2023/10/30 by Zijia Li, Li, Zijia, Hans-Peter Schröcker +3
Computer Science · Mathematics · #15A66 15A67 20G20 51B10 51F15 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2310.19325
openalex publication_date 2023/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new algorithm to decompose generic spinor polynomials into linear factors. Spinor polynomials are certain polynomials with coefficients in the geometric algebra of dimension three that parametrize rational conformal motions. The factorization algorithm is based on the "kinematics at infinity" of the underlying rational motion. Factorizations exist generically but not generally and are typically not unique. We prove that generic multiples of non-factorizable spinor polynomials admit factorizations and we demonstrate at hand of an example how our ideas can be used to tackle the hitherto unsolved problem of "factorizing" algebraic motions.