TensoriaCalc - 處理偽黎曼張量分析問題的使用者導向Mathematica套件;TensoriaCalc, an user-oriented Mathematica package to tackle semi-Riemannian tensor calculus problems

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题名:	TensoriaCalc - 處理偽黎曼張量分析問題的使用者導向Mathematica套件;TensoriaCalc, an user-oriented Mathematica package to tackle semi-Riemannian tensor calculus problems
作者:	陳威澔;Chen, Wei-Hao
贡献者:	物理學系
关键词:	TensoriaCalc;張量微積分;廣義相對論;Mathematica套件;微分幾何;TensoriaCalc;tensor calculus;General Relativity;Mathematica package;Differential Geometry
日期:	2023-07-28
上传时间:	2024-09-19 15:56:04 (UTC+8)
出版者:	國立中央大學
摘要:	TensoriaCalc是一個使用者導向的Mathematica套件，首先是由我的導師瞿怡仁所建構的，並且由我顯著地擴展套件。經由使用者提供度量張量以及坐標系，可以快速算出重要的幾何張量如克里斯多福符號、愛因斯坦張量等，微分幾何及張量分析中的常見運算如: 張量收縮、座標轉換、投影、偏導數、協變導數、外微分、李導數亦是可使用的功能。在本文中，我將解釋TensoriaCalc的基本運作及使用方式，並展示新添加的功能與建構的思路。最後，我將呈現如何使用TensoriaCalc來計算數個廣義相對論及微分幾何中經典的問題。;TensoriaCalc is an user-oriented Mathematica package developed to tackle tensor calculus problems. By giving a metric tensor and the coordinate set, the users can rapidly obtain tensor components of geometric objects such as Christoffel symbols, Einstein tensors, etc. Operations in tensor calculus and differential geometry, such as contraction, coordinate transformation, projection, partial derivative, covariant derivative, exterior derivative, Lie derivative, etc., are also available. In this paper, I will explain the basic structure of this package, firstly constructed by Yi-Zen Chu and significantly expanded by me. Also, the track of thought of my newly added functionality or structure will be presented. Eventually, I will show how to use TensoriaCalc to calculate several classic problems in General Relativity and Differential Geometry.
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