SymPy | Partition.RGS_generalized() in Python

Partition.RGS_generalized() : RGS_generalized() is a sympy Python library function that calculates the m + 1 generalized unrestricted growth strings (string where a[i] is the block in which element i occurs) and then return it as rows in matrix.

Restricted growth strings – string in which each character, a_i results in the Block (B_i) in which the corresponding element belongs.

Syntax : sympy.combinatorics.partitions.Partition.RGS_generalized()

Return : generalized unrestricted growth strings as row of matrix.

Code #1 : RGS_generalized() Example

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# Python code explaining
# SymPy.RGS_generalized()

# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.partitions import RGS_generalized

# Using from sympy.combinatorics.partitions.Partition.RGS_generalized() method
p = RGS_generalized(3)

print ("Row of Matrix : \n", p)

Output :

Row of Matrix :
Matrix([[1, 1, 1, 1], [1, 2, 3, 0], [2, 5, 0, 0], [5, 0, 0, 0]])

Code #2 : RGS_generalized() Example

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# Python code explaining
# SymPy.RGS_generalized()

# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.partitions import RGS_generalized

# Using from sympy.combinatorics.partitions.Partition.RGS_generalized() method
p = RGS_generalized(-1)

print ("Row of Matrix : \n", p)

Output :

Row of Matrix :
Matrix(0, 0, [])