HP Prime Graphing Calculator User Guide
Edition1 Part Number NW280-2001 Legal Notices This manual and any examples contained herein are provided "as is" and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, noninfringement and fitness for a particular purpose. Portions of this software are copyright 2013 The FreeType Project (www.freetype.org). All rights reserved.
Copyright © 2013 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws.
Contents Preface Manual conventions ................................................................ 9 Notice ................................................................................. 10 1 Getting started Before starting ...................................................................... 11 On/off, cancel operations...................................................... 12 The display .......................................................................... 13 Sections of the display ..........
4 Exam Mode Modifying the default configuration..................................... 62 Creating a new configuration ............................................. 63 Activating Exam Mode ........................................................... 64 Cancelling exam mode...................................................... 66 Modifying configurations........................................................ 66 To change a configuration .................................................
6 Function app Getting started with the Function app .................................... 111 Analyzing functions ............................................................. 118 The Function Variables......................................................... 122 Summary of FCN operations ................................................ 124 7 Advanced Graphing app Getting started with the Advanced Graphing app ................... 126 Plot Gallery ...........................................................
Plot types ....................................................................... 219 Setting up the plot (Plot Setup view)................................... 221 Exploring the graph ........................................................ 221 11 Statistics 2Var app Getting started with the Statistics 2Var app............................. 223 Entering and editing statistical data ....................................... 228 Numeric view menu items ................................................
15 Parametric app Getting started with the Parametric app ................................. 271 16 Polar app Getting started with the Polar app ......................................... 277 17 Sequence app Getting started with the Sequence app .................................. 281 Another example: Explicitly-defined sequences ....................... 285 18 Finance app Getting Started with the Finance app..................................... 287 Time value of money (TVM) ..............................
App menu .......................................................................... 347 Function app functions..................................................... 348 Solve app functions ......................................................... 349 Spreadsheet app functions ............................................... 349 Statistics 1Var app functions............................................. 363 Statistics 2Var app functions............................................. 365 Inference app functions...
24 Lists Create a list in the List Catalog ............................................. 451 The List Editor................................................................. 453 Deleting lists ....................................................................... 455 Lists in Home view............................................................... 455 List functions ....................................................................... 457 Finding statistical values for lists .............................
28 Basic integer arithmetic The default base.................................................................. 582 Changing the default base ............................................... 583 Examples of integer arithmetic............................................... 584 Integer manipulation ............................................................ 585 Base functions ..................................................................... 586 A Glossary B Troubleshooting Calculator not responding .....
Preface Manual conventions The following conventions are used in this manual to represent the keys that you press and the menu options that you choose to perform operations. • A key that initiates an unshifted function is represented by an image of that key: e,B,H, etc.
• Items you can select from a list, and characters on the entry line, are set in a non-proportional font, as follows: Function, Polar, Parametric, Ans, etc. • Cursor keys are represented by =, \, >, and <. You use these keys to move from field to field on a screen, or from one option to another in a list of options. • Error messages are enclosed in quotation marks: “Syntax Error” Notice This manual and any examples contained herein are provided as-is and are subject to change without notice.
1 Getting started The HP Prime Graphing Calculator is an easy-to-use yet powerful graphing calculator designed for secondary mathematics education and beyond. It offers hundreds of functions and commands, and includes a computer algebra system (CAS) for symbolic calculations. In addition to an extensive library of functions and commands, the calculator comes with a set of HP apps.
When the calculator is on, a battery symbol appears in the title bar of the screen. Its appearance will indicate how much power the battery has. A flat battery will take approximately 4 hours to become fully charged. Battery Warning Adapter Warning • To reduce the risk of fire or burns, do not disassemble, crush or puncture the battery; do not short the external contacts; and do not dispose of the battery in fire or water.
The Home View Home view is the starting point for many calculations. Most mathematical functions are available in the Home view. Some additional functions are available in the computer algebra system (CAS). A history of your previous calculations is retained and you can re-use a previous calculation or its result. To display Home view, pressH. The CAS View CAS view enables you to perform symbolic calculations.
Sections of the display Title bar History Entry line Menu buttons Home view has four sections (shown above). The title bar shows either the screen name or the name of the app you are currently using—Function in the example above. It also shows the time, a battery power indicator, and a number of symbols that indicate various calculator settings. These are explained below. The history displays a record of your past calculations. The entry line displays the object you are currently entering or modifying.
Getting started Annunciator Meaning (Continued) CAS [White] You are working in CAS view, not Home view. A...Z [orange] In Home view The Alpha key is active. The character shown in orange on a key will be entered in uppercase when a key is pressed. See “Adding text” on page 23 for more information. In CAS view The Alpha–Shift key combination is active. The character shown in orange on a key will be entered in uppercase when a key is pressed. See “Adding text” on page 23 for more information. a...
Annunciator 1U [Yellow] [Time] [Green with gray border] Meaning (Continued) The user keyboard is active. The next key press will enter the customized object associated with the key. See “The User Keyboard: Customizing key presses” on page 516 for more information. Current time. The default is 24-hour format, but you can choose AM–PM format. See “Home settings” on page 30 for more information. Battery-charge indicator. Navigation The HP Prime offers two modes of navigation: touch and keys.
Touch gestures In addition to selection by tapping, there are other touchrelated operations available to you: To quickly move from page to page, flick: Place a finger on the screen and quickly swipe it in the desired direction (up or down). To pan, drag your finger horizontally or vertically across the screen. To quickly zoom in, make an open pinch: Place the thumb and a finger close together on the screen and move them apart. Only lift them from the screen when you reach the desired magnification.
The keyboard The numbers in the legend below refer to the parts of the keyboard described in the illustration on the next page.
1 2 17 16 3 4 5 15 14 13 12 11 10 6 7 9 8 Context-sensitive menu A context-sensitive menu occupies the bottom line of the screen. The options available depend on the context, that is, the view you are in. Note that the menu items are activated by touch.
There are two types of buttons on the context-sensitive menu: • menu button: tap to display a pop-up menu. These buttons have square corners along their top (such as in the illustration above). • command button: tap to initiate a command. These buttons have rounded corners (such as in the illustration above). Entry and edit keys The primary entry and edit keys are: 20 Keys Purpose N to r Enter numbers O or J Cancels the current operation or clears the entry line.
Getting started Keys Purpose (Continued) Sv Relations palette: Displays a palette of comparison operators and Boolean operators. Sr Special symbols palette: Displays a palette of common math and Greek characters. Sc Automatically inserts the degree, minute, or second symbol according to the context. C Backspace. Deletes the character to the left of the cursor. It will also return the highlighted field to its default value, if it has one. SC Delete.
Keys Purpose (Continued) Sa Displays all the available characters. To enter a character, use the cursor keys to highlight it, and then tap . To select multiple characters, select one, tap , and continue likewise before pressing . There are many pages of characters. You can jump to a particular Unicode block by tapping and selecting the block. You can also flick from page to page.
Adding text The text you can enter directly is shown by the orange characters on the keys. These characters can only be entered in conjunction with the A and S keys. Both uppercase and lowercase characters can be entered, and the method is exactly the opposite in CAS view than in Home view.
Math keys The most common math functions have their own keys on the keyboard (or a key in combination with the S key). Example 1: To calculate SIN(10), press e10 and press E. The answer displayed is –0.544… (if your angle measure setting is radians). Example 2: To find the square root of 256, press Sj 256 and press E. The answer displayed is 16. Notice that the S key initiates the operator represented in blue on the next key pressed (in this case √ on the j key).
Example: Suppose you want to find the cube root of 945: 1. In Home view, press F. 2. Select . The skeleton or framework for your calculation now appears on the entry line: 3. Each box on the template needs to be completed: 3>945 4. Press E to display the result: 9.813… The template palette can save you a lot of time, especially with calculus calculations. You can display the palette at any stage in defining an expression. In other words, you don’t need to start out with a template.
degrees; and enters ″ if the previous entry is a value in minutes. Thus entering: 36Sc40Sc20Sc yields 36°40′20″. See “Hexagesimal numbers” on page 26 for more information. Fractions The fraction key (c) cycles through thee varieties of fractional display. If the current answer is the decimal fraction 5.25, pressing c converts the answer to the common fraction 21/4. If you press c again, the answer is converted to a mixed number (5 + 1/4). If pressed again, the display returns to the decimal fraction (5.
Note that the degree and minute entries must be integers, and the minute and second entries must be positive. Decimals are not allowed, except in the seconds. Note too that the HP Prime treats a value in hexgesimal format as a single entity. Hence any operation performed on a hexagesimal value is performed on the entire value. For example, if you enter 10°25′ 26″ 2, the whole value is squared, not just the seconds component. The result in this case is 108°39′ 26.8544″ .
5. Press E The result is 8.0000E15. This is equivalent to 8 × 1015. Menus A menu offers you a choice of items. As in the case shown at the right, some menus have submenus and sub-submenus. To select from a menu There are two techniques for selecting an item from a menu: • direct tapping and • using the arrow keys to highlight the item you want and then either tapping or pressing E. Note that the menu of buttons along the bottom of the screen can only be activated by tapping.
To close a menu A menu will close automatically when you select an item from it. If you want to close a menu without selecting anything from it, press O or J. Toolbox menus The Toolbox menus (D) are a collection of menus offering functions and commands useful in mathematics and programming. The Math, CAS, and Catlg menus offer over 400 functions and commands. The items on these menus are described in detail in chapter 21, “Functions and commands”, starting on page 307.
Reset input form fields To reset a field to its default value, highlight the field and press . To reset all fields to their default values, press SJ (Clear). C System-wide settings System-wide settings are values that determine the appearance of windows, the format of numbers, the scale of plots, the units used by default in calculations, and much more. There are two system-wide settings: Home settings and CAS settings. Home settings control Home view and the apps.
Page 1 Setting Options Angle Measure Degrees: 360 degrees in a circle. Radians: 2 radians in a circle. The angle mode you set is the angle setting used in both Home view and the current app. This is to ensure that trigonometric calculations done in the current app and Home view give the same result. Number Format The number format you set is the format used in all Home view calculations. Standard: Full-precision display. Fixed: Displays results rounded to a number of decimal places.
Setting Options (Continued) Entry Textbook: An expression is entered in much the same way as if you were writing it on paper (with some arguments above or below others). In other words, your entry could be two-dimensional. Algebraic: An expression is entered on a single line. Your entry is always one-dimensional. RPN: Reverse Polish Notation. The arguments of the expression are entered first followed by the operator. The entry of an operator automatically evaluates what has already been entered.
Setting Options (Continued) Decimal Mark Dot or Comma. Displays a number as 12456.98 (dot mode) or as 12456,98 (comma mode). Dot mode uses commas to separate elements in lists and matrices, and to separate function arguments. Comma mode uses semicolons as separators in these contexts. Setting Options Font Size Choose between small, medium, and large font for general display. Calculator Name Enter a name for the calculator.
Setting Options (Continued) Time Set the time and choose a format: 24-hour or AM–PM format. The checkbox at the far right lets you choose whether to show or hide the time on the title bar of screens. Date Set the date and choose a format: YYYY/MM/DD, DD/MM/YYYY, or MM/DD/YYYY. Color Theme Light: black text on a light back- ground Dark: white text on a dark back- ground At the far right is a option for you to choose a color for the shading (such as the color of the highlight).
Specifying a Home setting This example demonstrates how to change the number format from the default setting—Standard—to Scientific with two decimal places. 1. Press SH (Settings) to open the Home Settings input form. The Angle Measure field is highlighted. 2. Tap on Number Format (either the field label or the field). This selects the field. (You could also have pressed \ to select it.) 3. Tap on Number Format again. A menu of number format options appears. 4. Tap on Scientific.
Mathematical calculations The most commonly used math operations are available from the keyboard (see “Math keys” on page 24). Access to the rest of the math functions is via various menus (see “Menus” on page 28). Note that the HP Prime represents all numbers smaller than 1 × 10–499 as zero. The largest number displayed is 9.99999999999 × 10499. A greater result is displayed as this number. Where to start The home base for the calculator is the Home view (H).
• RPN (Reverse Polish Notation). [Not available in CAS view.] The arguments of the expression are entered first followed by the operator. The entry of an operator automatically evaluates what has already been entered. Thus you will need to enter a two-operator expression (as in the example above) in two steps, one for each operator: Step 1: 5 h – the natural logarithm of 5 is calculated and displayed in history. Step 2: Szn – is entered as a divisor and applied to the previous result.
If you make a mistake while entering an expression, you can: Example • delete the character to the left of the cursor by pressing C • delete the character to the right of the cursor by pressing SC • clear the entire entry line by pressing O or J.
The following examples show the use of parentheses, and the use of the cursor keys to move outside a group of objects enclosed within parentheses. Algebraic precedence Entering ... Calculates … e 45+Sz sin 45 + e45>+Sz sin 45 + Sj85 >s 9 85 9 Sj85s9 85 9 The HP Prime calculates according to the following order of precedence. Functions at the same level of precedence are evaluated in order from left to right. 1. Expressions within parentheses.
Explicit and implied multiplication Implied multiplication takes place when two operands appear with no operator between them. If you enter AB, for example, the result is A*B. Notice in the example on page 38 that we entered 14Sk8 without the multiplication operator after 14. For the sake of clarity, the calculator adds the operator to the expression in history, but it is not strictly necessary when you are entering the expression.
Tip Using the clipboard Pressing S= takes you straight to the very first entry in history, and pressing S\ takes you straight to the most recent entry. Your last four expressions are always copied to the clipboard and can easily be retrieved by pressing SZ. This opens the clipboard from where you can quickly choose the one you want. Note that expressions and not results are available from the clipboard. Note too that the last four expressions remain on the clipboard even if you have cleared history.
You can repeat the previous calculation simply by pressing E. This can be useful if the previous calculation involved Ans. For example, suppose you want to calculate the nth root of 2 when n is 2, 4, 8, 16, 32, and so on. 1. Calculate the square root of 2. Sj2E 2. Now enter √Ans. SjS+E This calculates the fourth root of 2. 3. Press E repeatedly. Each time you press, the root is twice the previous root. The last answer shown in the illustration at the right is 32 2 .
Example: To assign 2 to to the variable A: Szj AaE Your stored value appears as shown at the right. If you then wanted to multiply your stored value by 5, you could enter: Aas5E. You can also create your own variables in Home view. For example, suppose you wanted to create a variable called ME and assign 2 to it. You would enter: Szj AQAcE A message appears asking if you want to create a variable called ME. Tap or press E to confirm your intention.
Complex numbers You can perform arithmetic operations using complex numbers. Complex numbers can be entered in the following forms, where x is the real part, y is the imaginary part, and i is the imaginary constant, – 1 : • (x, y) • x + yi (except in RPN mode) • x – yi (except in RPN mode) • x + iy (except in RPN mode), or • x – iy (except in RPN mode) To enter i: • press ASg or • press Sy. There are 10 built-in variables available for storing complex numbers. These are labeled Z0 to Z9.
screen with as a menu item, you can select an item on that screen to send it to another HP Prime. You use one of the supplied USB cables to send objects from one Micro-A: sender Micro-B: receiver HP Prime to another. This is the micro-A–micro B USB cable. Note that the connectors on the ends of the USB cable are slightly different. The micro-A connector has a rectangular end and the micro-B connector has a trapezoidal end.
Online Help W Press to open the online help. The help initially provided is context-sensitive, that is, it is always about the current view and its menu items. For example, to get help on the Function app, press I, . select Function, and press W From within the help system, tapping displays a hierarchical directory of all the help topics. You can navigate through the directory to other help topics, or use the search facility to quickly find a topic. You can find help on any key, view, or command.
2 Reverse Polish Notation (RPN) The HP Prime provides you with three ways of entering objects in Home view: • Textbook An expression is entered in much the same way was if you were writing it on paper (with some arguments above or below others). In other words, your entry could be twodimensional, as in the following example: • Algebraic An expression is entered on a single line. Your entry is always one-dimensional.
The same entry-line editing tools are available in RPN mode as in algebraic and textbook mode: • Press C to delete the character to the left of the cursor. • Press SC to delete the character to the right of the cursor. • Press J to clear the entire entry line. • Press SJ to clear the entire entry line. History in RPN mode The results of your calculations are kept in history. This history is displayed above the entry line (and by scrolling up to calculations that are no longer immediately visible).
bottom. In RPN mode, your history is ordered chronologically by default, but you can change the order of the items in history. (This is explained in “Manipulating the stack” on page 51.) Re-using results There are two ways to re-use a result in history. Method 1 deselects the copied result after copying; method 2 keeps the copied item selected. Method 1 1. Select the result to be copied. You can do this by pressing = or \ until the result is highlighted, or by tapping on it. 2. Press E.
However, you could also have entered the arguments separately and then, with a blank entry line, entered the operator ( ). Your history would look like this before entering the operator: s If there are no entries in history and you enter an operator or function, an error message appears. An error message will also appear if there is an entry on a stack level that an operator needs but it is not an appropriate argument for that operator.
Manipulating the stack A number of stack-manipulation options are available. Most appear as menu items across the bottom the screen. To see these items, you must first select an item in history: PICK Copies the selected item to stack level 1. The item below the one that is copied is then highlighted. Thus if you tapped four times, four consecutive items will be moved to the bottom four stack levels (levels 1–4). ROLL There are two roll commads: • Tap to move the selected item to stack level 1.
DUPN Duplicates all items between (and including) the highlighted item and the item on stack level 1. If, for example, you have selected the item on stack level 3, selecting DUPN duplicates it and the two items below it, places them on stack levels 1 to 3, and moves the items that were duplicated up to stack levels 4 to 6. Echo Places a copy of the selected result on the entry line and leaves the source result highlighted.
3 Computer algebra system (CAS) A computer algebra system (CAS) enables you to perform symbolic calculations. By default, CAS works in exact mode, giving you infinite precision. On the other hand, non-CAS calculations, such as those performed in HOME view or by an app, are numerical calculations and are often approximations limited by the precision of the calculator (to 12 significant digits in the case of the HP Prime). For example, 1--- + 2--- yields 3 7 the approximate answer .
The menu buttons in CAS view are: : assigns an object to a variable • • : applies common simplification rules to reduce an expression to its simplest form. For example, c simplify(ea + LN(b*e )) yields b * EXP(a)* EXP(c). • : copies a selected entry in history to the entry line • : displays the selected entry in full-screen mode, with horizontal and vertical scrolling enabled. The entry is also presented in textbook format.
Example 1 To find the roots of 2x2 + 3x – 2: 1. With the CAS menu open, select Polynomial and then Find Roots. The function proot() appears on the entry line. 2. Between the parentheses, enter: 2Asj+3 Asw2 3. Press E. Example 2 To find the area under the graph of 5x2 – 6 between x =1 and x = 3: 1. With the CAS menu open, select Calculus and then Integrate. The function int() appears on the entry line. 2. Between the parentheses, enter: 5Asjw6 oAso1o 3 3. Press E.
Page 1 56 Setting Purpose Angle Measure Select the units for angle measurements: Radians or Degrees. Number Format (first drop-down list) Select the number format for displayed solutions: Standard or Scientific or Engineering Number Format (second dropdown list) Select the number of digits to display in approximate mode (mantissa + exponent).
Setting Purpose (Cont.) Complex Select this to allow complex results in variables. Use √ If checked, second order polynomials are factorized in complex mode or in real mode if the discriminant is positive. Use i If checked, the calculator is in complex mode and complex solutions will be displayed when they exist. If not checked, the calculator is in real mode and only real solutions will be displayed.
Setting the form of menu items Setting Purpose (Cont.) Recursive Replacement Specify the maximum number of embedded variables allowed in a single evaluation in a program. See also Recursive Evaluation above. Recursive Function Specify the maximum number of embedded function calls allowed. Epsilon Any number smaller than the value specified for epsilon will be shown as zero. Probability Specify the maximum probability of an answer being wrong for non-deterministic algorithms.
functions to be presented by their command name, deselect the Menu Display option on the second page of the Home Settings screen (see “Home settings” on page 30). To use an expression or result from Home view When your are working in CAS, you can retrieve an expression or result from Home view by tapping Z and selecting Get from Home. Home view opens. Press = or \ until the item you want to retrieve is highlighted and press E. The highlighted item is copied to the cursor point in CAS.
60 Computer algebra system (CAS)
4 Exam Mode The HP Prime can be precisely configured for an examination, with any number of features or functions disabled for a set period of time. Configuring a HP Prime for an examination is called exam mode configuration. You can create and save multiple exam mode configurations, each with its own subset of functionality disabled. You can set each configuration for its own time period, with or without a password.
Modifying the default configuration A configuration named Default Exam appears when you first access the Exam Mode screen. This configuration has no functions disabled. If only one configuration is needed, you can simply modify the default exam configuration.
An expand box at the left of a feature indicates that it is a category with sub-items that you can individually disable. (Notice that there is an expand box beside System Apps in the example shown above.) Tap on the expand box to see the sub-items. You can then select the sub-items individually. If you want to disable all the sub-item, just select the category. You can select (or deselect) an option either by tapping on the check box beside it, or by using the cursor keys to scroll to it and tapping . 6.
5. Tap , select Copy from the menu and enter a name for the new configuration. See “Adding text” on page 23 if you need help with entering alphabetic characters. 6. Tap twice. 7. Tap . The Exam Mode Configuration screen appears. 8. Select those features you want disabled, and make sure that those features you don’t want disabled are not selected. 9. When you have finished selecting the features to be disabled, tap .
To activate exam mode: 1. If the Exam Mode screen is not showing, press SH, tap and tap . 2. If a configuration other than Default Exam is required, choose it from the Configuration list. 3. Select a time-out period from the Timeout list. Note that 8 hours is the maximum period. If you are preparing to supervise a student examination, make sure that the time-out period chosen is greater than the duration of the examination. 4. Enter a password of between 1 and 10 characters.
mode, with the specified disabled features not accessible to the user of that calculator. 9. Repeat from step 7 for each calculator that needs to have its functionality limited. Cancelling exam mode If you want to cancel exam mode before the set time period has elapsed, you will need to enter the password for the current exam mode activation. 1. If the Exam Mode screen is not showing, press SH, tap and tap . 2. Enter the password for the current exam mode activation and tap twice.
To return to the default configuration 1. Press SH. The Home Settings screen appears. 2. Tap . 3. Tap . The Exam Mode screen appears. 4. Choose Default Exam from the Configuration list. 5. Tap , select Reset from the menu and tap to confirm your intention to return the configuration to its default settings. Deleting configurations You cannot delete the default exam configuration (even if you have modified it). You can only delete those that you have created. To delete a configuration: 1.
68 Exam Mode
5 An introduction to HP apps Much of the functionality of the HP Prime is provided in packages called HP apps. The HP Prime comes with 18 HP apps: 10 dedicated to mathematical topics or tasks, three specialized Solvers, three function Explorers, a spreadsheet, and an app for recording data streamed to the calculator from an external sensing device. You launch an app by first pressing I (which displays the Application Library screen) and tapping on the icon for the app you want.
App name Use this app to: (Cont.) Linear Solver Find solutions to sets of two or three linear equations. Parametric Explore parametric functions of x and y in terms of t. Example: x = cos (t) and y = sin(t). Polar Explore polar functions of r in terms of an angle . Example: r = 2 cos 4 Quadratic Explorer Explore the properties of quadratic equations and test your knowledge.
With one exception, all the apps mentioned above are described in detail in this user guide. The exception is the DataStreamer app. A brief introduction to this app is given in the HP Prime Quick Start Guide. Full details can be found in the HP StreamSmart 410 User Guide. Application Library Apps are stored in the Application Library, displayed by pressing I. To open an app 1. Open the Application Library. 2. Find the app’s icon and tap on it.
You can change the sort order of the built-in apps to: • Alphabetically The app icons are sorted alphabetically by name, and in ascending order: A to Z. • Fixed Apps are displayed in their default order: Function, Advanced Graphing, Geometry … Polar, and Sequence. Customized apps are placed at the end, after all the built-in apps. They appear in chronological order: oldest to most recent. To change the sort order: 1. Open the Application Library. 2. Tap . 3.
App views Most apps have three major views: Symbolic, Plot, and Numeric. These views are based on the symbolic, graphic, and numeric representations of mathematical objects. They are accessed through the Y, P, and M keys near the top left of the keyboard. Typically these views enable you to define a mathematical object—such as an expression or an open sentence—plot it, and see the values generated by it.
App Use the Symbolic view to: (Cont.) Linear Solver Not used Parametric Specify up to 10 parametric functions of x and y in terms of t. Polar Specify up to 10 polar functions of r in terms of an angle . Quadratics Explorer Not used Sequence Specify up to 10 sequence functions. Solve Specify up to 10 equations. Spreadsheet Not used Statistics 1Var Specify up to 5 univariate analyses. Statistics 2Var Specify up to 5 multivariate analyses.
Plot view The table below outlines what is done in the Plot view of each app. App Use the Plot view to: Advanced Graphing Plot and explore the open sentences selected in Symbolic view. Finance Display an amortization graph. Function Plot and explore the functions selected in Symbolic view. Geometry Create and manipulate geometric constructions. Inference View a plot of the test results. Linear Explorer Explore linear equations and test your knowledge of them.
Plot Setup view The table below outlines what is done in the Plot Setup view of each app. 76 App Use the Plot Setup view to: Advanced Graphing Modify the appearance of plots and the plot environment. Finance Not used Function Modify the appearance of plots and the plot environment. Geometry Modify the appearance of the drawing environment. Inference Not used Linear Explorer Not used Linear Solver Not used Parametric Modify the appearance of plots and the plot environment.
Numeric view The table below outlines what is done in the Numeric view of each app. App Use the Numeric view to: Advanced Graphing View a table of numbers generated by the open sentences selected in Symbolic view. Finance Enter values for time-value-of-money calculations. Function View a table of numbers generated by the functions selected in Symbolic view. Geometry Perform calculations on the geometric objects drawn in Plot view.
App Use the Numeric view to: (Cont.) Triangle Solver Enter known data about a triangle and solve for the unknown data. Trig Explorer Not used Numeric Setup view The table below outlines what is done in the Numeric Setup view of each app. 78 App Use the Numeric Setup view to: Advanced Graphing Specify the numbers to be calculated according to the open sentences specified in Symbolic view, and set the zoom factor. Finance Not used.
App Use the Numeric Setup view to: (Cont.) Spreadsheet Not used Statistics 1Var Not used Statistics 2Var Not used Triangle Solver Not used Trig Explorer Not used Quick example The following example uses all six app views and should give you an idea of the typical workflow involved in working with an app. The Polar app is used as the sample app. Open the app 1. Open the Application Library by pressing I. 2. Tap once on the icon of the Polar app. The Polar app opens in Symbolic View.
Symbolic Setup view 4. Press SY. 5. Select Radians from the Angle Measure menu. Plot view 6. Press P. A graph of the equation is plotted. However, as the illustration at the right shows, only a part of the petals is visible. To see the rest you will need to change the plot setup parameters. Plot Setup View 7. Press SP. 8. Set the second RNG field to 4 by entering: >4Sz ( 9. Press P to return to Plot view and see the complete plot.
Numeric View The values generated by the equation can be seen in Numeric view. 10. Press M. Suppose you want to see just whole numbers for ; in other words, you want the increment between consecutive values in the column to be 1. You set this up in the Numeric Setup view. Numeric Setup View 11. Press SM. 12. Change the to 1. NUMSTEP field 13. Press M to return to Numeric view.
Add a definition With the exception of the Parametric app, there are 10 fields for entering definitions. In the Parametric app there are 20 fields, two for each paired definition. 1. Highlight an empty field you want to use, either by tapping on it or scrolling to it. 2. Enter your definition. If you need help, see “Definitional building blocks” on page 82. 3. Tap or press E when you have finished. Your new definition is added to the list of definitions.
• From Home variables Some Home variables can be incorporated into a symbolic definition. To access a Home variable, press a, tap , select a category of variable, and select the variable of interest. Thus you could have a definition that reads F1(X)=X2+Q. (Q is on the Real sub-menu of the Home menu.) Home variables are discussed in detail in chapter 28, “Troubleshooting”, beginning on page 507. • From app variables All settings, definitions, and results, for all apps, are stored as variables.
