IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-585-33247-5_9.html

Solving Systems of Equations

In: Algorithms for Computer Algebra

Author

Listed:
  • K. O. Geddes

    (University of Waterloo)

  • S. R. Czapor

    (Laurentian University)

  • G. Labahn

    (University of Waterloo)

Abstract

In this chapter we consider the classical problem of solving (exactly) a system of algebraic equations over a field F. This problem, along with the related problem of solving single univariate equations, was the fundamental concern of algebra until the beginning of the “modern” era (roughly, in the nineteenth century); it remains today an important, widespread concern in mathematics, science and engineering. Although considerable effort has been devoted to developing methods for numerical solution of equations, the develop- ment of exact methods is also well motivated. Obviously, exact methods avoid the issues of conditioning and stability. Moreover, in the case of nonlinear systems, numerical methods cannot guarantee that all solutions will be found (or prove that none exist). Finally, many systems which arise in practice contain “free” parameters and hence must be solved over non-numerical domains.

Suggested Citation

  • K. O. Geddes & S. R. Czapor & G. Labahn, 1992. "Solving Systems of Equations," Springer Books, in: Algorithms for Computer Algebra, chapter 0, pages 389-428, Springer.
    • Handle: RePEc:spr:sprchp:978-0-585-33247-5_9
    DOI: 10.1007/978-0-585-33247-5_9
    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_9. 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.