Add one Hermite series to another in Python

To add one Hermite series to another, use the polynomial.hermite.hermadd() method in Python NumPy. The method returns an array representing the Hermite series of their sum. Returns the sum of two Hermite series c1 + c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. The parameters c1 and c2 are 1-D arrays of Hermite series coefficients ordered from low to high.

Syntax

numpy.polynomial.hermite.hermadd(c1, c2)

Parameters

• c1, c2 ? 1-D arrays of Hermite series coefficients ordered from low to high

Example

Let's create two Hermite series and add them together ?

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

# Create 1-D arrays of Hermite 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)

# Add one Hermite series to another
print("\nResult (sum)....\n", H.hermadd(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 (sum)....
 [4. 4. 4.]

Adding Hermite Series of Different Lengths

The method can handle Hermite series of different lengths ?

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

# Create Hermite series of different lengths
c1 = np.array([1, 2, 3, 4])
c2 = np.array([5, 6])

print("First series:", c1)
print("Second series:", c2)

# Add the series
result = H.hermadd(c1, c2)
print("\nSum:", result)

First series: [1 2 3 4]
Second series: [5 6]

Sum: [6. 8. 3. 4.]

How It Works

The hermadd() function performs element-wise addition of the coefficients. When series have different lengths, the shorter series is treated as having zero coefficients for the missing higher-order terms.

Conclusion

The polynomial.hermite.hermadd() method efficiently adds two Hermite series by summing their coefficients element-wise. It handles series of different lengths automatically by padding with zeros.