## Saturday, May 30, 2015

### HP Prime and TI-84 Plus: Runge Kutta 4th Order

HP Prime and TI-84 Plus:  Runge Kutta 4th Order

The Runge Kutta 4th Order is a method for solving differential equations involving the form:  dy/dx = f(x,y), where:

x_n+1 = x_n + h
y_n+1 = y_n + (k1 + 2*k2 + 2*k3 + k4)/6

Where:

k1 = h * f(x_n, y_n)
k2 = h * f(x_n + h/2, y_n + k1/2)
k3 = h * f(x_n + h/2, y_n + k2/2)
k4 = h * f(x_n + h, y_n + k3)

Variables used:

A = x_n
B = y_n
C = x_n+1
D = y_n+1
H = step
K = k1
L = k2
M = k3
N = k4

Results are stored in lists L1 and L2.  L1 represents the x coordinates, L2 represents the y coordinates.

This adopts the RK4 method that I programmed for the Casio fx-5800p, which you can see here:  http://edspi31415.blogspot.com/2015/01/fx-5800p-runge-kutta-4th-order-method.html

The screen shots show the example dy/dx = x^2 + y^2/3, with initial conditions y(0) = 1.  10 steps are plotted with step size 0.1.

HP Prime:  DIFFTBL and RK4

Both DIFFTBL and RK4 return the same output.  The difference is that DIFFTBL uses an Input box and no-pass through arguments and RK4 uses five pass-through arguments.  This way, RK4 could be used as a subroutine.

Both return the results in a matrix, M1.  Rev. 7820 firmware is used.

DIFFTBL:
EXPORT DIFFTBL()
BEGIN
// EWS 2015-05-29
HAngle:=0;
// Input
LOCAL f;

INPUT({{f,[8]},A,B,H,S},"Data Input",
{"dy/dx=","x0=","y0=","Step=",
"# Steps="});
L1:={A}; L2:={B};
// Main Loop
FOR I FROM 1 TO S DO
// k1
X:=A;
Y:=B;
K:=H*EVAL(f);
// k2
X:=A+H/2;
Y:=B+K/2;
L:=H*EVAL(f);
// k3
Y:=B+L/2;
M:=H*EVAL(f);
// k4
X:=A+H;
Y:=B+M;
N:=H*EVAL(f);
// point
A:=A+H;
B:=B+(K+2*L+2*M+N)/6;
L1:=CONCAT(L1,{A});
L2:=CONCAT(L2,{B});
END;
M1:=list2mat(CONCAT(L1,L2),
SIZE(L1));
M1:=TRN(M1);
RETURN M1;

END;

RK4:
EXPORT RK4(f,A,B,H,S)
BEGIN
// EWS 2015-05-29
HAngle:=0;
// Input

L1:={A}; L2:={B};
// Main Loop
FOR I FROM 1 TO S DO
// k1
X:=A;
Y:=B;
K:=H*EVAL(f);
// k2
X:=A+H/2;
Y:=B+K/2;
L:=H*EVAL(f);
// k3
Y:=B+L/2;
M:=H*EVAL(f);
// k4
X:=A+H;
Y:=B+M;
N:=H*EVAL(f);
// point
A:=A+H;
B:=B+(K+2*L+2*M+N)/6;
L1:=CONCAT(L1,{A});
L2:=CONCAT(L2,{B});
END;
M1:=list2mat(CONCAT(L1,L2),
SIZE(L1));
M1:=TRN(M1);
RETURN M1;

END;

TI-84 Plus:  DIFFPLOT

DIFFPLOT plots the results in a statistics xy-plot.  The equation variable Y0 is used, but subsequently deleted.  I left out any color commands to make this easily adoptable for both the monochrome and color TI-84 Plus calculators.

Do not forget to enclose dy/dx in quotes, unless an input error occurs

Disp "DIFF. EQUATION"
Disp "Y₀=DY/DX"
Disp "USE QUOTES"
Input Y₀
Input "X0=",A
Input "Y0=",B
Input "STEP=",H
Input "NO. STEPS=",S
{A}→L₁
{B}→L₂
For(I,1,S)
A→X:B→Y
H*Y₀→K
A+H/2→X:B+K/2→Y
H*Y₀→L
B+L/2→Y
H*Y₀→M
A+H→X:B+M→Y
H*Y₀→N
A+H→A
B+(K+2*L+2*M+N)/6→B
augment(L₁,{A})→L₁
augment(L₂,{B})→L₂
End
FnOff 0
PlotsOn 1
Plot1(xyLine,L₁,L₂)
ZoomStat

This blog is property of Edward Shore.  2015.

