Conversations in Math: What can we learn about a function by looking at the sequence of output values?
What can we learn about a function with domain and codomain a finite field by looking at the sequence of output values?
Dr. Manuel Lopez
Associate Professor
School of Mathematical Sciences, RIT
Learn about a function with domain and codomain a finite field by looking at the sequence of output values.
Abstract:
The assertion that a function f : X→ X is determined by the set of ordered pairs (x, f(x)) seems reasonable but it doesn't hold for Fq, a finite field with q=p^n many elements (p a prime). An undergraduate and I approached functions f : Fq→Fq with the view point of limiting our initial knowledge to the ordered pairs generated by the function. A project presented at the Undergraduate Research Symposium sought to characterize the structure of all polynomials f : Fp → Fp, p a prime, which output only quadratic residues (and possibly zero) and which can be represented by a polynomial of degree 2 or less. We found a binary operation that makes this set into a group. Now we pursue the goal of finding what can be determined about the irreducibility of polynomials of degree less than p over Fp=Fq from its input-output pairs.
Intended Audience:
Undergraduates and graduates. Those with interest in the topic.
Event Snapshot
When and Where
Who
Open to the Public
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No