7^(h<XdZddlmZddlmZddlmZddlmZGddZ d Z d Z y ) a Interval Arithmetic for plotting. This module does not implement interval arithmetic accurately and hence cannot be used for purposes other than plotting. If you want to use interval arithmetic, use mpmath's interval arithmetic. The module implements interval arithmetic using numpy and python floating points. The rounding up and down is not handled and hence this is not an accurate implementation of interval arithmetic. The module uses numpy for speed which cannot be achieved with mpmath. ) int_valued) fuzzy_and) nsimplify)intervalMembershipceZdZdZdddZedZedZdZdZ d Z d Z d Z d Z d ZdZdZeZdZdZdZdZeZdZdZdZdZdZdZy)intervala: Represents an interval containing floating points as start and end of the interval The is_valid variable tracks whether the interval obtained as the result of the function is in the domain and is continuous. - True: Represents the interval result of a function is continuous and in the domain of the function. - False: The interval argument of the function was not in the domain of the function, hence the is_valid of the result interval is False - None: The function was not continuous over the interval or the function's argument interval is partly in the domain of the function A comparison between an interval and a real number, or a comparison between two intervals may return ``intervalMembership`` of two 3-valued logic values. 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