Casio fx-991 CW: Solving Linear Systems of Complex Numbers

Casio fx-991 CW: Solving Linear Systems of Complex Numbers

Introduction

The fx-991 CW is a capable calculator. It even handles complex number calculations and linear systems up to four variables. So we should be able to handle problems such as:

(A + Bi) * (x + yi) + (C + Di) * (z + ti) = E + Fi

(G +Hi) * (x + yi) + (J + Ki) * (z + ti) = L + Mi

where i=√-1 and A, B, C, D, E, F, G, H, J, K, L, and M are real and imaginary parts of complex numbers.

Well, yes. But the Equation mode does not allow for complex numbers, and the complex mode handles arithmetic and rectangular/polar conversions. True. However, all is not lost.

If we multiply the left side of both equations, we get:

(A * x – B * y + C * z – D * t) + (B * x + A * y + D * z + C * t)i = E + Fi

(G * x – H * y + J * z – K * t) + (H * x + G * y + K * z + J * t)i = L + Mi

Equating the real and imaginary parts, we get four equations since the real and imaginary parts are separated by addition.

A * x – B * y + C * z – D * t = E (real part)

B * x + A * y + D * z + C * t = F (imaginary part)

G * x – H * y + J * z – K * t = L (real part)

H * x + G * y + K * z + J * t = M (imaginary part)

In this form, we can use the linear system solver of the fx-991CW (as well as many other calculators).

In matrix form:

[ [ A, -B, C, D ] [ [ x ]   [ [ E ]

[ B, A, D, C ]   * [ y ]  = [ F ]

[ G, -H, J, -K ]   [ z ]    [ L ]

[ H, G, K, J ] ]   [ t ] ]  [ M ] ]

Casio fx-991CW: Algorithm

Step 1. Press the [ HOME ] key and select Equation.

Step 2. Select Simul Equation.

Step 3. Select 4 Unknowns.

Step 4. Set up the equations as follows:

A * x – B * y + C * z – D * t = E

B * x + A * y + D * z + C * t = F

G * x – H * y + J * z – K * t = L

H * x + G * y + K * z + J * t = M

Step 5. Press [ EXE ], or [ SHIFT ] [ EXE ] (≈) for all approximate solutions. Scroll to see the results x, y, z, and t. In the default setting, every answer, except for x is expressed in standard form. I’m not sure why this is. This is your solution to x + yi and z + ti.

Step 6. To do a new calculation, press [ EXE ] again.

Examples

Example 1:

(6 + 4i) * (x + yi) + (2 + 5i) * (z + ti) = 11 + 63i

(8 + 14i) * (x + yi) + (16 + 7i) * (z + ti) = 213 + 105i

Set up the four equations as:

6x – 4y + 2z – 5t = 11

4x + 6y + 5z + 2t = 63

8x -14y + 16z – 7t = 213

14x + 8y + 7z + 16t = 105

Results:

x ≈ -1.682508574

y = -2109 / 2041 ≈ -1.033317001

z = 2239 / 157 ≈ 14.2611465

t = 363 / 157 ≈ 2.312101911

x + yi ≈ -1.682508574 – 1.033317001i

z + ti ≈ 14.2611465 + 2.312101911i

Example 2:

(3 + 3i) * (x + yi) + (-9 + 7i) * (z + ti) = -4 + 2i

(-5 + 3i) * (x + yi) +(2 + 8i) * (z + ti) = 11 + 0i

Set up the four equations as:

3x – 3y - 9z – 7t = -4

3x + 3y + 7z - 9t = 2

-5x - 3y + 2z – 8t = 11

3x - 5y + 8z + 2t = 0

Results:

x ≈ -1.252444271

y = -1245 / 5114 ≈ -0.2434493547

z = 2131 / 5114 ≈ 0.4166992569

t = -2029 / 5114 ≈ -0.3967540086

x + yi ≈ -1.252444271 – 0.2434493547i

z + ti ≈ 0.4166992569 – 0.3967540086i

Until next time, take care,

Eddie

All original content copyright, © 2011-2025. 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.

