chapter 1: Working with numbers

1.1 Basic Mathematical Operations

… code-block:: python

>>> 1 + 2
3
>>> 1 + 3.5
4.5
>>> -1 + 2.5
1.5
>>> 100 – 45
55
>>> -1.1 + 5
3.9

>>> 3 * 2
6
>>> 3.5 * 1.5
5.25

>>> 3 / 2
1.5
>>> 4 / 2
2.0

>>> 3 // 2
1

>>> -3 // 2
-2

>>> 9 % 2
1

>>> 2 ** 2
4
>>> 2 ** 10
1024
>>> 1 ** 10
1

>>> 8 ** (1/3)
2.0

>>> 5 + 5 * 5
30
>>> (5 + 5) * 5
50

1.2 Labels: Attaching Names to Numbers

… code-block:: python

>>> a = 3
>>> a + 1
4
>>> a = 5
>>> a + 1
6

1.3 Different Kinds of Numbers

… code-block:: python

>>> type(3)
<class 'int'>
>>> type(3.5)
<class 'float'>
>>> type(3.0)
<class 'float'>

>>> int(3.8)
3
>>> int(3.0)
3

>>> float(3)
3.0

1.4 Working with Fractions

… code-block:: python

u >>> from fractions import Fraction v >>> f = Fraction(3, 4) w >>> f Fraction(3, 4)

>>> Fraction(3, 4) + 1 + 1.5
3.25

>>> Fraction(3, 4) + 1 + Fraction(1/4)
Fraction(2, 1)

1.5 Complex Numbers

… code-block:: python

>>> a = 2 + 3j
>>> type(a)
<class 'complex'>

>>> a = complex(2, 3)
>>> a
(2 + 3j)

>>> b = 3 + 3j
>>> a + b
(5 + 6j)
>>> a - b
(-1 + 0j)

>>> a * b
(-3 + 15j)
>>> a / b
(0.8333333333333334 + 0.16666666666666666j)

>>> z = 2 + 3j
>>> z.real
2.0
>>> z.imag
3.0

>>> z.conjugate()
(2 - 3j)

>>> (z.real ** 2 + z.imag ** 2) ** 0.5
3.605551275463989

>>> abs(z)
3.605551275463989

1.6 Getting User Input

… code-block:: python

u >>> a = input() v 1

>>> a
w '1'

>>> s1 = 'a string'
>>> s2 = "a string"

>>> a = '1'
>>> int(a) + 1
2
>>> float(a) + 1
2.0

>>> int('2.0')
Traceback (most recent call last):
File "<pyshell#26>", line 1, in <module>
int('2.0')
ValueError: invalid literal for int() with base 10: '2.0'

>>> a = float(input())
3/4
Traceback (most recent call last):
File "<pyshell#25>", line 1, in <module>
a=float(input())
ValueError: could not convert string to float: '3/4'

1.8 Handling Exceptions and Invalid Input

… code-block:: python

>>> try:
a = float(input('Enter a number: '))
except ValueError:
print('You entered an invalid number')

Enter a number: 3/4 u You entered an invalid number

>>> a = input('Input an integer: ')

>>> a = int(input())
1
>>> a + 1
2

>>> a = int(input())
1.0
Traceback (most recent call last):
File "<pyshell#42>", line 1, in <module>
a=int(input())
ValueError: invalid literal for int() with base 10: '1.0'

>>> 1.1.is_integer()
False

>>> 1.0.is_integer()
True

1.9 Fractions and Complex Numbers as Input

… code-block:: python

>>> a = Fraction(input('Enter a fraction: '))
Enter a fraction: 3/4
>>> a
Fraction(3, 4)

>>> a = Fraction(input('Enter a fraction: '))
Enter a fraction: 3/0
Traceback (most recent call last):
File "<pyshell#2>", line 1, in <module>
a = Fraction(input('Enter a fraction: '))
File "/usr/lib64/python3.3/fractions.py", line 167, in __new__
raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
ZeroDivisionError: Fraction(3, 0)

>>> try:
a = Fraction(input('Enter a fraction: '))
except ZeroDivisionError:
print('Invalid fraction')
Enter a fraction: 3/0
Invalid fraction

>>> z = complex(input('Enter a complex number: '))
Enter a complex number: 2+3j
>>> z
(2+3j)

