Differentiate a polynomial in Python

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To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy. Return the polynomial coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the polynomial 1 + 2*x + 3*x**2 while [[1,2],[1,2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y.

The method returns the Polynomial coefficients of the derivative. The 1st parameter, c is an array of polynomial coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. The 2nd parameter, m are number of derivatives taken, must be non-negative. (Default: 1)

The 3rd parameter is scl. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter is axis. It's the axis over which the derivative is taken. (Default: 0). The result is (d/dx)(c) = 2 + 6x + 12x**2

Steps

At first, import the required library −

import numpy as np
from numpy.polynomial import polynomial as P

Create an array of polynomial coefficients i.e. 1 + 2x + 3x**2 + 4x**3 −

c = np.array([1,2,3,4])

Display the coefficient array −

print("Our coefficient Array...",c)

Check the Dimensions −

print("Dimensions of our Array...",c.ndim)

Get the Datatype −

print("Datatype of our Array object...",c.dtype)

Get the Shape −

print("Shape of our Array object...",c.shape)

To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy −

print("Result...",P.polyder(c))

Example

import numpy as np
from numpy.polynomial import polynomial as P

# Create an array of polynomial coefficients i.e.
# 1 + 2x + 3x**2 + 4x**3
c = np.array([1,2,3,4])

# Display the coefficient array
print("Our coefficient Array...",c)

# Check the Dimensions
print("Dimensions of our Array...",c.ndim)

# Get the Datatype
print("Datatype of our Array object...",c.dtype)

# Get the Shape
print("Shape of our Array object...",c.shape)

# To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy.
# Return the polynomial coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the polynomial 1 + 2*x + 3*x**2 while [[1,2],[1,2]] represents 1 + 1*x + 2*y + 2*x*y if axis=0 is x and axis=1 is y.

print("Result...",P.polyder(c))

Output

Our coefficient Array...
[1 2 3 4]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(4,)

Result...
[ 2. 6. 12.]
Updated on 01-Mar-2022 05:48:28