JavaScript is disabled for your browser. Some features of this site may not work without it.
  • About K
  • Academics
  • Admission
  • Alumni Relations
  • Giving to K
  • News & Events
  • Student Life
  • HORNET HIVE
  • ATHLETICS
  • SITEMAP
  • WEBMAIL
    • Login
    View Item 
    •   CACHE Homepage
    • Academic Departments, Programs, and SIPs
    • Mathematics
    • Mathematics Senior Integrated Projects
    • View Item
    •   CACHE Homepage
    • Academic Departments, Programs, and SIPs
    • Mathematics
    • Mathematics Senior Integrated Projects
    • View Item

    Algorithmic Methods for Computing Monomial Invariants of Abelian Groups

    Thumbnail
    View/Open
    Searchable PDF/Kalamazoo College Only (562.0Kb)
    Date
    2022-06-01
    Author
    Rizzolo, Lucas
    Metadata
    Show full item record
    Abstract
    Given some arbitrary polynomial ring, an invariant polynomial is a polynomial that is unchanged by the action of a group G. We investigate the ring of invariant polynomials under the action of some abelian groups with the goal of finding generators for this ring. When considering an abelian group, we can always find a basis such that the action is diagonal, so there exists monomial generators mi for the invariant ring. By Noether’s degree bound, the minimal set of generating monomials ⟨m1, . . . ,mk⟩ is finite and the degree of each generating monomial mi is less than |G|. Motivated by the previous work of Gandini and Derksen, we present new theoretical approaches to find invariants of Abelian groups. In combination with the theory, we can apply exact algorithmic approaches and deploy parallel programming methods to create various algorithms for computing the minimal generating set of invariants for the ring of invariants. Finally, we present the Gandini-Ratliff-Rizzolo algorithm, a seeded generation algorithm for computing invariants.
    URI
    https://cache.kzoo.edu/handle/10920/43753
    Collections
    • Mathematics Senior Integrated Projects [274]

    Browse

    All of CACHECommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Login

    DSpace software copyright © 2002-2023  DuraSpace
    DSpace Express is a service operated by 
    Atmire NV
    Logo

    Kalamazoo College
    1200 Academy Street
    Kalamazoo Michigan 49006-3295
    USA
    Info 269-337-7000
    Admission 1-800-253-3602

    About K
    Academics
    Admission
    Alumni Relations
    Giving to K
    News & Events
    Student Life
    Sitemap
    Map & Directions
    Contacts
    Directories
    Nondiscrimination Policy
    Consumer Information
    Official disclaimer
    Search this site


    Academic Calendars
    Apply
    Bookstore
    Crisis Response
    Employment
    Library
    Registrar
    DSpace Express is a service operated by 
    Atmire NV