Factorization of Motion Polynomials
This work solves a theoretical problem in algebraic geometry or computational mathematics, likely incremental as it builds on existing factorization concepts.
The paper addresses the problem of factorizing monic, bounded motion polynomials, proving existence of factorizations after potential multiplication with a real polynomial and providing two algorithms for computation, with the second offering optimal degree.
In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial factor and factorizations. The first algorithm is conceptually simpler but may require a high degree of the polynomial factor. The second algorithm gives an optimal degree.