## Thursday, May 28, 2015

### HP Prime, TI-84 Plus, Casio Prizm: Julian Day Shortcut Formulas

Julian Day Shortcut Formulas

Here are a couple of formulas that can be used to quickly get the Julian Day.  (I haven't figured how to include the time yet).

HP Prime (Rev. 7820):

yyyy:  four digit year, mm:  two digit month, dd: two digit day.  The international date format is used.

From December 31, 1899:

JD = DDAYS(1899.1231,yyyy.mmdd) + 2415020

Alternatively, from November 16, 1858:

JD = DDAYS(1858.1116, yyyy.mmdd) + 2.4E6

TI-84 (and BA II  Plus to that extent):

Dates are good from January 1, 1950 to December 31, 2049:

JD = dbd(1.0150, mm.ddyy) + 2433283

The days between dates function (dbd) is accessed by pressing [ APPS ], [ 1 ], [ALPHA], [ x^-1] (D).

Casio Prizm and fx-Graphing calculators:

Dates are good from January 1, 1901 to December 31, 2099:

JD = Days_Prd(1,1,1901,mm,dd,yyyy) + 2415386

Where to find Days_Prd:  [ OPTN ], ( > ) (until you see the FINANCE sub menu), (FINANCE), ( > ), (DAYS), (PRD)

Source:
"Julian Day"  http://en.wikipedia.org/wiki/Julian_day   Retrieved May 28, 2015

Eddie

This blog is property of Edward Shore.  2015.

## Saturday, May 23, 2015

### Review: TI-84 Plus CE

Review:  TI-84 Plus CE

 TI-84 Plus CE

Calculator Information:

Calculator:  TI-84 Plus CE
Manufacturer:  Texas Instruments

Price:  \$119 - \$135

Availability:  Currently online through select distributors.  I purchased mine from the Bach Company (website: http://www.bachcompany.com/ ).  For a complete list of vendors, check the Texas Instruments calculator website at http://education.ti.com/en/us/purchase/purchase  .   It should be available at popular retail stores, in many colors, by the time the next school year (2015-2016) comes around.

Current OS:  5.0.1.0012.

What’s in the package?

TI-84 Plus CE, standard mini-USB charging cable, calculator to calculator cable, warranty information, getting standard guide (fold out card), and a short operation manual (fold out card).  The full manual is found online from the TI Calculator website.

If you want to see a video introduction of it, click this link:  https://www.youtube.com/watch?v=F7OAG3dNpzE

Key Features:

*  For those of you new to the TI-83/84 Plus family, the TI-84 Plus CE is the latest incarnation.  Like 2013’s TI-84 Plus C Silver Edition, the TI-84 Plus CE is a color graphing calculator, that has a rechargeable battery.

* If you know how to operate any of the TI-83 or TI-84 calculators and are considering either an upgrade or adding this calculator to your collection, you will feel right at home operating the TI-84 Plus CE.  In general, you have the same interface and syntax (for most commands).  The best part is that the TI Basic programs (with few exceptions) can easily be transferred to the TI-84 Plus CE from older calculators.

* Mathematical features:

Mathematical:  All the standard scientific functions, integer and fractional part extraction, numeric derivative, numeric integral, numerical summation, and numerical solver.

Complex Numbers:  arithmetic, power, roots, exponential, and logarithmic.

Graphing:  Function, Parametric, Polar, Sequential

Matrices:  Up to 10 matrices can be stored. Operations include determinant, transpose, inverse, row operations, and generation of identity and random integers.

Lists:  6 default list names but you can add more.  List operations include cumulative sum, sum of the list, dimension, and change between elements.

Statistics:  1 and 2 variable.  The regressions available are med-med, linear (two forms), quadratic, cubic, quartic, exponential, logarithmic, power, logistic, and sinusoidal.

Programming: TI-Basic, Assembly, and Applications.

Distributions:  Normal (with inverse), T (with inverse), Chi Square, F, Binomial, Poisson, and Geometric.

Colors:  Up to 15 different colors for graphing and displaying text can be used.

* Memory:  Archive 3 MB (1.92 MB available after the OS and default included apps), RAM:  154,000 bytes.

* Applications Included:  Finance (basic), CabriJr (geometry), Conics, Vernier EasyData (for classroom peripherals), Inequalz*, Periodic (table), PlySlmt2 (polynomial and simultaneous equation solver), Prob Sim (probability simulator), SciTools*, and Transfrm (dynamic graphing by including A, B, C, etc in functions).

