HP 50g / 49g+ / 48gII graphing calculator advanced user’s reference manual H Edition 2 HP part number F2228-90010 Printed Date: 2009/7/14
Notice REGISTER YOUR PRODUCT AT: www.register.hp.com 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, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO.
Contents Contents ............................................................................................................................................................................................... 1 1. RPL Programming.......................................................................................................................................................................1-1 Understanding Programming .....................................................................................
Fibonacci Numbers..................................................................................................................................................................2-1 FIB1 (Fibonacci Numbers, Recursive Version)...........................................................................................................2-1 FIB2 (Fibonacci Numbers, Loop Version....................................................................................................................
→ARRY...................................................................................................................................................................................3-15 ASIN.........................................................................................................................................................................................3-15 ASIN2C...........................................................................................................................
→COL .....................................................................................................................................................................................3-39 COL→ .....................................................................................................................................................................................3-39 COL–..............................................................................................................................
DIFF.........................................................................................................................................................................................3-59 DIFFEQ ..................................................................................................................................................................................3-59 DIR ............................................................................................................................
EXP2POW..............................................................................................................................................................................3-79 EXPAN....................................................................................................................................................................................3-79 EXPAND .................................................................................................................................
GROBADD ..........................................................................................................................................................................3-101 GXOR....................................................................................................................................................................................3-101 *H........................................................................................................................................
KER........................................................................................................................................................................................3-123 KERRM .................................................................................................................................................................................3-123 KEY...............................................................................................................................
MATHS..................................................................................................................................................................................3-143 MATR ....................................................................................................................................................................................3-143 MAX.................................................................................................................................
PA2B2 ....................................................................................................................................................................................3-162 PARAMETRIC ....................................................................................................................................................................3-162 PARITY.....................................................................................................................................
PURGE..................................................................................................................................................................................3-182 PUSH......................................................................................................................................................................................3-183 PUT ...............................................................................................................................
RND .......................................................................................................................................................................................3-205 RNRM....................................................................................................................................................................................3-206 ROLL ............................................................................................................................
SINH ......................................................................................................................................................................................3-226 SINV.......................................................................................................................................................................................3-226 SIZE .........................................................................................................................
TABVAR ...............................................................................................................................................................................3-247 →TAG...................................................................................................................................................................................3-247 TAIL...................................................................................................................................
UPDIR ...................................................................................................................................................................................3-265 UTPC .....................................................................................................................................................................................3-265 UTPF.............................................................................................................................
√ (Square Root).................................................................................................................................................................3-286 ∫ (Integrate).......................................................................................................................................................................3-288 ? (Undefined)...................................................................................................................................
Series and Parallel C (2, 7) .............................................................................................................................................5-12 Series and Parallel L (2, 8)..............................................................................................................................................5-13 Capacitive Energy (2, 9) .........................................................................................................................................
Angular Motion (8, 4).....................................................................................................................................................5-36 Circular Motion (8, 5).....................................................................................................................................................5-36 Terminal Velocity (8, 6) ........................................................................................................................................
A. B. C. D. BetaTesting ........................................................................................................................................................................6-3 CD→...................................................................................................................................................................................6-3 →CD..............................................................................................................................
E. F. G. H. I. J. K. ALRMDAT ..............................................................................................................................................................................D-2 βENTER...................................................................................................................................................................................D-3 CST ..............................................................................................................
1 1.RPL Programming If you’ve used a calculator or computer before, you’re probably familiar with the idea of programs. Generally speaking, a program is something that gets the calculator or computer to do certain tasks for you — more than a built-in command might do. In the HP 48gII, HP 49g+, and HP 50g calculators, a program is an object that does the same thing.
Examples of Program Actions Program « 1 2 » Results 2: 1: « "Hello" { A B } » 2: 1: "Hello" { A B } « '1+2' » 1: '1+2' « '1+2' →NUM » 1: 3 « « 1 2 + » » 1: « 1 2 + » « « 1 2 + » EVAL » 1: 3 1 2 Programs can also contain structures. A structure is a program segment with a defined organization. Two basic kinds of structure are available: Local variable structure.
Entering and Executing Programs A program is an object — it occupies one level on the stack, and you can store it in a variable. To enter a program: 1. Press @%.The PRG annunciator appears, indicating program-entry mode is active. 2. Enter the commands and other objects (with appropriate delimiters) in order for the operations you want the program to execute. Press # to separate consecutive numbers. Press ™ to move past closing delimiters. 3.
To stop an executing program: Press −. Example: Enter a program that takes a radius value from the stack and calculates the volume of a sphere of radius r using V= 4 π 3 r3 If you were going to calculate the volume manually after entering the radius on the stack, you might press these keys: 3Q!ì*4`3/*@ï Enter the same keystrokes in a program. (@ë just starts a new line.) @% 3Q!ì*4#3/* @ë @ï Put the program on the stack. ` Store the program in variable VOL.
Example: Enter a program SPH that calculates the volume of a spherical cap of height h within a sphere of radius R using values stored in variables H and R. 1 2 V = --- πh ( 3r – h ) 3 In this and following chapters on programming, “stack diagrams” show what arguments must be on the stack before a program is executed and what results the program leaves on the stack. Here’s the stack diagram for SPH.
This is the program: « '1/3*π*H^2*(3*R-H)' →NUM » Now use SPH to calculate the volume of a spherical cap of radius r = 10 and height h = 3. First, store the data in the appropriate variables. Then select the VAR menu and execute the program. The answer is returned to level 1 of the stack. 10 O R K 3OHK J %SPH% Viewing and Editing Programs You view and edit programs the same way you view and edit other objects — using the command line. To view or edit a program: 1.
Save the edited version of SPH in the variable. Then, to verify that the changes were saved, view SPH in the command line. `J!%SPH% @%SPH% ˜ Press − to stop viewing. Creating Programs on a Computer It is convenient to create programs and other objects on a computer and then load them into the calculator. If you are creating programs on a computer, you can include “comments” in the computer version of the program. To include a comment in a program: Enclose the comment text between two @ characters.
For example, if the stack looks like this: then → a creates local variable a = 20. → ab creates local variables a = 6 and b = 20. → abc creates local variables a = 10, b = 6, and c = 20. The defining procedure then uses the local variables to do calculations. Local variable structures have these advantages: The → command stores the values from the stack in the corresponding variables — you don’t need to explicitly execute STO.
Evaluating Local Names Local names are evaluated differently from global names. When a global name is evaluated, the object stored in the corresponding variable is itself evaluated. (You’ve seen how programs stored in global variables are automatically evaluated when the name is evaluated.) When a local name is evaluated, the object stored in the corresponding variable is returned to the stack but is not evaluated.
Example: In the following program excerpt, the defining procedure for local variables d, e, and f calls a program that you previously created and stored in global variable P1. Program: Comments: « : → a b c « a b + c + → d e f 'P1+a/(d*e+f)' Defines local variables d, e, f. Local variables a, b, c and d, e, f are available in this procedure. The defining procedure executes the program stored in variable P1.
If a program begins with a local variable structure and has a program as the defining procedure, the complete program acts like a user-defined function in two ways: it takes numeric or symbolic arguments, and takes those arguments either from the stack or in algebraic syntax. However, it does not have a derivative. (The defining program must, like algebraic defining procedures, return only one result to the stack.
If neither object is an algebraic or a name, returns 1. if the two objects are the same type and have the same value, or 0. otherwise. For example, if 6 is stored in X, X 5 < puts 6 and 5 on the stack, then removes them and returns 0.. (Lists and programs are considered to have same value if the objects they contain are identical. For strings, “less than” means “alphabetically previous.
Testing Object Types The TYPE command (!°%TEST% L %TYPE%) takes any object as its argument and returns the number that identifies that object type. For example, "HELLO" TYPE returns 2, the value for a string object. See the table of object types in chapter 3, in the TYPE command, to find calculator objects and their corresponding type numbers. Testing Linear Structure The LININ command (!°%TEST% !«%LININ%) takes an algebraic equation on level 2 and a variable on level 1 as arguments and returns 1.
« … IF test-clause THEN true-clause ELSE false-clause END … » IF … THEN … ELSE … END executes either the true-clause sequence of commands if the test-clause is true, or the false-clause sequence of commands if the test-clause is false. If the test-clause is an algebraic, it’s automatically evaluated to a number — you don’t need →NUM or EVAL. IF begins the test-clause, which leaves a test result on the stack. THEN removes the test result from the stack.
To enter CASE 7 END in a program: 1. Press !°%BRCH% !%CASE% to enter CASE … THEN …END…END 2. For each additional test-clause, move the cursor after a test-clause END and press @%CASE% to enter THEN … END. Conditional Examples These examples illustrate conditional structures in programs. Example: One Conditional Action. The programs below test the value in level 1 — if the value is positive, it’s made negative.
Example: Two Conditional Actions. This program takes a value x from the stack and calculates (sin x)/x. At x = 0 the division would error, so the program returns the limit value 1 in this case. « → x « IF 'x‹0' THEN x SIN x / ELSE 1 END » » The following version uses IFTE algebraic syntax: « → x 'IFTE(x‹0,SIN(x)/x,1' » Example: Two Conditional Actions. This program multiplies two numbers together if they’re both nonzero — otherwise, it returns the string “ZERO”.
Example: Multiple Conditional Actions. The following program stores the level 1 argument in a variable if the argument is a string, list, or program. Program: « → y « CASE y TYPE 2 SAME THEN y 'STR' STO END y TYPE 5 SAME THEN y 'LIST' STO END y TYPE 8 SAME THEN y 'PROG' STO END END » » Comments: Defines local variable y. Starts the defining procedure. Starts the case structure. Case 1: If the argument is a string, stores it in STR. Case 2: If the argument is a list, stores it in LIST.
The START 7 NEXT Structure The syntax for this structure is « … start finish START loop-clause NEXT … » START … NEXT executes the loop-clause sequence of commands one time for each number in the range start to finish. The loop-clause is always executed at least once.
The START 7 STEP Structure The syntax for this structure is « … start finish START loop-clause increment STEP … » START … STEP executes the loop-clause sequence just like START … NEXT does — except that the program specifies the increment value for the counter, rather than incrementing by 1. The loop-clause is always executed at least once.
The FOR 7 NEXT Structure The syntax for this structure is « … start finish FOR counter loop-clause NEXT … » FOR … NEXT executes the loop-clause program segment one time for each number in the range start to finish, using local variable counter as the loop counter. You can use this variable in the loop-clause. The loop-clause is always executed at least once.
The FOR 7 STEP Structure The syntax for this structure is « … start finish FOR counter loop-clause increment STEP … » FOR … STEP executes the loop-clause sequence just like FOR … NEXT does — except that the program specifies the increment value for counter, rather than incrementing by 1. The loop-clause is always executed at least once.
Example: The following program takes n from the stack, and returns the series of numbers 1, 2, 4, 8, 16, …, n. If n isn’t in the series, the program stops at the last value less than n. « 1 SWAP FOR n n n STEP » The first n is the local variable declaration for the FOR loop. The second n is put on the stack each iteration of the loop. The third n is used by STEP as the step increment.
Example: The following program calculates n + 2n +3n + … for a value of n. The program stops when the sum exceeds 1000, and returns the sum and the coefficient of n. Program: Comments: « DUP 1 → n s c Duplicates n, stores the value into n and s, and initializes c to 1. « Starts the defining procedure. DO 'c' INCR n * 's' STO+ UNTIL s 1000 > Starts the loop-clause. Increments the counter by 1. (See Using Loop Counters.) Calculates c × n and adds the product to s. Starts the test-clause.
The WHILE 7 REPEAT 7 END Structure The syntax for this structure is « … WHILE test-clause REPEAT loop-clause END … » WHILE … REPEAT … END repeatedly evaluates test-clause and executes the loop-clause sequence if the test is true. Because the test-clause is executed before the loop-clause, the loop-clause is not executed if the test is initially false.
Using Loop Counters For certain problems you may need a counter inside a loop structure to keep track of the number of loops. (This counter isn’t related to the counter variable in a FOR … NEXT/STEP structure.) You can use any global or local variable as a counter. You can use the INCR or DECR command to increment or decrement the counter value and put its new value on the stack.
Using Summations Instead of Loops For certain calculations that involve summations, you can use the Σ function instead of loops. You can use Σ with stack syntax or with algebraic syntax. Σ automatically repeats the addition for the specified range of the index variable — without using a loop structure. Example: The following programs take an integer upper limit n from the stack, then find the summation. One program uses a FOR … NEXT loop — the other uses Σ.
Using Flags You can use flags to control calculator behavior and program execution. You can think of a flag as a switch that is either on (set) or off (clear). You can test a flag’s state within a conditional or loop structure to make a decision. Because certain flags have unique meanings for the calculator, flag tests expand a program’s decision-making capabilities beyond that available with comparison and logical functions. Types of Flags The calculator has two types of flags: System flags.
Example: System Flag. The following program sets an alarm for June 6, 2007 at 5:05 PM. It first tests the status of system flag –42 (Data Format flag) in a conditional structure and then supplies the alarm date in the current date format, based on the test result. Example: Program: Comments: « THEN 6.152007 Tests the status of flag –42, the Date Format flag. If flag –42 is clear, supplies the date in month/day/year format. ELSE 15.062007 If flag –42 is set, supplies the date in day.month.year format.
To recall the current flag states: Execute RCLF (!°L %MODES% %FLAG% L%RCLF% ). RCLF returns a list containing four 64-bit binary integers representing the current states of the lower and upper groups of system and user flags: { #nsystem-lower #nuser-lower #nsystem-upper #nuser-upper } To change the current flag states: 1. Enter the flag-state argument — see below 2. Execute STOF (!°L %MODES% %FLAG% L%STOF% ).
Program: Comments: « → a b 'π^2*(b^2-a^2)' Creates local variables a and b. Calculates the surface area. →NUM » Converts algebraic to a number. ` O TORSA K Puts the program on the stack. Stores the program in TORSA. Here is a stack diagram and program listing for TORSV. Level 2 Level 1 → Level 1 a b → volume Program: Comments: « → a b Creates local variables a and b. « a b TORSA b a - * 4 / Starts a program as the defining procedure.
Single-Stepping through a Program It’s easier to understand how a program works if you execute it step by step, observing the effect of each step. Doing this can help you debug your own programs or understand programs written by others. To single-step from the start of a program: 1. Put the program or program name in level 1 (or the command line). 2. Press !°LL%RUN% %DBUG% to start and immediately suspend execution. HLT appears in the status area. 3.
To single-step from the middle of a program: 1. Insert a HALT command in the program where you want to begin single-stepping. 2. Execute the program normally. The program stops when the HALT command is executed, and the HLT annunciator appears. 3. Take any action: To see the next program step displayed in the status area and then executed, press %SST%. To display but not execute the next one or two program steps, press %NEXT%. To continue with normal execution, press !=.
Single-Step Operations Key Programmable Command Description !°LL%RUN% : %DBUG% DBUG Starts program execution, then suspends it as if HALT were the first program command. Takes as its argument the program or program name in level 1. Executes the next object or command in the suspended program. %SST% %SST°% Same as %SST%, except if the next program step is a subroutine, single-steps to the first step in that subroutine. %NEXT% Displays the next one or two objects, but does not execute them.
To artificially cause a built-in error to occur in a program: 1. Enter the error number (as a binary integer or real number) for the error. 2. Enter the DOERR command (PRG ERROR menu). If DOERR is trapped in an IFERR structure (described in the next topic), execution continues. If it’s not trapped, execution is abandoned at the DOERR command and the error message appears. To analyze an error in a program: To get the error number for the last error, execute ERRN (PRG ERROR menu).
Making an Error Trap You can construct an error trap with one of the following conditional structures: IFERR … THEN … END. IFERR … THEN … ELSE … END. The IFERR 7 THEN 7 END Structure The syntax for this structure is « … IFERR trap-clause THEN error-clause END … » The commands in the error-clause are executed only if an error is generated during execution of the trap-clause.
The IFERR 7 THEN 7 ELSE 7 END Structure The syntax for this structure is « … IFERR trap-clause THEN error-clause ELSE normal-clause END … » The commands in the error-clause are executed only if an error is generated during execution of the trap-clause. If an error occurs in the trap-clause, the error is ignored, the remainder of the trap-clause is skipped, and program execution jumps to the error-clause.
Input A program can stop for user input, then resume execution, or can use choose boxes or input forms (dialog boxes) for input. You can use several commands to get input: PROMPT (!=to resume). DISP FREEZE HALT (!=to resume). INPUT (`to resume). INFORM CHOOSE Data Input Commands Key Command Description !°L %IN% : %INFOR% INFORM Creates a user-defined input form. %NOVAL% NOVAL Place holder for the INFORM command. Returned when a value is not present in an input form field.
Example: If you execute this program segment « "ABC?" PROMPT » the display looks like this: Example: The following program, TPROMPT, prompts you for the dimensions of a torus, then calls program TORSA (from page 1-29) to calculate its surface area. You don’t have to enter data on the stack prior to program execution. Program: Comments: « "ENTER a, b IN ORDER:" Puts the prompting string on the stack.
Continue the program. != Note that when program execution is suspended by PROMPT, you can execute calculator operations just as you did before you started the program. If the outer radius b of the torus in the previous example is measured as 0.83 feet, you can convert that value to inches while the program is suspended for data input by pressing .83 `12 *, then !=.
(The in the previous program is the calculator’s representation for the newline character after you enter a program on the stack.) Using INPUT, ENTER for Input INPUT lets you use the stack area for prompting, lets you supply default input, and prevents the user from using normal stack operations or altering data on the stack. To enter INPUT in a program: 1. Enter a string (with "" delimiters) to be displayed as a prompt at the top of the stack area. 2.
The following program, VSPH, calculates the volume of a sphere. VSPH prompts for the radius of the sphere, then cubes it and multiplies by 4/3 π. VSPH executes INPUT to prompt for the radius. INPUT sets Program-entry mode when program execution pauses for data entry. Program: Comments: « "Key in radius" Specifies the prompt string. "" Specifies the command-line string. In this case, the command line will be empty.
To include INPUT options: Use a list (with {} delimiters) as the command-line argument for INPUT. The list can contain one more of the following: Command-line string (with "" delimiters). Cursor position as a real number or as a list containing two real numbers. Operating options ALG, Œ, or V. In its general form, the level 1 argument for INPUT is a list that specifies the content and interpretation of the command line.
To process the result string from INPUT: For simple input, use OBJ→ to convert the string into its corresponding objects. For sensitive input, use the V option for INPUT to check for valid objects, then use OBJ→ to convert the string into those objects. For special input, process the input as a string object, possibly extracting data as substrings. Example: The program VSPH on page 1-41 uses an empty command-line string.
Execute TINPUT to calculate the surface area of a torus of inner radius a = 10 and outer radius b = 20. J %TINPU% Key in the value for a, press ˜ to move the cursor to the next prompt, then key in the value for b. 10 ˜20 Continue program execution. ` Example: The following program executes INPUT to prompt for a social security number, then extracts two strings: the first three digits and last four digits. The level 1 argument for INPUT specifies: A command-line string with dashes.
Program: Comments: « "Key in S.S. #" { " - " -1 } INPUT DUP 1 3 SUB SWAP 8 11 SUB Prompt string. Command-line string (3 spaces before the first -, 2 spaces between, and 4 spaces after the last -). Suspends the program for input. Copies the result string, then extracts the first three and last four digits in string form. » O SSEC ‰ Stores the program in SSEC. Using INFORM and CHOOSE for Input You can use input forms (dialog boxes), and choose boxes for program input.
You can specify a help message and the type of data that must be entered in field by entering field specifications as lists. For example, { { "Name:" "Enter your name" 2 } } defines the Name field, displays Enter your name across the bottom of the input form, and accepts only object type 2 (strings) as input. To set up a choose box: 1. Enter a title string for the choose box. 2. Enter a list of items.
Program: Comments: "ADD A NAME" { { "NAME:" "ENTER NAME" 2 } { "PHONE:" "ENTER A PHONE NUMBER" 2 } } { } { } { } INFORM REPEAT Creates an input form that gets the name and phone number. The two fields accept only strings (object type 2). DUP IF { NOVAL } HEAD POS THEN DROP "Complete both fields before pressing OK" MSGBOX ELSE 1 →LIST NAMES + SORT 'NAMES' STO Checks if either field in the new entry is blank. END END END Ends the IF structure, the WHILE loop, and the CASE statement.
You can delete names and numbers by editing the NAMES variable. To improve upon this program, create a delete name routine. Beeping to Get Attention To enter BEEP in a program: 1. Enter a number that specifies the tone frequency in hertz. 2. Enter a number that specifies the tone duration in seconds. 3. Enter the BEEP command (!°L%OUT% L menu). « … frequency duration BEEP … » BEEP takes two arguments from the stack: the tone frequency from level 2 and the tone duration from level 1.
Using KEY for Keystroke Input You can use KEY inside an indefinite loop to “pause” execution until any key — or a certain key — is pressed. To enter a KEY loop in a program 1. Enter the loop structure. 2. In the test-clause sequence, enter the KEY command (PRG IN menu) plus any necessary test commands. 3. In the loop-clause, enter no commands to give the appearance of a “paused” condition. KEY returns 0 to level 1 when the loop begins.
Labeling Output with Tags To label a result with a tag: 1. Put the output object on the stack. 2. Enter a tag — a string, a quoted name, or a number. 3. Enter the →TAG command (PRG TYPE menu). « … object tag →TAG … » →TAG takes two arguments — an object and a tag — from the stack and return a tagged object. Example: The following program TTAG is identical to TINPUT, except that it returns the result as AREA: value.
Example: The following program TSTRING is identical to TINPUT, except that it converts the program result to a string and appends a labeling string to it. Program: Comments: « "Key in a, b" { ":a: :b:" {1 0} V} INPUT OBJ→ TORSA →STR "Area = " SWAP + CLLCD 1 DISP 3 FREEZE Converts the result to a string. Enters the labeling strings. Swaps and adds the two strings. Displays the resultant string, without its delimiters, in line 1 of the display. » `OTSTRING ‰ Stores the program in TSTRING.
You must acknowledge a message box by pressing %OK% or −. Using Menus with Programs You can use menus with programs for different purposes: Menu-based input. A program can set up a menu to get input during a halt in a program and then resume executing the same program. Menu-based application. A program can set up a menu and finish executing, leaving the menu to start executing other related programs. To set up a built-in or library menu: 1. Enter the menu number. 2.
The program remains halted until it’s resumed by a CONT command, such as by pressing !æ. If you create a custom menu for input, you can include a CONT command to automatically resume the program when you press the menu key. Example: The following program activates page 1 of the MODES ANGL menu and prompts you to set the angle mode. After you press the menu key, you have to press !æto resume execution.
1.25 !æ Example: The following program, EIZ, constructs a custom menu to emulate the HP Solve application for a capacitive electrical circuit. The program uses the equation E = IZ, where E is the voltage, I is the current, and Z is the impedance. Because the voltage, current, and impedance are complex numbers, you can’t use the HP Solve application to find solutions.
Store the voltage value. Then key in and store the current value. Solve for the impedance. %%E%% !Ü .37 ~@6 68 %%I%% !%%Z%% Recall the current and double it. Then find the voltage. @%%I%% 2 *%%I%% !%%E%% Press (!&H)%FMT% %STD% and L %MODES %ANGLE %RECT% to restore Standard and Rectangular modes. Turning Off the Calculator from a Program To turn off the calculator in a program: Execute the OFF command (PRG RUN menu). The OFF command turns off the calculator.
2 2.RPL Programming Examples The programs in this chapter demonstrate basic programming concepts. These programs are intended to improve your programming skills, and to provide supplementary functions for your calculator. At the end of each program, the program’s checksum and size in bytes are listed to help make sure you typed the program in correctly. (The checksum is a binary integer that uniquely identifies the program based on its contents).
Techniques used in FIB1 IFTE (if -then-else function). The defining procedure for FIB1 contains the conditional function IFTE, which can take its argument either from the stack or in algebraic syntax. Recursion. The defining procedure for FIB1 is written in terms of FIB1, just as Fn is defined in terms of Fn-1 and Fn-2. FIB1 program listing Program: Comments: « → n 'IFTE(n‰1, n, FIB1(n-1)+FIB1(n-2))' Defines local variable n. The defining procedure, an algebraic expression.
FIB2 program listing Program: Comments: « → n « IF n 1 ‰ THEN n ELSE Creates a local variable structure. If n ≤ 1, then Fn = n; otherwise … 0 1 Puts F0 and F1 on the stack. 2 n START DUP From 2 to n does the following loop: Copies the latest F (initially F1) ROT Gets the previous F (initially F0) + Calculates the next F (initially F2) NEXT Repeats the loop. SWAP DROP Drops Fn-1. END » » `O FIB2 K Ends the ELSE clause. Ends the defining procedure. Stores the program in FIB2.
FIBT (Comparing Program-Execution Time) FIB1 calculates intermediate values Fi more than once, while FIB2 calculates each intermediate Fi only once. Consequently, FIB2 is faster. The difference in speed increases with the size of n because the time required for FIB1 grows exponentially with n, while the time required for FIB2 grows only linearly with n. FIBT executes the TICKS command to record the execution time of FIB1 and FIB2 for a given value of n.
Example: Calculate F13 and compare the execution time for the two methods. Select the VAR menu and do the calculation. J 13 %FIBT% F13 is 233. FIB2 takes fewer seconds to execute than FIB1 (far fewer if n is large). (The times required for the calculations depend on the contents of memory and other factors, so you may not get the exact times shown above.