TI-84 CE and TI-86: Matrix Row Statistics

TI-84 CE and TI-86: Matrix Row Statistics

Introduction

The program MROWST will take a matrix and a desired row and calculate three statistics points:

* Sum of the row

* Mean of the row

* Difference Vector: row – mean for each element

TI-84 CE Program MROWST

Matrices used: [ J ] (entry matrix), [ I ] (difference vector)

Input “MATRIX? “, [ J ]

Input “ROW? “, R

dim([ J ])

Ans(2) → D

0 → S

For(I, 1, D)

S + [ J ](R, I) → S

End

S / D → M

{1, D} → dim([ I ])

For(I, 1, D)

[ J ](R, I) – M → [ I ](1, I)

End

ClrHome

Disp “SUM: “ + toString(S)

Disp “MEAN: “ + toString(M)

Disp “DIFF VECTOR:”

Pause [ I ]

TI-86 Program MROWST

Matrices used: MJ (entry matrix), MD (difference vector), mone (vector of ones)

Input “Matrix? “, MJ

Input “Row? “, R

dim MJ

Ans(2) → D

D → dim mone

Fill(1, mone)

dot(mone, MJ(R)) → S

S / dim mone → M

MJ(R) - (M * mone) → MD

ClLCD

Disp “Sum:”, S

Disp “Mean:”, M

Disp “Diff Vector:”

Pause MD

Example

Matrix:

[ [ -9, -4, -1, -9, 4 ]

[ -9, -7, -4, -4, 9 ]

[ 7, 1, -9, -7, 8 ] ]

Row 1:

Sum: -1

Mean: -0.2

Difference Vector: [ 9.2, -3.8, -0.8, -8.8, 4.2 ]

Row 2:

Sum: -15

Mean: -3

Difference Vector: [ -6, -4, -1, -1, 12 ]

Row 3:

Sum: 0

Mean: 0

Difference Vector: [ 7, 1, -9, -7, 8 ]

Source:

Stuerke, Cecil. “Demonstration of Principal Component Analysis on TI-86” IEEE 2008

Eddie

Quick update: Starting October 5, 2024, my schedule will allow me to blog once a week. Regular posts will go live every Saturday. Thank you for your support and compliments. I wish you all well.

All original content copyright, © 2011-2024. 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.

Spotlight: Sharp EL-5200

 Spotlight: Sharp EL-5200

As we come on the 13^th (April 16) anniversary of this blog, I want to thank you. Blogging about mathematics and calculators is a joy in my life and I’m grateful for your support.

Today’s spotlight is about an early graphing calculator, which is a rare collector’s item today: the Sharp EL-5200, also known as the Sharp EL-9000.

Quick Facts

Model: EL-5200/EL-9000

Company: Sharp

Timeline: 1986 – late 1980s

Type: Graphing, Programmable

Memory: 5,120 bytes

Power: 2 x CR2032 batteries

Keyboard

There are excellent reviews and articles on the Sharp EL-5200/EL-9000, please check out the Sources section below.

The EL-5200 is a folding calculator which is housed in a wallet. On the left side, we have the scientific keys, the arrow keys, memory keys, and the numeric keypad. The keys are the normal calculator keys.

On the right side, there are the alphabetic keys and the utility keys. I think the key style on the right side is a membrane keyboard, but I am not sure.

The Four Main Modes

The four main modes of the Sharp EL-5200 are, which are listed in switch order:

STAT mode

COMP mode

AER II mode

AER I mode

AER II and AER I modes are programming mode, which is called the Algebraic Expression Reserve mode. The AER I mode is the classic AER mode while AER II is the newer version of programming mode.

The manual to the EL-9000 can be downloaded here: http://basic.hopto.org/basic/manual/Sharp%20EL-9000%20EN.pdf

STAT Mode

This is the calculator's statistics mode. Upon switching to this mode, we have the option of storing data points. Data points are stored in array S while basic statistics are stored in array Z. The basic statistics stored in array Z are:

Z[1] = n

Z[2] = Σx

Z[3] = Σx^2

Z[4] = Σxy

Z[5] = Σy

Z[6] = Σy^2

Be aware when you decide to store data, it takes up programming memory.

