HP49G GRAPHING CALCULATOR ADVANCED USER’S GUIDE Version 1 HP 49G ciLe.; (¿M' (iik 0 IT fl • ^ ’ < ► /¡'0 0 4V c <3 (3 fl « oaaaa o a ^ /3 a G Ej lZj Ll^i CEJ 1-?lJ J QD vIaj Caj l~ j G?1 ZJ2 CjJ Li-J C±..
Contents Preface vii Material covered................................................................................... vii The HP 49G documentation set ........................................................viii Chapter 1: Entering commands 1-1 Keyboard entry.................................................................................... 1-1 Subject-specific menus ....................................................................... 1-1 Sub-menus................................................
Chapter 4: The Stack 4-1 Using the stack .................................................................................... 4-1 Example stack calculations ................................................................4-2 Using a one-argument command................................................ 4-2 Using a multi-argument command ............................................ 4-3 Multi-conmrand calculations.......................................................
Chapter 6: Unit objects 6-1 Ovei^view of the Units application.................................................. 6-1 Unit objects .......................................................................................... 6-2 To create a imit object.................................................................... 6-2 To assemble a imit object from the stack...................................... 6-3 Unit prefixes ...................................................................................
Chapter 9: Lists and Sequences 9-1 Creating Lists....................................................................................... 9-1 To enter a list from the keyboard.................................................9-1 To assemble a list from a set of stack objects ...............................9-1 To append a new object to the beginning of a list ....................9-1 To append a new object to the end of a list ............................... 9-2 List Processing................................
Chapter 11: Memory 11-1 How memory is structured.............................................................. 11-1 Accessing port contents.................................................................... 11-2 Backup objects.................................................................................... 11-2 Backing up and restoring HOME ............................................... 11-3 Storing and deleting backup objects ..........................................
Chapter 13: Customization 13-1 Creating menus.................................................................................. 13-1 To create a custom menu............................................................ 13-1 To display a custom menu.......................................................... 13-2 Customizing the keyboard......................................................... 13-2 User mode ........................................................................................
Preface This guide contains infomiation on the advanced fimctionality of the HP 49G. It is a supplement to the Pocket Guide and User’s Guide that is shipped with the HP 49G. Material covered This guide contains the following information: • Chapter 1, Entering commands contains information on the different ways that you can enter and use commands. • Chapter 2, System flags contains information on using the HP 49G’s flags, and the conunands to control them.
• Chapter 14, Computer algebra commands describes each of the computer algebra commands that the calculator contains, and what each command does. The HP 49G documentation set The HP 49G docmnentation set is a mixture of hard copy documentation and documentation available from the HP Calculators web site. You can find all of the documentation for the HP 49G on the HP Calculators web site, at the following address: http://www.hp.com/calculators/graphing/49g_info.
Chapter 1 Entering commands There are a ramrber of ways you can enter a command: • by pressing the key or keys for the command • by selecting the command from a subject-specific menu ® by selecting the command from the command catalog • by typing the command on the command line. Keyboard entry The most commonly needed commands can be entered directly from the keyboard by pressing one or two keys. For example, to enter the SIN command, press the (SIN) key; to enter the LOG command, press (r)(iog).
units menu i arithmetic menu i complex number menu (0 SEE)) base menu (0 {№ Tliese subject-specific menus have keys allocated to them on the keyboard. There are many other subject-specific menus. For example, the math menu and the various Computer Algebra System sub-menus can be selected from the Applications menu: 1. Press ®. The Applications menu is displayed. 2. Press ®. The last page of the Applications menu is displayed. 3.
Entering a command From a sub-menu 1 With the main menu displayed, highlight the name of the sub-menu. You can do this by: ® pressing ® imtil the sub-menu name is highlighted or • pressing the number key that corresponds to the number of the sub-menu. For example, to highlight the REAL sub-menu in the above example you could press 5.) 2. Press OK or (ENTER). The sub-menu is displayed. 3. Highlight the name of the command you want to enter.
Command catalog The HP 49G provides a single choose list that contains all its commands. This is called the command catalog. Displaying the command catalog 1. Press A choose list is displayed. This is the command catalog. RAD CATAlD(i: 6S3 CtiHHADDS ■ :hoh K HCH ¿1 2. Locate the command that you want to enter. (See the next section.) isnsiKn 3. Press OK or (MS)If you are working in algebraic mode, the command you selected appears on the command line ready for you to specify arguments.
commands are displayed in your currently selected system font. If, for example, you have chosen System 8 as your current system font, you will see only four commands per page. Searching For a command in the command catalog The majority of commands can be selected from the command catalog by searching on the first character of the command’s name. 1. Press the keys for the first character—or first few characters—of the command’s name. For example, to find tire HALFTAN command, type (SM) H or (EES (M) HA.
While the alpha keyboard is active, you can also search for a command that begins with a special character by typing that character and then one or more of the next alphabetical characters. The keystrokes for non-alphabetic characters can be fomid in the Characters catalog. For example, the keystrokes for Z are 0 and S. Therefore, to search for the E+ command in the command catalog, you display the catalog and press 0 S. The Characters catalog- accessed by pressing chapter 2 of the User’s Guide.
Chapter 2 System Flags System flags provide you with some control over how the HP 49G behaves and displays infomiation. For example, by setting flag -60, you can lock the alpha keyboard by pressing (SM) once rather than twice. Clearing flag -60 retimrs the mode to its default setting (where (IPHA) must be pressed twice to lock the alpha keyboard). Displaying system Flags 1. Press (MODE) to display the Calculator Modes input form. 2. Press FLAGS.
Setting and clearing Flags Method 1 Use this method only if the flag you want to change is listed in the System Flags list. 1. With the System Flags list displayed, higlilight the flag that you want to set or clear. You can do this by either: ® pressing the ® or ® keys imtil the flag you want is highlighted or • typing the first digit of the number of the flag. See the previous section for instructions on displaying the flags. 2. Press CHK.
Setting or clearing several Flags at once In algebraic mode, the syntax is: command^llist}') In RPN mode, enter a list of the flags you want to set or clear on the first level of the stack and then enter the appropriate command. For example, to set flags -19 and-40 in algebraic mode, you enter SF({-19,-401) and press (ENTER). In RPN mode, you enter {-19 ^0} onto level 1 of the stack, enter SF onto the command line and press (ENTER').
Flag commands The flag commands are listed and explained in the table below. The flag commands enable you to set and clear flags as well as having a value returned that indicates the status of a specified flag: 1 if the flag is set, 0 if the flag is clear. Description Command SF Sets the specified flag. CF Clears the specified flag. FS? Returns true (1) if the specified flag is set and false (0) if the flag is clear.
Chapter 3 Command line operations The command line is where you enter and edit conunands and objects. The HP 49G provides numerous tools to assist you when working on the conunand line. Some of these tools have their own key; others can be selected from the command line editor’s Tool menu. Activating the command line The way you activate the command line depends on whether you intend to create a new object or edit an existing object. To create a new object, just start typing.
Positioning the cursor Wlien editing the object on the command line, you will almost always need to reposition the cursor. Main methods: single-line command line Press @ or ® to move the cursor left or right respectively. To go directly to the last chai'acter on the command line, press or 0®. To go directly to the first character on the command line, press 0® or 0® .
Helpful commands and sub-menus Like all other HP 49G applications, the command line editor has its own Tool menu. This menu is displayed by pressing (TOOp while the command line is active (that is, while the cursor is blinking). You then select a command by pressing the corresponding fmrction key. The conunands that provide ways of positioning the cursor are: -SKIP Moves the cursor to the beginning of the current word (that is, to the beginning of the word in which the cursor is currently placed).
The Find command is on the Search sub-menu. You can use this command to send the ciu'sor to the character or character string you specify. See “Find” on page 3-8 for more information. FIND Selecting characters The HP 49G provides a number of commands that work on selected text (such as copy and cut). To select characters, you mark the beginning of the selection and the end of the selection. 1. Position the cursor at the beginning of your selection.
Editing the command Line Deleting characters The simplest way to delete a character is to position the cm'sor to the immediate right of the character and press @Other ways of deleting characters are provided by commands on the Tool menu for the command line editor. The menu is displayed by pressing when the command line is active.
Inserting characters By default, any character you enter on the command line will be inserted between the characters on either side of the cursor. To replace characters rather than insert them, you de-activate insert mode. Each character you enter will then replace—that is, overwrite—the character directly below the cursor. To de-activate (or activate) insert mode: 1. With the conunand line active, press (TOOp.fiSP KVZ HEK R= 'K' tHPHEi____ 2. If the INS conunand is not displayed, press imtil it is.
Evaluating components oF the command line If there is a component of your object that could be evaluated—such as a mathematical expression—^you can select the component and evaluate it. The result of tlie evaluation replaces the component. To evaluate a component, make sure that the Tool menu for the command line editor is displayed. (Press (TOOp if it is not.) 1. Select the component of the object that you want to evaluate. See “Selecting characters” on page 3-4 for instructions. 2.
Find and replace Tlie HP 49G provides a number of search aird replace commands to help you edit multiline objects (such as arrays and programs). These are available from the Search menu (which is a sub-menu of the Tool menu). 1. With an object on the command line, press (TOOD. 2. Press (HxT) to display the second page of the Tool menu. 3. Press SEARCH. A choose list appears listing the find and replace options. Find RAD ÎH0H 2. Rep lace.. S.Find next H.Rep lace Selection S.Replace-^Find Rext e.
