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Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. This paper presents a method of computing the normal form of quaternionic polynomials under the conjugate-alternating order, and defines basis-free quaternionic polynomial algebra and conjugate-free quaternionic polynomial algebra under conjugate-separating orders, which can be used in classifying and computing multivariate quaternionic polynomials.

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Normal Forms of Coordinate-Free Quaternionic Polynomials

  • 会议论文

  • 发表日期：

    2026年

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  • Hongbo Li,
  • Zhengyang Wang,
  • Yue Liu,
  • Lei Huang,
  • Changpeng Shao

摘要

Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. This paper presents a method of computing the normal form of quaternionic polynomials under the conjugate-alternating order, and defines basis-free quaternionic polynomial algebra and conjugate-free quaternionic polynomial algebra under conjugate-separating orders, which can be used in classifying and computing multivariate quaternionic polynomials.