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 

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 

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