5. If you do not want a case sensitive search, press CHK. The tick in the Case Sensitive field is deleted. Your search will now look for both the upper-case and lower-case versions of the characters you entered into the Search For field. 6. Press OK or (ENTER) to begin the search. If your search string is found, it will be highlighted on the command line; otherwise a message is displayed infonning you that your search string cannot be foimd.
Replace The Replace command searches through the object on the command line and highlights the first instance of a character or character string that matches your search string (that is, the character or character string you specify). You can then replace that string with another string. The Replace command begins searching from the position of the cursor.
10. Press OK or (ENTER) to begin the search. If your search string is found, it will be highlighted on the command line; othei-wise a message is displayed informing you that your search string cannot be formd. 11. If you don’t want to replace the current selection but want to continue looking for your search string, select FIND NEXT from the Search menu and repeat this procedure from step 10.
Command Line information The command line editor Tool menu also provides general infonnation about the object on the command line and the position of the cursor. To see this infonnation, press INFO. A screen entitled “Connnand Line” appears. Km%mm ■CoHHondLine i tiriii: KpOSition: VpOfition: Position: Line 5i2C: 7 Text Sx2is Sth Si2«: 7 Hen m'j ■ 13 H Clip Set. la L1 aHD Si2i: Ji2i: 0 0 The fields on this screen are: # Lines The nimiber of lines over which the object extends.
Styles You can set the style of a command line entry to bold, italic, underlined, or inverted, or to any combination of these characteristics. You can also choose a different font for the entiy. To do this, make sure that the command line is active and the Tool menu for the conunand line editor is displayed. (Press (TOOp if it is not.) 1. If the STYLES command is not displayed, press (NXD luitil it is. 2.
Chapter 4 The Stack The HP 49G keeps a record of the objects you enter and the results of your operations. In algebraic mode this record is called history; in RPN mode it is called the stack. Using the stack Entries on the stack are niunbered (as in the RMi KVZ HEK R= 'K' example at tire riglrt). Air entry on the stack is ■ CHOHE? __________ 58 referred to as being on a particular level. The ___ 6 level is the number of the line on which the ■J8745 93.514704726 entiy appears.
In RPN mode, you enter: In other words, in RPN mode 52 and 3 are entered onto the stack before the conunand is entered; 52 must be on level 2 and 3 on level 1 before the command is executed. -Jd U____________ _____________ 3 Strictly speaking, the last (or only) argument does not need to be on the stack before you execute a command in RPN mode. You can execute a command with the last (or only) argument still on the command line. Therefore, the second (BW) in the example immediately above can be omitted.
Using a multi-argument command Method 1 1. Enter the arguments, pressing (ENTER) after each one. 2. Execute the command. Example: To calculate 23 x 97 1. Enter 23 and press (0 2. Enter 97 and press (B 23 is now on level 2 of the stack and 97 is on level 1. 2! l: 23 97 3. Press @. In this example, the order in which you enter the arguments does not affect the answer. However, this is not always the case with two-argument conunands.
Multi-command calculations Because the result of a calculation is retained on the stack, you can easily perform complex calculations by accumulating the results of sub calculations on the stack and then treating these results as the arguments m a fmther calculation. Example: To calculate 13^ - (17 x 19) + | 1. Enter 1300. The result—169—appears on level 1 of the stack. 2. Enter 17 and press (ENTER). 3. Enter 19 and press (ENT0. 4. Press ®.
Chapter 5 Matrices and linear algebra The HP 49G has extensive capabilities for entering and manipulating anrays. An array object can be a vector or matrix. Many of the matrix operations described in this chapter also apply to vectors. Wherever this is the case, the more general term array is used instead of m ati'ix. By default, Matrix Writer will interpret a one-row array as a vector rather than as a matrix. If you want a one-row array interpreted as an array, press VEC first.
Method 2: the GOTO command 1. Press GOTO. The Matrix Writer input form is displayed. Note that the GOTO command is on the second page of the Matrix Writer menu, so you may need to press (NXT) to display it. 2. Enter the row number of the cell you want to go to. 3. Press (ENTER). 4. Enter the cohmm number of the cell you want to go to. 5. Press (EiiER). 6. Press OK or (ENTER). The matrix is redisplayed and the cursor is now in the cell whose rowcolumn coordinates you specified. To edit an array 1.
To make the cells narrower or wider • Press ^WID to make the cells nan"ower. More columirs ai'e displayed. ® Press WID-^ to make the cells wider. Fewer colmrms are displayed. Note that these commands modify the width of all columns, not just the column with the highlighted cell. To control how the cursor moves aFter an entry By default, the cursor moves to the adjacent cell in the next column after you place an object in a cell.
Manipulating columns and rows To insert a column 1. Move the cursor to the column where you wairt the new coliuun to appear. 2. Press +COL. A coliurm of zeros is inserted. Note that the +COL command is on the second page of the menu, so you may need to press (NXT) to display it. You can also add a column to an an’ay without using Matrix Writer. See “To insert one or more new columns into an array” on page 511. To add a column to the right oF the last column of data 1.
To add a row below the bottom row oF data 1. Move the cursor to the row below the last row of data. Pressing 0 ® will move the cursor directly to the last row of data. You then press ® to move to the next row. 2. Enter an object. 3. Press (TOER) to move your object to the highlighted cell. The rest of the row fills with zeros and your array now includes this new row. To delete a row 1. Move the cursor to the row you want to delete. 2. Press-ROW. To delete the contents of a selection of cells 1.
Summary oF Matrix Writer operations Key Description EDIT Places the contents of the ciuTent cell on the command line for editing. VEC For one-row arrays, toggles between vector entry and matrix entry. If this command is selected, one-row arrays are entered onto the command line as vectors (example: [ 1 2 3 ]); if it’s not selected, one-row arrays are entered as matrices (example: [ [ 1 2 3 ]]). ^WID Decreases the width of all cells. WID^ Increases the width of all cells.
Advanced matrix operations Creating special matrices To create an array Riled with a given constant 1. Select the Constant Array command. 0 (WTRICESl CREATE CON 2. For the first argument of the command, enter either: • a list containing the dimensions of the desired constant array: { roivs, cohmins } or • an existing array. .3. For the second argument, enter the constant that you want in the array. 4. Press®®).
To create an array filled with random integers 1. Select tlie Random Matrix comnaaird. 0 {Bm CREATE RANM 2. Enter either: • a list containing the dimensions of the desired random matrix: { rows, columns } or ® an existing array. 3. Press (ENTER). The result is a random aiTay of the specified dimensions (or of the dimensions of the specified array). The elements are integers within the range -9 to 9. Assembling matrices To assemble a matrix by rows From a series of vectors 1.
To assemble a matrix with a particular diagonal From a vector 1. Select the Vector-to-Matrix Diagonal conmiand. 0 {MS§) create diag^ 2. Enter the vector containing the diagonal elements. 3. Enter either: • a list containing the dimensions of the desired matrix: {nrws columns] or • a real number representing the number of rows and columns in the desired square matrix. 4. Press (HI). The result is a matrix of the desired dimensions using the elements of the vector as the diagonal elements of the matrix.
Disassembling matrices To disassemble a matrix into its elements 1. Select the Object-to-Stack conomand. 0 (PRG) TYPE OBJ-> 2. Enter or select the matrix you want to disassemble. 3. Press (EB. The matrix is disassembled in row-major order. A list indicating the dimensions of the matrix is also returned. To disassemble a matrix into row vectors 1. Select the Matrix-to-Rows command. 0 CREATE ROW ^ROW 2. Enter or select the matrix you want to disassemble. 3. Press (ENTER).
Inserting rows and columns To insert one or more new rows into a matrix 1. Select the Insert Row command. 0 (MATRICES) CRBTATE ROW ROW+ 2. Enter or select the ari’ay you want to modify. 3. Enter the vector or matrix that you want to insert. An inserted array must have the same number of cohunns as the array into which it is being inserted. 4. Enter the row number you want the first (or only) inserted row to be. 5. Press (ENTER).
Extracting rows and columns To extract a particular row From an array 1. Select the Delete Row command. 0 (illCES) CREATE ROW ROW- 2. Enter or select the array with the row you want to extract. 3. Enter the number of the row you want to extract. 4. Press The result is the array without tlie extracted row, and the extracted row as a vector. To extract a particular column From an array 1. Select the Delete Coluimr conuuand. 0 (MATRICES) CREATE COLUMN COL- 2.
To swap two columns in an array 1. Select the Colmim Swap command, 0 (MfiCB) CREATE COLUMN CSWP 2. Entei" or select the matrix with the coluimis you want to swap. 3. Enter the number of the one of the columns you want to swap. 4. Enter the number of the other column you want to swap. 5. Press (ENTER). The result is the array with the two specified columns swapped. Extracting and replacing elements oF matrices To extract the element at a specified position 1. Select the Get Element command.
Characterizing matrices Matrix calculations are often sensitive to special characteristics of the matrices used. The HP 49G has a number of commands that return characteristics of matrices. Note that some commands are only defined for square matrices, some for any rectangular matrix.
Keys (Continued) R (iWRICES) OPERATIONS SRAD R (MATRICES) OPERATIONS OOND 0 (MATRICES) OPERATIONS RANK 0 CMATRICES) OPERATIONS DET 0 (MATRICES) OPERATIONS TRACE Matrices and linear algebra Description Returns the spectral radius of a square matrix. The spectral radius is the absolute value of the largest eigenvalue of the matrix. Retimis the cohmm-norm condition number of a square matrix.
