Python Program to Remove Small Trailing Coefficients from Chebyshev Polynomial

Given a Chebyshev Polynomial, the task is to Remove Small Trailing Coefficients from Chebyshev Polynomial in Python and NumPy.

Example

Input: [-1, 0, 2, 0]

Output: [-1.  0.  2.]

Explanation: One dimensional array in which trailing zeroes are removed.

NumPy.polynomial.Chebyshev method

Python provides a method called NumPy.polynomial.Chebyshev removes the trailing zeroes in a polynomial. This method accepts a one-dimensional (1D) array that consists of coefficients of a polynomial starting from lower order to higher order and returns a one-dimensional (1D) array in which trailing zeroes are removed. Let’s consider a polynomial 0x³+2x²+0x-1 and for the given polynomial, the coefficient array is [-1, 0, 2, 0] starting from lower-order constant to higher-order x³. The chebtrim method will remove the trailing zeroes and return the resultant coefficient array.

Syntax: numpy.polynomial.chebyshev.chebtrim(arr)

Parameter:

• arr: 1-d array of coefficients.

Returns: trimmed ndarray.

Example 1:

Python program to remove the small trailing coefficients for the polynomial 0x³+2x²+0x-1.

Python3

# import necessary packages
import numpy as np
import numpy.polynomial.chebyshev as c

# create 1D array of
# coefficients for the given polynomial
coeff = np.array([-1, 0, 2, 0])

# returns array where trailing zeroes
# got removed
print(c.chebtrim(coeff))

Output:

The x³ coefficient is removed because there is no significance for the higher-order term as its coefficient is zero.

[-1.  0.  2.]

Example 2:

Python program to remove the small trailing coefficients for the polynomial 0x⁵+0x⁴+x³-x²+10x+0.

Python3

# import necessary packages
import numpy as np
import numpy.polynomial.chebyshev as c

# create 1D array of coefficients for the given polynomial
coeff = np.array([0, 10, -1, 1, 0, 0])

# returns array where trailing zeroes got removed
print(c.chebtrim(coeff))

Output:

The coefficients of x⁴ and x⁵ are removed by the chebtrim method from the input array of coefficients.

[ 0. 10. -1.  1.]

Example 3:

Python program to remove the small trailing coefficients for the polynomial 4x⁴+3x³-2x²-1x+0.

Python3

# import necessary packages
import numpy as np
import numpy.polynomial.chebyshev as c

# create 1D array of coefficients for the
# given polynomial
coeff = np.array([0, -1, -2, 3, 4])

# returns array where trailing zeroes got removed
print(c.chebtrim(coeff))

Output:

Here no coefficients are removed by the chebtrim method as there are no trailing zeroes.

[ 0. -1. -2.  3.  4.]