Divide One Chebyshev Series by Another in Python

To divide one Chebyshev series by another, use the polynomial.chebyshev.chebdiv() method in Python Numpy. The method returns arrays of Chebyshev series coefficients representing the quotient and remainder.

Returns the quotient-with-remainder of two Chebyshev series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series T_0 + 2*T_1 + 3*T_2. The parameters c1 and c2 are 1-D arrays of Chebyshev series coefficients ordered from low to high.

Steps

At first, import the required libraries -

import numpy as np
from numpy.polynomial import chebyshev as C

Create 1-D arrays of Chebyshev series coefficients −

c1 = np.array([1,2,3])
c2 = np.array([3,2,1])

Display the arrays of coefficients −

print("Array1...\n",c1)
print("\nArray2...\n",c2)

Display the datatype −

print("\nArray1 datatype...\n",c1.dtype)
print("\nArray2 datatype...\n",c2.dtype)

Check the Dimensions of both the arrays −

print("\nDimensions of Array1...\n",c1.ndim)
print("\nDimensions of Array2...\n",c2.ndim)

Check the Shape of both the arrays −

print("\nShape of Array1...\n",c1.shape)
print("\nShape of Array2...\n",c2.shape)

To divide one Chebyshev series by another, use the polynomial.chebyshev.chebdiv() method in Python −

print("\nResult (division)....\n",C.chebdiv(c1,c2))

Example

import numpy as np
from numpy.polynomial import chebyshev as C

# Create 1-D arrays of Chebyshev series coefficients
c1 = np.array([1,2,3])
c2 = np.array([3,2,1])

# Display the arrays of coefficients
print("Array1...\n",c1)
print("\nArray2...\n",c2)

# Display the datatype
print("\nArray1 datatype...\n",c1.dtype)
print("\nArray2 datatype...\n",c2.dtype)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",c1.ndim)
print("\nDimensions of Array2...\n",c2.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n",c1.shape)
print("\nShape of Array2...\n",c2.shape)

# To divide one Chebyshev series by another, use the polynomial.chebyshev.chebdiv() method in Python Numpy
print("\nResult (division)....\n",C.chebdiv(c1,c2))

Output

Array1...
[1 2 3]

Array2...
[3 2 1]

Array1 datatype...
int64

Array2 datatype...
int64

Dimensions of Array1...
1

Dimensions of Array2...
1

Shape of Array1...
(3,)

Shape of Array2...
(3,)

Result (division)....
(array([3.]), array([-8., -4.]))