• From app functions Some of the functions on the App menu can be incorporated into a definition. The App menu is one of the Toolbox menus (D). The following definition incorporates the app function PredY: F9(X)=X2+Statistics_2Var.PredY(6). • From the Catlg menu Some of the functions on the Catlg menu can be incorporated into a definition. The Catlg menu is one of the Toolbox menus (D). The following definition incorporates a command from that menu and an app variable: F6(X)=X2+INT(Root).
You can tell if a definition is selected by the tick (or checkmark) beside it. A checkmark is added by default as soon as you create a definition. So if you don’t want to plot or evaluate a particular definition, highlight it and tap . (Do likewise if you want to re-select a deselected function.) Choose a color for plots Each function and open sentence can be plotted in a different color. If you want to change the default color of a plot: 1. Tap the colored square to the left of the function’s definition.
Symbolic view: Summary of menu buttons Button Purpose Copies the highlighted definition to the entry line for editing. Tap when done. To add a new definition—even one that is replacing an existing one—highlight the field and just start entering your new definition. Selects (or deselects) a definition. [Function only] [Advanced Graphing only] [Advanced Graphing only] Enters the independent variable in the Function app. You can also press d. Enters an X in the Advanced Graphing app. You can also press d.
Common operations in Symbolic Setup view [Scope: all apps] The Symbolic Setup view is the same for all apps. Its primary purpose is to allow you to override three of the system-wide settings specified on the Home Settings window. Press SY to open Symbolic Setup view. Override system-wide settings 1. Tap once on the setting you want to change. You can tap on the field name or the field. 2. Tap again on the setting. A menu of options appears. 3. Select the new setting.
Common operations in Plot view Plot view functionality that is common to many apps is described in detail in this section. Functionality that is available only in a particular app is described in the chapter dedicated to that app. Press P to open Plot view. Zoom [Scope: Advanced Graphing, Function, Parametric, Polar, Sequence, Solve, Statistics 1 Var, and Statistics 2Var. Also, to a limited degree, Geometry.] Zooming redraws the plot on a larger or smaller scale.
Zoom keys There are two zoom keys: pressing + zooms in and pressing w zooms out. The extent of the scaling is determined by the ZOOM FACTOR settings (explained above). Zoom menu In Plot view, tap an option. (If displayed, tap and tap is not .) The zoom options are explained in the following table. Examples are provided on “Zoom examples” on page 91. Option Result Center on Cursor Redraws the plot so that the cursor is in the center of the screen. No scaling occurs.
Box zoom Option Result (Cont.) Square Changes the vertical scale to match the horizontal scale. This is useful after you have done a box zoom, X zoom or Y zoom. Autoscale Rescales the vertical axis so that the display shows a representative piece of the plot given the supplied x axis settings. (For Sequence, Polar, parametric, and Statistics apps, autoscaling rescales both axes.) The autoscale process uses the first selected function to determine the best scale to use.
Views menu The most commonly used zoom options are also available on the Views menu. These are: • Autoscale • Decimal • Integer • Trig. These options—which can be applied whatever view you are currently working in—are explained in the table immediately above. Testing a zoom with split-screen viewing A useful way of testing a zoom is to divide the screen into two halves, with each half showing the plot, and then to apply a zoom only to one side of the screen.
Note that there is an Unzoom option on the Zoom menu. Use this to return a plot to its pre-zoom state. If the Zoom menu is not shown, tap .
Y Out Y Out Square Square Notice that in this example, the plot on left has had a Y In zoom applied to it. The Square zoom has returned the plot to its default state where the X and Y scales are equal. Autoscale Autoscale Decimal Decimal Notice that in this example, the plot on left has had a X In zoom applied to it. The Decimal zoom has reset the default values for the x-range and yrange.
Trig Trig Trace [Scope: Advanced Graphing, Function, Parametric, Polar, Sequence, Solve, Statistics 1 Var, and Statistics 2Var.] The tracing functionality enables you to move a cursor (the trace cursor) along the current graph. You move the trace cursor by pressing < or >. You can also move the trace cursor by tapping on or near the current plot. The trace cursor jumps to the point on the plot that is closest point to where you tapped.
To evaluate a definition One of the primary uses of the trace functionality is to evaluate a plotted definition. Suppose in Symbolic view you have defined F1(X) as (X – 1)2 – 3. Suppose further that you want to know what the value of that function is when X is 25. 1. Open Plot view (P). 2. If the menu at the bottom of the screen is not open, tap . 3. If more than one definition is plotted, ensure that the trace cursor is on the plot of the definition you want to evaluate.
Plot view: Summary of menu buttons Button Purpose Displays a menu of zoom options. See “Zoom options” on page 88. / A toggle button for turning off and turning on trace functionality. See “Trace” on page 94. Displays an input form for you to specify a value you want the cursor to jump to. The value you enter is the value of the independent variable. [Function only] Displays a menu of options for analyzing a plot. See “Analyzing functions” on page 118.
configuration options are spread across two pages. Tap to move from the first to the second page, and to return to the first page. Tip When you go to Plot view to see the graph of a definition selected in Symbolic view, there may be no graph shown. The likely cause of this is that the spread of plotted values is outside the range settings in Plot Setup view. A quick way to bring the graph into view is to press V and select Autoscale. This also changes the range settings in Plot Setup view.
Setup field Purpose (Cont.) S*MARK Sets the graphic that will be used to represent a data point in a scatter plot. A different graphic can be used for each of the five analyses that can be plotted together. XRNG Sets the initial range of the x-axis. Note that here are two fields: one for the minimum and one for the maximum value. In Plot view the range can be changed by panning and zooming. YRNG Sets the initial range of the y-axis.
Setup field METHOD [Not in either statistics app] Purpose (Cont.) Sets the graphing method to adaptive, fixed-step segments, or fixed-step dots. Explained below. Graphing methods The HP Prime gives you the option of choosing one of three graphing methods. The methods are described below, with each applied to the function f(x) = 9*sin(ex). • adaptive: this gives very accurate results and is used by default. With this method active, some complex functions may take a while to plot.
Restore default settings [Scope: Advanced Graphing, Function, Parametric, Polar, Sequence, Solve, Statistics 1 Var, Statistics 2Var, Geometry.] To restore one field to its default setting: 1. Select the field. 2. Press C. To restore all default settings, press SJ. Common operations in Numeric view [Scope: Advanced Graphing, Function, Parametric, Polar] Numeric view functionality that is common to many apps is described in detail in this section.
x-values will be 10, 10.1, 10.2, 10.3, 10.4, etc. (Zooming out does the opposite: 10, 10.4, 10,8, 11.2 etc. becomes10, 11.6, 13.2, 14.8, 16.4, etc.). Before zooming Zoom options After zooming In Numeric view, zoom options are available from two sources: • the keyboard • the menu in Numeric view. Note that any zooming you do in Numeric view does not affect Plot view, and vice versa.
The zoom options are explained in the following table. Option Result In The increment between consecutive values of the independent variable becomes the current value divided by the NUMZOOM setting. (Shortcut: press +.) Out The increment between consecutive values of the independent variable becomes the current value multiplied by the NUMZOOM setting. (Shortcut: press w.) Decimal Restores the default NUMSTART and NUMSTEP values: 0 and 0.1 respectively.
3. Tap . Numeric view is refreshed, with the value you entered in the first row and the result of the evaluation in a cell to the right. In this example, the result is 389373. Custom tables If you choose Automatic for the NUMTYPE setting, the table of evaluations in Numeric view will follow the settings in the Numeric Setup view. That is, the independent variable will start with the NUMSTART setting and increment by the NUMSTEP setting.
Numeric view: Summary of menu buttons Button Purpose To modify the increment between consecutive values of the independent variable in the table of evaluations. See page 100. [BuildYourOwn only] [BuildYourOwn only] [BuildYourOwn only] To edit the value in the selected cell. To overwrite the value in the selected cell, you can just start entering a new value without first tapping . Only visible if NUMTYPE is set to BuildYourOwn. See “Custom tables” on page 103.
Button Purpose (Cont.) Displays a menu for you to choose to display the evaluations of 1, 2, 3, or 4 defintions. If you have more than four definitions seelcted in Symbolic view, you can press > to scroll rightwards and see more columns. Pressing < scrolls the columns leftwards. Common operations in Numeric Setup view [Scope: Advanced Graphing, Function, Parametric, Polar, Sequence] Press SM to open Numeric Setup view.
To help you set a starting number and increment that matches the current Plot view, tap . Restore default settings To restore one field to its default setting: 1. Select the field. 2. Press C. To restore all default settings, press SJ. Combining Plot and Numeric Views You can display Plot view and Numeric view side-by-side. Moving the tracing cursor causes the table of values in Numeric view to scroll. You can also enter a value in the X column.
To add a note to an app: 1. Open the app. 2. Press SI (Info). If a note has already been created for this app, its contents are displayed. 3. Tap and start writing (or editing) your note. The format and bullet options available are the same as those in the Note Editor (described in “The Note Editor” on page 490). 4. To exit the note screen, press any key. Your note is automatically saved. Creating an app The apps that come with the HP Prime are built in and cannot be deleted.
Like built-in apps, customized apps can be sent to another HP Prime calculator. This is explained in “Sharing data” on page 44. Customized apps can also be reset, deleted, and sorted just as built-in apps can (as explained earlier in this chapter). Note that the only apps that cannot be customized are the: Example • Linear Explorer • Quadratic Explorer and • Trig Explorer apps. Suppose you want to create a customized app that is based on the built-in Sequence app.
Sequence app—see chapter 17, “Sequence app”, beginning on page 281. As well as cloning a built-in app—as described above—you can modify the internal workings of a customized app using the HP Prime programming language. See “Customizing an app” on page 522. App functions and variables Functions App functions are used in HP apps to perform common calculations. For example, in the Function app, the Plot view Fcn menu has a function called SLOPE that calculates the slope of a given function at a given point.
Suppose you are in Home view and want to retrieve the mean of a data set recently calculated in the Statistics 1Var app. 1. Press a. This opens the Variables menu. From here you can access Home variables, user-defined variables, and app variables. 2. Tap . This opens a menu of app variables. 3. Select Statistics 1Var > results > MeanX. The current value of the variable you chose now appears on the entry line. You can press E to see its value.
6 Function app The Function app enables you to explore up to 10 realvalued, rectangular functions of y in terms of x; for 2 example, y = 1 – x and y = x – 1 – 3 . Once you have defined a function you can: • create graphs to find roots, intercepts, slope, signed area, and extrema, and • create tables that show how functions are evaluated at particular values. This chapter demonstrates the basic functionality of the Function app by stepping you through an example.
Open the Function app 1. Open the Function app. I Select Function Recall that you can open an app just by tapping its icon. You can also open it by using the cursor keys to highlight it and then pressing E. The Function app starts in Symbolic view. This is the defining view. It is where you symbolically define (that is, specify) the functions you want to explore. The graphical and numerical data you see in Plot view and Numeric view are derived from the symbolic expressions defined here.
5. Decide if you want to: – give one or more function a custom color when it is plotted – evaluate a dependent function – deselect a definition that you don’t want to explore – incorporate variables, math commands and CAS commands in a definition. For the sake of simplicity we can ignore these operations in this example. However, they can be useful and are described in detail in “Common operations in Symbolic view” on page 81.
Trace a graph By default, the trace functionality is active. This enables you to move a cursor along a graph. If more than two graphs are shown, the graph that is the highest in the list of functions in Symbolic view is the graph that will be traced by default. Since the linear equation is higher than the quadratic function in Symbolic view, it is the graph on which the tracing cursor appears by default. 8. Trace the linear function. > or < Note how a cursor moves along the plot as you press the buttons.
Note • Use options on the Zoom menu to zoom in or out, horizontally or vertically, or both, etc. • Use options on the View menu (V) to select a predefined view. Note that the Autoscale option attempts to provide a best fit, showing as many of the critical features of each plot as possible. By dragging a finger horizontally or vertically across the screen, you can quickly see parts of the plot that are initially outside the set x and y ranges. This is easier than resetting the range of an axis.
You can also choose whether the table of data in Numeric view is automatically populated or whether it is populated by you typing in the particular x-values you are interested in. These options—Automatic or BuildYourOwn—are available from the Num Type list. They are explained in detail in “Custom tables” on page 103. 13. Press SJ(Clear) to reset all the settings to their defaults. 14.
expressions selected in Symbolic view: 1–x and (x–1)2 –3. You can also scroll through the columns of the dependant variables (labeled F1 and F2 in the illustration above). You can also scroll the table vertically or horizontally using tap and drag gestures. To go directly to a value 17. Place the cursor in the X column and type the desired value. For example, to jump straight to the row where x = 10: 10 To access the zoom options Other options Numerous zoom options are available by tapping .
Analyzing functions The Function menu ( ) in Plot view enables you to find roots, intersections, slopes, signed areas, and extrema for any function defined in the Function app. If you have more than one function plotted, you may need to choose the function of interest beforehand. Display the Plot view menu The Function menu is a sub-menu of the Plot view menu.
Note the button. If you tap this button, vertical and horizontal dotted lines are drawn through the current position of the tracer to highlight its position. Use this feature to draw attention to the cursor location. You can also choose a blinking cursor in Plot Setup. Note that the functions in the Fcn menu all use the current function being traced as the function of interest and the current tracer xcoordinate as an initial value.
3. Choose the function whose point of intersection with the currently selected function you wish to find. The coordinates of the intersection are displayed at the bottom of the screen. Tap on the screen near the intersection, and repeat from step 2. The coordinates of the intersection nearest to where you tapped are displayed at the bottom of the screen. To find the slope of the quadratic function We will now find the slope of the quadratic function at the intersection point. 1.
To find the signed area between the two functions We’ll now find the area between the two functions in the range – 1.3 x 2.3 . 1. Tap and select Signed area. 2. Specify the start value for x: Tap and press Q1.3 E. 3. Tap . 4. Select the other function as the boundary for the integral. (If F1(X) is the currently selected function, you would choose F2(X) here, and vice versa.) 5. Specify the end value for x: Tap and press 2.3E. The cursor jumps to x = 2.
Shortcut: When the Goto option is available, you can display the Go To screen simply by typing a number. The number you type appears on the entry line. Just tap to accept it. To find the extremum of the quadratic 1. To calculate the coordinates of the extremum of the quadratic equation, move the tracing cursor near the extremum of interest (if necessary), tap and select Extremum. The coordinates of the extremum are displayed at the bottom of the screen.
To access Function variables The Function variables are available in Home view and in the CAS, where they can be included as arguments in calculations. They are also available in Symbolic view. 1. To access the variables, press a, tap and select Function. 2. Select Results and then the variable of interest. The variable’s name is copied to the insertion point and its value is used in evaluating the expression that contains it. You can also enter the value of the variable instead of its name by tapping .
Summary of FCN operations 124 Operation Description Root Select Root to find the root of the current function nearest to the tracing cursor. If no root is found, but only an extremum, then the result is labeled Extremum instead of Root. The cursor is moved to the root value on the x-axis and the resulting x-value is saved in a variable named Root. Extremum Select Extremum to find the maximum or minimum of the current function nearest to the tracing cursor.
7 Advanced Graphing app The Advanced Graphing app enables you to define and explore the graphs of symbolic open sentences in x, y, both or neither. You can plot conic sections, polynomials in standard or general form, inequalities, and functions. The following are examples of the sorts of open sentences you can plot: 1. x2/3 – y2/5 = 1 2. 2x – 3y ≤ 6 3. mod x = 3 2 y 2 2 4. sin x + y – 5 > sin 8 atan -- x 5. x2 + 4x = –4 6.
Example 3 Example 4 Example 5 Example 6 Getting started with the Advanced Graphing app The Advanced Graphing app uses the customary app views: Symbolic, Plot, and Numeric described in chapter 5. For a description of the menu buttons available in this app, see: • “Symbolic view: Summary of menu buttons” on page 86 • “Plot view: Summary of menu buttons” on page 96, and • “Numeric view: Summary of menu buttons” on page 104.
Open the app 1. Open the Advanced Graphing app: I Select Advanced Graphing The app opens in the Symbolic view. Define the open sentence 2. Define the open sentence: jn2> w7 n 10 > + 3 jn4> w n 10 >+ n5 >w 10 <0 E Note that displays the relations palette from which relational operators can be easily selected. This is the same palette that appears if you press Sv. 3.
Set up the plot You can change the range of the x- and y-axes and the spacing of the interval marks along the axes. 4. Display Plot Setup view: SP (Setup) For this example, you can leave the plot settings at their default values. If your settings do not match those in the illustration at the right, press SJ (Clear) to restore the default values. See “Common operations in Plot Setup view” on page 96 for more information about setting the appearance of plots. Plot the selected definitions 5.
8. Tap . The definition as you entered it in Symbolic view appears at the bottom of the screen. 9. Tap . The definition is now editable. 10.Change the < to = and tap . Notice that the graph changes to match the new definition. The definition in Symbolic view also changes. 11.Tap to drop the definition to the bottom of the screen so that you can see the full graph. The definition is converted from textbook mode to algebraic mode to save screen space.
The tracer does not extend beyond the current Plot view window. The table below contains brief descriptions of each option. 130 Trace option Description Off Turns tracing off so that you can move the cursor freely in Plot view Inside Constrains the tracer to move within a region where the current relation is true. You can move in any direction within the region. Use this option for inequalities, for example.
Numeric view The Numeric view of most HP apps is designed to explore 2variable relations using numerical tables. Because the Advanced Graphing app expands this design to relations that are not necessarily functions, the Numeric view of this app becomes significantly different, though its purpose is still the same. The unique features of the Numeric view are illustrated in the following sections. 12.Press Y to return to Symbolic view and define V1 as Y=SIN(X).
Numeric Setup Although you can configure the X- and Y-values shown in Numeric view by entering values and zooming in or out, you can also directly set the values shown using Numeric setup. 15. Display the Numeric Setup view: SM(Setup) You can set the starting value and step value (that is, the increment) for both the X-column and the Y-column, as well as the zoom factor for zooming in or out on a row of the table.
Trace Edge 16.Tap and select Edge. Now the table shows (if possible) pairs of values that make the relation true. By default, the first column is the Y-column and there are multiple X-columns in case more than one X-value can be paired with the Y-value to make the relation true. Tap to make the first column an X-column followed by a set of Y-columns. In the figure above, for Y=0, there are 10 values of X in the default Plot view that make the relation Y=SIN(X) true.
Plot Gallery A gallery of interesting graphs—and the equations that generated them—is provided with the calculator. You open the gallery from Plot view: 1. With Plot view open, press the Menu key. Note that you press the Menu key here, not the Menu touch button on the screen. 2. From the menu, select Visit Plot Gallery. The first graph in the Gallery appears, along with its equation. 3. Press > to display the next graph in the Gallery, and continue likewise until you want to close the Gallery. 4.
8 Geometry The Geometry app enables you to draw and explore geometric constructions. A geometric construction can be composed of any number of geometric objects, such as points, lines, polygons, curves, tangents, and so on. You can take measurements (such as areas and distances), manipulate objects, and note how measurements change.
Preparation 1. Press SH. 2. On the Home Setting screen set the number format to Fixed and the number of decimal places to 3. Open the app and plot the graph 3. Press I and select Geometry. If there are objects showing that you don’t need, press SJ and confirm your intention by tapping . 4. Select the type of graph you want to plot. In this example we are plotting a simple sinusoidal function, so choose: > Plot > Function 5.
Add a tangent 8. We will now add a tangent to the curve, making point B the point of tangency: > More > Tangent 9. Tap on point B, press E and then press J. A tangent is drawn through point B. (Depending on where you placed point B, your illustration might be different from the one at the right.) We’ll now make the tangent stand out by giving it a bright color. 10. If the curve is selected, tap a blank area of the screen to deselect, and then tap on the tangent to select it. 11.
finger completes the move and deselects the point. In this case there is no way to cancel the move unless you have activated keyboard shortcuts, which provides you with an undo function. (Shortcuts are described on page 147.) Create a derivative point The derivative of a graph at any point is the slope of its tangent at that point. We’ll now create a new point that will be constrained to point B and whose ordinate value is the derivative of the graph at point B.
point B (referred to as GB in Symbolic view) and the later is to constrained to the slope of C (referred to as GC in Symbolic view). 19. You should have point() on the entry line. Between the parentheses, add: abscissa(GB),slope(GC) You can enter the commands by hand, or choose them from one of two Toolbox menus: App > Measure, or Catlg. 20.Tap . The definition of your new point is added to Symbolic view.
tangent changes in Plot view, the value of the slope is automatically updated in Numeric view. 26. With the new calculation highlighted in Numeric view, tap . Selecting a calculation in Numeric view means that it will also be displayed in Plot view. 27. Press P to return to Plot view. Notice the calculation that you have just created in Numeric view is displayed at the top left of the screen. Let’s now add two more calculations to Numeric view and have them displayed in Plot view. 28.
Trace the derivative Point D is the point whose ordinate value matches the derivative of the curve at point B. It is easier to see how the derivative changes by looking at a plot of it rather than comparing subsequent calculations. We can do that by tracing point D as it moves in response to movements of point B. First we’ll hide the calculations so that we can better see the trace curve. 35. Press M to return to Numeric view. 36.
Creating or selecting an object always involves at least two steps: tap and press E. Only by pressing E do you confirm your intention to create the point or select an object. When creating a point, you can tap on the screen and then use the cursor keys to accurately position the point before pressing E. Note that there are on-screen instructions to help you.
four vertices are named D, E, G, and H. Moreover, each of the six segments is also given a name: I, J, K, L, M, and N. These names are not displayed in Plot view, but you can see them if you go to Symbolic view (see “Symbolic view in detail” on page 148). Naming objects and parts of objects enables you to refer to them in calculations. This is explained in “Numeric view in detail” on page 150. You can rename an object. See “Symbolic Setup view” on page 150.
Coloring objects An object is colored black by default (and cyan when it is selected). If you want to change the color of an object: 1. Select the object whose color you want to change. 2. Press Z. 3. Select Change Color. The Choose Color palette appears. 4. Select the color you want. 5. Press J. Filling objects An object with closed contours (such as a circle or polygon) can be filled with color. 1. Press Z. 2. Select Fill with Color. The Select Object menu appears. 3.
Clearing an object To clear one object, select it and tap C. Note that an object is distinct from the points you entered to create it. Thus deleting the object does not delete the points that define it. Those points remain in the app. For example, if you select a circle and press C, the circle is deleted but the center point and radius point remain. If you tap C when no object is selected, a list of objects appears. Tap on the one you want to delete.
Plot view: buttons and keys Button or key Purpose Various scaling options. See “Zoom” on page 88. Tools for creating various types of points. See “Points” on page 153 Tools for creating various types of lines. See “Line” on page 156 Tools for creating various types of polygons. See “Polygon” on page 157 Tools for creating various types of curves and plots. See “Curve” on page 158 Tools for geometric transformations of various kinds. See “Geometric transformations” on page 161.
The fields and options are: • X Rng: Two fields for entering the minimum and maximum x-values, thereby giving the default horizontal range. As well as changing this range on the Geometry Plot Setup screen, you can change it by panning and zooming. • Y Rng: Two fields for entering the minimum and maximum y-values, thereby giving the default vertical range. As well as changing this range on the Geometry Plot Setup screen, you can change it by panning and zooming.
Key g j B r n t Result in Plot view (Continued) Selects the intersection drawing tool. Follow the instructions on the screen (or see page 154). Selects the line drawing tool. Follow the instructions on the screen (or see page 156). Selects the point drawing tool. Follow the instructions on the screen (or see page 153). Selects the segment drawing tool. Follow the instructions on the screen (or see page 156). Selects the triangle drawing tool. Follow the instructions on the screen (or see page 157).
Note Calculations referencing geometry variables can be made in the CAS or in the Numeric view of the Geometry app (explained below on page 150). You can change the definition of an object by selecting it, tapping , and altering one or more of its defining parameters. The object is modified accordingly in Plot view.
Deleting an object As well as deleting an object in Plot view (see page 145) you can delete an object in Symbolic view. 1. Highlight the definition of the object you want to delete. 2. Tap or press C. To delete all objects, press SJ. Symbolic Setup view The Symbolic view of the Geometry app is common with many apps. It is used to override certain system-wide settings. For details, see “Symbolic Setup view” on page 74.
You could have entered the command and object name manually, that is, without choosing them from menus. If you enter object names manually, remember that the name of the object in Plot view must be given a “G” prefix if it is used in any calculation. Thus the circle named C in Plot view must be referred to as GC in Numeric view and Symbolic view. 5. Press 6. Tap E or tap . The area is displayed. . 7. Enter radius(GC) and tap . The radius is displayed.
grouped according to their type, with each group given its own menu. If you are building a calculation, you can select an object from one of these variables menus. The name of the selected object is placed at the insertion point on the entry line. Getting object properties As well as employing functions to make calculations in Numeric view, you can also get various parameters of objects just by tapping and specifying the object’s name.
Geometric objects The geometric objects discussed in this section are those that can be created in Plot view. Objects can also be created in Symbolic view—more, in fact, than in Plot view—but these are discussed in “Geometry functions and commands” on page 165. In Plot view, you choose a drawing tool to draw an object. The tools are listed in this section. Note that once you select a drawing tool, it remains selected until you deselect it.
placed on a circle will remain on that circle regardless of how you move the point. If there is no object where you tap, a point is created if you then press E. Midpoint Tap where you want one point to be and press E. Tap where you want the other point to be and press E. A point is automatically created midway between those two points. If you choose an object first—such as a segment—choosing the Midpoint tool and pressing E adds a point midway between the ends of that object.
Erase Trace Erases all trace lines, but leaves the definition of the trace points in Symbolic view. While a Trace definition is still in Symbolic view, if you move the point again, a new trace line is created. Center Tap a circle and press E. A point is created at the center of the circle. Element 0 .. 1 Element 0 .. 1 has a number of uses. You can use it to place a constrained point on a object (whether previously created or not).
Line Segment Tap where you want one endpoint to be and press E. Tap where you want the other endpoint to be and press E. A segment is drawn between the two end points. Keyboard shortcut: r Ray Tap where you want the endpoint to be and press E. Tap a point that you want the ray to pass through and press E. A ray is drawn from the first point and through the second point. Line Tap at a point you want the line to pass through and press E. Tap at another point you want the line to pass through and press E.
Parallel Tap on a point (P) and press E. Tap on a line (L) and press E. A new line is draw parallel to L and passing through P. Perpendicular Tap on a point (P) and press E. Tap on a line (L) and press E. A new line is draw perpendicular to L and passing through P. Tangent Tap on a curve (C) and press E. Tap on a point (P) and press E. If the point (P) is on the curve (C), then a single tangent is drawn. If the point (P) is not on the curve (C), then zero or more tangents may be drawn.
four vertices are automatically calculated and the regular hexagon is drawn. Special Eq. triangle Produces an equilateral triangle. Tap at one vertex and press E. Tap at another vertex and press E. The location of the third vertex is automatically calculated and the triangle is drawn. Square Tap at one vertex and press E. Tap at another vertex and press E. The location of the third and fourth vertices are automatically calculated and the square is drawn. Parallelogram Tap at one vertex and press E.
Special Circumcircle A circumcircle is the circle that passes through each of the triangle’s three vertices, thus enclosing the triangle. Tap at each vertex of the triangle, pressing E after each tap. Incircle An incircle is a circle that is tangent to each of a polygon’s sides. The HP Prime can draw an incircle that is tangent to the sides of a triangle. Tap at each vertex of the triangle, pressing E after each tap.
Locus Takes two points as its arguments: the first is the point whose possible locations form the locus; the second is a point on an object. This second point drives the first through its locus as the second moves on its object. In the example at the right, circle C has been drawn and point D is a point placed on C (using the Point On function described above). Point I is a translation of point D. Choosing Curve > Special > Locus places locus( on the entry line.
Geometric transformations The Transform menu—displayed by tapping —provides numerous tools for you to perform transformations on geometric objects in Plot view. You can also define transformations in Symbolic view Translation A translation is a transformation of a set of points that moves each point the same distance in the same direction. T: (x,y) → (x+a, y+b). You must create a vector to indicate the distance and direction of the translation. You then choose the vector and the object to be translated.
