Create math_utils.py

utils/math_utils.py

@@ -0,0 +1,59 @@
+import numpy as np
+from scipy.linalg import expm
+
+def calculate_wormhole_stability(matrix_a, matrix_b):
+    """
+    Calculate the stability of a wormhole using the eigenvalues of the matrices A and B.
+
+    Args:
+        matrix_a (numpy array): Matrix A representing the wormhole's gravitational field.
+        matrix_b (numpy array): Matrix B representing the wormhole's exotic matter distribution.
+
+    Returns:
+        float: The stability of the wormhole (0 = unstable, 1 = stable).
+    """
+    eigenvalues_a = np.linalg.eigvals(matrix_a)
+    eigenvalues_b = np.linalg.eigvals(matrix_b)
+    stability = np.dot(eigenvalues_a, eigenvalues_b) / (np.linalg.norm(eigenvalues_a) * np.linalg.norm(eigenvalues_b))
+    return stability
+
+def optimize_faster_than_light_travel(trajectory, mass_ratio):
+    """
+    Optimize a faster-than-light travel trajectory using the Alcubierre Warp Drive metric.
+
+    Args:
+        trajectory (numpy array): The initial trajectory of the spacecraft.
+        mass_ratio (float): The mass ratio of the spacecraft to the exotic matter.
+
+    Returns:
+        numpy array: The optimized trajectory.
+    """
+    # Calculate the Alcubierre Warp Drive metric
+    metric = np.array([[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]])
+    metric[0, 0] = 1 - mass_ratio * np.exp(-(trajectory[0] ** 2 + trajectory[1] ** 2 + trajectory[2] ** 2) / (2 * mass_ratio ** 2))
+
+    # Optimize the trajectory using a genetic algorithm
+    from scipy.optimize import differential_evolution
+    bounds = [(0, 1), (0, 1), (0, 1), (0, 1)]
+    result = differential_evolution(lambda x: -np.linalg.norm(np.dot(metric, x)), bounds)
+    optimized_trajectory = result.x
+
+    return optimized_trajectory
+
+def calculate_quantum_entanglement(state_vector):
+    """
+    Calculate the quantum entanglement of a state vector using the von Neumann entropy.
+
+    Args:
+        state_vector (numpy array): The state vector of the quantum system.
+
+    Returns:
+        float: The quantum entanglement of the state vector.
+    """
+    # Calculate the density matrix
+    density_matrix = np.outer(state_vector, state_vector)
+
+    # Calculate the von Neumann entropy
+    entropy = -np.trace(np.dot(density_matrix, np.log2(density_matrix)))
+
+    return entropy