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)
