Paco Arjonilla: HP 35S Program Suite

 Paco Arjonilla:  HP 35S Program Suite

On today's blog post, I am going to highlight a recent suite of programs, written by Paco Arjonilla, is designed to compliment the rich function set of the HP 35S calculator.

Each category will have a set of programs of functions.  Stack diagrams are provided in the documentation.  Each category belongs to a single label.

Label P:  vector functions (includes norm, cross product, 3 x 3 determinant) - 149 steps

Label G:  complex numbers (conjugate, polar/rectangular conversions, construct and break down complex numbers) - 48 steps

Label Q:  quaternions (construction, angle, rotation) - 80 steps

Label K:  quadratic equation solver - 28 steps

Label H:  save stack data to variables - 55 steps

Label I:  recall saved stack - 55 steps

Label J:  stack operations (push and pop the x stack, delete the x stack, clear reserved memory registers, copy memory registers) - 159 steps

Paco's website also has a cheat sheet which can be downloaded as a PDF file.

For the programs and for license information, click here:  

http://www.pacoarjonilla.es/HP-35s.html

Special thanks to Paco Arjonilla.

Eddie 

All original content copyright, © 2011-2022.  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. 

Casio fx-CG50: Discrete Fourier Transform

Casio fx-CG50: Discrete Fourier Transform

Making the Discrete Transforms and Back Again

Given a set of numbers, either real or complex:

{x_0, x_1, x_2, x_3, ... , x_n-1}  (small X)

can be transformed using a discrete transform by the sum:

X_k = Σ( x_m * e^(-2 * π * k * m * i ÷ n), m = 0, n - 1)

with i = √(-1)  (big X)

We can do the reverse:

x_k = 1 ÷ n * Σ( X_m * e^(2 * π * k * m * i ÷ n), m = 0, n - 1)

On the Casio fx-CG50, lists start with marker 1 instead of 0, so a slight adjustment in the programs below are needed.

On the programs:

List 25 = small x

List 26 = big X

Casio fx-CG50 Program:  DFT  (Discrete Fourier Transform)

Menu "FORMAT","a+bi",1,"r∠θ",2

Lbl 1:a+bi:Goto 3

Lbl 2:r∠θ:Goto 3

Lbl 3

"DFT"

"E. SHORE, 2022"

"SMALL X (List 25)"?→List 25

Dim List 25→N

List 25→List 26

For 1→K To N

0→S

For 1→J To N

List 25[J]→A

S+A×e^(-2×π×i×(K-1)×(J-1)÷N)→S

Next

S→List 26[K]

Next

"BIG X (List 26)"⊿

List 26

Note:  i = √(-1), [SHIFT] [ 0 ]

Casio fx-CG50 Program:  IDFT  (Inverse Discrete Fourier Transform)

Menu "FORMAT","a+bi",1,"r∠θ",2

Lbl 1:a+bi:Goto 3

Lbl 2:r∠θ:Goto 3

Lbl 3

"INVERSE DFT"

"E. SHORE, 2022"

"BIG X (List 26)"?→List 26

Dim List 26→N

List 26→List 25

For 1→K To N

0→S

For 1→J To N

List 26[J]→A

S+A×e^(2×π×i×(K-1)×(J-1)÷N)→S

Next

S÷N→List 25[K]

Next

"SMALL X (List 25)"⊿

List 25

Note:  i = √(-1), [SHIFT] [ 0 ]

Example Transforms

List 25 (small x):  {2, 4, 6, 8}

List 26 (big X):  {20, -4+4i, -4, -4-4i}

List 25 (small x): {5 + i, 6 + 2i, 7 + 3i, 8 + 4i, 9 + 5i}

List 26 (big X), approximate: 

{35 + 15i, -5.941 + 0.941i, -3.3123 -1.6877i, -1.6877 - 3.3123i, 0.941 - 5.941i}

Source:

Discrete Fourier Transform. Brilliant.org. Retrieved May 7, 2022, from https://brilliant.org/wiki/discrete-fourier-transform/

All original content copyright, © 2011-2022.  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. 

Retro Review: Radio Shack EC-4035

Retro Review:   Radio Shack EC-4035

Quick Facts:

Model:  EC-4035

Company:  Radio Shack

Equivalent Of:  Casio fx-580

Years:  1986-1991

Type:  Scientific

Batteries: 1 x CR-2032

Operating Mode:  AOS

Memory Registers: 7  (K1 - K6, M)

Number of Digits: 10 (display), 8 in fractions, 2 digit exponents are in the top right of the display (10^xx)

Contrast Wheel

Features

*  Trigonometry, logarithmic functions

*  Base conversions with Boolean algebra

*  Engineering and Units mode

*  Single variable and linear regression  (y = A + Bx)

*  Gamma function

*  Complex numbers

*  6 constant memories (Kin/Kout) complete with storage arithmetic

The Radio Shack EC-4035 (Casio fx-580) uses an AOS (postfix) operating mode,  instead of typing expressions as they are written.

Statistics Mode

In linear regression, the equation used is y = A + Bx, where A is the y-intercept and B is the slope.  The statistics mode uses the six constant memories as follows:

K1 = Σx^2

K2 = Σx

K3 = n

K4 = Σy^2

K5 = Σy

K6 = Σxy

Gamma Function

The EC-4035 has a gamma function (Γ), which accepts all real numbers except for negative integers (-1, -2, -3, etc, because the gamma function is undefined there).  I wish this was available on more scientific functions.  

