print (12*14)

print ( 5 ** 0.5 )

from math import *
print ( sqrt(5) )

""" root2.py 
    To compute the root of 5 
    written for Programming in Physics """

# import library
from math import *

# main program
print ( sqrt(5) )  # calculate square root

# Solving ax^2 + bx + c = 0 for a=1, b=3, c=-4
from math import *

print ( (-3 + sqrt(3*3 -4*1*(-4))) / (2*1) )
print ( (-3 - sqrt(3*3 -4*1*(-4))) / (2*1) )

# Solving ax^2 + bx + c = 0 for a=1, b=3, c=-4
from math import *

a = 1
b = 3
c = -4
print ( (-b + sqrt(b**2 -4*a*c)) / (2*a) )
print ( (-b - sqrt(b**2 -4*a*c)) / (2*a) )

# Solving ax^2 + bx + c = 0 for a=1, b=3, c=-4
from math import *

a = 1
b = 3
c = -4
D = b**2 -4*a*c # determinant

x1 = (-b + sqrt(D)) / (2*a) # 1st root 
x2 = (-b - sqrt(D)) / (2*a) # 2nd root
print ( x1, x2)

# Solving ax^2 + bx + c = 0
from math import *

a = 1
b = 3
c = -4
D = b*b-4*a*c # determinant

if D >= 0:
    # indented lines below executed only if expression is true
    x1 = (-b + sqrt(D)) / (2*a) # 1st root
    x2 = (-b - sqrt(D)) / (2*a) # 2nd root
    print (x1, x2)
print ("End of execution")

# Solving ax^2 + bx + c = 0
from math import *

a = 1
b = 3
c = -4
D = b*b-4*a*c # determinant

if D >= 0:
    # indented lines below executed only if expression is true
    x1 = (-b + sqrt(D)) / (2*a) # 1st root
    x2 = (-b - sqrt(D)) / (2*a) # 2nd root
    print (x1, x2)
else:
    print ( "no solution" )

print (0)
print (1)
print (2)
print (3)
print (4)

i = 0 

print (i)  # i = 0
i = i+1   

print (i)  # i = 1
i = i+1

print (i)  # i = 2
i = i+1

print (i)  # i = 3
i = i+1

print (i)  # i = 4
i = i+1

i = 0; 
while i < 5:
    print (i)  
    i = i+1   

# direct approach to calculate 5! (factorial of 5)
x = 1 * 2 * 3 * 4 * 5
print (x)

x = 1

i = 1; x = x * i # x=1  
i = 2; x = x * i # x=1.2
i = 3; x = x * i # x=1.2.3
i = 4; x = x * i # x=1.2.3.4
i = 5; x = x * i # x=1.2.3.4.5

print (x)

x = 1
i = 1

x = x * i; i = i + 1 # x=1  i=2
x = x * i; i = i + 1 # x=1.2  i=3
x = x * i; i = i + 1 # x=1.2.3  i=4
x = x * i; i = i + 1 # x=1.2.3.4  i=5
x = x * i; i = i + 1 # x=1.2.3.4.5  i=6

print (x)

# using while-loop to calculate n! (factorial of n)
n = 5
x = 1
i = 1
while i <= n:
    x = x * i
    i = i + 1
print (x)

# using while-loop to calculate n! (factorial of n)
n = 5
x = 1
i = 1
while i <= n:
    x = x * i
    i = i + i
print (x)

# using while-loop to calculate n! (factorial of n)
n = 5
x = 1
i = 1
while i <= n:
    x = x * i
    print ("x = ", x) # debugging
    i = i + i
    print ("i = ", i) # debugging
print (x)

x1 = 5
x2 = 3*2 
x3 = 5/4        # float point division
x4 = 8/4        # float point division
x5 = 7%4        # remainder
x6 = int(2.6)   # type conversion, truncating to integer
x7 = round(2.6) # round up to integer
x8 = 2**100     # a very large integer
print( x1, x2, x3, x4 )
print( x5, x6, x7, x8 )
print( type(5) )  # output data type of a value
print( type(x1), type(x3), type(x4) ) # output data type of variables

x1 = 6.022e23         # floating point constant assigned to x1
x2 = 1e300 * 1e100  # overflow -> inf.
x3 = 1e-300 / 1e100 # underflow -> 0
x4 = 1 + 1e-15       # -> 1.000000000000001 
x5 = 1 + 1e-16       # -> 1.0  (why not 1.0000000000000001 ?)
x6 = (1 + 0.1) -1    # -> 0.10000000000000009  (why not 0.1 ?)
print(x1, x2, x3, x4, x5, x6)

x = 3 < 4 
print( 3 > 4, x, x+1, type(x) )

s = "a"           # a string with one character, i.e. length = 1
print(s, ord(s))  # print the character and its ASCII code 
i = 97
print(i, chr(i))  # print the ASCII code and the represented character
print(chr(i+1))

