Math faculty and alumnus publish research article in international journal
Michael Keenan '16, Associate Professor Jim Beuerle and A.L. Hook Associate Professor Chad Awtrey published a research paper in the most recent issue of the International Journal of Pure and Applied Mathematics.
The most recent issue of International Journal of Pure and Applied Mathematics includes a new research paper by a team from Elon including Michael Keenan '16, Associate Professor Jim Beuerle and A.L. Hook Associate Professor Chad Awtrey.
The research team's article, "Algorithms for computing quartic Galois groups over fields of characteristic 0," developed theory for, designed and implemented a new algorithm for computing the symmetry properties of degree four polynomials whose coefficients come from sets that behave similarly to the rational numbers. These symmetries encode much of the arithmetic structure of the polynomial and its roots, which is why this task is of fundamental importance to mathematicians.
The team's algorithm also determines when there exist degree two polynomials that are associated to the degree four input polynomial. When such degree two polynomials exist, the algorithm returns this information as well.
In addition to developing new theory and algorithms, the paper also surveys other techniques that determine the symmetry properties of degree four polynomials. It is important to note that the other algorithms do not compute the associated information concerning related degree two polynomials.
Among all techniques surveyed, the team found that an algorithm due to Beuerle's doctoral advisor was computationally the fastest. This fact represents an important contribution to the field, since no previous comparison had taken place. While the team's algorithm was not the fastest, their method still represents an advancement since the algorithm computes associated degree two polynomials, when they exist.