Three keys are remapped as follows:

[ RM ]: CD. Clear data. Erases a data point.

[ ⇒M ] (x, y): Adds a comma between the x point and y point.

[ M+ ] DATA: Adds a data point.

The statistic variables are access through the second function ([2ndF]) of the numeric keypad and arithmetic keys.

Linear regression is offered in the form of y = a + bx. The variable a is the y-intercept while the variable b is the slope.

Adding × n before pressing [ M+ ] {DATA} adds the frequency to the data point.

Graphs of statistical data are available, including histograms, linear regression lines, and scatter plots.

Fairly simple.

COMP MODE

This is our calculation mode. In addition to our regular scientific calculator, which operates in algebraic mode, there are other sub-modes included in COMP Mode.

Graphing

We can graph up to two functions at one time. The [ RANGE ] key allows to set the range parameters, while the [ AUTO ] key sets the zoom level automatically. The [DRAW] key draws the graph.

For example, to draw y(x) = x^2 + 5 using automatic zoom, key in [ GRAPH ] [ X ] [ x^2 ] [ + ] 5 [ AUTO ] [ DRAW ].

The screen takes up the entire left hand of the screen. The screen shows one coordinate at a time, X or Y. Switch between the two with the key sequence [ 2ndF ] [ ↑ ] {X<>Y}.

Matrices

The EL-5200 can store up to 26 matrices A-Z. Operations include determinant, inverse, transpose, and matrix arithmetic. We can get to the arrays at any time by pressing [ 2ndF] [↓].

In fact, the [ 2ndF ] [ ↓ ] toggles between the text (calculator), graphics, and data/array screen.

The [ 2ndF ] [ A ] {DIM} sequence can set the dimensions of a matrix.

In the data screen, we see two elements at one time.

Base Conversions

Integers can be converted between four bases: hexadecimal, binary, decimal, and octal. (bases 16, 2, 10, and 8, respectively) Not much more than arithmetic is offered.

Running Programs

Finally, COMP mode is where we run AER programs. Scroll through the programs with the [ PRO ] button. Start programs and enter data at the prompts by using the [ COMP ] key.

AER I MODE

AER I mode is the classic programming mode for Sharp programming calculators. This mode is meant for simple calculations. The [ f()=/? ] key puts the input form     f( )=. Enter the variables in between the parenthesis, and the variables will automatically be prompted. For example f(AB)= prompts for the variable A, then B. Only global variables (A – Z) are used. Implied multiplication is allowed. This mode is similar to the AER mode of EL-5100 from 1979.

Example: Circular Radius and Circumference

Title:

CIR.1

Code:

M: f( R ) = π × R^2 ⇒ A, 2 × π × R ⇒ C

(spaces are added for readability)

AER II MODE

AER II is the full programming mode. In this mode, we can use both global and local variables, with local variables being the default. Local variables include lower case letters and subscript numbers. Subscript numbers are entered by the sequence [ 2ndF ] [ number key ]. In this mode, the [ f()=/? ] key adds a question mark to the variable and creates a prompt. Unlike AER I, implied multiplication is not allowed.

Example: Graphing a Sine Wave

Title:

Graph A×sin(Bx+C). Set radians mode.

Code:

M: A = ? B = ? C = ? GRAPH A × SIN (B × X + C) AUTO DRAW

(spaces are added for readability)

There is no Radians mode command, so the user has to set Radians mode during program execution.

Common to Both Program Modes

M: This is the main loop.

, (comma): Displays the result of a calculation and pauses the execution. Press [ COMP ] to continue.

␣ (open space) : Finishes a calculation without stopping.

◣ (right triangle): Ends the current program or subroutine.

↳ ↰ : Loop markers

(comparison) -Y→[(do if true)] -N→[(do if false)]: If Then Else Structure.

[ 2ndF ] {SUB}: Creates a new subroutine. Switch between subroutines and the main loop by pressing [ 2ndF ] [ ↑ ] or [ 2ndF ] [ ↓ ].

