Heuristic System Approach to the Hodge Conjecture: Insight from the CAS 6 Framework

# assume: NS_basis (20 vectors), T_basis (2 vectors), Gram matrices available

# build H2_basis = NS_basis + T_basis

# Build H2_tensor_basis = [e_i e_j for e_i,e_j in H2_basis]

# Function: project_to_T_tensor(vec_in_H2xH2_coords)

def project_to_T_tensor(vec):

    # indices: locate indices for t_it_j

    return [ vec[index(t1,t1)], vec[index(t1,t2)], vec[index(t2,t1)], vec[index(t2,t2)] ]

# For each candidate Z:

for Z in candidate_list:

    cohom_class_coords = compute_cohomology_class(Z)   # returns coords in H2H2 basis

    tvec = project_to_T_tensor(cohom_class_coords)