Dozenal RPN Calculator App for Android for Android Smartphones and Numworks Beta Firmware Version 25

 Dozenal Calculator App for Android Smartphones and Numworks Beta Firmware Version 25

Dozenal Calculator App for Android Smartphones

The Dozenal RPN Calculator app is by Unum Designum for the Android smartphones. It is a classical, four-level stack RPN (Reverse Polish Notation) app that operates in both dozenal (i.e. duodecimal, Base 12) and decimal (Base 10). The calculator app features a standard set of scientific functions:

* arithmetic, square, square root

* sin, cos, tan, and inverses

* e^x, 10^x, ln, log

* DMS/Decimal conversions and HMS/Hours conversions (not sure how there are two sets, since they seem to do the same thing)

* Pol/Rect conversions

* percent function (%)

* Stack functions: roll down, roll up, swap, last x

Originally Released: July 1, 2020

Last Updated: December 17, 2025 (as of January 22, 2026)

Version I am reviewing 1.0.11

The polar/rectangular conversions follow the conventional RPN calculator format:

	Rectangular	Polar
Y Stack:	Y	Θ
X Stack:	X	R

The percent function follows the conventional RPN calculator format:

	Before	After
Y Stack:	Y	Y
X Stack:	X	Y * X ÷ 100

However, the decimal/DMS (decimal-minute-seconds) and hours/HMS (hours-minute-seconds) follow up this format:

	Decimal/Hours	DMS/HMS
Z Stack:	0 after conversion	seconds
Y Stack:	0 after conversion	minutes
X Stack:	decimal/hours as a decimal	decimal/hours

Conversion between bases is just a matter of pressing [ f ] [ DOZ/DEC ].

Symbols:

* Upside down 2 (↊) represents 10 (Unicode 218A); commonly symbolized by X

* Backwards 3 (↋) represents 11 (Unicode 218B); commonly symbolized by E

(Unicode is from Wikipedia: https://en.wikipedia.org/wiki/Duodecimal)

Two constants provided by the Dozenal RPN app:

	Base 10 (e: 10^n)	Base 12 (e: 12^n)
π	3.141592653589793	3;184809493↋9186459↊↊
Planck	6.6206070149999999e-34	1;↊79611175↊0925342846e-27

App information: https://play.google.com/store/apps/details?id=dozecal.unumdesignum.com&hl=en_NZ#/

Numworks: Beta Firmware 25

Version 25 Information: https://www.numworks.com/calculator/update/version-25/

Nuwmorks has released a firmware update 25.1. It is a beta version software where new features are tested. To try it, Numworks is inviting Numworks users to download and become a beta test or us the beta emulator on the Numworks website.

Verison 25 Beta Emulator: https://www.numworks.com/calculator/update/version-25/

Please keep in mind that this emulator is probably only available for the testing period and may become unavaiable once the official release is made.

Major updates include:

* Data in the Statistics app can either be qualitative (data points, the way the statistics mode was always used) or categorial (data points always belong to specific categories, up to 10)

* The Grapher app can shade area of intersection for a given set of inequalities.

* The Grapher app also finds intersection points of conic sections and vertical lines.

* In the Calculations app, results with five or more decimal place will have at least a fractional approximation in the Additional Results quick tab.

* The degree and radian symbol/indicators are added to the Toolbox.

* Sequences have new notations.

* Installing this version will limit roll back deinstalls to versions 24.11 or later.

No word on any additions or changes to the Python app.

I have installed version 25 on my older Numworks calculator (N0110) so I can try them out.

HP 12C: An Improved Linear Regression Function (from Curvee RPN-45 SD)

HP 12C:  An Improved Linear Regression Function (from Curvee RPN-45 SD)

Curvee RPN-45 Simulator 

The Curvee RPN-45 from Curvee Software is an excellent app.  The RPN-45 SD app is the Super-45.   The Super-45 is a emulator of the classic HP 45 calculator from 1973 with the following enhancements:

*  The gold shift key becomes a double-shift key (gold/purple)

*  Complex Numbers

*  10 additional registers

*  Days between dates

*  Four solvers: 2 x 2 system of linear equations, 3 x 3 system of linear equations, quadratic equation, cubic equation

*  Expanded statistics including full linear regression analysis

I have purchased one on my iPod Touch (that is an iPhone without the "phone" part) for $1.99 (prices may vary).  There are versions for the iPhone and iPad.  

