"""
This is an implementation of logarithmic series in Python.
Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series
"""

def logarithmic_series(x: float, n_terms: int = 5, expand: bool = False) -> list:
    """
    Returns the logarithmic series for a number x (log x) upto n terms.
    
    Parameters:
        x: a floating point number for log(x)
        n_terms: number of terms to be computed
        expand: Set this flag to get the terms as real numbers, unset for unsolved expressions
    
    Examples:
        >>> logarithmic_series(3)
        ['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5']
        
        >>> logarithmic_series(-3)
        ['-(4^1)/1', '(4^2)/2', '-(4^3)/3', '(4^4)/4', '-(4^5)/5']
        
        >>> logarithmic_series(3, 10)
        ['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5', '-(2^6)/6', '(2^7)/7', '-(2^8)/8', '(2^9)/9', '-(2^10)/10']
        
        >>> logarithmic_series(3, expand=True)
        [2.0, -2.0, 2.6666666666666665, -4.0, 6.4]
    """
    n_times_x_minus_1: float = x-1
    n: int = 1
    series: list = []
    for _ in range(n_terms):
        if (expand):
            series.append(((-1)**(n+1))*(n_times_x_minus_1/n))
            n_times_x_minus_1 *= (x-1)
        else:
            sign: str = '-' if (-1)**(n+1) == -1 else ''
            term: str = sign+'('+str(x-1)+'^'+str(n)+')'+'/'+str(n)
            if (term.startswith("-(-")):
                term = '('+term[3::]
            elif (term.startswith("(-")):
                term = "-("+term[2::]
            series.append(term)
        n += 1
    return series

if (__name__ == "__main__"):
    import doctest
    doctest.testmod()