+

# SymPy | Permutation.rank () in Python

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

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

Return: lexicographic rank of the permutation

Code # 1: rank () Example

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

Output:

Permutation a - rank form: 2461