Python| sympy.reduced_totient() 方法

借助sympy.reduced_totient()方法，我们可以在 SymPy 中找到 Carmichael 约简函数或 lambda(n)。 reduce_totient(n)或$\lambda(n)$是最小的m > 0使得$k^m \equiv 1 \mod n$对于所有k与n互质。

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.

示例 #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)

输出：

lambda(8) =  2 

示例 #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)) 

输出：

lambda(30) =  4