间隔符号？

Question

我想为实数的间隔制作一个Python类。与数学符号最密切相关的语法是Interval([a, b))，或者甚至更好，Interval[a, b)来构造满足x的所有真实a <= x < b的区间。

是否可以构造一个可以处理这种语法的类？

Answer 1

无法修复＆＃34;通过创建自定义类，语法上无效的python。

我认为你在python中最接近数学区间符号的是

Interval('[a, b)')

如果您将间隔作为参数传递给函数，并且函数在使用它们之前将其参数转换为适当的类型，则这种方式会变得更加轻量级。例如：

def do_foo(interval, bar, baz):
    interval = Interval(interval)
    # do stuff

do_foo('[3,4)', 42, true)

Possible implementation：

import re

class Interval:
    def __init__(self, interval):
        """Initialize an Interval object from a string representation of an interval
           e.g: Interval('(3,4]')"""
        if isinstance(interval, Interval):
            self.begin, self.end = interval.begin, interval.end
            self.begin_included = interval.begin_included
            self.end_included = interval.end_included
            return
        number_re = '-?[0-9]+(?:.[0-9]+)?'
        interval_re = ('^\s*'
                       +'(\[|\()'  # opeing brecket
                       + '\s*'
                       + '(' + number_re + ')'  # beginning of the interval
                       + '\s*,\s*'
                       + '(' + number_re + ')'  # end of the interval
                       + '\s*'
                       + '(\]|\))'  # closing brecket
                       + '\s*$'
                      )
        match = re.search(interval_re, interval)
        if match is None:
            raise ValueError('Got an incorrect string representation of an interval: {!r}'. format(interval))
        opening_brecket, begin, end, closing_brecket = match.groups()
        self.begin, self.end = float(begin), float(end)
        if self.begin >= self.end:
            raise ValueError("Interval's begin shoud be smaller than it's end")
        self.begin_included = opening_brecket == '['
        self.end_included = closing_brecket == ']'
        # It might have been batter to use number_re = '.*' and catch exeptions float() raises instead

    def __repr__(self):
        return 'Interval({!r})'.format(str(self))

    def __str__(self):
        opening_breacket = '[' if self.begin_included else '('
        closing_breacket = ']' if self.end_included else ')'
        return '{}{}, {}{}'.format(opening_breacket, self.begin, self.end, closing_breacket)

    def __contains__(self, number):
        if self.begin < number < self.end:
            return True
        if number == self.begin:
            return self.begin_included
        if number == self.end:
            return self.end_included

Answer 2

您无法更改Python现有的语法规则（无需更改整个语言），但您可以接近您想要的内容：

class Interval(object):
    def __init__(self, left_bracket, a, b, right_bracket):
        if len(left_bracket) !=1 or left_bracket not in '[(':
            raise ValueError(
                'Unknown left bracket character: {!r}'.format(left_bracket))
        if len(right_bracket) !=1 or right_bracket not in '])':
            raise ValueError(
                'Unknown right bracket character: {!r}'.format(right_bracket))

        if a < b:
            self.lower, self.upper = a, b
        else:
            self.lower, self.upper = b, a

        self.left_bracket, self.right_bracket = left_bracket, right_bracket

        if left_bracket == '[':
            if right_bracket == ']':
                self._contains = (
                    lambda self, val: self.lower <= val <= self.upper)
            else:
                self._contains = (
                    lambda self, val: self.lower <= val <  self.upper)
        else:
            if right_bracket == ']':
                self._contains = (
                    lambda self, val:  self.lower < val <= self.upper)
            else:
                self._contains = (
                    lambda self, val:  self.lower < val <  self.upper)

    __contains__ = lambda self, val: self._contains(self, val)

    def __str__(self):
        return '{}{}, {}{}'.format(self.left_bracket, self.lower, self.upper,
                                   self.right_bracket)

    def __repr__(self):
        return '{}({!r}, {}, {}, {!r})'.format(self.__class__.__name__,
                self.left_bracket, self.lower, self.upper, self.right_bracket)

if __name__ == '__main__':
    interval1 = Interval('[', 1, 3, ']')  # closed interval
    interval2 = Interval('[', 1, 3, ')')  # half-open interval

    print('{} in {}? {}'.format(3, interval1,  3 in interval1))
    print('{} in {}? {}'.format(3, interval2,  3 in interval2))

输出：

3 in [1, 3]? True
3 in [1, 3)? False

注意：a和b参数可以是任何可以比较的类型。

Answer 3

你不能使这个确切的语法工作。但是你可以通过覆盖相关的比较方法来做这样的事情：

a <= Interval() < b

然后，整个表达式可以返回一个新的Interval对象，其中包含大于或等于a且严格小于b的所有内容。 Interval()本身可以解释为从负无穷大到正无穷大的完全开放区间（即所有实数的无界区间），而Interval() < b本身可以指从上方但不是从下方。

NumPy使用类似的技术进行数组比较操作（其中A＆lt; B表示＆＃34;返回1和0的数组，对应于A的每个元素是否小于B＆＃34的相应元素;）