TransForming matrices To transpose a matrix 1. Select the appropriate Transpose Matrix command: ® 0 EH) MATRIX MAKE TEN (if you want the conjugate transpose of a complex matrix), or ® 0 (WiCB] OPERATIONS TRAN (if you want transposition without conjugation). 2. Enter or select the array you want to transpose. 3. Press (ENTER) to transpose the matrix. The first row of the original matrix is now the first column, the original second row is now the second colmnn and so on. To invert a square matrix 1.
More matrix arithmetic Simple matrix arithmetic is covered in chapter 8 of the HP 49G User’s Guide. This section covers some of the other aritlimetic options. To change the sign of each element in a matrix 1. Press ©(lD. 2. With the cursor between the parentheses, enter or select the matrix. 3. Press To multiply a matrix and vector 1. Enter or select the matrix. 2. Press ®. 3. Enter or select the vector. The number of elements in the vector must equal the number of columns in the matrix. 4.
TransForming complex matrices To combine two real matrices into a complex matrix 1. Select the Real-to-Complex command. 0 (M® COMPLEX R^C 2. Enter or select the real matrix that will become the real part of the complex matrix. 3. Enter or select the real matrix that will become the imaginary part of the complex matrix. This matrix must have the same dimensions as the matrix entered at step 2. 4. Press (ITER). The two real matrices are combined to form a complex matrix.
To extract the matrix of imaginary parts From a complex matrix 1. Select the Imaginary Part function. 0 COMPLEX IM 2. Enter or select the complex matrix whose imaginary components you want to extract. 3. Press The result is a matrix comprising just the imaginary components of the complex matrix. Linear algebra topics The use of matrix functions to solve systems of linear equations is covered in chapter 8 of the HP 49G User’s Guide. This section covers other important linear algebra commands.
To compute the eigenvalues and eigenvectors For a square matrix 1. Select the Eigenvalues and Eigenvectors command. 0 (iliCES) EIGENVECTOR EGV 2. Enter or select the square (w. x n) matrix whose eigenvalues and eigenvectors you want to calculate. 3. Press (ENTER). The result is an n x n matrix of eigenvectors and an »-element vector of eigenvalues. To compute the singular values oF a matrix 1. Select the Singular Values command. 0 SID FACTORIZATION SVL 2. Enter or select the matrix. 3. Press (H).
To decompose or factor a matrix The HP 49G offers a set of matrix decomposition and factorization tools that you can use either alone or in program routines to solve specialized problems. These tools are explained in the following table: Keys Description H (MATRICES) FACTORIZATION LU Grout LU Decomposition. This procedure is used in the process of solving an exactly-determined system of linear equations, inverting a matrix, and computing the determinant of a square matrix.
Description Keys (Continued) R (MATRICES) FACTORIZATION Page 5-22 SVD Singular Value Decomposition. This command factors an m x n matrix A into an m X m orthogonal matrix U, an n X n orthogonal matrix V, and a vector S of the singular values of A such that A = US‘V (where S‘ is the m x n matrix fomied by using the elements of S as its diagonal elements).
Chapter 6 Unit objects The Units application contains a catalog of 127 imits that you can combine with real numbers to create unit objects. It also provides you with tools to manipulate unit objects. The Units application enables you to: • convert imits—for example, you can convert the imit object 10_ft to 120Jn or 3.048„m • factor imits—for example, you can factor 20_W with respect to 1__N and return 20_N*m/s • calculate with units—for example, you can add 10_ft/s to 10_mph and return 16.82_mph.
Unit objects A unit object has two parts: a real number and a unit expression (a single unit or multiplicative combination of imits). The two parts are linked by the imderscore character For example, 2_in (2 inches) and 8.303_gal/Ii (8.303 US gallons per hour) are imit objects. Like other object types, a unit object can be placed on the stack, stored in a variable, and used in algebraic expressions and programs.
To assemble a unit object from the stack 1. Place the number part of the unit object on level 2 of the stack and the mrit expression on level 1. The imit expression must be in the format n_unit where n is any real number and unit is the unit abbreviation (lb, in, m, etc.)2. Execute the ^UNIT command. You can execute the ^UNIT command by: ® pressing 0 (ilTS) TOOLS ->UNiT ® selecting it from the commands catalog ((CAT) ->IINIT) or • pressing 00 (i®)im)UNIT(Eii).
Converting units The HP 49G provides two commands for converting imit objects from one unit of measurement to another: ® CONVERT ® DBASE. Tire CONVERT command—which requires two arguments—can be used to convert one type of imit to any other similar miit. The DBASE conunand— which requires only one argument—is used to convert a imit object to its equivalent SI base imit: feet to metres, knots to metres per second, and so on.
To convert units to SI base units The CONVERT command discussed in the previous section can be used to convert to any specified units, SI units or otheiTvise. If you want to convert a rmit object to its equivalent SI base imits, the UBASE command is quicker, as it requires just one argument. 1. Press © @1) TOOLS UBASE. 2. Enter the unit object with the units that you want to convert. See “To create a miit object” on page 6-2 for instmctlons on creating unit objects. Example: 365_ft 3. Press (1.
The trigonometric operations SIN, COS, and TAN, operate only on unit objects with-planar ang-ular units: radians (r), degrees (°), grads (grad), arc-minutes (arcmin), or arc-seconds (arcs). Temperature units require special attention: see “Working with temperatiue imits” on page 6-8. Sample unit calculations The following examples assume that you are working in algebraic mode. Subtraction. To subtract 39 in from 4 ft: 1. Enter 4_ft. 2. Press Q. 3. Enter 39Jn. 4. Press (ENTER). The answer is 9„in.
Powers. To cube 2ft/s. 1. Enter (2_ft/s). Note that when you are in algebraic mode and raising a imit object to a power, the unit object must be entered in parentheses. 2. Press ©• 3. Enters. 4. Press (ITER). The answer is In RPN mode: follow steps 1, 3, and 2. Parentheses are not required around unit objects in RPN mode. Percentages. To find what percentage of 4.2cm^ is lin^: 1. Press 0 (MlB) real %t. 2. Enter l_in^3. 3. Press 0Q. 4. Enter 4.2_cm^3. 5. Press (EB). The answer is 25.6299725198.
Factoring unit expressions The UFACT command factors one unit within a unit object, returning a luiit object whose unit expression consists of the factored unit and the remaining SI base units. To Factor units within a unit expression 1. Press 0 ÌUN0 TOOLS UFACT 2. Enter the imit object with the original imits. Example; 74_pdl. 3. Press ©Q. 4. Enter any number (such as 1) and attach the imits you want to factor out. Example: 10g. 5. Press ¡Hi). Answer: 10.2308666238_kgm/s^.
Converting temperature units Conversions between the four temperature scales (K, °C, °F, and °R) involve additive constants as well as multiplicative factors. The additive constants are included in a conversion when the temperatiue units reflect actual temperature levels, and are ignored when the temperature units reflect temperature differences. • Pure temperature units (levels).
Example 2: Convert 25°C/min to °F/min. Note that unlike in the first example, in this example a relative temperature conversion will be performed. 1. Press 0 iOirS] TOOLS CONVERT. 2. Enter 25_°C/min. Note that °C/min is not available in the units catalog and so must be created. You can select °C from the units catalog, and then press 0 and type “min” to complete the compound unit. (Note that min must be entered in lower case.) 3. Press 0Q. 4. Enter l_°F/mm.
Chapter 7 Constants Library The constants libraiy contains a collection of conunonly used physical constants and quantities. You can use them in equations and programs. The following table lists the constants in the order they appear in the library. Abbrev Description iation Value (SI) NA Avogadro’s number 6.0221367E23 gmopl k Boltzmann constant 1.380658E-23 J/K Molar volume 22.4141 Pgmol R Universal gas constant 8.31451 J/(gmol-K) StdT Standard temperature 273.
Abbrev Description iation Value (SI) Proton rest mass 1.6726231E-27 kg mp/me 1836.152701 a Fine stmcture constant 0.00729735308 0 Magnetic flux qiiantiuTi 2.06783461E-15 Wb F Faraday constant 96485.309 C/gmol R.X. Rydberg constant 10973731.534 nci aO Bohr radius 0.0529177249 nm ,uB Bohr magneton 9.2740154E-24 J/T l-iN Nuclear magneton 5.0507866E-27 J/T ?t0 Photon wavelengtlr (cli/e) 1239.8425 nm fO Photon frequency (e/lr) 2.4179883E14 Hz Xc Compton wavelength 0.
To view the constants library 1. Press (№PS) CONSTANTS LIB. 2. Press (ENTER). In RPN mode: follow step 1 only. To view the value and units oF a particular constant 1. Highlight the constant whose value you want to see. You can either press ® or @ rmtil the constant is highlighted, or press (IM) followed by the first character of the constant’s abbreviation. For example, to quickly find the acceleration of gravity, enter (IM) 0 G.
To include a constant in an algebraic expression You can include a constant in an expression you are creating on the command line or in Equation Writer. 1. At the position in the expression where you want to include a constant, type CONST. 2. Press 00. 3. With the cursor between the parentheses, type the abbreviation for the constant. For example: 4.56*CONST(g). When the expression is evaluated, the constant is also evaluated. (In the above example, the answer, in SI units, is 44.718824jn/s^.
