#Algebraic equations over GF|2|


    # Convert the coefficients and constants to a numpy array

    # Solve the system of equations using Gaussian elimination

    # Check if the system has a solution


# Example usage



if __name__ == '__main__':
    import numpy as np
    def solve_algebraic_equations(coefficients, constants):
        A = np.array(coefficients)
        b = np.array(constants)
        augmented_matrix = np.column_stack((A, b))
        rref, _ = np.linalg.qr(augmented_matrix)
        rank_A = np.linalg.matrix_rank(A)
        rank_augmented = np.linalg.matrix_rank(augmented_matrix)
        if rank_A == rank_augmented:
            return True  # System has a solution
        else:
            return False  # System does not have a solution
    coefficients = [[1, 0, 1], [0, 1, 1], [1, 1, 0]]
    constants = [1, 0, 1]
    has_solution = solve_algebraic_equations(coefficients, constants)
    print("Has solution:", has_solution)
