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 approximate the partial Weyl closure of a holonomic module, where the closure is taken with respect to a subset of the variables. The method is based on a non-commutative generalization of Rabinowitsch's trick and yields a holonomic module included in the Weyl closure of the input system. 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运算：它将具有有理系数的微分算子系统转换为具有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预备步骤。本文引入了一种新算法来近似全纯模的部分Weyl闭包，其中闭包是针对变量的一个子集进行的。该方法基于Rabinowitsch技巧的非交换推广，并生成一个包含在输入系统Weyl闭包内的全纯模。该算法已在Julia包MultivariateCreativeTelescoping.jl中实现，相较于Singular和Macaulay2中现有的精确Weyl闭包算法，展现出显著的加速效果。