Chapter 8 Number bases Entering and displaying binary integers You can enter and display integers in one of four fonns: ® decimal (base 10) * hexadecimal (base 16) ® octal (base 8) or ® binary (base 2). You use the pound symbol (#) together with a suffix to indicate the base of a number. The suffixes are: d (decimal) h (hexadecimal) о (octal) and b (binary). For example, # 182d, # B6h, # 266o, and # 10110110b are all ways of representing 182.
The settings for flags -11 and -12 determine the current base. The DEC, HEX, OCT, and BIN commands control the settings of these flags: -11 Set Clear Set Hex Bin Clear Oct Dec -12 An annimciator on your default screen indicates the current base setting. To set the wordsize 1. Press 0(®STWS. 2. Key in the new wordsize (from 1 to 64). 3. Press (ENTER). In RPN mode: follow steps 2 and 1.
Binary integers are displayed on the HP 49G with a space after the # sign. You do not need to enter a space when creating a binary integer. If you specify a base other than the current base setting, the HP 49G converts the binary integer you entered to an integer to the base of the current setting. If you want to see the binary integer you entered, press 0 @D). For example, if your cmTent base setting is hexadecimal and you enter # 1101b, the calculator displays your entry as # Dh.
To convert a binary integer to a diFFerent number base 1. Press (CAT) n, where n is the command that represents the base you want to convert to: DEC, BIN, HEX, or OCT. 2. Enter the binary integer. 3. Press For example, to convert # 1101b to hexadecimal, enter HEX(# 1101b) and press (ENTER). In RPN mode: follow steps 2 and 1. Note that converting a binaiy integer to a different number base also changes the base setting to the base that you converted the integer to.
Using Boolean operators The HP 49G provides a number of commands that enable you to perfonu Boolean operations and comparisons on binary integers. These commands—available by pressing 0 (B^ LOGIC—are illustrated in the following table. The input syntax shown assumes that you are in algebraic mode. Examples Commands Input Output AND Logical bit-by-bit AND of two arguments. Compares corresponding bits and returns true (1) if both bits are 1.
Manipulating bits and bytes The following commands enable you to manipulate binaiy integers one bit or one byte at a time. The commands are available by pressing o (BASEjbit OR 0 (0E)byte. Unless otherwise stated, each example assumes the wordsize is set to 24. Example Commands Input ASR Arithmetic Shift Right. Per forms 1 bit arithmetic right shift. The most significant bit is regener ated. Output #1100010b #110001b # 1100b # 1001b # FFFFh # FFFFOOh RR Rotate Right.
Chapter 9 Lists and Sequences Creating Lists To enter a List From the keyboard 1. Press CQ}. The braces indicate the beginning and end of a list. 2. Enter the elements of the list, separating each with a comma (0Q). 3. Press (ENTER). Note that the list is displayed without commas. To assemble a list from a set oF stack objects If you are worMng in RPN mode, you can assemble a list from a contiguous set of objects already on the stack. 1.
To append a new object to the end oF a list 1. Enter or select the list. 2. Press 0. 3. Enter or select the new object. 4. Press (H). In RPN mode: follow steps 1, 3, and 2. List Processing To apply a one-argument command to each element in a list The order in which you enter the command and tire list depends on the type of function it is: prefix or postfix. A prefix function is one whose name or abbreviation usually comes before its arguments; for example, SIN^) and SQ(x, y).
If you are executing a postfix fxmction, or working in RPN mode, the steps you should take are given in the following table. Prefix Postfix Algebraic 1, 2, 3 2, 1,3 RPN 2, 3, 1 2, 1 Another example: To find the factorial of 3, 4, and 5 while working in algebraic mode. 1. Enter or select the list; ¡3, 4, 5). 2. Select the factorial command: Q (ME) PROBABILITY ! 3. Press (ENTER). The answer is {6, 24,120). To add corresponding elements of two Lists 1. Enter or select the first list.
To concatenate two lists To concatenate two lists is to form a list made up of the elements of botlr lists. The order of tire elements in each sub-list is preseiwed. 1. Enter the list whose elements will form the first part of the concatenated list. For example, {1, 2, 3| 2. Press©. 3. Enter the list whose elements will fomi the latter part of the concatenated list. For example, {4, 5, 6}. 4. Press (ENTER). The answer is {1, 2, 3, 4, 5, 6j. In RPN mode: follow steps 1, 3, and 2.
Applying a Function or program to a List The DOLIST coiranand enables you to run programs or execute fmrctions on groups of lists. To run a program or execute a Function on Lists When you are operating on a number of lists—especially long lists—it may be easier and clearer if you are in RPN mode (as in the case of the following example). 1. Enter the lists. 2. Enter the number of lists to be operated on.
Example: Find the 2-element moving average of {2, 4, 8, 16, SOj. 1. Enter the list. 2. Enter the frame index. In this example, the number is 2, as you want to find the average of tv)o nimibers each time. 3. Enter the program. «+ 2/» 4. Execute the DOSUB command. 0 {mg) LIST PROCEDURES DOSIJBS. The answer is ¡3, 6, 12, 33). To execute a function on every element of a list The STREAM command enables you to apply a fimction I'ecursively to every element in a list.
List Manipulations The following functions provide ways to manipulate the elements of a list: Function Description Q (MTHl LIST SORT Sorts the elements in a list in ascending order. In RPN mode, the list must be on level 1. 0 (MÌB) LIST EEVLIST Reverses the order of the elements in a list. In RPN mode, the list must be on level 1. 0 (PRGIlIST ELEMENTS HEAD Returns the first element in the list. In RPN mode, the list must be on level 1.
Function (Continued) Description 0 (flGlLIST ELEMENTS POS Returns the position of the first occurrence of an ele ment (argument 2/level 1) in a specified list (argument 1/level 2). For example: POS({2, 4, 6, 1, 2, 3, 4), 4) returns 2 (since the first occuiTence of 4 is at position 2 in the list. 0 (PEG) LIST RPN command to disassemble a list into its elements and return (to level 1) the number of elements that were in the list. Each element is placed on a separate level of the stack.
Sequences Sequence commands automate the generation of a list from the repeated execution of a fimction or program. To generate a sequence In algebraic mode: 1. Specify the sequential calculation command. 0 {PRG) LIST PROCEDURES SEQ. 2. Enter the function or program (or its name). 3. Enter the index variable name. 4. Enter tire initial value for the variable. 5. Enter the final value for the variable. 6. Enter tire step size of the increment.
If you had entered 2 for the step value at step 6, then every second integer in the specified range would have been included in the iterations, and the result would have been ¡225, 289, 361 j. To find the sum of the elements in a finite List 1. Select tire list sum command. 0 (MDi) LIST Slist 2. Enter or select the list. For example, ¡2, 4, 7]. 3. Press (ENTER). The answer is 13. In RPN mode: follow steps 2 and 1. To find the product of the elements in a finite list 1. Select the list product commaird.
Chapter 10 Advanced plotting options Labelling and relocating the axes To label the coordinate axes with the variable names The names of the independent and dependent variables, and the coordinates (in user-units) of the largest and smallest displayed values for each variable, can be added to the plot after it has been drawn. The figm'e below shows labels added to the plot of y X - 2 (assuming that you have used the default settings). To label the axes: 1. Press EDIT. 2.
To label the axes with user-defined labels 1. Select the axes command from the command catalog i 2. Enter a list containing the horizontal and vertical axis labels as strings: { "h-label" "v-label" } . For example: AXES({"Years", "Earnings"}). 3. Press (ENTER) to store the labels. 4. Press 0 (GRM) to display the plot again. 5. Press EDIT. 6. Press (NXT) to display the second page of the fmiction-key menu. 7. Press LABEL. To have the axes intersect at a point other than (0,0) 1.
The following diagram is of the same plot as in the previous illustration, but the axes now meet where x =1 and y =1. Plotting programs You can plot a program if it takes nothing from the stack, uses the independent variable in the program, and returns exactly one mrtagged number to the stack. Examples ® Real result. Equivalent to the expressions/(,x) (function plots) and 'r(6) (polar plots).
Plotting range vs. display range The plotting range is the range of the independent variable (or variables) over which the current equation is evaluated. If you don’t specify the plotting range, the HP 49G uses the a;-axis display range (specified by XRNG or by H-VIEW) as the plotting range.
4. Enter a complex niuxiber to indicate the coordinates, in user units, of the comer of PICT diagonally opposite the comer specified at step 2 above. For example, PDM((-6,-6), (6,9)). 5. Press (ENTER). Press 0 (GRM) to see the results of the re dimensioning of PICT. In RPN mode: follow steps 2, 4, and 1. To keep the same display ranges: 1. Press 0 (PRG) PICT PDM to select the PICT dimension command. 2. Enter a binary integer to indicate the horizontal size of PICT in pixels. 3. Press ©Q. 4.
Saving and Restoring Plots A plot consists of several components: • The plot picture (that is, a graphic object). • The current equation or equations (stored in the reserved variable EQ). • The current plot parameters (stored in the reserved variable PPAR and, in the case of three-dimensional plot types, VPAK). • Flag settings that determine plotting and display options. You have the option to save any or all of these plot components in a variable so that you cair retrieve them later.
To view a plot picture stored in a variable 1. Press (WR)2. Press the function key corresponding to the variable containing the plot picture. You may have to press (NXT) a number of times to display the variable you want. You may also have to change directories if the variable is not in the current directory. 3. Press ® to display the plot. To save a reconstructable version oF the current plot 1. After drawing the plot, press (CANCEp to return to your default screen. 2. Press 0(0]. 3. Press (WR). 4.