PAD program listing Program: Comments: « →STR WHILE DUP SIZE 22 < REPEAT " " SWAP + END Makes sure the object is in string form. (Strings are unaffected by this command.) Repeats if the string contains fewer than 22 characters. Loop-clause adds a leading space. End loop. » `OPAD K Stores the program in PAD. Checksum: # 6577d Bytes: 57.5 PAD is demonstrated in the program BDISP.
PRESERVE program listing Program: Comments: « RCLF Recalls the list of four 64-bit binary integers representing the status of the 128 system flags and 128 user flags. → f Stores the list in local variable f. « Begins the defining procedure. Starts the error trap. Executes the program placed on the stack as the level 1 argument. If the program caused an error, restores flags, shows the error, and aborts execution. Ends the error routine.
Techniques used in BDISP IFERR…THEN…END (error trap). To accommodate real-number arguments, BDISP includes the command R→B (real-to-binary). However, this command causes an error if the argument is already a binary integer. To maintain execution if an error occurs, the R→B command is placed inside an IFERR clause. No action is required when an error occurs (since a binary number is an acceptable argument), so the THEN clause contains no commands. Enabling LASTARG.
BDISP program listing Program: Comments: « Begins the main nested program. « DUP Makes a copy of n. -55 CF Clears flag –55 to enable LASTARG. Begins error trap. IFERR R→B Converts n to a binary integer. THEN END If an error occurs, do nothing (no commands in the THEN clause). → n « CLLCD Creates a local variable n and begins the defining program. Clears the display. « BIN » « OCT » Nested program for BIN. Nested program for OCT. « DEC » Nested program for DEC.
Example: Switch to DEC base, display #100 in all bases, and check that BDISP restored the base to DEC. Clear the stack and select the MTH BASE menu. Make sure the current base is DEC and enter #100. ‚· ‚ã%DEC% !â100 ` Execute BDISP. J %BDISP% Return to the normal stack display and check the current base. − ‚ã Although the main nested program left the calculator in BIN base, PRESERVE restored DEC base. To check that BDISP also works for real numbers, try 144.
Techniques used in %TILE FLOOR and CEIL. For an integer, FLOOR and CEIL both return that integer; for a noninteger, FLOOR and CEIL return successive integers that bracket the noninteger. SORT. The SORT command sorts the list elements into ascending order. %TILE program listing Program: Comments: « SWAP SORT DUP SIZE Brings the list to level 1 and sorts it. Copies the list, then finds its size. 1 + ROT % Calculates the position of the specified percentile.
Techniques used in MEDIAN Arrays, lists, and stack elements. MEDIAN extracts a column of data from ΣDAT in vector form. To convert the vector to a list, MEDIAN puts the vector elements on the stack and combines them into a list. From this list the median is calculated using %TILE. The median for the mth column is calculated first, and the median for the first column is calculated last. As each median is calculated, ROLLD is used to move it to the top of the stack.
Program: Comments: Combines all the medians into an m-element vector. Restores ΣDAT to its previous value. m →ARRY s STOΣ Ends the defining procedure. » » `OMEDIAN K Stores the program in MEDIAN. Checksum: # 256d Bytes: 140 Example: Calculate the median of the following data. 18 4 3 11 31 20 12 7 2 1 48 17 There are two columns of data, so MEDIAN will return a two-element vector. Enter the matrix.
MULTI (Multiple Execution) Given an object and a program that acts on the object, MULTI applies the program to the object repeatedly until the program no longer changes the object. Level 2 Level 1 → Level 1 object «program» → objectresult Techniques used in MULTI DO…UNTIL…END (indefinite loop). The DO clause contains the steps to be repeated. The UNTIL clause contains the test that repeats both clauses again (if false) or exits (if true). Programs as arguments.
EXCO (Expand and Collect Completely) EXCO repeatedly executes EXPAN on an algebraic until the algebraic doesn’t change, then repeatedly executes COLCT until the algebraic doesn’t change. In some cases the result will be a number. Expressions with many products of sums or with powers can take many iterations of EXPAN to expand completely, resulting in a long execution time for EXCO. Level 1 → Level 1 'algebraic' → 'algebraic' 'algebraic' → z Techniques used in EXCO Subroutines.
!Ü4 *Y+Z ™+ ! Ü 8 *X -5 *Z ™Q2 ` Select the VAR menu and start the program. J %EXCO% Minimum and Maximum Array Elements This section contains two programs that find the minimum or maximum element of an array: MNX uses a DO…UNTIL…END (indefinite) loop. MNX2 uses a FOR…NEXT (definite) loop. MNX (Minimum or Maximum Element—Version 1) MNX finds the minimum or maximum element of an array on the stack.
MNX program listing Program: Comments: « {{ « { « "MAX" 10 SF CONT » } "MIN" 10 CF CONT » }} TMENU "Sort for MAX or MIN?" PROMPT Defines the option menu. %MAX% sets flag 10 and continues execution. %MIN% clears flag 10 and continues execution. Displays the temporary menu and a prompt message. 1 GETI Gets the first element of the array. DO Begins the DO loop. ROT ROT GETI 4 ROLL DUP2 IF > 10 FS? XOR Puts the index and the array in levels 1 and 2, then gets the new array element.
Enter the matrix. !² 12 `56 `˜šš 45 `1 ` 9 `14 ` ` Select the VAR menu and execute MNX. J %MNX% Find the maximum element. %MAX% MNX2 (Minimum or Maximum Element—Version 2) Given an array on the stack, MNX2 finds the minimum or maximum element in the array. MNX2 uses a different approach than MNX: it executes OBJ→ to break the array into individual elements on the stack for testing, rather than executing GETI to index through the array.
MNX2 program listing Program: Comments: « {{ "MAX" « 10 SF CONT » } { "MIN" « 10 CF CONT » }} TMENU "Sort for MAX or MIN?" PROMPT DUP OBJ→ 1 SWAP OBJ→ Defines the temporary option menu. %MAX% sets flag 10 and continues execution. %MIN% clears flag 10 and continues execution. Displays the temporary menu and a prompting message. Copies the array. Returns the individual array elements to levels 2 through nm+1, and returns the list containing n and m to level 1. Sets the initial counter value.
!² 12 `56 `˜šš 45 `1 ` 9 `14 ` ` Select the VAR menu and execute MNX2. J %MNX2% Find the minimum element. %MIN% Applying a Program to an Array APLY makes use of list processing to transform each element of an array according to a desired procedure. The procedure applied to each element must be a program that takes exactly one argument (i.e. the element) and returns exactly one result (i.e. the transformed element).
Program: 1 CF a DUP SIZE DUP SIZE IF 1 == THEN 1 SF 1 + SWAP OBJ→ OBJ→ DROP 1 + ROLL ELSE DROP2 a OBJ→ END DUP OBJ→ DROP * SWAP OVER 2 + ROLLD →LIST 1 p DOSUBS OBJ→ 1 + ROLL IFERR IF 1 FS? THEN OBJ→ DROP →LIST END →ARRY THEN OBJ→ IF 1 FC?C THEN DROP END → n m « 1 n FOR i m →LIST 'm*(n-i)+i' EVAL ROLLD Comments: Make sure the flag 1 is clear to begin the procedure. Retrieve the dimensions of the array. Determine if the array is a vector.
Program: Comments: Repeat loop for the next row. Gather rows into a list, forming a list of lists (symbolic pseudo-array). Close the local variable structure and end the IFERR…THEN…END structure. Clear flag 1 before exiting the program. NEXT n →LIST » END 1 CF » » Stores the program in APLY. `OAPLY K Checksum: # 11132d Bytes: 314 Example: Apply the function, f(x) = Ax3-7 to each element x of the vector [ 3 -2 4 ].
nBASE program listing Program: Comments: « 1 CF 0 RND SWAP 0 RND RCLF Clear flag 1, round both arguments to integers and recall flag settings. → b n f Store the base, number and flag settings in local variables. Begin the outer local variable structure. « STD n LOG b LOG / Sets “standard” display mode and computes the ratio of the common logarithms of number and base. 10 RND Rounds result to remove imprecision in last decimal place.
Program: UNTIL 'm' EVAL 0 == END IF 1 FS?C THEN "0" + Comments: Repeat the DO...UNTIL loop until m = 0 (i.e. all decimal value have been accounted for). Is flag 1 set? Clear the flag after the test. Then add a placeholding zero to the result string. WHILE i 'k' EVAL - 0 ‹ Begin WHILE...REPEAT loop to determine if additional placeholding zeros are needed. Loop repeats as long as i≠k. REPEAT "0" + 1 'k' STO+ Add an additional placeholding zero and increment k before repeating the testclause.
NAMES (Check List for Exactly Two Names) If the argument for a program is a list (as determined by VFY), NAMES verifies that the list contains exactly two names. If the list does not contain exactly two names, an error message appears in the status area and program execution is aborted. Level 1 → { valid list } → { invalid list } → Level 1 (error message in status area) Techniques used in NAMES Nested conditionals. The outer conditional verifies that there are two objects in the list.
Checksum: # 10752d Bytes: 141.5 NAMES is demonstrated in the program VFY. VFY (Verify Program Argument) VFY verifies that an argument on the stack is either a name or a list that contains exactly two names. Level 1 → Level 1 'name' → 'name' { valid list } → { valid list } { invalid list } → { invalid list } (and error message in status area) invalid object → invalid object (and error message in status area) Techniques used in VFY Utility programs. VFY by itself has little use.
Program: argm TYPE 6. SAME NOT THEN "Not name or list" DOERR END END » » Comments: Tests if the argument is not a name. If so, displays an error message and aborts execution. Ends the CASE structure. Ends the defining procedure. Enters the program, then stores it in VFY. `OVFYK Checksum: # 31403d Bytes: 139.5 Example: Execute VFY to test the validity of the name argument BEN. (The argument is valid and is simply returned to the stack.
Techniques used in →RPN Recursion. The →RPN program calls itself as a subroutine. This powerful technique works just like calling another subroutine as long as the stack contains the proper arguments before the program calls itself. In this case the level 1 argument is tested first to be sure that it is an algebraic expression before →RPN is called again. Object Type-Checking. →RPN uses conditional branching that depends on the object type of the level 1 object. Nested program Structures.
Checksum: # 1522d Bytes: 189.5 Example: Convert the following algebraic expression to a series of objects in RPN syntax: 'A*COS(B+ƒ(C/D))-X^3'. OA *TB +R!Ü C /D ™™-X Q3 `%²RPN% Bessel Functions This section contains a program, BER, that calculates the real part Bern(x) of the Bessel function Jn (xe3πi/4). When n = 0, 4 8 (x ⁄ 2 ) (x ⁄ 2 ) Ber ( x ) = 1 – ----------------- + ----------------- – … 2 2 2! 4! Level 1 → Level 1 z → Ber(z) Techniques used in BER Local variable structure.
BER program listing Program: Comments: « → x Creates local variable x. « 'x/2' →NUM 2 1 → xover2 j sum « DO sum 'sum+(-1)^(j/2)* xover2^(2*j)/SQ(j!)' EVAL 2 'j' STO+ DUP 'sum' STO UNTIL == END sum » » » `OBER K Checksum: # 15837d Bytes: 203 Example: Calculate BER(3). J 3 %BER% Calculate BER(2) in algebraic syntax. O %BER% !Ü2 N 2-30 RPL Programming Examples Begins outer defining procedure. Enters x/2, the first counter value, and the first term of the series, then creates local variables.
Animation of Successive Taylor’s Polynomials This section contains three programs that manipulate graphics objects to display a sequence of Taylor’s polynomials for the sine function. SINTP draws a sine curve, and saves the plot in a variable. SETTS superimposes plots of successive Taylor’s polynomials on the sine curve plot from SINTP, and saves the resulting graphics objects in a list. TSA uses the ANIMATE command to display in succession each graphics object from the list built in SETTS.
SETTS (Superimposing Taylor’s polynomials) SETTS superimposes successive Taylor’s polynomials on a sine curve and stores each graphics object in a list. Techniques used in SETTS Structured programming. SETTS calls SINTP to build a sine curve and convert it to a graphics object. FOR…STEP (definite loop). SETTS calculates successive Taylor’s polynomials for the sine function in a definite loop. The loop counter serves as the value of the order of each polynomial. Programmatic use of PLOT commands.
TSA (Animating Taylor’s Polynomials) TSA displays in succession each graphics object created in SETTS. Techniques used in TSA Passing a global variable. Because SETTS takes several minutes to execute, TSA does not call SETTS. Instead, you must first execute SETTS to create the global variable TSL containing the list of graphics objects. TSA simply executes that global variable to put the list on the stack. ANIMATE.
Programmatic Use of Statistics and Plotting This section describes a program PIE you can use to draw pie charts. PIE prompts for single variable data, stores that data in the statistics matrix ΣDAT, then draws a labeled pie chart that shows each data point as a percentage of the total. Techniques used in PIE Programmatic use of PLOT commands. PIE executes XRNG and YRNG to define x- and y-axis display ranges in user units, and executes ARC and LINE to draw the circle and individual slices.
Program: Comments: (66,32) 20 0 6.28 ARC Draws the circle. PICT RCL →LCD Displays the empty circle. RCLΣ TOT / Recalls the statistics data matrix, computes totals, and calculates the proportions. Converts the proportions to percentages. DUP 100 * → prcnts Stores the percentage matrix in prcnts. « 2 π →NUM * * 0 Multiplies the proportion matrix by 2π, and enters the initial angle (0). → prop angle Stores the angle matrix in prop and angle in angle.
Program: prcnts n GET 1 RND →STR "%" + Comments: Gets the nth value from the percentage matrix, rounds it to one decimal place, and converts it to a string with “%” appended. 1 →GROB Converts the string to a graphics object. GOR DUP PICT STO Adds the label to the plot and stores the new plot. →LCD NEXT { } PVIEW » » flags STOF » 0 MENU Displays the updated plot. Ends the loop structure. Displays the finished plot. Restores the original flag status. Restores the previous menu.
Trace Mode This section contains two programs, αENTER and ßENTER, which together provide “trace mode” for the calculator using an external printer. To turn on “trace mode,” set flag –63 and activate User mode. To turn off “trace mode,” clear flag –63 or turn off User mode. Techniques used in αENTER and ßENTER Vectored ENTER. Setting flag –63 and activating User mode turns on vectored ENTER.
Inverse-Function Solver This section describes the program ROOTR, which finds the value of x at which f(x) = y. You supply the variable name for the program that calculates f(x), the value of y, and a guess for x (in case there are multiple solutions). Level 3 Level 2 Level 1 → Level 1 'function name' y x guess → x Techniques used in ROOTR Programmatic use of root-finder. ROOTR executes ROOT to find the desired x-value. Programs as arguments.
Example: Find the value of x for which X→FX equals 599.5. Use a guess in the vicinity of 1. Start by keying in X→FX : @å@é x †O3.7 *x Q3 +4.5 * x Q2 +3.9 *x +5 ` Store the program in X→FX, then enter the program name, the y-value 599.5, and the guess 1, and execute ROOTR: O X→FX K O J %X²FX% ` 599.5 ` 1 %ROOTR% Animating a Graphical Image Program WALK shows a small person walking across the display. It animates this custom graphical image by incrementing the image position in a loop structure.
Program: { # 0d # 25d } PICT OVER walk GXOR 5 MAXR FOR i i 131 MOD R→B # 25d 2 →LIST PICT OVER walk GXOR PICT ROT walk GXOR 0.2 WAIT 5 STEP » » `OWALK K Checksum: # 28684d Bytes: 250.0 Example: Send the small person out for a walk. J %WALK% Press − when you think the walker’s tired. 2-40 RPL Programming Examples Comments: Puts the first position on the stack and turns on the first image. This readies the stack and PICT for the loop. Starts the loop to generate horizontal coordinates indefinitely.
3 3.Full Command and Function Reference Introduction This chapter details the calculator’s commands and functions.
first case, it returns the numeric arccosine; in the second, it returns the symbolic arccosine expression of the argument. Some commands affect a calculator state — a mode, a reserved variable, a flag, or a display — without taking any arguments from the stack or returning any results to the stack. No stack diagrams are shown for these commands. Other commands may have more complicated input or output that is easier to explain in prose.
Computer Algebra System Commands and Functions The Computer Algebra System, or CAS, is a collection of operations that can be applied to algebraic expressions. The calculator’s operations can be used with numbers to produce numeric results, or with symbols to produce algebraic expressions. Algebraic expressions and equations can be written using the Equation Writer too.
Terms Used in Stack Diagrams Term Description arg Argument. [ array ] Real or complex vector or matrix. [ C-array ] Complex vector or matrix. date Date in form MM.DDYYYY or DD.MMYYYY. { dim } List of one or two array dimensions (real numbers). 'global' Global name. grob Graphics object. HMS A real-number time or angle in hours-minutes-seconds format. { list } List of objects. local Local name. [[ matrix ]] Real or complex matrix.
ABCUV Type: Description: Command Access: Arithmetic, !Þ POLYNOMIAL Input: Level 3/Argument 1: The polynomial corresponding to a. Level 2/Argument 2: The polynomial corresponding to b. Level 1/Argument 3: The value corresponding to c. Output: Level 2/Item 1: The solution corresponding to u. Level 1/Item 2: The solution corresponding to v. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
ACK has no effect on control alarms. Control alarms that come due are automatically acknowledged and saved in the system alarm list. Access: Flags: Input/Output: See also: ACKALL Type: Description: Access: Flags: Input/Output: See also: ACOS Type: Description: (Ó is the right-shift of the 9 key). …Ó TOOLS ALRM ACK Repeat Alarms Not Rescheduled (–43), Acknowledged Alarms Saved (–44) None ACKALL Command Acknowledge All Alarms Command: Acknowledges all past-due alarms.
Access: Flags: Input/Output: View these graphs with domain and range reversed to see how the domain of COS is restricted to make an inverse function possible. Consider the vertical band in the lower graph as the restricted domain Z = (x, y). COS sends this domain onto the whole complex plane in the range W = (u, v) = COS(x, y) in the upper graph. !¾ ( ¾ is the left-shift of the T key).
2 arc cos --- + arc cos ( x ) 3 Command: Result: See also: ACOSH Type: Description: ACOS2S(ACOS(2/3)+ACOS(X)) π/2-ASIN(2/3)+π/2-ASIN(X) ASIN2C, ASIN2T, ATAN2S Analytic Function Inverse Hyperbolic Cosine Analytic Function: Returns the inverse hyperbolic cosine of the argument. For real arguments x < 1, ACOSH returns the complex result obtained for the argument (x, 0). The inverse of ACOSH is a relation, not a function, since COSH sends more than one argument to the same result.
ADD Type: Description: Access: Flags: Input/Output: See also: Command Add List Command: Adds corresponding elements of two lists or adds a number to each of the elements of a list. ADD executes the + command once for each of the elements in the list. If two lists are the arguments, they must have the same number of elements as ADD will execute the + command once for each corresponding pair of elements.
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Express the result of the following addition in modulo 7. (x2+3x+6)+(9x+3) Note: Before trying this example, use the CAS modes input form to set the modulo to 7. Command: Result: ADDTMOD(X^2+3*X+6,9*X+3) X^2-2*X+2 ADDTOREAL Type: Command Description: Adds specified global names to the reserved variable REALASSUME.
AMORT Type: Description: Access: Flags: Input/Output: Command Amortize Command: Amortizes a loan or investment based upon the current amortization settings. Values must be stored in the TVM variables (I%YR, PV, PMT, and PYR). The number of payments n is taken from the input together with flag –14. @& Î TVM AMORT (Î is the left-shift of the 7key).
Input/Output: See also: ANIMATE Type: Description: Access: Input/Output: Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1 #n1 #n2 → #n3 “string1” “string2” → “string3” T/F1 T/F2 → 0/1 T/F 'symb' → 'T/F AND symb' 'symb' T/F → 'symb AND T/F'' 'symb1' NOT, OR, XOR 'symb2' → 'symb1 AND symb2' Command Animate Command: Displays graphic objects in sequence. ANIMATE displays a series of graphics objects (or variables containing them) one after the other.
characters), as might have been left on the stack by entries when running in algebraic mode, will be ignored. Access: !î Input/Output: ( îis the left-shift of the `key). Level 1/Argument 1 Level 1/Item 1 → n LAST, LASTARG, PICK See also: APPLY Type: Description: Access: Input/Output: Function Apply to Arguments Function: Creates an expression from the specified function name and arguments.
Access: Flags: !°LPICT ARC ( °is the left-shift of the Nkey). Angle Mode (–17 and –18). The setting of flags –17 and –18 determine the interpretation of xθ1 and xθ2 (degrees, radians, or grads).
ARIT Type: Description: Command Access: Catalog, …µ Flags: If the CHOOSE boxes flag is clear (flag –117 clear), displays the submenus as a numbered list. If the flag is set, displays the operations as a menu of function keys. See also: ALGB, CONSTANTS, DIFF, EXP&LN, INTEGER, MAIN, MATHS, MATR, MODULAR, POLYNOMIAL, REWRITE, TESTS, TRIGO ARRY→ Type: Description: Access: Input/Output: Displays a menu or list showing the three CAS submenus for arithmetical operations, INTEGER, MODULAR and POLYNOMIAL.
The inverse of SIN is a relation, not a function, since SIN sends more than one argument to the same result. The inverse relation for SIN is expressed by ISOL as the general solution: ASIN(Z)*(-1)^n1+π*n1 The function ASIN is the inverse of a part of SIN, a part defined by restricting the domain of SIN such that: • each argument is sent to a distinct result, and • each possible result is achieved. The points in this restricted domain of SIN are called the principal values of the inverse relation.
Input/Output: Level 1/Argument 1 Level 1/Item 1 z → asin z 'symb' → 'ASIN(symb)' See also: ACOS, ATAN, ISOL, SIN ASIN2C Type: Command Description: Transforms an expression by replacing asin(x) subexpressions with π/2–acos(x) subexpressions. Access: Trigonometry, …Ñ Input: An expression Output: The transformed expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
The principal branch used by the calculator for ASINH was chosen because it is analytic in the regions where the arguments of the real-valued function are defined. The branch cut for the complex-valued ASINH function occurs where the corresponding real-valued function is undefined. The principal branch also preserves most of the important symmetries. The graph for ASINH can be found from the graph for ASIN (see ASIN) and the relationship asinh z = –i asin iz.
Be careful not to reassign or suppress the keys necessary to cancel User mode. If this happens, exit User mode by doing a system halt (“warm start”): press and hold ‡and C simultaneously, releasing Cfirst. This cancels User mode.
Input: Level 1/Item 1: An expression giving the name of the global variable to be added to the REALASSUME list, and the assumption to be placed on it, or a list of such assumptions. Output: Level 1/Item 1: The input expression or list of expressions. Example: Add the CAS assumption that the global variable Z is real and positive.
Access: !À ( Àis the left-shift of the Ukey). Flags: Principal Solution (–1), Numerical Results (–3), Angle Mode (–17, –18) Input/Output: Level 1/Argument 1 See also: ACOS, ASIN, ISOL, TAN ATAN2S Type: Description: Command Level 1/Item 1 z → atan z 'symb' → 'ATAN(symb)' Transforms an expression by replacing atan(x) subexpressions with the following: x asin ------------------ x 2 + 1 Access: Trigonometry, …Ñ Input: An expression. Output: The transformed expression.
ATANH Type: Description: Access: Flags: Input/Output: Analytic Function Arc Hyperbolic Tangent Analytic Function: Returns the inverse hyperbolic tangent of the argument. For real arguments |x| > 1, ATANH returns the complex result obtained for the argument (x, 0). For a real argument x=±1, an Infinite Result exception occurs. If flag –22 is set (no error), the sign of the result (MAXR) matches that of the argument.
Input/Output: Level 1/Argument 1 Level 1/Item 1 → → → → x #n {xy} { #n #m } See also: ATTACH Type: Description: AXES, DRAX Command Attach Library Command: Attaches the library with the specified number to the current directory. Each library has a unique number. If a port number is specified, it is ignored. To use a library object, it must be in a port and it must be attached. A library object copied into RAM (such as through the PC Link) must be stored into a port using STO.
1 2 3 4 5 6 Result: AUTO Type: Description: Command Autoscale Command: Calculates a y-axis display range, or an x- and y-axis display range. The action of AUTO depends on the plot type as follows: Plot Type Scaling Action FUNCTION Samples the equation in EQ at 40 values of the independent variable, equally spaced through the x-axis plotting range, discards points that return ±∞, then sets the y-axis display range to include the maximum, minimum, and origin.
The argument for AXES (a complex number or list) is stored as the fifth parameter in the reserved variable PPAR. How the argument is used depends on the type of object it is: • If the argument is a complex number, it replaces the current entry in PPAR. • If the argument is a list containing any or all of the above variables, only variables that are specified are affected. atick has the same format as the argument for the ATICK command. This is the variable that is affected by the ATICK command.
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). See also: AXL, AXQ AXQ Type: Description: Command Access: Convert, !Ú Input: Level 2/Argument 1: An n×n matrix. Level 1/Argument 2: A vector containing n variables. Output: Level 2/Item 1: The corresponding quadratic form. Level 1/Item 2: The vector containing the variables. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
• ptype is a command name specifying the plot type. Executing the command BAR places the command name BAR in PPAR. • depend is a name specifying a label for the vertical axis. The default value is Y. A bar is drawn for each element of the column in ΣDAT. Its width is specified by res and its height is the value of the element. The location of the first bar can be specified by indep; otherwise, the value in (xmin, ymin) is used.
