PySymmetry - Python Symmetry

PySymmetry (Python Symmetry) is a comprehensive Python library for describing symmetries and their applications in physics.

Features

Quantum Physics Module (phys.quantum)

Complete quantum simulation framework with:

• State Representations: Ket, Bra, DensityMatrix, entangled states (Bell, GHZ, W)
• Hamiltonian Operators: Free particle, harmonic oscillator, hydrogen atom, spin systems
• Schrodinger Solvers: Exact diagonalization, sparse solvers, time evolution
• Symmetry Analysis: Parity, translation, selection rules, conserved quantities
• Interactive API: SceneBuilder for arbitrary quantum scenarios

Core Modules

• Group Theory: Abstract groups, finite groups, continuous groups (U(1), SU(2), SO(3), etc.)
• Lie Theory: Lie algebras, representations, root systems
• Linear Algebra: Matrix operations, eigendecomposition

Abstract Physics (abstract_phys)

Framework for physical symmetries:

• Symmetry operations (translation, rotation, parity, time reversal)
• Physical representations
• Conservation laws via Noether's theorem

Installation

pip install PySymmetry

Quick Start

Quantum Simulation

from PySymmetry.phys.quantum import SceneBuilder, simulate, QuantumAnalyzer

# Create a harmonic oscillator
scene = (SceneBuilder("Harmonic Oscillator")
         .add_electron(position=[0])
         .add_harmonic_potential(center=[0], k=1.0)
         .set_spatial_range(-10, 10)
         .set_grid_points(300)
         .build())

# Simulate
result = simulate(scene, num_states=5)

# Analyze
analyzer = QuantumAnalyzer(result.hamiltonian, result)
print(analyzer.generate_report())

Symmetry Analysis

from PySymmetry.phys.quantum import analyze, quick_report

# Full analysis
result = analyze(hamiltonian, simulation_result)

# Quick report
print(quick_report(hamiltonian, simulation_result))

Examples

See examples/ directory:

• quantum_examples.py - Basic quantum systems (hydrogen, square well, spin)
• interactive_demo.py - Arbitrary scenario simulation
• analysis_demo.py - Symmetry analysis demonstrations

Project Structure

PySymmetry/
├── src/
│   └── PySymmetry/
│       ├── core/                    # Core mathematics
│       │   ├── algebraic_structures/
│       │   ├── group_theory/
│       │   ├── lie_theory/
│       │   ├── matrix/
|       |   └── and more... 
│       │
│       ├── abstract_phys/           # Physical abstractions
│       │   ├── physical_objects/
│       │   ├── representation/
│       │   ├── symmetry_operations/
│       │   ├── symmetry_environments/
|       |   └── and more... 
│       │
│       └── phys/                   # Physics applications
│           └── quantum/             # Quantum module
│
├── examples/
├── tests/
├── pyproject.toml
└── README.md

Development Status

Version: 1.0.0

Completed

• Core mathematical layer (groups, Lie algebras, representations)
• Abstract physics framework (symmetries, operations)
• Quantum physics module (states, Hamiltonians, solvers, analysis)

In Progress

• Visualization tools
• Additional physics examples
• Performance optimization

Requirements

• Python >= 3.10
• numpy >= 1.24
• scipy >= 1.10

Optional

• matplotlib (visualization)
• sympy (symbolic computation)
• spglib (crystallography)

Contributing

Contributions welcome! Please:

1. Fork the repository
2. Create a feature branch
3. Run tests with pytest
4. Submit a pull request

License

MIT License - see LICENSE

Author

LDK (Cathylinlin)

• Email: bluejam001@163.com
• GitHub: https://github.com/cathylinlin/PySymmetry

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Explore the beautiful world of symmetries! 🎉