To reconstruct a plot from its stored version This procedure is best done in RPN mode. 1. Press®. 2. Press the function key associated with the variable that contains the stored version of the plot’s components. 3. Press 0 TYPE OBJ-> to disassemble the list and put the components onto the stack. 4. Press ® to delete the object on level 1. This is the number of items in the original list and is not needed m the procedure.
Chapter 11 Memory This section describes the memory structure of tire HP 49G. It describes how to create backup objects of data that you want to save, and how to use libraries to add functionality to the calculator. How memory is structured The HP 49G contains a total of 2.5 Mb of memory. Of this memory: • 1 Mb is used to hold the operating system. ® 1.5 Mb is used for performing the operations that you specify, and for storing data that you want to keep.
Unlike the HOME directory, port memory cannot be subdivided into directories. A port can only contain two types of objects: ® backup objects ® library objects. Accessing port contents In order to access the contents of the variables stored in the ports you can use File Manager. For details on how to use File Manager, refer to the User’s Guide. Alternatively, you can access the contents of libraries and ports, by pressing 0(DB).
You can use File Manager to copy and delete backup objects in a similar fashion to normal calculator objects. In addition, there are specific commands for manipulating backup objects. Backing up and restoring HOME You can back up and restore the contents of the entire HOME directory in a backup object. This includes all variables, and any key assignments and alanus that you have created.
Storing and deleting backup objects There are three ways to create a backup object: » Use File Manager to copy the object to a port. With this method, the backup object has the same name as the original object. ® Use the STO command to copy the object to a port, and assign it a name. See Coimnand Reference Part D for details of tire STO command. ® Use the ARCHIVE command to create a backup of the HOME directory, and assign a name to the backup object.
You can also execute an object from the command line as follows: ® In RPN mode: - To evaluate a backup object, enter: :Port_Number: Backup_Name variable_name EVAL - To recall a backup object to the command line, enter: :Port_Number: Backup_Name variable_name RCL ® In algebraic mode: - To evaluate a backup object, enter: EVAL(:Port_Number: Backup_Name variable_name) - To recall a backup object to the corraxiand line, enter: RCL{:Port_Number: Backup_Name variable^name You can also use 0® as described in
Library objects A library is a collection of objects that extend the calculator’s fimctionality. You can execute objects in a library, but you can neither view, nor edit them. You can obtain libraries from various web sites. Installing and attaching a library To install a libraiy, perfomr the following: 1. Copy the library to your HOME directory. - from a PC, use the Coimectivity Kit. - From another calculator, use the calculator-to-calculator connection cable. 2. Install the library in a port.
Deleting a library To delete a library from a port, use the following commands. In the commands, port^number is the number of the port you stored your object in and 1 ib_number is the library number of the library you want to purge. ® In RPN mode: :port_number: lib_number PURGE • In algebraic mode: PURGE(;port_number: lib_number) How the HP 49G manages memory The following section explains how the calculator manages memory in the various ports.
Port 2 Port 2 is part of the Flash ROM. As with port 1, it is not possible to store objects larger than 128KB. Flash ROM is organized as 8 areas of 128KB each and one area of 64KB. The method that the system uses to manage Flash ROM can sometimes affect operations in port 2. Wlien it erases data, the system must erase 128Kb areas at a time. It cannot erase single objects. When you delete an object from flash ROM, the object is simply flagged as deleted. It still occupies memory space.
Chapter 12 Date and time arithmetic Date and time Formats The following table illustrates the date and time formats available on the HP 49G. The time and date illustrated is 4;31;04PM on March 21, 2001. Format Clock Display Number Format Date: 03/21/2001 MontlVday/year fonnat 3.212001 21.03.2001 Day.month.year fonnat 21.032001 Time: 04:31:04P 12-hour format 16.3104 16:31:04 24-hour fonnat 16.3104 Table 12-1: Date and time formats To set the Format oF the date and time 1. Press 0 (JME]. 2.
You can also use this procedure to set the date and time. You can also set the date by set the time by executing the ^TIME coiraiiand. executing the ^date command, and Date and time tools Numerous tools for working with dates and times are available from the Time menu. Displaying the Time menu Tlrere are two ways to access this menu: 0 (TÍME) TOOLS ® hold down 0 while pressing (TÍME). ® press To copy the date to the stack or history 1. Display the Time menu (see above). 2. Press DATE. 3.
Calculating with dates To add days to a given date 1. Enter tire date in number format (see the table on page page 12-1). For example: 3.212001 (that is, March 21, 2001). 2. Press @D DATE+. 3. Enter a real number representing the number of days you want to add to the date entered at step 1. For example 13. 4. Press (ENTER). The answer is 4.032001 (that is, April 3, 2001). In RPN mode: follow steps 1, 3, and 2. To subtract days From a given date 1.
To determine the number oFdays between two dates 1. Press ® ddays. 2. Enter the first date in number format (see the table on page page 12-1). For example: 3.212001 (that is, Mai'ch 21, 2001). 3. Press 0Q. 4. Enter the second date, also in number format. For example 5.232001 (that is, May 23, 2001). 5. Press (ENTER). The answer is 63. In RPN mode: follow steps 2, 4, and 1. Calculating with times You can work with times expressed in decimal fonnat or in HMS fonuat.
To convert a time in HMS format to decimal Format 1. Press (CAT) HMS^. 2. Enter the time in HMS format. For example: 5.1231 (that is, 5 hours, 12 minutes, and 31 seconds). 3. Press®®). The answer is 5.20861111 hours. In RPN mode: follow steps 2 and 1. To add times in HMS format 1. Press (CAT) HMS+. 2. Enter one time in HMS format. For example: 5.1231 (that is, 5 hours, 12 minutes, and 31 seconds). 3. Press 0Q. 4. Enter the other time, also in HMS fonnat. For example: 4.
System time System time is kept in ticks of the clock. Each tick is 1/8192 of a second in duration. System time can be converted to standard time (in both decimal format and HMS format). To display system time 1. Press (d m S TOOLS TICKS. 2. Press (ENTER). System time is displayed as a binary number. In RPN mode: follow step 1. The TICKS command is useful for measming elapsed time. To convert system time to HMS time 1. Press 0 O BASE B^R. 2. Enter the system time as a binary number.
To calculate elapsed time in seconds 1. To prepare to start timing, press TOOLS TICKS. 2. To start timing, press (ENTER). 3. To prepare to stop timing, press 0 TOOLS TICKS. 4. To stop timing, press (ENTER). 5. Press Q. 6. Press (H@. 7. Select the result of step 2. 8. Press (ENTER) twice. 9. Press Q (mTFD base b^r. 10. Select the result of step 8. 11. Press (ENTER). 12. Press ©. 13. Enter 8192. 14. Press In RPN mode: follow steps 1, 2, press steps 5, 9, 13, and 12.
Chapter 13 Customization Creating menus The HP 49G enables you to create a custom menu. The menu can contain labels for operations, commands, and other objects that you create or group together for your convenience. A custom menu is identified by the reserved variable GST. Therefore, you create a custom menu by naming a list of menu items GST. You can also use the MENU command to store a list in GST.
To display a custom menu 1. Press 0 (SUH)The menu labels appear across the bottom of your screen. You access a menu item by pressing the corresponding function key. Customizing the keyboard You can assign alternative fiuictionality to any key on the keyboard (including alpha and shifted keys). This enables you to customize the keyboard to your particular needs. Your customized keyboard is called the user keyboard, and it is active whenever you are in user mode.
Assigning user keys You can assign commands and other objects to a user key (including shifted keys). To assign an object to a user key 1. Press &f) ASN. 2. Enter the object to be assigned to the user key. 3. Press 0Q. 4. Enter the key code that identifies the user key. The code is made up of the row number, column number, and shifted status. For example, 23.4 indicates the key at row 2 and column 3 when pressed with the (ALPHA) key. See the diagram below. 5. Press In RPN mode: follow steps 2, 4, and 1.
To assign a command to a user key 1. Press (OT) STOREYS. Between the parentheses, enter a list with the command name as the first element—enclosed within tick marks—and the user key code as the second element. User key codes are explained in the illustration above. For example: STOKEYS(j‘TIME()’, 31.0)). Press ® In RPN mode: follow steps 2 and 1.
To enable disabled keys 1. Press ® DB^LKEYS. 2. lype 0 (that is, zero). 3. Press In RPN mode: follow steps 2 and 1. If you assign or disable the keys necessary to re-enable keys, or necessary to cancel user mode, you will be stuck in user mode. You will then need to reboot the calculator by holding (ON), pressing and releasing (F3) and then releasing ' Recalling and editing user key assignments To recall the current user key assignments 1. Press (CM) RCLKEYS. 2. Press In RPN mode: follow step 1.
Chapter 14 Computer Algebra Commands This chapter details the computer algebra operations that are available on the HP 49G. For each operation, the following details are provided; Type: Fimction or command. Functions can be used as a part of an algebraic object and commands cannot. When working with functions or commands within Equation Writer: • When you apply a function to an expression, the fimction appears as part of the expression.
Flags: Details of how flag settings affect the operation of the function or command. Example: An example of the fimction or command. See also: Related fimctions or commands.
