app.py

import numpy as np

def generate_random_embedding(dim):
    return np.random.rand(dim)

# Example word embeddings (replace these with your actual embeddings)
num_embeddings = 5
embedding_dim = 3
embeddings = [generate_random_embedding(embedding_dim) for _ in range(num_embeddings)]

# Define a non-commutative product operation
def non_comm_product(embedding_a, embedding_b):
    return np.outer(embedding_a, embedding_b)

# Define the algebra (using non-commutative product)
def create_algebra(embeddings):
    n = len(embeddings)
    algebra = np.zeros((n, n, embedding_dim, embedding_dim))
    for i in range(n):
        for j in range(n):
            algebra[i, j] = non_comm_product(embeddings[i], embeddings[j])
    return algebra

algebra = create_algebra(embeddings)

# Example Hilbert space representation
# (In practice, this would require a more sophisticated mapping)
hilbert_space_representation = lambda x: x

# Define a simplified Dirac operator (In practice, this should be more complex)
def dirac_operator(embedding):
    return np.linalg.norm(embedding)

# Calculate Dirac operator for all embeddings
dirac_operators = [dirac_operator(embedding) for embedding in embeddings]

# Define a simplified Connes' metric (In practice, this should be more complex)
def connes_metric(dirac_a, dirac_b):
    return abs(dirac_a - dirac_b)

# Calculate the distance between all pairs of embeddings using Connes' metric
distance_matrix = np.zeros((num_embeddings, num_embeddings))
for i in range(num_embeddings):
    for j in range(num_embeddings):
        distance_matrix[i, j] = connes_metric(dirac_operators[i], dirac_operators[j])

print("Connes' metric distance matrix:")
print(distance_matrix)