A Geometric Algorithm for the Factorization of Spinor Polynomials
Rings and Algebras
2023-11-14 v2
Abstract
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.
Cite
@article{arxiv.2310.19325,
title = {A Geometric Algorithm for the Factorization of Spinor Polynomials},
author = {Zijia Li and Hans-Peter Schröcker and Johannes Siegele},
journal= {arXiv preprint arXiv:2310.19325},
year = {2023}
}