Reflection A reflection is a transformation which maps an object or set of points onto its mirror image, where the mirror is either a point or a line. A reflection through a point is sometimes called a half-turn. In either case, each point on the mirror image is the same distance from the mirror as the corresponding point on the original. In the example at the right, the original triangle D is reflected through point I. 1. Tap and select Reflection. 2.
Rotation A rotation is a mapping that rotates each point by a fixed angle around a center point. The angle is defined using the angle() command, with the vertex of the angle as the first argument. Suppose you wish to rotate the square (GC) around point K (GK) through figure to the right. 1. Press Y and tap 2. Tap ∡ LKM in the . and select Transform > Rotation. rotation() appears on the entry line. 3. Between the parentheses, enter: GK,angle(GK,GL,GM ),GC 4. Press E or tap . 5.
lengths of the corresponding segments. If k=1, then the lengths CA and CA’ are reciprocals. Suppose you wish to find the inversion of a circle (GC) with a point on the circle (GD) as center. 1. Tap and select More > Inversion. 2. Tap the point that is to be the center (GD) of the inversion circle and press E. 3. Enter the inversion ratio—use the default value of 1—and press E. 4. Tap on the circle( GC) and press E. You will see that the inversion is a line.
Geometry functions and commands The list of geometry-specific functions and commands in this section covers those that can be found by tapping in both Symbolic and Numeric view and those that are only available from the Catlg menu. The sample syntax provided has been simplified. Geometric objects are referred to by a single uppercase character (such as A, B,C and so on).
center Returns the center of a circle. center(circle) Example: center(circle(x2+y2–x–y)) gives point(1/2,1/2) division_point For two points A and B, and a numerical factor k, returns a point C such that C-B=k*(C-A). division_point(point1, point2, realk) Example: division_point(0,6+6*i,4) returns point (8,8) element Creates a point on a geometric object whose abscissa is a given value or creates a real value on a given interval. element(object, real) or element(real1..
isobarycenter Returns the hypothetical center of mass of a set of points. Works like barycenter but assumes that all points have equal weight. isobarycenter(point1, point2, …,pointn) Example: isobarycenter(–3,3,3*√3*i) returns point(3*√3*i/3), which is equivalent to (0,√3). midpoint Returns the midpoint of a segment. The argument can be either the name of a segment or two points that define a segment. In the latter case, the segment need not actually be drawn.
point2d Randomly re-distributes a set of points such that, for each point, x ∈ [–5,5] and y ∈ [–5,5]. Any further movement of one of the points will randomly re-distribute all of the points with each tap or direction key press. point2d(point1, point2, …, pointn) trace Begins tracing of a specified point. trace(point) stop trace Stops tracing of a specified point, but does not erase the current trace. This command is only available in Plot view.
bisector Given three points, creates the bisector of the angle defined by the three points whose vertex is at the first point. The angle does not have to be drawn in the Plot view. bisector(point1, point2, point3) Examples: bisector(A,B,C) draws the bisector of ∡ BAC. bisector(0,-4i,4) draws the line given by y=–x exbisector Given three points that define a triangle, creates the bisector of the exterior angles of the triangle whose common vertex is at the first point.
median_line Given three points that define a triangle, creates the median of the triangle that passes through the first point and contains the midpoint of the segment defined by the other two points. median_line(point1, point2, point3) Example: median_line(0, 8i, 4) draws the line whose equation is y=2x; that is, the line through (0,0) and (2,4), the midpoint of the segment whose endpoints are (0, 8) and (4, 0). parallel Draws a line through a given point that is parallel to a given line.
perpendicular Draws a line through a given point that is perpendicular to a given line. The line may be defined by its name, two points, or an expression in x and y. perpendicular(point, line) or perpendicular(point1, point2, point3) Examples: perpendicular(GA, GD) draws a line perpendicular to line D through point A. perpendicular(3+2i, GB, GC) draws a line through the point whose coordinates are (3, 2) that is perpendicular to line BC.
Polygon equilateral_triangle Draws an equilateral triangle defined by one of its sides; that is, by two consecutive vertices. The third point is calculated automatically, but is not defined symbolically. If a lowercase variable is added as a third argument, then the coordinates of the third point are stored in that variable. The orientation of the triangle is counterclockwise from the first point.
isosceles_triangle Draws an isosceles triangle defined by two of its vertices and an angle. The vertices define one of the two sides equal in length and the angle defines the angle between the two sides of equal length. Like equilateral_triangle, you have the option of storing the coordinates of the third point into a CAS variable.
polygon Draws a polygon from a set of vertices. polygon(point1, point2, …, pointn) Example: polygon(GA, GB, GD) draws ΔABD quadrilateral Draws a quadrilateral from a set of four points. quadrilateral(point1, point2, point3, point4) Example: quadrilateral(GA, GB, GC, GD) draws quadrilateral ABCD. rectangle Draws a rectangle given two consecutive vertices and a point on the side opposite the side defined by the first two vertices or a scale factor for the sides perpendicular to the first side.
Example rhombus(GA, GB, angle(GC, GD, GE)) draws a rhombus on segment AB such that the angle at vertex A has the same measure as ∡ DCE. right_triangle Draws a right triangle given two points and a scale factor. One leg of the right triangle is defined by the two points, the vertex of the right angle is at the first point, and the scale factor multiplies the length of the first leg to determine the length of the second leg.
Curve function Draws the plot of a function, given an expression in the independent variable x. Note the use of lowercase x. plotfunc(Expr) Example: Example: plotfunc(3*sin(x)) draws the graph of y=3*sin(x). circle Draws a circle, given the endpoints of the diameter, or a center and radius, or an equation in x and y. circle(point1, point2) or circle(point1, point 2-point1) or circle(equation) Examples: circle(GA, GB) draws the circle with diameter AB.
ellipse Draws an ellipse, given the foci and either a point on the ellipse or a scalar that is one half the constant sum of the distances from a point on the ellipse to each of the foci. ellipse(point1, point2, point3) or ellipse(point1, point2, realk) Examples: ellipse(GA, GB, GC) draws the ellipse whose foci are points A and B and which passes through point C. ellipse(GA, GB, 3) draws an ellipse whose foci are points A and B. For any point P on the ellipse, AP+BP=6.
incircle Draws the incircle of a triangle, the circle tangent to all three sides of the triangle. incircle(point1, point2, point3) Example: incircle(GA, GB, GC) draws the incircle of ΔABC. locus Given a first point and a second point that is an element of (a point on) a geometric object, draws the locus of the first point as the second point traverses its object.
inversion Draws the inversion of a point, with respect to another point, by a scale factor. inversion(point1, realk, point2) Example: inversion(GA, 3, GB) draws point C on line AB such that AB*AC=3. In this case, point A is the center of the inversion and the scale factor is 3. Point B is the point whose inversion is created.
rotation Rotates a geometric object, about a given center point, through a given angle. rotate(point, angle, object) Example: rotate(GA, angle(GB, GC, GD),GK) rotates the geometric object labeled K, about point A, through an angle equal to ∡ CBD. similarity Dilates and rotates a geometric object about the same center point.
Measure Plot angleat Used in Symbolic view. Given the three points of an angle and a fourth point as a location, displays the measure of the angle defined by the first three points. The measure is displayed, with a label, at the location in the Plot view given by the fourth point. The first point is the vertex of the angle. angleat(point1, point2, point3, point4) Example: In degree mode, angleat(point(0, 0), point(2√3, 0), point(2√3, 3), point(-6, 6)) displays “appoint(0,0)=30.
distanceatraw Works the same as distanceat, but without the label. perimeterat Used in Symbolic view. Displays the perimeter of a polygon or circle. The measure is displayed, with a label, at the given point in Plot view. perimeterat(polygon, point) or perimeterat(circle, point) Example: perimeterat(circle(x^2+y^2=1), point(-4,4)) displays “pcircle(x^2+y^2=1)= 2*π” at point (-4, 4) perimeteratraw Works the same as perimeterat, but without the label. slopeat Used in Symbolic view.
affix Returns the coordinates of a point or both the x- and y-lengths of a vector as a complex number. affix(point) or affix(vector) Example: if GA is a point at (1, –2), then affix(GA) returns 1–2i. angle Returns the measure of a directed angle. The first point is taken as the vertex of the angle as the next two points in order give the measure and sign. angle(vertex, point2, point3) Example: angle(GA, GB, GC) returns the measure of ∡ BAC.
Examples: If GA is defined to be the unit circle, then area(GA) returns . area(4-x^2/4, x=-4..4) returns 14.666… coordinates Given a vector of points, returns a matrix containing the x- and y-coordinates of those points. Each row of the matrix defines one point; the first column gives the x-coordinates and the second column contains the y-coordinates. coordinates([point1, point2, …, pointn])) distance Returns the distance between two points or between a point and a curve.
equation Returns the Cartesian equation of a curve in x and y, or the Cartesian coordinates of a point. equation(curve) or equation(point) Example: If GA is the point at (0, 0), GB is the point at (1, 0), and GC is defined as circle(GA, GB-GA), then equation(GC) returns x2 + y2 = 1. extract_measure Returns the definition of a geometric object. For a point, that definition consists of the coordinates of the point.
If GA is the point at (0, 0), GB is the point at (1, 0), and GC is defined as square(GA, GB-GA), then perimeter(GC) returns 4. radius Returns the radius of a circle. radius(circle) Example: If GA is the point at (0, 0), GB is the point at (1, 0), and GC is defined as circle(GA, GB-GA), then radius(GC) returns 1. Test is_collinear Takes a set of points as argument and tests whether or not they are collinear. Returns 1 if the points are collinear and 0 otherwise.
is_element Tests if a point is on a geometric object. Returns 1 if it is and 0 otherwise is_element(point, object) Example: 2 is_element(point (---2 -,----) , circle(0,1)) returns 1. 2 2 is_equilateral Takes three points and tests whether or not they are vertices of a single equilateral triangle. Returns 1 if they are and 0 otherwise. is_equilateral(point1, point2, point3) Example: is_equilateral(point(0,0), point(4,0), point(2,4)) returns 0.
is_parallel Tests whether or not two lines are parallel. Returns 1 if they are and 0 otherwise. is_parallel(line1, line2) Example: is_parallel(line(2x+3y=7),line(2x+3y=9) returns 1. is_parallelogram Tests whether or not a set of four points are vertices of a parallelogram. Returns 0 if they are not. If they are, then returns 1 if they form only a parallelogram, 2 if they form a rhombus, 3 if they form a rectangle, and 4 if they form a square.
is_square Tests whether or not a set of four points are vertices of a square. Returns 1 if they are and 0 otherwise. is_square(point1, point2, point3, point4) Example: is_square(point(0,0), point(4,2), point(2,6), point(-2,4)) returns 1. Other Geometry functions The following functions are not available from a menu in the Geometry app, but are available from the Catlg menu. convexhull Returns a vector containing the points that serve as the convex hull for a given set of points.
Example: harmonic_division(point(0, 0), point(3, 0), point(4, 0), p) returns point(12/5, 0) and stores it in the variable p is_harmonic Tests whether or not 4 points are in a harmonic division or range. Returns 1 if they are or 0 otherwise.
LineHorz Draws the horizontal line y=a. LineHorz(a) Example: LineHorz(-2) draws the horizontal line whose equation is y = –2 LineVert Draws the vertical line x=a. LineVert(a) Example: LineVert(–3) draws the vertical line whose equation is x = –3 open_polygon Connects a set of points with line segments, in the given order, to produce a polygon. If the last point is the same as the first point, then the polygon is closed; otherwise, it is open.
pole Returns the pole of the given line with respect to the given circle. pole(circle, line) Example: pole(circle(x^2+y^2=1), line(x=3)) returns point(1/3, 0) powerpc Given a circle and a point, returns the difference between the square of the distance from the point to the circle’’s center and the square of the circle’s radius.
single_inter Returns the intersection of curve1 and curve2 that is closest to point. single_inter(curve1, curve2, point) Example: single_inter(line(y=x),circle(x^2+y^2=1), point(1,1)) returns point(((1+i)* √2)/2) vector Creates a vector from point1 to point2. With one point as argument, the origin is used as the tail of the vector. vector(point1, point2) or vector(point) Example: vector(point(1,1), point(3,0)) creates a vector from (1, 1) to (3, 0). vertices Returns a list of the vertices of a polygon.
194 Geometry
9 Spreadsheet The Spreadsheet app provides a grid of cells for you to enter content (such as numbers, text, expressions, and so on) and to perform certain operations on what you enter. To open the Spreadsheet app, and select press Spreadsheet. I You can create any number of customized spreadsheets, each with its own name (see “Creating an app” on page 107). You open a customized spreadsheet in the same way: by pressing and selecting the particular spreadsheet.
3. Enter PRICE and tap first column PRICE. . You have named the entire 4. Select column B. Either tap on B or use the cursor keys to highlight the B cell. 5. Enter a formula for your commission (being 10% of the price of each item sold): S.PRICEs0.1E Because you entered the formula in the heading of a column, it is automatically copied to every cell in that column. At the moment only 0 is shown, since there are no values in the PRICE column yet. 6. Once again select the header of column B. 7.
11. To delete the dummy values, select cell A1, tap , press \ until all the dummy values are selected, and then press C. 12. Select cell C1. 13. Enter a label for your takings: S.ANTAKINGSE Notice that text strings, but not names, need to be enclosed within quotation marks. 14. Select cell D1. 15. Enter a formula to add up your takings: S.
23. Enter a label for your fixed costs: S.ANCOSTSE 24.In cell D5, enter 100. This is what you have to pay the landowner for renting the space for your stall. 25. Enter the label PROFIT in cell C7. 26. In cell D7, enter a formula to calculate your profit: S.D3 w D5E You could also have named D3 and D5—say, TOTCOM and COSTS respectively. Then the formula in D7 could have been =TOTCOM–COSTS. 27. Enter the label GOAL in cell E1.
32. Tap and select Color. 33. Choose a color for the contents of the selected cells. 34.Tap and select Fill. 35. Choose a color for the background of the selected cells. The most important cells in the spreadsheet will now stand out from the rest. The spreadsheet is complete, but you may want to check all the formulas by adding some dummy data to the PRICE column. When the profit reaches 250, you should see the value in D9 change from 0 to 1.
Cell references You can refer to the value of a cell in formulas as if it were a variable. A cell is referenced by its column and row coordinates, and references can be absolute or relative. An absolute reference is written as $C$R (where C is the column number and R the row number). Thus $B$7 is an absolute reference. In a formula it will always refer to the data in cell B7 wherever that formula, or a copy of it, is placed. On the other hand, B7 is a relative reference.
The following is a more complex example involving the naming of an entire column. 1. Select cell A (that is the header cell for column A). 2. Enter COST and tap . 3. Select cell B (that is the header cell for column B). 4. Enter S.COST*0.33 and tap . 5. Enter some values in column A and observe the calculated results in column B. Entering content You can enter content directly in the spreadsheet or import data from a statistics app.
underlying formula that generates the value, move your cursor to the cell. The entry line shows a formula if there is one. A single formula can add content to every cell in a column or row. For example, move to C (the heading cell for column C), enter S.SIN(Row)and press E. Each cell in the column is populated with the sine of the cell’s row number. A similar process enables you to populate every cell in a row with the same formula.
The column is filled with the data from the statistics app, starting with the cell selected at step 1. Any data in that column will be overwritten by the data being imported. You can also export data from the Spreadsheet app to a statistics app. See “Entering and editing statistical data” on page 215 for the general procedure. It can be used in both the Statistics 1Var and Statistics 2Var apps.
There are additional spreadsheet functions that you can use (mostly related to finance and statistics calculations). See “Spreadsheet app functions” on page 349. Copy and paste To copy one or more cells, select them and press SV (Copy). Move to the desired location and press SZ (Paste). You can choose to paste either the value, formula, format, both value and format, or both formula and format.
Referencing variables Any variable can be inserted in a cell. This includes Home variables, App variables, CAS variables and user variables. Variables can be referenced or entered. For example, if you have assigned 10 to P in Home view, you could enter =P*5 in a spreadsheet cell, press E and get 50. If you subsequently changed the value of P, the value in that cell automatically changes to reflect the new value. This is an example of a referenced variable.
Using the CAS in spreadsheet calculations You can force a spreadsheet calculation to be performed by the CAS, thereby ensuring that results are symbolic (and thus exact). For example, the formula =√Row in row 5 gives 2.2360679775 if not calculated by the CAS, and √5 if it is. You choose the calculation engine when you are entering the formula. As soon as you begin entering a formula, the key changes to or (depending on the last selection). This is a toggle key. Tap on it to change it from one to the other.
Buttons and keys Button or key Purpose Activates the entry line for you to edit the object in the selected cell. (Only visible if the selected cell has content.) Converts the text you have entered on the entry line to a name. (Only visible when the entry line is active.) / A toggle button that is only visible when the entry line is active. Both options force the expression to be handled by the CAS, but only evaluates it. Tap to enter the $ symbol. A shortcut when entering absolute references.
Formatting options The formatting options appear when you tap . They apply to whatever is currently selected: a cell, block, column, row, or the entire spreadsheet. The options are: • Name: displays an input form for you to give a name to whatever is selected • Number Format: Auto, Standard, Fixed, Scientific, or Engineering. See “Home settings” on page 30 for more details. • Font Size: Auto or from 10 to 22 point • Color: color for the content (text, number, etc.
Format Parameters Each format attribute is represented by a parameter that can be referenced in a formula. For example, =D1(1) returns the formula in cell D1 (or nothing if D1 has no formula). The attributes that can be retrieved in a formulas by referencing its associated parameter are listed below.
relevant cell. For example, wherever it is placed g5(1):=6543 enters 6543 in cell g5. Any previous content in g5 is replaced. Similarly, B3(5):=2 forces the contents of B3 to be displayed in medium font size. Spreadsheet functions As well as the functions on the Math, CAS and Catlg menus, you can use special spreadsheet functions. These can be found on the App menu, one of the Toolbox menus. Press D, tap and select Spreadsheet. The functions are described on “Spreadsheet app functions” on page 349.
10 Statistics 1Var app The Statistics 1Var app can store up to ten data sets at one time. It can perform one-variable statistical analysis of one or more sets of data. The Statistics 1Var app starts with the Numeric view which is used to enter data. The Symbolic view is used to specify which columns contain data and which column contains frequencies. You can also compute statistics in Home and recall the values of specific statistics variables.
2. Enter the measurement data in column D1: 160 E 165 E 170 E 175 E 180 E 3. Find the mean of the sample. Tap to see the statistics calculated from the sample data in D1. _ The mean (x ) is 170. There are more statistics than can be displayed on one screen. Thus you may need to scroll to see the statistic you are after. Note that the title of the column of statistics is H1. There are 5 data-set definitions available for onevariable statistics: H1–H5.
represent the data in Plot view: Histogram, Box and Whisker, Normal Probability, Line, Bar, or Pareto. Symbolic view: menu items The menu items you can tap on in Symbolic view are: Menu item Purpose Copies the column variable (or variable expression) to the entry line for editing. Tap when done. Selects (or deselects) a statistical analysis (H1–H5) for exploration. Enters D directly (to save you having to press two keys). Displays the current expression in textbook format in full-screen view.
7. Enter the name of the column that you will contain the frequencies (in this example, D2): 2 8. If you want to choose a color for the graph of the data in Plot view, see “Choose a color for plots” on page 85. 9. If you have more than one analysis defined in Symbolic view, deselect any analysis you are not currently interested in. 10. Return to Numeric view: M 11. In column D2, enter the frequency data shown in the table above: >5E 3E 8E 2E 1E 12.
13. Configure a histogram plot for the data. SP ((Setup) Enter parameters appropriate to your data. Those shown at the right will ensure that all the data in this particular example are displayed in Plot view. 14. Plot a histogram of the data. P Press > and < to move the tracer and see the interval and frequency of each bin. You can also tap to select a bin. Tap and drag to scroll the Plot view. You can also zoom in or out on the cursor by pressing + and w respectively.
1Var app open, return to Home view and enter Spreadsheet.A1:A10 D7 E. Whichever method you use, the data you enter is automatically saved. You can leave this app and come back to it later. You will find that the data you last entered is still available. After entering the data, you must define data sets—and the way they are to be plotted—in Symbolic view. Numeric view: menu items The menu items you can tap on in Numeric view are: Item Purpose Copies the highlighted item into the entry line.
Delete data Insert data • To delete a data item, highlight it and press C. The values below the deleted cell will scroll up one row. • To delete a column of data, highlight an entry in that column and press SJ(Clear). Select the column and tap . • To delete all data in every column, press SJ (Clear), select All columns, and tap . 1. Highlight the cell below where you want to insert a value. 2. Tap and enter the value.
you want to sort by income, then you make C2 the independent column and C1 the dependent column. 4. Specify any frequency data column. 5. Tap . The independent column is sorted as specified and any other columns are sorted to match the independent column. To sort just one column, choose None for the Dependent and Frequency columns. Computed statistics Tapping displays the following results for each dataset selected in Symbolic view.
Plotting You can plot: • Histograms • Box-and-Whisker plots • Normal Probability plots • Line plots • Bar graphs • Pareto charts Once you have entered your data and defined your data set, you can plot your data. You can plot up to five boxand-whisker plots at a time; however, with the other types, you can only plot one at a time. To plot statistical data 1. In the Symbolic view, select the data sets you want to plot. 2. From the Plotn menu, select the plot type. 3.
that bin is 6. The data set is defined by H3 in Symbolic view. You can see information about other bins by pressing > or <. Box-and-Whisker plot The left whisker marks the minimum data value. The box marks the first quartile, the median, and the third quartile. The right whisker marks the maximum data value. The numbers below the plot give the statistic at the cursor. You can see other statistics by pressing >or <.
Pareto chart A pareto chart places the data in descending order and displays each with its percentage of the whole. Setting up the plot (Plot Setup view) The Plot Setup view (SP) enables you to specify many of the same plotting parameters as other apps (such as X Rng and Y Rng). There are two settings unique to the Statistics 1Var app: Histogram width H Width enables you to specify the width of a histogram Histogram range H Rng enables you to specify the range of values for a set bin.
Plot view: menu items The menu items you can tap on in Plot view are: Button Purpose Displays the Zoom menu. Turns trace mode on or off. See “Zoom” on page 100.) Displays the definition of the current statistical plot. Shows or hides the menu.
11 Statistics 2Var app The Statistics 2Var app can store up to ten data sets at one time. It can perform two-variable statistical analysis of one or more sets of data. The Statistics 2Var app starts with the Numeric view which is used to enter data. The Symbolic view is used to specify which columns contain data and which column contains frequencies. You can also compute statistics in Home and in the Spreadsheet app. The values computed in the Statistics 2Var app are saved in variables.
Open the Statistics 2Var app 1. Open the Statistics 2Var app: I Select Statistics 2Var. Enter data 2. Enter the advertising minutes data in column C1: 2E1E3E5E5E4 E 3. Enter the resulting sales data in column C2: 1400E 920E 1100E 2265E 2890E 2200E Choose data columns and fit In Symbolic view, you can define up to five analyses of two-variable data, named S1 to S5. In this example, we will define just one: S1. The process involves choosing data sets and a fit type. 4.
5. Select a fit: From the Type 1 field select a fit. In this example, select Linear. 6. If you want to choose a color for the graph of the data in Plot view, see “Choose a color for plots” on page 85. 7. If you have more than one analysis defined in Symbolic view, deselect any analysis you are not currently interested in. Explore statistics 8. Find the correlation, r, between advertising time and sales: M The correlation is r=0.8995… 9. Find the mean advertising time ( x ).
10. Find the mean sales ( y ). The mean sales, y , is approximately $1,796. Press to return to Numeric view. Setup plot 11. Change the plotting range to ensure that all the data points are plotted (and to select a different data-point indicator, if you wish). SP(Setup) Q1E6 E Q 1000 E3200 E \ 500 E Plot the graph 12. Plot the graph. P Notice that the regression curve (that is, a curve to best fit the data points) is plotted by default.
Display the equation 13. Return to the Symbolic view. Y Note the expression in the Fit1 field. It shows that the slope (m) of the regression line is 425.875 and the y-intercept (b) is 376.25. Predict values Let’s now predict the sales figure if advertising were to go up to 6 minutes. 14. Return to the Plot view: P The trace option is active by default. This option will move the cursor from data point to data point as you press > or <.
The cursor jumps from whatever data point it was on to the regression curve. 16. Tap on the regression line near x = 6 (near the right edge of the display). Then press > until x = 6. If the x-value is not shown at the bottom left of the screen, tap . When you reach x = 6, you will see that the PREDY value (also displayed at the bottom of the screen) reads 2931.5. Thus the model predicts that sales would rise to $2,931.50 if advertising were increased to 6 minutes.
Whichever method you use, the data you enter is automatically saved. You can leave this app and come back to it later. You will find that the data you last entered is still available. After entering the data, you must define data sets—and the way they are to be plotted—in Symbolic view. Numeric view menu items The buttons you can tap on in Numeric view are: Button Purpose Copies the highlighted item to the entry line. Inserts a new cell above the highlighted cell (and gives it a value of 0).
Delete data Insert data • To delete a data item, highlight it and press C. The values below the deleted cell will scroll up one row. • To delete a column of data, highlight an entry in that column and press SJ(Clear). Select the column and tap . • To delete all data in every column, press SJ (Clear), select All columns, and tap . Highlight the cell below where you want to insert a value. Tap and enter the value.
Defining a regression model You define a regression model in Symbolic view. There are three ways to do so: Choose a fit • Accept the default option to fit the data to a straight line. • Choose a pre-defined fit type (logarithmic, exponential, and so on). • Enter your own mathematical expression. The expression will be plotted so that you can see how closely it fits the data points. 1. PressYto display the Symbolic view. 2.
Fit type Meaning (Continued) Logistic Fits the data to a logistic curve: L y = ------------------------ – bx 1 + ae where L is the saturation value for growth. You can store a positive real value in L, or—if L=0—let L be computed automatically. To define your own fit Quadratic Fits the data to a quadratic curve: y = ax2+bx+c. Needs at least three points.
Computed statistics When you tap , three sets of statistics become available. By default, the statistics involving both the independent and dependent columns are shown. Tap to see the statistics involving just the independent column or to display the statistics derived from the dependent column. Tap to return to the default view. The tables below describe the statistics displayed in each view.
The statistics displayed when you tap are: Statistic Definition x Mean of x- (independent) values. X Sum of x-values. X2 Sum of x2-values. sX The sample standard deviation of the independent column. X The population standard deviation of the independent column. serrX the standard error of the independent column The statistics displayed when you tap are: Statistic Definition y Mean of y- (dependent) values. Y Sum of y-values. Y Sum of y2-values.
necessary), the X Rng and Y Rng fields in Plot Setup view. (SP). 3. PressP. If the data set and regression line are not ideally positioned, Press V and select Autoscale. Autoscale can be relied upon to give a good starting scale which can then be adjusted later in the Plot Setup view. Tracing a scatter plot The figures below the plot indicate that the cursor is at the second data point of S1, at ((1, 920). Press>to move to the next data point and display information about it.
press \ a fourth time, you will return to the S1 scatter plot. If you are confused as to what you are tracing, just tap to see the definition of the object (scatter plot or fit) currently being traced. Plot view: menu items The menu items in Plot view are: Button Purpose Displays the Zoom menu. Turns trace mode on or off. Shows or hides a curve that best fits the data points according to the selected regression model.
Predicting values PredX is a function that predicts a value for X given a value for Y. Likewise, PredY is a function that predicts a value for Y given a value for X. In both cases, the prediction is based on the equation that best fits the data according to the specified fit type. You can predict values in the Plot view of the Statistics 2Var app and also in Home view. In Plot view 1. In the Plot view, tap to display the regression curve for the data set (if it is not already displayed). 2.
Tip In cases where more than one fit curve is displayed, the PredX and PredY functions use the first active fit defined in Symbolic view. Troubleshooting a plot If you have problems plotting, check the following: 238 • The fit (that is, regression model) that you intended to select is the one selected. • Only those data sets you want to analyze or plot are selected in Symbolic view. • The plotting range is suitable.