To create a new program, go to either AER I or AER II mode, press [ COMP ], enter the title. The title is not limited to eight characters. Since we do not have string or string functions, include descriptive information and reminders in the title (see the example in AEI II Mode above).

I find the symbols taking a bit getting used to because we have symbols instead of the regular If-Then-Else-End structure, For-Next loop, Lbl-Goto structure, etc. AER can store complex formulas and best are for simple number crunching.

Overall Thoughts

I like the separate alphabetic keys, but the membrane keyboard calls for extra care when using those keys. The number of features of the EL-5200 are very invented and advanced for 1986. I wish the AER programs had line returns instead everything smashed together in wrap around lines, but it is more for readability. The calculator has a nice, compact form and is fun to work with.

In the future I will be posting AER programs for the EL-5200. It’s rarity makes the EL-5200/EL-9000 collectible.

Sources

Calculator Culture. “Sharp EL-9000 Graphing Calculator from 1986” November 27, 2023.

https://www.youtube.com/watch?v=cw7Gp2Qrmtk

Gelhaus, Matthew & Taia Gelahus. “Sharp EL-5200” gelahus.net. Last Updated December 21, 2023. http://www.gelhaus.net/cgi-bin/page.py?loc:8bit/+content:EL-5200.html Retrieved March 1, 2024.

Magyarra, Váltás “History and Programming of AER Calculators”. Milestone in the History of Calculators. Virtual Museum of Calculators. 2016. Retrieved March 25, 2024. http://www.arithmomuseum.com/szamologep.php?id=25&lang=en

Sharp Corporation. Sharp Scientific Calculator Super Scientific Model EL-9000 Operation Manual. 1986 http://basic.hopto.org/basic/manual/Sharp%20EL-9000%20EN.pdf

(website hosted by hopto.org) (this the same manual for the EL-5200)

Eddie

All original content copyright, © 2011-2024. 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 15C: Vector Operations

HP 15C:   Vector Operations

Calculators covered:

* HP 15C

* HP 15C Limited Edition

* HP 15C Collector's Edition

* Apps, Swiss Micros DM 15

HP 15C:   Dot Product, Tensor Product, and Angle Between Vectors

Set vectors A and B as 3 x 1 vectors (3 rows, 1 column)

3 ENTER 1 dim A

3 ENTER 1 dim B

Dot Product  (LBL D)  

Dot product:  A ⋅ B = A^T B 

The result is a single number.

Code: 

001 : 42,21,14 : LBL D

002 : 45,16,11 : RCL MATRIX A

003 : 42,16, 4 : MATRIX 4

004 : 45, 16, 12 : RCL MATRIX B

005 : 42, 26, 13 : RESULT C

006 : 20 : ×

007 : 45,16,11 : RCL MATRIX A

008 : 42,16, 4 : MATRIX 4

009 : 45,13 : RCL C

010 : 43,32 : RTN

Tensor Product (LBL E)

Tensor product:  A ⊗ B = A B^T

The result is a 3 x 3 matrix

Code: 

011 : 42,21,15 : LBL E

012 : 45,16,11 : RCL MATRIX A

013 : 45,16,12 : RCL MATRIX B

014 : 42,16, 4 : MATRIX 4

015 : 42,26,13 : RESULT C

016 : 20 : ×

017 : 45,16,12 : RCL MATRIX B

018 : 41,16, 4 : MATRIX 4

019 : 42,16, 1 : MATRIX 1

020 : 45,16,13 : RCL MATRIX C

021 : 43, 32 : RTN

Angle Between Vectors (LBL 0)

θ = arccos( (A ⋅ B) ÷ (||A|| ||B||) )

Code:

022 : 42,21, 0 : LBL 0

023 : 32,14 : GSB D

024 : 45,16,11 : RCL MATRIX A

025 : 42,16, 8 : MATRIX 8

026 : 45,16,12 : RCL MATRIX B

027 : 42,16, 8 : MATRIX 8

028 : 20 : ×

029 : 10 : ÷

030 : 43,24 : COS^-1

031 : 43,32 : RTN

Notes:  

MATRIX 4:  Transposes a matrix, which it is stored in the original matrix slot.  