Inequalz:  Run this app and you are able to graph inequalities as well as equalities complete with shading.

SciTools:  This adds constants, conversions, and vector operations.  Vector operations are 2D and are drawn.  Operations available are addition, subtraction, dot product, and cross product. Data/Graphs wizard is a statistics interface.

MathPrint vs. Classic:  You can operate the TI-84 Plus CE in the classic mode, which the way older TI-83 Plus calculate, or in MathPrint.  In MathPrint, you can express calculations using templates.  With the faster processor, I don’t really think there is any advantage to using Classic mode any more (except for maybe to get used to syntax required for programming).

 TI 84 Plus CE in action

 SciTools app in action

What I like the Most:

* I am loving the increased amount of RAM that the TI-84 Plus CE has.  It has the most ram of any incarnation of the TI-83/84 family.  154,000 bytes are now available compared to the small 21,000 bytes that the TI-84 Plus C Silver Edition offered.

* The new software that is associated with the TI-84 Plus CE is the TI Connect CE.  Features include easily being able to take screen shots, transfer files, and even editing programs in the Connection software.  TI Connect CE works with the TI-84 Plus family and the TI-83 Plus fr (France’s edition of the TI-84 Plus), and TI-83 Premium CE (France’s version of the TI-84 Plus CE).

* The TI-84 Plus CE is at least three times faster than the predecessor.  And this is welcome.  The CE gets a new 48 Mhz ez80 processor. The internal RAM has doubled from 128 KB (which 21 KB-24 KB was available for the user) to 256 KB (154 KB available to the user), allowing for faster calculations.

* It may be settle, but I detect a better key press response rate.

* Like the previous C Silver Edition, the screen is crisp and clear.  The text is very easy to read.

* This is the thinnest TI-84 calculator ever.  Yet the CE fits comfortably in my hand and the keyboard is large with easy to read keys.

‘*  The QuickPlot&Fit-EQ feature (present on the previous C Silver Edition as well).  To use it, press the [graph] key.  The press the [stat] key, scroll up, and select E: QuickPlot&Fit-EQ under the CALC submenu.  Drop points using the [enter] key.  Once you are done, press [graph] (FITEQ) to fit the points.  Select the appropriate curve and the curve is plotted.  You can see whether the curve plotted works.  Results can be stored.

 QuckPlot&Fit-EQ in action:  I love this feature!

Being Nit Picky?

* The graph screen still has a border from the previous C Silver Edition.  I was hoping the calculator take advantage of the entire screen that the monochrome 84s did.

*  I would really still like to see vector functions make the Math or Vector menu, as well as trigonometric functions being allowed to handle complex numbers.  Maybe a future update?  (You can see my wish list here:  http://edspi31415.blogspot.com/2015/05/ti-84-plus-wish-list.html )

For a more technical review, please check out KermMartin’s review at cemetch.net:  http://www.cemetech.net/forum/viewtopic.php?t=11434

Verdict:

If you have been waiting to get a color graphing TI-84, then the wait has paid off.  The TI-84 CE is a delight to use, and the operation is fast and responsive.  I think only the black case TI-84 CEs are available, if you really want to have the CE in another color (red, dark blue, light blue, pink, purple, or gray), then it is a wait until Back to School season.

If you do not have a TI-84 and either are interested or need to get one for school, the CE is the version to consider, because you get the color, backlit screen, the rechargeable battery, and a large amount of RAM (user memory).

I think Texas Instruments has a winner with the TI-84 Plus CE.

Eddie

This blog is property of Edward Shore.  2015.

## Thursday, May 21, 2015

### Review: QuickGraph+ for iOS

App Information:
App: QuickGraph+
Platform: iOS
Created by KZLabs
Programmers: Alex Restrepo, Alejandro Montoya
Graphics: Giovanni Mojica

Cost: \$1.99 (I purchased it on 2015-05-18). There is a free version, which has a limited function set, but I am going to review the paid app.

Version in Review: 2.5.4

Key Features:

* Graph functions, inequalities, polar, spherical, cylindrical, and implicit statements in 2D and 3D.

* You can save graphs to the Camera roll, as well as use them in emails or tweets.

* Including the variable n in the expression will allow a dynamic graph. You can set he limits to n and the amount of steps between the limits.

* 2D functions, in the form of y=f(x), can be traced (tap the function and hold). When two or more functions are graphed, and one of them is traced, QuickGraph+ displays roots and intersections where appropriate. This is automatic.

What I Like the Most:

* Pressing the nine-square icon will bring up the table. This is available for the 2D graphs only.