12 Inference app The Inference app enables you to calculate confidence intervals and undertake hypothesis tests based on the Normal Z-distribution or Student’s t-distribution. In addition to the Inference app, the Math menu has a full set of probability functions based on various distributions (Chi-Square, F, Binomial, Poisson, etc.).
Symbolic view options The table below summarizes the options available in Symbolic view for the two inference methods: hypothesis test and confidence interval.
Select the inference method 2. Hypothesis Test is the default inference method. If it is not selected, tap on the Method field and select it. 3. Choose the type of test. In this case, select Z–Test: 1 from the Type menu. 4. Select an alternative hypothesis. In this case, select 0 from the Alt Hypoth menu. Enter data 5. Go to Numeric view to see the sample data. M The table below describes the fields in this view for the sample data.
The Numeric view is where you enter the sample statistics and population parameters for the situation you are examining. The sample data supplied here belong to the case in which a student has generated 50 pseudo-random numbers on his graphing calculator. If the algorithm is working properly, the mean would be near 0.5 and the population standard deviation is known to be approximately 0.2887. The student is concerned that the sample mean (0.
Importing statistics The Inference app can calculate confidence intervals and test hypotheses based on data in the Statistics 1Var and Statistics 2Var apps. The following example illustrates the process. A series of six experiments gives the following values as the boiling point of a liquid: 82.5, 83.1, 82.6, 83.7, 82.4, and 83.0 Based on this sample, we want to estimate the true boiling point at the 90% confidence level. Open the Statistics 1Var app 1. Clear unwanted data 2.
Calculate statistics 4. Calculate statistics: The statistics calculated will now be imported into the Inference app. 5. Tap to close the statistics window. Open the Inference app 6. Open the Inference app and clear the current settings. I Select Inference SJ Select inference method and type 7. Tap on the Method field and select Confidence Interval. 8. Tap on Type and select T-Int: 1 Import the data 9. Open Numeric view: M 10. Specify the data you want to import: Tap 244 .
11. From the App field select the statistics app that has the data you want to import. 12. In the Column field specify the column in that app where the data is stored. (D1 is the default.) 13. Tap . 14. Specify a 90% confidence interval in the C field. Display results numerically 15. Display the confidence interval in Numeric view: 16. Return to Numeric view: Display results graphically 17. Display the confidence interval in Plot view. P The 90% confidence interval is [82.48…, 83.28…].
The HP Prime hypothesis tests use the Normal Zdistribution or the Student’s t-distribution to calculate probabilities. If you wish to use other distributions, please use the Home view and the distributions found within the Probability category of the Math menu. One-Sample Z-Test Menu name Z-Test: 1 On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Results The results are: Result Test Z Test x P Critical Z Critical x Description Z-test statistic Value of x associated with the test Z-value Probability associated with the Z-Test statistic Boundary value(s) of Z associated with the level that you supplied Boundary value(s) of x required by the value that you supplied Two-Sample Z-Test Menu name Z-Test: 1 – 2 On the basis of two samples, each from a separate population, this test measures the strength of the evidence for a selected hypothesis a
Results The results are: Result Description Test Z Z-Test statistic Test x Difference in the means associated with the test Z-value P Probability associated with the Z-Test statistic Critical Z Boundary value(s) of Z associated with the level that you supplied Critical x Difference in the means associated with the level you supplied One-Proportion Z-Test Menu name Z-Test: On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected
Results The results are: Result Description Test Z Z-Test statistic Test p̂ Proportion of successes in the sample P Probability associated with the Z-Test statistic Critical Z Boundary value(s) of Z associated with the level that you supplied Critical p̂ Proportion of successes associated with the level you supplied Two-Proportion Z-Test Menu name Z-Test: 1– 2 On the basis of statistics from two samples, each from a different population, this test measures the strength of the evidence for
Results The results are: Result Description Test Z Z-Test statistic Test p̂ Difference between the proportions of successes in the two samples that is associated with the test Z-value P Probability associated with the Z-Test statistic Critical Z Boundary value(s) of Z associated with the level that you supplied Critical p̂ Difference in the proportion of successes in the two samples associated with the level you supplied One-Sample T-Test Menu name T-Test: 1 This test is used when th
Inputs Results The inputs are: Field name Definition x Sample mean s Sample standard deviation n Sample size 0 Hypotheticalpopulation mean Significance level The results are: Result Description Test T T-Test statistic Test x Value of x associated with the test t-value P Probability associated with the T-Test statistic DF Degrees of freedom Critical T Boundary value(s) of T associated with the level that you supplied Critical x Boundary value(s) of x required by the value t
Inputs Results 252 The inputs are: Field name Definition x1 Sample 1 mean x2 Sample 2 mean s1 Sample 1 standard deviation s2 Sample 2 standard deviation n1 Sample 1 size n2 Sample 2 size Significance level Pooled Check this option to pool samples based on their standard deviations The results are: Result Description Test T T-Test statistic Test x Difference in the means associated with the test t-value P Probability associated with the T-Test statistic DF Degrees of freedom
Confidence intervals The confidence interval calculations that the HP Prime can perform are based on the Normal Z-distribution or Student’s t-distribution. One-Sample Z-Interval Menu name Z-Int: This option uses the Normal Z-distribution to calculate a confidence interval for , the true mean of a population, when the true population standard deviation, , is known.
Inputs Results The inputs are: Field name Definition x1 Sample 1 mean x2 Sample 2 mean n1 Sample 1 size n2 Sample 2 size 1 Population 1 standard deviation 2 Population 2 standard deviation C Confidence level The results are: Result Description C Confidence level Critical Z Critical values for Z Lower Lower bound for Upper Upper bound for One-Proportion Z-Interval Menu name Z-Int: 1 This option uses the Normal Z-distribution to calculate a confidence interval for the p
Results The results are: Result Description C Confidence level Critical Z Critical values for Z Lower Lower bound for Upper Upper bound for Two-Proportion Z-Interval Menu name Z-Int: 1 – 2 This option uses the Normal Z-distribution to calculate a confidence interval for the difference between the proportions of successes in two populations.
One-Sample T-Interval Menu name T-Int: 1 This option uses the Student’s t-distribution to calculate a confidence interval for , the true mean of a population, for the case in which the true population standard deviation, , is unknown.
Inputs Results Inference app The inputs are: Result Definition x1 Sample 1 mean x2 Sample 2 mean s1 Sample 1 standard deviation s2 Sample 2 standard deviation n1 Sample 1 size n2 Sample 2 size C Confidence level Pooled Whether or not to pool the samples based on their standard deviations The results are: Result Description C Confidence level DF Degrees of freedom Critical T Critical values for T Lower Lower bound for Upper Upper bound for 257
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13 Solve app The Solve app enables you to define up to ten equations or expressions each with as many variables as you like. You can solve a single equation or expression for one of its variables, based on a seed value. You can also solve a system of equations (linear or non-linear), again using seed values. Note the differences between an equation and an expression: • An equation contains an equals sign.
One equation Suppose you want to find the acceleration needed to increase the speed of a car from 16.67 m/s (60 kph) to 27.78 m/s (100 kph) over a distance of 100 m. The equation to solve is: V 2 = U 2 +2AD. where V = final speed, U = initial speed, A = acceleration needed, and D = distance. Open the Solve app 1. Open the Solve app. I Select Solve The Solve app starts in Symbolic view, where you specify the equation to solve.
Enter known variables 4. Display the Numeric view. M Here you specify the values of the known variables, highlight the variable that you want to solve for, and tap . 5. Enter the values for the known variables. 2 7.7 8E1 6 .6 7E\1 0 0 E Note Some variables may already have values against them when you display the Numeric view. This occurs if the variables have been assigned values elsewhere. For example, in Home view you might have assigned 10 to variable U: 10 U.
Plot the equation The Plot view shows one graph for each side of the solved equation. You can choose any of the variables to be the independent variable by selecting it in Numeric view. So in this example make sure that A is highlighted. The current equation is V 2 = U 2 +2AD. The plot view will plot two equations, one for each side of the equation. One of these is Y = V 2, with V = 27.78, making Y = 771.7284. This graph will be a horizontal line. The other graph will be Y = U 2 +2AD with U =16.
Note By dragging a finger horizontally or vertically across the screen, you can quickly see parts of the plot that are initially outside the x and y ranges you set. Several equations You can define up to ten equations and expressions in Symbolic view and select those you want to solve together as a system. For example, suppose you want to solve the system of equations consisting of: Open the Solve app • X 2 + Y 2 = 16 and • X – Y = –1 1. Open the Solve app. I Select Solve 2.
variables, or let the calculator provide a solution. (Typically a seed value is a value that directs the calculator to provide, if possible, a solution that is closest to it rather than some other value.) In this example, let’s look for a solution in the vicinity of X = 2. 5. Enter the seed value in the X field: 2 The calculator will provide one solution (if there is one) and you will not be alerted if there are multiple solutions. Vary the seed values to find other potential solutions. 6.
Solution information When you are solving a single equation, the button appears on the menu after you tap . Tapping displays a message giving you some information about the solutions found (if any). Tap to clear the message. Message Meaning Zero The Solve app found a point where both sides of the equation were equal, or where the expression was zero (a root), within the calculator's 12-digit accuracy.
266 Message Meaning (Continued) Cannot find solution No values satisfy the selected equation or expression. Bad Guess(es) The initial guess lies outside the domain of the equation. Therefore, the solution was not a real number or it caused an error. Constant? The value of the equation is the same at every point sampled.
14 Linear Solver app The Linear Solver app enables you to solve a set of linear equations. The set can contain two or three linear equations. In a two-equation set, each equation must be in the form ax + by = k . In a three-equation set, each equation must be in the form ax + by + cz = k . You provide values for a, b, and k (and c in three-equation sets) for each equation, and the app will attempt to solve for x and y (and z in three-equation sets).
Note If the last time you used the Linear Solver app you solved for two equations, the two-equation input form is displayed. To solve a three-equation set, tap ; now the input form displays three equations. Define and solve the equations 2. You define the equations you want to solve by entering the coefficients of each variable in each equation and the constant term. Notice that the cursor is positioned immediately to the left of x in the first equation, ready for you to insert the coefficient of x (6).
Solve a two-bytwo system Note If the three-equation input form is displayed and you want to solve a twoequation set, tap . You can enter any expression that resolves to a numerical result, including variables. Just enter the name of a variable. For more information on assigning values to variables, see “Storing a value in a variable” on page 42. Menu items The menu items are: Linear Solver app • : moves the cursor to the entry line where you can add or change a value.
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15 Parametric app The Parametric app enables you to explore parametric equations. These are equations in which both x and y are defined as functions of t. They take the forms x = f t and y = gt . Getting started with the Parametric app The Parametric app uses the customary app views: Symbolic, Plot and Numeric described in chapter 5.
The graphical and numerical data you see in Plot view and Numeric view are derived from the symbolic functions defined here. Define the functions There are 20 fields for defining functions. These are labelled X1(T) through X9(T) and X0(T), and Y1(T) through Y9(T) and Y0(T). Each X function is paired with a Y function. 2. Highlight which pair of functions you want to use, either by tapping on, or scrolling to, one of the pair. If you are entering a new function, just start typing.
Set the angle measure Set the angle measure to degrees: 5. SY (Settings) 6. Tap the Angle Measure field and select Degrees. You could also have set the angle measure on the Home Settings screen. However, Home settings are system-wide. By setting the angle measure in an app rather than Home view, you are limiting the setting just to that app. Set up the plot 7. Open the Plot Setup view: SP (Setup) 8. Set up the plot by specifying appropriate graphing options.
Explore the graph The menu button gives you access to common tools for exploring plots: : displays a range of zoom options. (The + and w keys can also be used to zoom in and out.) : when active, enables a tracing cursor to be moved along the contour of the plot (with the coordinates of the cursor displayed at the bottom of the screen). : specify a T value and the cursor moves to the corresponding x and y coordinates. : display the functions responsible for the plot.
Display the numeric view 15. Display the Numeric view: M 16. With the cursor in the T column, type a new value and tap .The table scrolls to the value you entered. You can also zoom in or out on the independent variable (thereby decreasing or increasing the increment between consecutive values). This and other options are explained in “Common operations in Numeric view” on page 100. You can see the Plot and Numeric views side by side. See “Combining Plot and Numeric Views” on page 106.
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16 Polar app The Polar app enables you to explore polar equations. Polar equations are equations in which r—the distance a point is from the origin: (0,0)—is defined in terms of , the angle a segment from the point to the origin makes with the polar axis. Such equations take the form r = f . Getting started with the Polar app The Polar app uses the six standard app views described in chapter 5, “An introduction to HP apps”, beginning on page 69.
3. Define the expression 5cos(/2)cos()2. 5Szf dn2>> fd>j E Notice how the d key enters whatever variable is relevant to the current app. In this app the relevant variable is . 4. If you wish, choose a color for the plot other than its default. You do this by selecting the colored square to the left of the function set, tapping , and selecting a color from the color-picker.
8. Set up the plot by specifying appropriate graphing options. In this example, set the upper limit of the range of the independent variable to 4: Select the 2nd Rng field and enter 4Sz ( There are numerous ways of configuring the appearance of Plot view. For more information, see “Common operations in Plot Setup view” on page 96. Plot the expression 9. Plot the expression: Explore the graph 10. Display the Plot view menu.
If only one polar equation is plotted, you can see the equation that generated the plot by tapping . If there are several equations plotted, move the tracing cursor to the plot you are interested—by . pressing = or \—and then tap For more information on exploring plots in Plot view, see “Common operations in Plot view” on page 88. Display the Numeric view 11. Open the Numeric view: M The Numeric view displays a table of values for and R1.
17 Sequence app The Sequence app provides you with various ways to explore sequences. You can define a sequence named, for example, U1: • in terms of n • in terms of U1(n –1) • in terms of U1(n –2) • in terms of another sequence, for example, U2(n) or • in any combination of the above. You can define a sequence by specifying just the first term and the rule for generating all subsequent terms. However, you will have to enter the second term if the HP Prime is unable to calculate it automatically.
Open the Sequence app 1. Open the Sequence app: I Select Sequence The app opens in Symbolic view. Define the expression 2. Define the Fibonacci sequence: U 1 = 1 , U 2 = 1 , U n = U n – 1 + U n – 2 for n 2 .
6. Select Stairstep from the Seq Plot menu. 7. Set the X Rng maximum, and the Y Rng maximum, to 8 (as shown at the right). Plot the sequence 8. Plot the Fibonacci sequence: P 9. Return to Plot Setup view (SP) and select Cobweb, from the Seq Plot menu. 10.
Display Numeric view 11. Display Numeric view: M 12. With the cursor anywhere in the N column, type a new value and tap . The table of values scrolls to the value you entered. You can then see the corresponding value in the sequence. The example at the right shows that the 25th value in the Fibonacci sequence is 75,025.
Set up the table of values The Numeric Setup view provides options common to most of the graphing apps, although there is no zoom factor as the domain for the sequences is the set of counting numbers. See “Common operations in Numeric Setup view” on page 105 for more information. Another example: Explicitly-defined sequences In the following example, we define the nth term of a sequence simply in terms of n itself. In this case, there is no need to enter either of the first two terms numerically.
Plot the sequence 6. Plot the sequence: P Press E to see the dotted lines in the figure to the right. Press it again to hide the dotted lines. Explore the table of sequence values 286 7. View the table: M 8. Tap and select 1 to see the sequence values.
18 Finance app The Finance app enables you to solve time-value-of-money (TVM) and amortization problems. You can use the app to do compound interest calculations and to create amortization tables. Compound interest is accumulative interest, that is, interest on interest already earned. The interest earned on a given principal is added to the principal at specified compounding periods, and then the combined amount earns interest at a certain rate.
3. In the I%/YR field, type 5.5—the interest rate—and press E. 4. In PV field, type 19500 w 3000 and press E. This is the present value of the loan, being the purchase price less the deposit. 5. Leave P/YR and C/YR both at 12 (their default values). Leave End as the payment option. Also, leave future value, FV, as 0 (as your goal is to end up with a future value of the loan of 0). 6. Move the cursor to the PMT field and tap . The PMT value is calculated as –315.17.
The PV value is calculated as 15,705.85, this being the maximum you can borrow. Thus, with your $3,000 deposit, you can afford a car with a price tag of up to $18,705.85. Cash flow diagrams TVM transactions can be represented in cash flow diagrams. A cash flow diagram is a time line divided into equal segments representing the compounding periods. Arrows represent the cash flows. These could be positive (upward arrows) or negative (downward arrows), depending on the point of view of the lender or borrower.
The following cash flow diagram shows a loan from the lender's point of view: Cash flow diagrams also specify when payments occur relative to the compounding periods.The diagram to the right shows lease payments at the beginning of the period. This diagram shows deposits (PMT) into an account at the end of each period. Time value of money (TVM) Time-value-of-money (TVM) calculations make use of the notion that a dollar today will be worth more than a dollar sometime in the future.
There are seven TVM variables: Variable Description N The total number of compounding periods or payments. I%YR The nominal annual interest rate (or investment rate). This rate is divided by the number of payments per year (P/YR) to compute the nominal interest rate per compounding period. This is the interest rate actually used in TVM calculations. PV The present value of the initial cash flow. To a lender or borrower, PV is the amount of the loan; to an investor, PV is the initial investment.
payment. Find the size of the balloon payment—that is, the value of the mortgage after 10 years of payment. The following cash flow diagram illustrates the case of a mortgage with balloon payment: 1. Start the Finance app: I Select Finance 2. Return all fields to their default values: SJ 3. Enter the known TVM variables, as shown in the figure. 4. Highlight PMT and tap . The PMT field shows –984.10. In other words, the monthly payments are $948.10. 5.
Calculating amortizations Amortization calculations determine the amounts applied towards the principal and interest in a payment, or series of payments. They also use TVM variables. To calculate amortizations: 1. Start the Finance app. 2. Specify the number of payments per year (P/YR). 3. Specify whether payments are made at the beginning or end of periods. 4. Enter values for I%YR, PV, PMT, and FV. 5. Enter the number of payments per amortization period in the Group Size field.
2. Tap . 3. Scroll down the table to payment group 10. Note that after 10 years, $22,835.53 has been paid off the principal and $90,936.47 paid in interest, leaving a balloon payment due of $127,164.47. Amortization graph Press P to see the amortization schedule presented graphically. The balance owing at the end of each payment group is indicated by the height of a bar.
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19 Triangle Solver app The Triangle Solver app enables you to calculate the length of a side of a triangle, or the size of an angle in a triangle, from information you supply about the other lengths, angles, or both. You need to specify at least three of the six possible values—the lengths of the three sides and the size of the three angles—before the app can calculate the other values. Moreover, at least one value you specify must be a length.
2. If there is unwanted data from a previous calculation, you can clear it all by pressing SJ (Clear). Set angle measure Make sure that your angle measure mode is appropriate. By default, the app starts in degree mode. If the angle information you have is in radians and your current angle measure mode is degrees, change the mode to degrees before running the solver. Tap or depending on the mode you want. (The button is a toggle button.
Solve for the unknown values 4. Tap . The app displays the values of the unknown variables. As the illustration at the right shows, the length of the unknown side in our example is 3.22967… The other two angles have also been calculated. Choosing triangle types The Triangle Solver app has two input forms: a general input form and a simpler, specialized form for right-angled triangles.
Special cases The indeterminate case If two sides and an adjacent acute angle are entered and there are two solutions, only one will be displayed initially. In this case, the button is displayed (as in this example). You can tap to display the second solution and tap again to return to the first solution.
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20 The Explorer apps There are three explorer apps. These are designed for you to explore the relationships between the parameters of a function and the shape of the graph of that function. The explorer apps are: • Linear Explorer For exploring linear functions • Quadratic Explorer For exploring quadratic functions • Trig Explorer For exploring sinusoidal functions There are two modes of exploration: graph mode and equation mode.
form of the equation being explored at the top and, below it, the current equation of that form. The keys you can use to manipulate the graph or equation appear below the equation. The x- and y-intercepts are given at the bottom. There are two types (or levels) of linear equation available for you to explore: y = ax and y = ax + b. You choose between them by tapping or . The keys available to you to manipulate the graph or equation depend on the level you have chosen.
Equation mode Tap to enter equation mode. A dot will appear on the Eq button at the bottom of the screen. In equation mode, you use the cursor keys to move between parameters in the equation and change their values, observing the effect on the graph displayed. Press \ or = to decrease or increase the value of the selected parameter. Press > or < to select another parameter. PressQ to change the sign of a. Test mode Tap to enter test mode.
Quadratic Explorer app The Quadratic Explorer app can be used to investigate the behavior of y = a x + h 2 + v as the values of a, h and v change. Open the app PressI and select Quadratic Explorer. The left half of the display shows the graph of a quadratic function. The right half shows the general form of the equation being explored at the top and, below it, the current equation of that form. The keys you can use to manipulate the graph or equation appear below the equation.
Choose a general form by tapping the Level button— , and so on—until the form you want is displayed. The keys available to you to manipulate the graph vary from level to level. Equation mode Tap to move to equation mode. In equation mode, you use the cursor keys to move between parameters in the equation and change their values, observing the effect on the graph displayed. Press \ or = to decrease or increase the value of the selected parameter. Press > or < to select another parameter.
Trig Explorer app The Trig Explorer app can be used to investigate the behavior of the graphs y = a sin bx + c + d and y = a cos bx + c + d as the values of a, b, c and d change. The menu items available in this app are: • or : toggles between graph mode and equation mode or • : toggles between sine and cosine graphs • or : toggles between radians and degrees as the angle measure for x • or : toggles between translating the graph ( ), and changing its frequency or amplitude ( ).
Graph mode The app opens in graph mode. In graph mode, you manipulate a copy of the graph by pressing the cursor keys. All four keys are available. The original graph—converted to dotted lines—remains in place for you to easily see the result of your manipulations. When is chosen, the cursor keys simply translate the graph horizontally and vertically.
Test mode Tap to enter test mode. In test mode you test your skill at matching an equation to the graph shown. Test mode is like equation mode in that you use the cursor keys to select and change the value of one or more parameters in the equation. The goal is to try to match the graph that is shown. The app displays the graph of a randomly chosen sinusoidal function. Tap a Level button— , and so on—to choose between one of five types of sinusoidal equations.
21 Functions and commands Many mathematical functions are available from the calculator’s keyboard. These are described in “Keyboard functions” on page 309. Other functions and commands are collected together in the Toolbox menus (D).
– used in programming – used in the Matrix Editor – used in the List Editor – and some additional functions and commands See “Ctlg menu” on page 378. Although the Catlg menu includes all the programming commands, the Commands menu ( ) in the Program Editor contains all the programming commands grouped by category. It also contains the Template menu ( ), which contains the common programming structures.
Abbreviations used in this chapter In describing the syntax of functions and commands, the following abbreviations and conventions are used: Eqn: an equation Expr: a mathematical expression Fnc: a function Frac: a fraction Intgr: an integer Obj: signifies that objects of more than one type are allowable here Poly: a polynomial RatFrac: a rational fraction Val: a real value Var: a variable Parameters that are optional are given in square brackets, as in NORMAL_ICDF([,,]p).
The examples below show the results you would get in Home view. If you are in the CAS, the results are given in simplified symbolic format. For example: Sj 320 returns 17.88854382 in Home view, and 8*√5 in the CAS. +,w,s, n Add, subtract, multiply, divide. Also accepts complex numbers, lists, and matrices. value1 + value2, etc. h Natural logarithm. Also accepts complex numbers. LN(value) Example: LN(1) returns 0 Sh (ex) Natural exponential. Also accepts complex numbers.
efg Sine, cosine, tangent. Inputs and outputs depend on the current angle format: degrees or radians. SIN(value) COS(value) TAN(value) Example: TAN(45) returns 1 (degrees mode) Se(ASIN) Arc sine: sin–1x. Output range is from –90° to 90° or –/2 to /2. Inputs and outputs depend on the current angle format. Also accepts complex numbers. ASIN(value) Example: ASIN(1) returns 90 (degrees mode) Sf(ACOS) Arc cosine: cos–1x. Output range is from 0° to 180° or 0 to .
Sj Square root. Also accepts complex numbers. )√value Example: √320 returns 17.88854382 k x raised to the power of y. Also accepts complex numbers. value power Example: 2 8 returns 256 Sk The nth root of x. root√value Example: 3√8 returns 2 Sn Reciprocal. value -1 Example: 3 -1 returns .333333333333 Q- Negation. Also accepts complex numbers. -value Example: -(1+2*i) returns -1-2*i SQ(|x|) Absolute value. |value| |x+y*i| |matrix| For a complex number, |x+y*i| returns x2 + y2 .
Math menu Press D to open the Toolbox menus (one of which is the Math menu). The functions and commands available on the Math menu are listed as they are categorized on the menu. Numbers Ceiling Smallest integer greater than or equal to value. CEILING(value) Examples: CEILING(3.2) returns 4 CEILING(-3.2) returns -3 Floor Greatest integer less than or equal to value. FLOOR(value) Example: FLOOR(3.2) returns 3 FLOOR(-3.2) returns -4 IP Integer part. IP(value) Example: IP(23.
ROUND can also round to a number of significant digits if places is a negative integer (as shown in the second example below). Examples: ROUND(7.8676,2) returns 7.87 ROUND(0.0036757,-3) returns 0.00368 Truncate Truncates value to decimal places. Also accepts complex numbers. TRUNCATE(value,places) TRUNCATE can also round to a number of significant digits if places is a negative integer (as shown in the second example below). Examples: TRUNCATE(2.3678,2) returns 2.36 TRUNCATE(0.0036757,–3) returns 0.
press K. This opens the computer algebra system. If you want to return to Home view to make further calculations, press H. Minimum Minimum. The lesser of two values. MIN(value1,value2) Example: MIN(210,25) returns 25 Modulus Modulo. The remainder of value1/value2. value1 MOD value2 Example: 74 MOD 5 returns 4 Find Root Function root-finder (like the Solve app). Finds the value for the given variable at which expression most nearly evaluates to zero. Uses guess as initial estimate.
Real Part Real part x, of a complex number, (x+y*i). RE(x+y*i) Example: RE(3+4*i) returns 3 Imaginary Part Imaginary part, y, of a complex number, (x+y*i). IM(x+y*i) Example: IM(3+4*i) returns 4 Unit Vector Sign of value. If positive, the result is 1. If negative, –1. If zero, result is zero. For a complex number, this is the unit vector in the direction of the number. SIGN(value) SIGN((x,y)) Examples: SIGN(POLYEVAL([1,2,–25,–26,2],–2)) returns –1 SIGN((3,4)) returns (.6+.
SEC Secant: 1/cosx. SEC(value) ASEC Arc secant. ASEC(value) COT Cotangent: cosx/sinx. COT(value) ACOT Arc cotangent. ACOT(value) Hyperbolic The hyperbolic trigonometry functions can also take complex numbers as arguments. SINH Hyperbolic sine. SINH(value) ASINH Inverse hyperbolic sine: sinh–1x. ASINH(value) COSH Hyperbolic cosine COSH(value) ACOSH Inverse hyperbolic cosine: cosh–1x. ACOSH(value) TANH Hyperbolic tangent. TANH(value) ATANH Inverse hyperbolic tangent: tanh–1x.
Combination The number of combinations (without regard to order) of n things taken r at a time. COMB(n,r) Example: Suppose you want to know how many ways five things can be combined two at a time. COMB(5,2)returns 10. Permutation Number of permutations (with regard to order) of n things taken r at a time: n!/(n–r)!. PERM (n,r) Example: Suppose you want to know how many permutations there are for five things taken two at a time. PERM(5,2)returns 20. Random Number Random number.
Seed Sets the seed value on which the random functions operate. By specifying the same seed value on two or more calculators, you ensure that the same random numbers appear on each calculator when the random functions are executed. RANDSEED(value) Density Normal Normal probability density function. Computes the probability density at value x, given the mean, and standard deviation, of a normal distribution. If only one argument is supplied, it is taken as x, and the assumption is that =0 and =1.
