Convert a polynomial to Legendre series in Python

To convert a polynomial to a Legendre series, use the legendre.poly2lag() method in Python Numpy. Convert an array representing the coefficients of a polynomial ordered from lowest degree to highest, to an array of the coefficients of the equivalent Legendre series, ordered from lowest to highest degree. The method returns a 1-D array containing the coefficients of the equivalent Legendre series. The parameter pol, is a 1-D array containing the polynomial coefficients

Steps

At first, import the required library −

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

Create an array using the numpy.array() method −

c = np.array([1, 2, 3, 4, 5])

Display the array −

print("Our 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 convert a polynomial to a Legendre series, use the legendre.poly2lag() method in Python Numpy −

print("\nResult (polynomial to legendre)...\n",L.poly2leg(c))

Example

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

# Create an array using the numpy.array() method
c = np.array([1, 2, 3, 4, 5])

# Display the array
print("Our 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 convert a polynomial to a Legendre series, use the legendre.poly2lag() method in Python Numpy
print("\nResult (polynomial to legendre)...\n",L.poly2leg(c))

Output

Our Array...
   [1 2 3 4 5]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(5,)

Result (polynomial to legendre)...
   [3. 4.4 4.85714286 1.6 1.14285714]