Subtract one Hermite_e series from another in Python

To subtract one Hermite_e series from another, use the polynomial.hermite_e.hermesub() method in Python NumPy. The method returns an array representing the Hermite_e series of their difference (c1 - c2). The sequences of coefficients are ordered from lowest to highest degree term, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2.

Syntax

numpy.polynomial.hermite_e.hermesub(c1, c2)

Parameters

c1, c2: 1-D arrays of Hermite_e series coefficients ordered from low to high degree.

Example

Let's create two Hermite_e series and subtract one from another ?

import numpy as np
from numpy.polynomial import hermite_e as H

# Create 1-D arrays of Hermite_e 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 subtract one Hermite_e series from another
print("\nResult (difference)....\n", H.hermesub(c1, c2))

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 (difference)....
 [-2.  0.  2.]

How It Works

The hermesub() function performs element-wise subtraction of the coefficient arrays. For coefficients c1 = [1, 2, 3] and c2 = [3, 2, 1], the result is:

• Coefficient 0: 1 - 3 = -2
• Coefficient 1: 2 - 2 = 0
• Coefficient 2: 3 - 1 = 2

Different Array Lengths

When arrays have different lengths, the shorter array is padded with zeros ?

import numpy as np
from numpy.polynomial import hermite_e as H

# Arrays with different lengths
c1 = np.array([1, 2, 3, 4])
c2 = np.array([1, 2])

print("c1:", c1)
print("c2:", c2)
print("Difference:", H.hermesub(c1, c2))

c1: [1 2 3 4]
c2: [1 2]
Difference: [0. 0. 3. 4.]

Conclusion

The numpy.polynomial.hermite_e.hermesub() method efficiently subtracts Hermite_e series by performing element-wise subtraction of their coefficients. It automatically handles arrays of different lengths by padding with zeros.