Issue
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)
result: float
How do I get a Decimal square root of a negative Decimal number?
For a positive number we could use: Decimal (8).sqrt ()
The result is still a Decimal. But it doesn't work on negative numbers: Decimal (-8).sqrt ()
{InvalidOperation}[]
Solution
You could implement a ComplexDecimal()
class with that functionality.
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'>
and then you need to implement multiplication, division, etc. yourself, but that should be pretty straightforward.
Answered By - norok2 Answer Checked By - Candace Johnson (PHPFixing Volunteer)
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