如何在Python中获得负十进制数的十进制平方根？ [英] How do I get a Decimal square root of a negative Decimal number in Python?

问题描述

要获取负数的平方根，可以使用cmath.sqrt。但是结果的实部或imag部分仍然是浮点数：

To get the sqaure root of a negative number we could use cmath.sqrt. But either the real part or the imag part of the result is still a float:

type（cmath.sqrt（Decimal（-8）） .imag）

结果：浮点数

如何获得小数平方负数的根？

How do I get a Decimal square root of a negative Decimal number?

对于正数，我们可以使用：十进制（8）.sqrt（）

For a positive number we could use: Decimal (8).sqrt ()

结果仍然是小数。但是它不适用于负数：十进制（-8）.sqrt（）

The result is still a Decimal. But it doesn't work on negative numbers: Decimal (-8).sqrt ()

{InvalidOperation} []

{InvalidOperation}[]

推荐答案

您可以使用该方法实现 ComplexDecimal（）类功能。

You could implement a ComplexDecimal() class with that functionality.

下面是一些让您前进的代码：

Here is some code to get you going:

from decimal import Decimal


class ComplexDecimal(object):
    def __init__(self, value):
        self.real = Decimal(value.real)
        self.imag = Decimal(value.imag)

    def __add__(self, other):
        result = ComplexDecimal(self)
        result.real += Decimal(other.real)
        result.imag += Decimal(other.imag)
        return result

    __radd__ = __add__

    def __str__(self):
        return f'({str(self.real)}+{str(self.imag)}j)'

    def sqrt(self):
        result = ComplexDecimal(self)
        if self.imag:
            raise NotImplementedError
        elif self.real > 0:
            result.real = self.real.sqrt()
            return result
        else:
            result.imag = (-self.real).sqrt()
            result.real = Decimal(0)
            return result

x = ComplexDecimal(2 + 3j)
print(x)
# (2+3j)
print(x + 3)
# (5+3j)
print(3 + x)
# (5+3j)

print((-8) ** (0.5))
# (1.7319121124709868e-16+2.8284271247461903j)
print(ComplexDecimal(-8).sqrt())
# (0+2.828427124746190097603377448j)
print(type(ComplexDecimal(8).sqrt().imag))
# <class 'decimal.Decimal'>

然后您需要自己实现乘法，除法等，但这应该非常简单。

and then you need to implement multiplication, division, etc. yourself, but that should be pretty straightforward.

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