Why is not 'decimal.Decimal(1)' an instance of 'numbers.Real'?

Question

I try to check if a variable is an instance of a number of any type (int, float, Fraction, Decimal, etc.).

I cam accross this question and its answer: How to properly use python's isinstance() to check if a variable is a number?

However, I would like to exclude complex numbers such as 1j.

The class numbers.Real looked perfect but it returns False for Decimal numbers...

from numbers Real
from decimal import Decimal

print(isinstance(Decimal(1), Real))
# False

In contradiction, it works fine with Fraction(1) for example.

The documentation describes some operations which should work with the number, I tested them without any error on a decimal instance. Decimal objects cannot contains complex numbers moreover.

So, why isinstance(Decimal(1), Real) would return False?

Answer 1

So, I found the answer directly in the source code of cpython/numbers.py:

## Notes on Decimal
## ----------------
## Decimal has all of the methods specified by the Real abc, but it should
## not be registered as a Real because decimals do not interoperate with
## binary floats (i.e.  Decimal('3.14') + 2.71828 is undefined).  But,
## abstract reals are expected to interoperate (i.e. R1 + R2 should be
## expected to work if R1 and R2 are both Reals).

Indeed, adding Decimal to float would raise a TypeError.

In my point of view, it violates the principle of least astonishment, but it does not matter much.

As a workaround, I use:

import numbers
import decimal

Real = (numbers.Real, decimal.Decimal)

print(isinstance(decimal.Decimal(1), Real))
# True