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Python | SymPy Permutation.commutes_with() method
• Last Updated : 26 Aug, 2019

Permutation.commutes_with() : commutes_with()
is a sympy Python library function that checks whether the two permutations are commuting. 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.commutes_with()

Return :
checks whether the two permutations are commuting

Code #1 : commutes_with() Example

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

Output :

Permutation a – commutes_with form : False
Permutation b – commutes_with form : False

Code #2 : commutes_with() Example – Self Commutator

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

Output :

Permutation a – commutes_with form : True

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