1 [a b/c] 2 [ Γ ] returns 1.772453851  (√π).  

The factorial function (x!) still only accepts non-negative integers.  

Complex Numbers

In the complex mode (Mode 3), the available functions are:

*  arithmetic (+, -, ×, ÷)

*  reciprocal (1/x)

*  argument and absolute value 

*  conjugate (x + yi → x - yi)

*  powers and roots, x^2, √

The arrow key [ → ]  and the key sequence [ SHIFT ] ( ← ) can scroll complex numbers.   Complex numbers are entered in rectangular form.  

Units and Engineering Modes

Results and calculations can be made using Engineering units and certain Electronics symbols.  All are accessed by using the [ [Sym] ] key.  The symbol each key has is located on the bottom right of the key in navy blue.   

[ MODE ] [ . ]:  Engineering Mode.  Results are shown, when applicable, with engineering symbols, for instance:

n:  nano, 10^-9

μ:  micro, 10^-6

m:  milli, 10^-3

k:  kilo, 10^3

M:  mega, 10^6

G:  giga, 10^9

The mode can be turned off by pressing [ MODE ] [ . ].

[ MODE ] [ 0 ]:  Unit Mode.  This is an enhancement to engineering mode to add electronic units:

V:  volts

A:  amperes

S:  seconds

W:  watts

F:  farads

C:  coulombs

Ω:  ohms

The electronic units can be combined with engineering units.    Also, the appropriate unit is determined in calculations.    To leave Unit Mode, go to Comp Mode by pressing [ MODE ] [ 1 ]. 

Engineering and Unit Mode are neat modes and it's really geared for electronic engineering and physics calculations.

Final Thoughts

The features of the EC-4035 gives a pretty standard advanced scientific calculators with additional features geared towards electronic engineering.   

Perhaps the next perfect calculator for electronic engineering would be a combination of the EC-4035 (fx-580), Casio fx-61f, and Calculated Industries Electronic Calc Pro (5070).  

Source:

"casio fx-580"  Voidware.  http://www.voidware.com/calcs/fx580.htm  Last Accessed April 22, 2022. 

Until next time,

Eddie

All original content copyright, © 2011-2022.  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. 

Casio fx-9750GIIIl (and fx-CG 50): Ways to Solve Equations

An expert calculator user will be able to use the tools that the calculators has to offer.  Sometimes, the solutions may be found without the need of programming.

The calculator covered today is the Casio fx-9750GIII, which is named the Casio fx-9860GIII in countries outside of the United States.  I am very confident that the solving tools are available to most recent of Casio's graphing models, including the GII series, the first Prizm, and the current color graphing calculator fx-CG 50.

Solve vs SolveN

The functions Solve and SolveN are offered in the Run-Mat mode as well as a programming commands.  

Solve works with equations involving solving for X:

Solve( f(x) = g(x), guess for X)

If g(x) is omitted, then Solve uses f(x) = 0.  Numeric solutions are returned.

SolveN allows us to solve for any variable A-Z and Θ.   Instead of an initial guess, we can provide a lower and upper bound.  SolveN returns a list of solutions within the bound.  If the lower and upper bound are omitted, then the bounds are -9.999999999E99 and 9.999999999E99.

SolveN( left = right, variable, lower bound, upper bound)

If there is no right side given, then SolveN uses left = 0.   When possible, SolveN returns exact solutions:  fractions, square roots, and multiples of π.

Neither Solve or SolveN can return complex numbered answers.  

The Equation Mode

The Equation Mode allows for three type of solvers:

F1:  Simultaneous

F2:  Polynomial

F3:  Solver

On the fx-9750GIII, access the equation mode by pressing MENU, A.   The location of the Equation mode varies depending on the calculator.  

Simultaneous

Linear equations up to 6 x 6 systems can be solved.   Entries can be either real or complex, regardless of the Set Up.  The matrix is set up like this:

[   columns of coefficients (left)   |  (right) ]

For example:

a*x1 + b*x2 = s

c*x1 + d*x2 = t

shows:

1 2 3

1 [ a b s ]

2 [ c d t  ]

The current coefficients are stored in the variable matrix Sim Coef (S∙Cof), while the current solutions can be stored in the variable Sim Result (S∙Rlt).  These are read-only variables. Both variables can be found in the [VARS],[ F6 ] ( > ), [ F3 ] (EQUA) menu. 

Polynomial

The Casio graphing calculators can solve up to 6-degree polynomials.  Depending on the Set Up, the solutions can be restricted to real numbers or return complex numbered solutions.   However, none of the of coefficients in the polynomial to be solved can be complex numbers.

The current coefficients is stored in the variable matrix Poly Coef (P∙Cof), while the current solutions can be stored in the variable Poly Result (P∙Rlt).  These are read-only variables.   Both variables can be found in the [VARS],[ F6 ] ( > ), [ F3 ] (EQUA) menu. 

Solver

The solver will allow any equations with variables A-Z and Θ.  What is nice about this mode is that all the variables will be listed and you can select one variable to solve for.   Repeated scenarios can be explored without the need to recall the SolveN function.  

Those are some of the solving tools of the Casio graphing calculators.  Hopefully you find them useful.  

If there is an interest, I can explore ways to solve applications without the need for programming.

Eddie 

All original content copyright, © 2011-2022.  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.