TypeError: both arguments should be Rational instances when trying to use fractions

Question

So im trying to write a code that will solve general solutions in calculus and one of my values is a fraction with f1 = fractions.Fraction(2.0, period) but if I use 12.5 as the period it comes back with an error. Code:

from cmath import sin
import math
import re
import operator
import fractions
from decimal import Decimal

amplitude = input("What is the A value?: ")
period = input("What is the P value?: ")
ogperiod = float(period)
period = float(period)


f1 = fractions.Fraction(2.0, period)
print(f1)

But all I get is TypeError: both arguments should be Rational instances full error code:

TypeError                                 Traceback (most recent call last)
Input In [84], in <cell line: 27>()
     23 ogperiod = float(period)
     24 period = float(period)
---> 27 f1 = fractions.Fraction(2.0, period)
     28 print(f1)
     31 bpi = 2 * math.pi

File /opt/homebrew/Cellar/[email protected]/3.9.8/Frameworks/Python.framework/Versions/3.9/lib/python3.9/fractions.py:152, in Fraction.__new__(cls, numerator, denominator, _normalize)
    147     numerator, denominator = (
    148         numerator.numerator * denominator.denominator,
    149         denominator.numerator * numerator.denominator
    150         )
    151 else:
--> 152     raise TypeError("both arguments should be "
    153                     "Rational instances")
    155 if denominator == 0:
    156     raise ZeroDivisionError('Fraction(%s, 0)' % numerator)

TypeError: both arguments should be Rational instances

Answer 1

I found that one problem is to assign a float to period. Fraction class has a constructor that accepts two values (the numerator and the denominator) of a Rational class (see the documentation). Since Python version 3.2, there is the possibility of initialize a Fraction from a float but only using one parameter.

So, if you want to keep the 2 values (2.0 and period), you have to change 2.0 to 2 and use period as int (loosing precision). So, your code will be:

f1 = fractions.Fraction(2, int(period))

---

EDIT:

If you want to keep the precision of period, it's better to convert it to a fraction and do the fractional division to initialize f1. That is:

period = fractions.Fraction(period)
f1 = fractions.Fraction(2 * period.denominator, period.nominator)

Answer 2

The traceback tells you exactly what the problem is: both the numerator and denominator of the Fraction instance need to be rational numbers - that is, a number that is expressed as the ratio of two integers. Floats are not rational in and of themselves, due to the way they are implemented in hardware. See Is floating point math broken? for details.

Basically, the numerator and denominator of a fractions.Fraction instance need to be either ints or Fractions themselves.