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
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.permutations import 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))
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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
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.permutations import Permutation
a = Permutation([[ 2 , 4 , 0 ],
[ 3 , 1 , 2 ],
[ 1 , 5 , 6 ]])
print ( "Permutation a - commutator form : " , a.commutator(a))
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Output :
Permutation a – commutator form : Permutation([], size=7)
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