* Derivative of functions can be graphed and symbolic analyzed. We can take the following derivatives d/dx, d/dy, and d/dz. To see the symbolic analyzation, press the blue circular icon with the ellipsis (...). On the iPod Touch/iPhone version, a step by step analysis is shown.

* Speaking of analysis, you can enter numerical expressions and they will be automatically analyzed. Just press the [ + ] button and enter the expression. In this sense, this is a scientific calculator.

* You can store functions and graph statements in the app's built in library. The library is stocked with several graph statements when you download QuickGraph+ for the first time. The library is accessed by pressing the book icon. Graphs that are active are listed on top, and those not already stored can be by pressing the small book icon next to them.

* The modulus function (mod), can work with any real number, not just positive integers.

Being Nit Picky?

* Not being able to trace polar functions like regular functions.

* Not being able to trace functions that contain n or be analyzed.

Wish List:

* The ability to plot parametric functions, both in 2D and 3D.

Verdict:

This is a fun app and you can graphically explore functions, patterns, and inequalities. Sharing graphs is a plus. Not a bad way to spend \$1.99!

Eddie

This blog is property of Edward Shore. 2015

## Wednesday, May 20, 2015

### Fun with the GO-25 iOS App

Here are several short programs made with the GO-25 iOS app. Each one can be adopted into programming routines for other RPN calculators and apps.

Enjoy!

GO SCI-25 App

; atan2 function in radians. Store x to memory 1 and y to memory 2.
02 24 02 ; RCL 2
03 24 01 ; RCL 1
04 71 ; ÷
05 15 06 ; tan⁻¹
06 24 01 ; RCL 1
07 15 41 ; x<0
08 13 11 ; GTO 11
09 22 ; R↓
10 13 00 ; GTO 00
11 22 ; R↓
12 24 02 ; RCL 2
13 15 03 ; ABS
14 14 73 ; LASTx
15 71 ; ÷
16 15 73 ; Ï€
17 61 ; X
18 51 ; +
19 13 00 ; GTO 00

; signum function. sgn(stack x), x ≠ 0
01 15 03 ; ABS
02 14 73 ; LASTx
03 71 ; ÷
04 13 00 ; GTO 00

; Simple Simultaneous Equarions
; a + b = x
; a - b = y
; x → R1, y → R2, load before running
01 24 02 ; RCL 2
02 24 01 ; RCL 1
03 51 ; +
04 02 ; 2
05 71 ; ÷
06 74 ; R/S
07 24 01 ; RCL 1
08 24 02 ; RCL 2
09 41 ; -
10 02 ; 2
11 71 ; ÷
12 13 00 ; GTO 00

; t^2 + y*t + x = 0
; Enter y and x before running.
01 31 ; ENTER *may or may not be needed deepening on stack operations
02 04 ; 4
03 61 ; X
04 21 ; Swap xy
05 15 02 ; x^2
06 14 73 ; LASTx
07 32 ; CHS
08 23 01 ; STO 1
09 22 ; R↓
10 21 ; Swap xy
11 41 ; -
12 14 02 ; √
13 23 02 ; STO 2
14 24 01 ; RCL 1
15 24 02 ; RCL 2
16 51 ; +
17 02 ; 2
18 71 ; ÷
19 74 ; R/S
20 24 01 ; RCL 1
21 24 02 ; RCL 2
22 41 ; -
23 02 ; 2
24 71 ; ÷
25 13 00 ; GTO 00

; Hypotenuse Function
; hypot(x,y) = √(x^2 + y^2)
; Enter x and y on the stack.
01 15 02 ; x^2
02 21 ; Swap xy
03 15 02 ; x^2
04 51 ; +
05 14 02 ; √
06 13 00 ; GTO 00

; Approximate Speed of Sound in Dry Air (4 decimal places)
; Enter temperature in degrees Fahrenheit (°F). Results are in miles per hour.
; V ≈ .7456*(x-32) + 741.3087
01 31 ; ENTER
02 03 ; 3
03 02 ; 2
04 41 ; -
05 73 ; .
06 07 ; 7
07 04 ; 4
08 05 ; 5
09 06 ; 6
10 61 ; X
11 07 ; 7
12 04 ; 4
13 01 ; 1
14 73 ; .
15 03 ; 3
16 00 ; 0
17 08 ; 8
18 07 ; 7
19 51 ; +
20 13 00 ; GTO 00

