计算一个全微分算子模的偏韦尔闭包近似
Computing an approximation of the partial Weyl closure of a holonomic module
AI总结：
本文提出了一种计算全微分算子模偏韦尔闭包的算法，基于非交换泛化拉宾诺维奇技巧，实现速度快于现有算法。
摘要：
韦尔闭包是微分代数中的基本操作：它将具有有理系数的微分算子系统转换为等价的具有多项式系数的系统。除了编码系统奇点的更精细信息外，它还为许多符号积分算法提供了预备步骤。本文提出了一种新的算法，用于近似全微分算子模的偏韦尔闭包，其中闭包是相对于变量子集进行的。该方法基于非交换的拉宾诺维奇技巧泛化，并产生一个包含在输入系统韦尔闭包中的全微分算子模。该算法在Julia包MultivariateCreativeTelescoping.jl中实现，并在Singular和Macaulay2的现有精确韦尔闭包算法上显示出显著的速度提升。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
