ruffini.py

def ruffinis_rule(coefficients, factor):
    """Perform synthetic division and evaluate a polynomial at a factor."""
    deflated = np.empty(len(coefficients) - 1, dtype=complex)
    deflated[0] = coefficients[0]
    for i, coeff in enumerate(coefficients[1:-1], start=1):
        deflated[i] = coeff + deflated[i - 1] * factor
    evaluation = coefficients[-1] + deflated[-1] * factor
    return deflated, evaluation