numpy.poly1d() in Python

The numpy.poly1d() function helps to define a polynomial function. It makes it easy to apply “natural operations” on polynomials.

Syntax: numpy.poly1d(arr, root, var) 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. 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

For example: poly1d(3, 2, 6) = 3x² + 2x + 6 poly1d([1, 2, 3], True) = (x-1)(x-2)(x-3) = x³ – 6x² + 11x -6

Code 1 : Explaining poly1d() and its argument

Python3

# 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

Python3

# 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 polynomials : 
    2
1 x - 3 x + 2