Computations in the ring of quaternionic polynomials

DOI10.1016/j.jsc.2009.06.003zbMath1221.30104OpenAlexW2082126363MaRDI QIDQ1034546

Graziano Gentili, Alberto Damiano, Daniele C. Struppa

Publication date: 6 November 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2009.06.003

zbMATH Keywords

Gröbner basesBezout theoremquaternionic polynomialsnon-commutative syzygies

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (5)

A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames ⋮ An iterative method to compute the dominant zero of a quaternionic unilateral polynomial ⋮ Solution of a quadratic quaternion equation with mixed coefficients ⋮ Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves ⋮ The Moore-Penrose inverses of matrices over quaternion polynomial rings

Uses Software

• Plural
• SINGULAR

Cites Work

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• The fundamental theorem of algebra for Hamilton and Cayley numbers
• Zeros of regular functions and polynomials of a quaternionic variable
• On the multiplicity of zeroes of polynomials with quaternionic coefficients
• A new theory of regular functions of a quaternionic variable
• A new approach to Cullen-regular functions of a quaternionic variable
• On the Structure of the Set of Zeros of Quaternionic Polynomials
• Equations in Quaternions
• The Roots of a Quaternion
• The “fundamental theorem of algebra” for quaternions
• Zeros of quaternion polynomials

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