Python | SymPy Permutation.commutator() method

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)