; Area of a Polygon:
; Degrees mode is used. Stack:
; y: length
; x: sides
01 15 32 ; DEG
02 23 01 ; STO 1
03 21 ; Swap xy
04 15 02 ; x^2
05 61 ; X
06 01 ; 1
07 08 ; 8
08 00 ; 0
09 24 01 ; RCL 1
10 71 ; ÷
11 14 06 ; tan
12 04 ; 4
13 61 ; X
14 71 ; ÷
15 13 00 ; GTO 00

; Doppler Effect: calculated the effective frequency given:
; y: observed frequency in Hz
; x: change in velocity of the object in m/s, if the source is coming to you, enter this velocity as negative
01 31 ; ENTER
02 02 ; 2
03 09 ; 9
04 09 ; 9
05 07 ; 7
06 09 ; 9
07 02 ; 2
08 04 ; 4
09 05 ; 5
10 08 ; 8
11 71 ; ÷
12 01 ; 1
13 51 ; +
14 61 ; X
15 13 00 ; GTO 00

; Music Scale: Approximate frequency given for x half steps from Middle C (523 Hz)
01 31 ; ENTER
02 02 ; 2
03 31 ; ENTER
04 01 ; 1
05 02 ; 2
06 15 22 ; 1/x
07 14 03 ; y^x
08 21 ; Swap xy
09 14 03 ; y^x
10 05 ; 5
11 02 ; 2
12 03 ; 3
13 61 ; X
14 13 00 ; GTO 00

Eddie

This blog is property of Edward Shore. 2015

## Tuesday, May 19, 2015

### Review: Calculator C++ (Android)

App Information:
App: Calculator C++
Platform: Android
Created by serso
Translated to English by Sergey Solovyev

Cost: Free with ads or \$3.99 to remove ads from the graph and menu screens (well worth it in my opinion)

Version in Review: 2.1.2

Key Features:

* Calculator C++ has two setups: Simple and Engineering. The Engineering will give you the scientific calculator setup and give you freedom to switch angle modes, while Simple mode operates in Degrees mode and rounds all answers to five decimal places. You can change settings by rerunning the Start Wizard. My review will be on the app on the Engineering setup.

* The calculator operates in algebraic mode. Results are automatically calculated and updated in real time (you can turn this feature off in Settings-Calculation Settings).

* Expressions can include implicit multiplication. Hence, calculations such as 5(2+3) and 2.5cos(60°) are allowed. Just use it in the home area, when programming custom functions, make sure to include the multiplication signs (*).

* Shift functions are accessed by swipes, not a secondary (or tertiary) key. I admit this took getting used to, but it is a unique feature I have seen regarding shifted functions in any app I have used so far.

* Full complex number support, including trigonometric functions.

* Integer conversions between binary, octal, hexadecimal, and decimal. Except for octal, each of the bases have their own modes, with decimal mode being the default.

What I like the most:

* The ability to create functions. Either press the [f(x)] button, go to the MY section and press [ + ], or create the expression on the home screens and swipe up on the [f(x)] button. (Personally the former procedure works a lot better.). Need to edit a user-defined function? Press [f(x)] button, go to the MY section, hold on the function to edited and select Modify.

Caution: Only the variables x, y, t, and j (not sure i can be used since i represents the constant √-1) are available on the keyboard. However, you can use any letter or word (i.e. myvar, cost,temp) as arguments in user defined functions.

* Constants (via the [ Ï€,... ] button) are handled the same way. Eight constants are built in. An unusual one is he Î  (capital Ï€), which returns Ï€ in Radians mode, 180 in Degrees mode.

* The graphing engine, especially with the way Calculator C++ handles 3D function. Essentially to plot a function, just enter the function (2D or 3D), swipe down on the equals key ([ = ]).

* CAS functions! Symbolic derivative, integral*, sum, product, and simplification of some algebraic objects.

Being nit picky? Some things I didn't like so much:

* I wish the factorial function worked on more than positive integers. Either way, glad it's here.

* The lack of integer and fractional part functions, logic functions, and an if function for function programming. However, the presence of comparison functions may indicate that there is room for updates in the future.

* Integration is limited to basic functions, those whose anti-derivative can easily be found. This affects the numerical integral function as well (∫ab).

By the way...

Comparison Functions

Comparison functions are indicated by a two letter function instead of their usual symbols. If the comparison is true, the result is 1, otherwise it is 0. They are:

ap(x,y): Not sure what this one is. Maybe the same of eq? It seems to test that way.
eq(x,y): Test whether x = y
ge(x,y): Test whether x > y
gt(x,y): Test whether x ≥ y
le(x,y): Test whether x < y
lt(x,y): Test whether x ≤ y
ne(x,y): Test whether x ≠ y

Verdict:

This is a yes. I am really impressed with the interface, and how you can access functions by swipes, calculations update in real time, and the graphing engine.