For more information:  http://cuveesoft.ch/rpn45/en/index.html

The enhanced linear regression (L.R.) function on the Super-45 returns the following calculations to the four-level stack:

T:  covariance

Z:  correlation

Y:  slope

X:  intercept

The relationship between correlation (r) and covariance (cov):

cov(x,y) = r * sx * sy

sx = standard deviation of x-data

sy = standard deviation of y-data

The HP 12C mimics the enhanced L.R. function.   Yes, check out this app!

HP 12C Program:  Enhanced Linear Regression

The results are stored in the following registers:

R7 = intercept

R8 = Slope

R9 = correlation

R.0 = covariance

In addition, I added code to calculate population deviation:  σx in the x-stack, σy in the y-stack.

Step #: Code [ key ]

// linear regression function 

01:  1  [ 1 ]

02:  43, 1  [ x^,r ]

03:  34  [ x<>y ]

04:  44, 9 [ STO 9 ]

05:  43, 48  [ s ]

06:  20  [ × ]

07:  20  [ × ]

08:  44, 48, 0   [ STO  .  0  (decimal point, zero) ]

09:  0  [ 0 ]

10:  43, 2  [ y^, r ]

11:  44, 7  [ STO 7 ]

12:  1   [  1 ]

13:  43, 2  [ y^, r ]

14:  34  [ x<>y ]

15:  33  [ R↓ ]

16:  34  [ x<>y ]

17:  30  [ - ]

18:  44, 8 [ STO 8 ]

19:  45, 48, 0 [  RCL . 0  (decimal point, zero) ]

20:  45, 9  [ RCL 9 ]

21:  45, 8  [ RCL 8 ]

22:  45, 7  [ RCL 7 ]

23:  43, 33, 00 [ GTO 00 ]

// population deviation

24:  45, 1 [ RCL 1 ]

25:  36  [ ENTER ]

26:  36  [ ENTER ]

27:  1  [ 1 ]

28:  30  [ - ]

29:  10  [ ÷ ]

30:  43, 21  [ √ ]

31:  44, 0  [ STO 0 ]

32:  43, 48  [ s ]

33:  45, 0  [ RCL 0 ]

34:  10  [ ÷ ]

35:  34  [ x<>y ]

36:  45, 0  [ RCL 0 ]

37:  10  [ ÷ ]

38:  34  [ x<>y ]

39:  43, 33, 00 [ GTO 00 ]

Example

Fix 6 mode is set.  

Data:

(5.35, 10)

(5,70, 11)

(6.18, 12)

(6.55, 13)

(6.97, 14)

(7.36, 15)

After entering the data points:

[ f ] (PRGM) [ R/S ]

-3.162788 (intercept), [ R↓ ]

2.465287 (slope), [ R↓ ]

0.999396 (correlation, r), [ R↓ ]

1.418000 (covariance)  ( [ R↓ ] to return the stack to it's original configuration )

[ g ] (GTO) 24 [ R/S ]

0.692331 ( σx ) [ x<>y ]

1.707825 ( σy )

Eddie

All original content copyright, © 2011-2023.  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. 

HP Prime and TI 84 Plus CE: Jacobi Elliptic Functions

HP Prime and TI 84 Plus CE:  Jacobi Elliptic Functions

Introduction

Jacobian Elliptic Functions are a set of twelve functions denoted by XY(U, K) where X and Y stands of letters c, s, n, and d.  Today's blog post will focus on three of the common Jacobi Elliptic Functions:

Sine Amplitude:  sn(u,k)
Cosine Amplitude:  cn(u,k)
Delta Amplitude:  dn(u,k)

Where u is a real number and k is a parameter between -1 and 1 inclusive

To determine any of the Jacobian Elliptic Functions, the integral has to be solved for X:

U = ∫( 1/√(1 - K^2 * sin^2(T)) dT from T = 0 to T = X)

Solving for X will represent the function am(U,K).