Binomial Binomial probability density function. Computes the probability of k successes out of n trials, each with a probability of success of p. Returns Comb(n,k) if there is no third argument. Note that n and k are integers with k n . BINOMIAL(n,k,p) Example: Suppose you want to know the probability that just 6 heads would appear during 20 tosses of a fair coin. BINOMIAL(20,6,0.5) returns 0.0369644165039. Poisson Poisson probability mass function.
2 Cumulative 2 distribution function. Returns the lower-tail probability of the 2 probability density function for the value x, given n degrees of freedom. CHISQUARE_CDF(n,k) Example: CHISQUARE_CDF(2,6.1) returns 0.952641075609. F Cumulative Fisher distribution function. Returns the lower-tail probability of the Fisher probability density function for the value x, given numerator n and denominator d degrees of freedom. FISHER_CDF(n,d,x) Example: FISHER_CDF(5,5,2) returns 0.76748868087.
T Inverse cumulative Student's t distribution function. Returns the value x such that the Student's-t lower-tail probability of x, with n degrees of freedom, is p. STUDENT_ICDF(n,p) Example: STUDENT_ICDF(3,0.0246659214814) returns –3.2. 2 Inverse cumulative 2 distribution function. Returns the value x such that the 2 lower-tail probability of x, with n degrees of freedom, is p. CHISQUARE_ICDF(n,p) Example: CHISQUARE_ICDF(2,0.957147873133) returns 6.3.
Matrix These functions work on matrix data stored in matrix variables. They are explained in detail in chapter 25, “Matrices”, beginning on page 463. Special Beta Returns the value of the beta function ( for two numbers a and b. Beta(a,b) Gamma Returns the value of the gamma function ( for a number a. Gamma(a) Psi Returns the value of the nth derivative of the digamma function at x=a, where the digamma function is the first derivative of ln((x)).
CAS menu Press D to open the Toolbox menus (one of which is the CAS menu). The functions on the CAS menu are those most commonly used. Many more functions are available. See “Ctlg menu”, beginning on page 378. Note that the Geometry functions appear on the App menu. They are described in “Geometry functions and commands”, beginning on page 165. The result of a CAS command may vary depending on the CAS settings. The examples in this chapter assume the default CAS settings unless otherwise noted.
Substitute Substitutes a value for a variable in an expression. Syntax: subst(Expr,Var=value) Example: subst(x/(4-x^2),x=3) returns -3/5 Partial Fraction Performs partial fraction decomposition on a fraction. partfrac(RatFrac or Opt) Example: partfrac(x/(4-x^2)) returns (-1/2)/(x-2)-(1/2)/ ((x+2) Extract Numerator Simplified Numerator. For the integers a and b, returns the numerator of the fraction a/b after simplification.
Calculus Differentiate With one expression as argument, returns derivative of the expression with respect to x. With one expression and one variable as arguments, returns the derivative or partial derivative of the expression with respect to the variable. With one expression and more than one variable as arguments, returns the derivative of the expression with respect to the variables in the second argument.
Series Returns the series expansion of an expression in the vicinity of a given equality variable. With the optional third and fourth arguments you can specify the order and direction of the series expansion. If no order is specified the series returned is fifth order. If no direction is specified, the series is bidirectional.
Gradient Returns the gradient of an expression. With a list of variables as second argument, returns the vector of partial derivatives. grad(Expr,LstVar) Example: grad(2*x^2*y-x*z^3,[x,y,z]) gives [2*2*x*yz^3,2*x^2,-x*3*z^2] Hessian Returns the Hessian matrix of an expression.
F(b)–F(a) Returns F(b)–F(a). preval(Expr(F(var)),Real(a),Real(b),[Var]) Example: preval(x^2-2,2,3) gives 5 Limits Riemann Sum Returns in the neighborhood of n=+∞ an equivalent of the sum of Xpr(var1,var2) for var2 from var2=1 to var2=var1 when the sum is looked at as a Riemann sum associated with a continuous function defined on [0,1].
Inverse Laplace Returns the inverse Laplace transform of an expression. invlaplace(Expr,[Var],[IlapVar]) Example: ilaplace(1/(x^2+1)^2) returns ((-x)*cos(x))/ 2+sin(x)/2 FFT With one argument (a vector), returns the discrete Fourier transform in R. fft(Vect) With two additional integer arguments a and p, returns the discrete Fourier transform in the field Z/pZ, with a as primitive nth root of 1 (n=size(vector)). fft((Vector, a, p) Example: fft([1,2,3,4,0,0,0,0]) gives [10.0,0.414213562373-7.
Zeros With an expression as argument, returns the real zeros of the expression; that is, the solutions when the expression is set equal to zero. With a list of expressions as argument, returns the matrix where the rows are the real solutions of the system formed by setting each expression equal to zero.
Differential Equation Returns the solution to a differential equation. deSolve(Eq,[TimeVar],Var) Example: desolve(y''+y=0,y) returns G_0*cos(x)+G_1*sin(x) ODE Solve Ordinary Differential Equation solver. Solves an ordinary differential equation given by Expr, with variables declared in VectrVar and initial conditions for those variables declared in VectrInit.
texpand Expands a transcendental expression. texpand(Expr) Example: texpand(sin(2*x)+exp(x+y)) returns exp(x)*exp(y)+ 2*cos(x)*sin(x)) Exp & Ln ey*lnx → xy Returns an expression of the form en*ln(x) rewritten as a power of x. Applies en*ln(x)=xn. exp2pow(Expr) Example: exp2pow(exp(3*ln(x))) gives x^3 xy → ey*lnx Returns an expression with powers rewritten as an exponential. Essentially the inverse of exp2pow.
asinx → atanx Returns an expression with asin(x) rewritten as: x atan -------------------2- 1–x asin2atan(Expr) Example: asin2atan(2*asin(x)) returns x 2 atan -------------------2- 1–x sinx → cosx*tanx Returns an expression with sin(x) rewritten as cos(x)*tan(x). sin2costan(Expr) Example: sin2costan(sin(x)) gives tan(x)*cos(x) Cosine acosx → asinx Returns an expression with acos(x) rewritten as /2–asin(x).
Tangent atanx → asinx Returns an expression with atan(x) rewritten as: x asin -------------------2- 1–x atan2asin(Expr) Example: atan2asin(atan(2*x)) returns 2x asin --------------------------------2- 1 – 2 x atanx → acosx Returns an expression with atan(x) rewritten as: x --- – acos -------------------2- 2 1+x atan2acos(Expr) tanx → sinx/cosx Returns an expression with tan(x) rewritten as sin(x)/cos(x).
trigx → cosx Returns an expression simplified using the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x). Cos(x) is given precedence over sin(x) and tan(x) in the result. trigcos(Expr) Example: trigcos(sin(x)^4+sin(x)^2) returns cos(x)^43*cos(x)^2+2 trigx → tanx Returns an expression simplified using the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x). Tan(x) is given precedence over sin(x) and cos(x) in the result.
trigexpand Returns a trigonometric expression in expanded form. trigexpand(Expr) Example: trigexpand(sin(3*x)) gives (4*cos(x)^21)*sin(x) trig2exp Returns an expression with trigonometric functions rewritten as complex exponentials (without linearization). trig2exp(Expr) Example: trig2exp(sin(x)) returns –----i 1 exp i x – ------------------------ 2 exp i x Integer Divisors Returns the list of divisors of an integer or a list of integers.
GCD Returns the greatest common divisor of two or more integers. gcd(Intgr1, Intgr2,…) Example: gcd(32,120,636) returns 4 LCM Returns the lowest common multiple of two or integers. lcm(Intgr1, Intgr2,…) Example: lcm(6,4) returns 12 Prime Test if Prime Tests whether or not a given integer is a prime number. isPrime(Integer) Example: isPrime(19999) returns false Nth Prime Returns the nth prime number.
Division Quotient Returns the integer quotient of the Euclidean division of two integers. iquo(Intgr1, Intgr2) Example: iquo(63, 23) returns 2 Remainder Returns the integer remainder from the Euclidean division of two integers. irem(Intgr1, Intgr2) Example: irem(63, 23) returns 17 an MOD p For the three integers a, n, and p, returns an modulo p in [0, p−1]. powmod(a, n, p,[Expr],[Var]) Example: powmod(5,2,13) returns 12 Chinese Remainder Integer Chinese Remainder Theorem for two equations.
Coefficients Given a polynomial in x, returns a vector containing the coefficients. If the polynomial is in a variable other than x, then declare the variable as the second argument. With an integer as the optional third argument, returns the coefficient of the polynomial whose degree matches the integer. coeff(Poly, [Var], [Integer]) Examples: coeff(x^2-2) returns [1 0 -2] coeff(y^2-2, y, 1) returns 0 Divisors Given a polynomial, returns a vector containing the divisors of the polynomial.
Create Poly to Coef Given a polynomial, returns a vector containing the coefficients of the polynomial. With a variable as second argument, returns the coefficients of a polynomial with respect to the variable. With a list of variables as the second argument, returns the internal format of the polynomial. symb2poly(Expr,[Var]) or symb2poly(Expr, {Var1, Var2,…}) Example: symb2poly(x*3+2.1) returns [3 Coef to Poly 2.
Random Returns a vector of the coefficients of a polynomial of degree Integer and where the coefficients are random integers in the range –99 through 99 with uniform distribution or in an interval specified by Interval. Use with poly2symbol to create a random polynomial in any variable. randpoly(Integer, Interval, [Dist]), where Interval is of the form Real1..Real2. Example: randpoly(t, 8, -1..1) returns a vector of 9 random integers, all of them between –1 and 1.
Degree Returns the degree of a polynomial. degree(Poly) Example: degree(x^3+x) gives 3 Factor by Degree For a given polynomial in x of degree n, factors out xn and returns the resulting product. factor_xn(Poly) Example: factor_xn(x^4-1) gives x^4*(1-x^-4) Coef. GCD Returns the greatest common divisor (GCD) of the coefficients of a polynomial.
Special Cyclotomic Returns the list of coefficients of the cyclotomic polynomial of an integer. cyclotomic(Integer) Example: cyclotomic(20) gives [1 0 –1 0 1 0 –1 0 1] Groebner Basis Given a vector of polynomials and a vector of variables, returns the Groebner basis of the ideal spanned by the set of polynomials.
Lagrange Given a vector of abscissas and a vector of ordinates, returns the Lagrange polynomial for the points specified in the two vectors. This function can also take a matrix as argument, with the first row containing the abscissas and the second row containing the ordinates. lagrange([X1 X2…], [Y1 Y2…])) or X1 X2 ... Y1 Y2 ... lagrange Example: lagrange([1,3],[0,1]) gives (x-1)/2 Laguerre Given an integer n, returns the Laguerre polynomial of degree n.
Plot Function Used to define a function graph in the Symbolic view of the Geometry app. Plots the graph of an expression written in terms of the independent variable x. Note that the variable is lowercase. plotfunc(Expr) Example: plotfunc(3*sin(x)) draws the graph of y=3*sin(x) Implicit Used to define an implicit graph in the Symbolic view of the Geometry app. Plots the graph of an equation written in terms of the independent variable x and the dependent variable y. Note that the variables are lowercase.
ODE Used in the Symbolic view of the Geometry app. Draws the solution of the differential equation y’=f(x,y) that contains as initial condition the point (x0, y0). The first argument is the expression f(x,y), the second argument is the vector of variables (abscissa must be listed first), and the third argument is the initial condition {x0, y0}.
Function app functions The Function app functions provide the same functionality found in the Function app's Plot view under the FCN menu. All these operations work on functions. The functions may be expressions in X or the names of the Function app variables F0 through F9. AREA Area under a curve or between curves. Finds the signed area under a function or between two functions. Finds the area under the function Fn or below Fn and above the function Fm, from lower X-value to upper X-value.
Solve app functions The Solve app has a single function that solves a given equation or expression for one of its variables. En may be an equation or expression, or it may be the name of one of the Solve Symbolic variables E0–E9. SOLVE Solve. Solves an equation for one of its variables. Solves the equation En for the variable var, using the value of guess as the initial value for the value of the variable var.
The syntax for many, but not all, the spreadsheet functions follows this pattern: functionName(input,[optional parameters]) Input is the input list for the function. This can be a cell range reference, a simple list or anything that results in a list of values. One useful optional parameter is Configuration. This is a string that controls which values are output. Leaving the parameter out produces the default output. The order of the values can also be controlled by the order that they appear in the string.
AVERAGE Calculates the arithmetic mean of a range of numbers. AVERAGE([input]) For example, AVERAGE(B7:B23) returns the arithmetic mean of the numbers in the range B7 to B23. You can also specify a block of cells, as in AVERAG(B7:C23). An error is returned if a cell in the specified range contains a non-numeric object. AMORT Amortization. Calculates the principal, interest, and balance of a loan over a specified period. Corresponds to pressing in the Finance app.
STAT1 The STAT1 function provides a range of one-variable statistics. It can calculate all or any of x , Σ, Σ², s, s², σ, σ², serr, 2 xi – x , n, min, q1, med, q3, and max. STAT1(Input range, [mode], [outlier removal Factor], ["configuration"]) Input range is the data source (such as A1:D8). Mode defines how to treat the input. The valid values are: 1 = Single data. Each column is treated as an independent dataset. 2 = Frequency data.
For example if you specify "h n Σ x", the first column will contain row headers, the first row will be the number of items in the input data, the second the sum of the items and the third the mean of the data. If you do not specify a configuration string, a default string will be used. Notes: The STAT1 f function only updates the content of the destination cells when the cell that contains the formula is calculated.
7 y= L/(1 + a*exp(b*x)) 8 y= a*sin(b*x+c)+d 9 y= cx^2+bx+a 10 y= dx^3+cx^2+bx+a 11 y= ex^4+dx^3+cx^2+bx+a • Configuration: a string which indicates which values you want to place in which row and if you want row and columns headers. Place each parameter in the order that you want to see them appear in the spreadsheet. (If you do not provide a configuration string, a default one will be provided.
PredY Returns the predicted Y for a given x. PredY(mode, x, parameters) • Mode governs the regression model used: 1 y= sl*x+int 2 y= sl*ln(x)+int 3 y= int*exp(sl*x) 4 y= int*x^sl 5 y= int*sl^x 6 y= sl/x+int 7 y= L/(1 + a*exp(b*x)) 8 y= a*sin(b*x+c)+d 9 y= cx^2+bx+a 10 y= dx^3+cx^2+bx+a 11 y= ex^4+dx^3+cx^2+bx+a • PredX Parameters is either one argument (a list of the coefficients of the regression line), or the n coefficients one after another. Returns the predicted x for a given y.
HypZ1mean The one-sample Z-test for a mean. HypZ1mean( x , n,0,,,mode, [”configuration”]) The input parameters can be a range reference, a list of cell references, or a simple list of values. Mode: Specifies which alternative hypothesis to use: • 1: < 0 • 2: > 0 • 3: ≠ 0 Configuration: a string that controls what results are shown and the order in which they appear. An empty string "" displays the default: all results, including headers.
Mode: Specifies which alternative hypothesis to use: • 1: 1 < 2 • 2: 1 > 2 • 3: 1 ≠ 2 • Configuration: a string that controls what results are shown and the order in which they appear. An empty string "" displays the default: all results, including headers. The options in the configuration string are separated by spaces.
• Configuration: a string that controls what results are shown and the order in which they appear. An empty string "" displays the default: all results, including headers. The options in the configuration string are separated by spaces.
• prob: the lower-tail probability • cZ: The critical Z-value associated with the input α-level • cp1: The lower critical value of associated with the critical Z-value • cp2: The upper critical value of associated with the critical Z-value Example: HypZ2prop(21, 26, 50, 50, 0.05, 1, "") HypT1mean The one-sample t-test for a mean.
HypT2mean The two-sample T-test for the difference of two means. HypT2mean((x1,x2,s1,s2n1,n2,pooled,mode, [”configuration”]) Pooled: Specifies whether or not the samples are pooled • 0: not pooled • 1: pooled Mode: Specifies which alternative hypothesis to use: • 1: 1 < 2 • 2: 1 > 2 • 3: 1 ≠ 2 Configuration: a string that controls what results are shown and the order in which they appear. An empty string "" displays the default: all results, including headers.
• h: header cells will be created • Z: the critical Z-value • zXl: the lower bound of the confidence interval • zXh: the upper bound of the confidence interval • std: the standard deviation Example: ConfZ1mean(0.461368, 50, 0.2887, 0.95, "") ConfZ2mean The two-sample Normal confidence interval for the difference of two means. ConfZ2mean( x 1 , x 2 , n1, n2,s1,s2,C, [”configuration”]) Configuration: a string that controls what results are shown and the order in which they appear.
• zXh: the upper bound of the confidence interval • zXm: the midpoint of the confidence interval • std: the standard deviation Example: ConfZ1prop(21, 50, 0.95, "") ConfZ2prop The two-sample Normal confidence interval for the difference of two proportions. ConfZ2prop(x1,x2,n1,n2,C,[”configuration”]) Configuration: a string that controls what results are shown and the order in which they appear. An empty string "" displays the default: all results, including headers.
Example: ConfT1mean(0.461368, 0.2776, 50, 0.95, "") ConfT2mean The two-sample Student’s T confidence interval for the difference of two means. ConfT2mean( x 1 , x 2 , s1,s2,n1, n2,C,pooled, [”configuration”]) Configuration: a string that controls what results are shown and the order in which they appear. An empty string "" displays the default: all results, including headers. The options in the configuration string are separated by spaces.
Do1VStats Do1-variable statistics. Performs the same calculations as tapping in the Numeric view of the Statistics 1Var app and stores the results in the appropriate Statistics 1Var app results variables. Hn must be one of the Statistics 1Var app Symbolic view variables H1-H5. Do1VStats(Hn) Example: Do1VStats(H1) executes summary statistics for the currently defined H1 analysis. SetFreq Set frequency.
Statistics 2Var app functions The Statistics 2Var app has a number of functions. Some are designed to calculate summary statistics based on one of the statistical analyses (S1-S5) defined in the Symbolic view of the Statistics 2Var app. Others predict X- and Y-values based on the fit specified in one of the analyses. PredX Predict X. Uses the fit from the first active analysis (S1-S5) found to predict an x-value given the y-value. PredX(value) PredY Predict Y.
SetIndep Set independent column. Sets the independent column for one of the statistical analyses S1-S5 to one of the column variables C0-C9. SetIndep(Sn,Cn) Example: SetIndep(S1, C2) sets the Independent Column field for the S1 analysis to use the data in list C2. Inference app functions The Inference app has a single function that returns the same results as tapping in the Numeric view of the Inference app. The results depend on the contents of the Inference app variables Method, Type, and AltHyp.
Example: HypZ1mean(0.461368, 50, 0.5, 0.2887, 0.05, 1) returns {1, -.9462…, 0.4614, 0.8277…, 1.6448…, 0.5671…} HYPZ2mean The two-sample Z-test for means.
Mode: Specifies which alternative hypothesis to use: • 1: < 0 • 2: > 0 • 3: ≠ 0 Example: HypZ1prop(21, 50, 0.5, 0.05,1) returns {1, -1.1313…, 0.42, 0.8710…, 1.6448…, 0.6148…} HypZ2prop The two-sample Z-test for proportions.
Mode: Specifies which alternative hypothesis to use: • 1: < 0 • 2: > 0 • 3: ≠ 0 Example: HypT1mean(0.461368, 0.2776, 50, 0.5, 0.05, 1) returns {1, -.9462…, 0.4614, 0.8277…, 1.6448…, 0.5671…} HypT2mean The two-sample T-test for means.
ConfZ1mean The one-sample Normal confidence interval for a mean. Returns a list containing (in order): • The lower critical Z-value • The lower bound of the confidence interval • The upper bound of the confidence interval ConfZ1mean( x ,n,, C) Example: ConfZ1mean(0.461368, 50, 0.2887, 0.95) returns {1.9599…, 0.3813…, 0.5413…} ConfZ2mean The two-sample Normal confidence interval for the difference of two means.
ConfZ2prop The two-sample Normal confidence interval for the difference of two proportions. Returns a list containing (in order): • The lower critical Z-value • The lower bound of the confidence interval • The upper bound of the confidence interval ConfZ2prop(x1,x2,n1,n2,C) Example: ConfZ2prop(21, 26, 50, 50, 0.95) returns {-1.9599…, -0.2946…, 0.0946…)} ConfT1mean The one-sample Student’s T confidence interval for a mean.
Finance app functions The Finance app uses a set of functions that all reference the same set of Finance app variables. These correspond to the fields in the Finance app Numeric view. There are 5 main TVM variables, 4 of which are mandatory for each of these functions, as they each solve for and return the value of the fifth variable to two decimal places. DoFinance is the sole exception to this syntax rule.
CalcIPYR Solves for the interest rate per year of an investment or loan. CalcIPYR(NbPmt,PV,PMTV,FV[,PPYR,CPYR, BEG]) Example: CalcIPYR(360, 150000, -948.10, -2.25) returns 6.50 CalcNbPmt Solves for the number of payments in an investment or loan. CalcNbPmt(IPYR,PV,PMTV,FV[,PPYR,CPYR,BEG]) Example: CalcNbPmt(6.5, 150000, -948.10, -2.25) returns 360.00 CalcPMT Solves for the value of a payment for an investment or loan. CalcPMT(NbPmt,IPYR,PV,FV[,PPYR,CPYR,BEG]) Example: CalcPMT(360, 6.5, 150000, -2.
Linear Solver app functions The Linear Solver app has 3 functions that offer the user flexibility in solving 2x2 or 3x3 linear systems of equations. Solve2x2 Solves a 2x2 linear system of equations. Solve2x2(a, b, c, d, e, f) Solves the linear system represented by: ax+by=c dx+ey=f Solve3x3 Solves a 3x3 linear system of equations. Solve3x3(a, b, c, d, e, f, g, h, i, j, k, l) Solves the linear system represented by: ax+by+cz=d ex+fy+gz=h ix+jy+kz=l LinSolve Solve linear system.
AAS Angle-Angle-Side. Takes as arguments the measures of two angles and the length of the side opposite the first angle and returns a list containing the length of the side opposite the second angle, the length of the third side, and the measure of the third angle (in that order). AAS(angle,angle,side) Example: AAS(30, 60, 1) in degree mode returns {1.732…, 2, 90} ASA Angle-Side-Angle.
SSS Side-Side-Side Takes as arguments the lengths of the three sides of a triangle and returns the measures of the angles opposite them, in order. SSS(side,side,side) Example: SSS(3, 4, 5) in degree mode returns {36.8…, 53.1…, 90} DoSolve Solves the current problem in the Triangle Solver app. The Triangle Solver app must have enough data entered to ensure a successful solution; that is, there must be at least three values entered, one of which must be a side length.
Quadratic Explorer functions SOLVE Solve quadratic. Given the coefficients of a quadratic equation ax2+bx+c=0, returns the real solutions. SOLVE(a, b, c) Example: SOLVE(1,0,-4) returns {-2, 2} DELTA Discriminant. Given the coefficients of a quadratic equation ax2+bx+c=0, returns the value of the discriminant in the Quadratic Formula.
Example: With the Function app as the current app, CHECK(1) checks the Function app Symbolic view variable F1. The result is that F1(X) is drawn in the Plot view and has a column of function values in the Numeric view of the Function app. With another app as the current app, you would have to enter Function.CHECK(1). UNCHECK Un-Check. Un-checks—that is, deselects—the Symbolic view variable corresponding to Digit. Used primarily in programming to de-activate symbolic view definitions in apps.
described in “Keyboard functions” on page 309. Those that are also on the CAS menu are described in “CAS menu” on page 324. The functions and commands specific to the Geometry app are described in “Geometry functions and commands” on page 165, and those specific to programming are described in “Program commands” on page 527. The matrix functions are described in “Matrix functions” on page 475and the list functions are described in “List functions” on page 457.
+ Addition symbol. Returns the sum of two numbers, the term-byterm sum of two lists or two matrices, or adds two strings together. − Subtraction symbol. Returns the difference of two numbers, or the term-by-term subtraction of two lists or two matrices. .* List or matrix multiplication symbol. Returns the term-by-term multiplication of two lists or two matrices. List1.*List2 or Matrix1.*Matrix2 Example: [[1,2],[3,4]].*[[3,4],[5,6]] gives [[3,8],[15,24]] ./ List or matrix division symbol.
