Python: Complex Number Arithmetic and Lambert Function
07-14-2021, 02:42 PM
Post: #1 Eddie W. Shore Senior Member Posts: 1,251 Joined: Dec 2013
Python: Complex Number Arithmetic and Lambert Function
Complex Number Arithmetic

The HP Prime App "Python-Complex Arithmetic" performs the four arithmetic functions on two complex numbers.

Code:
from cmath import *
print("Complex Number Arithmetic")
x1=float(input("real_1: "))
# input values are not auto printed
print(x1)
y1=float(input("imag_y: "))
print(y1)
z1=complex(x1,y1)
print("z1 = "+str(z1))

x2=float(input("real_2: "))
print(x2)
y2=float(input("imag_2: "))
print(y2)
z2=complex(x2,y2)
print("z2 = "+str(z2))

print()
print("z1 + z2 = "+str(z1+z2))
print("z1 - z2 = "+str(z1-z2))
print("z1 * z2 = "+str(z1*z2))
print("z1 / z2 = "+str(z1/z2))

Lambert W Function

The HP Prime App "Python-Lambert W Function" approximates the Lambert W function. The Python script estimates w given complex number z using Newtons Method:

w * e^w = z

Code:
from cmath import *
print("Lambert W Function - approx")
print("w * exp(w) = z, find w")
zr=float(input("z_real: "))
print(zr)
zj=float(input("z_imag: "))
print(zj)
z=complex(zr,zj)
w0=complex(1,1)
w1=complex(1,1)

while abs(w1)>1*10**-10:
w1=(w0*exp(w0)-z)/(exp(w0)+w0*exp(w0))
w0=w0-w1

# round low parts to zero
# z.real, z.imag are read only
wr=w0.real
if abs(wr)<1*10**-10:
wr=0
wj=w0.imag
if abs(wj)<1*10**-10:
wj=0
w0=complex(wr,wj)

print("w = "+str(w0))

Example:

Result: approx -1.223152769062088e-06+1.57079554811127j

Input: 2+3j
Result: approx 1.090076534485791+0.5301397207748389j

Source:
Wikipedia. "Lambert W Function" Last updated June 13, 2021.
https://en.wikipedia.org/wiki/Lambert_W_function Retrieved July 9, 2021