MATRIX 8:  The 2-norm of a matrix.   It is calculated by taking a square root of the sum of the square of each element.  √(Σ( A_r,c ^ 2,  r = 1 to n and c = 1 to m))

For the dot and tensor products, I transpose the appropriate matrix back to the 3 x 1 form after the calculation.

Example

A = [ [ 4 ], [ 5 ], [ -2 ] ]

B = [ [ -3 ], [ 9 ], [ 8 ] ]

Dot Product:  GTO D R/S

Result:  17

Tensor Product:   GTO E R/S

Result:

[ [ -12, 36, 32 ], [ -15, 45, 40 ], [ 6, -18, -16 ] ]

Angle Between Vectors:  GTO 0 R/S

Result:  78.2166°

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. 

TI-84 Plus CE: Using Matrices for "Tax Table" Calculations

TI-84 Plus CE:   Using Matrices for "Tax Table" Calculations

How The Matrix is Set Up

Each row represents a tier or a bracket.  

First column:  Lower Limit.  This is the test variable.  The first tier often will have the lower tier of 0.

Second and subsequent columns:    Variables that are associated with that tier.

Let's demonstrate this with an example.

Example Tax Bracket

This matrix has four brackets (four rows).  The algorithm starts with the last (bottom) row and tests whether the input is greater or equal to the test variable.  

According to the table, the tax rate changes at income level at $30,000, $90,000, and $270,000, with the top tax rate of 9% effective for all income excess of $270,000.

If the income is $29,999.99, the first tier of 3% is used.  If the income goes to $30,000.00, the next tier is activated.

The program ITAX, which uses this type of setup, goes "backwards".  It tests from the highest tier down.  

For example:  Income = $50,000

Start at tier 4 (bottom row). 

Is 50,000 > 270,000?  No, go to tier 3. (move one row up)

Is 50,000 > 90,000?  No, go to tier 2.  (move one row up) 

Is 50,000 > 30,000?  Yes, use the variables from tier 2.

Tax:  (50,000 - 30,000) × 5% + 900 = 20,000 × 5% + 900 = 1,900

Matrix wise:   (income - M[2,1]) * M[2,2] ÷ 100 + M[2,3]

Programs

There are two programs that illustrate this method:  

ITAX:  Income Tax Bracket.  Bracket is stored in Matrix [ A ] and has three columns:

Column 1:  lower limit of each bracket

Column 2:  tax rate for that bracket

Column 3:  additional "minimum" tax.   

BAROMET:  Calculates the air pressure and density based on height.  Scientific information is stored in Matrix [ J ].  

Column 1:  height in meters

Column 2:  mass density in kg/m^3

Column 3:  standard temperature in K

Column 4:  static pressure in Pa

If you are working in US Units, the height is converted to meters first.  After the calculation, the results are converted back into US units. 

You can download both programs here (zip file):  

https://drive.google.com/file/d/1ZCtMcJgZDLUGnrAHE6cPAkWBQQj1aHKc/view?usp=sharing

Source

"Barometric formula."  Wikipedia.  Last edited July 13, 2023.  Retrieved July 16, 2023.   https://en.wikipedia.org/wiki/Barometric_formula

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 15C: Quadratic Regression

HP 15C:  Quadratic Regression

Setup, Normal Equations, and Registers Used

This program fits bivariate date (x,y) to the quadratic polynomial:

y = c + b * x + a * x^2

This program uses the matrix feature of the HP 15C.  