<> = Inequality test. Returns 1 if the inequality is true, and 0 if the inequality is false. Equality symbol. Connects two members of an equation. == Equality test. Returns 1 if the left side and right side are equal, and 0 otherwise. > Strict greater than inequality test. Returns 1 if the left side of the inequality is greater than the right side, and 0 otherwise. Note that more than two objects can be compared. See comment above regarding <. >= Greater than or equal inequality test.
algvar Returns the matrix of the symbolic variable names used in an expression. The list is ordered by the algebraic extensions required to build the original expression. algvar(Expr) Example: algvar(sqrt(x)+y) gives y x AND Logical And. Returns 1 if the left and right sides both evaluate to true and returns 0 otherwise. Expr1 AND Expr2 Example: 3 +1==4 AND 4 < 5 returns 1 append Appends an element to a list or vector.
basis Given a matrix, returns the basis of the linear subspace defined by the set of vectors in the matrix. basis(Matrix)) Example: basis([[1,2,3],[4,5,6],[7,8,9],[10,11,12]]) gives [[-3,0,3],[0,-3,-6]] black blue Used in the Symbolic view of the Geometry app. In the definition of a geometric object, including the statement “display=black” specifies that the object defined will be drawn in black. Used in the Symbolic view of the Geometry app.
charpoly Returns the coefficients of the characteristic polynomial of a matrix. With only one argument, the variable used in the polynomial is x. With a variable as second argument, the polynomial returned is in terms of that variable. charpoly(Mtrx,[Var]) Example: 2 charpoly 1 2 z returns z – 5 z – 2 3 4 chrem Returns a vector containing the Chinese remainders for two sets of integers, contained in either two vectors or two lists.
companion Returns the companion matrix of a polynomial. companion(Poly,Var) Example: companion(x^2+5x-7,x) returns 0 7 1 –5 compare Compares objects, and returns 1 if type(arg1)
contains Given a list or vector and an element, returns the index of the first occurrence of the element in the list or vector; if the element does not appear in the list or vector, returns 0. contains((List, Element) or contains(Vector, Element) Example: contains({0,1,2,3},2) returns 3 CopyVar Copies the first variable into the second variable without evaluation. CopyVar(Var1,Var2) correlation Returns the correlation of the elements of a list or matrix.
covariance_ correlation Returns a vector containing both the covariance and the correlation of the elements of a list or matrix. covariance_correlation(List) or covariance_correlation(Matrix) Example: 1 2 covariance_correlation 1 1 4 7 cpartfrac returns 11 33 ------- ------------------3 6 31 Returns the result of partial fraction decomposition of a rational fraction in the complex field.
delcols Given a matrix and an integer n, deletes the nth column from the matrix and returns the result. If an interval of two integers is used instead of a single integer, deletes all columns in the interval and returns the result. delcols(Matrix, Integer) or delcols(Matrix, Intg1..Intg2) Example: 1 2 3 1 3 7 8 9 7 9 delcols 4 5 6 2 returns 4 6 delrows Given a matrix and an integer n, deletes the nth row from the matrix and returns the result.
egcd Given two polynomials, A and B, returns three polynomials U, V and D such that: U(x)*A(x)+V(x)*B(x)=D(x), where D(x)=GCD(A(x),B(x)), the greatest common divisor of polynomials A and B. The polynomials can be provided in symbolic form or as lists of coefficients in descending order. Without a third argument, it is assumed that the polynomials are expressions of x. With a variable as third argument, the polynomials are expressions of it.
evalc Returns a complex expression written in the form real+i*imag. evalc(Expr) Example: 1 x iy - returns ------------------- – -----------------evalc ---------------- 2 2 2 2 x+yi evalf x +y x +y Given an expression and a number of significant digits, returns the numerical evaluation of the expression to the given number of significant digits. With just an expression, returns the numerical evaluation based on the CAS settings. evalf(Expr,[Integer]) Example: evalf(2/3) gives 0.
exponential_ regression Given a set of points, returns a vector containing the coefficients a and b of y=b*a^x, the exponential which best fits the set of points. The points may be the elements in two lists or the rows of a matrix. exponential_regression(Matrix) or exponential_regression(List1, List2) Example: 1.0 2.0 exponential_regression 0.0 1.0 returns 4.0 7.0 1.60092225473,1.10008339351 EXPR Parses the string String into a number or expression.
fMax Given an expression in x, returns the value of x for which the expression has its maximum value. Given an expression and a variable, returns the value of that variable for which the expression has its maximum value. fMax(Expr,[Var]) Example: fMax(-x^2+2*x+1,x) gives 1 fMin Given an expression in x, returns the value of x for which the expression has its minimum value. Given an expression and a variable, returns the value of that variable for which the expression has its minimum value.
fsolve Returns the numerical solution of an equation or a system of equations. With the optional third argument you can specify a guess for the solution or an interval within which it is expected that the solution will occur. With the optional fourth argument you can name the iterative algorithm to be used by the solver. fsolve(Expr,Var,[Guess or Interval],[Method]) Example: fsolve(cos(x)=x,x,-1..1,bisection_solver) gives [0.
gramschmidt Given a basis of a vector subspace, and a function that defines a scalar product on this vector subspace, returns an orthonormal basis for that function. gramschmidt(Vector, Function) Example: 1 gramschmidt 1 1 + x p q p q dx –1 returns 1 1 + x – 1--------------------------2 6 ------3 green Used in the Symbolic view of the Geometry app.
head Returns the first element of a given vector, sequence or string. head(Vector) or head(String) or head(Obj1, Obj2,…) Example: head(1,2,3) gives 1 Heaviside Returns the value of the Heaviside function for a given real number (i.e. 1 if x>=0, and 0 if x<0). Heaviside(Real) Example: Heaviside(1) gives 1 hyp2exp Returns an expression with hyperbolic terms rewritten as exponentials.
id Returns a vector containing the solution to the identity function for the argument(s). id(Object1, [Object2,…]) Example: id([1 identity 2], 3, 4) returns [[1 2] 3 4] Given an integer n, returns the identity matrix of dimension n. identity(Integer) Example: 1 0 0 identity(3) returns 0 1 0 0 0 1 iegcd Returns the extended greatest common divisor of two integers.
iPart Returns a real number without its fractional part or a list of real numbers each without its fractional part. iPart(Real) or iPart(List) Example: iPart(4.3) returns 4 iquorem Returns the Euclidean quotient and remainder of two integers. iquorem(Integer1, Integer2) Example: iquorem(63, 23) returns [2, 17] jacobi_symbol Returns the Jacobi symbol of the given integers.
length Returns the length of a list, string or set of objects. length(List) or length(String) or length(Object1, Object2,…) Example: length([1,2,3]) gives 3 lgcd Returns the greatest common divisor of a set of integers or polynomials, contained in a list, a vector, or just entered directly as arguments. lgcd(List) or lgcd(Vector) or lgcd(Integer1, Integer2, …) or lgcd(Poly1, Poly2, …) Example: lgcd([45,75,20,15]) gives 5 lin Returns an expression with the exponentials linearized.
list2mat Returns a matrix of n columns made by splitting a list into rows, each containing n terms. If the number of elements in the list is not divisible by n, then the matrix is completed with zeros. list2mat(List, Integer) Example: 1 list2mat({1,8,4,9},1) returns 8 4 9 lname Returns a list of the variables in an expression. lname(Expr) Example: lname(exp(x)*2*sin(y)) gives [x,y] lnexpand Returns the expanded form of a logarithmic expression.
logistic_ regression Returns y, y', C, y'max, xmax, and R, where y is a logistic function (the solution of y'/y=a*y+b), such that y(x0)=y0 and where [y'(x0),y'(x0+1)...] is the best approximation of the line formed by the elements in the list L. logistic_regression(Lst(L),Real(x0),Real(y0)) Example: logistic_regression([0.0,1.0,2.0,3.0,4.0],0.0 ,1.0) gives [-17.77/(1+exp(0.496893925384*x+2.82232341488+3.14159265359* i)),-2.48542227469/(1+cosh(0.496893925384*x+2.82232341488+3.
Example: matpow([[1,2],[3,4]],n) gives [[(sqrt(33)3)*((sqrt(33)+5)/2)^n*-6/(-12*sqrt(33))+((sqrt(33))-3)*((-(sqrt(33))+5)/2)^n*6/(12*sqrt(33)),(sqrt(33)-3)*((sqrt(33)+5)/ 2)^n*(-(sqrt(33))-3)/(-12*sqrt(33))+((sqrt(33))-3)*((-(sqrt(33))+5)/2)^n*((sqrt(33))+3)/(12*sqrt(33))],[6*((sqrt(33)+5)/2)^n*-6/(12*sqrt(33))+6*((-(sqrt(33))+5)/2)^n*6/(12*sqrt(33)),6*((sqrt(33)+5)/2)^n*((sqrt(33))-3)/(-12*sqrt(33))+6*(((sqrt(33))+5)/2)^n*(-(sqrt(33))+3)/(12*sqrt(33))]] MAXREAL mean Returns the maximum real number that t
modgcd Uses the modular algorithm to return the greatest common divisor of two polynomials. modgcd(Poly1,Poly2) Example: modgcd(x^4-1,(x-1)^2) gives x-1 mRow Given an expression, a matrix, and an integer n, multiplies row n of the matrix by the expression.
nDeriv Given an expression, a variable of differentiation, and a real number h, returns an approximate value of the derivative of the expression, using f’(x)=(f(x+h)–f(x+h))/(2*h). Without a third argument, the value of h is set to 0.001; with a real as third argument, it is the value of h. With a variable as the third argument, returns the expression above with that variable in place of h. nDeriv(Expr,Var, Real) or nDeriv(Expr, Var1, Var2) Example: nDeriv(f(x),x,h) returns (f(x+h)-(f(x-h)))*0.
order_size Returns the remainder (O term) of a series expansion: limit(x^a*order_size(x),x=0)=0 if a>0. order_size(Expr) pa2b2 Takes a prime integer n congruent to 1 modulo 4 and returns [a,b] such that a^2+b^2=n. pa2b2(Integer) Example: pa2b2(17) gives [4 1] pade Returns the Pade approximation of an expression, i.e. a rational fraction P/Q such that P/Q=Expr mod x^(n+1) or mod N with degree(P)
plotparam Used in the Geometry app Symbolic view. Takes a complex expression in one variable and an interval for that variable as arguments. Interprets the complex expression f(t)+i*g(t) as x=f(t) and y=g(t) and plots the parametric equation over the interval specified in the second argument. plotparam(f(Var)+i*g(Var), Var= Interval) Example: plotparam(cos(t)+i*sin(t), t=0..2*π) plots the unit circle plotpolar Used in the Geometry app Symbolic view.
pole Given a circle and a line, returns the point for which the line is polar with respect to the circle. pole(Crcle,Line) Example: pole(circle(0, 1), line(1+i, 2)) returns point(1/2,1/2) POLYCOEF Returns the coefficients of a polynomial with roots given in the vector or list argument. POLYCOEF(Vector) or POLYCOEF(List) Example: POLYCOEF({-1, 1}) returns {1, 0, -1} POLYEVAL Given a vector or list of coefficients and a value, evaluates the polynomial given by those coefficients at the given value.
polygonscatterplot Used in the Geometry app Symbolic view. Given an n × m matrix, draws and connects the points (xk, yk), where xk is the element in row k and column 1, and yk is the element in row k and column j (with j fixed for k=1 to n rows). Thus, each column pairing generates its own figure, resulting in m-– figures. polygonscatterplot(Matrix) Example: 1 2 3 polygonscatterplot 2 0 1 draws two figures, each –1 2 3 with three points connected by segments.
power_regression Given a set of points defined by two lists, returns a vector containing the coefficients m and b of y=b*x^m, the monomial which best approximates the given points. power_regression(List1, List2) Example: power_regression({1, 2, 3, 4}, {1, 4, 9, 16}) returns [2 1] powerpc Given a circle and a point, returns the real number d2–r2, where d is the distance between the point and the center of the circle, and r is the radius of the circle.
propfrac Returns a fraction or rational fraction A/B simplified to Q+r/ B, where R
quartile3 Given a list or vector, returns the third quartile of the elements of the list or vector. Given a matrix, returns the third quartile of the columns of the matrix. quartile3(List) or quartile3(Vector) or quartile3(Matrix) Example: quartile3([1,2,3,5,10,4]) returns 5 quartiles Returns a matrix containing the minimum, first quartile, median, third quartile, and maximum of the elements of a list or vector. With a matrix as argument, returns the 5-number summary of the columns of the matrix.
randperm Given a positive integer, returns a random permutation of [0,1,2,...,n–1]. randperm(Intg(n)) Example: randperm(4) returns a random permutation of the elements of the vector [0 1 2 3] ratnormal Rewrites an expression as an irreducible rational fraction.
reduced_conic Takes a conic expression and returns a vector with the following items: • The origin of the conic • The matrix of a basis in which the conic is reduced • 0 or 1 (0 if the conic is degenerate) • The reduced equation of the conic • A vector of the conic’s parametric equations reduced_conic(Expr, [Vector]) Example: reduced_conic(x^2+2*x-2*y+1) returns 1 0 0 1 2 1 1 2 1 y 2 x 1 i 2 x x i x x 4 4 0.
residue Returns the residue of an expression at a value. residue(Expr, Var, Value) Example: residue(1/z,z,0) returns 1 restart Purges all the variables. restart(NULL) resultant Returns the resultant (i.e. the determinant of the Sylvester matrix) of two polynomials. resultant(Poly1, Poly2, Var) Example: resultant(x^3+x+1, x^2-x-2,x) returns -11 revlist Reverses the order of the elements in a list or vector.
rowAdd Given a matrix and two integers, returns the matrix obtained from the given matrix after the row indicated by the second integer is replaced by the sum of the rows indicated by the two integers. rowAdd(Matrix, Integer1, Integer2) Example: 1 2 1 2 5 6 5 6 rowAdd 3 4 1 2 returns 4 6 rowDim Returns the number of rows of a matrix.
select Given a Boolean expression in a single variable and a list or vector, tests each element in the list or vector and returns a list or vector containing the elements that satisfy the Boolean. select(Expr, List) or select(Expr, Vector) Example: select(x→x>=5,[1,2,6,7]) gives [6,7] seq Given an expression, a variable defined over an interval, and a step value, returns a vector containing the sequence obtained when the expression is evaluated within the given interval using the given step.
simult Returns the solution to a system of linear equations or several systems of linear equations presented in matrix form. In the case of one system of linear equations, takes a matrix of coefficients and a column matrix of constants, and returns the column matrix of the solution. simult(Matrix1, Matrix2) Example: simult 3 1 – 2 returns – 2 3 2 sincos 2 4 Returns an expression with the complex exponentials rewritten in terms of sin and cos.
stddevp Returns the population standard deviation of the elements of a list or a list of the population standard deviations of the columns of a matrix. The optional second list is a list of weights. stddevp(List1, [List2]) or stddevp(Vector1, [Vector2]) or stddevp(Matrix) Example: stddevp({1,2,3}) gives 1 sto Stores a real or string in a variable. sto((Real or Str),Var) sturmseq Returns the Sturm sequence for a polynomial or a rational fraction.
sylvester Returns the Sylvester matrix of two polynomials. sylvester(Poly1, Poly2, Var) Example: sylvester(x2-1,x3-1,x) table gives 1 0 0 1 0 0 1 0 0 1 –1 0 1 0 0 0 –1 0 –1 0 0 0 –1 0 –1 Defines an array where the indexes are strings or real numbers. table(SeqEqual(index_name=element_value)) tail Given a list, string, or sequence of objects, returns a vector with the first element deleted.
trunc Given a value or list of values, as well as an integer n, returns the value or list truncated to n decimal places. If n is not provided, it is taken as 0. Accepts complex numbers. trunc(Real, Integer) or trunc(List, Integer) Example: trunc(4.3) gives 4 tsimplify Returns an expression with transcendentals rewritten as complex exponentials. tsimplify(Expr) Example: tsimplify(exp(2*x)+exp(x)) gives exp(x)^2+exp(x) type Returns the type of an expression (e.g. list, string).
vpotential Given a vector V and a vector of variables, returns the vector U such that curl(U)=V. vpotential(Vector1, Vector2) Example: vpotential([2*x*y+3,x2-4*z,-2*y*z],[x,y,z]) returns when XOR 0 –2 x y z 1 3 4 x z – --- x + 3 y 3 Used to introduce a conditional statement. Exclusive or. Returns 1 if the first expression is true and the second expression is false or if the first expression is false and the second expression is true. Returns 0 otherwise.
Inserts a template for a summation expression. Inserts a minus sign. Inserts a square root sign. Inserts a template for an antiderivative expression. Inequality test. Returns 1 if the left and right sides are not equal and 0 if they are equal. Less than or equal inequality test. Returns 1 if the left side of the inequality is less than the right side or if the two sides are equal, and 0 otherwise. Greater than or equal inequality test.
3. In the Function field, enter the function. eAA>+fAB>AC New fields appear below your function, one for each variable used in defining it. You need to decide which ones are to be input arguments for your functions and which ones are global variables whose values are not input within the function. In this example, we’ll make A and B input variables, so our new function takes two arguments. The value of C will be provided by global variable C (which by default is zero). 4.
22 Variables Variables are objects that have names and contain data. They are used to store data, either for later use or to control settings in the Prime system. There are four types of variables, all of which can be found in the Vars menu by pressing a: • Home variables • CAS variables • App variables • User variables The Home and app variables all have names reserved for them. They are also typed; that is, they can contain only certain types of objects.
you evaluate that result (using the EVAL command), the CAS will now return {2,4,6}. User variables are explicitly created by the user. You create user variables either in a program or by assignment in Home view. User variables created in a program are either declared as local or exported as global. User variables created by assignment or exported from a program will show up in the Vars User menu. Local variables exist only within their own program.
Working with user variables Example 2: Create a variable called ME and assign 2 to it. 1. Press H to display Home view. 2. Assign 2 to ME: Szj AQAcE 3. A message appears asking if you want to create a variable called ME. Tap or press E to confirm your intention. You can now use that variable in subsequent calculations: ME*3 will yield 29.6…, for example. Example 3: You can also store objects in variables using the assignment operator: Name:=Object.
Entering HAngle:=0 E forces the setting to return to radians. You can see what value has been assigned to a variable—whether Home, app, or user—by entering its name in Home view and pressing E. You can enter the name letter by letter, or choose the variable from the Variables menu by pressing a. More about the Vars menu Besides the four variable menus, the Vars menu contains a toggle. If you want the value of a variable instead of its name when you choose it from the Vars menu, tap .
Qualifying variables Some app variable names are shared by multiple apps. For example, the Function app has a variable named Xmin, but so too does the Polar app, the Parametric app, the Sequence app, and the Solve app. Although named identically, these variables usually hold different values. If you attempt to retrieve the contents of a variable that is used in more than one app by entering just its name in Home view, you will get the contents of that version of the variable in the current app.
Home variables The Home variables are accessed by pressing a and tapping . Category Real Names A to Z and For example, 7.45 Complex A Z0 to Z9 For example, 2+3×i Z1 or (2,3) Z1 (depending on your Complex number settings) List L0 to L9 For example, {1,2,3} Matrix L1. M0 to M9 Store matrices and vectors in these variables. For example, [[1,2],[3,4]] Graphics G0 to G9 Settings HAngle M1.
App variables The app variables are accessed by pressing a and tapping . They are grouped below by app. (You can find then grouped by view—Symbolic, Numeric, Plot, —in “Variables and Programs” on page 556.) Note that if you have customized a built-in app, your app will appear on the App variables menu under the name you gave it. You access the variables in a customized app in the same way that you access the variables in built-in apps.
Results variables Extremum Contains the value from the last use of the Extremum function from the menu in the Plot view of the Function app. The app function EXTREMUM does not store results to this variable. Isect Contains the value from the last use of the Isect function from the menu in the Plot view of the Function app. The app function ISECT does not store results to this variable. Root Contains the value from the last use of the Root function from the menu in the Plot view of the Function app.
Spreadsheet app variables Category Names Numeric ColWidth RowHeight Row Cell Col AAngle AComplex ADigits AFormat Modes Solve app variables Variables Category Names Symbolic E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Plot Axes Cursor GridDots GridLines Labels Method Recenter Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Modes AAngle AComplex ADigits AFormat 431
Advanced Graphing app variables Category Names Symbolic V1 V2 V3 V4 V5 V6 V7 V8 V9 V0 Plot Axes Cursor GridDots GridLines Labels Recenter Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric NumXStart NumYStart NumXStep NumYStep NumIndep AAngle AComplex ADigits AFormat Modes 432 NumType NumXZoom NumYZoom Variables
Statistics 1Var app variables Category Names Results NbItem MinVal Q1 MedVal Q3 MaxVal X X2 MeanX sX X serrX Symbolic H1 H2 H3 H4 H5 H1Type H2Type H3Type H4Type H5Type Plot Axes Cursor GridDots GridLines Hmin Hmax Hwidth Labels Recenter Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric D1 D2 D3 D4 D5 D6 D7 D8 D9 D0 Modes AAngle AComplex ADigits AFormat [explained below] Variables 433
Results NbItem Contains the number of data points in the current 1variable analysis (H1-H5). MinVal Contains the minimum value of the data set in the current 1-variable analysis (H1-H5). Q1 Contains the value of the first quartile in the current 1variable analysis (H1-H5). MedVal Contains the median in the current 1-variable analysis (H1-H5). Q3 Contains the value of the third quartile in the current 1variable analysis (H1-H5).
Statistics 2Var app variables Category Names Results NbItem Corr CoefDet sCov Cov XY MeanX X X2 sX X serrX MeanY Y Y2 sY Y serrY Symbolic S1 S2 S3 S4 S5 S1Type S2Type S3Type S4Type S5Type Plot Axes Cursor GridDots GridLines Labels Method Recenter Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric C1 C2 C3 C4 C5 C6 C7 C8 C9 C0 Modes AAngle AComplex ADigits AFormat [explained below] Variables 435
Results NbItem Contains the number of data points in the current 2variable analysis (S1-S5). Corr Contains the correlation coefficient from the latest calculation of summary statistics. This value is based on the linear fit only, regardless of the fit type chosen. CoefDet Contains the coefficient of determination from the latest calculation of summary statistics. This value is based on the fit type chosen. sCov Contains the sample covariance of the current 2-variable statistical analysis (S1-S5).
Y Contains the sum of the dependent values (Y) of the current 2-variable statistical analysis (S1-S5). Y2 Contains the sum of the squares of the dependent values (Y) of the current 2-variable statistical analysis (S1-S5). sY Contains the sample standard deviation of the dependent values (Y) of the current 2-variable statistical analysis (S1S5). Y Contains the population standard deviation of the dependent values (Y) of the current 2-variable statistical analysis (S1-S5).
Results CritScore Contains the value of the Z- or t-distribution associated with the input -value CritVal1 Contains the lower critical value of the experimental variable associated with the negative TestScore value which was calculated from the input -level. CritVal2 Contains the upper critical value of the experimental variable associated with the positive TestScore value which was calculated from the input -level. DF Contains the degrees of freedom for the t-tests.
Parametric app variables Variables Category Names Symbolic X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Plot Axes Cursor GridDots GridLines Labels Method Recenter Tmin Tmax Tstep Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric NumStart NumStep NumType NumZoom Modes AAngle AComplex ADigits AFormat 439
Polar app variables Category Names Symbolic R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Plot min max step Axes Cursor GridDots GridLines Labels Method Recenter Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric NumIndep NumStart NumStep NumType NumZoom Modes AAngle AComplex ADigits AFormat Finance app variables Category Names Numeric CPYR BEG FV IPYR NbPmt PMTV PPYR PV GSize Modes 440 AAngle AComplex ADigits AFormat Variables
Linear Solver app variables a. Category Names Numeric LSystem LSolutiona Modes AAngle AComplex ADigits AFormat Contains a vector with the last solution found by the Linear Solver app.
Trig Explorer app variables Category Names Modes AAngle AComplex ADigits AFormat Sequence app variables 442 Category Names Symbolic U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Plot Axes Cursor GridDots GridLines Labels Nmin Nmax Recenter Xmax Xmin Xtick Xzoom Ymax Ymin Ytick Yzoom Numeric NumIndep NumStart NumStep NumType NumZoom Modes AAngle AComplex ADigits AFormat Variables
23 Units and constants Units A unit of measurement—such as inch, ohm, or Becquerel—enables you to give a precise magnitude to a physical quantity. You can attach a unit of measurement to any number or numerical result. A numerical value with units attached is referred to as a measurement. You can operate on measurements just as you do on numbers without attached units. The units are kept with the numbers in subsequent operations. The units are on the Units menu. Press SF (Units) and, if necessary, tap .
Prefixes The Units menu includes an entry that is not a unit category, namely, Prefix. Selecting this option displays a palette of prefixes. Y: yotta Z: zetta E: exa P: peta T: tera G: giga M: mega k: kilo h: hecto D: deca d: deci c: centi m: milli : micro n: nano p: pico f: femto a: atto z: zepto y: octo Unit prefixes provide a handy way of entering large or small numbers. For example, the speed of light is approximately 300,000 m/s.
Example Suppose you want to add 20 centimeters and 5 inches and have the result displayed in centimeters. 1. If you want the result in cm, enter the centimeter measurement first. 20 SF (Units) Select Length Select cm 2. Now add 5 inches. + 5 SF Select Length Select in E The result is shown as 32.7 cm. If you had wanted the result in inches, then you would have entered the 5 inches first. 3. To continue the example, let’s divide the result by 4 seconds.
4. Now convert the result to kilometers per hour. SF Select Speed Select km/h E The result is shown as 0.2943 kilometers per hour. Unit tools There are a number of tools for managing and operating on units. These are available by pressing SF and tapping . CONVERT Converts one unit to another unit of the same category. CONVERT(5_m,1_ft) returns 16.4041994751_ft You can also use the last answer as the first argument in a new conversion calculation. Pressing S+ places the last answer on the entry line.
UFACTOR Unit factor conversion. Converts a measurement using a compound unit into a measurement expressed in constituent units. For example, a Coulomb—a measure of electric charge—is a compound unit derived from the SI base units of Ampere and second: 1 C = 1 A * 1 s. Thus: UFACTOR(100_C,1_A)) returns 100_A*s USIMPLIFY Unit simplification. For example, a Joule is defined as one kg*m2/s2.
3. Select Physics. 4. Select c: 299792458. 5. Square the speed of light and evaluate the expression. jE Value or measurement? You can enter just the value of a constant or the constant and its units (if it has units). If is showing on the screen, the value is inserted at the cursor point. If is showing on the screen, the value and its units are inserted at the cursor point. In the example at the right, the first entry shows the Universal Gas Constant after it was chosen with showing.
List of constants Category Name and symbol Math e MAXREAL MINREAL i Units and constants Chemistry Avogadro, NA Boltmann, k molar volume, Vm universal gas, R standard temperature, StdT standard pressure, StdP Phyics Stefan-Boltzmann, speed of light, c permittivity, 0 permeability, 0 acceleration of gravity, g gravitation, G Quantum Planck, h Dirac, electronic charge, q electron mass, me q/me ratio, qme proton mass, mp mp/me ratio, mpme fine structure, magnetic flux, Faraday, F Rydberg, R
450 Units and constants
24 Lists A list consists of comma-separated real or complex numbers, expressions, or matrices, all enclosed in braces. A list may, for example, contain a sequence of real numbers such as {1,2,3}. Lists represent a convenient way to group related objects. You can do list operations in Home and in programs. There are ten list variables available, named L0 to L9, or you can create your own list variable names. You can use them in calculations or expressions in Home or in a program.
2. Tap on the name you want to assign to the new list (L1, L2, etc.). The list editor appears. If you’re creating a new list rather than changing, make sure you choose a list with out any elements in it. 3. Enter the values you want in the list, pressingE after each one. Values can be real or complex numbers (or an expression). If you enter a expression, it is evaluated and the result is inserted in the list. 4. When done, press Sp(List) to return to the List catalog, or press Hto go to Home view.
The List Editor The List Editor is a special environment for entering data into lists. There are two ways to open the List Editor once the List Catalog is open: List Editor: Buttons and keys • Highlight the list and tap • Tap the name of the list. or When you open a list, the following buttons and keys are available to you: Button or Key Purpose Copies the highlighted list item into the entry line. Inserts a new value—with default zero—before the highlighted item.
To edit a list 1. Open the List Catalog. Sp(List) 2. Tap on the name of the list (L1, L1,etc.). The List Editor appears. 3. Tap on the element you want to edit. (Alternatively, press = or \ until the element you want to edit is highlighted.) In this example, edit the third element so that it has a value of 5. 5 To insert an element in a list 454 Suppose you want to insert a new value, 9, in L1(2) in the list L1 shown to the right.
Select L1(2), that is, the second element in the list. 9 Deleting lists To delete a list In the List Catalog, use the cursor keys to highlight the list and press C. You are prompted to confirm your decision. Tap or press E. If the list is one of the reserved lists L0-L9, then only the contents of the list are deleted. The list is simply stripped of its contents. If the list is one you have named (other than L0-L9), then it is deleted entirely. To delete all lists In the List Catalog, press SJ (Clear).
4. When you have finished entering the elements, press E. The list is added to History (with any expressions among the elements evaluated). To store a list You can store a list in a variable. You can do this before the list is added to History, or you can copy it from History. When you’ve entered a list in the entry line or copied it from History to the entry line, tap , enter a name for the list and press E.
To send a list You can send lists to another calculator or a PC just as you can apps, programs, matrices, and notes. See “Sharing data” on page 44 for instructions. List functions List functions are found on the Math menu. You can use them in Home and in programs. You can type in the name of the function, or you can copy the name of the function from the List category of the Math menu. Press D 6 to select the List category in the left column of the Math menu.
Menu format By default, a List function is presented on the Math menu using its descriptive name, not its common command name. Thus the shorthand name CONCAT is presented as Concatenate and POS is presented as Position. If you prefer the Math menu to show command names instead, deselect the Menu Display option on page 2 of the Home Settings screen (see page 26).
Reverse Creates a list by reversing the order of the elements in a list. REVERSE(list) Example: REVERSE({1,2,3}) returns {3,2,1} Concatenate Concatenates two lists into a new list. CONCAT(list1,list2) Example: CONCAT({1,2,3},{4}) returns {1,2,3,4}. Position Returns the position of an element within a list. The element can be a value, a variable, or an expression. If there is more than one instance of the element, the position of the first occurrence is returned.
LIST Creates a new list composed of the first differences of a list; that is, the differences between consecutive elements in the list. The new list has one less element than the original list. The differences for {x1, x2, x3,... xn-1, xn} are {x2 –x1, x3–x2 ,... xn –xn–1}. LIST(list1) Example: In Home view, store {3,5,8,12,17,23} in L5 and find the first differences for the list. Sq 3,5,8,12,17,23 > A j 5E D Select List Select List Aj5E LIST Calculates the sum of all elements in a list.
Finding statistical values for lists To find statistical values—such as the mean, median, maximum, and minimum of a list—you create a list, store it in a data set and then use the Statistics 1Var app. Example In this example, use the Statistics 1Var app to find the mean, median, maximum, and minimum values of the elements in the list L1, being 88, 90, 89, 65, 70, and 89. 1. In Home view, create L1. Sq 88, 90, 89, 65, 70,89 > Aj 1E 2. In Home view, store L1 in D1.
4. In the Symbolic view, specify the data set whose statistics you want to find. Y By default, H1 will use the data in D1, so nothing further needs to be done in Symbolic view. However, if the data of interest were in D2, or any column other than D1, you would have to specify the desired data column here. 5. Calculate the statistics. M 6. Tap when you are done. See the chapter 10, “Statistics 1Var app”, beginning on page 211, for the meaning of each statistic.
25 Matrices You can create, edit, and operate on matrices and vectors in the Home view, CAS, or in programs. You can enter matrices directly in Home or CAS, or use the Matrix Editor. Vectors Vectors are one-dimensional arrays. They are composed of just one row. A vector is represented by single brackets; for example, [1 2 3]. A vector can be a real number vector, or a complex number vector such as [1+2*i 7+3*i]. Matrices Matrices are two-dimensional arrays.