>>> z = complex(input('Enter a complex number: '))
Enter a complex number: 2 + 3j
Traceback (most recent call last):
File "<pyshell#43>", line 1, in <module>
z = complex(input('Enter a complex number: '))
ValueError: complex() arg is a malformed string

1.10 Writing Programs That Do the Math for You

Calculating the Factors of an Integer

… code-block:: python

>>> def is_factor(a, b):
if b % a == 0:
return True
else:
return False

>>> is_factor(4, 1024)
True

>>> for i in range(1, 4):
print(i)

>>> for i in range(5):
print(i)

>>> for i in range(1,10,2):
print(i)

‘’’ Find the factors of an integer ‘’’ def factors(b): u for i in range(1, b+1): if b % i == 0: print(i) if __name__ == ‘__main__’: b = input(‘Your Number Please: ‘) b = float(b) v if b > 0 and b.is_integer(): factors(int(b)) else: print(‘Please enter a positive integer’)

Your Number Please: 25 1 5 25

Your Number Please: 15.5 Please enter a positive integer

Generating Multiplication Tables

… code-block:: python

‘’’ enhanced_multi_table.py

Multiplication table printer: Enter the number and the number of multiples to be printed ‘’‘

def multi_table(a, n):

for i in range(1, n+1):

print(‘{0} x {1} = {2}’.format(a, i, a*i))

if __name__ == ‘__main__’:

try:

a = float(input(‘Enter a number: ‘)) n = float(input(‘Enter the number of multiples: ‘)) if not n.is_integer() or n < 0:

print(‘The number of multiples should be a positive integer’)

else:

multi_table(a, int(n))

except ValueError:

print(‘You entered an invalid input’)

Converting Units of Measurement

… code-block:: python

‘’’ enhanced_unit_converter_exit_power.py

Unit converter:

Miles and Kilometers Kilograms and Pounds Celsius and Fahrenheit

‘’‘

def print_menu():

print(‘1. Kilometers to Miles’) print(‘2. Miles to Kilometers’) print(‘3. Kilograms to Pounds’) print(‘4. Pounds to Kilograms’) print(‘5. Celsius to Fahrenheit’) print(‘6. Fahrenheit to Celsius’)

def km_miles():

km = float(input(‘Enter distance in kilometers: ‘)) miles = km / 1.609

print(‘Distance in miles: {0}’.format(miles))

def miles_km():

miles = float(input(‘Enter distance in miles: ‘)) km = miles * 1.609

print(‘Distance in kilometers: {0}’.format(km))

def kg_pounds():

kg = float(input(‘Enter weight in kilograms: ‘)) pounds = kg * 2.205

print(‘Weight in pounds: {0}’.format(pounds))

def pounds_kg():

pounds = float(input(‘Enter weight in pounds: ‘)) kg = pounds / 2.205

print(‘Weight in kilograms: {0}’.format(kg))

def cel_fahren():

celsius = float(input(‘Enter temperature in celsius: ‘)) fahrenheit = celsius* (9 / 5) + 32 print(‘Temperature in fahrenheit: {0}’.format(fahrenheit))

def fahren_cel():

fahrenheit = float(input(‘Enter temperature in fahrenheit: ‘)) celsius = (fahrenheit - 32)*(5/9) print(‘Temperature in celsius: {0}’.format(celsius))

if __name__ == ‘__main__’:

print_menu()

while True:

choice = input(‘Which conversion would you like to do? ‘)

if choice == ‘1’:

km_miles()

if choice == ‘2’:

miles_km()

if choice == ‘3’:

kg_pounds()

if choice == ‘4’:

pounds_kg()

if choice == ‘5’:

cel_fahren()

if choice == ‘6’:

fahren_cel()

answer = input(‘Do you want to exit? (y) for yes ‘) if answer == ‘y’:

break

Finding the Roots of a Quadratic Equation

… code-block:: python

‘’’ Quadratic equation root calculator ‘’’ def roots(a, b, c):

D = (b*b - 4*a*c)**0.5 x_1 = (-b + D)/(2*a) x_2 = (-b - D)/(2*a) print(‘x1: {0}’.format(x_1)) print(‘x2: {0}’.format(x_2))

if __name__ == ‘__main__’:

a = input(‘Enter a: ‘) b = input(‘Enter b: ‘) c = input(‘Enter c: ‘) roots(float(a), float(b), float(c))