# numpy.poly1d() in Python

• 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

 `# 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```

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