Then:
sn(U,K) = sin(X)
cn(U,K) = cos(X)
dn(U,K) = √(1 - K^2 * sin^2(X))

Radian angles are used. 

HP Prime App:  Jacobi Elliptic Functions

Download here:  https://drive.google.com/open?id=1qQ253ri88IyZIwYvKd5kEAIe2Bkgfyl_

In a different approach, I have created a custom app, which is based on the Solver App named Jacobi Elliptic Functions, which you can download on the link above.

Symb View:  The four equations that are used for this app.  Leave all four checked.

Num View:  This is where you enter U and K.  Leave these boxes unchecked.  Press or touch (Solve) to get the other values am (X), sn (S), cn (C), and dn (D). 

If you want to program ths app yourself, please see the screen shots above. 

TI-84 Plus CE Program:  ELLIPFX

Download here:  https://drive.google.com/open?id=16DTb2m2o2kwo1sJ6s_NGGJ_M9bgxsOvZ

"EWS 2020-01-22"
Radian
.5→X:1→F:1→N
ClrHome
Disp "JACOBIAN ELLIPTIC","­1≤K and K≤1"
Prompt U,K
Repeat abs(N/F)≤1E­10
fnInt((1-K^2*sin(T)^2)^(­-1/2),T,0,X)-U→N
(1-K^2*sin(X)^2)^(­-1/2)→F
X-N/F→X
End
sin(X)→S
cos(X)→C
√(1-K^2*sin(X)^2)→D
ClrHome
Disp "U="+toString(U)
Disp "K="+toString(K)
Disp "AM="+toString(X)
Disp "SN="+toString(S)
Disp "CN="+toString(C)
Disp "DN="+toString(D)

Examples

Example 1:
U = 3
K = 0.5

Results:
AM(U,K) = 2.772166899
SN(U,K) = 0.3610799872
CN(U,K) = -0.932534848
DN(U,K) = 0.9835676442

Example 2:
U = 1.5
K = 0

Results:
AM(U,K) = 1.5
SN(U,K) = 0.9974949866
CN(U,K) = 0.0707372017
DN(U,K) = 1

Sources

"Jacobi elliptic functions"  Wikipeida.  https://en.wikipedia.org/wiki/Jacobi_elliptic_functions  Retrieved December 23, 2019

"Jacobi elliptic function sn,cn,dn (chart) Calculator"  Ke!san Online Calculator https://keisan.casio.com/exec/system/1180573437  Retrieved January 22, 2020


Eddie

All original content copyright, © 2011-2020.  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.

HP Prime: TrigPlot App (HP Prime Custom app Tutorial)

HP Prime: TrigPlot App  (HP Prime Custom app Tutorial)

Introduction

Here is another example custom app, the TrigPlot, which plots the following equation:

y = A * sin(Bx + C) + D * cos(Ex + F) + G * sin(Hx + I)^2 + J * cos(Kx + L)^2

where all angles are in radians.  The app uses the global variables A through L. 

Keys

[ Num ]:  The user enters values for A – L.  They must be real (not complex or have a √(-1) component)

[ Plot ]:  Enter plot parameters and choose the color of the plot (purple, blue, green, gold, red).  The plot is against a black background.

[ View ], Erase A-L:  Sets the variables A through L to 0 (zero).

[ Info ]:  Displays information about the app

Notes

The Info section introduces the user to the app’s concept:

Info()

BEGIN

// This is when the user presses

// Shift+Apps (Info), use Print

// commands

PRINT();

PRINT("TrigPlot App");

PRINT("------------");

PRINT("By Edward Shore");

PRINT("------------");

PRINT("This app plots the equation");

PRINT("Y = A*SIN(B*X+C) + D*COS(E*X+F) +");

PRINT("G*SIN(H*X+I)^2 + J*COS(K*X+L)^2");

PRINT("------------");

PRINT("February 2018");

END;

To ensure the app always runs in Radians mode, I store the value 1 to AAngle during startup (START).  In addition, I added the Info(); to show the Info screen.