Computer algebra command categories The following is an index of the computer algebra commands, listed in menu order. Algebra commands EXPAND......................14-19 FACTOR...................... 14-21 LNCOLLECT...............14-42 LIN ..............................14-41 SOLVE ........................14-57 SUBST ........................14-58 TEXPAND ..................14-63 Arithmetic commands DIVIS .......................... 14-15 FACTORS....................14-22 LGCD .........................
Calculus commands Derivation and integration commands CURL............................. 14-11 DERIV............................ 14-12 DERVX........................... 14-12 DIV ................................ 14-13 FOURIER....................... 14-23 HESS............................... 14-27 IBP................................... 14-30 INTVX............................ 14-34 LAPL.............................. 14-37 PREVAL ........................ 14-47 RESULTANT ................
Trigonometry commands AC0S2S .............................14-6 ASIN2C............................. 14-8 ASIN2T..............................14-8 ATAN2S ...........................14-8 HALFTAN...................... 14-27 SINCOS .......................... 14-57 TAN2SC ......................... 14-61 Computer Algebra Commands TAN2SC2 ............. .......... 14-61 TCOLLECT .......... .......... 14-62 TEXPAND ...................... 14-63 TLIN................................. 14-63 TRIG .......................
Alphabetical command list The following pages contain the commands in alphabetical order. See “Computer algebra conunand categories” on page 14-3 to view the commands in the order that they appear on the menus. ABCUV Type: Command Description: Returns a solution in polynomials u and v of miMro =c where a and b are polynomials, and c is a value. Arithmetic, RiMiTH) polynomial Access: Input: Output: Level 3/Argument 1: The polynomial corresponding to a.
Example: Simplify the following expression: a rc cos + arc cos (x) Command: AC0S2S(ACOS(2/3)+ACOS(X)) Result: n/2-ASIN{2/3) +Tt/2-ASIN(X) See also: ASIN2C ASIN2T ATAN2S ADDTMOD Type: Fimction Description: Adds two expressions or values, modulo the current modulus. Arithmetic, 0(ARjTH) MODULO Access: Input: Output: Level 2/Argmnent 1: The first expression. Level 1/Argument 2: The second expression. The sum of the two expressions, modulo the current modulus.
ASIN2C Type: Command Description: Transfonns an expression by replacing asin(ir) sub expressions with Tc/2-acos(a;) sub expressions. Access: Trigonometry, ©(HI) Input: An expression. Output: The transfonned expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). ASIN2T Type: Command Description: Transfonns an expression by replacing asin(a') sub expressions with the following: atan I ~x" Access: Trigonometry, Input: An expression.
Flags: Exact mode must be set (flag -105 clear). Niiiueric mode must not be set (flag -03 clear). AXL Type: Command Description: Access: Converts a list to an array, or an array to a list. Convert, (^(CONVSf) Input: A list or an array. Output: If the input is a list, returns the con'esponding array. If the input is an array, returns the corresponding list. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
AXQ Type: Command Description: Converts a square matrix into the associated quadratic form. Access: Convert, RSlfflf) Input: Level 2/Argiunent 1: An nxn matrix. Level 1/Argument 2: A vector containing n variables. Output: Level 2/Itein 1: The corresponding quadratic fonn. Level 1/Item 2: The vector containing the variables. Flags: Exact mode must be set (flag -105 clear). Niuneric mode must not be set (flag -03 clear).
CHINREM Type: CoiTUTiand Description: Solves a system of simultaneous polynomial congruences in the ring Z[x]. Access: Arithmetic, R1(MTR] polynomial Input: Level 2/Argiunent 1: A vector of the first congruence (expression and modulus). Level 1/Argument 2: A vector of the second congruence (expression and modulus). Output: A vector of the solution congruence (expression and modulus). Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
Example: Find the curl of the following vector function: 2 "I T (\' = X yi + x~yj + y^zky Command: Result: See Also: CURL ( [ X " 2 * Y , [2 * X * Y , X''2*Y, Y^2*z] , [X, Y, z] ) , Y^2 ] DIV HESS DERIV Type: Function Description: Returns the partial derivatives of a fimction, with respect to the specified variables. Access: Calculus, 0{® DERIV. & INTEG Input: Level 2/Ai'gument 1: A fimction or a list of fimctions. Level 1/Argument 2: A variable, or a vector of variables.
Output: The derivative, or a vector of the derivatives, of the function or functions. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). See also: DERIV DESOLVE Type: Command Descriptiou: Solves certain first-order ordinary differential equations with respect to the current variable. Access: Symbolic solve, 0(SSv) Input: Level 2/Argument 1: A first-order differential equation. Level 1/Argument 2: The function to solve for.
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Find the divergence of the following vector fimction: l 9 9 V = y [ + X y j + _y z k Command: Result: See also: DIV([X^2*Y, X^2*Y, Y^2*Z],[X,Y,Z]) Y*2*X+X^2+Y^2 CURL, HESS DIV2 Type: Command Description: Performs euclidean division on two expressions. Stepby-step mode is available with this command. Access: Arithmetic, (nl (MTH)polynomial Input: Level 2/Argiiment 1: The dividend.
Output: Level 2/Item 1: The quotient. Level 1/Item 2: The remainder. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Find the result of — ----- , modulo the default modulus, 3. V-' + 4 X- - 1 Command: DIV2MOD(X^3+4,X^2-l) Result: {X X+1} DIVIS Type: Command Description: Returns a list of divisors of a polynomial or an integer. Access: Arithmetic, 0 ® B Input: A polynomial or an integer.
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Modulo the default modulus, 3, divide 5a’^+4x+2 by a-2+1. Command: DIVMOD(5*X^2+4*X+2,X^2+l) Result: -{ ( X ^ 2 - X + l ) / X " 2 + l ) ) DIVPC Type: Command Description: Returns a Taylor polynomial for the quotient of two expressions. Access: Calculus, (3&S) LIMITS & SERIES Input: Level 3/Ai'gument 1: The nmuerator expression. Level 2/Argument 2; The denominator expression.
Access: Arithixietic, RiM) POLYNOMIAL Input: Level 2/Argiiment 1: The expression coiTesponding to a in the equation. Level 1/Argiiment 2: The expression corresponding to b in the equation. Output: Level 3/Item 1: The result corresponding to c in the equation. Level 2/Item 2: The result corresponding to u in the equation. Level 1/ltem 3: The result corresponding to v in the equation. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
EULER Type: Function Description: For a given integer, retimrs the niunber of integers less than the integer that are co-prime with the integer. (Euler’s 4> fimction.) Access: RiliTH) INTEGER Input: A non-negative integer. Output: The number of positive integers, less than, and co-prime with, the integer. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
EXPAN Type: Command Description: Expands and simplifies an algebraic expression. This conunand is identical to the EXPAND command. It is included to ensure backward-compatibility with the HP 48-series calculators. Access: Catalog, (¡M) Input: An expression Output: The expanded and simplified expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
EXPANDMOD Type: Function Description: Expands and simplifies an algebraic expression, modulo the current modulus. Access: AR!TH] MODULO Input: An expression. Ontpnt: The expanded and simplified expression modulo the current modulus. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Expand the following expression and give the result modulo 3 (the default modulo setting): (.T+3)(.
See also: SINCOS FACTOR Type: Command Description: Factorizes a polynomial or an integer: • The fimction expresses a polynomial as the product of in’educible polynomials. • The fimction expresses an integer as the product of prime numbers. Access: Algebra, 0{ALG) Input: An expression or an integer. Output: The factorized expression, or the integer expressed as the product of prime numbers. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
Command: FACTORMOD { X ^ ' 2 + 2 ) Result: (X+1)*(X-1) FACTORS Type: Command Description: For a value or expression, returns a list of prime factors and their multiplicities. Access: Arithmetic, 0®]]) Input: A value or expression. Output: A list of prime factors of the value or expression, with each factor followed by its multiplicity. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example 1: Find the prime factors of 100.
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Find the rational polynomial corresponding to the following set of roots and poles: 1,2, 3,-1 Command: FCOEF{ [ 1 , 2 , 3 , - 1 ] Result: (X-1)^2/(X-3) See also: ) FROOTS FOURIER Type: Fimction Description: Returns the coefficient of a complex Fourier series expansion. The PERIOD variable must be in the current path, and set to hold L, the period of the input fimction.
If complex mode is set (flag -103 set), FROOTS looks for complex solutions as well as real solutions. If approximate mode is set (flag -105 set) FROOTS searches for niuneric roots. See also: FCOEF FXND Type: Command Description: Splits an object iirto a numerator and a denominator. Access: Catalog, (C@ Input: A fraction, or an object that evaluates to a fraction. Output: The object split into numerator and denominator. Level 2/Item 1: The niunerator. Level 1/Item 2: The denominator.
D contains the coefficients of the diagonal representation. Level 2/Argument 3: The diagonal representation of the quadratic form. Level 1/Argument 4: A list of the vaiiables. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
GCDMOD Type: Function Description: Finds the greatest common divisor of two polynomials modulo the current modulus. Access: Arithmetic, Input: Level 2/Argument 1: A polynomial expression. Level 1/Argument 2: A polynomial expression. Output: The greatest common divisor of the two expressions modulo the current modulus. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
HALFTAN Type: Command Description: Transforms an expression by replacing sin(ar), cos(a:) and tan(a:) sub expressions with tan(a;/2) terms. Access: Trigonometry, Input: An expression Output: The transformed expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). HERMITE Type: Function Description: Returns the nth Hermite polynomial. Access: Arithmetic, R(MTH) POLYNOMIAL Input: A non-negative integer.
