We can ask whether a polynomial is irreducible over a particular field. If we consider the iteration of this polynomial (that is composing the polynomial with itself) we can explore if it remains irreducible over that base field. This phenomenon is called dynamical irreducibility or stability. We will explore what tools we have to discuss irreducibility over iteration and how to use SageMath to explore this question. This work will showcase work done by PRiME (Pomona Research in Mathematics Experience) students and Rethinking Number Theory working group.
Dynamic irreducibility over finite fields
Bianca Thompson, Westminster UniversityAuthors: Jamie Juul, Bella Tobin, Swati, Cigole Thomas, Tori Day, Rebecca DeLand, Malike Conteh, Michaela Fitzgerald, Sarah Szafranski, and Jasmine Camero
2023 AWM Research Symposium
Number Theory at Primarily Undergraduate Institutions [Organized by Bella Tobin and Leah Sturman]