Creating and storing matrices The Matrix Catalog contains the reserved matrix variables M0-M9, as well as any matrix variables you have created in Home or CAS views (or from a program if they are global). Once you select a matrix name, you can create, edit, and delete matrices in the Matrix Editor. You can also send a matrix to another HP Prime. To open the Matrix Catalog, pressSt(Matrix). In the Matrix Catalog, the size of a matrix is shown beside the matrix name. (An empty matrix is shown as 1*1.
Working with matrices To open the Matrix Editor To create or edit a matrix, go to the Matrix Catalog, and tap on a matrix. (You could also use the cursor keys to highlight the matrix and then press .) The Matrix Editor opens. Matrix Editor: Buttons and keys The buttons and keys available in the Matrix Editor are.: Button or Key Purpose Copies the highlighted element to the entry line. Inserts a row of zeros above, or a column of zeros to the left, of the highlighted cell.
To create a matrix in the Matrix Editor 1. Open the Matrix Catalog: St(Matrix) 2. If you want to create a vector, press = or \ until the matrix you want to use is highlighted, tap , and then press E. Continue from step 4 below. 3. If you want to create a matrix, either tap on the name of the matrix (M0–M9), or press = or \ until the matrix you want to use is highlighted and then press E. Note that an empty matrix will be shown with a size of 1*1 beside its name. 4.
Matrices in Home view You can enter and operate on matrices directly in Home view. The matrices can be named or unnamed. Enter a vector or matrix in Home or CAS views directly in the entry line. 1. Press S u ([]) to start a vector or matrix. The matrix template will appear, as shown in the figure to the right. 2. Enter a value in the square. Then press > to enter a second value in the same row, or press \ to move to the second row.
entry line or copied it from History to the entry line, tap , enter a name for it and press E. The variable names reserved for vectors and matrices are M0 through M9. You can always use a variable name you devise to store a vector or matrix. The new variable will appear in the Vars menu under . The screen at the right shows the matrix 2.5 729 16 2 being stored in M5.
To store one element In Home view, enter value, tap , and then enter matrixname(row,column). For example, to change the element in the first row and second column of M5 to 728 and then display the resulting matrix: 728 AQ5 R1o 2 E An attempt to store an element to a row or column beyond the size of the matrix results in re-sizing the matrix to allow the storage. Any intermediate cells will be filled with zeroes.
Example 1. Select the first matrix: St (Matrix) Tap M1 or highlight it and press E. 2. Enter the matrix elements: 1E2 E3E 4E 3. Select the second matrix: St (Matrix) Tap M2 or highlight it and press E. 4. Enter the matrix elements: EE E E 5 6 7 8 5. In Home view, add the two matrices you have just created. HA Q1 + A Q2 E To multiply and divide by a scalar For division by a scalar, enter the matrix first, then the operator, then the scalar.
To multiply two matrices To multiply the two matrices that you created for the previous example, press the following keys: AQ1 sA Q2E To multiply a matrix by a vector, enter the matrix first, then the vector. The number of elements in the vector must equal the number of columns in the matrix. To raise a matrix to a power You can raise a matrix to any power as long as the power is an integer. The following example shows the result of raising matrix M1, created earlier, to the power of 5.
This operation is not a mathematical division: it is a leftmultiplication by the inverse of the divisor. M1/M2 is equivalent to M2–1 * M1. To divide the two matrices you created for the previous example, press the following keys: A Q1 n A Q2 To invert a matrix You can invert a square matrix in Home view by typing the matrix (or its variable name) and pressing SnE. You can also use the INVERSE command in the Matrix category of the Math menu.
2. Create the vector of the three constants in the linear system. 5E7E1 E 3. Return to the Matrix Catalog. St The size of M1 should be showing as 3. 4. Select and clear M2, and re-open the Matrix Editor: [Press \ or = to select M2] C E 5. Enter the equation coefficients. 2E3E [Tap in cell R1, C3.
6. Return to Home view and left-multiply the constants vector by the inverse of the coefficients matrix: HA Q2 S ns A Q1E The result is a vector of the solutions: x = 2, y = 3 and z = –2. An alternative method is to use the RREF function (see page 476). Matrix functions and commands Functions Functions can be used in any app or in Home view. They are listed on the Math menu under the Matrix category. They can be used in mathematical expressions—primarily in Home view—as well as in programs.
The matrix commands are designed to support programs that use matrices. The matrix commands are listed in the Matrix category of the Commands menu in the Program Editor. They are also listed in the Catalog menu, one of the Toolbox menus. Press D and tap to display the commands catalog. The matrix functions are described in the following sections of this chapter; the matrix commands are described in the chapter Programming (see page 544).
RREF Reduced Row-Echelon Form. Changes a rectangular matrix to its reduced row-echelon form. RREF(matrix) Example: RREF 1 – 2 1 returns 1 0 0.2 3 4 –1 0 1 – 0.4 Create Make Creates a matrix of dimension rows × columns, using expression to calculate each element. If expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J.
Random Given two integers, n and m, and a matrix name, creates an n x m matrix that contains random integers in the range −99 through 99 with a uniform distribution and stores it in the matrix name. randMat(MatrixName,n,m) Example: RANDMAT(M1,2,2) returns a 2x2 matrix with random integer elements, and stores it in M1. Jordan Returns a square nxn matrix with expr on the diagonal, 1 above and 0 everywhere else.
Vandermonde Returns the Vandermonde matrix. Given a vector [n1, n2 … nj], returns a matrix whose first row is [(n1)0, (n1)1, (n1)2, …,(n1)j-1]. The second row is [(n2)0, (n2)1, (n2)2, …,(n2)j-1], etc. vandermonde(vector) Example: 11 1 vandermonde([1 3 5]) returns 1 3 9 1 5 25 Basic Norm Returns the Frobenius norm of a matrix. |matrix| Example: 1 2 returns 5.47722557505 34 Row Norm Row Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row.
Spectral Norm Spectral Norm of a square matrix. SPECNORM(matrix) Example: SPECNORM 1 2 returns 5.46498570422 34 Spectral Radius Spectral Radius of a square matrix. SPECRAD(matrix) Example: SPECRAD 1 2 returns 5.37228132327 34 Condition Condition Number. Finds the 1-norm (column norm) of a square matrix. COND(matrix) Example: COND 1 2 returns 21 34 Rank Rank of a rectangular matrix.
Trace Finds the trace of a square matrix. The trace is equal to the sum of the diagonal elements. (It is also equal to the sum of the eigenvalues.) TRACE(matrix) Example: TRACE 1 2 returns 5 34 Advanced Eigenvalues Displays the eigenvalues in vector form for matrix. EIGENVAL(matrix) Example: EIGENVAL 1 2 returns: 34 5.37228 – 0.37228 . Eigenvectors Eigenvectors and eigenvalues for a square matrix. Displays a list of two arrays.
Diagonal Given a list, returns a matrix with the list elements along its diagonal and zeroes elsewhere. Given a matrix, returns a vector of the elements along its diagonal. diag(list) or diag(matrix) Example: diag 1 2 returns 1 4 34 Cholesky For a numerical symmetric matrix A, returns the matrix L such that A=L*tran(L).
Hessenberg Matrix reduction to Hessenberg form. Returns [P,B] such that B=inv(P)*A*P. hessenberg(Mtrx(A)) Example: 123 In CAS view, hessenberg 4 5 6 789 returns Smith 100 0 4 - 1 7 010 1 29 --- 2 7 7 39 --- 8 7 0 278 ----- 3 49 7 Smith normal form of a matrix with coefficients in Z: returns U,B,V such that U and V invertible in Z, B is diagonal, B[i,i] divides B[i+1,i+1], and B=U*A*V.
Factorize LQ LQ Factorization. Factorizes a m × n matrix into three matrices L, Q, and P, where {[L[m × n lowertrapezoidal]],[Q[n × n orthogonal]], [P[m × m permutation]]}and P*A=L*Q. LQ (matrix) Example: LQ 1 2 returns 34 2.2360 0 , 0.4472 0.8944 , 1 0 4.9193 0.8944 0.8944 – 0.4472 0 1 LSQ Least Squares. Displays the minimum norm least squares matrix (or vector) corresponding to the system matrix1*X=matrix2.
QR QR Factorization. Factorizes an m×n matrix A numerically as Q*R, where Q is an orthogonal matrix and R is an upper triangular matrix, and returns R. R is stored in var2 and Q=A*inv(R) is stored in var1. QR(matrix A,var1,var2) Example: QR 1 2 returns 34 0.3612 0.9486 3.1622 4.4271 1 0 , , 0 0.6324 0 1 0.9486 –0.3162 SCHUR Schur Decomposition. Factorizes a square matrix into two matrices. If matrix is real, then the result is {[[orthogonal]],[[upper-quasi triangular]]}.
SVL Singular Values. Returns a vector containing the singular values of matrix. SVL(matrix) Example: SVL 1 2 returns 5.4649 0.3659 34 Vector Cross Product Cross Product of vector1 with vector2. CROSS(vector1, vector2) Example: CROSS 1 2 , 3 4 returns 0 0 – 2 Dot Product Dot Product of two arrays, matrix1 and matrix2. DOT(matrix1, matrix2) Example: DOT 1 2 , 3 4 returns 11 L2 Norm Returns the l2 norm (sqrt(x1^2+x2^2+...xn^2)) of a vector.
Max Norm Returns the l∞ norm (the maximum of the absolute values of the coordinates) of a vector. maxnorm(Vect or Mtrx) Example: maxnorm 1 2 3 – 4 returns 4 Examples Identity Matrix You can create an identity matrix with the IDENMAT function. For example, IDENMAT(2) creates the 2×2 identity matrix [[1,0],[0,1]]. You can also create an identity matrix using the MAKEMAT (make matrix) function.
which can then be stored as a 3 4 real matrix in any matrix variable. M1 is used in this example. You can then use the RREF function to change this to reduced-row echelon form, storing it in any matrix variable. M2 is used in this example. The reduced row echelon matrix gives the solution to the linear equation in the fourth column.
488 Matrices
26 Notes and Info The HP Prime has two text editors for entering notes: • The Note Editor: opens from within the Note Catalog (which is a collection of notes independent of apps). • The Info Editor: opens from the Info view of an app. A note created in the Info view is associated with the app and stays with it if you send the app to another calculator. The Note Catalog Subject to available memory, you can store as many notes as you want in the Note Catalog. These notes are independent of any app.
Button or Key Purpose (Continued) Save: creates a copy of the selected note and prompts you to save it under a new name. Rename: renames the selected note. Sort: sorts the list of notes (sort options are alphabetical and chronological). Delete: deletes the selected note. Clear: deletes all notes. Send: sends the selected note to another HP Prime. C SJ Deletes the selected note. Deletes all notes in the catalog. The Note Editor The Note Editor is where you create and edit notes.
2. Create a new note. 3. Enter a name for your note. In this example, we’ll call the note MYNOTE. AA MYNOTE 4. Write your note, using the editing keys and formatting options described in the following sections. When you are finished, exit the Note Editor by pressing H or pressing I and opening an app. Your work is automatically saved. To access your new note, return to the Notes Catalog.
Note Editor: buttons and keys The following buttons and keys are available while you are adding or editing a note. Button or Key Purpose Opens the text formatting menu. See “Formatting options” on page 494. Provides bold, italic, underline, full caps, superscript and subscript options. See “Formatting options” on page 494 A toggle button that offers three types of bullet.
Button or Key Entering uppercase and lowercase characters E Starts a new line. SJ(Clear) Erases the entire note. a Menu for entering variable names, and the contents of variables. D Menu for entering math commands. Sa (Chars) Displays a palette of special characters. To type one, highlight it and tap or press E. To copy a character without closing the Chars menu, select it and tap . The following table below describes how to quickly enter uppercase and lowercase characters.
Keys Purpose (Continued) SA With lowercase locked, make all characters uppercase until the mode is reset A Reset lowercase lock mode The left side of the notification area of the title bar will indicate what case will be applied to the character you next enter. Text formatting Formatting options You can enter text in different formats in the Note Editor. Choose a formatting option before you start entering text. The formatting options are described in “Formatting options” below.
Category Font Style Bullets • • • • • • Bold Italic Underline Strikethrough Superscript Subscript • • ◦ • • • [Cancels bullet] You can insert a mathematical expression in textbook format into your note, as shown in the figure to the right. The Note Editor uses the same 2D editor that the Home and CAS views employ, activated via the menu button. Δ Inserting mathematical expressions Options (Continued) 1. Enter the text you want.
To import a note You can import a note from the Note Catalog into an app’s Info view and vice versa. Suppose you want to copy a note named Assignments from the Note Catalog into the Function Info view: 1. Open the Note Catalog. SN 2. Select the note Assignments and tap 3. Open the copy options for copying to the clipboard. SV (Copy)) The menu buttons change to give you options for copying: : Marks where the copying or cutting is to begin. end.
27 Programming in HP PPL This chapter describes the HP Prime Programming Language (HP PPL). In this chapter you’ll learn about: • programming commands • writing functions in programs • using variables in programs • executing programs • debugging programs • creating programs for building custom apps • sending a program to another HP Prime HP Prime Programs An HP Prime program contains a sequence of commands that execute automatically to perform a task.
Some built-in commands employ an alternative syntax whereby function arguments do not appear in parentheses. Examples include RETURN and RANDOM. Program Structure Programs can contain any number of subroutines (each of which is a function or procedure). Subroutines start with a heading consisting of the name, followed by parentheses that contain a list of parameters or arguments, separated by commas. The body of a subroutine is a sequence of statements enclosed within a BEGIN–END; pair.
Open the Program Catalog Press Sx (Program) to open the Program Catalog. The Program Catalog displays a list of program names. The first item in the Program Catalog is a built-in entry that has the same name as the active app. This entry is the app program for the active app, if such a program exists. See “App programs” on page 520 for more information. Program Catalog: buttons and keys Button or Key Purpose Opens the highlighted program for editing.
Button or Key Purpose (Continued) Save creates a copy of the selected program with a new name you are prompted to give. Rename renames the selected program. Sort sorts the list of programs. (Sort options are alphabetical and chronological). Delete deletes the selected program. Clear deletes all programs. Transmits the highlighted program to another HP Prime. Debugs the selected program. Runs the highlighted program. 500 S= or S\ Moves to the beginning or end of the Program Catalog.
Creating a new program In the following few sections, we will create a simple program that counts to three as an introduction to using the Program editor and its menus. 1. Open the Program Catalog and start a new program. Sx (Program) 2. Enter a name for the program. AA (to lock alpha mode) MYPROGRAM . 3. Press again. A template for your program is then automatically created.
The Program Editor Until you become familiar with the HP Prime commands, the easiest way to enter commands is to select them from ), or from the Commands the Catalog menu (D menu in the Program Editor ( ). To enter variables, symbols, mathematical functions, units, or characters, use the keyboard keys. Program Editor: buttons and keys The buttons and keys in the Program Editor are: Button or Key Meaning Checks the current program for errors.
Button or Key Meaning (Continued) Press J to return to the main menu. The commands in this menu are described in “Commands under the Cmds menu”, beginning on page 534. Opens a menu from which you can select common programming commands. The commands are grouped under the options: • Block • Branch • Loop • Variable • Function Press J to return to the main menu. The commands in this menu are described in “Commands under the Tmplt menu”, beginning on page 528.
Button or Key Meaning (Continued) S> and S< Moves the cursor to the end (or beginning) of the current line. You can also swipe the screen. S= and S\ Moves the cursor to the start (or end) of the program. You can also swipe the screen. A> and A< Moves the cursor one screen right (or left). You can also swipe the screen. E Starts a new line. C Deletes the character to the left of the cursor. SC Deletes the character to the right of the cursor. SJ Deletes the entire program. 1.
In this example we’ll select a LOOP command from the menu. 3. Select Loop and then select FOR from the sub-menu. Notice that a FOR_FROM_TO_DO _ template is inserted. All you need do is fill in the missing information. 4. Using the cursor keys and keyboard, fill in the missing parts of the command. In this case, make the statement match the following: FOR N FROM 1 TO 3 DO 5. Move the cursor to a blank line below the FOR statement. 6. Tap to open the menu of common programming commands. 7.
8. Fill in the arguments of the MSGBOX command, and type a semicolon at the end of the command (S+). 9. Tap to check the syntax of your program. 10. When you are finished, press Sx to return to the Program Catalog or H to go to Home view. You are ready now to execute the program. Run a Program From Home view, enter the name of the program. If the program takes parameters, enter a pair of parentheses after the program name with the parameters inside them each separated by a comma.
4. Tap three times to step through the FOR loop. Notice that the number shown increments by 1 each time. After the program terminates, you can resume any other activity with the HP Prime. If a program has arguments, when you press a screen appears prompting you to enter the program parameters. Multi-function programs If there is more than one EXPORT function in a program, when is tapped a list appears for you to choose which function to run.
1. In the Program Catalog, select MYPROGRAM. Sx Select MYPROGRAM 2. Tap . If there is more than one EXPORT function in a file, a list appears for you to choose which function to debug. While debugging a program, the title of the program or intra-program function appears at the top of the display. Below that is the current line of the program being debugged. The current value of each variable is visible in the main body of the screen.
The message box appears. Note that when each message box is displayed, you still have to dismiss it by tapping or pressing E. Tap and press E repeatedly to execute the program step-by-step. Tap to close the debugger at the current line of the program, or tap to run the rest of the program without using the debugger. Edit a program You edit a program using the Program Editor, which is accessible from the Program Catalog. 1. Open the Program Catalog. Sx 2.
: Cut the selection. : Copy the selection. 4. Select what you want to copy or cut (using the options listed immediately above). 5. Tap or . 6. Return to the Program Catalog and open the target program. 7. Move the cursor to where you want to insert the copied or cut code. 8. Press SZ (Paste). The clipboard opens. What you most recently copied or cut will be first in the list and highlighted already, so just tap . The code will be pasted into the program, beginning at the cursor location.
To share a program You can send programs between calculators just as you can send apps, notes, matrices, and lists. See “Sharing data” on page 44. The HP Prime programming language The HP Prime programming language allows you to extend the capabilities of the HP Prime by adding programs, functions and variables to the system. The programs you write can be either standalone or attached to an app. The functions and variables you create can be either local or global.
variables is given in chapter 22, “Variables”, beginning on page 423.) In a program you can declare variables for use only within a particular function. This is done using a LOCAL declaration. The use of local variables enables you to declare and use variables that will not affect the rest of the calculator. Local variables are not bound to a particular type; that is, you can store floating-point numbers, integers, lists, matrices, and symbolic expressions in a variable with any local name.
Note that EXPORT command for the variable RADIUS appears before the heading of the function where RADIUS is assigned. After you execute this program, a new variable named RADIUS appears on the USER GETRADIUS section of the Variables menu. Qualifying the name of a variable The HP Prime has many system variables with names that are apparently the same. For example, the Function app has a variable named Xmin, but so too does the Polar app, the Parametric app, the Sequence app, and the Solve app.
Program ROLLDIE We’ll first create a program called ROLLDIE. It simulates the rolling of a single die, returning a random integer between 1 and whatever number is passed into the function. In the Program Catalog create a new program named ROLLDIE. (For help, see page 501.) Then enter the code in the Program Editor. EXPORT ROLLDIE(N) BEGIN RETURN 1+RANDINT(N-1); END; The first line is the heading of the function.
L2(roll)+1 ▶ L2(roll); END; END; By omitting the EXPORT command when a function is declared, its visibility can be restricted to the program within which it is defined.
FOR k FROM 1 TO n DO ROLLDIE(sides)+ROLLDIE(sides) ▶ roll; results(roll)+1 ▶ results(roll); END; RETURN results; END; ROLLDIE(N) BEGIN RETURN 1+RANDINT(N-1); END; In Home view you would enter ROLLMANY(100,6) L5 and the results of the simulation of 100 rolls of two sixsided dice would be stored in list L5. The User Keyboard: Customizing key presses You can assign alternative functionality to any key on the keyboard, including to the functionality provided by the shift and alpha keys.
To activate persistent user mode, press SWSW. Notice that U appears in the title bar. The user keyboard will now remain active until you press SW again. If you are in user mode and press a key that hasn’t been re-assigned, the key’s standard operation is performed. Re-assigning keys Suppose you want to assign a commonly used function—such as ALOG—to its own key on the keyboard. Simply create a new program that mimics the syntax in the image at the right.
Tip Key names A quick way to write a program to re-assign a key is to press Z and select Create user key when you are in the Program Editor. You will then be asked to press the key (or key combination) you want to re-assign. A program template appears, with the internal name of the key (or key combination) added automatically. The first line of a program that re-assigns a key must specify the key to be reassigned using its internal name. The table below gives the internal name for each key.
Internal name of keys and key states (Continued) (Continued) (Continued) Key Programming in HP PPL Name S A + key + key AS + key n K_Div KS_Div KA_Div KSA_Div .
Internal name of keys and key states (Continued) (Continued) (Continued) Key Name S A + key + key AS + key W K_Help – KA_Help KSA_Help Z K_Menu KS_Menu KA_Menu KSA_Menu J K_Esc KS_Esc KA_Esc KSA_Esc K K_Cas KS_Cas KA_Cas KSA_Cas D K_Math KS_Math KA_Math KSA_Math F K_Templ KS_Templ KA_Templ KSA_Templ R K_Paren KS_Paren KA_Paren KSA_Paren B K_Eex KS_Eex KA_Eex KSA_Eex s K_Mul KS_Mul KA_Mul KSA_Mul S – – – – X K_Space KS_Space KA_Space KSA_Space App
Using dedicated program functions Redefining the View menu There are nine dedicated program function names, as shown in the table below. These functions are called when the corresponding keys shown in the table are pressed. These functions are designed to be written into a program that controls an app and used in the context of that app.
Customizing an app When an app is active, its associated program appears as the first item in the Program Catalog. It is within this program that you put functions to create a custom app. A useful procedure for customizing an app is illustrated below: 1. Decide on the HP app that you want to customize. The customized app inherits all the properties of the HP app. 2. Go to the Applications Library (I), highlight the HP app, tap and save the app with a unique name. 3.
1. In the Application Librray, select the Statistics 1Var app but don’t open it. I Select Statistics 1Var. 2. Tap . 3. Enter a name for the new app (such as DiceSimulation.) 4. Tap twice. The new app appears in the Application Library. 5. Open the Program Catalog. Sx 6. Tap the program to open it. Each customised app has one program associated with it. Initially, this program is empty. You customize the app by entering functions into that program.
These views will be activated by pressing M and P, but the function Plot() in our app program will actually launch the latter view after doing some configuration. Before entering the following program, press S I to open the Info editor and enter the text shown in the figure. This note will be attached to the app and will be displayed when the user selects the Start option from the View menu (or presses S I).
FOR k FROM 1 TO ROLLS DO roll:=ROLLDIE(SIDES)+ROLLDIE (SIDES); D2(roll-1):= D2(roll-1)+1; END; Xmin:= -0.1; Xmax:= MAX(D1)+1; Ymin:= −0.
BEGIN Xmin:=-0.1; Xmax:= MAX(D1)+1; Ymin:= −0.1; Ymax:= MAX(D2)+1; STARTVIEW(1,1); END; Symb() BEGIN SetSample(H1,D1); SetFreq(H1,D2); H1Type:=1; STARTVIEW(0,1); END; The ROLLMANY() routine is an adaptation of the program presented earlier in this chapter. Since you cannot pass parameters to a program called through a selection from a custom View menu, the exported variables SIDES and ROLLS are used in place of the parameters that were used in the previous versions.
2. Press V to see the custom app menu. Here you can reset the app (Start), set the number of sides of the dice, the number of rolls, and execute a simulation. 3. Select Set Rolls and enter 100. 4. Select Set Sides and enter 6. 5. Select Roll Dice. You will see a histogram similar to the own shown in the figure. 6. Press M to see the data and P to return to the histogram. 7. To run another simulation, press V and select Roll Dice. Program commands This section describes each program command.
Commands under the Tmplt menu Block The block commands determine the beginning and end of a sub-routine or function. There is also a Return command to recall results from sub-routines or functions. BEGIN END Syntax: BEGIN command1; command2;…; commandN; END; Defines a command or set of commands to be executed together. In the simple program: EXPORT SQM1(X) BEGIN RETURN X^2-1; END; the block is the single RETURN command. If you entered SQM1(8) in Home view, the result returned would be 63.
CASE Syntax: CASE IF test1 THEN commands1 END; IF test2 THEN commands2 END; … [DEFAULT commands] END; Evaluates test1. If true, executes commands1 and ends the CASE. Otherwise, evaluates test2. If true, executes commands2 and ends the CASE. Continues evaluating tests until a true is found. If no true test is found, executes default commands, if provided.
Example 1: This program determines which integer from 2 to N has the greatest number of factors. EXPORT MAXFACTORS(N) BEGIN LOCAL cur,max,k,result; 1 ▶ max;1 ▶ result; FOR k FROM 2 TO N DO SIZE(CAS.idivis(k)) ▶ cur; IF cur(1) > max THEN cur(1) ▶ max; k ▶ result; END; END; MSGBOX("Max of "+ max +" factors for "+result); END; In Home, enter MAXFACTORS(100).
RECT(); xincr := (Xmax - Xmin)/318; yincr := (Ymax - Ymin)/218; FOR X FROM Xmin TO Xmax STEP xincr DO FOR Y FROM Ymin TO Ymax STEP yincr DO color := RGB(X^3 MOD 255,Y^3 MOD 255, TAN(0.1*(X^3+Y^3)) MOD 255); PIXON(X,Y,color); END; END; WAIT; END; FOR DOWN Syntax: FOR var FROM start DOWNTO finish DO commands END; Sets variable var to start, and for as long as this variable is more than or equal to finish, executes the sequence of commands, and then subtracts 1 (decrement) from var.
END; d+1▶ d; END; RETURN sum==n; END; The following program displays all the perfect numbers up to 1000: EXPORT PERFECTNUMS() BEGIN LOCAL k; FOR k FROM 2 TO 1000 DO IF ISPERFECT(k) THEN MSGBOX(k+" is perfect, press OK"); END; END; END; REPEAT Syntax: REPEAT commands UNTIL test; Repeats the sequence of commands until test is true (not 0).
Variable These commands enable you to control the visibility of a user-defined variable. LOCAL Local. Syntax: LOCAL var1,var2,…varn; Makes the variables var1, var2, etc. local to the program in which they are found. EXPORT Syntax: EXPORT var1, var2, …, varn; Exports the variables var1, var2, etc. so they are globally available and appear on the User menu when you press a and select . Function These commands enable you to control the visibility of a user-defined function. EXPORT Export.
Commands under the Cmds menu Strings A string is a sequence of characters enclosed in double quotes (""). To put a double quote in a string, use two consecutive double quotes. The \ character starts an escape sequence, and the character(s) immediately following are interpreted specially. \n inserts a new line and two backslashes insert a single backslash. To put a new line into the string, press E to wrap the text at that point. ASC Syntax: ASC (string) Returns a list containing the ASCII codes of string.
STRING Syntax: STRING (object); Returns a string representation of object. The result varies depending on the type of object. Examples: String Result string(F1), when F1(X) = COS(X) "COS(X)" STRING(2/3) 0.666666666667 string(L1) when L1 = {1,2,3} "{1,2,3}" string(M1) when M1 = "[[1,2,3],[4,5,6]]" 1 2 3 4 5 6 INSTRING Syntax: INSTRING (str1,str2) Returns the index of the first occurrence of str2 in str1. Returns 0 if str2 is not present in str1.
MID Syntax: MID(str,pos, [n]) Extracts n characters from string str starting at index pos. n is optional, if not specified, extracts all the remainder of the string. Example: MID("MOMOGUMBO",3,5) returns "MOGUM", MID("PUDGE",4) returns "GE" ROTATE Syntax: ROTATE(str,n) Permutation of characters in string str. If 0 <=n < DIM(str), shifts n places to left. If –DIM(str) < n <= –1, shifts n spaces to right. If n > DIM(str) or n < –DIM(str), returns str.
coordinates using the Cartesian plane defined in the current app by the variables Xmin, Xmax, Ymin, and Ymax. The remaining thirteen work with pixel coordinates where the pixel 0,0 is the top left pixel of the GROB, and 320, 240 is the bottom right. Functions in this second set have a _P suffix to the function name. C→PX Converts from Cartesian coordinates to screen coordinates.
