With the help of sympy.bell() method, we can find Bell number and Bell polynomials in SymPy.
bell(n) –
Syntax: bell(n)
Parameter:
n – It denotes the order of the bell number.Returns: Returns the nth bell number.
Example #1:
# import sympy from sympy import * n = 5print("Value of n = {}".format(n)) # Use sympy.bell() method nth_bell = bell(n) print("Value of nth bell number : {}".format(nth_bell)) |
Output:
Value of n = 5 Value of nth bell number : 52
bell(n, k) –
Syntax: bell(n, k)
Parameter:
n – It denotes the order of the bell polynomial.
k – It denotes the variable in the bell polynomial.Returns: Returns the expression of the bell polynomial or its value.
Example #2:
# import sympy from sympy import * n = 5k = symbols('x') print("Value of n = {} and k = {}".format(n, k)) # Use sympy.bell() method nth_bell_poly = bell(n, k) print("The nth bell polynomial : {}".format(nth_bell_poly)) |
Output:
Value of n = 5 and k = x The nth bell polynomial : x**5 + 10*x**4 + 25*x**3 + 15*x**2 + x
Example #3:
# import sympy from sympy import * n = 5k = 3print("Value of n = {} and k = {}".format(n, k)) # Use sympy.bell() method nth_bell_poly = bell(n, k) print("The nth bell polynomial value : {}".format(nth_bell_poly)) |
Output:
Value of n = 5 and k = 3 The nth bell polynomial value : 1866
bell(n, k, (x1, x2, x3, …)) –
Syntax: bell(n, k, (x1, x2, x3, …))
Parameter:
n – It denotes the order of the bell polynomial of second kind.
k – It is a parameter in the bell polynomial of second kind.
(x1, x2, x3, …) – It denotes the tuple of variable symbols.Returns: Returns the Bell polynomials of the second kind.
Example #4:
# import sympy from sympy import * n = 5k = 3variables = symbols('x:6')[1:] print("Value of n = {}, k = {} and variables = {}".format(n, k, variables)) # Use sympy.bell() method nth_bell_poly = bell(n, k, variables) print("The nth bell polynomial of second kind : {}".format(nth_bell_poly)) |
Output:
Value of n = 5, k = 3 and variables = (x1, x2, x3, x4, x5) The nth bell polynomial of second kind : 10*x1**2*x3 + 15*x1*x2**2
