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Differentiate a polynomial and multiply each differentiation by a scalar in Python
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/d(-x))(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...\n",c)Check the Dimensions −
print("\nDimensions of our Array...\n",c.ndim)Get the Datatype −
print("\nDatatype of our Array object...\n",c.dtype)Get the Shape −
print("\nShape of our Array object...\n",c.shape)To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy −
print("\nResult...\n",P.polyder(c, scl = -1))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...\n",c)
# Check the Dimensions
print("\nDimensions of our Array...\n",c.ndim)
# Get the Datatype
print("\nDatatype of our Array object...\n",c.dtype)
# Get the Shape
print("\nShape of our Array object...\n",c.shape)
# To differentiate a polynomial, use the polynomial.polyder() method in Python Numpy.
print("\nResult...\n",P.polyder(c, scl = -1))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.]
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