def dataframe_to_tsfile(dataframe: pd.DataFrame,
                        file_path: str,
                        table_name: Optional[str] = None,
                        time_column: Optional[str] = None,
                        tag_column: Optional[list[str]] = None,
                        ):
    """
    Write a pandas DataFrame to a TsFile by inferring the table schema from the DataFrame.
    This function automatically infers the table schema based on the DataFrame's column
    names and data types, then writes the data to a TsFile.
    Parameters
    ----------
    dataframe : pd.DataFrame
        The pandas DataFrame to write to TsFile.
        - If a 'time' column (case-insensitive) exists, it will be used as the time column.
        - Otherwise, the DataFrame index will be used as timestamps.
        - All other columns will be treated as data columns.
    file_path : str
        Path to the TsFile to write. Will be created if it doesn't exist.
    table_name : Optional[str], default None
        Name of the table. If None, defaults to "table".
    time_column : Optional[str], default None
        Name of the time column. If None, will look for a column named 'time' (case-insensitive),
        or use the DataFrame index if no 'time' column is found.
    tag_column : Optional[list[str]], default None
        List of column names to be treated as TAG columns. All other columns will be FIELD columns.
        If None, all columns are treated as FIELD columns.
    Returns
    -------
    None
    Raises
    ------
    ValueError
        If the DataFrame is empty or has no data columns.
    """