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+--- Thread: [HP41] Lambda Modular function; question (/thread-19366.html)
[HP41] Lambda Modular function; question - floppy - 12-31-2022 12:17 PM
Hello,
is anywhere a program to calculate the points of lambda with an HP41? RPN or RPN in MOD or Microcode in MOD? with complex numbers.
In Wiki, there is a curve https://en.wikipedia.org/wiki/Modular_lambda_function#/media/File:Lambda_function.svg
First I would like to calculate several points of
a) lambda(i*x) then
b) (e^(1/e))*(1-lambda(i*x)) then..
x between 0 and 10.
Any advise is welcome.
(if none exists in HP41 - or HP71 -, I will look at other calculator or PC-computing)
RE: [HP41] Lambda Modular function; question - Ángel Martin - 01-07-2023 11:15 AM
Here's a quick & dirty routine using 12 terms of the q-expansion and the 41Z.
More terms would be needed for better accuracy near the origin in the imaginary axis.
Input: Im(z) in Y, Re(z) in X
Code:
01*LBL "ZML"
02 ZENTER^
03 PI
04 0
05 Z*
06 ZEXP
07 ENTER^
08 ENTER^
09 ENTER^
10 13504512
11 CHS
12 *
13 5702208
14 +
15 *
16 2320128
17 -
18 *
19 904784
20 +
21 *
22 335872
23 -
24 *
25 117632
26 +
27 *
28 38400
29 -
30 *
31 11488
32 +
33 *
34 3072
35 -
36 *
37 704
38 +
39 *
40 128
41 -
42 *
43 16
44 +
45 *
46 ENDRE: [HP41] Lambda Modular function; question - floppy - 01-07-2023 05:38 PM
Thanks. For comparison in python.
Code:
import math as math
from mpmath import *
import matplotlib.pyplot as plt
import numpy as np
#
mp.dps = 25
mp.pretty = True
#
# Knowledge
# https://mpmath.org/doc/current/functions/elliptic.html
# https://mpmath.org/doc/current/functions/hypergeometric.html
# green curve = https://en.wikipedia.org/wiki/Modular_lambda_function#/media/File:Lambda_function.svg
# https://en.wikipedia.org/wiki/Modular_lambda_function
#
def func_fromk(p_in):
# because p_in must be a number and not an array from np..
return kfrom(tau=p_in*j)
#
N = 50
Wide = 3.
X = np.arange(0.,Wide,Wide/N)
Y1 = np.zeros(N)
Y2 = np.zeros(N)
#
# Y1 equal this? https://www.desmos.com/calculator/00bdl5omnf?lang=de
#
for i in range(N):
Y1[i]=(1-((np.abs(func_fromk((Wide/N)*i)))**2))*((np.exp(1))**(1/(np.exp(1))))
Y2[i]=(np.abs(func_fromk((Wide/N)*i)))**2
#
plt.plot(X,Y1,'r-')
plt.plot(X,Y2,'g-')
#
plt.xlabel('X')
plt.ylabel('.. of X*j (green) and (1-(..of (X*j)))*(e**(1/e)))')
plt.title('lambda of ..')
plt.grid()
# https://matplotlib.org/stable/gallery/lines_bars_and_markers/psd_demo.html#sphx-glr-gallery-lines-bars-and-markers-psd-demo-py
Steps=0.2
Xticks = np.arange(0, Wide, Steps)
plt.xticks(Xticks)
Yticks = np.arange(0, 1.8, Steps)
plt.yticks(Yticks)
plt.show()