. BOCHER, Introduction to higher algebra. The MacMillan C., New York (1907).

    Google Scholar 

  2. S.Y. KU, R.J. ADLER, Computing polynomial resultants. CACM, 12, 1 (Jan 1969), 23–30.

    Google Scholar 

  3. G.E. COLLINS, Subresultant and reduced polynomial remainder sequence. J. ACM Vol. 14, n. 1, (Jan 1967).

    Google Scholar 

  4. R.E. KALMAN, Some computational problems and methods related to invariant factors and control theory. Computational problems in abstract algebra, Ed. J. Leech, Pergamon, London (1970).

    Google Scholar 

  5. S. BARNETT, Matrices in control theory. Van Nostrand Reinhold C., London (1971).

    Google Scholar 

  6. G.E. COLLINS, The calculation of multivariate polynomial resultant. J. ACM. Vol 18, n. 4, (Oct 1971) 515–532.

    Article  Google Scholar 

  7. J.V. USPENSKY, Theory of equations. New York, Toronto, London, Mc. Graw-Hill Book Company, Inc., 1948.

    Google Scholar 

  8. D.E. KNUTH, The art of computer programming. Vol. 2: "Seminumerical algorithms", Addison Wesley, Reading, Mass., 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica, Via Buonarroti 12, 00185, Roma, Italy

    L. Bordoni, A. Colagrossi & A. Miola

Authors
  1. L. Bordoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Colagrossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Miola
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jacques Calmet

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bordoni, L., Colagrossi, A., Miola, A. (1982). Linear algebraic approach for computing polynomial resultant. In: Calmet, J. (eds) Computer Algebra. EUROCAM 1982. Lecture Notes in Computer Science, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11607-9_27

Download citation

  • DOI: https://doi.org/10.1007/3-540-11607-9_27

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11607-3

  • Online ISBN: 978-3-540-39433-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation