SymPy | Permutation.rank() in Python

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Permutation.rank() : rank() is a sympy Python library function that returns the lexicographic rank of the permutation.

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

Return : lexicographic rank of the permutation

Code #1 : rank() Example

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

Output :

Permutation a – rank form : 16
Permutation b – rank form : 191

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

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