The normal equations that are solved are:

n * c + Σx * b + Σx^2 * a = Σy

Σx *c + Σx^2 * b + Σx^3 *a = Σxy

Σx^2 * c + Σx^3 * b + Σx^4 * a = Σ(x^2 y)

Matrix A = 

[ [ n, Σx, Σx^2 ]

[ Σx, Σx^2, Σx^3 ]

[ Σx^2, Σx^3, Σx^4 ] ]

Matrix B = 

[ [ Σy ]

[ Σxy ]

[ Σ(x^2 y) ] ]

Matrix C = (Matrix B)^-1 Matrix A

[ [ c ] 

[ b ] 

[ a ] ]

Registers Used:

R0:  x data point, row pointer

R1:  y data point, column pointer

Default Statistics Registers:

R2:  n

R3:  Σx

R4:  Σx^2

R5:  Σy

R6:  Σy^2

R7:  Σxy

Additional Statistics Registers:

R8:  Σx^3

R9:  Σx^4

R.0:  Σ(x^2 y)   ("register point zero":  press the decimal point before the 0)

Instructions

1.  Run label A to clear the matrices and registers.  This needs to be done in order to get the most accurate results.  Zero is displayed to indicate when the calculator is ready.  

2.  For each point, enter y data point, press [ ENTER ], x data point, and run label B.  The number of data points (n) will be displayed.  

3.  To calculate the coefficients, run label C.   The coefficients c, b, and a are displayed in order.

Matrix Operations Used

MATRIX 0:  clear all the matrices 

MATRIX 1:  sets the row and counter pointer to 1,1.   

User Mode Set:  automatically advances the pointer to the right row by row.   In programs, turning on and off User Mode is not a step.  However, storage and recall operations in User Mode are marked with a "u" after the step number.  Be careful because if a matrix's pointers (row in R0 and column in R1) return to (1,1), while in USER mode, the next program is skipped.  A special acknowledgement to Torsten for pointing this to me.  

HP 15C Program Code: Quadratic Regression 

Program Memory:  67 steps, 90 bytes

Needs 15 additional memory registers to store the three matrices.

Comments begin with a hash symbol.  #

#  Label A:   Initialization

001 :  42,21,11 :   LBL A

002 :  42,34 :  CLEAR REG

003 :  42,16, 0 :  MATRIX 0

004 :  0 :   0

005 :  43,32  : RTN

# Label B:  Data Entry and Processing

006 : 42,21,12 :  LBL B

007 : 44, 0 :   STO 0

008 :  43,11 : x^2

009 :  34  :  x<>y

010 :  44, 1  : STO 1

011 :  20  :  ×

012 :  44,40,.0 :  STO+ .0  (# store-add to register point zero)

013 :  45, 0  : RCL 0  

014 :  3 :  3

015 :  14 : y^x

016 :  44,40, 8 :  STO+ 8

017 :  45,20, 0 :  RCL× 0

018 :  44,40, 9 : STO+ 9

019 :  45, 1 : RCL 1

020 :  45, 0 : RCL 0

021 :  49  : Σ+

022 :  43,32 : RTN

# Label C:  Calculation

023 : 42,21,13 : LBL C

024 : 3 :  3

025 : 36 : ENTER

026 : 42,23,11 : DIM A

027 : 42,16, 1 : MATRIX A

# Matrix A - Row 1

# Turn on USER Mode ( [ f ] [ RCL ] (USER))

028 : 45, 2 : RCL 2

029 u 44,11 :  STO A

030 : 45, 3 : RCL 3

031 u 44,11 : STO A

032 :  45, 4 :  RCL 4

033 u 44,11 : STO A

# Matrix A - Row 2

034 : 45, 3 : RCL 3

035 u 44,11 : STO A

036 : 45, 4 :  RCL 4

037 u 44,11 : STO A

038 :  45, 8 : RCL 8

039 u 44,11 : STO A

# Matrix A - Row 3

040 : 45, 4 : RCL 4

041 u 44,11 : STO A

042 : 45, 8:  RCL 8

043 u 44,11 : STO A

044 : 45, 9 : RCL 9

045 u 44,11 : STO A

# Turn off USER Mode (unless the next step would be skipped unnecessarily)

# Matrix B

046 : 42,16, 1 : MATRIX 1

047 : 3 :  3

048 : 36 : ENTER

049 : 1 : 1

# Turn on USER Mode

050 : 42,23,12 : DIM B

051 : 45, 5 : RCL 5

052 u 44,12 : STO B

053 : 45, 7 : RCL 7

054 u 44,12 : STO B

055 : 45,.0 : RCL .0   (# recall registers point-zero)

