Quadratic Spinor Polynomials with Infinitely Many Factorizations

2024/02/22 by Zijia Li, Li, Zijia, Hans-Peter Schröcker +5
Computer Science · Mathematics · #15A66 #15A67 #51B10 #51F15 #53A05 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2402.14347

openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions. Factorizations of spinor polynomial corresponds to the decomposition of the rational motion into elementary motions. Generic spinor polynomials allow for a finite number of factorizations. We present two examples of quadratic spinor polynomials that admit infinitely many factorizations. One of them, the circular translation, is well-known. The other one has only been introduced recently but in a different context. We not only compute all factorizations of these conformal motions but also interpret them geometrically.

Related

• A Geometric Algorithm for the Factorization of Spinor Polynomials
• Quadratic Motion Polynomials With Irregular Factorizations
• Motion Polynomials Admitting a Factorization with Linear Factors
• The Geometry of Quadratic Quaternion Polynomials in Euclidean and Non-Euclidean Planes
• Factorization of Motion Polynomials