Input/Output: Level 1/Argument 1 → nbaudrate See also: BEEP Type: Description: Access: Flags: Input/Output: See also: BESTFIT Type: Description: Level 1/Item 1 CKSM, PARITY, TRANSIO Command Beep Command: Sounds a tone at n hertz for x seconds. The frequency of the tone is subject to the resolution of the built-in tone generator. The minimum frequency is 1 Hz and the maximum frequency in 15000 Hz. An input that doesn’t round to an integer within this range will cause the BEEP command to be skipped.
BINS Type: Description: Command Sort into Frequency Bins Command: Sorts the elements of the independent column (XCOL) of the current statistics matrix (the reserved variable ΣDAT) into (nbins + 2) bins, where the left edge of bin 1 starts at value xmin and each bin has width xwidth. BINS returns a matrix containing the frequency of occurrences in each bin, and a 2-element array containing the frequency of occurrences falling below or above the defined range of x-values.
Input/Output: See also: BUFLEN Type: Description: Access: Input/Output: Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1 { #n1 #m1 } { #n2 #m2 } → (x1, y1) (x2, y2) → ARC, LINE, TLINE Command Buffer Length Command: Returns the number of characters in the calculator’s serial input buffer and a single digit indicating whether an error occurred during data reception.
If # n ≥ # 1000000000000 (base 10), only the 12 most significant decimal digits are preserved in the resulting mantissa. ( ãis the right-shift of the 3key). Access: …ãB→R Flags: Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12) Input/Output: Level 1/Argument 1 Level 1/Item 1 → #n See also: C$ Type: Description: n R→B Access: Example 1: Command Counted String Command: Enters C$ on the command line to help with the manual entry of a string object.
CASCMD Type: Description: Access: See also: CASE Type: Description: Command Displays a list of CAS operations. Selecting one with OK displays a description, related operations, an example of the operation, and the option to copy the example to the command line. More details are given in Appendix C and Appendix H of the User’s Guide. If level 1 of the stack contains a string, the list of CAS operations will be displayed beginning at this point.
CEIL Type: Function Description: Ceiling Function: Returns the smallest integer greater than or equal to the argument. Access: !´REAL LL CEIL ( ´ is the left-shift of the Pkey).
Input/Output: Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1 x y → 100(y – x)/x x 'symb' → '%CH(x,symb)' 'symb' x → '%CH(symb,x)' 'symb1' 'symb2' → '%CH(symb1, symb2)' x_unit y_unit → 100(y_unit – x_unit)/x_unit x_unit 'symb' → '%CH(x_unit,symb)' Example 1: → 'symb' x_unit '%CH(symb,x_unit)' 1_m 500_cm %CH returns 400, because 500 cm represents an increase of 400% over 1 m. Example 2: 100_K 150_K %CH returns 50.
Example: Find the Cholesky factorization of: 11 15 Command: Result: CHOOSE Type: Description: CHOLESKY 1 1 15 1 1 0 2 Command Create User-Defined Choose Box Command: Creates a user-defined choose box. CHOOSE creates a standard single-choice choose box based on the following specifications: Variable Access: Input/Output: Function “prompt” A message that appears at the top of choose box. If “prompt” is an empty string (“”), no message is displayed.
Access: Input/Output: The character codes are an extension of ISO 8859/1. Codes 128 through 160 are unique to the calculator. See Appendix J for a complete list of characters and character codes. The default character ā is supplied for all character codes that are not part of the normal calculator’s display character set. Character code 0 is used for the special purpose of marking the end of the command line. Attempting to edit a string containing this character causes the error Can't Edit Null Char.
CLEAR Type: Description: Access: Input/Output: Command Clear Command: Removes all objects from the stack or history. To recover a cleared stack or history, press …¯ (the right-shift of the Mkey) before executing any other operation. There is no programmable command to recover the stack or history. …· (·is the right-shift of the ƒkey). Leveln/Argument 1 ... Level 1/Argumentn objn ...obj1 See also: CLKADJ Type: Description: Access: Input/Output: Leveln/Item 1 ...
Access: …µCLOSEIO Input/Output: None See also: BUFLEN, OPENIO CLΣ Type: Description: Command Purges the current statistics matrix (reserved variable ΣDAT). Access: …µCLΣ Input/Output: None See also: RCLΣ, STOΣ, Σ+, Σ– CLUSR Type: Description: Access: Command Clear Variables Command: Provided for compatibility with the HP 28 series. CLUSR is the same as CLVAR. See CLVAR. None. Must be typed in.
→COL Type: Description: Access: Command Matrix to Columns Command: Transforms a matrix into a series of column vectors and returns the vectors and a column count, or transforms a vector into its elements and returns the elements and an element count. →COL introduces no rounding error. !´MATRIX COL →COL ( ´ is the left-shift of the Pkey). !Ø CREATE COLUMN →COL ( Ø is the left-shift of the 5key). Input/Output: Level 1/Argument 1 See also: COL→ Type: Description: Access: Leveln+1/Item 1 ...
COL+ Type: Description: Access: Command Insert Column Command: Inserts an array (vector or matrix) into a matrix (or one or more elements into a vector) at the position indicated by nindex, and returns the modified array. The inserted array must have the same number of rows as the target array. nindex is rounded to the nearest integer. The original array is redimensioned to include the new columns or elements, and the elements at and to the right of the insertion point are shifted to the right.
Example: Factorize the following: 2 x + 5x + 6 Command: Result: See also: COLΣ Type: Description: Access: Input/Output: COLLECT(X^2+5*X+6) (X+2)(X+3) COLCT, EXPAND, FACTOR Command Column Sigma Command: Specifies the independent-variable and dependent-variable columns of the current statistics matrix (the reserved variable ΣDAT). COLΣ combines the functionality of XCOL and YCOL.
Access: The constant value is a real or complex number taken from argument 2/level 1. The resulting array is either a new array, or an existing array with its elements replaced by the constant, depending on the object in argument 1/level 2. • Creating a new array: If argument 1/level 2 contains a list of one or two integers, CON returns a new array. If the list contains a single integer ncolumns, CON returns a constant vector with n elements.
Example: See also: The following program computes the above rule of thumb for the number of accurate digits: « DUP SIZE 1 GET LOG SWAP COND LOG + 11 SWAP - » SNRM, SRAD, TRACE CONIC Type: Description: Command Conic Plot Type Command: Sets the plot type to CONIC. When the plot type is CONIC, the DRAW command plots the current equation as a secondorder polynomial of two real variables. The current equation is specified in the reserved variable EQ.
Input/Output: Level 1/Argument 1 Level 1/Item 1 x → x (x, y) → (x, –y) [ R-array ] → [ R-array ] [ C-array ]1 → [ C-array ]2 See also: → 'symb' 'CONJ(symb)' [ (3,4) (7,2) ] CONJ returns [ (3,-4) (7,-2) ] A square matrix A containing complex elements is said to be Hermitian if AH = A, where AH is the same as a normal transpose except that the complex conjugate of each element is used. The following program returns 1 if the input matrix is Hermitian, and a 0 if it is not.
CONT Type: Description: Command Continue Program Execution Command: Resumes execution of a halted program. Since CONT is a command, it can be assigned to a key or to a custom menu. Access: !æ ( æis the left-shift of the ‡key). Input/Output: None Example: The program « "Enter A, press { CONT }" { CONT } MENU PROMPT » displays a prompt message, builds a menu with the CONT command assigned to the first menu key, and halts the program for data input.
COS Type: Description: Analytic Function Cosine Analytic Function: Returns the cosine of the argument. For real arguments, the current angle mode determines the number’s interpretation as an angle, unless the angular units are specified. For complex arguments, cos(x + iy) = cosx coshy – i sinx sinhy. If the argument for COS is a unit object, then the specified angular unit overrides the angle mode to determine the result. Integration and differentiation, on the other hand, always observe the angle mode.
Input/Output: Level 1/Argument 1 See also: CR Type: Description: Level 1/Item 1 → COLΣ, CORR, PCOV, PREDX, PREDY, XCOL, YCOL xcovariance Command Carriage Right Command: Prints the contents, if any, of the printer buffer. When printing to the serial port (flag –34 set), CR sends to the printer a string that encodes the line termination method. The default termination method is carriage-return/linefeed. The string is the fourth parameter in the reserved variable PRTPAR.
Access: !Ø CREATE COLUMN CSWP !´MATRIX COL CSWP ( Ø is the left-shift of the 5key). ( ´ is the left-shift of the Pkey). Input/Output: See also: Level 3/Argument 1 Level 2/Argument 2 Level 1/Argument 3 [[ matrix ]]1 ncolumni ncolumnj → [[ matrix ]]2 nelementi nelementj → [ vector ]2 [ vector ]1 COL+, COL–, RSWP Level 1/Item 1 CURL Type: Description: Function Access: Calculus, !ÖDERIV. & INTEG. Input: Level 2/Argument 1: A three-dimensional vector function of three variables.
Access: !´VECTOR L CYLIN Input/Output: None See also: RECT, SPHERE C→PX Type: Description: ( ´ is the left-shift of the Pkey). Command Complex to Pixel Command: Converts the specified user-unit coordinates to pixel coordinates. The user-unit coordinates are derived from the (xmin, ymin) and (xmax, ymax) parameters in the reserved variable PPAR. Access: !°LPICT LC→PX Input/Output: ( °is the left-shift of the Nkey).
Flags: Date Format (–42) Input/Output: Level 1/Argument 1 Example: See also: →DATE Type: Description: Access: Flags: Input/Output: Level 1/Item 1 → date If the current date is May 12, 2010, if flag –42 is clear, and if the display mode is Standard, DATE returns 5.12201. (The trailing zeros are dropped.) DATE+, DDAYS, TIME, TSTR Command Set Date Command: Sets the system date to date. date has the form MM.DDYYYY or DD.MMYYYY, depending on the state of flag –42. MM is month, DD is day, and YYYY is year.
Input/Output: Level 1/Argument 1 Level 1/Item 1 « program » or 'program name' See also: DDAYS Type: Description: Access: Flags: Input/Output: See also: DEC Type: Description: Access: → HALT, NEXT Command Delta Days Command: Returns the number of days between two dates. If the argument 1/level 2 date is chronologically later than the argument 2/ level 1 date, the result is negative. The range of allowable dates is October 15, 1582, to December 31, 9999.
DEDICACE Type: Description: Function Access: Catalog, …µ Example: In algebraic mode, the message can be extended. Try: DEDICACE(Salutations) DEF Type: Function Displays a greeting from the CAS team and dedication to all HP calculator users. Description: Defines a variable or a function. Works like the DEFINE command, except that it returns a result and can be included in an algebraic expression.
Input/Output: Level 1/Argument 1 Level 1/Item 1 → 'name=exp' Example 1: Example 2: See also: DEG Type: Description: Access: → 'name(name1 ... namen)=exp(name1 ... namen)' 'A=2*X' DEFINE stores '2*X' in variable A. 'A(X,Y)=2*X+3/Y' DEFINE creates a user-defined function A. The contents of A is the program « → X Y '2*X+3/Y' » DEF, STO, UNASSIGN Command Degrees Command: Sets Degrees angle mode. DEG clears flags –17 and –18, and displays the DEG annunciator.
…&9 ALRM DELALARM Input/Output: Level 1/Argument 1 See also: DELAY Type: Description: nindex FINDALARM, RCLALARM, STOALARM Level 1/Item 1 → Command Delay Command: Specifies how many seconds the calculator waits between sending lines of information to the printer. Setting flag –34 directs printer output to the serial port. In this case, flag –33 must be clear.
Input/Output: Level 1/Argument 1 See also: DEPND Type: Description: Access: Input/Output: xkey → { xkey1, ... ,xkey n } → 0 → 'S' → ASN, RCLKEYS, STOKEYS Command Dependent Variable Command: Specifies the dependent variable (and its plotting range for TRUTH plots). The specification for the dependent variable name and its plotting range is stored in the reserved variable PPAR as follows: • If the argument is a global variable name, that name replaces the dependent variable entry in PPAR.
See also: CLEAR, DROPN DERIV Type: Description: Function Access: Calculus, P CALCULUS or !ÖDERIV. & INTEG. Input: Level 2/Argument 1: A function or a list of functions. Level 1/Argument 2: A variable, or a vector of variables. The variable or variables must not exist as variables stored in the current directory nor directories above it. Output: The derivative, or a vector of the derivatives, of the function or functions. Flags: Exact mode must be set (flag –105 clear).
(See the description of dn and Chapter 16 of the User’s Guide for an explanation of the use of “d1” for a derivative.) Result: See also: DET Type: Description: Access: Flags: Input/Output: {Y(X)=(1/5*EXP(5*X)+cC0)*(1/EXP(X)^2)} dn, LDEC Command Determinant Function: Returns the determinant of a square matrix. The argument matrix must be square. DET computes the determinant of 1 × 1 and 2 × 2 matrices directly from the defining expression for the determinant.
DIAG→ Type: Description: Access: Command Vector to Matrix Diagonal Command: Takes an array and a specified dimension and returns a matrix whose major diagonal elements are the elements of the array. Real number dimensions are rounded to integers. If a single dimension is given, a square matrix is returned. If two dimensions are given, the proper order is { number of rows, number of columns }. No more than two dimensions can be specified.
Command: DIAGMAP 1 1 , << → X<> >> 0 2 or DIAGMAP([[1,1],[0,2]],exp(X)) Result: EXP ( 1 ) – EXP ( 1 ) + EXP ( 2 ) 0 EXP ( 2 ) DIFF Type: Description: Command Access: Catalog, …µ Flags: If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
– If axes contains any strings other than 0, 1 or n, the DIFFEQ plotter uses the default strings 0 and 1, and plots the independent variable on the horizontal axis and the dependent variable on the vertical. • ptype is a command name specifying the plot type. Executing the command DIFFEQ places the command name DIFFEQ in PPAR.
for input. The FREEZE command can be used to cause the object to persist in the display until a key is pressed. ( °is the left-shift of the Nkey). Access: !°LOUT DISP Input/Output: Example: See also: DISPXY Type: Description: Access: Input/Output: Level 2/Argument 1 Level 1/Argument 2 obj n DISTRIB Type: Description: Access: Input: Output: Flags: → The program « "ENTER Data Now" 1 DISP 7 FREEZE HALT » displays ENTER Data Now at the top of the display, “freezes” the entire display, and halts.
DIV Type: Description: Command Access: Calculus, !ÖDERIV. & INTEG. Input: Level 2/Argument 1: An array representing a vector function. Level 1/Argument 2: An array containing the variables. Output: The divergence of the vector function with respect to the specified variables. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Example: Find the divergence of the following vector function: Returns the divergence of a vector function.
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). 3 Example: Command: Result: x +4 ------------2 – 1 x Find the result of , modulo 3. DIV2MOD(X^3+4,X^2-1) {X X+1} DIVIS Type: Description: Command Access: Arithmetic, !Þor PARITH Input: A polynomial or an integer. Output: A list containing the expressions or integers that exactly divide into the input. Flags: Exact mode must be set (flag –105 clear).
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Incremental power mode must be set (flag –114 set). Example: Find the fourth degree Taylor polynomial for the following: 3 x + 4x + 12 ----------------------------11 11x + 1 Command: Result: DIVPC(X^3+4*X+12,11*X^11+1,4) 12+4*X+X^3 See also: TAYLOR0, TAYLR, SERIES dn Type: Description: Function Differential of a function with respect to its argument n.
Input/Output: Level 1/Argument 1 Example: See also: DOERR Type: Description: Access: Input/Output: Level 1/Item 1 DO → UNTIL → END T/F → The following program counts down from 100 to 0 and leaves the integers 100 to 0 on the stack: « 100 'A' STO A DO 'A' DECR UNTIL 'A==0' END 'A' PURGE » END, UNTIL, WHILE Command Do Error Command: Executes a “user-specified” error, causing a program to behave exactly as if a normal error had occurred during program execution.
Input/Output: Ln+2/A1 ... L3/An–2 L2/An+1 L1/An+2 { list }1 ... { list }n n « program » → { results } { list }1 ... { list }n n command → { results } { list }1 ... { list }n n name → { results } { list }1 ... { list }n+1 « program » → { results } { list }1 ... { list }n+1 command → { results } { list }1 ... { list }n+1 name → { results } Level 1/Item 1 L = Level; A = Argument See also: { 1 2 3 } { 4 5 6 } { 7 8 9 } 3 « + * » DOLIST returns { 11 26 45 }.
Access: Input/Output: command ENDSUB. Both of these commands return an Undefined Local Name error if executed when DOSUBS is not active. DOSUBS returns the Invalid User Function error if the object at level 1/argument 3 is a user program that does not contain only one command and does not have a user-defined function structure.
DRAW Type: Description: Access: Flags: Input/Output: See also: Command Operation Draw Plot Command: Plots the mathematical data in the reserved variable EQ or the statistical data in the reserved variable ΣDAT, using the specified x- and y-axis display ranges. The plot type determines if the data in the reserved variable EQ or the data in the reserved variable ΣDAT is plotted. DRAW does not erase PICT before plotting; execute ERASE to do so. DRAW does not draw axes; execute DRAX to do so.
DROITE Type: Description: Function Access: Catalog, …µ Input: Level 2/Argument 1: The first point, in the form a+b *i, or (a,b), where a and b must be numbers, or variables or expressions that evaluate to numbers. Level 1/Argument 2: The second point, in the form c+d *i, or (c,d), where c and d must be numbers, or variables or expressions that evaluate to numbers. Output: Level 1/Item 1: An equation for the straight line through the two points. The general form is Y=(d-b)/(c-a)*(X-a)+b.
Input/Output: Level 2 See also: DROPN Type: Description: Access: Level 1 obj1 CLEAR, DROP, DROPN obj2 Level 1 → RPL Command Drop n Objects Command: Removes the first n + 1 objects from the stack (the first n objects excluding the integer n itself). !°STACK LL DROPN ( °is the left-shift of the Nkey). ISTACK LL DROPN Input/Output: Leveln+1 ... Level 2 See also: DTAG Type: Description: Access: Input/Output: Level 1 obj1 ...
Input/Output: L2 L1 obj2 obj1 → L4 L3 L2 L1 obj2 obj1 obj2 obj1 L = Level See also: DUP, DUPN, PICK DUPDUP Type: Description: Access: RPL Command Duplicates an object twice. Same as DUP DUP. !°STACK LL DUPDUP ( °is the left-shift of the Nkey).
When evaluated, e returns its numerical representation if flag –2 or –3 is set; otherwise, e returns its symbolic representation. The number returned for e is the closest approximation to 12-digit accuracy. For exponentiation, use the expression 'EXP(x)' rather than e^x, since the function EXP uses a special algorithm to compute the exponential to greater accuracy. Even though the calculator often displays 'EXP(x)' as e^x, it’s still 'EXP(x)' internally.
Example: Find the polynomials for u, v, and c, where c is the greatest common divisor of a and b such that: 2 u(x + 1) + v(x – 1) = c Command: Result: See also: EGV Type: Description: EGCD(X^2+1,X-1) {2,1,-(X+1)} IEGCD, ABCUV Command Eigenvalues and Eigenvectors Command: Computes the eigenvalues and right eigenvectors for a square matrix. The resulting vector EVal contains the computed eigenvalues. The columns of matrix EVec contain the right eigenvectors corresponding to the elements of vector EVal.
See the IF, CASE, IFERR, DO, and WHILE keyword entries for more information. Access: !°BRANCH IF/CASE/DO/WHILE END ( °is the left-shift of the Nkey). Input/Output: None See also: IF, CASE, DO, ELSE, IFERR, REPEAT, THEN, UNTIL, WHILE ENDSUB Type: Description: Command Ending Sublist Command: Provides a way to access the total number of sublists contained in the list used by DOSUBS. Returns an Undefined Local Name error if executed when DOSUBS is not active.
Example: Command: Result: EQNLIB Type: Description: Access: Input/Output: See also: EQW Type: Description: Access: Replace with zero the terms smaller than EPS in the expression: 10-13x + 10-2 EPSX0(1E-13*X+.01) 0*X+.01 Command Starts the Equation Library application. GEQUATION LIBRARY None MSOLVR, SOLVEQN Command Opens Equation Writer, where you can edit an expression. Puts an object into the Equation Writer. …µEQW (Non-programmable access is via ˜ when there is an algebraic object on the stack.
ERR0 Type: Description: Command Clear Last Error Number Command: Clears the last error number so that a subsequent execution of ERRN returns # 0h, and clears the last error message. ( °is the left-shift of the Nkey). Access: !°LLERROR ERR0 Input/Output: None See also: DOERR, ERRM, ERRN ERRM Type: Description: Access: Input/Output: Command Error Message Command: Returns a string containing the error message of the most recent calculator error. ERRM returns the string for an error generated by DOERR.
EVAL Type: Description: Command Evaluate Object Command: Evaluates the object. The following table describes the effect of the evaluation on different object types. Effect of Evaluation Object Type Local Name Recalls the contents of the variable. Global Name Calls the contents of the variable: • A name is evaluated. • A program is evaluated. • A directory becomes the current directory. • Other objects are put on the stack.
Access: Catalog, …µ Input: An equation. Output: Level 2/Item 1: The expression to the left of the “=” sign in the original equation, or, if the input is an expression and not an equation, the independent variable. Level 1/Item 2: The expression to the right of the “=” sign in the original equation, or, if the input is an expression, the expression. Flags: Numeric mode must not be set (flag –3 clear).
Input/Output: Level 1/Argument 1 See also: ALOG, EXPM, LN, LOG EXP2HYP Type: Description: Function Level 1/Item 1 z → ez 'symb' → 'EXP(symb)' Converts expressions involving the exponential function into expressions with hyperbolic functions. Access: Catalog, …µ Input: An expression Output: The rewritten expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Flags: Numerical Results (–3), Exact Mode (–105) Input/Output: Level 1/Argument 1 Level 1/Item 1 x → x 'symb1' → 'symb2' Example 1: Example 2: See also: → (x, y) 'A^(B+C)' EXPAN returns 'A^C*A^B' '(X+Y)^2' EXPAN returns 'X^2+2*Y*X+Y^2' COLCT, EXPAND, ISOL, QUAD, SHOW EXPAND Type: Command (x, y) Description: Expands and simplifies an algebraic expression.
EXPFIT Type: Description: Command Exponential Curve Fit Command: Stores EXPFIT as the fifth parameter in the reserved variable ΣPAR, indicating that subsequent executions of LR are to use the exponential curve fitting model. LINFIT is the default specification in ΣPAR. Access: …µ EXPFIT Input/Output: None See also: BESTFIT, LR, LINFIT, LOGFIT, PWRFIT EXPLN Type: Description: Transforms the trigonometric terms in an expression to exponential and logarithmic terms.
Access: Input/Output: xpoint, ypoint, and zpoint are real numbers that set the x-, y-, and z-coordinates as the eye-point from which to view a 3D plot’s view volume. The y-coordinate must always be 1 unit less than the view volume’s nearest point (ynear of YVOL). These coordinates are stored in the reserved variable VPAR.
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 –3 clear). Results including complex terms are returned if complex mode is set (flag –103 set).
FANNING Type: Description: Access: Flags: Input/Output: See also: FAST3D Type: Description: Function Fanning Friction Factor Function: Calculates the Fanning friction factor of certain fluid flows. FANNING calculates the Fanning friction factor, a correction factor for the frictional effects of fluid flows having constant temperature, cross-section, velocity, and viscosity (a typical pipe flow, for example). xx/D is the relative roughness (the ratio of the conduit roughness to its diameter).
Access: …µFAST3D Input/Output: None See also: BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPEFIELD, TRUTH, WIREFRAME, YSLICE FCOEF Type: Command Description: From an array of roots and multiplicities/poles, returns a rational polynomial with a leading coefficient of 1, with the specified set of roots or poles, and with the specified multiplicities.
Input/Output: Level 1/Argument 1 Example: See also: FDISTRIB Type: Description: Level 1/Item 1 → nflag number If flag –44 is set, -44 FC?C returns 0 to level 1 and clears flag –44. CF, FC?, FS? FS?C, SF 0/1 Command Performs a full distribution of multiplication and division with respect to addition and subtraction in a single step. Access: !Ú Input: An expression.
Access: !´L FFT FFT Input/Output: ( ´ is the left-shift of the Pkey). Level 1/Argument 1 [ array ]1 See also: IFFT FILER Type: Description: Command Opens File Manager. Access: !¡ Level 1/Item 1 → [ array ]2 ( ¡ is the left-shift of the Gkey). …µFILER Input/Output: None FINDALARM Type: Command Description: Find Alarm Command: Returns the alarm index nindex of the first alarm due after the specified time.
Access: Fix mode shows n digits to the right of the fraction mark (decimal point), where 0 ≤ n ≤ 11. (Values for n outside this range are rounded to the nearest integer.) A number is displayed or printed as (sign) mantissa, where the mantissa can be of any form. However, the calculator automatically displays a number in scientific mode if either of the following is true: • The number of digits to be displayed exceeds 12. • A nonzero value rounded to n decimal places otherwise would be displayed as zero.
Access: …µ FONT6 Input/Output: Level 1/Argument 1 Level 1/Item 1 → See also: FONT7 Type: Description: Access: Input/Output: FONT7, FONT8, →FONT, FONT→ Function Font Function: Returns the system FONT7 object. You use this in conjunction with the →FONT command to set the system font to type 7. …µFONT7 Level 1/Argument 1 Level 1/Item 1 → See also: FONT8 Type: Description: Access: Input/Output: Font object FONT6, FONT8, →FONT, FONT→ Function Font Function: Returns the system FONT8 object.
