论文标题
多元多项式的有效Q-Integer线性分解
Efficient q-Integer Linear Decomposition of Multivariate Polynomials
论文作者
论文摘要
我们提出了两种新算法，用于计算多元多项式的Q-Integer线性分解。这样的分解对于通过创意望远镜的Q-Hyperainemometric符号总结以及描述俄勒冈 - 苏摩理论的Q-counterpart是必不可少的。我们的这两种算法都仅需要基本整数和多项式算术，并适用于包含整数环的任何独特的分解域。在多元整数多项式的情况下，对我们的算法和两种先前的算法进行了完整的复杂性分析，表明我们的算法具有更好的理论性能。还包括枫木实现，这表明我们的算法在实践中的速度也比以前的算法要快得多。
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and for describing the q-counterpart of Ore-Sato theory. Both of our algorithms require only basic integer and polynomial arithmetic and work for any unique factorization domain containing the ring of integers. Complete complexity analyses are conducted for both our algorithms and two previous algorithms in the case of multivariate integer polynomials, showing that our algorithms have better theoretical performances. A Maple implementation is also included which suggests that our algorithms are also much faster in practice than previous algorithms.
