PYTHON ONLY, PLEASE FOLLOW DIRECTIONS GIVEN! DIRECTIONS: import stdio import sys

Question

PYTHON ONLY, PLEASE FOLLOW DIRECTIONS GIVEN!

DIRECTIONS:

import stdio
import sys

# Returns the GCD of p and q, computed using Euclid's algorithm.
def _gcd(p, q):
return p if q == 0 else _gcd(q, p % q)

class Rational:
"""
Represents a rational number.
"""

def __init__(self, x, y=1):
"""
Constructs a new rational given its numerator and denominator.
"""

d = _gcd(x, y)
self._x = ...
self._y = ...

def __add__(self, other):
"""
Returns the sum of self and other.
"""

...

def __sub__(self, other):
"""
Returns the difference of self and other.
"""

...

def __mul__(self, other):
"""
Returns the product of self and other.
"""

...

def __abs__(self):
"""
Return the absolute value of self.
"""

...

def __str__(self):
"""
Returns a string representation of self.
"""

a, b = self._x, self._y
if a == 0 or b == 1:
return str(a)
if b < 0:
a *= -1
b *= -1
return str(a) + '/' + str(b)

# Test client [DO NOT EDIT]. Reads an integer n as command-line argument and
# writes the value of PI computed using Leibniz series:
# PI/4 = 1 - 1/3 + 1/5 - 1/7 + ... + (-1)^n/(2n-1).
def _main():
n = int(sys.argv[1])
total = Rational(0)
sign = Rational(1)
for i in range(1, n + 1):
total += sign * Rational(1, 2 * i - 1)
sign *= Rational(-1)
stdio.writeln(4.0 * total._x / total._y)

if __name__ == '__main__':
_main()

Problem 5. (Rational Number) Define a data type rational in rational.py that represents a rational number, ie, a number of the form a/b where a and b 0 are integers. The data type must support the following API method description Rational (x, y) new rational r from the numerator r and denominator y sum of r and s r 8 difference of r and s product of r and s abs(r) absolute value of r the string representation of r as 'x/y str (r) Use the private function -gedo to ensure that the numerator and denominator never have any common factors. For example, the rational number 2/4 must be represented as 1/2. python. rational .py 100 3.13159290356

Explanation / Answer

import stdio
import sys

# Returns the GCD of p and q, computed using Euclid's algorithm.
def _gcd(p, q):
return p if q == 0 else _gcd(q, p % q)

class Rational:
"""
Represents a rational number.
"""
def __init__(self, x, y=1):
"""
Constructs a new rational given its numerator and denominator.
"""
d = _gcd(x, y)
self._x = x/d
self._y = y/d
def __add__(self, other):
"""
Returns the sum of self and other.
"""
x = self._x*other._y + self._y*other._x
y = self._y*other._y
rec = Rational(x, y)
return rec
def __sub__(self, other):
"""
Returns the difference of self and other.
"""
x = self._x*other._y - self._y*other._x
y = self._y*other._y
rec = Rational(x, y)
return rec
def __mul__(self, other):
"""
Returns the product of self and other.
"""
x = self._x*other._x
y = self._y*other._y
rec = Rational(x, y)
return rec
def __abs__(self):
"""
Return the absolute value of self.
"""
x = abs(self._x)
y = abs(self._y)
rec = Rational(x, y)
return rec
def __str__(self):
"""
Returns a string representation of self.
"""
a, b = self._x, self._y
if a == 0 or b == 1:
return str(a)
if b < 0:
a *= -1
b *= -1
return str(a) + '/' + str(b)

# Test client [DO NOT EDIT]. Reads an integer n as command-line argument and
# writes the value of PI computed using Leibniz series:
# PI/4 = 1 - 1/3 + 1/5 - 1/7 + ... + (-1)^n/(2n-1).
def _main():
n = int(sys.argv[1])
total = Rational(0)
sign = Rational(1)
for i in range(1, n + 1):
total += sign * Rational(1, 2 * i - 1)
sign *= Rational(-1)
stdio.writeln(4.0 * total._x / total._y)
if __name__ == '__main__':
_main()

# code link: https://paste.ee/p/TkBxj

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