FOR Type: Description: Access: Input/Output: Command Operation FOR Definite Loop Structure Command: Starts FOR … NEXT and FOR … STEP definite loop structures. Definite loop structures execute a command or sequence of commands a specified number of times. • A FOR … NEXT loop executes a program segment a specified number of times using a local variable as the loop counter. You can use this variable within the loop.
FOURIER Type: Description: Function Access: Calculus !ÖDERIV. & INTEG. Input: Level 1/Argument 2: An expression in terms of the current variable Level 2/Argument 1: The number, n, of the coefficient to return. Output: The nth Fourier coefficient of the expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Complex mode must be set, that is, flag –103 must be set.
Access: Input/Output: Display Area Value Code Status area 1 History/Stack/Command-line area 2 Menu area 4 So, for example, 2 FREEZE freezes the history/stack/command-line area, 3 FREEZE freezes the status area and the history/stack/command-line area, and 7 FREEZE freezes all three areas. Values of ndisplay area ≥ 7 or ≤ 0 freeze the entire display (are equivalent to value 7).
!° LMODES FLAG FS? !& H FLAG FS? ( °is the left-shift of the Nkey). Input/Output: Level 1/Argument 1 → nflag number See also: FS?C Type: Description: Access: Level 1/Item 1 0/1 CF, FC?, FC?C, FS?C, SF Command Flag Set? Clear Command: Tests whether the system or user flag specified by nflag number is set, and returns a corresponding test result: 1 (true) if the flag is set or 0 (false) if the flag is clear. After testing, clears the flag. !°TEST LLFS?C ( °is the left-shift of the Nkey).
otherwise, the values in (xmin, ymin) and (xmax, ymax)(the display range) are used. Lines are drawn between plotted points unless flag –31 is set. If EQ contains an expression or program, the expression or program is evaluated in Numerical Results mode for each value of the independent variable to give the values of the dependent variable. If EQ contains an equation, the plotting action depends on the form of the equation, as shown in the following table.
GAMMA Type: Description: Function Evaluate the Γ function at the given point. For a positive integer x, Γ(x) is equal to (x +1)! GAMMA differs from the FACT and ! functions because it allows complex arguments. The Γ function is defined by Γ(x ) = +∞ – t ∫0 e ⋅t x–1 dt . Access: Input: Output: Flags: !´LSPECIAL A real or complex number, x. Γ(x). If the input x is an integer greater than 100, returns the symbolic expression GAMMA(x).
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Find a Grœbner basis of the ideal polynomial generated by the polynomials: x2 + 2xy2, xy + 2y3 – 1 Command: Result: GBASIS([X^2 + 2*X*Y^2, X*Y + 2*Y^3 – 1], [X,Y]) [X, 2*Y^3-1] Note this is not the minimal Grœbner basis, as the leading coefficient of the second term is not 1; the algorithm used avoids giving results with fractions.
Access: !°LIST ELEMENTS GET Input/Output: Example 1: Example 2: Example 3: See also: GETI Type: Description: Access: Flags: ( °is the left-shift of the Nkey).
Input/Output: L2/A1 L1/A2 L3/I1 L2/I2 L1/I3 [[ matrix ]] nposition1 → [[ matrix ]] nposition2 zget [[ matrix ]] { nrow, mcolumn }1 → [[ matrix ]] { nrow, mcolumn }2 zget 'namematrix' nposition1 → 'namematrix' nposition2 zget 'namematrix' { nrow, mcolumn }1 → 'namematrix' { nrow, mcolumn }2 zget [ vector ] nposition → [ vector ] nposition2 zget [ vector ] {nposition1 } → [ vector ] {nposition2 } zget 'namevector' nposition1 → 'namevector nposition2 zget 'namevec
Input/Output: None See also: DEG, RAD GRAMSCHMIDT Type: Command Description: Finds an orthonormal base of a vector space with respect to a given scalar product. Access: Matrices, !Ø LVECTOR Input: Level 2/Argument 1: A vector representing a basis of a vector space. Level 1/Argument 2: A function that defines a scalar product in that space. This can be given as a program, or as the name of a variable containing the definition of the function.
Result: See also: -1 Note this is the remainder of the input polynomial modulo the term x in the Grœbner basis GBASIS GRIDMAP Type: Description: Command GRIDMAP Plot Type Command: Sets the plot type to GRIDMAP. When plot type is set GRIDMAP, the DRAW command plots a mapping grid representation of a 2-vector-valued function of two variables. GRIDMAP requires values in the reserved variables EQ, VPAR, and PPAR.
Input/Output: Level 2/Argument 1 Level 1/Argument 2 obj ncharsize Level 1/Item 1 → grob Example: This program: « 'Y=3*X^2' 0 →GROB PICT STO { } PVIEW » returns a graphics object to the stack representing the Equation Writer application picture of 'Y=3*X^2', then stores the graphics object in PICT and shows it in the graphics display with scrolling activated.
GROB 5 x 5 11A040A011 GXOR LASTARG GXOR » turns on (makes dark) every pixel in PICT, then superimposes a 5 x 5 graphics object on PICT at pixel coordinates { # 0d # 0d }. Each on-pixel in the 5 by 5 graphics object turns off (makes light) the corresponding pixel in PICT. Then, the original picture is restored by executing GXOR again with the same arguments. See also: *H Type: Description: GOR, REPL, SUB Command Multiply Height Command: Multiplies the vertical plot scale by xfactor.
Access: !°LL RUN & DEBUG HALT Input/Output: None See also: CONT, KILL HEAD Type: Description: Access: ( °is the left-shift of the Nkey). Command First Listed Element Command: Returns the first element of a list or string. !°LCHARS LHEAD !°LIST ELEMEN LHEAD ( °is the left-shift of the Nkey). ( °is the left-shift of the Nkey). …± LHEAD (± is the right-shift of the Nkey). Input/Output: Level 1/Argument 1 { obj1, ...
HERMITE Type: Description: Function Access: Arithmetic, !ÞPOLY L Input: A non-negative integer. Output: The corresponding polynomial expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Example: Command: Result: See also: Find the Hermite polynomial with degree 4. HESS Type: Description: Returns the nth Hermite polynomial.
Input/Output: None See also: BIN, DEC, OCT, RCWS, STWS HILBERT Type: Description: Command Access: Matrices, !Ø CREATE Lor !´ MATRX 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 –3 clear). Example: Find the order 3 Hilbert matrix. Command: HILBERT(3) Result: See also: Returns a square Hilbert matrix of the specified order.
• depend is a name specifying a label for the vertical axis. The default value is Y. The frequency of the data is plotted as bars, where each bar represents a collection of data points. The base of each bar spans the values of the data points, and the height indicates the number of data points. The width of each bar is specified by res. The overall maximum and minimum values for the data can be specified by indep; otherwise, the values in (xmin, ymin) and (xmax, ymax) are used.
Access: The format for HMS (a time or an angle) is H.MMSSs, where: • H is zero or more digits representing the integer part of the number (hours or degrees). • MM are two digits representing the number of minutes. • SS are two digits representing the number of seconds. • s is zero or more digits (as many as allowed by the current display mode) representing the decimal fractional part of seconds. …ÓTools LHMS+ ( Ó is the right-shift of the 9 key).
HOME Type: Description: Access: Command HOME Directory Command: Makes the HOME directory the current directory. …µ HOME !& J Input/Output: None See also: CRDIR, PATH, PGDIR, UPDIR HORNER Type: Description: Command Executes a Horner scheme on a polynomial. That is, for a given polynomial P, and a number r, HORNER returns QUOT(P/(x–r)), r and also P(r) Access: Arithmetic, !ÞPOLY L Input: Level 2/Argument 1: A polynomial, P. Level 1/Argument 2: A number, r.
Output: Level 2/Item 1: The value for u. Level 1/Item 2: The value for v. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Find a solution in integers of the equation: 6a + 11b = 3 Command: Result: IABCUV(6,11,3) {6,-3} See also: ABCUV, IEGCD IBASIS Type: Description: Command Access: Matrices, !Ø L VECTOR Input: Two lists of vectors Output: A list of vectors.
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
• If the argument is a name, the name must identify a variable containing a square matrix. In this case, the elements of the matrix are replaced by those of the identity matrix (complex if the original matrix is complex). Access: !Ø ( Ø is the left-shift of the 5key). CREATE IDN !´MATRIX MAKE IDN ( ´ is the left-shift of the Pkey).
See also: IF Type: Description: ABCUV, EGCD, IABCUV Command Operation IF Conditional Structure Command: Starts IF … THEN … END and IF … THEN … ELSE … END conditional structures. Conditional structures, used in combination with program tests, enable a program to make decisions. • IF … THEN … END executes a sequence of commands only if a test returns a nonzero (true) result. The syntax is: IF test-clause THEN true-clause END IF begins the test clause, which must return a test result to the stack.
3 The key buffer is cleared. 4 If any or all of the display is “frozen” (by FREEZE), that state is cancelled. 5 If Last Arguments is enabled, the arguments to the command that caused the error are returned to the stack. 6 Program execution jumps to the error clause. The commands in the error clause are executed only if an error is generated during execution of the trap clause.
Access: !´LFFT IFFT Input/Output: ( ´ is the left-shift of the Pkey). Level 1/Argument 1 Level 1/Item 1 → [ array ]1 See also: IFT Type: Description: FFT Command IF-THEN Command: Executes obj if T/F is nonzero. Discards obj if T/F is zero. IFT lets you execute in stack syntax the decision-making process of the IF … THEN … END conditional structure. The “true clause” is obj in argument 2 (level 1).
Access: Calculus, !ÖDIFFERENTIAL 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 –3 clear). Radians mode must be set (flag –17 set).
INCR Type: Description: Access: Input/Output: Command Increment Command: Takes a variable, adds 1, stores the new value back into the original variable, and returns the new value. The value in name must be a real number or an integer. !°MEMORY ARITHMETIC INCR ( °is the left-shift of the Nkey). Level 1/Argument 1 Example: See also: INDEP Type: Description: Level 1/Item 1 → 'name' If 35.7 is stored in A, 'A' INCR returns 36.7.
Variable Function {s1 s2 … sn} Field definitions. A field definition (sx) can have two formats: “label”, a field label, or { “label” “helpInfo” type0 type1 … typen }, a field label with optional help text that appears near the bottom of the screen, and an optional list of valid object types for that field. If object types aren’t specified, all object types are valid. For information about object types, see the TYPE command.
Access: Input/Output: In its general form, the second argument (level 1) for INPUT is a list that specifies the content and interpretation of the command line. The list can contain one or more of the following parameters, in any order: • "command-line prompt", whose contents are placed on the command line for prompting when the program pauses.
Example: Command: Result: Find the integral of sin(x) with respect to x, at the point where x=y. See also: INTVX, RISCH INTEGER Type: Description: Command Access: Catalog, …µ Flags: If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
Input/Output: Level 1/Argument 1 Level 1/Item 1 z → 1/z [[ matrix ]] → [[ matrix ]]–1 'symb' → 'INV(symb)' x_unit → 1/x_1/unit See also: SINV, / INVMOD Type: Description: Function Access: Arithmetic, !ÞMODULO L Input: An object. Output: The modular inverse of the object. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Example: Solve the following for x, modulo the default modulus, 13.
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). See also: QUOT, IDIV2 IREMAINDER Type: Function Description: Returns the remainder of an integer division. Access: PARITH or Arithmetic, !ÞINTEGER L Input: Level 2/Argument 1: The numerator. Level 1/Argument 2: The denominator. Output: The remainder. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Example 1: Analyze the isometry given by the matrix 0 –1 –1 0 Command: ISOM([[0,-1] [-1,0]]) Result: { [1, 1] –1}, meaning the matrix represents a symmetry in the line y = –x, and this is an indirect isometry. 1 – 3 --- ---------2 2 Example 2: Command: Result: Analyze the isometry given by the matrix 3 ------2 1 --2 ISOM([[1/2, -√3/2][√3/2, 1/2]]) { π/3, 1 }, meaning the matrix represents a rotation of π/3 radians, and this is a direct isometry.
vector or a list of Jordan chains, each of them ending with an "Eigen:"-tagged eigenvector). Level 1/Item 4: An array of the eigenvalues, with multiplicities Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Access: Input/Output: Unlike WAIT, which returns a three-digit number that identifies alpha and shifted keyboard planes, KEY returns the row-column location of any key pressed, including !, …, and ~. !°LIN KEY ( °is the left-shift of the Nkey). Level 1/Argument 1 Level 2/Item 1 Level 1/Item 2 xn m 1 → → Example: See also: KEYEVAL Type: Description: Access: Input/Output: 0 The program « DO UNTIL KEY END 81 SAME » returns 1 to the stack if the ! key is pressed while the indefinite loop is running.
KEYTIME→ Type: Description: Access: Input/Output: Command Displays the current keytime value. Keytime is the time after a keypress during which further keypresses will not be actioned. It is measured in ticks. If you experience key bounce, you can increase the value of keytime. …µ KEYTIME→ Level 1/Argument 1 Level 1/Item 1 → See also: KGET Type: Description: Access: Flags: Input/Output: →KEYTIME Command Kermit Get Command: Used by a local Kermit to get a Kermit server to transmit the named object(s).
2. If axes parameter is not a list, then the independent variable name in PPAR is used. The vertical axis name is chosen in the following priority order: 1. If the axes parameter in PPAR is a list, then the y-axis element from that list is used. 2. If axes is not a list, then the dependent variable name from PPAR is used. Access: …µ LABEL Input/Output: None See also: AXES, DRAW, DRAX LAGRANGE Type: Description: Command Returns the interpolating polynomial of minimum degree for a set of pairs of values.
LAP Type: Description: Function Access: Calculus, !Ö DIFFERENTIAL EQNS Input: An expression. Output: The Laplace transform of the expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Command: Result: Find the Laplace transform of ex. See also: ILAP, LAPL LAPL Type: Description: Command Access: !Ö DERIV & INTEG L Input: Level 2/Argument 1:An expression.
LASTARG Type: Description: Access: Command Returns copies of the arguments of the most recently executed command. The objects return to the same stack levels that they originally occupied. Commands that take no arguments leave the current saved arguments unchanged. When LASTARG follows a command that evaluates an algebraic expression or program, the last arguments saved are from the evaluated algebraic expression or program, not from the original command.
Output: The least common multiple of the objects. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Find the least common multiple of the following two expressions: 2 x –1 x–1 Command: Results: LCM(X^2-1,X-1) X^2-1 See also: GCD LCXM Type: Description: Command Access: Catalog, …µ Input: Level 3/Argument 1: The number of rows you want in the resulting matrix.
Result: COS(X)*(cC0 -X)+(cC1 — -1)*SIN(X) See also: DESOLVE LEGENDRE Type: Description: Function Access: Arithmetic, !Þ POLYNOMIAL LL Input: An integer, n. Output: The nth Legendre polynomial. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Example: Command: Result: Find the Legendre polynomial with degree 4. See also: HERMITE, TCHEBYCHEFF LGCD Type: Description: Function Access: Arithmetic, !Þ L Input: A list of expressions or values.
Access: …µ LIBS Input/Output: Level 1/Argument 1 Level 1/Item 1 → See also: ATTACH, DETACH lim Type: Description: Function Access: Calculus, !Ö LIMITS&SERIES Input: Level 2/Argument 1: An expression. {“title”, nlib, nport, ...,“title”, nlib, nport } Returns the limit of a function as its argument approaches a specified value. Expands and simplifies an algebraic expression.
Example: Linearize the following expression: x y 4 x(e e ) Command: Result: See also: LIN(X*(EXP(X)*EXP(Y))^4) X*EXP(4X+4Y) TEXPAND LINE Type: Command Operation Description: Draw Line Command: Draws a line in PICT between the input coordinates. Access: !°LPICT LINE ( °is the left-shift of the Nkey).
Input/Output: None See also: BESTFIT, EXPFIT, LOGFIT, LR, PWRFIT LININ Type: Description: Access: Input/Output: Function Linear Test Function: Tests whether an algebraic is structurally linear for a given variable.
Input/Output: Leveln+1/Argument1 7Level2/Argumentn Level1/Argumentn+1 Level 1/Item 1 Example: → obj1 … objn n { obj1, … ,objn } The program « DEPTH →LIST 'A' STO » combines the entire contents of the stack into a list that is stored in variable A. See also: →ARRY, LIST→, →STR, →TAG, →UNIT ∆LIST Type: Description: Access: Input/Output: Command List Differences Command: Returns the first differences of the elements in a list. Adjacent elements in the list must be suitable for mutual subtraction.
For x = 0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set, –MAXR is returned. The inverse of EXP is a relation, not a function, since EXP sends more than one argument to the same result. The inverse relation for EXP is the general solution: LN(Z)+2*π*i*n1 The function LN is the inverse of a part of EXP, a part defined by restricting the domain of EXP such that: each argument is sent to a distinct result, and each possible result is achieved.
Input/Output: Level 1/Argument 1 z See also: LNAME Type: Description: Access: Input: Output: Flags: Example: Command: Result: See also: 'symb' ALOG, EXP, ISOL, LNP1, LOG Level 1/Item 1 → ln z → 'LN(symb)' Command Returns the variable names contained in a symbolic expression. Catalog, …µ A symbolic expression. Level 2/Argument 1: The original expression. Level 1/Argument 2: A vector containing the variable names.
Flags: Numerical Results (–3), Infinite Result Exception (–22) Input/Output: Level 1/Argument 1 Level 1/Item 1 x → ln (x + 1) 'symb' → 'LNP1(symb)' See also: EXPM, LN LOCAL Type: Description: Command Access: Catalog, …µ Input: Level 1/Argument 1: A list of one or more local variable names (names beginning with the local variable identifier ←), each one followed by an equals sign and the value to be stored in it. Any variable not followed by an equal sign and a value is set equal to zero.
Input/Output: Level 1/Argument 1 See also: LOGFIT Type: Description: Level 1/Item 1 z → log z 'symb' → 'LOG(symb)' ALOG, EXP, ISOL, LN Command Logarithmic Curve Fit Command: Stores LOGFIT as the fifth parameter in the reserved variable ΣPAR, indicating that subsequent executions of LR are to use the logarithmic curve-fitting model. LINFIT is the default specification in ΣPAR.
Model Transformation Logarithmic y = b + m ln(x) Exponential ln(y) = ln(b) + mx Power ln(y) = ln(b) + m ln(x) Access: …µ LR Input/Output: Level 1/Argument 1 Level 2/Item 1 Level 1/Item 2 → See also: LSQ Type: Description: Access: Flags: Input/Output: See also: LU Type: Description: Access: Intercept: x1 Slope: x2 BESTFIT, COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, PREDX, PREDY, PWRFIT, XCOL, YCOL Command Least Squares Solution Command: Returns the minimum norm least squares solution t
Input/Output: Level 1/Argument 1 See also: [[ matrix ]]A DET, INV, LSQ, / LVAR Type: Command → Level 3/Item 1 Level 2/Item 2 Level 1/Item 3 [[ matrix ]]L [[ matrix ]]U [[ matrix ]]P Description: Returns a list of variables in an algebraic object. Differs from LNAME above in that functions of variables, such as COS(X) or LN(AB) are returned, instead of the variable names, X or AB. INV() and SQ() are not treated as functions. Compare the example here with the same example in LNAME.
MAIN Type: Command Description: Displays the main menu (or list) of CAS operations. This displays the CASCFG command, the ALGB, ARIT, DIFF, EXP&LN, MATHS MATR, REWRITE and TRIGO menu commands described in this part of the Command Reference, and the CMPLX and SOLVER menu commands described in the Full Command and Function Reference (Chapter 3). Other menus are not shown because they are within the submenus given by MAIN. More details are given in Appendix K of the User’s Guide.
The pattern 'symbpat' and replacement 'symbrepl' can be normal expressions; for example, you can replace .5 with 'SIN(π/6)'. You can also use a “wildcard” in the pattern (to match any subexpression) and in the replacement (to represent that expression). A wildcard is a name that begins with &, such as the name '&A', used in replacing 'SIN(&A+&B)' with 'SIN(&A)*COS(&B)+COS(&A)*SIN(&B)'. Multiple occurrences of a particular wildcard in a pattern must match identical subexpressions.
Input/Output: Level 2/Argument 1 Level 1/Argument 2 'symb1' { 'symbpat', 'symbrepl' } → Level 2/Item 1 Level 1/Item 2 'symb2' 0/1 Example 1: → 'symb1' { 'symbpat', 'symbrepl', 'symbcond' } 'symb2' 0/1 This sequence: 'SIN(π/6)' { 'SIN(π/6)' '1/2' } ↑MATCH returns '1/2' to level 2 and 1 (indicating a replacement was made) to level 1. Example 2: This sequence: 'SIN(X+π)' { 'SIN(&A+π)' '-SIN(&A)' } ↑MATCH returns '-SIN(X)' to level 2 and 1 to level 1.
Example 1: 10 -23 MAX returns 10. Example 2: -10 -23 MAX returns -10. Example 3: 1_m 9_cm MAX returns 1_m. See also: MIN MAXR Type: Description: Access: Flags: Input/Output: Function Maximum Real Function: Returns the symbolic constant MAXR or its numerical representation 9.99999999999E499. MAXR is the largest real number that can be represented by the calculator. !´L CONSTANTS LMAXR ( ´ is the left-shift of the Pkey).
MEAN Type: Description: Command Mean Command: Returns the mean of each of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT). The mean is returned as a vector of m real numbers, or as a single real number if m = 1. The mean is computed from the formula: 1 n --- ∑ x i ni = 1 Access: where xi is the ith coordinate value in a column, and n is the number of data points.
Access: than a list or name containing a list is supplied to MENU, a Bad Argument Type error will occur when the calculator attempts to display the custom menu. A full list of all menus can be found in Appendix H of this reference. !&H [MENU] MENU !°LMODES [MENU] MENU ( °is the left-shift of the Nkey).
108-113 114-119 120-125 126-131 132-137 138-140 Example: Command: Result: EXLR DIV2MOD RREFMOD CASCFG DIFF ∞ LNAME POWMOD MODSTO MAIN ARIT PROMPTSTO ADDTMOD INVMOD MENUXY ALGB SOLVER VER SUBTMOD GCDMOD KEYEVAL CMPLX EXP&LN MULTMOD EXPANDMOD GROBADD TRIGO EPSX0 DIVMOD FACTORMOD SCROLL MATR ? Display a menu containing ATAN2S, ASIN2T, ASIN2C and ACOS2S. MENUXY(34,37) The four functions are displayed above the A to D keys. In Algebraic mode, NOVAL is returned as item 1.
Use the number or arrow keys to cross the battlefield one square at a time (use 7, 9, 1, and 3to move diagonally.) You can exit the game at any time by pressing −(the $ key). To interrupt and save a game, press K. This creates a variable MHpar in the current directory and ends the game. If MHpar exists when you start MINEHUNT, the interrupted game resumes and MHpar is purged. You can change the number of mines in the battlefield by creating a variable named Nmines containing the desired number.
Input/Output: Level 1/Argument 1 See also: MINΣ Type: Description: Access: Input/Output: Level 1/Item 1 → 'MINR' → 1.00000000000E–499 e, i, MAXR, π Command Minimum Sigma Command: Finds the minimum coordinate value in each of the m columns of the current statistics matrix (reserved variable ΣDAT). The minima are returned as a vector of m real numbers, or as a single real number if m = 1.
Example 2: Command: Result: See also: MOD Type: Description: Access: Flags: Input/Output: Find the matrix for a rotation with axis [1 1 1] and angle π/3 radians combined with a reflection in the plane x + y + z = 0 MKISOM({ [1, 1, 1],π/3}, -1) then simplify with EXPAND(ANS(1)) 0 –1 0 0 0 –1 –1 0 0 ISOM Function Modulo Function: Returns a remainder defined by: x mod y = x – y floor (x/y) Mod (x, y) is periodic in x with period y. Mod (x, y) lies in the interval [0, y) for y > 0 and in (y, 0] for y < 0.
MOLWT Type: Description: Function Returns the molecular weight for the specified molecular formula. It takes the formula as a string (such as "H2O") or name (with certain restrictions, such as 'H2O'). It returns the molecular weight. It chooses to use or not use units according to the Units Usage flag (flag 61: SI units if clear, no units if set). You can store a molecular formula in a variable, then use the variable name with MOLWT.
Input/Output: Level 1/Argument 1 See also: MSLV Type: Description: “message” CHOOSE, INFORM, PROMPT Level 1/Item 1 → Command Numerically approximates a solution to a system of equations. Searches for a solution accurate to 12 digits, regardless of the display setting. Underdetermined and overdetermined systems are rejected. Complex solutions will be looked for if any of the inputs contain complex values.
variable Mpar that is used during the solution process. Mpar contains the equation set plus additional information. See appendix D, “Reserved Variables”, for information about Mpar. Access: …µ MSOLVR Input/Output: None See also: EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, MUSER MULTMOD Type: Description: Function Access: Arithmetic, !Þ MODULO L Input: Level 2/Argument 1: A number or an expression. Level 1/Argument 2: A number or an expression.
NDIST Type: Description: Command Normal Distribution Command: Returns the normal probability distribution (bell curve) at x based on the mean m and variance v of the normal distribution. NDIST is calculated using this formula: 2 (x – m) – ------------------2v e ndist ( m, v, x ) = --------------------2πv Access: !´LPROBABILITY L NDIST Input/Output: See also: NDUPN Type: Description: Access: ( ´ is the left-shift of the Pkey).
