SymPy | Permutation.signature() in Python

Permutation.signature() : signature() is a sympy Python library function that returns the signature of the permutation needed to place the elements of the permutation in canonical order.
Signature = (-1)^<number of inversions>

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

Return : signature of the permutation.



Code #1 : signature() Example

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

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Output :

Permutation a – signature form : 1
Permutation b – signature form : -1

Code #2 : signature() Example

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

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Output :

Permutation a – signature form : 1




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