X = [1, 4, 9, 16, 25, 36] # create a list of integers
print(X)                  # output whole list
print(X[0], X[4])         # output elements 0 and 4

L = [ 1, 3.1416, True, "A", "Hello" ]
print(type(L), type(L[0]), type(L[1]), type(L[2]), type(L[3]), type(L[4]))

X = [1, 4, 9, 16, 25, 36] # create a list of integers
X[1]=5; print(X)          # modify element 1
X.append(49); print(X)    # append a value as last element
X.insert(3,10); print(X)  # insert a value as element 3
del X[3]; print(X)        # delete element 3
X.remove(36); print(X)    # remove the first occurence element by value

R = range(5)  # create a range
print( R, type(R) )
X = list(R)   # convert the range to a list
print( X, type(X) )

print( list( range(10) ) )     # from 0 to 9
print( list( range(0,10) ) )   # from 0 to 9, i.e. same as range(10)
print( list( range(1,11) ) )   # from 1 to 10
print( list( range(1,11,2) ) ) # from 1 to 10 with a step 2

# solving ax^2 + bx + c = 0 for a=1, b=3, c=-4
from math import *

a=1
b=3
c=-4

if a != 0: 
    # quadratic equation
    D = b*b-4*a*c
    if D >= 0:
        x1 = (-b + sqrt(D))/(2*a) # 1st root
        x2 = (-b - sqrt(D))/(2*a) # 2nd root
        print(x1, x2)
else:
    # linear equation
    if b != 0:
        x1 = - c/b
        print(x1) # root

# Total mass of N balls
N = 100        # no. of balls
M = 0          # partial sum, which becomes total mass
i=0            # ball counter
while i < N:   # repeat N times
    m = i      # m_i (mass of i-th ball)
    M += m     # i.e. M=M+m ( add m_i to partial sum )
    i += 1     # i.e. i=i+1 ( increase ball counter )
print(M)

for i in range(5):
    print(i, end = " ")

# Total mass of N balls
N = 100             # no. of balls
M = 0               # partial sum, which becomes total mass
for i in range(N):  # repeat N times
    m = i           # m_i (mass of i-th ball)
    M += m          # i.e. M=M+m ( add m_i to partial sum )
print(M)

L = [1, 1, 2, 3, 5, 8, 13]  # creates a variable of type 'list'
for i in L:
    print(i, end = " ")

# Possible outcomes when rolling 2 dice with nested loops
for i in range(1,7):
    for j in range(1,7):
        print(i, j)

# A deck of cards
for suit in [ 'diamonds', 'clubs', 'hearts', 'spades' ]:
    for number in [ 'A', '2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K' ]:
        print( number, ' of ', suit )

from math import *

r=1
area = 4*pi*r**2 
volume = 4/3*pi*r**3
print(r, area, volume)

r=3
area = 4*pi*r**2 
volume = 4/3*pi*r**3
print(r, area, volume)

r=7
area = 4*pi*r**2 
volume = 4/3*pi*r**3
print(r, area, volume)

from math import *

def Sphere():  # defining a function
    area = 4*pi*r**2 
    volume = 4/3*pi*r**3
    print(r, area, volume)

r=1
Sphere() # calling the function

r=3
Sphere() # calling the function

r=7
Sphere() # calling the function

from math import *

def Sphere(r):  # defining a function
    area = 4*pi*r**2 
    volume = 4/3*pi*r**3
    print(r, area, volume)

Sphere(1)  # r=1
Sphere(3)  # r=3
Sphere(7)  # r=7

from math import *

def Sphere(r, rho):  # defining a function
    area = 4*pi*r**2 
    volume = 4/3*pi*r**3
    mass = rho * volume
    print(r, area, volume, mass)

Sphere(1, 7.87)  # r=1, rho=7.87
Sphere(3, 8.96)  
Sphere(7, 11.36) 

def sqr(x):
    y = x**2
    print(y)

sqr(1.5)

from math import *

def sqr(x):
    y = x**2
    return y  # return a value to the calling line

sum = sqr(1.5) * sin(pi/6)  # the line which calls the function sqr
print(sum)

from math import *

def Sphere(r, rho):  # defining a function
    volume = 4/3*pi*r**3
    mass = rho * volume
    return mass

m1 = Sphere(1, 7.87) 
m2 = Sphere(3, 8.96)  
m3 = Sphere(7, 11.36) 
print (m1+m2+m3)

from math import *

def Sphere(r, rho):  # defining a function
    volume = 4/3*pi*r**3
    mass = rho * volume
    return volume, mass  # returning a list of 2 values