See also: NEWOB Type: Description: Access: Flags: ABS, CONJ, NOT, SIGN Command New Object Command: Creates a new copy of the specified object. NEWOB has two main uses: • NEWOB enables the purging of a library or backup object that has been recalled from a port. NEWOB creates a new, separate copy of the object in memory, thereby allowing the original copy to be purged.
Command: Result: See also: NIP Type: Description: Access: NEXTPRIME(145) 149 ISPRIME?, PREVPRIME RPL command Drops the (n–1)th argument, where n is the number of arguments or items on the stack. (that is, the object on level 2 of the stack). This is equivalent to executing SWAP followed by DROP in RPN mode. !° STACK LLNIP ( °is the left-shift of the Nkey).
NOVAL is used to mark an empty field in a user-defined dialog box created with the INFORM command. INFORM defines fields sequentially. If default values are used for those fields, the defaults must be defined in the same order as the fields were defined. To skip over (not provide defaults for) some of the fields, use the NOVAL command. After INFORM terminates, NOVAL is returned if a field is empty and OK or ` is selected.
The number of a character can be found by accessing the Characters tool (…±) and highlighting that character. The number appears near the bottom of the screen. These are also listed in Appendix J of this manual. Access: !°TYPE LNUM !° LCHARS NUM …&N NUM ( °is the left-shift of the Nkey). ( °is the left-shift of the Nkey).
!°LIST OBJ→ …&NL OBJ→ !°LCHARS LOBJ→ ( °is the left-shift of the Nkey). ( °is the left-shift of the Nkey). Input/Output: Leveln+1/Item1 Level 1/Argument 1 Example: See also: Level2/Itemn Level1/Itemn+1 x y (x, y) → { obj1, ... ,objn } → obj1 … objn n [ x1, ... ,xn ] → x1 … xn {n} [[ x1 1, ... ,xm n ]] → x1 1 … xm n { m, n } “obj” → 'symb' → x_unit → evaluated object arg1 ...
Access: See also: OPENIO Type: Description: Access: Flags: Input/Output: See also: OR Type: Description: The character set in the HP 82240A Infrared Printer does not match the character set of the calculator: • 24 characters in the calculator’s character set are not available in the HP 82240A Infrared Printer. (From the table in Appendix J, these characters are numbers 129, 130, 143-157, 159, 166, 169, 172, 174, 184, and 185.) The HP 82240A prints a in substitution.
bit1 bit2 bit1 OR bit2 0 0 0 0 1 1 1 0 1 1 1 1 • An argument that is a string is treated as a sequence of bits, using 8 bits per character (that is, using the binary version of the character code). The two string arguments must be the same length. When the arguments are real numbers or symbolics, OR simply does a true/false test. The result is 1 (true) if either or both arguments are nonzero; it is 0 (false) if both arguments are zero. This test is usually done to compare two test results.
Access: !°STACK OVER Input/Output: Level 2 See also: P2C Type: Description: ( °is the left-shift of the Nkey). Level 1 → obj1 obj2 PICK, ROLL, ROLLD, ROT, SWAP Level 3 Level 2 Level 1 obj1 obj2 obj1 Command Takes a list representing a permutation as an argument, and returns the permutation decomposed into lists that represent cycles. Access: !Þ PERM Input: A list representing a permutation.
• (xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper right corner of the display range). The default value is (6.5,3.2) for the HP 48gII and (6.5,4.0) for the HP 50g and 49g+. • indep is a list containing a name that specifies the independent variable, and two numbers specifying the minimum and maximum values for the independent variable (the plotting range). Note that the default value is X.
PARSURFACE Type: Command Description: PARSURFACE Plot Type Command: Sets plot type to PARSURFACE. When plot type is set to PARSURFACE, the DRAW command plots an image graph of a 3vector-valued function of two variables. PARSURFACE requires values in the reserved variables EQ, VPAR, and PPAR.
Result: See also: PATH Type: Description: Access: Input/Output: 1/2/(X-1)+-1/2/(X+1) PROPFRAC Command Current Path Command: Returns a list specifying the path to the current directory. The first directory is always HOME, and the last directory is always the current directory. If a program needs to switch to a specific directory, it can do so by evaluating a directory list, such as one created earlier by PATH. ( °is the left-shift of the Nkey).
PCONTOUR Type: Description: Command PCONTOUR Plot Type Command: Sets the plot type to PCONTOUR. When plot type is set PCONTOUR, the DRAW command plots a contour-map view of a scalar function of two variables. PCONTOUR requires values in the reserved variables EQ, VPAR, and PPAR.
Access: …µ PCOV Input/Output: Level 1/Argument 1 Level 1/Item 1 → See also: PDIM Type: Description: xpcovariance COLΣ, CORR, COV, PREDX, PREDY, XCOL, YCOL Command PICT Dimension Command: Replaces PICT with a blank PICT of the specified dimensions. If the arguments are complex numbers, PDIM changes the size of PICT and makes the arguments the new values of (xmin, ymin) and (xmax, ymax) in the reserved variable PPAR. Thus, the scale of a subsequent plot is not changed.
PERTBL Type: Description: Access: Flags: Input/Output: See also: PEVAL Type: Description: Access: Input/Output: Command Starts the Periodic Table. It doesn’t affect the stack. G PERIODIC TABLE PERTBL Units Usage (61), Units Type (60) None MOLWT, PERINFO, PTPROP Command Polynomial Evaluation Command: Evaluates an n-degree polynomial at x.
Input/Output: L3 L2 L1 obj1 obj2 obj3 → L4 L3 L2 L1 obj1 obj2 obj3 obj1 L = Level; A = Argument; I =Item Example: See also: PICT Type: Description: 333 22 1 PICK3 returns 333 22 1 333. PICK, OVER, DUP Command PICT Command: Puts the name PICT on the stack. PICT is the name of a storage location in calculator memory containing the current graphics object. The command PICT enables access to the contents of that memory location as if it were a variable.
Input/Output: None PIX? Type: Description: Command Pixel On? Command: Tests whether the specified pixel in PICT is on; returns 1 (true) if the pixel is on, and 0 (false) if the pixel is off. Access: !° LPICT L PIX? Input/Output: ( °is the left-shift of the Nkey). Level 1/Argument 1 See also: Level 1/Item 1 (x,y) → 0/1 { #n #m } → 0/1 PIXON, PIXOFF PIXOFF Type: Command Description: Pixel Off Command: Turns off the pixel at the specified coordinate in PICT. ( °is the left-shift of the Nkey).
Flags: I/O Device (–33), I/O Messages (–39), I/O Device for Wire (–78). The I/O Data Format flag (– 35) can be significant if the server sends back more than one packet. Input/Output: Level 2/Argument 1 Example 1: Example 2: See also: PLOT Type: Description: Access: Input: Output: Example: Command: Result: Level 1/Argument 2 Level 1/Item 1 → “data” “type” “response” A PKT command to send a generic directory request is "D" "G" PKT.
Access: …µ PMIN Input/Output: Level 1/Argument 1 See also: Level 1/Item 1 → (x,y) PDIM, PMAX, XRNG, YRNG PMINI Type: Description: Command Access: Matrices, ! Ø LEIGENVECTORS Input: An nxn matrix A. Output: A matrix whose first zero-row contains the minimal polynomial of A. In step-by-step mode, PMINI shows the row-reduction steps. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Step-by-step mode can be set (flag –100 set).
• res is a real number specifying the interval, in user-unit coordinates, between values of the independent variable. The default value is 0, which specifies an interval of 2 degrees, 2 grads, or π/90 radians. • axes is a list containing one or more of the following, in the order listed: a complex number specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark annotation, and two strings specifying labels for the horizontal and vertical axes. The default value is (0,0).
POS Type: Description: Access: Command Position Command: Returns the position of a substring within a string or the position of an object within a list. If there is no match for obj or substring, POS returns zero. !°LCHARS POS ( °is the left-shift of the Nkey). !°LIST ELEM POS ( °is the left-shift of the Nkey).
Output: The result from applying the distributive property of exponentiation over multiplication. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Example: Command: Result: Expand (X+1)3. POWEXPAND((X+1)^3) (X+1)·(X+1)·(X+1) POWMOD Type: Description: Function Access: Arithmetic, !Þ MODULO L Input: Level 2/Argument 1: The object. Level 1/Argument 2: The exponent. Output: The result of the object raised to the exponent, modulo the current modulus.
Access: Flags: …µ PR1 I/O Device (–33), Printing Device (–34), Double-spaced Printing (–37), Linefeed (–38), I/O Device for Wire (–78). If flag –34 is set, flag –33 must be clear.
PREDY Type: Description: Command Predicted y-Value Command: Returns the predicted dependent-variable value ydependent, based on the independent-variable value xindependent, the currently selected statistical model, and the current regression coefficients in the reserved variable ΣPAR. The value is predicted using the regression coefficients most recently computed with LR and stored in the reserved variable ΣPAR.
Result: 135/4 PREVPRIME Type: Function Description: Given an integer, finds the closest prime number smaller than the integer. Like ISPRIME?, it uses a pseudoprime check for large numbers. Access: Arithmetic, !Þ INTEGER L Input: An integer or an expression that evaluates to an integer. Output: The closest prime number smaller than the integer. Example: Command: Result: Find the closest, smaller prime number to 145.
Input/Output: Level 1/Argument 1 Level 1/Item 1 → “global” See also: PROOT Type: Description: PROMPT, STO Command Polynomial Roots Command: Returns all roots of an n-degree polynomial having real or complex coefficients. For an nth-order polynomial, the argument must be a real or complex array of length n + 1 containing the coefficients listed from highest order to lowest. The result is a real or complex vector of length n containing the computed roots.
PRST Type: Description: Command Print Stack Command: Prints all objects in the stack, starting with the object on the highest level. Objects are printed in multiline printer format. See the PR1 entry for a description of multiline printer format. Access: …µ PRST Flags: I/O Device (–33), Printing Device (–34), Double-spaced Printing (–37), Linefeed (–38), I/O Device for Wire (–78). If flag –34 is set, flag –33 must be clear. Generally, flag –38 should be clear.
PSDEV Type: Description: Command Population Standard Deviation Command: Calculates the population standard deviation of each of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT). PSDEV returns a vector of m real numbers, or a single real number if m = 1.
PTAYL Type: Description: Function Access: Arithmetic, !Þ POLYNOMIAL LL Input: Level 2/Argument 1: A polynomial, P. Level 1/Argument 2: A number, a. Output: A polynomial, Q such that Q(x – a)=P(x). Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Find the polynomial Q(x) such that Q(x-2)=x2+3x+2.
number can be replaced with the wildcard character &, in which case the calculator will search ports 0 through 2, and then main memory for the named backup object. A library object must be detached before it can be purged from the HOME directory. Neither a library object nor a backup object can be purged if it is currently “referenced” internally by stack pointers (such as an object on the stack, in a local variable, on the LAST stack, or on an internal return stack). This produces the error Object in Use.
Input/Output: Example 1: Example 2: Example 3: See also: PUTI Type: Description: Access: Flags: Level 3/Argument 1 Level 2/Argument 2 Level 1/Argument 3 Level 1/Item 1 [[ matrix ]]1 nposition zput → [[ matrix ]]2 [[ matrix ]]1 { nrow mcol } zput → [[ matrix ]]2 'namematrix' nposition zput → 'namematrix' { nrow mcol } zput → [ vector ]1 nposition zput → [ vector ]2 [ vector ]1 { nposition } zput → [ vector ]2 'namevector' nposition zput → 'namevector' { nposition }
Input/Output: L3/A1 L2/A2 L1/A3 L2/I1 L1/I2 [[ matrix ]]1 nposition1 zput → [[ matrix ]]2 nposition2 [[ matrix ]]1 { nrow mcol }1 zput → [[ matrix ]]2 { nrow mcol }2 'namematrix' nposition1 zput → 'namematrix' nposition2 'namematrix' { nrow mcol }1 zput → 'namematrix' { nrow mcol }2 [ vector ]1 nposition1 zput → [ vector ]2 nposition2 [ vector ]1 { nposition1 } zput → [ vector ]2 { nposition2 } 'namevector' nposition1 zput → 'namevector' nposition2 'namevector'
If nport = 0, then memory is bytes of available main RAM; otherwise memory is bytes of available RAM in the specified port. Access: …µPVARS Input/Output: Level 1/Argument 1 See also: PVIEW Type: Description: Access: Level 2/Item 1 Level 1/Item 2 nport → { :nport :namebackup ... } memory nport → { :nport :nlibrary ... } memory PVARS, VARS Command PICT View Command: Displays PICT with the specified coordinate at the upper left corner of the graphics display.
PX→C Type: Description: Access: Input/Output: Command Pixel to Complex Command: Converts the specified pixel coordinates to user-unit coordinates. The user-unit coordinates are derived from the (xmin, ymin) and (xmax, ymax) parameters in the reserved variable PPAR. The coordinates correspond to the geometrical center of the pixel. ( °is the left-shift of the Nkey).
Input/Output: Level 1/Argument 1 Example: See also: qr Type: Description: Access: Input/Output: x → 'a/b*̟' x → 'a/b' 'symb1' → 'symb2' (x,y) → 'a/b*̟ + c/d*̟*i' → (x,y) 'a/b + c/d*i' In Fix mode to three decimal places, 6.2832 →Qπ returns '44/7'. In Standard mode, however, 6.2832 →Qπ returns '3927/625'. →Q, /, XQ, π Command qr Factorization of a square Matrix Command: Returns the qr factorization of an n × n matrix.
Input/Output: Level 2/Argument 1 Level 1/Argument 2 'symb1' 'global' COLCT, EXPAN, ISOL, SHOW, SOLVE See also: QUOT Type: Description: Function Access: Arithmetic, !Þ POLYNOMIAL !« Input: Level 2/Argument 1: The numerator polynomial. Level 1/Argument 2: The denominator polynomial. Output: The quotient of the Euclidean division. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
QXA Type: Description: Command Access: !Ø Input: Level 2/Argument 1: A quadratic form. Level 1/Argument 2: A vector containing the variables. Output: Level 2/Item 1: The quadratic form expressed in matrix form. Level 1/Item 2: The vector containing the variables. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Access: Flags: Input/Output: Rank is computed by calculating the singular values of the matrix and counting the number of non-negligible values. If all computed singular values are zero, RANK returns zero. Otherwise RANK consults flag –54 as follows: • If flag –54 is clear (the default), RANK counts all computed singular values that are less than or equal to 1.E–14 times the largest computed singular value. • If flag –54 is set, RANK counts all nonzero computed singular values.
Input/Output: See also: RCEQ Type: Description: Access: Input/Output: Level 2/Argument 1 Level 1/Argument 2 z1 [ array ] [ array ] z 'symb' 'symb1' #n1 n1 #n1 x_unit1 x x_unit 'symb' x_unit z2 {[ matrix ]] z 'symb' z 'symb2' n2 #n2 #n2 y_unit2 y_unit y x_unit 'symb' Level 1/Item 1 → → → → → → → → → → → → → → z1/z2 [[ array × matrix–1]] [ array/z ] 'z/symb' 'symb/z' 'symb1/symb2' #n3 #n3 #n3 (x/y)_unit1/unit2 (x/y)_1/unit (x/y)_unit 'symb/x_unit' 'x_unit/symb' / Command Recall from EQ Command: Ret
by a constant xfactor, adds this product to element j of the vector, and returns the modified vector. RCIJ rounds the row numbers to the nearest integer, and treats vector arguments as column vectors. Access: !Ø CREATE ROW RCIJ ( Ø is the left-shift of the 5key). !´ MATRIX ROW RCIJ ( ´ is the left-shift of the Pkey).
Access: …ÓTools ALRM RCLALARM ( Ó is the right-shift of the 9 key). …&9ALRM RCLALARM „°LLTIME ALRM RCLALARM ( °is the left-shift of the Nkey). Input/Output: Level 1/Argument 1 See also: RCLF Type: Description: Access: Flags: Input/Output: nindex DELALARM, FINDALARM, STOALARM Level 1/Item 1 → Command Recall Flags Command: Returns a list of integers representing the states of the system and user flags, respectively.
Executing RCLMENU when the current menu is a user-defined menu (build by TMENU) returns 0.01 (in 2 Fix mode), indicating “Last menu”. Access: „&HMENU RCLMENU „°LMODES MENU RCLMENU( °is the left-shift of the Nkey). Input/Output: Level 1/Argument 1 Level 1/Item 1 → Example: See also: xmenu If the third page of the PRG STACK menu is currently active, RCLMENU returns 73.03. MENU, TMENU RCLVX Type: Description: Command Access: Catalog, …µ Input: None.
If the list contains a single number nelements, the result is an n-element vector. If the list contains two numbers nrows and mcols, the result is an n × m matrix. Elements taken from the argument vector or matrix preserve the same row order in the resulting vector or matrix. If the result is dimensioned to contain fewer elements than the argument vector or matrix, excess elements from the argument vector or matrix at the end of the row order are discarded.
Input/Output: Level 1/Argument 1 See also: RECN Type: Description: Access: Flags: Level 1/Item 1 x → x x_unit → x (x,y) → x [ R-array ] → [ R-array ] [ C-array ] → [ R-array ] 'symb' → 'RE(symb') C→R, IM, R→C Command Receive Renamed Object Command: Prepares the calculator to receive a file from another Kermit server device, and to store the file in a specified variable. RECN is identical to RECV except that the name under which the received data is stored is specified.
I/O Device flag (–33), I/O Data Format (–35), RECV Overwrite (–36), I/O Messages (–39), I/O Device for Wire (–78) Input/Output: None See also: BAUD, CKSM, FINISH, KGET, PARITY, RECN, SEND, SERVER, TRANSIO Flags: REF Type: Description: Command Access: Matrices, !Ø Input: A real or complex matrix. Output: The equivalent matrix in echelon form. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
REORDER Type: Description: Function Given a polynomial expression and a variable, reorders the variables in the expression in the order of powers set on the CAS Modes screen, that is, either in increasing or decreasing order. Access: Catalog, …µ Input: Level 2/Argument 1: The polynomial expression. Level 1/Argument 2: The variable with respect to which the reordering is performed. Output: The reordered expression. Flags: Exact mode must be set (flag –105 clear).
Input/Output: Example 1: Example 2: Example 3: See also: RES Type: Description: Level 3/Argument 1 Level 2/Argument 2 Level 1/Argument 3 Level 1/Item 1 [[ matrix ]]1 nposition [[ matrix ]]2 → [[ matrix ]]3 [[ matrix ]]1 { nrow, ncolumn } [[ matrix ]]2 → [[ matrix ]]3 [ vector ]1 nposition [ vector ]2 → [ vector ]3 { listtarget } nposition { list1 } → { listresult } “stringtarget” nposition “string1” → “stringresult” grobtarget (#n, #m) grob1 → grobresult grobtarget (x
Plot Type Default Interval PCONTOUR RES does not apply POLAR 2°, 2 grads, or π/90 radians SCATTER RES does not apply SLOPEFIELD RES does not apply WIREFRAME RES does not apply YSLICE 2 pixels (plots a point in every other column of pixels) Access: …µ RES Input/Output: Level 1/Argument 1 Level 1/Item 1 → ninterval See also: RESTORE Type: Description: Access: Input/Output: → #ninterval BAR, CONIC, DIFFEQ, FUNCTION, GRIDMAP, HISTOGRAM, PARAMETRIC, PARSURFACE, PCONTOUR, POLAR, SCATTER, SLOPE
Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Complex mode must be set (flag –103 set) if either input contains complex terms. Example: Obtain the resultant of the two polynomials x3-px+q and 3x2-p. Command: Result: RESULTANT(X^3-P*X+Q, 3*X^2-P) 27*Q^2-4*P^3 REVLIST Type: Command Description: Reverse List Command: Reverses the order of the elements in a list. Access: !°LIST PROCEDURES REVLIST ( °is the left-shift of the Nkey).
RKF Type: Description: Access: Input/Output: Command Solve for Initial Values (Runge–Kutta–Fehlberg) Command: Computes the solution to an initial value problem for a differential equation, using the Runge-Kutta-Fehlberg (4,5) method. RKF solves y'(t) = f(t,y), where y(t0) = y0.
• error displays the absolute error for that step. A zero error indicates that the Runge–Kutta– Fehlberg method failed and that Euler’s method was used instead. The absolute error is the absolute value of the estimated error for a scalar problem, and the row (infinity) norm of the estimated error vector for a vector problem. (The latter is a bound on the maximum error of any component of the solution.
Input/Output: Level 1/Argument 1 Level 1/Item 1 → #n1 See also: RLB Type: Description: Access: Flags: Input/Output: #n2 RLB, RR, RRB Command Rotate Left Byte Command: Rotates a binary integer one byte to the left. The leftmost byte of #n1 becomes the rightmost byte of #n2. RLB is equivalent to executing RL eight times. … ã L BYTE RLB (ã is the right-shift of the 3key).
See also: RNRM Type: Description: Access: TRNC Command Row Norm Command: Returns the row norm (infinity norm) of its argument array. The row norm is the maximum (over all rows) of the sums of the absolute values of all elements in each row. For a vector, the row norm is the largest absolute value of any of its elements. !Ø OPERATIONS LRNRM ( Ø is the left-shift of the 5key). !´ MATRIX NORMALIZE RNRM ( ´ is the left-shift of the Pkey).
ROOT Type: Description: Access: Input/Output: ROT Type: Description: Access: Input/Output: Command Root-Finder Command: Returns a real number xroot that is a value of the specified variable global for which the specified program or algebraic object most nearly evaluates to zero or a local extremum. ROOT is the programmable form of the HP Solve application. guess is an initial estimate of the solution.
ROW+ Type: Description: Access: Command Insert Row Command: Inserts an array into a matrix (or one or more numbers into a vector) at the position indicated by nindex, and returns the modified matrix (or vector). The inserted array must have the same number of columns as the target array. nindex is rounded to the nearest integer. The original array is redimensioned to include the new columns or elements, and the elements at and below the insertion point are shifted down.
RPL> Type: Description: Access: Input/Output: Command User RPL program function. This function allows for the entry and execution of User RPL programs while in algebraic mode. While RPL programs can be written in algebraic mode without the use of this function, some RPL constructs, such as FOR…NEXT loops, will produce an error message if not preceded by the RPL> function.
rref Type: Description: Command Access: PSOLVE, Matrices, !Ø Input: A matrix. Output: Level 2/Item 1: The pivot points. Reduces a matrix to row-reduced echelon form, and provides a list of pivot points. LINEAR SYSTEMS Level 1/Item 2: An equivalent matrix in row reduced echelon form. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear) If flag –126 is clear (the default), row reduction is done with the last column.
RREFMOD Type: Description: Command Access: Catalog, …µ 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 –3 clear). If flag –126 is clear (the default), row reduction is done with the last column. If the flag is set, row reduction is done without reducing the last column, but the last column will be modified by the reduction of the rest of the matrix.
The derivative of the function with respect to y (∂f/∂y) is –4y, and the derivative of the function − 2t with respect to t (∂f/∂t) is . (1 + t 2 ) 2 1. Store the independent variable’s initial value, 0, in T. 2. Store the dependent variable’s initial value, 0, in Y. 1 3. Store the expression, − 2 y 2 , in F. 2 1+ t 4. Store ∂f/∂y, –4y, in FY. − 2t 5. Store ∂f/∂t, , in FT. (1 + t 2 ) 2 6. Enter these five items in a list: { T Y F FY FT }. 7. Enter the tolerance.
Access: Input/Output: RRKSTEP will use the Euler method to compute the next solution step and will consider the error tolerance satisfied. The Rosenbrock method will fail if the current independent variable is zero and the stepsize ≤ 2.5 × 10-499 or if the variable is nonzero and the stepsize is 2.5 × 10-11 times its magnitude. The Runge–Kutta–Fehlberg method will fail if the current independent variable is zero and the stepsize ≤ 1.3 × 10-498 or if the variable is nonzero and the stepsize is 1.
• B and Z must both be vectors or both be matrices. • B and Z must have the same number of columns if they are matrices. RSD is typically used for computing a correction to Z, where Z has been obtained as an approximation to the solution X to the system of equations AX = B. Access: !Ø OPERATIONS LRSD ( Ø is the left-shift of the 5key). !´ MATRIX LRSD ( ´ is the left-shift of the Pkey).
R→C Type: Description: Command Real to Complex Command: Combines two real numbers or real arrays into a single complex number or complex array. The first input represents the real element(s) of the complex result. The second input represents the imaginary element(s) of the complex result. Array arguments must have the same dimensions. Access: !°TYPE L R→C Input/Output: See also: R→D Type: Description: Access: Flags: Input/Output: ( °is the left-shift of the Nkey).
Input/Output: Level 2/Argument 1 Example 1: Example 2: Example 3: See also: Level 1/Argument 2 obj1 obj2 { A B } (4,5) SAME returns 0. { A B } { B A } SAME returns 0. "CATS" "CATS" SAME returns 1. TYPE, == Level 1/Item 1 → 0/1 SBRK Type: Description: Command Serial Break Command: Interrupts serial transmission or reception. SBRK is typically used when a problem occurs in a serial data transmission.
Executing SCALEW changes the x-axis display range—the xmin and xmax components of the first two complex numbers in the reserved variable PPAR. The plot origin (the user-unit coordinate of the center pixel) is not changed.
