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README.md
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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. 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. 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 ## Features
- Vector and Matrix operations - Vector and Matrix operations
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- Unitary Matrix: `CategoryOf<IDim>.OnField<Complex>.FDiagonalMatrix` - Unitary Matrix: `CategoryOf<IDim>.OnField<Complex>.FDiagonalMatrix`
- Special Unitary Matrix: `CategoryOf<IDim>.OnField<Complex>.FSpecialUnitaryMatrix` - 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. Be cautious when using `FSpecialUnitaryMatrix.Log`, as this may not behave as the general logarithm function.
## Requirements ## Requirements
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dotnet nuget add source --name hangman-lab https://git.hangman-lab.top/api/packages/hzhang/nuget/index.json dotnet nuget add source --name hangman-lab https://git.hangman-lab.top/api/packages/hzhang/nuget/index.json
``` ```
## Usage ## Usage
### Example 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): You can use tensors (vectors and matrices) with predefined dimensions (e.g., 2, 3, 4) and predefined fields (e.g., double, complex):