Normalization of Quaternionic Polynomials

TL;DR

This paper develops a normalization method for quaternionic polynomials by establishing their generating ideal, computing a Groebner basis for pure imaginary variables, and explicitly describing their normal forms.

Contribution

It introduces a generating ideal for quaternionic polynomials, computes a Groebner basis for pure imaginary cases, and explicitly characterizes their normal forms.

Findings

Generated ideal of quaternionic polynomials established

Groebner basis computed for pure imaginary variables

Explicit normal forms of quaternionic polynomials described

Abstract

Quaternionic polynomials are generated by quaternionic variables and the quaternionic product. This paper proposes the generating ideal of quaternionic polynomials in tensor algebra, finds the Groebner base of the ideal in the case of pure imaginary quaternionic variables, and describes the normal forms of such quaternionic polynomials explicitly.