• ptype is a command name specifying the plot type. Executing the command SCATTER places the name SCATTER in ptype. • depend is a name specifying the dependent variable. The default value is Y.
Access: …µ SCLΣ Input/Output: None See also: AUTO, SCATRPLOT SCONJ Type: Description: Access: Input/Output: Command Store Conjugate Command: Conjugates the contents of a named object. The named object must be a number, an array, or an algebraic object. For information on conjugation, see CONJ. !°MEMORY ARITHMETIC LSCONJ ( °is the left-shift of the Nkey). Level 1/Argument 1 Level 1/Item 1 → 'name' See also: SCROLL Type: Description: Access: Input/Output: CONJ, SINV, SNEG Command Displays any object.
Access: Flags: Data is always sent from a local Kermit, but can be sent either to another local Kermit (which must execute RECV or RECN) or to a server Kermit. To rename an object when sending it, include the old and new names in an embedded list. …µ SEND I/O Device flag (–33), I/O Data Format (–35), I/O Messages (–39), I/O Device for Wire (–78) If flag –35 is clear (ASCII transfer), the translation setting also has an effect.
Level 1/Argument 3: The order for the series expansion. The minimum value is 2, and the maximum value is 20. Output: Level 2/Item 1: A list containing the limit as a value and as the equivalent expression, an expression approximating the function near the limit point, and the order of the remainder. These are expressed in terms of a small parameter h. Level 1/Item 2: An expression for h in terms of the original variable. Flags: Exact mode must be set (flag –105 clear).
Access: Input/Output: User flags are numbered 1 through 128. System flags are numbered –1 through –128. See Appendix C for a listing of system flags and their flag numbers. ( °is the left-shift of the Nkey).
G(x + 1) – G(x) = f(x) where x is the specified variable. Access: !ÖDERIV L Input: Level 2/Argument 1: A function Level 1/Argument 2: The variable to calculate the antiderivative with respect to. Output: The discrete antiderivative of the function. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Access: Flags: Input/Output: !´ REAL LSIGN ( ´ is the left-shift of the Pkey). …ßL SIGN Numerical Results (–3) ( ß is the right-shift of the 1key). Level 1/Argument 1 Level 1/Item 1 z1 → z2 x_unit → xsign 'symb' → Example 1: Example 2: See also: 'SIGN(symb)' 32_ft SIGN returns 1. (1,1) SIGN returns (.707106781187,.707106781187). ABS, MANT, XPON SIGNTAB Type: Command Description: Tabulates the sign of a rational function of the current CAS variable.
See also: EGCD SIMPLIFY Type: Command Description: Simplifies an expression. Access: !Ú Input: An expression Output: An equivalent simplified expression. SIMPLIFY follows an extensive built-in set of rules, but these might not give exactly the simplification the user expects. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set). Must be in complex mode (flag –103 set). Example: Command: Result: Express eix in trigonometric terms. See also: EXPLN SINH Type: Description: Access: Flags: Input/Output: SINCOS(EXP(i*X)) COS(X)+iSIN(X) Analytic function Hyperbolic Sine Analytic Function: Returns the hyperbolic sine of the argument. For complex arguments, sinh(x + iy) = sinhx cosy + i coshx siny. …Ñ HYPERBOLIC SINH (Ñ is the right-shift of the 8key).
Input/Output: Level 1/Argument 1 See also: SL Type: Description: Access: Flags: Input/Output: Level 2/Item 1 “string” → n integer → n { list } → n [ vector ] → {n} [[ matrix ]] → { n m} 'symb' → n grob → #nwidth #mheight PICT → #nwidth #mheight x_unit CHR, NUM, POS, REPL, SUB → n Command Shift Left Command: Shift a binary integer one bit to the left. The most significant bit is shifted out to the left and lost, while the least significant bit is regenerated as a zero.
When plot type is set to SLOPEFIELD, the DRAW command plots a slope representation of a scalar function with two variables. SLOPEFIELD requires values in the reserved variables EQ, VPAR, and PPAR. VPAR has the following form: { xleft xright ynear yfar zlow zhigh xmin xmax ymin ymax xeye yeye zeye xstep ystep } For plot type SLOPEFIELD, the elements of VPAR are used as follows: • xleft and xright are real numbers that specify the width of the view space.
Input/Output: Level 1/Argument 1 Level 1/Item 1 → See also: [ array ] ABS, CNRM, COND, RNRM, SRAD, TRACE xspectralnorm SOLVE Type: Command Description: Finds zeros of an expression equated to 0, or solves an equation. Access: Symbolic solve, !Î, P SOLVE, …×L Input: Level 2/Argument 1: The expression or equation. A list of equations and expressions can be given too, each will be solved for the same variable. Level 1/Argument 2: The variable to solve for.
Input/Output: Level 3/Argument 1 Level 2/Argument 2 Level 1/Argument 3 n m 0/1 See also: EQNLIB, MSOLVR SOLVER Type: Description: Access: Command Displays a menu of commands used in solving equations. …µ SOLVER Level 1/Item 1 → If the CHOOSE boxes flag is clear (flag –117 clear), displays the operations as a numbered list. If the flag is set, displays the operations as a menu of function keys.
Input/Output: Level 1/Argument 1 → { list }1 See also: Level 1/Item 1 { list }2 REVLIST SPHERE Type: Description: Command Spherical Mode Command: Sets spherical coordinate mode. SPHERE sets flags –15 and –16. In spherical mode, vectors are displayed as polar components. Access: „&H ANGLE SPHERE Input/Output: None See also: CYLIN, RECT SQ Type: Description: Access: Flags: Input/Output: Analytic function Square Analytic Function: Returns the square of the argument.
The spectral radius of a matrix is a measure of the size of the matrix, and is equal to the absolute value of the largest eigenvalue of the matrix. Access: !Ø OPERATIONS L L SRAD !´ MATRIX NORMALIZE SRAD (Ø is the left-shift of the 5key). ( ´ is the left-shift of the Pkey). Input/Output: Level 1/Argument 1 [[ matrix ]]n×n See also: SRB Type: Description: Access: Flags: Input/Output: Level 1/Item 1 → COND, SNRM, TRACE Command Shift Right Byte Command: Shifts a binary integer one byte to the right.
Access: Flags: Input/Output: Note that BUFLEN also clears the above-mentioned framing, overrun, and overflow errors. Therefore, SRECV cannot detect an input-buffer overflow after BUFLEN is executed, unless more characters were received after BUFLEN was executed (causing the input buffer to overflow again). SRECV also cannot detect framing and UART overrun errors cleared by BUFLEN.
See also: START Type: Description: Access: Input/Output: NEXT, SST Command Operation START Definite Loop Structure Command: Begins START … NEXT and START … STEP definite loop structures. Definite loop structures execute a command or sequence of commands a specified number of times. • START … NEXT executes a portion of a program a specified number of times.
Access: …µ STD Input/Output: None Example: The following table provides examples of numbers displayed in Standard mode: Number See also: STEP Type: Description: Representable With 12 Digits? Displayed As 1011 100000000000 Yes (integer) 1012 1.E12 No 10-11 .000000000001 Yes 1.2 x 10-11 1.23E-11 No 12.345 12.345 Yes ENG, FIX, SCI Command Operation STEP Command: Defines the increment (step) value, and ends definite loop structure. See the FOR and START keyword entries for more information.
Input/Output: Level 1/Argument 1 → xseconds See also: STO Type: Description: Access: Input/Output: Example 1: Example 2: Example 3: See also: STOALARM Type: Description: Level 1/Item 1 0 BUFLEN, CLOSEIO, SBRK, SRECV, XMIT → Command Store Command: Stores an object into a specified variable or object. Storing a graphics object into PICT makes it the current graphics object. To create a backup object, store the obj into the desired backup location (identified as :nport:namebackup).
nindex is a real integer identifying the alarm based on its chronological position in the system alarm list. (Ó is the right-shift of the 9 key).
Input/Output: Level 1/Argument 1 Level 1/Item 1 { obj1, xkey 1, ... objn, xkey n } → { S, obj1, xkey 1, ... objn, xkey n } → 'S' → See also: ASN, DELKEYS, RCLKEYS STORE Type: Description: Function Stores a number in a global variable. Given an expression as input, STORE evaluates the expression and stores the numerical value, unlike DEF which stores the expression. Access: Catalog, …µ Input: Level 2/Argument 1: A number or an expression that evaluates to a numeric value.
Input/Output: Level 2/Argument 1 See also: STO– Type: Description: Access: Input/Output: See also: STO* Type: Description: Access: Input/Output: See also: STO/ Type: Description: obj 'name' STO–, STO*, STO/, + Level 1/Argument 2 'name' obj Level 1/Item 1 → → Command Store Minus Command: Calculates the difference between a number (or other object) and the contents of a specified variable, and stores the new value in the specified variable.
Access: Input/Output: See also: STOΣ Type: Description: Access: Input/Output: Using STO/ to divide one array by another array or to divide an array by a number (where obj is an array or a number and name is the global name of an array) requires less memory than using the stack to divide them. !°MEMORY ARITHMETIC STO/ ( °is the left-shift of the Nkey).
Input/Output: Level 1/Argument 1 Level 1/Item 1 → obj Example: See also: STREAM Type: Description: Access: Input/Output: “obj” →STR can create special displays to label program output or provide prompts for input. The sequence "Result = " SWAP →STR + 1 DISP 1 FREEZE displays Result = object in line 1 of the display, where object is a string form of an object taken from level 1.
See also: STURMAB STURMAB Type: Command Description: For a polynomial P and a closed interval [a, b], STURMAB determines the number of zeroes P has in [a, b] Access: Arithmetic, !ÞPOLYNOMIAL !« Input: A polynomial P Output: A list containing a number that is the same sign as P(a) and the number of zeroes P has in [a, b]. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set).
Access: !°LIST SUB Input/Output: ( °is the left-shift of the Nkey).
Input: Level 2/Argument 1: The object or number to be subtracted from. Level 1/Argument 2: The object or number to subtract. Output: The result of the subtraction, modulo the current modulus. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). SVD Type: Description: Command Singular Value Decomposition Command: Returns the singular value decomposition of an m × n matrix. SVD decomposes A into 2 matrices and a vector.
DUP, DUPN, DUP2, OVER, PICK, ROLL, ROLLD, ROT See also: SYSEVAL Type: Description: Command Evaluate System Object Command: Evaluates unnamed operating system objects specified by their memory addresses. WARNING: Use extreme care when executing this function. Using SYSEVAL with random addresses will almost always cause a memory loss. Do not use this function unless you know what you are doing.
Example: Convert this system to a matrix: X–Y=0 2X + Y = 5 Command: Result: %T Type: Description: Access: Flags: Input/Output: Example 1: Example 2: See also: SYST2MAT([X-Y, 2*X+Y=5],[X, Y]) 1 –1 0 2 1 –5 Function Percent of Total Function: Returns the percent of the first argument that is represented by the second argument. If both arguments are unit objects, the units must be consistent with each other.
Result: TABVAR Type: { X^2+1,{{1, 2, 3},{2, 5, 10}}} Command Description: For a function of the current variable, with a rational derivative, computes the variation table, that is the turning points of the function and where the function is increasing or decreasing. Access: PGRAPH L, !ÖGRAPH L Input: An expression in terms of the current variable, which has a rational derivative. Output: Level 3/Item 1: The original rational function. Level 2/Item 2: A list of two lists.
See also: TAN Type: Description: HEAD Analytic function Tangent Analytic Function: Returns the tangent of the argument. For real arguments, the current angle mode determines the number’s interpretation as an angle, unless the angular units are specified. For a real argument that is an odd-integer multiple of 90 in Degrees mode, an Infinite Result exception occurs. If flag –22 is set (no error), the sign of the result (MAXR) matches that of the argument.
Input: An expression Output: The transformed expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Replace tan(x) terms in the function: ( tan ( x ) ) 2 Command: Result: TAN2SC(TAN(X)^2) (SIN(X)/COS(X))^2 See also: HALFTAN, TAN2CS2, TAN2SC2 TAN2SC2 Type: Command Description: Replaces tan(x) terms in an expression with sin(2x)/1+cos(2x) terms.
TAYLOR0 Type: Description: Function Access: Calculus, !Ö LIMITS & SERIES, PCALC L Input: An expression Output: The Taylor expansion of the expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Command: Result: Obtain the fourth-order Taylor series expansion of cos(x) at x=0.
TCOLLECT Type: Description: Command Access: Trigonometry, …ÑL Input: An expression with trigonometric terms. Output: The simplified expression. Flags: Exact mode must be set (flag –105 clear). Numeric mode must not be set (flag –3 clear). Radians mode must be set (flag –17 set). Example: Collect terms in the expression: Linearizes products in a trigonometric expression by collecting sine and cosine terms, and by combining sine and cosine terms of the same argument.
TEVAL Type: Description: Access: Input/Output: Function For the specified operation, performs the same function as EVAL, and returns the time taken to perform the evaluation as well as the result. …µ TEVAL Level 1/Argument 1 Object → Level 2/Item 2 Level 1/Item 1 result time taken See also: EVAL TEXPAND Type: Description: Command Access: !Ð, PALG, PTRIG, …×L, …ÑL, PLEXPLN Input: An expression. Output: The transformation of the expression. Flags: Exact mode must be set (flag –105 clear).
TICKS Type: Command Description: Ticks Command: Returns the system time as a binary integer, in units of 1/8192 second. Access: …ÓTOOLS TICKS ( Ó is the right-shift of the 9 key).
Input/Output: See also: TDELTA TLIN Type: Description: Command Level 2/Argument 1 Level 1/Argument 2 xinitial ydelta → xfinal x_unit1 y_unit2delta → x_unit1final x_unit 'symb' → 'TINC(x_unit, symb)' 'symb' y_unitdelta → 'TINC(symb, y_unitdelta)' 'symb1' 'symb2' → 'TINC(symb1, symb2)' Linearizes and simplifies trigonometric expressions. Note that this function does not collect sin and cos terms of the same angle. Access: PTRIG, Trigonometry, …ÑL Input: An expression.
TMENU Type: Description: Access: Input/Output: Command Temporary Menu Command: Displays a built-in menu, library menu, or user-defined menu. TMENU works just like MENU, except for user-defined menus (specified by a list or by the name of a variable that contains a list). Such menus are displayed like a custom menu and work like a custom menu, but are not stored in reserved variable CST. Thus, a menu defined and displayed by TMENU cannot be redisplayed by evaluating CST.
Access: !Ø OPERATIONS LLTRAN Input/Output: ( Ø is the left-shift of the 5key). Level 1/Argument 1 See also: TRANSIO Type: Description: Level 1/Item 1 [[ matrix ]] → 'name' → [[ matrix ]]transpose CONJ, TRN Command I/O Translation Command: Specifies the character translation option. These translations affect only ASCII Kermit transfers and files printed to the serial port.
Result: 2 1 L N( X + 1 ) + 2 × i × A TA N -- x -----------------------------------------------------------------------------2 See also: TRIGCOS, TRIGSIN, TRIGTAN TRIGCOS Type: Command Description: Simplifies a trigonometric expression by applying the identity: 2 2 ( sin x ) + ( cos x ) = 1 Returns only cosine terms if possible. Access: Trigonometry, …ÑLL Input: An expression with trigonometric terms. Output: The transformed expression. Flags: Exact mode must be set (flag –105 clear).
Access: Trigonometry, …ÑLL 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 –3 clear). Radians mode must be set (flag –17 set).
Input/Output: Example 1: Example 2: See also: Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1 z1 ntruncate → z2 z1 'symbtruncate' → 'TRNC(z1,symbtruncate)' 'symb1' ntruncate → 'TRNC(symb1,ntruncate)' 'symb1' 'symbtruncate' → 'TRNC(symb1,symbtruncate)' [ array ]1 ntruncate → [ array ]2 x_unit ntruncate → y_unit → x_unit 'symbtruncate' 'TRNC(x_unit,symbtruncate)' (4.5792,8.1275) 2 TRNC returns (4.57,8.12). [ 2.34907 3.96351 2.73453 ] -2 TRNC returns [ 2.3 3.9 2.7 ].
• indep is a name specifying the independent variable on the horizontal axis, or a list containing such a name and two numbers specifying the minimum and maximum values for the independent variable (the horizontal plotting range). The default value is X. • res is a real number specifying the interval (in user-unit coordinates) between plotted values of the independent variable on the horizontal axis, or a binary integer specifying that interval in pixels.
Input/Output: Example: See also: TVARS Type: Description: Access: Input/Output: Level 2/Argument 1 Level 1/Argument 2 date time Level 1/Item 1 → “DOW DATE TIME“ With flags –42 and –41 clear, 2.061990 14.55 TSTR returns "TUE 02/06/90 02:55:00P". DATE, TICKS, TIME Command Typed Variables Command: Lists all global variables in the current directory that contain objects of the specified types. If the current directory contains no variables of the specified types, TVARS returns an empty list.
Input/Output: Level 1/Argument 1 'TVM variable' Level 1/Item 1 → xTVM variable See also: AMORT, TVM, TVMBEG, TVMEND TYPE Type: Description: Command Type Command: Returns the type number of an object, as shown in the following table: Object Type: Number: User objects: Real number Complex number Character string Real array Complex array List Global name Local name Program Algebraic object Binary integer Graphics object Tagged object Unit object XLIB name Directory object Library Object Type: Numb
UFACT Type: Command Description: Factor Unit Command: Factors the level 1 unit from the unit expression of the level 2 unit object. Access: !Ú UNITS TOOLS UFACT ( Ú is the left-shift of the 6key). Input/Output: Level 2/Argument 1 Example: See also: Level 1/Argument 2 x1_unit1 x2_unit2 1_W 1_N UFACT returns 1_N*m/s.
Input: Level 1/Item 1: The name of a global variable, or a list of global names, to be removed from the REALASSUME list. Output: Level 1/Item 1: The same name or list of names as was input, even if any of the named variables were not in REALASSUME. Example: Command: Result: Remove the variables S1 and S2 which are include in the REALASSUME list by default.
UNROT Type: Description: RPL Command Changes the order of the first three objects on the stack. The order of the change is the opposite to that of the ROT command. ( °is the left-shift of the Nkey). Access: !° STACK UNROT Input/Output: L3 Example: See also: L2 L1 obj3 obj2 obj1 333 22 1 UNROT returns 1 333 22. OVER, PICK, ROLL, ROLLD, SWAP, ROT → L3 L2 L1 obj1 obj3 obj2 UNTIL Type: Description: Command UNTIL Command: Starts the test clause in a DO … UNTIL … END indefinite loop structure.
Input/Output: Level 2/Argument 1 See also: UTPF Type: Description: Level 1/Argument 2 n UTPF, UTPN, UTPT Level 1/Item 1 → x utpc(n,x) Command Upper Snedecor’s F Distribution Command: Returns the probability utpf(n1, n2, x) that a Snedecor’s F random variable is greater than x, where n1 and n2 are the numerator and denominator degrees of freedom of the F distribution.
Input/Output: Level 3/Argument 1 See also: UTPT Type: Description: Level 2/Argument 2 Level 1/Argument 3 v x m UTPC, UTPF, UTPT For any value z, z z Γ --- = --- – 1 ! 2 2 ∞ 2 t ∫x 1 + ---n- n+1 – -----------2 dt , where ! is the factorial command. Level 1/Argument 2 x Level 1/Item 1 → See also: n UTPC, UTPF, UTPN UVAL Type: Description: Function Unit Value Function: Returns the numerical part of a unit object.
Input/Output: L1/A1 [xy] [ xr, ytheta ] [ x1 , x2 , x3 ] [ x1, xtheta, xz ] [ x1, xtheta, xphi ] [ x1, x2, ..., xn ] (x, y) (xr, ytheta) → → → → → → → → Ln/I1 ... L3/In–2 L2/In–1 L1/In x1 x1 x1 x1 ... xn–2 x xr x2 xtheta xtheta xn–1 x xr y ytheta x3 xz xphi xn y ytheta L = Level; A = Argument; I = item Example 1: Example 2: Example 3: See also: →V2 Type: Description: With flag –16 clear (Rectangular mode), (2,3) V→ returns 2 to level 2 and 1 to level 1.
Mode Result Rectangular (flag –16 clear) [ x1 x2 x3 ] Polar/Cylindrical (flag –15 clear and –16 set) [ x1 xtheta xz ] Polar/Spherical (flag –15 and –16 set) [ x1 xtheta xphi ] Access: !´ VECTOR →V3 Flags: Coordinate System (–15 and –16) Input/Output: Example 1: Example 2: Example 3: See also: ( ´ is the left-shift of the Pkey).
The variance (equal to the square of the standard deviation) is returned as a vector of m real numbers, or as a single real number if m = 1. The variances are computed using this formula: 1 ------------ ⋅ n–1 n ∑ (xi – x) 2 i=1 where xi is the ith coordinate value in a column, the number of data points.
VISIT Type: Command Description: For a specified variable, opens the contents in the command-line editor. Access: …µ VISIT or „˜ Input/Output: Level 1/Argument 1 Level 1/Item 1 → A variable name See also: VISITB Type: Description: Access: Input/Output: VISITB, EDIT, EDITB Command For a specified variable, opens the contents in the most suitable editor for the object type. For example, if the specified variable holds an equation, the equation is opened in Equation Writer.
However, obtaining the curl of the above result, and then applying VPOTENTIAL to it again will give the same result. See also: VTYPE Type: Description: CURL, POTENTIAL Command Variable Type Command: Returns the type number of the object contained in the named variable. If the named variable does not exist, VTYPE returns –1. For a table of the objects’ type numbers, see the entry for TYPE. Access: !° TYPE L L VTYPE Input/Output: ( °is the left-shift of the Nkey).
Input/Output: Level 1/Argument 1 Example 1: Example 2: See also: WHILE Type: Description: Access: Input/Output: Level 1/Item 1 x → 0 → xkey –1 → xkey This program: « "Press [1] to add Press any other key to subtract" 1 DISP 0 WAIT IF 92.1 SAME THEN + ELSE - END » displays a prompting message and halts program execution until a key is pressed. If the 1 key (location 92.1) is pressed, two numbers on the stack are added. If any other key is pressed, two numbers on the stack are subtracted.
VPAR has the following form: { xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep } For plot type WIREFRAME, the elements of VPAR are used as follows: • xleft and xright are real numbers that specify the width of the view space. • ynear and yfar are real numbers that specify the depth of the view space. • zlow and zhigh are real numbers that specify the height of the view space. • xmin and xmax are not used. • ymin and ymax are not used.
Code Description 5 A Deep Sleep wakeup (for example, $, Alarm). 6 Not used 7 A 5-nibble word (CMOS test word) in RAM was corrupt. (This word is checked on every interrupt, but it is used only as an indicator of potentially corrupt RAM.) 8 Not used 9 The alarm list is corrupt. A System RPL jump to #0. B The card module was removed (or card bounce).
Access: …µΣX2 Input/Output: Level 1/Argument 1 Level 1/Item 1 → See also: ΣX^2 Type: Description: Sum of X2 NΣ, ΣX, XCOL, ΣXY, ΣY, ΣY2 Command Sum of Squares of x-Values Command: Sums the squares of the values in the independentvariable column of the current statistical matrix. ΣX^2 is provided for compatibility with the HP 28. ΣX^2 is the same as ΣX2; see its listing for details.
Access: Flags: Input/Output: After receiving an XOFF command (with transmit pacing in the reserved variable IOPAR set), XMIT stops transmitting and waits for an XON command. XMIT resumes transmitting if an XON is received before the time-out set by STIME elapses; otherwise, XMIT terminates, returns a 0, and stores "Timeout" in ERRM.
Flags: Input/Output: !´ BASE L LOGIC XOR ( ´ is the left-shift of the Pkey). Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12) Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1 #n1 #n2 → #n3 “string1” “string2” → “string3” T/F1 T/F2 → 0/1 T/F 'symb' → 'T/F XOR symb' 'symb' T/F → 'symb XOR T/F' 'symb1' 'symb2' → 'symb1 XOR symb2' See also: AND, NOT, OR XPON Type: Description: Function Exponent Function: Returns the exponent of the argument.
Example 1: Command: Results: Express .3658 in rational format, in Std mode: Example 2: Command: Results: Express .3658 in rational format, in Fix 4 mode: Example 3: Command: Results: Express 1.04719755120 in rational format, in Eng 11 mode: See also: →Q, →Qπ XRECV Type: Description: Access: Flags: Input/Output: XQ(.3658) 1829/5000 XQ(.3658) √(19/142) XQ(1.04719755120) 1/3*π Command XModem Receive Command: Prepares the calculator to receive an object via XModem.
Input/Output (RPN): Level 2 Level 1 Level 1 y x → x y 'symb1' 'symb2' → 'XROOT(symb2,symb1)' 'symb' x → 'XROOT(x,symb)' y 'symb' → 'XROOT(symb,y)' y_unit x → y_unit 'symb' → Argument 1 Argument 2 y x → y x 'symb1' 'symb2' → 'XROOT(symb1,symb2)' 'symb' x → 'XROOT(symb,x)' y 'symb' → 'XROOT(y,symb)' x y_unit → 'symb' y_unit → x y _unit1/x 'XROOT(symb,y_unit)' Input/Output (ALG): XSEND Type: Description: Access: Flags: Input/Output: Level 1 XSERV Type: De
M Get the calculator memory L: List the files in the current directory Access: See also: XVOL Type: Description: Access: Input/Output: …µ XSERV BAUD, RECN, RECV, SEND XRECV, XGET, XPUT Command X Volume Coordinates Command: Sets the width of the view volume in the reserved variable VPAR. xleft and xright set the x-coordinates for the view volume used in 3D plots. These values are stored in the reserved variable VPAR.
