Jayce-Ping / SpTm

A Wolfram Mathematica Package for Differential Geometry and General Relativity Calculations.

Space-Time (SpTm)

A Wolfram Mathematica Package for Differential Geometry and General Relativity Calculations.

• 中文

• English

中文

谨以此纪念我的微分几何与广义相对论的入门导师——梁灿彬教授。

简介

• Space-Time是一个关于微分几何和广义相对论计算的Mathematica程序包。

• 你可以使用一种符合书写习惯的方式输入带有抽象指标的张量表达式，并对其进行一些化简和计算。

• 在选取坐标系并设置了张量的分量后，你可以计算得到表达式的分量。

• 你可以计算一些常用张量的分量，如：黎曼张量、里奇张量、爱因斯坦张量等。

• 具体使用方法和例子见Documentation_CN.nb。

安装

这里介绍两种安装和使用的方法：

• 任意打开一个Mathematica笔记本，执行

  URLDownload["https://raw.githubusercontent.com/Jayce-Ping/SpTm/main/SpTm.wl", FileNameJoin[{$UserBaseDirectory, "Applications", "SpTm.wl"}]]

  在这之后，在任何笔记本中导入SpTm只需要执行<<SpTm`或 Needs["SpTm`"]即可。

• 将SpTm.wl文件下载至当前目录，在当前目录下新建笔记本，在笔记本中执行

  Get[FileNameJoin[{NotebookDirectory[], "SpTm.wl"}]]

  即可

另外，由Brock University的Barak Shoshany所开发的OGRe程序包也是一个很优秀的微分几何与广义相对论的计算程序包。

English

In honor of my introductory tutor in Differential Geometry and General Relativity, Prof. Canbin Liang.

Introduction

• Space-Time is a Mathematica package for Differential Geometry and General Relativity calculations.

• You can input tensor expressions with abstract indices in a customary way, and do some simplifications and calculations.

• Given a coordinate system and the components of tensors set, you can calculate the components of the expression.

• You can calculate the components of some common tensors, such as Riemann tensor, Ricc tensor and Einstein tensor, etc.

• For details and examples of use, see Documentation_EN.nb.

Installation

Here are two ways to install and use:

• Open any Mathematica notebook, run

  URLDownload["https://raw.githubusercontent.com/Jayce-Ping/SpTm/main/SpTm.wl", FileNameJoin[{$UserBaseDirectory, "Applications", "SpTm.wl"}]]

  After this, to import SpTm in any notebook just execute <<SpTm` or Needs["SpTm`"].

• Download SpTm.wl to the current directory, create a new Notebook, and run

  Get[FileNameJoin[{NotebookDirectory[], "SpTm.wl"}]]

  in the notebook.

In addition, the OGRe, developed by Barak Shoshany of Brock University, is also an excellent package for calculating differential geometry and general relativity.