Vieta’s formulae for regular polynomials of a quaternionic variable
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Fabio Vlacci
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.
Funding
The author was partially supported by Progetto MIUR di Rilevante Interesse Nazionale 2010–2011 “Varietà reali e complesse: geometria, topologia e analisi armonica” and by G.N.S.A.G.A of Istituto nazionale di Alta Matematica I.N.d.A.M. “F. Severi”
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© 2017 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Ricci solitons on four-dimensional Lorentzian Walker manifolds
- The exterior splash in PG(6, q): carrier conics
- Central figure-8 cross-cuts make surfaces cylindrical
- Vieta’s formulae for regular polynomials of a quaternionic variable
- On characterizations of sausages via inequalities and roots of Steiner polynomials
- On maximal symplectic partial spreads
- Helly numbers of algebraic subsets of ℝd and an extension of Doignon’s Theorem
- A maximum problem of S.-T. Yau for variational p-capacity
- Drapeable unit arcs fit in the unit 30° sector
- Uniform Lie algebras and uniformly colored graphs
- A Krasnosel’skii-type theorem for an enlarged class of orthogonal polytopes
Articles in the same Issue
- Frontmatter
- Ricci solitons on four-dimensional Lorentzian Walker manifolds
- The exterior splash in PG(6, q): carrier conics
- Central figure-8 cross-cuts make surfaces cylindrical
- Vieta’s formulae for regular polynomials of a quaternionic variable
- On characterizations of sausages via inequalities and roots of Steiner polynomials
- On maximal symplectic partial spreads
- Helly numbers of algebraic subsets of ℝd and an extension of Doignon’s Theorem
- A maximum problem of S.-T. Yau for variational p-capacity
- Drapeable unit arcs fit in the unit 30° sector
- Uniform Lie algebras and uniformly colored graphs
- A Krasnosel’skii-type theorem for an enlarged class of orthogonal polytopes