L = Sphere(1, 7.87)  # assign list to variable L
v1 = L[0]            # extract values from list
m1 = L[1]

v2, m2 = Sphere(3, 8.96)  # assign list's values directly to variables
v3, m3 = Sphere(7, 11.36) 

print(v1+v2+v3, m1+m2+m3)

print( "A quote (\' or \") can be included in a string" )
print( "1\t10\t100\n1000\t10000\t100000") # output a simple table of numbers

s1 = "joining" + " strings"  # add two strings
s2 = s1[8:14]  # substring of characters 8 to 14
s3 = s1[8:]    # substring of characters 8 to end of string
s4 = s1[0:-4]  # substring of characters 0 to 4th last character.
print(s1 + '\n' + s2 + '\n' + s3 + '\n' + s4)

x = 1
y = 3
print( f"{x} / {y} = {x/y}")  # an expression inside { } will be evaluated 
print( f"{x:10d}{y:10d}") # controlling width
print( f"{x/y:10.3g}{x/y:10.3g} {x/y*1e10:.3g}")  # controlling width and no. of s.f.

S = input("Please enter your message: ")
print( S, type(S) )

S = input("Enter two numbers: ")
s1, s2 = S.split()       # splitting string into words
print( s1, s2, s1+s2 )   # adding (i.e. joining) strings, rather than adding numbers
x=float(s1); y=float(s2) # converting string to float
print( x, y, x+y )       # adding numbers

ofile = open("numbers.txt", "w")
for i in range(10):
    ofile.write( str(i) + " ")
ofile.close()

from math import *

def f(x):
    return (1/sqrt(2*pi)) * exp(-x**2/2)

ofile = open("normal.txt", "w")
x = -5
while x <= 5:
    ofile.write( str(x) + " " + str(f(x)) + "\n" )
    x += 0.01
ofile.close()

infile = open("normal.txt", "r")
sum=0
for line in infile:
    s1, s2 = line.split()
    x=float(s1); y=float(s2)
    sum += y
print(sum)
infile.close()

import numpy as np
L = [1, 4, 9, 16, 25, 36]   # create a list of integers
X1 = np.array(L); print(X1) # convert to array
X2 = np.append( X1, [49, 64]); print(X2)  # append elements to array
X3 = X2[1:7]; print(X3)  # extract sub-array of elements 1 to 7
X4 = X3[:-2]; print(X4)  # extract sub-array from elements 0 excluding last 2

import numpy as np
X = np.arange(4);         # creates an array, analogous to range
print(X, X+1, 2*X, X**2)  # simple algebric operations of array elements
print(np.exp(X))          # mathematic function for array elements
print(np.sum(X))          # sum up all elements
Y =np.linspace(2,8,4);    # creates an array with 4 equally spaced points
print(Y, X+Y, X*Y)        # simple algebric oerpations of array elements

import numpy as np
X = np.array( [[1, 2, 3], 
               [4, 5, 6]]) # convert a list of list to a 2D array
print(X)        # output entire array
print(X[0,1])   # output element at row 0, column 1

# calculate and plot normal distribution (run in google colab)
from math import *
import matplotlib.pyplot as plt  
import numpy as np  

X = np.linspace(-5,5,101)            # create array of values from -5 to 5 with 101 elements
Y = 1/sqrt(2*pi) * np.exp( -X**2/2 ) # calculate P(x) for each element in X

plt.plot(X, Y)                       # plot a graph
plt.xlabel('x')  
plt.ylabel('P(x)')  
plt.title('Normal distribution')   
plt.savefig('Normal_distribution.jpg')   

class Complex:                 # define a complex data type
    def __init__(self, x, y):  # initialization function of complex variable
        self.re = x            # creates variable re within the complex variable
        self.im = y            # creates variable im within the complex variable

z1 = Complex(1, 1)       # creates a complex variable       
z2 = Complex(1, 2)       # creates another complex variable
z2.im = 5                # variables within complex variable can be modified
zsum = Complex( z1.re + z2.re, z1.im + z2.im )  # addition of complex two variables
print(zsum.re, zsum.im)  # output complex variable by outputing components

class Complex:                 # define a complex data type
    def __init__(self, x, y):  # initialization function of complex variable
        self.re = x            # creates variable re within the complex variable
        self.im = y            # creates variable im within the complex variable

    def add(self, z):          # a method for addition
        return Complex(self.re + z.re, self.im + z.im)

    def __add__(self, z):      # an operator for addition
        return Complex(self.re + z.re, self.im + z.im)

    def __str__(self):         # convert the number to a string, used by print()
        return str(self.re) + '+' + str(self.im) + 'i'

z1 = Complex(1, 1)           
z2 = Complex(1, 3)
print( z1, z2, z1.add(z2) )  # addition using a method
print( z1, z2, z1 + z2 )     # addition using an operator