# Divide one Legendre series by another in Python

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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.]))