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 much faster in practice than previous algorithms.

我们提出了两种新的算法来计算多元多项式的q整数线性分解。这种分解对于通过创造性伸缩处理q超几何符号求和以及描述q是必不可少的-Ore-Sato理论的对立面。我们的两种算法都只需要基本整数和多项式算法，并且可用于包含整数环的任何唯一分解域。在多元整数多项式的情况下，对我们的算法和两个以前的算法都进行了完整的复杂度分析，这表明我们的算法具有更好的理论性能。还包括Maple实现，这表明我们的算法在实践中比以前的算法要快得多。