Pixels and Cartesian ARC_P ARC Syntax; ARC(G, x, y, r [ , a1, a2, c]) ARC_P(G, x, y, r [ , a1, a2, c]) Draws an arc or circle on G, centered on point x,y, with radius r and color c starting at angle a1 and ending on angle a2. G can be any of the graphics variables and is optional. The default is G0 r is given in pixels. c is optional and if not specified black is used. It should be specified in this way: #RRGGBB (in the same way as a color is specified in HTML).
sx2, sy2 are optional and if not specified will be the bottom right of the srcGRB. sx1, sy1 are optional and if not specified will be the top left of srcGRB. dx1, dy1 are optional and if not specified will be the top left of trgtGRB. c can be any color specified as #RRGGBB. If it is not specified, all pixels from srcGRB will be copied. Note Using the same variable for trgtGRB and srcGRB can be unpredictable when the source and destination overlap.
GROBW_P GROBW Syntax: GROBW(G) GROBW_P(G) Returns the width of G. G can be any of the graphics variables and is optional. The default is G0. INVERT_P INVERT Syntax: INVERT([G, x1, y1, x2, y2]) INVERT_P([G, x1, y1, x2, y2]) Executes a reverse video of the selected region. G can be any of the graphics variables and is optional. The default is G0. x2, y2 are optional and if not specified will be the bottom right of the graphic. x1, y1 are optional and if not specified will be the top left of the graphic.
PIXON_P PIXON Syntax: PIXON([G], x, y [ ,color]) PIXON_P([G], x, y [ ,color]) Sets the color of the pixel G with coordinates x,y to color. G can be any of the graphics variables and is optional. The default is G0, the current graphic. Color can be any color specified as #RRGGBB. The default is black.
EXPORT BOX() BEGIN RECT(); RECT_P(40,90,#0 00000); WAIT; END; The program below also uses the RECT_P command. In this case, the pair of arguments 320 and 240 correspond to x2 and y2. The program produces are rectangle with a black edge and a red fill.
TEXTOUT_P TEXTOUT Syntax: TEXTOUT(text [ ,G], x, y [ ,font, c1, width, c2]) TEXTOUT_P(text [ ,G], x, y [ ,font, c1, width, c2]) Draws text using color c1 on graphic G at position x, y using font. Do not draw text more than width pixels wide and erase the background before drawing the text using color c2. G can be any of the graphics variables and is optional. The default is G0. Font can be: 0: current font selected on the Homes Settings screen, 1: small font 2: large font.
TEXTOUT_P(K ,35,0,2,#FFFFFF, 100,#333399); TEXTOUT_P(A ,90,30,2,#000000,100, #99CC33); sign*-1 ▶ sign; K+1 ▶ K; UNTIL 0; END; END; The program executes until the user presses O to terminate. Matrix The matrix commands described in this section are in addition to the matrix functions described in “Matrix functions and commands” on page 474. Some matrix commands take as their argument the matrix variable name on which the command is applied.
EDITMAT Syntax: EDITMAT(name) Starts the Matrix Editor and displays the specified matrix. If used in programming, returns to the program when user presses . Even though this command returns the matrix that was edited, EDITMAT cannot be used as an argument in other matrix commands. REDIM Syntax: REDIM(name, size) Redimensions the specified matrix (name) or vector to size. For a matrix, size is a list of two integers (n1,n2). For a vector, size is a list containing one integer (n).
App Functions These commands allow you to launch any HP app, bring up any view of the current app, and change the options in the View menu. STARTAPP Syntax: STARTAPP("name") Starts the app with name. This will cause the app program’s START function to be run, if it is present. The app’s default view will be started. Note that the START function is always executed when the user taps in the Application Library. This also works for user-defined apps. Example: STARTAPP("Function") launches the Function app.
You can also launch views that are not specific to an app by specifying a value for n that is less than 0: Home Screen:-1 Home Settings:-2 Memory Manager:-3 Applications Library:-4 Matrix Catalog:-5 List Catalog:-6 Program Catalog:-7 Notes Catalog:-8 VIEW Syntax: VIEW ("string"[,program_name]) BEGIN Commands; END; Adds a custom option to the View menu. When string is selected, runs program_name. See “The DiceSimulation program” on page 524.
BITSL Syntax: BITSL(int1 [,int2]) Bitwise Shift Left. Takes one or two integers as input and returns the result of shifting the bits in the first integer to the left by the number places indicated by the second integer. If there is no second integer, the bits are shifted to the left by one place. Examples: BITSL(28,2) returns 112 BITSL(5) returns 10. BITSR Syntax: BITRL(int1 [,int2]) Bitwise Shift Right.
GETBITS Syntax: GETBITS(#integer) Returns the number of bits used by integer, expressed in the default base. Example: GETBITS(#22122) returns #20h or 32 R→B Syntax: R→B(integer) Converts a decimal integer (base 10) to an integer in the default base. Example: R→B(13) returns #1101b (if the default base is binary) or #Dh (if the default base is hexadecimal). SETBITS Syntax: SETBITS(#integer[m] [,bits]) Sets the number of bits to represent integer. Valid values are in the range –64 to 65.
Returns true (not zero) if the user selects an object, otherwise return false (0). Example: CHOOSE (N,"PickHero", "Euler","Gauss ","Newton"); IF N==1 THEN PRINT("You picked Euler"); ELSE IF N==2 THEN PRINT("You picked Gauss");ELSE PRINT("You picked Newton"); END; END; After execution of CHOOSE, the value of N will be updated to contain 0, 1, 2, or 3. The IF THEN ELSE command causes the name of the selected person to be printed to the terminal.
Keys 0–13 { 0 1 3 6 2 7 8 9 12 5 11 4 13 10 Keys 14–19 Keys 20–25 Keys 26–30 Keys 31–35 Keys 36–40 Keys 41–45 Keys 46–50 Figure 27-1: Numbers of the keys INPUT Syntax: INPUT(var [,"title", "label", "help", reset]); Opens a dialog box with the title text title, with one field named label, displaying help at the bottom and using the reset value if S J is pressed. Updates the variable var if the user taps and returns 1. If the user taps , it does not update the variable, and returns 0.
ISKEYDOWN Syntax: ISKEYDOWN(key_id); Returns true (non-zero) if the key whose key_id is provided is currently pressed, and false (0) if it is not. MOUSE Syntax: MOUSE[(index)] Returns two lists describing the current location of each potential pointer (or empty lists if the pointers are not used). The output is {x , y, original z, original y, type} where type is 0 (for new), 1 (for completed), 2 (for drag), 3 (for stretch), 4 (for rotate), and 5 (for long click).
PRINT Syntax: PRINT(expression or string); Prints the result of expression or string to the terminal. The terminal is a program text output viewing mechanism which is displayed only when PRINT commands are executed. When visible, you can press \ or = to view the text, Cto erase the text and any other key to hide the terminal. Pressing O stops the interaction with the terminal. PRINT with no argument clears the terminal. There are also commands for outputting data in the Graphics section.
More %CHANGE Syntax: %CHANGE(x,y) The percentage change in going from x to y. Example: %CHANGE(20,50) returns 150. %TOTAL Syntax: %TOTAL(x,y) The percentage of x that is y. Example: %TOTAL(20,50) returns 250. CAS Syntax: CAS.function() or CAS.variable Executes the function or returns the variable using the CAS. EVALLIST Syntax: EVALLIST({list}) Evaluates the content of each element in a list and returns an evaluated list.
second list. The plus operator between them adds the two elements until there are no more pairs. With two lists, the numbers appended to & can have two digits; in this case, the first digit refers to the list number (in order from left to right) and the second digit can still only be from 1 to 9 inclusive. EXECON can also begin operating on a specified element in a specified list.
TYPE Syntax: TYPE(object) Returns the type of the object: 0: Real 1: Integer 2: String 3: Complex 4: Matrix 5: Error 6: List 8: Function 9: Unit 14.?: cas object. The fractional part is the cas type. Variables and Programs The HP Prime has four types of variables: Home variables, App variables, CAS variables, and User variables. You can retrieve these variables from the Variable menu (a).
variables represent the definitions and settings you make when working with apps interactively. As you work through an app, the app functions may store results in app variables as well. In a program, app variables are used to edit an app’s data to customize it and to retrieve results from the app’s operation. CAS variables are similar to the Home real variables A–Z, except that they are lowercase and designed to be used in CAS view and not Home view.
App variables Not all app variables are used in every app. S1Fit, for example, is only used in the Statistics 2Var app. However, many of the variables are common to the Function, Advanced Graphing, Parametric, Polar, Sequence, Solve, Statistics 1Var, and Statistics 2Var apps. If a variable is not available in all of these apps, or is available only in some of these apps (or some other app), then a list of the apps where the variable can be used appears under the variable name.
GridLines Turns the background line grid in Plot View on or off. In Plot Setup view, check (or uncheck) GRID LINES. In a program, type: Hmin/Hmax Statistics 1Var 0 GridLines—to turn the grid lines on (default). 1 GridLines—to turn the grid lines off. Defines the minimum and maximum values for histogram bars. In Plot Setup view for one-variable statistics, set values for HRNG. In a program, type: n 1 Hmin n 2 Hmax where n 1 n 2 Hwidth Statistics 1Var Sets the width of histogram bars.
Nmin/Nmax Sequence Defines the minimum and maximum values for the independent variable. Appears as the N RNG fields in the Plot Setup view. In Plot Setup view, enter values for N Rng. In a program, type: n1 Nmin n2 Nmax where n 1 n 2 Recenter Recenters at the cursor when zooming. From Plot-Zoom-Set Factors, check (or uncheck) Recenter. In a program, type: 0 Recenter— to turn recenter on (default). 1 Recenter— to turn recenter off.
step Polar Sets the step size for the independent variable. In Plot Setup view, enter a value for Step. In a program, type: n step where n 0 Tmin/Tmax Parametric Sets the minimum and maximum independent variable values. In Plot Setup view, enter values for T Rng. In a program, type: n1 Tmin n2 Tmax where n 1 n 2 Tstep Parametric Sets the step size for the independent variable. In Plot Setup view, enter a value for T Step.
Ymin/Ymax Sets the minimum and maximum vertical values of the plot screen. In Plot Setup view, enter the values for Y Rng. In a program, type: n1 Ymin n2 Ymax where n 1 n 2 Xzoom Sets the horizontal zoom factor. In Plot View, press then Factors,select it and tap Zoom and tap . . Scroll to Set . Enter the value for X In a program, type: n Xzoom where n 0 The default value is 4. Yzoom In Plot View, tap Factors and tap and tap . then . Scroll to Set .
E0...E9 Solve Contains an equation or expression. In Symbolic view, select one of E0 through E9 and enter an expression or equation. The independent variable is selected by highlighting it in Numeric view. In a program, type (for example): X+Y*X-2=Y▶ E1 F0...F9 Function Contains an expression in X. In Symbolic View, select one of F0 through F9 and enter an expression. In a program, type (for example): SIN(X) ▶ F1 H1...
Method Inference Determines whether the Inference app is set to calculate hypothesis test results or confidence intervals. In Symbolic view, make a selection for Method. In a program, type: R0...R9 Polar 0 Method—for Hypothesis Test 1 Method—for Confidence Interval Contains an expression in . In Symbolic view, select one of R0 through R9 and enter an expression. In a program, type (for example): SIN( ) R1 S1...
Type Inference Determines the type of hypothesis test or confidence interval. Depends upon the value of the variable Method. From Symbolic View, make a selection for Type. Or, in a program, store the constant number from the list below into the variable Type.
Numeric view variables C0...C9 Statistics 2Var Contain lists of numerical data. In Numeric view, enter numerical data in C0 through C9. In a program, type: LIST Cn where n = 0 , 1, 2, 3 ... 9 and LIST is either a list or the name of a list. D0...D9 Statistics 1Var Contain lists of numerical data. In Numeric view, enter numerical data in D0 through D9. In a program, type: LIST Dn where n = 0 , 1, 2, 3 ... 9 and LIST is either a list or the name of a list.
NumYStart Advanced Graphing Sets the starting value for the Y-values in a table in Numeric view. From Numeric Setup view, enter a value for NUMYSTART. In a program, type: n NumStep Function Parametric Polar Sequence NumYStart Sets the step size (increment value) for the independent variable in Numeric view. From Numeric Setup view, enter a value for NUMSTEP.
NumXZoom Advanced Graphing Sets the zoom factor for the values in the X column in the Numeric view. From Numeric Setup view, type in a value for NUMXZOOM. In a program, type: n NumXZoom where n 0 NumYZoom Advanced Graphing Sets the zoom factor for the values in the Y column in the Numeric view. From Numeric Setup view, type in a value for NUMYZOOM. In a program, type: n NumYZoom where n 0 Inference app variables The following variables are used by the Inference app.
Mean1 Sets the value of the mean of a sample for a 1-mean hypothesis test or confidence interval. For a 2-mean test or interval, sets the value of the mean of the first sample. From Numeric view, set the value of x or x 1 . In a program, type: n Mean2 Mean1 For a 2-mean test or interval, sets the value of the mean of the second sample. From Numeric view, set the value of x2 . In a program, type: n 0 Mean2 Sets the assumed value of the population mean for a hypothesis test.
Pooled Determine whether or not the samples are pooled for tests or intervals using the Student’s T-distribution involving two means. From the Numeric view, set the value of Pooled. In a program, type: s1 0 Pooled—for not pooled (default). 1 Pooled—for pooled. Sets the sample standard deviation for a hypothesis test or confidence interval. For a test or interval involving the difference of two means or two proportions, sets the sample standard deviation of the first sample.
x1 Sets the number of successes for a one-proportion hypothesis test or confidence interval. For a test or interval involving the difference of two proportions, sets the number of successes of the first sample. From the Numeric view, set the value of x1. In a program, type: n x2 x1 For a test or interval involving the difference of two proportions, sets the number of successes of the second sample. From the Numeric view, set the value of x2.
IPYR Interest per year. Sets the annual interest rate for a cash flow. From the Numeric view of the Finance app, enter a value for I%YR. In a program, type: n IPYR where n 0 NbPmt Number of payments. Sets the number of payments for a cash flow. From the Numeric view of the Finance app, enter a value for N. In a program, type: n NbPmt where n 0 PMTV Payment value. Sets the value of each payment in a cash flow. From the Numeric view of the Finance app, enter a value for PMTV.
GSize Group size. Sets the size of each group for the amortization table. From the Numeric view of the Finance app, enter a value for Group Size. In a program, type: n GSize Linear Solver app variables The following variables are used by the Linear Solver app. They correspond to the fields in the app's Numeric view. LSystem Contains a 2x3 or 3x4 matrix which represents a 2x2 or 3x3 linear system. From the Numeric view of the Linear Solver app, enter the coefficients and constants of the linear system.
SideC The length of Side c. Sets the length of the side opposite the angle C. From the Triangle Solver Numeric view, enter a positive value for c. In a program, type: n SideC where n 0 AngleA The measure of angle A. Sets the measure of angle A. The value of this variable will be interpreted according to the angle mode setting (Degrees or Radians). From the Triangle Solver Numeric view, enter a positive value for angle A. In a program, type: n AngleA where n 0 AngleB The measure of angle B.
RECT Corresponds to the status of in the Numeric view of the Triangle Solver app. Determines whether a general triangle solver or a right triangle solver is used. From the Triangle Solver view, tap . In a program, type: 0RECT—for the general Triangle Solver 1RECT—for the right Triangle Solver Home Settings variables The following variables (except Ans) are found in Home Settings. The first four can all be over-written in an app's Symbolic Setup view.
HComplex Date Sets the complex number mode for the Home view. In Home Settings, check or uncheck the Complex field. Or, in a program, type: 0 HComplex—for OFF. 1 HComplex—for ON. Contains the system date. The format is YYYY.MMDD. This format is used irrespective of the format set on the Home Settings screen. On page 2 of Home Settings, enter values for Date. In a program, type: YYYY.
Entry Contains an integer that indicates the entry mode. In Home Settings, select an option for Entry. In a program, enter: 0 Entry—for Textbook 1 Entry—for Algebraic 2 Entry—for RPN Integer Base Bits Returns or sets the integer base. In Home Settings, select an option for the first field next to Integers. In a program, enter: 0 Base—for Binary 1 Base—for Octal 2 Base—for Decimal 3 Base—for Hexadecimal Returns or sets the number of bits for representing integers.
Symbolic Setup variables The following variables are found in the Symbolic setup of an app. They can be used to overwrite the value of the corresponding variable in Home Settings. AAngle Sets the angle mode. From Symbolic setup, choose System, Degrees, or Radians for angle measure. System (default) will force the angle measure to agree with that in Home Settings. In a program, type: AComplex 0 AAngle—for System (default). 1 AAngle—for Degrees. 2 AAngle—for Radians.
AFormat Defines the number display format used for number display in the Home view and to label axes in the Plot view. From Symbolic setup, choose Standard, Fixed, Scientific, or Engineering in the Number Format field. In a program, store the constant number into the variable AFormat.
580 Programming in HP PPL
28 Basic integer arithmetic The common number base used in contemporary mathematics is base 10. By default, all calculations performed by the HP Prime are carried out in base 10, and all results are displayed in base 10. However, the HP Prime enables you to carry out integer arithmetic in four bases: decimal (base 10), binary, (base 2), octal (base 8), and hexadecimal (base 16). For example, you could multiply 4 in base 16 by 71 in base 8 and the answer is E4 in base 16.
represents 22810. In this case, the base marker h indicates that the number is to interpreted as a hexadecimal number: E416. Note that with integer arithmetic, the result of any calculation that would return a remainder in floating-point arithmetic is truncated: only the integer portion is presented. Thus #100b/#10b gives the correct answer: #10b (since 410/210 is 210). However, #100b/ #11b gives just the integer component of the correct result: #1b.
Note that if you change the default base, any calculation in history that involves integer arithmetic for which you did not explicitly add a base marker will be resisplayed in the new base. In the example at the right, the first calculation explicitly included base markers (b for each operand). The second calculation was a copy of the first but without the base markers. The default base was then changed to hex.
Examples of integer arithmetic The operands in integer arithmetic can be of the same base or of mixed bases. Integer calculation Decimal equivalent #10000b+#10100b =#100100b 16 + 20 = 36 #71o–#10100b = #45o 57 – 20 = 37 #4Dh * #11101b = #8B9h 77 × 29 = 2233 #32Ah/#5o = #A2h 810/5 = 162 Mixed-base arithmetic With one exception, where you have operands of different bases, the result of the calculation is presented in the base of the first operand.
Integer manipulation The result of integer arithmetic can be further analyzed, and manipulated, by viewing it in the Edit Integer dialog. 1. In Home view, use the cursor keys to select the result of interest. 2. Press Sw (Base). The Edit Integer dialog appears. The Was field at the top shows the result you selected in Home view. The hex and decimal equivalents are shown under the Out field, followed by a bit-by-bit representation of the integer.
: returns the one’s complement (that is, each bit in the specified wordsize is inverted: a 0 is replaced by 1 and a 1 by 0. The new integer represented appears in the Out field (and in the hex and decimal fields below it). : activates edit mode. A cursor appears and you can move abut the dialog using the cursor keys. The hex and decimal fields can be modified, as can the bit representation. A change in one such field automatically modifies the other fields. : closes the dialog and saves your changes.
Appendix A Glossary Glossary app A small application, designed for the study of one or more related topics or to solve problems of a particular type. The built-in apps are Function, Advanced Graphing, Geometry, Spreadsheet, Statistics 1Var, Statistics 2Var, Inference, DataStreamer, Solve, Linear Solver, Triangle Solver, Finance, Parametric, Polar, Sequence, Linear Explorer, Quadratic Explorer, and Trig Explorer. An app can be filled with the data and solutions for a specific problem.
588 command An operation for use in programs. Commands can store results in variables, but do not display results. expression A number, variable, or algebraic expression (numbers plus functions) that produces a value. function An operation, possibly with arguments, that returns a result. It does not store results in variables. The arguments must be enclosed in parentheses and separated with commas. Home view The basic starting point of the calculator. Most calculations can be done in Home view.
Glossary matrix A two-dimensional array of real or complex numbers enclosed by square brackets. Matrices can be created and manipulated by the Matrix Editor and stored in the Matrix Catalog. Vectors are also handled by the Matrix Catalog and Editor. menu A choice of options given in the display. It can appear as a list or as a set of touch buttons across the bottom of the display. note Text that you write in the Note Editor. It can be a general, standalone note or a note specific to an app.
590 Glossary
Appendix B Troubleshooting Calculator not responding If the calculator does not respond, you should first try to reset it. This is much like restarting a PC. It cancels certain operations, restores certain conditions, and clears temporary memory locations. However, it does not clear stored data (variables, apps, programs, etc.). To reset Turn the calculator over and insert a paper clip into the Reset hole just above the battery compartment cover. The calculator will reboot and return to Home view.
Operating limits Operating temperature: 0 to 45C (32 to 113F). Storage temperature: –20 to 65C (– 4 to 149F). Operating and storage humidity: 90% relative humidity at 40C (104F) maximum. Avoid getting the calculator wet. The battery operates at 3.7V with a capacity of 1500mAh (5.55Wh). Status messages The table below lists the most common general error messages and their meanings. Some apps and the CAS have more specific error messages that are selfexplanatory.
Troubleshooting Message Meaning (Continued) Syntax error The function or command you entered does not include the proper arguments or order of arguments. The delimiters (parentheses, commas, periods, and semi-colons) must also be correct. Look up the function name in the index to find its proper syntax. No functions checked You must enter and check an equation in the Symbolic view before entering the Plot view. Receive error Problem with data reception from another calculator. Resend the data.
594 Troubleshooting
Appendix C Product regulatory information Federal Communications Commission notice This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation.
Declaration of Conformity for products Marked with FCC Logo, United States Only This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation. If you have questions about the product that are not related to this declaration, write to: Hewlett-Packard Company P.O.
European Union Regulatory Notice Products bearing the CE marking comply with the following EU Directives: • Low Voltage Directive 2006/95/EC • EMC Directive 2004/108/EC • Ecodesign Directive 2009/125/EC, where applicable CE compliance of this product is valid if powered with the correct CE-marked AC adapter provided by HP.
Japanese Notice Korean Class Notice Disposal of Waste Equipment by Users in Private Household in the European Union 598 This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment.
Chemical Substances HP is committed to providing our customers with information about the chemical substances in our products as needed to comply with legal requirements such as REACH (Regulation EC No 1907/2006 of the European Parliament and the Council). A chemical information report for this product can be found at: http://www.hp.
600 Product regulatory information
Index A adapter 12 adaptive graphing 99 Advanced Graphing app 69, 125–134 Plot Gallery 134 trace options 129 variables, summary of 432 algebra functions 324–325 algebraic entry 32, 36, 47 algebraic precedence 39 alternative hypothesis 240 amortization 293–294 angle measure 31, 56 annunciators 14 Ans (last answer) 41 antilogarithm common 310 natural 310 app commands 546 creating 107, 134, 522 customizing See app, creating definition of 587 deleting 72 functions See functions HP apps See apps, HP library 7
buttons command 20 menu 20 See also menu buttons C cables 45 calculations CAS 54, 324–347 confidence intervals 253 financial 287–294 geometric 150 in Home view 36, 309–323 statistical 218, 233 with units 444 calculus functions 326–330 CAS 53–59 calculations using 54, 324–347 functions algebra 324–325 calculus 326–330 integer 337–339 plot 346–347 polynomial 339–345 rewrite 332–337 solve 330–332 menu 324–347 settings 30, 55 view 13 cash flow 289 Catlg menu 378–421 cells entering content 201 formatting 208 i
decimal mark 33 decimal zoom 90, 93, 102 default settings, restoring 21, 87, 100, expression defining 82, 112 extremum 122, 132 define your own fit 232 degree symbol 21 deleting apps 72 characters 21 lists 455 matrices 464 notes 490 programs 500 statistical data 217, 230 determinant 475 dilation 162 display 13 annunciators 14 clearing 13 engineering 31 fixed 31 fraction 31 menu buttons 14 parts of 14 scientific 31 standard 31 DMS format 21 document conventions 9 drag 17 drawing commands 536–544 F 106 E
keyboard 309–312 Linear Explorer 376 Linear Solver 374 number 313–314 plot 346–347 polynomial 339–345 probability 317–322 rewrite 332–337 solve 330–332 Solve app 349 spreadsheet 210, 349–363 Statistics 1Var 363–364 Statistics 2Var 365–366 Triangle Solver 374–376 G geometric objects 153–160 geometric transformations 161–164 Geometry app 69, 135–193 commands 165–193 creating objects in Plot view 141 in Symbolic view 148 functions 165–193 naming objects 142 objects, types of 153–160 Plot view, menu buttons 1
Inference app 69, 239–257 confidence intervals 253–257 functions 366–371 hypothesis tests 245–252 importing statistics 243 variables Numeric 568 Results 438 summary of 437 Info, Solve app 265 input form 29 insufficient memory 592 insufficient statistics data 592 integer 32 integer arithmetic 581 integer base 56 integer commands, programming 547 integer functions 337–339 integer zoom 90, 93, 102 integer, editing 585–586 intercepts 132 invalid dimension 592 statistics data 592 K keyboard 18 customizing 516
matrix calculations 463 negating elements 472 raised to a power 471 reduced-row echelon 486 singular value decomposition 485 storing 464, 468, 469 swap row 545 transposing 486 variables 428, 463 maximum real number 36 measurements See units 443 menu App 307 CAS 324–347 Catlg 378–421 context sensitive 20 Math 313–323 shortcuts 28 User 307 menu buttons 20 in Linear Solver app 269 in Numeric view 104 in Plot view general 96 Geometry app 146 in Spreadsheet app 207 in Statistics 1Var app 213, 216 in Statistics 2
physics constants 449 pinch 17 plot box-and-whisker 220 cobweb 281 color of 85 defined in Geometry app 160 functions 346–347 line 220 one-variable statistics 219 pareto 221 stairsteps 281 statistical data one-variable 219 two-variable 234 Plot and Numeric views together 106 Plot Gallery 134 Plot Setup view 76 common operations in 96–100 Plot view 75 common operations in 88–95 in Geometry app 141 menu buttons 96, 146 variables 558–562 zoom 88–94 points 153 Polar app 70, 277–280 variables 440 polygons 157 pol
Sequence app 70, 281–286 graph types 281 variables 442 settings 30, 428 CAS 30, 55 sharing data 44 shift keys 22 shortcut palettes 20 shortcuts in Geometry 147 in menus 28 Solve app 70, 259–266 functions 349 limitations 264 messages 265 one equation 260 several equations 263 variables, summary of 431 solve functions 330–332 sort apps 71, 72 special symbols palette 21, 25 split-screen viewing 91, 106 Spreadsheet app 70, 195–210 cell referencing 200 entering content 201 external functions 203 external referen
T tables, custom 103 template key 24 templates 20 test mode See exam mode text 23 textbook entry 32, 33, 36, 47 theme 34 time 16, 34 time-value-of-money problems 287 title bar 14 Toolbox menus 29, 307 touch options 16 trace 94–95, 129 transformations, geometric 161–164 Triangle Solver app 70, 295–298 functions 374–376 variables Numeric 573 summary of 441 Trig Explorer app 70, 304–306 trig zoom 90, 94, 102 trigonometric fit 232 functions 316 troubleshooting 591 turn on and off 12 TVM problems 287 Two-Propor
views definition of 589 in apps 73 Numeric 77 Numeric Setup 78 Plot 75 Plot Setup 76 Symbolic 73 Symbolic Setup 74 Views menu 91, 521 610 W wireless network 34 wordsize 583 Z Z-Intervals 253–255 zoom examples of 91–94 factors 88 in Numeric view 100–102 in Plot view 88–94 keys for 89, 101 types of 89–90, 102 Index
