Python | SymPy Permutation.index() method

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Permutation.index() : index() is a sympy Python library function that returns the index value of the permutation in argument.

Index of a permutation = Sum of all subscripts j such that permutation[j] is greater than permutation[j+1].

Syntax :
sympy.combinatorics.permutations.Permutation.index()

Return :
index value of the permutation

Code #1 : index() Example

# Python code explaining 
# SymPy.Permutation.index() 
  
# importing SymPy libraries 
from sympy.combinatorics.partitions import Partition 
from sympy.combinatorics.permutations import Permutation 
  
# Using from sympy.combinatorics.permutations.Permutation.index() method  
  
# creating Permutation 
a = Permutation([[2, 0], [3, 1]]) 
  
b = Permutation([1, 3, 5, 4, 2, 0]) 
  
  
print ("Permutation a - index form : ", a.index()) 
print ("Permutation b - index form : ", b.index()) 

Output :

Permutation a – index form : 1
Permutation b – index form : 9

Code #2 : index() Example – 2D Permutation

# Python code explaining 
# SymPy.Permutation.index() 
  
# importing SymPy libraries 
from sympy.combinatorics.partitions import Partition 
from sympy.combinatorics.permutations import Permutation 
  
# Using from sympy.combinatorics.permutations.Permutation.index() method  
  
# creating Permutation 
a = Permutation([[2, 4, 0],  
                 [3, 1, 2], 
                 [1, 5, 6]]) 
  
  
print ("Permutation a - index form : ", a.index()) 