# Turn off USER Mode (unless the next step would be skipped unnecessarily and in this case, an Error 11 would occur)

056 :  44,12 : STO B

# Matrix C - Results

057 : 42,26,13 : RESULT C

058 : 45,16,12 : RCL MATRIX B

059 : 45,16,11 : RCL MATRIX A

060 : 10 : ÷

061 : 42,16, 1 : MATRIX 1

062 u 45,13 : RCL C

063 : 31 : R/S

064 u 45,13 : RCL C

065 : 31 : R/S

066 u 45,13 : RCL C

067 : 43,32 : RTN

Examples

Example 1:

(3, 1.3)

(4, 1.6)

(5, 1.5)

(6, 1.4)

c = -0.54

b = 0.92

a = -0.1

y = -0.54 + 0.92 x - 0.1 x^2

Example 2:

(0, 99.856)

(3, 97.232)

(5, 93.481)

(7, 96.005)

(10, 102.008)

c ≈ 100.3437

b ≈ -2.5318

a ≈ 0.2495

y ≈ 100.3437 - 2.5318 x + 0.2495 x^2

Enjoy!

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. 

Announcement: HP 15C Collector's Edition

 Announcement:  HP 15C Collector's Edition

The HP 15C Returns

Hewlett Packard and Moravia is bringing back the HP 15C Calculator with the HP 15C Collector's Edition, which is set to be delivered starting the summer of 2023.  

The HP 15C is a RPN (Reverse Polish Notation) programming scientific calculator, first released in in 1982 and has the following features:  

*  Matrices:  Store up to 5 matrices.  Operations include determinant, inverse, norm, and transpose.  

*  Complex Numbers:  The set of complex numbers includes powers, logarithms, and trigonometry.

*  Numerical integration

*  Solve:  Finding the roots of functions

*  Standard Scientific functions:  polar/rectangular conversions, trigonometry, powers, roots, logarithms, linear regression, fraction and integer parts, hyperbolic functions

*  Programming:  Keystroke with labels, comparison tests

The HP 15C Collector's Edition has the following improvements from the original and Limited Edition of the HP 15C:

*  There are now 99 memory registers, up from 67

*  There is now a memory capacity of 672 steps, up from 448

*  The new processor promises a faster speed 

*  The Collector's Edition comes with a printed manual, which can be downloaded from Calculator Store's website here:  https://www.thecalculatorstore.com/epages/eb9376.sf/en_US/?ObjectPath=/Shops/eb9376/Products/%22HP-15c%20%23INT%22

From browsing the PDF file of the manual, the manual looks nice and it's detailed. 

For details, credit, and discussion, click on Klass' original post is on the Museum of HP Calculators (MoHPC) here:  https://www.hpmuseum.org/forum/thread-19886.html

Pre-Orders

The HP 15C Collector's Edition is set to be delivered starting at the end of June 2023.   At this moment, Moravia Consulting, a licensee for HP Calculators, has two stores offering pre-sales:

Eduwinkel:  (Netherlands) (Price:  129,95 Euros as of 5/3/2023*)

https://www.eduwinkel.nl/hp-15c-collectors-edition-calculator.html

The Calculator Store:  (Spain) (Price: 129,99 Euros as of 5/3/2023*)

English:  

https://www.thecalculatorstore.com/epages/eb9376.sf/en_US/?ObjectPath=Categories

Spanish:  

https://www.thecalculatorstore.com/epages/eb9376.sf/es_ES/?ObjectPath=Categories

* Prices do not include delivery charges but does include value added tax (VAT).  Depending where the customer is from VAT may be subtracted from the price.  

Source:

Kuperus, Klaas.   "NEW: HP 15C Collectors Edition"  MoHPC (Museum of HP Calculators)   May 2, 2023.  https://www.hpmuseum.org/forum/thread-19886.html

I have pre-ordered a HP 15C Collector's Edition and can't wait to work with it.  

Disclaimer:  No compensation has been received for this post.  

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.