From 0c3bd83eaaafa4b929b8154ad916464f0fa8d41d Mon Sep 17 00:00:00 2001
From: hzhang <hzhang@hangman-lab.top>
Date: Tue, 10 Dec 2024 21:36:25 +0000
Subject: [PATCH] improve: fix readme

---
 README.md | 25 ++++++++++++++++++++++---
 1 file changed, 22 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index 87834e9..6047762 100644
--- a/README.md
+++ b/README.md
@@ -3,6 +3,25 @@
 Skeleton is a computational library built with .NET 8.0, primarily designed to handle special complex matrices of small sizes (like 3x3) but supports matrices of any dimension over any custom field.  
 Other modules such as morphisms, groups, rings, and fields are under development.
 
+---
+
+## Table of Contents
+
+- [Features](#features)
+- [Planned Features](#planned-features)
+- [Supported Matrix Types](#supported-matrix-types)
+- [Requirements](#requirements)
+- [Installation](#installation)
+- [Usage](#usage)
+    - [Example Usage](#example-usage)
+    - [Simplifying with Aliases](#simplifying-with-aliases)
+    - [Custom Dimension and Field](#custom-dimension-and-field)
+        - [Custom Dimension](#custom-dimension)
+        - [Custom Field](#custom-field)
+- [License](#license)
+
+---
+
 ## Features
 
 - Vector and Matrix operations
@@ -24,7 +43,7 @@ Other modules such as morphisms, groups, rings, and fields are under development
 - Unitary Matrix: `CategoryOf<IDim>.OnField<Complex>.FDiagonalMatrix`
 - Special Unitary Matrix: `CategoryOf<IDim>.OnField<Complex>.FSpecialUnitaryMatrix`
 
-**Note**: The types `CategoryOf<>.OnField<>.FLieUnitaryMatrix` and `CategoryOf<>.OnField<>.FSpecialLieUnitaryMatrix` may not represent matrices as their names imply. Instead, they denote congruence classes of \( \{ \log(x) \ | \ x \in SU \} \), where all eigenvalues lie within \((-π, π)\).  
+**Note**: The types `CategoryOf<>.OnField<>.FLieUnitaryMatrix` and `CategoryOf<>.OnField<>.FSpecialLieUnitaryMatrix` may not represent matrices as their names imply. Instead, they denote congruence classes of \( \{ \log(x) \ | \ x \in SU \} \), where all eigenvalues lie within \((-\pi, \pi)\).  
 Be cautious when using `FSpecialUnitaryMatrix.Log`, as this may not behave as the general logarithm function.
 
 ## Requirements
@@ -46,8 +65,8 @@ Alternatively, add the NuGet source:
 dotnet nuget add source --name hangman-lab https://git.hangman-lab.top/api/packages/hzhang/nuget/index.json
 ```
 
-
 ## Usage
+
 ### Example Usage
 You can use tensors (vectors and matrices) with predefined dimensions (e.g., 2, 3, 4) and predefined fields (e.g., double, complex):
 
@@ -148,4 +167,4 @@ ScalarFieldStructureProvider.Register(new CustomFieldStructure());
 
 <!-- Definitions -->
 [author]: https://hangman-lab.top
-[license]: license
\ No newline at end of file
+[license]: license