IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-585-33247-5_10.html

Gröbner Bases for Polynomial Ideals

In: Algorithms for Computer Algebra

Author

Listed:
  • K. O. Geddes

    (University of Waterloo)

  • S. R. Czapor

    (Laurentian University)

  • G. Labahn

    (University of Waterloo)

Abstract

We have already seen that, among the various algebraic objects we have encountered, polynomials play a central role in symbolic computation. Indeed, many of the (higher-level) algorithms discussed in Chapter 9 (and later in Chapters 11 and 12) depend heavily on com putation with multivariate polynomials. Hence, considerable effort has been devoted to improving the efficiency of algorithms for arithmetic, GCD's and factorization of polynomials. It also happens, though, that a fairly wide variety of problems involving polynomials (among them, simplification and the solution of equations) may be formulated in terms of polynomial ideals. This should come as no surprise, since we have already used particular types of ideal bases (i.e. those derived as kernels of homomorphisms) to obtain algorithms based on interpolation and Hensel's lemma. Still, satisfactory algorithmic solutions for many such problems did not exist until the fairly recent development of a special type of ideal basis, namely the Gröbner basis.

Suggested Citation

  • K. O. Geddes & S. R. Czapor & G. Labahn, 1992. "Gröbner Bases for Polynomial Ideals," Springer Books, in: Algorithms for Computer Algebra, chapter 0, pages 429-471, Springer.
    • Handle: RePEc:spr:sprchp:978-0-585-33247-5_10
    DOI: 10.1007/978-0-585-33247-5_10
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-0-585-33247-5_10. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.