Affiliation:
1. DiMaI “U. Dini” , Università di Firenze , Viale Morgagni 67/a, 50134 , Firenze , Italy
Abstract
Abstract
Vieta’s classical formulae explicitly determine the coefficients of a polynomial p ∈ 𝔽[x] in terms of the roots of p, where 𝔽 is any commutative ring. In this paper, Vieta’s formulae are obtained for slice-regular polynomials over the noncommutative algebra of quaternions, by an argument which essentially relies on induction, without invoking quasideterminants or noncommutative symmetric functions.
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1. Zeros;Springer Monographs in Mathematics;2022