isepg

Functions for computations related to the inverse symplectic eigenvalue for a graph

Symplectic Eigenvalues Computation

This repository provides implementations for computing:

• Symplectic eigenvalues of positive definite Hermitian matrices
• Symplectic matrices that diagonalize these matrices
• Williamson decomposition

Quick Start

# Install dependencies
pip install -r requirements.txt

# Run tests
python3 test_symplectic_eigenvalues.py

# Run examples
python3 examples.py

Files

• symplectic_eigenvalues.py - Python/NumPy implementation
• symplectic_eigenvalues.sage - SageMath implementation
• symplectic_eigenvalues.mac - Maxima implementation (symbolic computation)
• test_symplectic_eigenvalues.py - Test suite
• examples_maxima.mac - Maxima examples
• SYMPLECTIC_EIGENVALUES.md - Detailed documentation

Example Usage

import numpy as np
from symplectic_eigenvalues import symplectic_eigenvalues

# Compute symplectic eigenvalues of a matrix
A = np.array([[3, 1, 0, 0], 
              [1, 3, 0, 0], 
              [0, 0, 3, 1], 
              [0, 0, 1, 3]], dtype=float)

eigenvalues = symplectic_eigenvalues(A)
print("Symplectic eigenvalues:", eigenvalues)
# Output: [2.0, 4.0]

For more details, see SYMPLECTIC_EIGENVALUES.md.