ΣY Type: Description: Access: Input/Output: Command Sum of y-Values Command: Sums the values in the dependent variable column of the current statistical matrix (reserved variable ΣDAT). The dependent variable column is specified by YCOL, and is stored as the second parameter in the reserved variable ΣPAR. The default dependent variable column number is 2.
YRNG Type: Description: Access: Input/Output: Command y-Axis Display Range Command: Specifies the y-axis display range. The y-axis display range is stored in the reserved variable PPAR as ymin and ymax in the complex numbers (xmin, ymin) and (xmax, ymax). These complex numbers are the first two elements of PPAR and specify the coordinates of the lower left and upper right corners of the display ranges. The default values of ymin and ymax are –3.1 and 3.2, respectively for the HP 48gII and -3.9 and 4.
YVOL Type: Description: Access: Input/Output: Command Y Volume Coordinates Command: Sets the depth of the view volume in the reserved variable VPAR. The variables ynear and yfar are real numbers that set the y-coordinates for the view volume used in 3D plots. ynear must be less than yfar. These values are stored in the reserved variable VPAR.
ZFACTOR Type: Description: Function Gas Compressibility Z Factor Function: Calculates the gas compressibility correction factor for non-ideal behavior of a hydrocarbon gas. xTr is the reduced temperature: the ratio of the actual temperature (T) to the pseudocritical temperature (Tc). (Calculate the ratio using absolute temperatures.) xTr must be between 1.05 and 3.0. yPr is the reduced pressure: the ratio of the actual pressure (P) to the pseudocritical pressure (Pc). yPr must be between 0 and 30.
Input/Output: Level 2/Argument 1 See also: Level 1/Argument 2 w z 'symb' 'symb1' x_unit x_unit EXP, ISOL, LN, XROOT z 'symb' z 'symb2' y 'symb' Level 1/Item 1 → → → → → → wz 'z^(symb)' '(symb)^z' 'symb1^('symb2)' xy_unity '(x_unit)^(symb)' | (Where) Type: Function Description: Where Function: Substitutes values for names in an expression.
The principal branch used by the calculator for √ was chosen because it is analytic in the regions where the arguments of the real-valued inverse function are defined. The branch cut for the complex-valued square root function occurs where the corresponding real-valued function is undefined. The principal branch also preserves most of the important symmetries. The graphs below show the domain and range of √.
∫ (Integrate) Type: Function Description: Integral Function: Integrates an integrand from lower limit to upper limit with respect to a specified variable of integration. The algebraic syntax for ∫ parallels its stack syntax: ∫ (lower limit, upper limit, integrand, name) where lower limit, upper limit, and integrand can be real or complex numbers, unit objects, names, or algebraic expressions. Evaluating ∫ in Symbolic Results mode (flag –3 clear) returns a symbolic result.
example you could define $=1_? Then other currencies could be defined as multiples or fractions of 1_? The calculator has symbols for Yen, Pounds and Euros; other currencies could be defined using their names. The unit conversion system would then check conversions between them for consistency because ? is recognized as a base unit.
Access: Input/Output: • To enter one data point with a single coordinate value, the argument for Σ+ must be a real number. • To enter one data point with multiple coordinate values, the argument for Σ+ must be a vector with m real coordinate values. • To enter several data points, the argument for Σ+ must be a matrix of n rows of m real coordinate values. In each case, the coordinate values of the data point(s) are added as new rows to the current statistics matrix (reserved variable ΣDAT).
flag –2 or flag –3 is set (to return numerical results), then evaluating 'SIN(π)' returns the numerical approximation –2.06761537357E–13. Access: !ì ( ìis the left-shift of the #key). Flags: Symbolic Constants (–2), Numerical Results (–3) Input/Output: Level 1/Argument 1 See also: Level 1/Item 1 → '̟' → 3.
∞ Γ(x + 1) = ∫e –t x t dt 0 and defined for other values of x by analytic continuation: Γ(x + 1) = n Γ(x) Access: !´ L PROBABILITY ! ( ´ is the left-shift of the Pkey). Flags: Numerical Results (–3), Underflow Exception (–20), Overflow Exception (–21) Input/Output: Level 1/Argument 1 See also: Level 1/Item 1 n → n! x → Γ(x + 1) 'symb' → '(symb!)' COMB, PERM % (Percent) Type: Function Description: Percent Function: Returns x percent of y.
The calculator handles units by attaching the unit to a numeric value using the underscore symbol. For example, the value of 3 kilometers is shown as 3_km, and is created by entering 3 and then the underscore character, followed by attaching the kilometer unit. Access: Input: Output: …Ý (Ý is the right-shift of the -key). Numeric value Numeric value ready for a unit attachment «» (Program delimiters) Type: Object Description: Program delimiter object: Enters a pair of program delimiter objects.
Input/Output: See also: Level 2/Argument 1 Level 1/Argument 2 x #n1 “string1” x 'symb' 'symb1' x_unit1 x_unit 'symb' y #n2 “string2” 'symb' x 'symb2' y_unit2 'symb' x_unit Level 1/Item 1 → → → → → → → → → 0/1 0/1 0/1 'x < symb' 'symb < x' 'symb1 < symb2' 0/1 'x_unit < symb' 'symb < x_unit' ≤, >, ≥, ==, ≠ ≤ (Less than or Equal) Type: Function Description: Less Than or Equal Function: Tests whether one object is less than or equal to another object.
> (Greater than) Type: Function Description: Greater Than Function: Tests whether one object is greater than another object. The function > returns a true test result (1) if the first argument is greater than the second argument, or a false test result (0) otherwise. If one object is a symbolic (an algebraic or a name), and the other is a number or symbolic or unit object, > returns a symbolic comparison expression that can be evaluated to return a test result.
Access: Flags: Input/Output: See also: example, that “a” is greater than or equal to “B”, since “B” is character code 66, and “a” is character code 97. For unit objects, the two objects must be dimensionally consistent and are converted to common units for comparison. If you use simple temperature units, the calculator assumes the values represent temperatures and not differences in temperatures. For compound temperature units, the calculator assumes temperature units represent temperature differences.
Input/Output: See also: Level 2/Argument 1 Level 1/Argument 2 obj1 obj2 → 0/1 (x,0) x → 0/1 x (x,0) → 0/1 z 'symb' → 'z ≠ symb' 'symb' z → 'symb ≠ z' 'symb2' → 'symb1 ≠symb2' 'symb1' SAME, TYPE, <, ≤, >,≥, ==, = Level 1/Item 1 * (Multiply) Type: Function Description: Multiply Analytic Function: Returns the product of the arguments. The product of a real number a and a complex number (x, y) is the complex number (xa, ya).
Input/Output: See also: Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1 z1 z2 → z1 z2 [[ matrix ]] [ array ] → [[ matrix × array ]] z [ array ] → [ z × array ] [ array ] z → [ array × z ] z 'symb' → 'z * symb' 'symb' z → 'symb * z' 'symb1' 'symb2' → 'symb1 *symb2' #n1 n2 → #n3 n1 #n2 → #n3 #n1 #n2 → #n3 x_unit y_unit → xy_unitx × unity x y_unit → xy_unit x_unit y → xy_unit 'symb' x_unit → 'symb * x_unit' x_unit 'symb' → 'x_unit * symb' +,
Access: Flags: Input/Output: Example 1: Example 2: Example 3: Example 4: See also: and %T treat temperatures as differences, without any additive constant, but require both arguments to be either absolute (K and ºR), both ºC, or both ºF. No other combinations are allowed.
Access: Flags: Input/Output: Example 1: Example 2: Example 3: See also: The difference of two binary integers is a binary integer that is the sum of the first argument and the two’s complement of the second argument. The difference of two unit objects is a unit object with the same dimensions as the second argument. The units of the two arguments must be consistent. Common usage is ambiguous about some units of temperature.
ax ay ---------------, ---------------- 2 2 2 2 x +y x +y A complex number (x, y) divided by a real number a returns the complex number (x/a, y/a). A complex number (x1, y1) divided by another complex number (x2, y2) returns this complex quotient: x 1 x 2 + y 1 y 2 y 1 x 2 – x 1 y 2 - , -------------------------- -------------------------- 2 2 x2 + y2 x +y 2 2 2 2 An array B divided by a matrix A solves the system of equations AX=B for X; that is, X = A–1 B.
Common usage is ambiguous about some units of temperature. When ºC or ºF represents a thermometer reading, then the temperature is a unit with an additive constant: 0 ºC = 273.15 K, and 0ºF = 459.67ºR. But when ºC or ºF represents a difference in thermometer readings, then the temperature is a unit with no additive constant: 1ºC=1 K and 1ºF = 1ºR. The arithmetic operators +, –, %, %CH, and %T treat temperatures as differences, without any additive constant.
Input/Output: See also: Level 2/Argument 1 Level 1/Argument 2 obj1 obj2 → 0/1 (x,0) x → 0/1 x (x,0) → 0/1 z 'symb' → 'z == symb' 'symb' z → 'symb == z' 'symb2' → 'symb1 == symb2' 'symb1' SAME, TYPE, <, ≤, >, ≥, ≠ Level 1/Item 1 (Store) Type: Command Description: Store Command: Stores an object into a specified variable. To create a backup object, store the obj into the desired backup location (identified as :nport:namebackup). will not overwrite an existing backup object.
See also: « → x y z 'x*y/2+z' » is a user-defined function. Like a built-in function, a user-defined function can take its arguments in stack syntax or algebraic syntax, and can take symbolic arguments. In addition, a user-defined function is differentiable if its defining procedure is an algebraic expression that contains only differentiable functions.
4 4.Computer Algebra System CAS Settings Selecting CAS Settings CAS settings are selected using the CAS MODES input form, described in Chapter 1 of the User’s Manual. Selecting a mode is equivalent to setting or clearing one of the system flags, the flag numbers are given in the “Flags” part of the operation descriptions. Pressing the L key in the CAS MODES input form displays a menu that allows the user to calculate settings.
• • • • • • • • • • • • • • • Many CAS commands will give numeric results instead of symbolic results if numeric mode is set instead of being cleared. Though these results may be correct, they will not be what the user wants if a symbolic result is needed. For this reason, the Flags section of most operation descriptions says that numeric mode should not be set.
Using the CAS Examples and Help In addition to the examples in this Command Reference, the built-in CAS help provides examples of CAS operations. • If an operation is selected from the operations catalog, …µ, and if help is available, then pressing the !HELP key shows help information. Pressing the %OK% menu key copies the operation to the command line, ready for use.
Computer algebra command categories listed by menu CAS operations are listed here in order of the keyboard menus they appear in. These menus can be selected from the CAS menu in G, or directly from the keyboard. A few CAS operations appear in more than one menu. Many CAS commands are also available from the P menu, or from the „´ menu; these menus are not listed here, to avoid duplication. The CAS has its own menu commands too, they are included in the alphabetical list of commands.
HERMITE .......................... 3-103 HORNER .......................... 3-108 LAGRANGE .......................... 3-126 LCM .......................... 3-128 LEGENDRE .......................... 3-130 PARTFRAC .......................... 3-164 PCOEF .......................... 3-165 PROOT .......................... 3-179 PTAYL .......................... 3-182 QUOT .......................... 3-189 RESULTANT .......................... 3-201 REMAINDER.......................... 3-198 STURM ......................
Calculus commands Derivation and integration commands, !ÖDERIV. & INTEG. CURL ..........................3-48 DERIV ..........................3-56 DERVX ..........................3-56 DIV ..........................3-62 FOURIER ..........................3-91 HESS ..........................3-104 IBP ..........................3-109 INTVX ..........................3-119 LAPL ..........................3-127 PREVAL ..........................3-177 RISCH ..........................3-202 SIGMA ........................
Exp and Lin commands, !Ð EXPLN .......................... 3-81 EXPM .......................... 3-81 LIN .......................... 3-131 LNCOLLECT .......................... 3-136 LNP1 .......................... 3-136 TEXPAND .......................... 3-252 TSIMP .......................... 3-260 Matrix-related commands Create, !Ø CREATE AUGMENT .......................... 3-23 IDN .......................... 3-110 CON .......................... 3-41 →DIAG .......................... 3-58 DIAG→ ..............
TRACE TRAN ..........................3-255 ..........................3-255 Operations, !Ø FACTORIZATION LQ ..........................3-138 LU ..........................3-139 QR ..........................3-188 qr ..........................3-188 SCHUR ..........................3-218 SVD ..........................3-244 SVL ..........................3-244 Quadratic form, !Ø QUADRATIC FORM AXQ ..........................3-26 CHOLESKY ..........................3-34 GAUSS ..........................3-95 QXA ......
Symbolic solve commands, !Î DESOLVE ISOL LDEC LINSOLVE SOLVEVX SOLVE ZEROS .......................... 3-56 .......................... 3-121 .......................... 3-129 .......................... 3-133 .......................... 3-229 .......................... 3-229 .......................... 3-284 Trigonometry commands Hyperbolic, ACOSH ASINH ATANH COSH SINH TANH …Ñ HYPERBOLIC .......................... 3-8 .......................... 3-17 .......................... 3-22 ..........................
Convert commands, !Ú Unit conversion tools, !Ú CONVERT ..........................3-45 UBASE ..........................3-262 UVAL ..........................3-267 UFACT ..........................3-263 →UNIT ..........................3-264 Base conversion tools, !Ú UNITS TOOLS BASE All operations in the BASE submenus are described in Chapter 3. Trigonometric conversions, !Ú ACOS2S ..........................3-7 ASIN2C ..........................3-17 ASIN2T ..........................3-17 ATAN2S ..............
Matrix convert, !Ú MATRIX CONVERT AXL .......................... 3-25 AXQ .......................... 3-26 QXA .......................... 3-190 SYST2MAT .......................... 3-245 Other CAS operations, …µ These operations are in other menus, as described in Access for each one, or can be accessed with …µ. Other mathematics operations DEGREE .......................... 3-53 DOMAIN .......................... 3-66 DROITE .......................... 3-69 dn .......................... 3-64 EPSX0 ............
CAS menu commands, …µ These commands display menus or lists of CAS operations. ALGB ..........................3-10 ARIT ..........................3-15 CONSTANTS ..........................3-44 DIFF ..........................3-59 EXP&LN ..........................3-81 INTEGER ..........................3-119 MAIN ..........................3-141 MATHS ..........................3-143 MATR ..........................3-143 MENUXY ..........................3-146 MODULAR ..........................3-150 POLYNOMIAL ....
5 5.Equation Reference The Equation Library consists of 15 subjects and more than 100 titles. Each subject and title has a number that you can use with SOLVEQN to specify the set of equations. These numbers are shown in parentheses after the headings. See the end of this section for references given in each subject. Remember that some equations are estimates and assume certain conditions. See the references or other standard texts for assumptions and limitations of the equations.
Subject, var (subj, title) Pic EQ Pg COLUMNS AND BEAMS, 22 **********(1)***** Elastic Buckling (1,1) Y 4 5-4 Eccentric Columns (1,2) Y 2 5-4 Simple Deflection (1,3) Y 1 5-5 Simple Slope (1,4) Y 1 5-5 Simple Moment (1,5) Y 1 5-6 Simple Shear (1,6) Y 1 5-6 Cantilever Deflection (1,7) Y 1 5-7 Cantilever Slope (1,8) Y 1 5-7 Cantilever Moment (1,9) Y 1 5-7 Cantilever Shear (1,10) Y 1 5-8 ELECTRICITY, 47 ****************(2)***** Coulomb's Law (2,1) N 1 5-10 Ohm's Law and Power (2,2) N 4 5-10 Voltage Divider (2,3)
Columns and Beams (1) Variable º σcr σmax Description Eccentricity (offset) of load Critical stress Maximum stress θ Slope at x A Cross-sectional area a Distance to point load c Distance to edge fiber (Eccentric Columns), or Distance to applied moment (beams) E Modulus of elasticity I Moment of inertia K Effective length factor of column L Length of column or bean M Applied moment Mx Internal bending moment at x P Load (Eccentric Columns), or Point load (beams) Pcr Critical load r
Elastic Buckling (1, 1) These equations apply to a slender column (K L / r > 100) with length factor K. Equations: 2 π ⋅E⋅A Pc r = --------------------2-⋅L K ----------- r 2 π ⋅E⋅I Pc r = -------------------2(K ⋅ L ) Pcr A σ c r = -------- r = I --A Example: Given: L=7.3152_m, r=4.1148_cm, E=199947961.502_kPa, A=53.0967_cm^2, K=0.7, I=8990598.7930_mm^4. Solution: Pcr=676.6019_kN, σcr=127428.2444_kPa.
Simple Deflection (1, 3) Equation: y = P ⋅ (L – a ) ⋅ x -------------------------------- ⋅ ( x 6 ⋅ L ⋅ E ⋅ I 2 + (L – a) 2 2 – L 2 ) 2 L c M ⋅ x x – ------------ ⋅ c – ----------- – --- – ----------- 6 ⋅ L 3 2 ⋅ L E ⋅ I w ⋅ x – -------------------- ⋅ ( L 24 ⋅ E ⋅ I 3 + x 2 ⋅ (x – 2 ⋅ L )) Example: Given: L=20_ft, E=29000000_psi, I=40_in^4, a=10_ft, P=674.427_lbf, c=17_ft, M=3687.81_ft∗lbf, w=102.783_lbf/ft, x=9_ft. Solution: y= -0.6005_in.
Example: Given: L=20_ft, E=29000000_psi, I=40_in^4, a=10_ft, P=674.427_lbf, c=17_ft, M=3687.81_ft∗lbf, w=102.783_lbf/ft, x=9_ft. Solution: Θ= -0.0876_°. Simple Moment (1, 5) Equation: P ⋅ ( L – a) ⋅ x M ⋅ x w ⋅ x Mx = -------------------------------- + ------------ + ----------- ⋅ ( L – x ) L L 2 Example: Given: L=20_ft, a=10_ft, P=674.427_lbf, c=17_ft, M=3687.81_ft∗lbf, w=102.783_lbf / ft, x=9_ft. Solution: Mx=9782.
Cantilever Deflection (1, 7) Equation: 2 2 2 P⋅x M⋅x w⋅x 2 2 y = ----------------- ⋅ ( x – 3 ⋅ a ) + ----------------- – -------------------- ⋅ ( 6 ⋅ L – 4 ⋅ L ⋅ x + x ) 6⋅E⋅I 2 ⋅ E ⋅ I 24 ⋅ E ⋅ I Example: Given: L=10_ft, E=29000000_psi, I=15_in^4, P=500_lbf, M=800_ft∗lbf, a=3_ft, c=6_ft, w=100_lbf/ft, x=8_ft. Solution: y= -0.3316_in.
Equation: 2 2 W Mx = P ⋅ ( x – a ) + M – ----- ⋅ ( L – 2 ⋅ L ⋅ x + x ) 2 Example: Given: L=10_ft, P=500lbf, M=800_ft∗lbf, a=3_ft, c=6_ft, w=100_lbf/ft, x=8_ft. Solution: Mx= -200_ft∗lbf Cantilever Shear (1, 10) Equation: V = P + w ⋅ (L – x ) Example: Given: L=10_ft, P=500lbf, a=3_ft, x=8_ft, w=100_lbf/ft.
Electricity (2) Variable Description ∈r Relative permittivity µr Relative permeability ω Angular frequency ω0 Resonant angular frequency φ φp ,φs ρ Phase angle Parallel and series phase angles Resistivity ∆I Current change ∆t Time change ∆V Voltage change A C, C1, C2 Cp,Cs Wire cross-section area (Wire Resistance), or Solenoid cross-section area (Solenoid Inductance), or Plate area (Plate Capacitor) Capacitance Parallel and series capacitances d Plate separation E Energy F Force bet
Variable Qp,Qs r R,R1,R2 ri,ro Rp,Rs t ti,tf Description Parallel and series quality factors Charge distance Resistance Inside and outside radii Parallel and series resistances Time Initial and final times V Voltage, or Total voltage (Voltage Divider) V1 Voltage across R1 Vi,Vf Initial and final voltages Vmax Maximum voltage XC Reactance of capacitor XL Reactance of inductor Reference: 3. Coulomb’s Law (2, 1) This equation describes the electrostatic force between two charged particles.
Voltage Divider (2, 3) Equation: R1 V1 = V ⋅ --------------------- R1 + R2 Example: Given: R1=40_Ω, R2=10_Ω, V=100_V. Solution: V1=80_V. Current Divider (2, 4) Equation: R2 I1 = I ⋅ --------------------- R1 + R2 Example: Given: R1=10_Ω, R2=6_Ω, I=15_A. Solution: I1=5.6250_A.
Example: Given: ρ=0.0035_Ω∗cm, L=50_cm, A=1_cm^2. Solution: R=0.175_Ω. Series and Parallel R (2, 6) Equation: 1 1 1 ------- = ------- + ------Rp R1 R2 R s = R1 + R2 Example: Given: R1=2_Ω, R2=3_Ω. Solution: Rs=5_Ω, Rp=1.2000_Ω. Series and Parallel C (2, 7) Equations: 1 1 1 ------ = ------- + ------Cs C1 C2 Cp = C1 + C2 Example: Given: C1=2_µF, C2=3_µF. Solution: Cs=1.2000_µF, Cp=5_µF.
Series and Parallel L (2, 8) Equations: 1 1 1 ------- = ------- + ------Lp L1 L2 Ls = L1 + L2 Example: Given: L1=17_mH, L2=16.5_mH, Solution: Ls=33.5000_mH, Lp=8.3731_mH. Capacitive Energy (2, 9) Equation: 2 C⋅V E = --------------2 Example: Given: E=0.025_J, C=20_µF. Solution: V=50_V. Inductive Energy (2, 10) Equation: 2 L⋅I E = -----------2 Example: Given: E= 4_J, L=15_mH. Solution: I=23.0940_A.
RLC Current Delay (2, 11) The phase delay (angle) is positive for current lagging voltage. Equations: 1 1 -------- – ------XC XL ---TA N( φp ) = 1 --R XL – XC TA N( φ s ) = ----------------------R 1 X C = -----------ω⋅C XL = ω ⋅ L ω = 2⋅π⋅f Example: Given: f= 1107_Hz, C=80_µf, L=20_ mH, R=5_Ω. Solution: ω=672.3008_r/s, φs= -45.8292_°, φp= -5.8772_°, XC=18.5929_Ω, XL=13.4460_Ω.
DC Inductor Voltage (2, 14) These equations approximate the dc voltage induced in an inductor by a change in current in a certain time interval. Equations: ∆I V = –V ⋅ ----- ∆t ∆V = – If – Ii ∆t = tf – ti Example: Given: L=100_mH, V=52_V, ∆t=32_µs, Ii=23_A, ti=0_s. Solution: ∆I= -0.0166_A, If=22.9834_A, tf=32_µs. RC Transient (2, 15) Equation: V = Vf – ( Vf – Vi ) ⋅ e –t -----------R⋅C Example: Given: Vi=0_V, C=50_µF, Vf=10_V, R=100_ω, t=2_ms. Solution: V=3.2968_V.
Solution: I=0.0072_A. Resonant Frequency (2, 17) Equation: 1 L⋅C ω 0 = --------------- 1 C Qs = --- ⋅ --R L C Qp = R ⋅ --L ω 0 = 2 ⋅ π ⋅ f0 Example: Given: L=500_mH, C=8_µF, R=10_ω. Solution: ω0=500_r / s, Qs=25.0000, Qp=0.0400, f0=79.5775_Hz. Plate Capacitor (2, 18) Equation: ∈0 ⋅ ∈ r ⋅ A C = -----------------------d Example: Given: C=25_µF, ∈r=2.26, A=1_cm^2. Solution: d=8.0042E-9_cm.
Example: Given: ∈r=1, ro=1_cm, ri=.999_cm, L=10_cm. Solution: C=0.0056_µF. Solenoid Inductance (2, 20) Equation: 2 L = µ0 ⋅ µr ⋅ n ⋅ A ⋅ h Example: Given: µr=2.5, n=40_1/cm, A= .2_cm^2, h=3_cm. Solution: L=0.0302_mH. Toroid Inductance (2, 21) Equation: 2 µ0 ⋅ µr ⋅ N ⋅ h ro L = ------------------------------------ ⋅ LN ---- ri 2⋅π Example: Given: µr=1, N=5000, h=2_cm, ri= .2_cm, ro=4_cm. Solution: L=69.3147_mH.
Sinusoidal Voltage (2, 22) Equations: V = V ma x ⋅ S IN(ω ⋅ t + φ) ω = 2⋅π⋅f Example: Given: Vmax=110_V, t=30_µs, f=60_Hz, φ=15_°. Solution: ω=376.9911_r/s, V=29.6699_V. Sinusoidal Current (2, 23) Equations: I = Ima x ⋅ S IN( ω ⋅ t + φ) ω = 2⋅π⋅f Example: Given: t=32_s, Imax=10_A, ω=636_r/s, φ=30_°. Solution: I=9.5983_A, f=101.2225_Hz.
Variable Re v1, v2 Description Reynolds number Initial and final velocities vavg Average velocity W Power input y1, y2 Initial and final heights References: 3,6,9. Pressure at Depth (3, 1) This equation describes hydrostatic pressure for an incompressible fluid. Depth h is positive downwards from the reference. Equation: P = P0 + ρ ⋅ g ⋅ h Example: Given: h=100_m, ρ=1025.1817_kg/m^3, P0=1_atm. Solution: P=1106.6848_kPa.