Function Bonus:

Here are some custom functions I programmed with the Calculator C++ app:

Hypotenuse function:
hypot(a,b)
Value: √(a^2 + b^2)
Parameter order: a, b

Permutation:
perm(x,y)
Value: x!/(x-y)!
Parameter order: x, y

Combination:
comb(x,y)
Value: x!/(y!*(x-y)!)
Parameter order: x, y

ATAN2(x,y) function (angle, argument):
This where the capital Î  constant comes in handy. Recall that Î  adjusts its value whether the app is in degrees mode or radians mode. On the android keyboard that I have (I think it's standard), I access the ?123 keyboard, then =\< keyboard, the hold down the Ï€ button to get Î .

atan2(x,y) = atan(y/x) + sgn(y)*Î *le(x,0)

The sgn is the sign function.

Roots of the Quadratic Equation (two functions):

Area of a Circle:
circlearea(x) = x^2*Ï€

(The constant Ï€ should be available on any Android keyboard. I am working on a Droid phone from Motorola).

Eddie

This blog is property of Edward Shore. 2015

P.S. The TI-84+ CE is on its way! :)

## Saturday, May 16, 2015

### TI-84 Plus Wish List

TI-84 Plus Wish List

 TI-84 Plus C Silver Edition in action

While awaiting the delivery of the next generation TI-84 Plus (TI-84 Plus CE), it has been a while since TI has upgraded the operating software of the TI-84 family, both the monochrome and color editions.  Hopefully, Texas Instruments has an update of the operator software in the near future.

Here is my wish list, should Texas Instruments decide to update the software for the TI-84 family:

Applies to both the Monochrome and Color TI-84s:

* Eigenvalues and eigenvector functions for matrices, even if these functions have an upper limit on what the matrix size can be (6 x 6, 10 x 10, etc.).

* Expand complex number support to include trigonometric functions.  The TI-84 already supports complex number arguments for the logarithm, exponential, square root, and power functions.

* A quick polynomial solver function.  The TI-85 and TI-86 had a poly function where you can enter a list that represents the polynomial’s coefficients.  For example, poly {3,2,-5} returned {1, -1.666666667}.  This would be a super command for programming applications.

* Vectors.  Many advanced math classes, starting in pre-calculus, teach vectors and their operations.  Functions can include, at the minimum, dot product, cross product, and the norm. These functions can be added to the Matrix menu.

* Expand the days between dates (dbd function from the Finance App) to include four-digit years.  With the current setup, the dbd function restricts dates from 1950 to 2049.

* Allow lower case text.

* Add the string commands (sub, Equ>String, String>Equ) to the PRGM I/O menu.

* Allow the factorial function (!) to include non-positive integers.

For the Color TI-84s:

* Add a RGB (red, green, blue) function.  This would allow users to use all the colors that the TI-84 instead of merely just 15.  The RGB function could be tacked on to the Vars, Color menu as the last option after the built-in 15 colors.

* Allow the Output command to show text in color.  The color can be an optional fourth argument which either takes the name of one of the 15 preset colors, it’s color value, or color determined by the RGB function.

If you are reading this Texas Instruments, please consider these suggestions and thank you for your time.  By the way, the TI Connect CE software is excellent; I love the interface and ease of connectivity.

A Musical Bonus

While out in Los Angeles, I came across this mini piano calculator at The Green Bean in the Eagle Rock community.  It is basic, solar, and fun to look at.  I only wish the keys were not so rubbery.  Oh well, it is fun to look at and play with.  Here is a picture:

 Mini Piano Calculator

Thank you to all my readers, followers, and commentators.  It is always appreciated!

Eddie

This blog is property of Edward Shore.  2015.

## Friday, May 15, 2015

### HP Prime Firmware 7820 Released

HP Prime Software Version 7820

DISCLAIMER: I am not an employee of Hewlett Packard.

Rev. 7820, 4/27/2015.

The above link provides files for the calculator, connectivity kit, and emulator.

Shout out to Tim Wessman, cyrille de brÃ©bisson, and the HP Calculator Group.

Let’s take a look at some of the new features with Version 7820 (4/27/2015):

Draw a Function

This blows me away.  I don’t think posting still pictures shows this new feature justice.   You can sketch a function by your finger (or mouse if you are using the hardware), and Prime draws a function that fits your sketch.  Furthermore, the function is defined and can be analyzed just as if you typed the functions on the Symb screen.  The sketch function draws functions of the following types:  linear, quadratic, exponential, natural logarithmic, and sinusoidal. To access this feature, go to the Plot screen, select Menu, then
Fcn, and Sketch… (option 1).

