论文标题
计算机代数中的特征类
Characteristic Classes in Computer Algebra
论文作者
论文摘要
我们开发一个框架，使用符号演算在计算机代数系统中计算特征类及其形式。为了做到这一点，我们利用Chern-Weil方法，在这种方法中，DE RHAM共同体中的矢量束的特征类别是通过任意联系获得的。一路上，我们实施了向量束的概念，它们的部分和连接以及Sagemath中的混合差异形式。最后，我们讨论了Jupyter笔记本中暴露的一些申请示例，并最终解决了计算成本的问题。
We develop a framework to compute characteristic classes and their forms in the computer algebra system SageMath using symbolic calculus. In order to do this, we make use of the Chern-Weil approach in which characteristic classes of vector bundles in the de Rham cohomology are obtained by arbitrary connections. Along the way, we implement the notion of vector bundles, their sections and connections as well as mixed differential forms in SageMath. We conclude by discussing some application examples exposed in Jupyter Notebook and eventually address the issue of computational cost.
