Python | SymPy Permutation.inversion_vector()

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Permutation.inversion_vector() : inversion_vector() is a sympy Python library function that returns the inversion_vector value of the permutation in argument.
The inversion vector includes those elements whose value indicates the no. of elements in the permutation that are < it and lie on its right hand side.

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

Return :
inversion_vector value of the permutation

Code #1 : inversion_vector() Example

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

Output :

Permutation a – inversion_vector form : [2, 2, 0] Permutation b – inversion_vector form : [1, 2, 3, 2, 1]

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

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