论文标题
用于分解季节多项式分解的算法
An Algorithm for the Factorization of Split Quaternion Polynomials
论文作者
论文摘要
我们提出了一种算法，以将所有因素化为分离季节的单变量多项式的线性因子，前提是存在这样的分解。该算法的失败等同于非实现性，我们还根据对不可脱离的分裂四元素的统治的几何解释。但是，裂开四元多项式的合适的真实多项式倍数仍然可以分解，我们描述了如何找到这些真实的多项式。分裂的四元素多项式描述了双曲机平面中的合理运动。用线性因子分解对应于合理运动分解为双曲线旋转的分解。由于使用真实多项式的乘法不会改变运动，因此这种分解始终是可能的。我们的一些想法可以转移到多项式运动的分解理论中。这些是具有实际规范多项式的双重四季度的多项式，它们描述了欧几里得运动学中的理性运动。我们传递用于分裂四个裂缝的技术，以计算某些双重四元素多项式的新因素化。
We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we present also geometric interpretations in terms of rulings on the quadric of non-invertible split quaternions. However, suitable real polynomial multiples of split quaternion polynomials can still be factorized and we describe how to find these real polynomials. Split quaternion polynomials describe rational motions in the hyperbolic plane. Factorization with linear factors corresponds to the decomposition of the rational motion into hyperbolic rotations. Since multiplication with a real polynomial does not change the motion, this decomposition is always possible. Some of our ideas can be transferred to the factorization theory of motion polynomials. These are polynomials over the dual quaternions with real norm polynomial and they describe rational motions in Euclidean kinematics. We transfer techniques developed for split quaternions to compute new factorizations of certain dual quaternion polynomials.