START()

BEGIN

// This happens when the app is started.

// Set the app to radians angle mode.

AAngle:=1;

// This is a specific app mode setting

// unlike HAngle

// Also run the Info screen

Info();

END;

The Plot portion of app is based on the Pixel Plot program (see http://edspi31415.blogspot.com/2018/02/hp-prime-pixel-plot-how-to-change.html ) where pixels are plotted.

HP Prime Program:  TrigPlot (in app TrigPlot)

#pragma mode( separator(.,;) integer(h32) )

//Symb()

//BEGIN

// MSGBOX("Symb");

//END;

Plot()

BEGIN

// runs the Plot routine

// set color scheme

LOCAL col1;

col1:={#BF00FFh,#7DF9FFh,

#00FF00h,#D4AF37h,#FF0000h};

// Radians

HAngle:=0;

// localize variables

LOCAL xm,xn,ym,yn;

LOCAL xs,ys,xp,yp;

LOCAL x,y,ch;

// input screen

INPUT({

xm,xn,ym,yn,

{ch,

{"Purple","Blue","Green",

"Gold","Red"}}},

"TrigPlot Setup: Plot",

{"x-min: ","x-max: ",

"y-min: ","y-max: ",

"Color: "});

// set black background

RECT_P(0);

// calulate the scale

xs:=(xn-xm)/320;

ys:=(yn-ym)/−220;

// drawing

// color choice

LOCAL c1:=col1[ch];

// axis information

LOCAL st1,st2;

st1:="x:["+xm+","+xn+"]";

st2:="y:["+ym+","+yn+"]";

TEXTOUT_P(st1,0,0,2,#C0C0C0h);

TEXTOUT_P(st2,0,20,2,#C0C0C0h);

// function

FOR x FROM xm TO xn STEP xs DO

// function

y:=A*SIN(B*x+C)+D*COS(E*x+F)+

G*SIN(H*x+I)^2+J*COS(K*x+L)^2;

// point→pixel, plot

xp:=(x-xm)/xs;

yp:=(y-yn)/ys;

PIXON_P(xp,yp,c1);

END;

// freeze screen

FREEZE;

END;

Num()

BEGIN

// This is where all the variables are

// entered, in one easy spot. A-L are

// global in this application.

INPUT({A,B,C,D,E,F,G,H,I,J,K,L},

"TrigPlot Variables");

END;

//SymbSetup()

//BEGIN

// MSGBOX("SymbSetup");

//END;

//PlotSetup()

//BEGIN

// MSGBOX("PlotSetup");

//END;

//NumSetup()

//BEGIN

// MSGBOX("NumSetup");

//END;

Info()

BEGIN

// This is when the user presses

// Shift+Apps (Info), use Print

// commands

PRINT();

PRINT("TrigPlot App");

PRINT("------------");

PRINT("By Edward Shore");

PRINT("------------");

PRINT("This app plots the equation");

PRINT("Y = A*SIN(B*X+C) + D*COS(E*X+F) +");

PRINT("G*SIN(H*X+I)^2 + J*COS(K*X+L)^2");

PRINT("------------");

PRINT("February 2018");

END;

START()

BEGIN

// This happens when the app is started.

// Set the app to radians angle mode.

AAngle:=1;

// This is a specific app mode setting

// unlike HAngle

// Also run the Info screen

Info();

END;

//RESET()

//BEGIN

//MSGBOX("RESET");

//END;

//VIEW "Views", Views()

//BEGIN

// MSGBOX("Views");

//END;

VIEW "Erase A-L", ERASEAL()

BEGIN

A:=0; B:=0; C:=0; D:=0; E:=0; F:=0;

G:=0; H:=0; I:=0; J:=0; K:=0; L:=0;

END;

Examples

Example 1:  y = 2 sin(x + 2) – 3 cos x

A = 2, B = 1, C = 2, D = -3, E = 1 (the rest are zero)

Example 2:  y = 2 cos(2x) + 1.5 * cos^2 x

D = 2, E = 2, J = 1.5, K = 1 (the rest are zero)

Eddie

This blog is property of Edward Shore, 2018.