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). See also: CURL DIV HILBERT Type: Command Description: Returns a square Hilbert matrix of the specified order. Access: Matrices, RQiMTRICES] CREATE Input: A positive integer, representing the order. Output: The Hilbert matrix of the specified order. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Find the order 3 Hilbert matrix.
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: For r = 3, find the result of executing a Homer scheme on the following polynomial: j; + X + i Command: HORNER(X^2+X+l,3) Results: (X+4,3,13) I^R Type: Command Description: Converts an integer into a real number. Access: Catalog, &) Input: Level 1/Argument 1: Ar integer. Output: Level 1/ltem 1: The integer converted to a real number. Flags: Exact mode must be set (flag -105 clear).
See also: ABCUV lEGCD IBERNOULLI Type: Fimction Description: Returns the nth Bernoulli number for a given integer. Access: Catalog, @D Input: Level 1/Ai'giuuent 1: an integer. Output: Level 1/Item 1: The corresponding nth Bernoulli number for the integer. Flags: Numeric mode must not be set (flag -03 clear). IBP Type: Command Description: Performs integration by parts on a function.
Level 2: x*COS (X) Level 1: S I N ( X ) Result: Level 2: S I N ( X ) . X Level 1: - S I N ( X ) Command 2: Apply the INTVX conamand to level 1, - S I N Result: Level 2: S I N ( X ) Level 1: C O S ( X ) (X) .X Command 3: Press 0 to add the result to the value at level 2 to obtain the final result. Result: See also: SIN (X) . (X)+COS (X) INTVX INT PREVAL RISCH ICHINREM Type: Command Deseriptlon: Solves a system of two congruences in integers using the Chinese Remainder theorem.
IDIV2 Type: Command Description: For two integers, a and b, returns the integer part of a/h, and the remainder, r. Access: Arithmetic, RiWTH] integer Input: Level 2/Ai'giiment 1: a. Level 1/Argument 2: 6. Output: Level 2/Item 1: The integer part of a/b. Level 1/Item 2: The remainder. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Return the integer part and the remainder of 11632/864.
ILAP Type: Function Description: Returns the inverse Laplace transform of an expression. The expression must evaluate to a rational fraction. Access: Calculus, 0(SQ) differential eqns Input: A rational expression. Output: The inverse Laplace transformation of the expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
INTVX Type: Function Description: Finds the antiderivative of a fimction symbolically, with respect to the current default variable. Access: Calculus, 0(£1£) deriv. & integ Input: An expression. Output: The antiderivative of the expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
IQUOT Type: Fimction Description: Returns the integer quotient of two integers. That is, given two integers, a and b, returns the integer q, such that: a = qb + r, and 0< ? - < b Access: Arithmetic, R(MfH) integer Input: Level 2/Item 1: The dividend. Level 1/Item 2: The divisor. Output: The integer quotient. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). See also: NEXTPRIME PREVPRIME JORDAN Type: Command Description: Computes the eigenvalues, eigenvectors, minimum polynomial, and characteristic polynomial of a matrix. Access: Matrices. ROwrISeigenvectors Input: An n X n matrix. Output: Level 4/Item 1: The minimiun polynomial. Level 3/Item 2: The characteristic polynomial.
Command: LAGRANGE { ' 3 4 2 6 „ , Result; 7 8 9 8x"-63x‘+151X-60 ------------- -------------- LAP Type: Fimction Description: Performs a Laplace transform on an expression with respect to the current default variable. Access: Calculus, R(ClC) DIFFERENTIAL EQNS Input: An expression. Output: The Laplace transform of the expression. Flags: Exact mode must be set (flag -105 clear). Nmneric mode must not be set (flag -03 clear). Example: Find the Laplace transform of o'*.
Command; L A P L ( E X P { X ) *COS (Z*Y) , [X,Y, Z] ) EXPAND(ANS(1)) Result: - ( (Y^2 + Z^2-l) *EXP (X) *COS (Z*Y) LCM Type: Function Description; Returns the least conunon multiple of two objects. Access: Arithmetic, R (aItH)polynomial Input: Level 2/Argument 1: An expression, a number, or object that evaluates to a number. Level 1/Argument 2: An expression, a number, or object that evaluates to a number. Output: The least conunon multiple of the objects.
Output: The resulting matrix. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Build a 2 x 3 matrix with ajj=i+2j. Command: Result: LCXM{2,3 , <<-»! J ' I + 2*J' >>) 3 57 4 68 LDEC Type: Command Description: Solves a linear differential equation with constant coefficients, or a system of first order linear differential equations with constant coefficients.
Command: LEGENDRE{4) Result: (35*X^4-30*X^2+3)/8 LGCD Type: Function Description: Returns the greatest conunon divisor of a list of expressions or values. Access: Arithmetic, 0®H) Input: A list of expressions or values. Output: Level 2/Item 1: The list of elements. Level 1/Item 2: The greatest common divisor of the elements. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
UN Type: Command Description: Linearizes expressions involving exponential terms. Access: Exponential and logarithm, 0(И1) Input: An expression. Output: The linearized expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Linearize the following expression: x{e e ) Command: LIN(X*(EXP{X)*EXP(Y))^4) Result: X*EXP(4X+4Y) LINSOLVE Type: Command Description: Solves a system of linear equations.
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). See also: LVAR LNCOLLECT Type: Command Description: Simplifies an expression by collecting logarithmic tenns. Access: Algebra, 0($G) Input: An expression. Output: The simplified expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Simplify the following expression: 2(ln(.
MAD Type: Command Description: Returns details of a square matrix. Access: Matrices, R Input: A square matrix Output: Level 4/Item 1: The determinant. Level 3/Item 2: The formal inverse. Level 2/Item 3: The matrix coefficients of the polynomial, p, defined by (a'i-a)p(.r)=?n,(x)i, where a is the matrix, and m is the characteristic polynomial of a. Level 1/Item 4: The characteristic polynomial. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). MULTMOD Type: Function Description: Performs modulai' multiplication of two objects, modulo the ciuTent modulus. Access: Aritlrmetic, FiKMiTti] MODULO Input: Level 2/Argument 1: A number or an expression. Level l/Argiuuent 2: A number or an expression. Output: The result of modular multiplication of the two objects, modulo the current modulus. Flags: Exact mode must be set (flag -105 clear).
PA2B2 Type: Command Description: Takes a prime number, p, such thatp=2 or p = 1 modulo 4, and returns a Gaussian integer a + ib such thatp = a,^ + b^. This fimction is useful for factorizing Gaussian integers. Access: Arithmetic, R(STh) integer Input: A prime number, p, such that p=2 or p = 1 modulo 4 Output: A Gaussian integer a+ib such that p=a^+h^ Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
PCAR Type: Command Description: Returns the characteristic polynomial of an n x n matrix. Access: Matrices, R(MAlilS) EIGENVECTORS Input: A square matrix. Output: The characteristic polynomial of the matrix. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Find the characteristic polynomial of the following matrix: 58 16 41 8 _-4 -4 -11.
PREVAL Type: Function Description: With respect to the current default variable, returns the difference between the values of a fimction at two specified values of the variable. PREVAL can be used in conjunction with INTVX to evaluate definite integrals. See the example below. Access: Calculus, 0(® DERIV. & INTEG. Input: Level 3/Ai'gument 1: A fimction. Level 2/Argument 2: The lower boimd. Level 3/Argiunent 1: The upper boimd. The bounds can be expressions. Output: The result of the evaluation.
See also: ISPRIME? NEXTPRIME PROPFRAC Type: Command Description: Splits an improper fraction into an integer part and a fraction part. Access: Input: Arithmetic, RiM] Output: Flags: A proper fraction. Example: Express the following as a proper fraction: An improper fraction, or an object that evaluates to an improper fraction. Exact mode must be set (flag -105 clear). Niuneric mode must not be set (flag -03 clear).
Psi Type: Function Description: Calculates the digamma function in one point. The digainina fimction is the derivative of the natiual logarithm (In) of the gamma fimction. The fimction can be represented as follows: T(z) = ^(Inr(z)) = ^ dz F(z) Access: Input: Output: Flags: Catalog, (QM) Level 2/Argiiment 1: A complex expression Level 1/Argument 2: A non-negative integer. The digamma fimction at the specified point. Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
Output: Flags: Example: The quotient of the Euclidean division. Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). 3 2 Find the quotient of the division of x + 6x + 1 lx + 6 by x^ + 5x + 6 . Command: Q U O T ( X ^ 3 Result: X+1 See also: + 6*X""2 + ll*x+6, X"2 + 5*X+6) REMAINDER QXA Type: Description: Access: Input: Command Expresses a quadratic form in matrix form. Catalog, (MD Level 2/Argument 1: A quadratic form.
Output: Flags: Level 1/Item 1: The real number converted to an integer. See also: I^R Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). REF Type: Description: Access: Input: Output: Flags: See also: Command Reduces a matrix to echelon fonn. Matrices. H (MATRiCES) LINEAR SYSTEMS A matrix. The equivalent matrix in echelon fonn. Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
Input: Level 2/Ai'gument 1: Tlie polynomial expression. Level 1/Argument 2: The variable with respect to which the reordering is performed. Output: Flags: The reordered expression. Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). RESULTANT Type: Pimction Description: Returns the resultant of two polyiromials of the current variable. That is, it returns the determinant of the Sylvester matrices of the two polynomials.
