The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the singularities of the system, it serves as a preparatory step for many algorithms in symbolic integration. A new algorithm is introduced to compute a holonomic submodule of the partial Weyl closure of a finite-rank module, where the closure is taken with respect to a subset of the variables. The method relies on a non-commutative analogue of Rabinowitsch's trick. The algorithm is implemented in the Julia package MultivariateCreativeTelescoping.jl and shows substantial speedups over existing exact Weyl closure algorithms in Singular and Macaulay2.

翻译：Weyl闭包是代数分析中的基本操作：它将有理系数的微分算子系统转化为多项式系数的等价系统。除了编码系统奇点的更精细信息外，它还是符号积分中许多算法的准备步骤。本文引入一种新算法，用于计算有限秩模的偏Weyl闭包的全纯子模（其中闭包是针对变量子集取的）。该方法依赖于Rabinowitsch技巧的非交换类比。该算法已在Julia包MultivariateCreativeTelescoping.jl中实现，与Singular和Macaulay2中现有的精确Weyl闭包算法相比，显示出显著的加速效果。