Divide one Legendre series by another in Python

To divide one Legendre series by another, use the polynomial.legendre.legdiv() method in Python Numpy. The method returns quo, rem of Legendre series coefficients representing the quotient and remainder.

Returns the quotient-with-remainder of two Legendre series c1 / c2. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Legendre series coefficients ordered from low to high.

Steps

At first, import the required library −

import numpy as np from numpy.polynomial import laguerre as L

Create 1-D arrays of Legendre series coefficients −

c1 = np.array([2,3,4]) c2 = np.array([4,3,2])

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 Legendre series by another, use the polynomial.legendre.legdiv() method in Python Numpy −

print("\nResult (division)....\n",L.legdiv(c1, c2))

Example

import numpy as np from numpy.polynomial import legendre as L # Create 1-D arrays of Legendre series coefficients c1 = np.array([2,3,4]) c2 = np.array([4,3,2]) # 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 Legendre series by another, use the polynomial.legendre.legdiv() method in Python Numpy print("\nResult (division)....\n",L.legdiv(c1, c2))

Output

Array1...    [2 3 4] Array2...    [4 3 2] 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([2.]), array([-6., -3.]))