Example: Find the antiderivative of the following function, with respect to y: y +3y + 2 Command: Result: See also: RISCH(Y''3-3*Y+2,Y) l/3*Y"3+3/2*Y"2+2*Y IBP INT INTVX RREF Type: Description: Access: Input: Output: Flags: Command Reduces a matrix to row-reduced echelon form. Matrices. RfWSlS) LINEAR SYSTEMS A matrix. An equivalent matrix in row reduced echelon fonn. Exact mode must be set (flag -105 clear). Niuneric mode must not be set (flag -03 clear).
RREFMOD Type: Command Description: Performs modular row-reduction to echelon form on a matrix, modulo the current modulus. Access: Catalog, {CAT) Input: A matrix. Output: The modular row-reduced matrix. The modulo value is set using the Modes CAS input form. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
SEVAL Type: Function Description: In the given expression, evaluates any existing variables that the expression contains and substitutes these back into the expression. Access: Catalog, (CM) Input: Level 1/Item 1: An algebraic expression. Output: The expression with existing variables evaluated. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
See also: SIGMA, RISCH SIGNTAB Type: Command Description: Tabulates the sign of a rational function of one variable. Access: Catalog, (Cl) Input: An algebraic expression. Output: A list containing, the points where the expression changes sign, and for each point, the sign of the expression between the points. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
SINCOS Type: Command Description: Converts complex logarithmic and exponential expressions to expressions with trigonometric terms. Access: Trigonometry, F](WG) Input: An expression with complex linear and exponential terms. Output: The expression with logarithmic and exponential sub expressions converted to trigonometric and inverse trigonometric expressions. Flags: Exact mode must be set (flag -105 clear). Nmneric mode must not be set (flag -03 clear). Must be in complex mode (flag -103 set).
SOLVEVX Type: Description: Command Finds zeros of an expression with respect to the cun-ent variable, or solves an equation with respect to the ciuxent variable. (You use the CAS modes input fonn to set the ciuTent variable.) Access: Symbolic solve, 0{Ssj3 Input: A fmiction or equation in tire current variable. Output: A list of zeros or solutions. Flags: For a symbolic result, clear the CAS modes Numeric option (flag -03 clear).
Example: Substitute X = z+l for X in the following expression, and apply the EXPAND command to simplify the result: + 3x + l Command: SUBST { X - ' 2 + 3 * X + 7 , X = Z + 1 ) EXPAND(ANS(1)) Result: Z"2+5*Z+11 SUBTMOD Type: Function Description: Performs a subtraction, modulo the current modulus. Access: Arithmetic, 0 ® B Input: Level 2/Argument 1: The object or number to be subtracted from. Level 1/Argmnent 2: The object or number to subtract.
TABVAL Type: Command Description: For an expression and a list of values, returns the results of substituting the values for the default variable in the expression. Access: Catalog, Input: Level 2/Argument 1: An algebraic expression in tenns of the cun'ent variable. Level 1/Argument 2: A list of values for which the expression is to be evaluated. Output: Level 2/Item 1: The algebraic expression.
Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). TAN2SC Type: Command Description: Replaces tan(,r) sub-expressions with sin(a:)/(l-cos(2a:) or (l-cos(2x))/sin(2.x). Access: Trigonometry, 0011) Input: An expression Output: The transformed expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). TAN2SC2 Type: Corrauand Description: Replaces tan(ar) terms in an expression with sin(2.
TAYLORO Type: Function Description: Performs a fourth-order Taylor expansion of an expression at a; = 0. Access: Calculus, 0(® LIMITS & SERIES Input: An expression Output: The Taylor expansion of the expression. Flags: Exact mode must be set (flag -105 clear). Nmneric mode must not be set (flag -03 clear). TCHEBYCHEFF Type: Function Description: Returns the nth Tchebycheff polynomial. Access: Catalog, (CM) Input: A non-negative integer, n. Output: The nth Tchebycheff polynomial.
TEXPAND Type: Command Description: Expands transcendental fimctions. Access: Trigonometry, 0QlG) Input: An expression. Output: The transfonnation of the expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). Example: Simplify the followmg expression: ln(sin(.
TRAN Type: Command Description: Returns the transpose of a matrix. Access: Matrices, H (MATRICES) OPERATIONS Input: A matrix. Output: The transposed matrix. Flags: Exact mode must be set (flag -105 clear). Niuneric mode must not be set (flag -03 clear).
TRIGCOS Type: Command Description: Simplifies a trigonometric expression by applying the identity: 2 (sinx) +(cosx) = 1 2 Returns only cosine terms if possible. Access: Trigonometry, (r^(T^ Input: An expression with trigonometric terms. Output: The transformed expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear).
Output: The transformed expression. Flags: Exact mode must be set (flag -105 clear). Numeric mode must not be set (flag -03 clear). See also: TRIGCOS, TRIGSIN TRUNC Type: Coimnand Description: Trimcates a series expansion. Access: Catalog, (MD Input: Level 2/Argiiment 1: The expression that you want to truncate. Level 1/Argiiment 2: The expression to truncate with respect to.
VANDERMONDE Type: Command Description; Builds a Vandermonde matrix from a list of objects. That is, for a list of n objects, the command creates an n x n matrix. The row in the matrix consists of the list items raised to the power of (i-l). Access: Matrices, (^(RSCES) CREATE Input: A list of objects. Output: The corresponding Vandermonde matrix. Flags; Exact mode must be set (flag -105 clear). Nmneric mode must not be set (flag -03 clear).
XNUM Type: Command Description: Converts an object or a list of objects to approximate nmneric format. Access: Catalog, Input: An object or list of objects. Output: The objects in numeric fonnat. Example: Find the approximate value of n/2, 3e, and 4cos(2). Command: XNUM{ { T C / 2 , 3 * e , 4*C0S ( 2 } ) Results: {1.5707963268 8.15484548538 1.66458734619} XQ Type: Command Description: Converts a number, or a list of numbers in decimal format, to rational format.
ZEROS Type: Command Description: Returns the zeros of a function of one variable, without multiplicity. Access: Symbolic solve, R(SM) Input: Level 2/Argument 1: An expression. Level 1/Arguinent 2: The variable to solve for. Ontpnt: The solution or solutions for the expression equated to 0. Flags: For a symbolic result, clear the CAS modes Nmueric option (flag -03 clear).
Index A ABCUV 14-6 AC0S2S 14-6 ADDTMOD 14-7 algebra, linear 5-19 AND 8-5 array 5-1 adding columns 5-4 adding rows 5-4 column norm 5-14 delete colunm 5-4 delete row 5-5 dimensions 5-14 redimension 5-16 row nonn 5-14 spectral nonn 5-14 ASIN2C 14-8 ASIN2T 14-8 ATAN2S 14-8 axes,labelling 10-1 AXL 14-9 AXM 14-9 AXQ 14-10 backup objects 11-2 backup 11-4 storing 11-4 using data in 11-4 base binary 8-1 flag settings 8-2 hexadecimal 8-1 setting 8-1 binary integer 8-1 aritlrmetic 8-3 conversion to 8-4 entemrg 8-2 ne
D date display 12-2 format 12-1 dates calculating with 12-3 decompose matrix 5-21 decomposition Schur 5-21 singular value 5-22 deleting characters 3-5 DERIV 14-12 DERVX 14-12 DESOLVE 14-13 determinant 5-15 disabUirg keys 13-4 display range 10-4 DIV 14-13 DIV2 14-14 DIV2MOD 14-14 DIVIS 14-15 DIVMOD 14-15 DIVPC 14-16 editing 3-5 array 5-2 EGCD 14-16 eigenvalues 5-19 eigenvectors 5-19 EPSXO 14-17 ERAXI 11-1 EULER 14-18 EXLR 14-18 EXPAN 14-19 EXPAND 14-19 EXPANDMOD 14-20 EXPLN 14-20 FACTOR 14-21 factoring uni
invert matrix 5-16 INVMOD 14-34 IQUOT 14-35 IRAM 11-1 IREMAINDER 14-35 ISPRIME? 14-35 M MAD 14-43 matrix 5-1 add rows 5-11 assembling 5-8 column-norm condition 5-15 complex 5-18 decompose 5-21 determinant 5-15 diagonal 5-9 disassemble 5-10 factor 5-21 factorization 5-21 Frobenius norm 5-14 invert 5-16 random 5-8 rank 5-15 J JORDAN 14-36 L label user-defined 10-1 label axes 10-1 labels 3-3 LAGRANGE 14-36 LAP 14-37 LAPL 14-37 LCM 14-38 LCXM 14-38 LDEC 14-39 LEGENDRE 14-39 LGCD 14-40 library attaching 11-5
PCAE 14-46 PICT, size of 10-4 plots recalling 10-7 restoring 10-6 saving 10-6 plotting range 10-4 ports 11-1 0 11-7 1 11-7 2 11-7 contents of 11-8 postfix function 9-2 POWMOD 14-46 prefix function 9-2 PRBVAL 14-47 PREVPRIME 14-47 programs, plotting 10-3 PROPFRAC 14-48 PSI 14-48 Psi 14-49 PTAYL 14-49 QUOT 14-49 QXA 14-60 R R-->I 14-50 random matrix 5-8 rank 5-15 redimension array 5-16 REF 14-51 REMAINDER 14-51 REORDER 14-51 replace 3-8, 3-10 restoring 11-3 RESULTANT 14-52 reverse Polish notation See RPN RI
s''';
