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README.md
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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.
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Other modules such as morphisms, groups, rings, and fields are under development.
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---
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## Table of Contents
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- [Features](#features)
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- [Planned Features](#planned-features)
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- [Supported Matrix Types](#supported-matrix-types)
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- [Requirements](#requirements)
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- [Installation](#installation)
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- [Usage](#usage)
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- [Example Usage](#example-usage)
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- [Simplifying with Aliases](#simplifying-with-aliases)
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- [Custom Dimension and Field](#custom-dimension-and-field)
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- [Custom Dimension](#custom-dimension)
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- [Custom Field](#custom-field)
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- [License](#license)
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---
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## Features
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- Vector and Matrix operations
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@@ -24,7 +43,7 @@ Other modules such as morphisms, groups, rings, and fields are under development
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- Unitary Matrix: `CategoryOf<IDim>.OnField<Complex>.FDiagonalMatrix`
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- Special Unitary Matrix: `CategoryOf<IDim>.OnField<Complex>.FSpecialUnitaryMatrix`
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**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 \((-π, π)\).
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**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 \((-\pi, \pi)\).
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Be cautious when using `FSpecialUnitaryMatrix.Log`, as this may not behave as the general logarithm function.
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## Requirements
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@@ -46,8 +65,8 @@ Alternatively, add the NuGet source:
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dotnet nuget add source --name hangman-lab https://git.hangman-lab.top/api/packages/hzhang/nuget/index.json
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```
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## Usage
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### Example Usage
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You can use tensors (vectors and matrices) with predefined dimensions (e.g., 2, 3, 4) and predefined fields (e.g., double, complex):
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@@ -148,4 +167,4 @@ ScalarFieldStructureProvider.Register(new CustomFieldStructure());
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<!-- Definitions -->
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[author]: https://hangman-lab.top
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[license]: license
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[license]: license
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