Date Functions

One of my favorite calculator functions of all time is the days between dates function.  Usually, this function is found mostly on financial calculators and some graphing calculators.  I am happy to report that the days between dates function (DDAYS) has finally made it to the HP Prime (a user program is no longer needed).
DDAYS(date1, date2):  calculate the days between date1 and date2.  Dates follow this format:  yyyy.mmdd.  This is the international date format (ISO standard): year, month, date.

DATEADD(date, n):  This determines the date n days from the specified date, where n can be positive (determining a future date) or negative (determining a past date).

DAYOFWEEK(date):  Returns the day of the week of a certain date.
1 – Monday
2 – Tuesday
3 – Wednesday
4 – Thursday
5 – Friday
6 – Saturday
7 – Sunday

These functions are found in the catalog or if you are in programming mode, through the Cmds-More menu.

Product Template

A new template to calculate the product of the function is added.  This template works well in both the Home and the CAS modes.

Pie Graph and Other 1-Variable Stat Plots

The HP Prime has an official pie graph feature in the Statistics1Var app.  Additional plots also include dot, stem and leaf, and control.  Stem and leaf plots are tables where numbers are arranged by their last digit (leaf) by their first digit(s) (stem).

Renaming of Columns, Mark Options in the Statistics Apps

Columns that used in the Statistics1Var and Statistics2Var apps are no longer restricted to the names C0 – C9.   Each column can contain up to 10,000 entries.  In the Symb menu, you can determine the color of the regression curve (2Var) and the markers.

To note, the symbolic variables of the Statistics2Var have changed.  Gone are the S1Type through the S5Type.  The variables S1 through S5 have been expanded.  S1 through S5 are lists containing the following items:

{ independent column,  dependent column, frequency column (can be blank), regression equation, plot type, color of the plot, mark type, color of the mark}

Plot Types:
1 – Linear
2 – Logarithmic
3 – Exponential
4 – Power
5 – Exponent
6 – Inverse
7 – Logistic
9 – Cubic
10 – Quartic
11 – Trigonometric
12 – Median-Median (new plot type)
13 – User Defined

Mark Types:
1 – small open circles
2 -  boxes
3 -  thin “X”s
4 -  crosses
5 -  thick diamonds
6 -  thick “X”s
7 -  solid circles
8 -  thin diamonds
9 -  large open circles

Expanded EDITLIST and EDITMAT

Both EDITLIST and EDITMAT have expanded capabilities.  You can add a title and make said list/matrix read-only.  The general format is:

EDITLIST(list variable or list, title as a string, read-only indicator)

EDITMAT(matrix variable or matrix, title as a string, read-only indicator)

The read-only indicator only needs to have any number other than zero to make such object read-only.  Both the title and read-only indicator arguments are optional.

Universal Setting Variables and Application Basic Setting Variables

The HP Prime now differentiates between universal setting variables (HAngle, HFormat, etc.) from application specific setting variables (AAngle, AFormat, etc.).

New density, cumulative, and inverse (lower tail) distribution functions are available for the following distributions:

Exponential: exponential, exponential_cdf, exponential_icdf
Geometric:  GEOMETRIC, GEOMETRIC_CDF, GEOMETRIC_ICDF
Negative Binomial: negbinomial, negbinomial_cdf, negbinomial_icdf
Uniform:  uniform, uniform_cdf, uniform_icdf
Weibull:  weibull, weibull_cdf, weibull_icdf

All these functions can be found in the catalog.

Additional random number generators based on the binomial, chi square, fisher, geometric, Poisson, and student distribution has been added in the catalog.  The new random generators have the prefix “rand”.

Programming:  Running the Programs through the Catalog ([Shift] + [ 1 ]) allows non-real input

It used to be that if you ran programs through the Program Catalog, we could only input real numbers as entries.   Thankfully, that is no longer the case.  Now we can input lists, matrices, and complex numbers.

One Directional Limits

The limit function now allows the use of plus and minus symbols to determine one-directional limits.  It won’t sing One Direction songs though (thankfully!).

This is just a few of the new features.  There is A LOT more detailed information about the above and all the new features, including improved copy and paste procedures, 1 way ANOVA analysis, display of graphic objects G0 through G9 on the home screen, and upper and lower case text conversion functions, included in the documentation of the new firmware.

