HP Prime Python: Complex Number Arithmetic and Lambert Function
HP Prime Python: Complex Number Arithmetic and Lambert Function - and Firmware Update!
Firmware Update!
There is a new firmware update (10/1/2021) - v. 14596 for both the Hardware versions (Version 1 and Version 2) of the HP Prime. The link to the MHPoC entry and download links:
HPMoC Thread:
https://www.hpmuseum.org/forum/thread-17538-post-152707.html#pid152707
HP Prime Hardware 1 Download:
https://www.hpcalc.org/details/7469
HP Prime Hardware 2 Download:
https://www.hpcalc.org/details/7783
Now on to complex numbers and the Lambert function.
Python File Introduction
Complex Number Arithmetic
The HP Prime App "Python-Complex Arithmetic" performs the four arithmetic functions on two complex numbers.
Script:
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))
Example:
x1 = 9
y1 = -8 (use [ +/- ] to enter negative numbers)
x2 = -1
y2 = 4
Results:
z1 = 9-8j
z2 = -1+4j
z1 + z2 = 8-4j
z1 - z2 = 10-12j
z1 * z2 = 23+44j
z1 / z2 = -2.411764705882353-1.647058823529412j
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
Script:
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:
Input: -1.57079362679 (about π/2)
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
Download both apps here (zip file):
https://drive.google.com/file/d/1MX5G-1MJidb2ZmoBVe57GpiUnYvY5BqD/view?usp=sharing
Eddie
All original content copyright, © 2011-2021. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
