Equations in quaternions

Maria Irene Falcão

November 12, 2019

Quaternions were introduced in 1843 by the Irish mathematician William Rowan Hamilton (1805-1865) as a generalization of complex numbers. Apart from their theoretical importance as the first example of a non-commutative algebra, quaternions have become a powerful tool for modeling and solving problems in classical fields of mathematics, engineering and physics.

Since the well-known work of Niven in the 1940’s “Equations in quaternions”, there has been a growing interest in studying the problem of characterizing and computing the zeros of quaternionic polynomials. While the factorization theory of quaternionic polynomials has been developed a long time ago, the design of algorithms for polynomial computation gained attention only recently.

In this talk we will give an overview of some theoretical and computational polynomial problems in quaternionic context.