• Skip to main content
  • Skip to after header navigation
  • Skip to site footer
ERN: Emerging Researchers National Conference in STEM

ERN: Emerging Researchers National Conference in STEM

  • About
    • About AAAS
    • About the NSF
    • About the Conference
    • Partners/Supporters
    • Project Team
  • Conference
  • Abstracts
    • Undergraduate Abstract Locator
    • Graduate Abstract Locator
    • Abstract Submission Process
    • Presentation Schedules
    • Abstract Submission Guidelines
    • Presentation Guidelines
  • Travel Awards
  • Resources
    • Award Winners
    • Code of Conduct-AAAS Meetings
    • Code of Conduct-ERN Conference
    • Conference Agenda
    • Conference Materials
    • Conference Program Books
    • ERN Photo Galleries
    • Events | Opportunities
    • Exhibitor Info
    • HBCU-UP/CREST PI/PD Meeting
    • In the News
    • NSF Harassment Policy
    • Plenary Session Videos
    • Professional Development
    • Science Careers Handbook
    • Additional Resources
    • Archives
  • Engage
    • Webinars
    • ERN 10-Year Anniversary Videos
    • Plenary Session Videos
  • Contact Us
  • Login

Some new criteria for absolute irreducibility of multivariate polynomials over finite fields

Undergraduate #29
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Session: 4
Room: Senate

Yaniel Rivera - University of Puerto Rico in Cayey
Co-Author(s): Yaziel Rivera, University of Puerto Rico, Cayey, Puerto Rico,Moises Delgado, University of Puerto Rico, Cayey, Puerto Rico,



A multivariate polynomial defined over a field K is absolutely irreducible if it is irreducible over the algebraic closure of the field. Finding criteria to test absolute irreducibility is fundamental for applications in pure and applied mathematics as algebraic geometry, combinatorics, coding theory, cryptography, finite geometry, etc. Some well known mathematical problems that have been solved, or partially solved, by proving absolute irreducibility includes exceptional APN conjecture. There are very few practical criteria for absolute irreducibility known so far. In this research we introduce novel techniques based on the 2 higher-degree terms of polynomials and introduce new absolute irreducibility criteria for multivariate polynomials over finite fields. As a consequence of our techniques, a bound for the number of absolutely irreducible factors of some multivariate polynomials is presented.

Funder Acknowledgement(s): Puerto Rico Louis Stokes Alliance For Minority Participation (PR-LSAMP)

Faculty Advisor: Moises Delgado, moises.delgado@upr.edu

Role: Experimented with polynomials of multiple variables for their factorizations and irreducibility using properties of finite fields (using the computer algebra system, SageMath). Investigated new techniques for irreducibility and absolute irreducibility over those polynomials. I’ve managed to find some unique patterns for univariate polynomials that were useful to show irreducibility. Develop a sketch of a proof for why x^n + F(y), where F(y) is any polynomial of the variable y, is absolutely irreducible. I’m now working the general case for F(x) + F(y) been absolutely irreducible.

Sidebar

Abstract Locators

  • Undergraduate Abstract Locator
  • Graduate Abstract Locator

This material is based upon work supported by the National Science Foundation (NSF) under Grant No. DUE-1930047. Any opinions, findings, interpretations, conclusions or recommendations expressed in this material are those of its authors and do not represent the views of the AAAS Board of Directors, the Council of AAAS, AAAS’ membership or the National Science Foundation.

AAAS

1200 New York Ave, NW
Washington,DC 20005
202-326-6400
Contact Us
About Us

  • LinkedIn
  • Facebook
  • Instagram
  • Twitter
  • YouTube

The World’s Largest General Scientific Society

Useful Links

  • Membership
  • Careers at AAAS
  • Privacy Policy
  • Terms of Use

Focus Areas

  • Science Education
  • Science Diplomacy
  • Public Engagement
  • Careers in STEM

Focus Areas

  • Shaping Science Policy
  • Advocacy for Evidence
  • R&D Budget Analysis
  • Human Rights, Ethics & Law

© 2023 American Association for the Advancement of Science