Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts

Program for Find sum of even factors of a number

import math

def sumofFactors(n) :

if (n % 2 != 0) :

return 0

res = 1

for i in range(2, (int)(math.sqrt(n)) + 1) :

count = 0

curr_sum = 1

curr_term = 1

while (n % i == 0) :

count= count + 1

n = n // i

if (i == 2 and count == 1) :

curr_sum = 0

curr_term = curr_term * i

curr_sum = curr_sum + curr_term

res = res * curr_sum

if (n >= 2) :

res = res * (1 + n)

return res

n = 18

print(sumofFactors(n))


Program for Legendre\’s Conjecture

import math

def isprime( n ):

i = 2

for i in range (2, int((math.sqrt(n)+1))):

if n%i == 0:

return False

return True

def LegendreConjecture( n ):

print ( "Primes in the range ", n*n

, " and ", (n+1)*(n+1)

, " are:" )

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

if(isprime(i)):

print (i)

n = 50

LegendreConjecture(n)


Finding sum of digits of a number until sum becomes single digit

import math

def digSum( n):

sum = 0

while(n > 0 or sum > 9):

if(n == 0):

n = sum

sum = 0

sum += n % 10

n /= 10

return sum

n = 1234

print (digSum(n))


Program for Product of unique prime factors of a number

import math

def productPrimeFactors(n):

product = 1

if (n % 2 == 0):

product *= 2

while (n%2 == 0):

n = n/2

for i in range (3, int(math.sqrt(n)), 2):

if (n % i == 0):

product = product * i

while (n%i == 0):

n = n/i

if (n > 2):

product = product * n

return product

n = 44

print (int(productPrimeFactors(n)))


Legendre's Conjecture program

import math

def isprime( n ):

i = 2

for i in range (2, int((math.sqrt(n)+1))):

if n%i == 0:

return False

return True

def LegendreConjecture( n ):

print ( "Primes in the range ", n*n

, " and ", (n+1)*(n+1)

, " are:" )

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

if(isprime(i)):

print (i)

n = 50

LegendreConjecture(n)



Program to find LCM

def calculate_lcm(x, y):  

    if x > y:  

        greater = x  

    else:  

        greater = y  

    while(True):  

        if((greater % x == 0) and (greater % y == 0)):  

            lcm = greater  

            break  

        greater += 1  

    return lcm    

num1 = int(input("Enter first number: "))  

num2 = int(input("Enter second number: "))  

print("The L.C.M. of", num1,"and", num2,"is", calculate_lcm(num1, num2))  


Solving linear mathematical equations with two variable

import numpy as np
A=np.array([[1.5,1],[3.75,4]])
B=np.array([1800,900])
x=np.linalg.solve(A,B)
print("Values of A and B variables:",x)
h=np.allclose(np.dot(A, x), B)
print("Substitution of two variables in equation to validate:",h)

Mathematical operators on Numpy Array and List

import numpy as np

a = np.array([1, 2, 3])
print(type(a))           
print('Numpy Array:\n',a)
print('Addition of Numpy Arrays with constant:\n',a+13)
print('Addition of Numpy Arrays:\n',a+a)
print('Multiplication of Numpy Arrays with constant:\n',a*3)
print('Multiplication of Numpy Arrays with another:\n',a*a)
print('Divison of Numpy Arrays with constant:\n', a/3)
print('Divison of Numpy Arrays with another:\n', a/a)
print('Power of Numpy Arrays with constant:\n', a**4)
print('Power of Numpy Arrays with another:\n', a**a)
print('Remainder of Numpy Arrays with constant:\n',a%2)
print('Remainder of Numpy Arrays with another:\n',a%a)
print('Subtraction of Numpy Arrays with constant:\n', a-1)
print('Subtraction of Numpy Arrays with another:\n', a-a)

try:
  a1=[1, 2, 3]
  print('\n',type(a1))
  print('Common List:\n', a1)
  print('Addition of Lists:\n',a1+a1)
  print('Multiplication of List with constant:\n',a1*3)
  print(a1+13) #error
  print(a1*a1) #error
  print(a1/3) #error
  print(a1/a1) #error
  print(a1**4) #error
  print(a1*a1) #error
  print(a1%2) #error
  print(a1%a1) #error
  print(a1-1) #error
  print(a1-a1) #error
except TypeError:
  print('TypeError')
 

Perimeter and area of a circle and finding Natural Exponential Function

import math
r=int(raw_input('Enter the radius of circle:'))
perimeter=2*math.pi*r
print 'Perimeter of a circle :',perimeter
area=math.pi*(r**2)
print 'Area of acircle :',area

x=int(raw_input('Enter the value of x in y=e**x:'))
y=math.e**x
print 'Natural Exponential Function value :',y

Trigonometric Functions

import math
d=int(raw_input('Enter the angle in degree:'))
x= math.radians(d)
print 'Corresponding Radians is:',x           #Converts angle from degrees to radians.
f1=math.acos(x)                                                          # Return the arc cosine of x
print 'acos',f1
f2=math.asin(x)                                                           #Return the arc sine of x
print 'asin',f2
f3=math.atan(x)                                                          #Return the arc tangent of x
print 'atan',f3
f4=math.cos(x)                                                            #Return the cosine of x
print 'cos',f4
f5=math.sin(x)                                                             #Return the sine of x
print 'sin',f5
f6= math.tan(x)                                                            # Return the tangent of x
print 'tan',f6

u=int(raw_input('Enter the value of x:'))
v=int(raw_input('Enter the value of y:'))
e=math.hypot(u, v)                                                 #Return the Euclidean norm, sqrt(u*u + v*v)
print 'The Euclidean norm:',e