numpy.poly1d() in Python (original) (raw)

Last Updated : 09 Aug, 2022

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

import numpy as np

p1 = np.poly1d([ 1 , 2 ])

p2 = np.poly1d([ 4 , 9 , 5 , 4 ])

print ("P1 : ", p1)

print ("\n p2 : \n", p2)

print ("\n\np1 at x = 2 : ", p1( 2 ))

print ("p2 at x = 2 : ", p2( 2 ))

print ("\n\nRoots of P1 : ", p1.r)

print ("Roots of P2 : ", p2.r)

print ("\n\nCoefficients of P1 : ", p1.c)

print ("Coefficients of P2 : ", p2.coeffs)

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

import numpy as np

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