numpy.poly1d() in Python

numpy.poly1d(arr, root, var): This function helps to define a polynomial function. It makes it easy to apply “natural operations” on polynomials.

Parameters :
-> arr : [array_like] The polynomial coefficients are given in decreasing order of powers. If the second parameter (root) is set to True then array values are the roots of the polynomial equation.
For example- poly1d(3, 2, 6) = 3x² + 2x + 6
poly1d([1, 2, 3], True) = (x-1)(x-2)(x-3) = x³ – 6x² + 11x -6

-> root : [bool, optional] True means polynomial roots. Default is False.
-> var : variable like x, y, z that we need in polynomial [default is x].

Arguments :
c : Polynomial coefficient.
coef : Polynomial coefficient.
coefficients : Polynomial coefficient.
order : Order or degree of polynomial.
o : Order or degree of polynomial.
r : Polynomial root.
roots : Polynomial root.

Return: Polynomial and the operation applied

Code 1 : Explaining poly1d() and its argument

# Python code explaining 
# numpy.poly1d() 
  
# importing libraries 
import numpy as np 
  
# Constructing polynomial 
p1 = np.poly1d([1, 2]) 
p2 = np.poly1d([4, 9, 5, 4]) 
  
print ("P1 : ", p1) 
print ("\n p2 : \n", p2) 
  
# Solve for x = 2 
print ("\n\np1 at x = 2 : ", p1(2)) 
print ("p2 at x = 2 : ", p2(2)) 
  
# Finding Roots 
print ("\n\nRoots of P1 : ", p1.r) 
print ("Roots of P2 : ", p2.r) 
  
# Finding Coefficients 
print ("\n\nCoefficients of P1 : ", p1.c) 
print ("Coefficients of P2 : ", p2.coeffs) 
  
# Finding Order 
print ("\n\nOrder / Degree of P1 : ", p1.o) 
print ("Order / Degree of P2 : ", p2.order) 

Output :

P1 :   
1 x + 2

 p2 : 
    3     2
4 x + 9 x + 5 x + 4


p1 at x = 2 :  4
p2 at x = 2 :  82


Roots of P1 :  [-2.]
Roots of P2 :  [-1.86738371+0.j         -0.19130814+0.70633545j -0.19130814-0.70633545j]


Coefficients of P1 :  [1 2]
Coefficients of P2 :  [4 9 5 4]


Order / Degree of P1 :  1
Order / Degree of P2 :  3

Code 2 : Basic mathematical operation on polynomial

# Python code explaining 
# numpy.poly1d() 
  
# importing libraries 
import numpy as np 
  
# Constructing polynomial 
p1 = np.poly1d([1, 2]) 
p2 = np.poly1d([4, 9, 5, 4]) 
  
print ("P1 : ", p1) 
print ("\n p2 : \n", p2) 
  
print ("\n\np1 ^ 2 : \n", p1**2) 
print ("p2 ^ 2 : \n", np.square(p2)) 
  
p3 = np.poly1d([1, 2], variable = 'y') 
print ("\n\np3 : ", p3) 
  
  
print ("\n\np1 * p2 : \n", p1 * p2) 
print ("\nMultiplying two polynimials : \n",  
       np.poly1d([1, -1]) * np.poly1d([1, -2])) 

Output :

P1 :   
1 x + 2

 p2 : 
    3     2
4 x + 9 x + 5 x + 4


p1 ^ 2 : 
    2
1 x + 4 x + 4
p2 ^ 2 : 
 [16 81 25 16]


p3 :   
1 y + 2


p1 * p2 : 
    4      3      2
4 x + 17 x + 23 x + 14 x + 8

Multiplying two polynimials : 
    2
1 x - 3 x + 2

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