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# Python | SymPy Permutation.commutator() method

• Last Updated : 26 Aug, 2019

Permutation.commutator() : commutator() is a sympy Python library function that returns the commutator of the partition. Suppose ‘a’ and ‘b’ are part of ‘C’, then the commutator of a and b is the ‘C’ identity iff a and b commute, i.e. ab == ba.

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

Return :
commutator of the partition

Code #1 : commutator() Example

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

Output :

Permutation a – commutator form : Permutation([3, 1, 2, 5, 4, 0])
Permutation b – commutator form : Permutation([5, 1, 2, 0, 4, 3])

Code #2 : commutator() Example – Self Commutator

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

Output :

Permutation a – commutator form : Permutation([], size=7)

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