标题： Macaulay2中的连接矩阵 显示英文标题

标题： Connection Matrices in Macaulay2

摘要： 本文中，我们描述了 Macaulay2 软件包 ConnectionMatrices 的理论基础，并解释了如何使用它。 对于 Weyl 代数中的有限全纯秩左理想，我们实现了与某个消去项序相关的连接形式的线性偏微分方程组的计算，该消去项序依赖于选定的正权向量。 我们还实现了有理函数域上的基变换的规范变换。 我们用实例演示了所有实现的算法。 显示英文摘要

摘要： In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of finite holonomic rank, we implement the computation of the encoded system of linear PDEs in connection form with respect to an elimination term order that depends on a chosen positive weight vector. We also implement the gauge transformation for carrying out a change of basis over the field of rational functions. We demonstrate all implemented algorithms with examples.