Mathematically, a fraction can be defined as the ratio a/b, where a and b are integers and b is non zero.
In this challenge, we are going to implement a Fraction class and some methods to support arithmetic and comparison operations on them. Write a Fraction class that meets the following requirements:
Initialisation: Create a Fraction object with a as numerator and b as denominator, e.g. Fraction(5, 6) where a = 5 and b = 6. Validate that a and b are both integers and b is non-zero. If not, print the error message shown below and do not create any variables. The numerator and denominator should also be stored in factorized form, e.g. 4/6 should be stored as 2/3.
Representation: It should be possible to print a Fraction or obtain a string representation of it via the str built-in function. For a positive fraction, this should return the string "x/y" e.g. "5/4". If the fraction is negative, return "- x/y" e.g. "- 5/9" (note the space after the - sign). If the fraction has failed to initialize, detect this (it shouldn't have any instance variables) and return the string "Initialisation Failed".
Arithmetic Operations: Implement suitable methods to support +, -, *, and / operations between two fractions with the usual arithmetic meaning. Return the appropriate factorised Fraction e.g Fraction(2, 3) * Fraction(2, 5) should return Fraction(4, 15). A division operation could result in a zero denominator and this should be catered for by printing the error message described in the initialization section and returning None. If the result of an operation is a negative fraction, return the numerator as the negative integer.
Comparison Operations: Implement suitable methods to compare two Fraction objects using operators ==,!=, <, >, <= and >= with the usual meanings. For ==, apply a tolerance factor of 10^-7.
Instance Method: Implement instance method decimal. This should return the decimal equivalent of the Fraction object to up to seven decimal places e.g. Fraction(1/4).decimal() -> 0.25.
Class Method: Implement class method fraction(decimal) which returns a Fraction object equivalent to decimal to up to seven decimal places e.g. Fraction.fraction(2.5) -> Fraction(5, 2). If the parameter decimal is an integer, set the denominator in Fraction to 1.
str(Fraction(2, -3)) ➞ ""- 2/3"
str(Fraction(3, 0)) ➞ "Initialisation Failed"
# Should print "numerator must be an integer and denominator a non zero integer".
Fraction(1, 5) + Fraction(3, 10) ➞ Fraction(1, 2)
Fraction(5, 2) * Fraction(6, -10) ➞ Fraction(-3, 2)
Fraction(0, 3) / Fraction(0, 5) ➞ None
# Should print "numerator must be an integer and denominator a non zero integer".
Fraction(-4, 5) > Fraction(-3, 5) ➞ False
Fraction(10, 9) < Fraction(2, 1) ➞ True
Fraction.fraction(11) ➞ Fraction(11, 1)
Fraction(5, 9).decimal() ➞ 0.5555556You will need to use a technique called operator overloading to successfully complete this challenge. This requires the use of what are termed magic or dunder methods in Python (Resources have a useful link for these). If you need to brush up on arithmetic with fractions, there's a link for that too.