Equations: 2 2 ∆P v 2 – v 1 ------ + ----------------------- + g ⋅ ∆y = 0 2 ρ 2 A2 2 v 2 ⋅ 1 – ------- A1 ∆P ------ + -------------------------------------------- + g ⋅ ∆y = 0 2 ρ 2 A2 2 v 1 ⋅ ------- – 1 A1 ∆P ------ + --------------------------------------------- + g ⋅ ∆y = 0 2 ρ ∆P = P 2 – P 1 ∆y = y 2 – y 1 M = ρ⋅Q Q = A1 – v1 Q = A2 – v2 2 2 π ⋅ D1 A 1 = ----------------4 π ⋅ D2 A 2 = ----------------4 Example: Given: P2=25_psi, P1=75_psi, y2=35_ft, y1=0_fr, D1=18_in,
Example: Given: P2=30_psi, P1=65_psi, y2=100_ft, y1=0_ft, ρ=64_lb/ft^3, D1=24_in, hL=2.0_ft^2/s^2, W=25_hp, v1=100_ft / s. Solution: Q=18849.5559_ft^3/min, M=1206371.5790_lb/min, ∆P=-35_psi, ∆y=100_ft, v2=93.1269_ft /s, A1=452.3893_in^2, A2=485.7773_in^2, D2=24.8699_in. Flow in Full Pipes (3, 4) These equations adapt Bernoulli’s equation for flow in a round, full pipe, including power input (or output) and frictional losses. (See “FANNING” in Chapter 3.
Variable Description A Projected area relative to flow ar Centripetal acceleration at r at Tangential acceleration at r Cd Drag coefficient E Energy F Force at r or x, or Spring force (Hooke’s Law), or attractive force (Law of Gravitation), or Drag force (Drag force) I Moment of inertia k Spring constant Ki,Kf Initial and final kinetic energies m, m1, m2 N Mass Rotational speed Ni, Nf Initial and final rotational speeds P Instantaneous power Pavg Average power r Radius from rota
Angular Mechanics (4, 2) Equations: 2 1 Ki = --- ⋅ I ⋅ ω i 2 τ = I⋅α W = Kf – Ki P =τ ⋅ ω ω = 2⋅π⋅N at = α ⋅ r 2 1 Kf = -- ⋅ I ⋅ ω f 2 W Pa v g = ----t ω i = 2 ⋅ π ⋅ Ni W = r ⋅Θ ω f = ω i +α ⋅ t ω f = 2 ⋅ π ⋅ Nf Example: Given: I=1750_lb∗in^2, Θ =360_°, r=3.5_in, α=10.5_r/min^2, ωi=0_r / s. Solution: r=1.1017E–3_ft_∗lbf, Ki=0_ft∗lbf, W=6.9221E–3_ft∗lbf, Kf=6.9221E–3_ft∗lbf, at=8.5069E–4_ft/s^2, Ni=0_rpm, ωf=11.4868_r/min, t=1.0940_min, Nf=1.8282_rpm, Pavg=1.9174E–7_hp.
1D Elastic Collisions (4, 5) Equations: m1 – m2 v1f = ---------------------- ⋅ v1i m1 + m2 2 ⋅ m1 v2f = ---------------------- ⋅ v1i m1 + m 2 Example: Given: m1=10_kg, m2=25_kg, vli=100_m/s. Solution: v1f=-42.8571_m/s, v2f=57.1429_m/s. Drag Force (4, 6) Equation: 2 ρ⋅v F = C d ⋅ ------------ ⋅ A 2 Example: Given: Cd=.05, ρ=1000_kg/m^3, A=7.5E6_cm^2, v=35_m/s. Solution: F=22968750_N.
Gases (5) Variable Description λ Mean free path ρ Flow density ρ0 Stagnation density A Flow area At Throat area d Molecular diameter k Specific heat ratio M Mach number m Mass MW Molecular weight n Number of moles, or Polytropic constant (Polytropic Processes) P Pressure, or Flow pressure (Isentropic Flow) P0 Stagnation pressure Pc Pseudocritical pressure Pi, Pf Initial and final pressures T Temperature, or Flow temperature (Isentropic Flow) T0 Stagnation temperature Tc
Example: Given: T=16.85_°C, P=1_atm, V=25_1, MW=36_g/gmol. Solution: n=1.0506_gmol, m=3.7820E-2_kg. Ideal Gas State Change (5, 2) Equation: Pf ⋅ Vf Pi ⋅ Vi ---------------- = ---------------Tf Ti Example: Given: Pi=1.5_kPa, Pf=1.5kPa, Vi=2_l, Ti=100_°C, Tf=373.15_K. Solution: Vf=2_1. Isothermal Expansion (5, 3) These equations apply to an ideal gas. Equations: Vf W = n ⋅ R ⋅ T ⋅ LN ------ Vi m = n ⋅ MW Example: Given: Vi=2_l, Vf=125_l, T=300_°C, n=0.25_gmol, MW=64_g/gmol. Solution: W=4926.
Equations: k ----------- P T k–1 ------ = ------ P0 T0 T 2 ------ = -------------------------------------2T0 2 + (k – 1 ) ⋅ M 1 ----------- T k–1 --ρ ---- = ------ T0 ρ0 k+1 ----------------------- 2 ⋅ (k – 1) 2 A 1 2 k–1 ----- = ---- ⋅ ----------- ⋅ 1 + ----------- ⋅ M At M k+1 2 Example: Given: k=2, M=.9, T0=26.85_°C, T=373.15_K, ρ0=100_kg/m^3, P0=100_kPa, A=1_cm^2. Solution: P=464.1152_kPa, At=0.9928_cm^2, ρ=215.4333_kg/m^3.
Kinetic Theory (5, 8) These equations describe properties of an ideal gas. Equations: 2 n ⋅ MW ⋅ vrms P = --------------------------------------3⋅V vrms = 1 λ = --------------------------------------------------n ⋅ NA 2 2 ⋅ π ⋅ ---------------- ⋅ d V 3⋅R⋅T ------------------MW m = n ⋅ MW Example: Given: P=100_kPa, V=2_1, T=26.85_°C, MW=18_g/gmol, d=2.5_nm. Solution: vrms=644.7678_m/s, m=1.4433E–3_kg, n=0.0802_gmol, λ=1.4916_nm.
Heat Capacity (6, 1) Equations: Q = m ⋅ c ⋅ ∆T Q = m ⋅ c ⋅ ( Tf – Ti ) Example: Given: ∆T=15_°C, Ti=0_°C, m=10_kg, Q=25_kJ. Solution: Tf=15_°C, c=.1667_kJ/(kg∗K) Thermal Expansion (6, 2) Equations: δ = α ⋅ L ⋅ ∆T δ = α ⋅ L ⋅ ( Tf – Ti ) Example: Given: ∆T=15_°C, L=10_m, Tf=25_°C, δ=1_cm. Solution: Ti=10_°C, α=6.6667E–5_1/°C. Conduction (6, 3) Equations: k⋅A q = ----------- ⋅ ∆T L k⋅A q = ----------- ⋅ ( Th – Tc ) L Example: Given: Tc=25_°C, Th=75_°C, A=12.5_m^2, L=1.5_cm, k=0.
Convection (6, 4) Equations: q = h ⋅ A ⋅ ∆T q = h ⋅ A ⋅ ( Th – Tc ) Example: Given: Tc= 300_K, A=200_m^2, h=0.005_W/(m^2∗K), q=10_W. Solution: ∆T=10_°C, Th=36.8500_°C. Conduction + Convection (6, 5) If you have fewer than three layers, give the extra layers a zero thickness and any nonzero conductivity. The two temperatures are fluid temperatures – if instead you know a surface temperature, set the corresponding convective coefficient to 10499.
Black Body Radiation (6, 6) (See “F0λ” in Chapter 3.) Equations: eb = σ ⋅ T 4 f = F0 λ ( λ 2 ; T ) – F0 λ ( λ 1 ; T ) e B1 2 f ⋅ e b = λ ma x ⋅ T = c 3 q = eb ⋅ A Example: Given: T=1000_°C, λ1=1000_nm, λ2=600_nm, A=1_cm^2. Solution: λmax=2276.0523_nm, eb=148984.2703_W/m^2, f=.0036, eb12=537.7264_W/m^2, q=14.8984_W.
Straight Wire (7, 1) The magnetic field calculation differs depending upon whether the point is inside or outside the wire. Equation: 0 r I ---------⋅---µ --------⋅--B = µ 2⋅π⋅r Example: Given: µr=1, rw= 0.25_cm, r=0.2_cm, I=25_A. Solution: B= 0.0016_T. Force between Wires (7, 2) The force between wires is positive for an attractive force (for currents having the same sign).
Magnetic (B) Field in Solenoid (7, 3) Equation: B = µ0 ⋅ µr ⋅ I ⋅ n Example: Given: µr=10, n=50, I=1.25_A. Solution: B=0.0785_T. Magnetic (B) Field in Toroid (7, 4) Equation: 0⋅ r⋅I⋅N 2 ------------µ --------------------- ⋅ --------------B = µ ro + r i 2⋅π Example: Given: µr=10, N=50, ri=5_cm, ro=7_cm, I=10_A. Solution: B=1.6667E–2_T.
Motion (8) Variable Description α Angular acceleration ω Angular velocity (Circular Motion), or Angular velocity at t (Angular Motion) ω0 Initial angular velocity ρ Fluid density θ Angular position at t θ0 Initial angular position (Angular Motion), or Initial vertical angel (Projectile Motion) a Acceleration A Projected horizontal area ar Centripetal acceleration at r Cd Drag coefficient m Mass M Planet mass N Rotational speed R Horizontal range (Projectile Motion), or Planet ra
Linear Motion (8, 1) Equations: 1 2 x = x0 + v0 ⋅ t + --- ⋅ a ⋅ t 2 1 2 x = x0 + v ⋅ t + --- ⋅ a ⋅ t 2 1 x = x0 + --- ⋅ ( v0 + v ) ⋅ t 2 v = v0 + a ⋅ t Example: Given: x0=0_m, x=100_m, t=10_s, v0=1_m/s Solution: v=19_m/s, a=1.8_m/s^2. Object in Free Fall (8, 2) Equations: 2 1 y = y0 + v0 ⋅ t + --- ⋅ g ⋅ t 2 2 1 2 y = y0 + v ⋅ t + --- ⋅ g ⋅ t 2 2 v = v0 + 2 ⋅ g ⋅ ( y + y0 ) v = v0 + g ⋅ t Example: Given: y0=1000_ft, y=0_ft, v0=0_ft/s Solution: t=7.8843_s, v= -253.6991_ft/s.
Angular Motion (8, 4) Equations: 1 2 θ = θ 0 + ω 0 ⋅ t + -- ⋅ α ⋅ t 1 2 2 θ = θ 0 + ω ⋅ t + -- ⋅ α ⋅ t 1 2 θ = θ 0 + -- ⋅ ( ω 0 + ω ) ⋅ t 2 ω = ω 0 +α ⋅ t Example: Given: Θ 0=0_°, ω0=0_r/min, α=1.5_r/min^2, t=30_s. Solution: Θ =10.7430_°, ω= 0.7500_r/min. Circular Motion (8, 5) Equations: 2 v a r = ---r v r ω = -- ω = 2⋅π⋅N Example: Given: r=25_in, v=2500_ft/s Solution: ω=72000_r/min, ar=3000000_ft/s^2, N=11459.1559_rpm.
Optics (9) Variable Description θ1 Angle of incidence θ2 Angle of refraction θB Brewster angle θc Critical angle f Focal length m Magnification n, n1, n2 Index of refraction r, r1, r2 Radius of curvature u Distance to object v Distance to image For reflection and refraction problems, the focal length and radius of curvature are positive in the direction of the outgoing light (reflected or refracted). The object distance is positive in front of the surface.
Critical Angle (9, 2) Equation: n1 S IN( θ c ) = ----n2 Example: Given: n1=1, n2=1.5. Solution: θc=41.8103_°. Brewster’s Law (9, 3) The Brewster angle is the angle of incidence at which the reflected wave is completely polarized. Equations: n2 TA N( θ B ) = ----n1 θ B + θ 2 = 90 Example: Given: n1=1, n2=1.5. Solution: θ B=56.3099_°, θ 2=33.6901_°.
Spherical Reflection (9, 4) Equations: 1 1 1 --- + --- = --u v f 1 f = --- ⋅ r 2 –v m = -----u Example: Given: u=10_cm, v=300_cm, r=19.35_cm. Solution: m=-30, f=9.6774_cm. Spherical Refraction (9, 5) Equation: n1 n2 n2 – n1 ------ + ------ = -----------------u v r Example: Given: u=8_cm, v=12_cm, r=2_cm, n1=1. Solution: n2=1.5000. Thin Lens (9, 6) r1 is for the front surface, and r2 is for the back surface.
Equations: 1 1 1 --- + --- = --u v f 1 1 1 --- = ( n – 1 ) ⋅ ----- – ----- r1 r2 f –v m = -----u Example: Given: r1=5_cm, r2=20_cm, n=1.5, u=50_cm. Solution: f=13.3333_cm, v=18.1818_cm, m= -0.3636.
Mass-Spring System (10, 1) Equations: ω = k ---m 2⋅π T = ---------ω ω = 2⋅π⋅f Example: Given: k=20_N/m, m=5_kg. Solution: ω=2_r/s. T=3.1416_s, f=.3183_Hz. Simple Pendulum (10, 2) Equations: ω = g --L 2⋅π T = ---------- ω ω = 2⋅π⋅ f Example: Given: L=15_cm. Solution: ω=8.0856_r/s. T= 0.7771_s, f=1.2869_Hz.
Conical Pendulum (10, 3) Equations: ω = g -h h = L ⋅ C OS ( θ ) 2⋅π T = ---------- ω ω = 2⋅π⋅f Example: Given: L=25_cm, h=20_cm. Solution: θ=36.899_°, T= 0.8973_s, ω=7.0024 r/s, f=1.1145_Hz. Torsional Pendulum (10, 4) Equations: w = G⋅J ----------L⋅I 2⋅π T = ---------- ω ω = 2⋅π⋅f Example: Given: G=1000_kPa, J=17_mm^4, L=26_cm, I=50_kg∗m^2. Solution: ω=1.1435E°–3_r/s, f=1.8200E–4_Hz, T=5494.4862_s.
Example: Given: xm=10_cm, ω=15_r/s, φ=25_°, t=25_µs. Solution: x=9.0615_cm, v= -0.6344_m/s, a= -20.3884_m/s^2, f= 2.3873_Hz.
Circle (11, 1) Equations: A = π⋅r 4 2 π⋅r I = -----------4 C = 2⋅π⋅r 4 π⋅r J = -----------2 Id = I + A ⋅ d 2 Example: Given: r=5_cm, d=1.5_cm. Solution: C=31.4159_cm, A=78.5398_cm^2, I=4908738.5_mm^4, J=9817477.0_mm^4, Id=6675884.4_mm^4. Ellipse (11, 2) Equations: 2 A = π⋅b⋅h 2 b +h C = 2 ⋅ π ⋅ ----------------2 π⋅b⋅h 2 2 J = ------------------ ⋅ ( b + h ) 4 3 π⋅b⋅h I = -------------------4 Id = I + A ⋅ d 2 Equations: Example: Given: b=17.85_µm, h=78.9725_µin, d=.00000012_ft.
Rectangle (11, 3) Equations: 3 A = b⋅h P = 2⋅b+2⋅h b⋅h 2 2 J = ---------- ⋅ ( b + h ) 12 b⋅h I = ------------12 Id = I + A ⋅ d 2 Example: Given: b=4_chain, h=7_rd, d=39.26_in. Set guesses for I, J, and Id in km^4. Solution: A=28328108.2691_cm^2, P=23134.3662_cm, I=2.9257E–7_km^4, J=1.8211E–6_km^4, Id=2.9539E– 7_km^4.
Circular Ring (11, 5) Equations: 2 π 4 4 I = --- ⋅ ( ro – ri ) 4 2 A = π ⋅ ( ro – ri ) π 4 4 J = --- ⋅ ( ro – ri ) 2 Id = I + A ⋅ d 2 Example: Given: ro=4_µ, ri=25.0Å, d=.1_mil. Solution: A=3.0631E–7_cm^2, I=1.7038E–10_mm^4, J=3.4076E–10_mm^4, Id=3.0648E–10_mm^4.
Solid Geometry (12) Variable Description A Total surface area b Base length d Distance to rotation axis in z direction h Height in z direction (Cone, Cylinder), or Height in y direction (Parallelepiped) I, Ixx Moment of inertia about x axis Id Moment of inertia in x direction at d Izz Moment of inertia about z axis m Mass r Radius t Thickness in z direction V Volume Reference: 4.
Cylinder (12, 2) Equations: 2 2 A = 2⋅π⋅r +2⋅π⋅r⋅h V = π⋅r ⋅h 1 2 Izz = --- ⋅ m ⋅ r 2 2 2 1 1 Ixx = --- ⋅ m ⋅ r + ------ ⋅ m ⋅ h 4 12 Id = Ixx + m ⋅ d 2 Example: Given: r=8.5_in, h=65_in, m=12000_lbs, d=2.5_in. Solution: V=14753.7045_in^3, A=3925.4200_in^2, Izz=4441750_lb∗in^2, Izz=433500_lb∗in^2, Id=4516750_lb∗in^2.
Sphere (12, 4) Equations: 3 4 V = --- ⋅ π ⋅ r 3 A = 4⋅π⋅r 2 2 2 I = --- ⋅ m ⋅ r 5 Id = I + m ⋅ d 2 Example: Given: d=14_cm, m=3.75_kg, Id=486.5_lb∗in^2. Solution: r=21.4273_cm, V=41208.7268_cm^3, A=5769.5719_cm^2, I=0.0689_kg∗m^2.
Solid State Devices (13) Variable Description αF Forward common-base current gain αR Reverse common-base current gain γ Body factor λ Modulation parameter µn Electron mobility φp Fermi potential ∆L Length adjustment (PN Step Junctions), or Channel encroachment (NMOS Transistors) ∆W Width adjustment (PN Step Junctions), or Width contraction (NMOS Transistors) a Channel thickness Aj Effective junction area BV Breakdown voltage Cj Junction capacitance per unit area Cox Silicon dioxid
Variable Js L Le Description Saturation current density Drawn mask length (PN Step Junctions), or Drawn gate length (NMOS Transistors), or Channel length (JFETs) Effectives gate length NA P-side doping (PN Step Junctions), or Substrate doping (NMOS Transistors) ND N-side doping (PN Step Junctions), or N-channel doping (JFETs) T Temperature tox Gate silicon dioxide thickness Va Applied voltage VBC Base-to-collector voltage VBE Base-to-emitter voltage Vbi Built-in voltage VBS Substrate volt
PN Step Junctions (13, 1) These equations for a silicon PN-junction diode use a “two-sided step-junction” model–the doping density changes abruptly at the junction. The equation assume the current density is determined by minority carries injected across the depletion region and the PN junction is rectangular in its layout, The temperature should be between 77 and 500 K. (See “SIDENS” in Chapter 3.
NMOS Transistors (13, 2) These equations for a silicon NMOS transistor use a two-port network model. They include linear and nonlinear regions in the device characteristics and are based on a gradual-channel approximation (the electric fields in the direction of current flow are small compared to those perpendicular to the flow). The drain current and transconductance calculations differ depending on whether the transistor is in the linear, saturated, or cutoff region.
Bipolar Transistors (13, 3) These equations for an NPN silicon bipolar transistor are based on large-signal models developed by J.J. Ebers and J.L. Moll. The offset-voltage calculation differs depending on whether the transistor is saturated or not. The equations also include the special conditions when the emitter-base or collector-base junction is open, which are convenient for measuring transistor parameters.
Equations: k⋅T ND V b i = ---------- ⋅ L N -------- q ni xdm ax = 2 ⋅ ε si ⋅ ε 0 ------------------------- ⋅ ( V b i – V G S + V D S ) q ⋅ ND a⋅W G 0 = q ⋅ N D ⋅ µ n ⋅ ------------ L 2 2 ⋅ s i ⋅ 0 I D = G 0 ⋅ V D S – -- ⋅ --------ε------------ε-----2 3 q ⋅ ND ⋅ a 3 3 --- 2 2 ( Vbi – VGS + VD S ) – ( Vb i – VG S) 2 q ⋅ ND ⋅ a V D s a t = -------------------------- – ( V b i – V G S ) 2 ⋅ ε si ⋅ ε 0 2 q ⋅ ND ⋅ a V t = V b i – ------------------------2 ⋅ ε si ⋅ ε 0
Stress Analysis (14) Variable Description δ Elongation ∈ Normal strain γ Shear strain φ Angle of twist σ Normal stress σ1 Maximum principal normal stress σ2 Minimum principal normal stress σavg Normal stress on place of maximum shear stress σx Normal stress in x direction σx1 Normal stress in rotated-x direction σy Normal stress in y direction σy1 Normal stress in rotated-y direction τ Shear stress τ max Maximum shear stress τ x1y1 Rotated shear stress τ xy θ Shear stress Ro
Normal Stress (14, 1) Equations: σ = E⋅∈ δ ∈ = -L-- P σ = --A Example: Given: P=40000_lbf, L=1_ft, A=3.14159265359_in^2, E=10E6_psi, Solution: δ=0.0153_in, ∈ =0.0013, σ=12732.3954_psi. Shear Stress (14, 2) Equations: τ = G⋅γ r⋅ γ = -------φ-L T⋅r τ = -----J---- Example: Given: L=6_ft, r=2_in, J=10.4003897419_in^4, G=12000000_psi, τ =12000_psi. Solution: T=5200.1949_ft∗lbf, φ=2.0626_°, γ =5.7296E–2_°. Stress on an Element (14, 3) Stresses and strains are positive in the directions shown.
Equations: σ x +σ y σ x – σ y σ x 1 = --------------------- + --------------------- ⋅ C OS ( 2 ⋅ θ ) + τx y ⋅ S IN( 2 ⋅ θ ) 2 2 σ x 1 +σ y 1 = σ x + σ y σ x –σ y τx 1 y 1 = – ----------2----------- ⋅ S IN( 2 ⋅ θ ) + τx y ⋅ σ y Example: Given: σx=15000_kPa, σy=4755_kPa, τ xy=7500_kPa, θ=30_°. Solution: σx1=18933.9405_kPa, σy1=821.0595_kPa, τ x1y1= -686.2151_kPa.
Waves (15) Variable Description β Sound level λ Wavelength ω Angular frequency ρ Density of medium B Bulk modulus of elasticity f Frequency I Sound intensity k Angular wave number s Longitudinal displacement at x and t sm Longitudinal amplitude t Time v Speed of sound in medium (Sound Waves), or Wave speed (Transverse Waves, Longitudinal Waves) x Position y Transverse displacement at x and t ym Transverse amplitude Reference: 3.
Sound Waves (15, 3) Equations: v = B --- ρ I β = 10 ⋅ LOG ------ 10 2 2 1 I = -- ⋅ ρ ⋅ v ⋅ ω ⋅ s m 2 ω = 2⋅π⋅f Example: Given: sm=10_cm, ω=6000_r/s, B=12500_kPa, ρ=65_kg/m^3. Solution: v=438.5290_m/s, I=5130789412.97_W/m^2, β=217.018_dB, f=954.9297_Hz.
References 1. Dranchuk, P.M., R.A. Purvis, and D.B. Robinson. “Computer Calculations of Natural Gas Compressibility Factors Using the Standing and Katz Correlation,” In Institute of Petroleum Technical Series, no. IP 74-008. 1974. 2. Gere, James M., and Stephen P. Timoshenko. Mechanics of Materials, 2d ed. PWS Engineering, Boston, 1984. 3. Halliday, David, and Robert Resnick. Fundamentals of Physics, 3d ed. John Wiley & Sons, 1988. 4. Meriam, J. L., and L. G. Kraige. Engineering Mechanics, 2d ed.
6 6.The Development Library Introduction Built into the calculator is a set of functions not accessible to the user by default. These functions are in a library that contains low level development tools mainly designed for use in developing System RPL and assembly programs. In order to enable this library, you must attach it with the command 256 ATTACH or by setting flag –86. When the library is attached after the next warmstart (or reset), it appears in the APPS menu.
Development Library Command Reference A→ → Description: Address out command: Returns the object stored at a specific address. Input/Output: Level 1/Argument 1 Example: #n #3A57Ch A→ returns SIN. Level 1/Item 1 → obj →A Description: Get address command: Returns the address of an object. Input/Output: Level 1/Argument 1 Example: A→ →H Description: Level 1/Item 1 → obj { SIN } OBJ→ DROP →A returns #3A57Ch.
ARM→ Description: MASD ARM assembly disassembler command: Disassembles a Code object or a range of memory addresses containing ARM machine language to produce the assembly language source code. Read later in this chapter for more details. Input/Output: Level 1/Argument 1 Example: ASM Description: Level 1/Item 1 → "string" Code ARM→ might return " ADD R0 R0 obj R0 MOV R0 R1 @".
→CD Description: Hex to code command: Returns the code (Assembly program) object represented by an hex string. A hex string is a string that only contains the characters ‘0’ to ‘9’ and ‘A’ to ‘F’. Input/Output: Level 1/Argument 1 Example: Level 1/Item 1 → Code "8F507621301641468…" →CD returns Code. “string” COMP→ → