Python sympy.subs() method

Python | sympy.reduced_totient() method

Last Updated : 17 Sep, 2019

With the help of sympy.reduced_totient() method, we can find the Carmichael reduced totient function or lambda(n) in SymPy. reduced_totient(n) or $\lambda(n)$ is the smallest m > 0 such that $k^m \equiv 1 \mod n$ for all k relatively prime to n.

Syntax: reduced_totient(n) Parameter: n – It denotes an integer. Returns: Returns the smallest integer m > 0 such that k^m % n is equal to 1 for all k relatively prime to n.

Example #1:

# import reduced_totient() method from sympy 
from sympy.ntheory import reduced_totient 
  
n = 8
  
# Use reduced_totient() method  
reduced_totient_n = reduced_totient(n)  
      
print("lambda({}) =  {} ".format(n, reduced_totient_n))  
# 1 ^ 2 = 1 (mod 8), 3 ^ 2 = 9 = 1 (mod 8), 
# 5 ^ 2 = 25 = 1 (mod 8) and 7 ^ 2 = 49 = 1 (mod 8) 

Output:

lambda(8) =  2

Example #2:

# import reduced_totient() method from sympy 
from sympy.ntheory import reduced_totient 
  
n = 30
  
# Use reduced_totient() method  
reduced_totient_n = reduced_totient(n)  
      
print("lambda({}) =  {} ".format(n, reduced_totient_n))  

Output:

lambda(30) =  4

Python sympy.subs() method

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