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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def add_time_variables(df, reindex = True):
 """ Return a DataFrame with variables for weekday index, weekday name, timedelta through day, fraction through day, hours through day and days through week added, optionally with the index set to datetime and the variable `datetime` removed. It is assumed that the variable `datetime` exists. """

    if not "datetime" in df.columns:
        log.error("field datetime not found in DataFrame")
        return False
    df["datetime"]             = pd.to_datetime(df["datetime"])
    df["month"]                = df["datetime"].dt.month
    df["month_name"]           = df["datetime"].dt.strftime("%B")
    df["weekday"]              = df["datetime"].dt.weekday
    df["weekday_name"]         = df["datetime"].dt.weekday_name
    df["time_through_day"]     = df["datetime"].map(
                                     lambda x: x - datetime.datetime.combine(
                                         x.date(),
                                         datetime.time()
                                     )
                                 )
    df["fraction_through_day"] = df["time_through_day"].map(
                                     lambda x: x / datetime.timedelta(hours = 24)
                                 )
    df["hour"]                 = df["datetime"].dt.hour
    df["hours_through_day"]    = df["fraction_through_day"] * 24
    df["days_through_week"]    = df.apply(
                                     lambda row: row["weekday"] + row["fraction_through_day"],
                                     axis = 1
                                 )
    df["days_through_year"]    = df["datetime"].dt.dayofyear
    df.index                   = df["datetime"]
    #del df["datetime"]
    return df