All the future programs posted on this blog will be done using the Version 7820 firmware.

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The Museum of HP Calculators

Here a great place to discuss calculators, specifically HP calculators.  It is a really great place for HP calculator owners.  The link to the forum is here:  http://www.hpmuseum.org/forum/.

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Eddie

This blog is property of Edward Shore.  2015.

## Monday, May 11, 2015

### HP Prime and TI-84 Plus C Silver Edition: Pie Charts

HP Prime and TI-84 Plus C Silver Edition:  Pie Charts

Both programs take an argument a list up to 15 segments long.

 PIECHART, HP Prime

HP Prime:  PIECHART

Notes:
* The % character is either retrieved by pressing [Shift], [Vars] (Chars), or typed if you are using the emulator.
*  The program sets the calculator to Radian and Standard modes.

EXPORT PIECHART(l1)
BEGIN
// Pie Chart EWS
// 2015-05-11

// initialization
LOCAL l2,l3,colors,s,k,Î¸,c;

HAngle:=0;

// Standard Mode
HFormat:=0;

// set colors (15)
colors:={#FFh,#FF0000h,#0h,
#FF00FFh,#FF00h,#FFA500h,
#964B00h,#80h,#87CEEBh,
#FFFF00h,#FFFFFFh,#C0C0C0h,
#808080h,#404040h,#101010h};
c:=1;

// error conditions
IF SIZE(l1)>15 THEN
MSGBOX("The list is too long.");
KILL;
END;

// calculations
l2:=l1;
FOR k FROM 2 TO SIZE(l1) DO
l2[k]:=l2[k]+l2[k-1];
END;

l2:=2*Ï€*l2/Î£LIST(l1);
l2:=CONCAT({0},l2);
s:=SIZE(l2);

// window setup
Xmin:=−10; Xmax:=10;
Ymin:=−10; Ymax:=10;
RECT();

// draw pie graph
FOR k FROM 1 TO s-1 DO
FOR Î¸ FROM l2[k] TO l2[k+1]
STEP Ï€/200 DO
LINE(2.5,0,5*COS(Î¸)+2.5,5*SIN(Î¸),
colors[c]);
END;
c:=c+1;
END;

// display legends and percentages
l3:=l1/Î£LIST(l1)*100;

FOR k FROM 1 TO SIZE(l1) DO
TEXTOUT(STRING(l1[k]),-10,10-(k-1),
2,colors[k]);
TEXTOUT(STRING(l3[k],2,1)+"%",
-6,10-(k-1),2,colors[k]);
END;

WAIT(0);
END;

 Pie Chart (PIE84), TI 84 Plus C Silver Edition

TI-84 Plus C Silver Edition

Notes:
*  Comments in this program will be marked with double slashes (//).  Do not type them in.  They are there only to explain parts of the program.  I intend to leave comments in every program publish from here on out if explanation is warranted.
* To type the percentage sign:  [ 2ND ], [ANGLE], 1 (°), [ ÷ ], [ . ].  There is no native percent sign (%) on the TI-84, this is the best I can do.
*  Float and Radian modes are set.

// Initialization, turn off axes
FnOff
Float
AxesOff

// ask for list of data
Input L₁
If dim(L₁)>15:Then
Disp "L₁>15":Stop
End

// calculation
2Ï€*cumSum(L₁)/sum(L₁)→L₂
augment({0},L₂)→L₂
dim(L₂)→S

// set color variables
10→C
10→D
L₁/sum(L₁)*100→L₃

// prepare draw screen
ZStandard
ClrDraw

// draw the pie chart
For(I,1,S-1)
For(Î¸,L₂(I),L₂(I+1),Ï€/100)
Line(2.5,0,5cos(Î¸)+2.5,5sin(Î¸),1,C)
End
C+1→C
End

// draw the legend, draw commands have to remain together
For(K,1,dim(L₃))
TextColor(D)
Text(12K,0,round(L₃(K),1))
Text(12K,30,"°/.")
D+1→D
End
Pause

// turn axes on, Disp by itself just shows the home screen
AxesOn
FnOn
Disp

Hope you find this program useful!

In TI-84 Plus CE news.  I heard back from the company I ordered my CE from and I am to expect delivery around May 25.  I plan to give a review of it at the end of May if not early June.

Take care,

Eddie

This blog is property of Edward Shore.  2015.

### TI-Nspire: Templates to Plot Functions, Parametric Equations, and Sequences

TI-Nspire:  Templates to Plot Functions, Parametric Equations, and Sequences Introduction The following are sample templates to plot functi...