Python | SymPy Permutation.get_precedence_matrix() method

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Permutation.get_precedence_matrix() : get_precedence_matrix() is a sympy Python library function that calculates the precedence matrix for the permutation in argument by calculating the precedence distance between the two.

p and q represent n jobs. The precedence metric counts the no. of times a job n is preceded by job m in both p and q. This is a commutative matrix.

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

Return :
calculates the precedence matrix for the permutation

Code #1 : get_precedence_matrix() Example

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

Output :

a – get_precedence_matrix :
Matrix([[0, 1, 0, 1, 1, 1],
[0, 0, 0, 0, 1, 1],
[1, 1, 0, 1, 1, 1],
[0, 1, 0, 0, 1, 1],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0]])

b – get_precedence_matrix :
Matrix([[0, 0, 0, 0, 0, 0],
[1, 0, 1, 0, 1, 1],
[1, 0, 0, 0, 1, 1],
[1, 1, 1, 0, 1, 1],
[1, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 1, 0]])

Code #2 : get_precedence_matrix() Example – 2D Permutation

# Python code explaining 
# SymPy.Permutation.get_precedence_matrix() 
  
# importing SymPy libraries 
from sympy.combinatorics.partitions import Partition 
from sympy.combinatorics.permutations import Permutation 
  
# Using from  
# sympy.combinatorics.permutations.Permutation.get_precedence_matrix() method  
  
# creating Permutation 
a = Permutation([[2, 4, 0],  
                 [7, 1, 3], 
                 [8, 5, 6]]) 
  
b = Permutation([[8, 4, 0],  
                 [2, 7, 0], 
                 [1, 6, 7]]) 
      
print ("a get_precedence_matrix : \n", a.get_precedence_matrix()) 
  
print ("\nb get_precedence_matrix : \n", b.get_precedence_matrix()) 

Output :

a get_precedence_matrix :
Matrix([[0, 1, 0, 0, 0, 1, 1, 0, 1],
[0, 0, 0, 0, 0, 1, 0, 0, 0],
[1, 1, 0, 1, 1, 1, 1, 1, 1],
[1, 1, 0, 0, 1, 1, 1, 1, 1],
[1, 1, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 1, 0, 0, 1],
[1, 1, 0, 0, 0, 1, 1, 0, 1],
[0, 1, 0, 0, 0, 1, 0, 0, 0]])

b get_precedence_matrix :
Matrix([[0, 0, 0, 0, 1, 0, 0, 0, 0],
[1, 0, 1, 1, 1, 1, 0, 1, 0],
[1, 0, 0, 0, 1, 1, 0, 1, 0],
[1, 0, 1, 0, 1, 1, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 1, 0, 0, 1, 0],
[1, 1, 1, 1, 1, 1, 0, 1, 0],
[1, 0, 0, 0, 1, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 1, 1, 1, 0]])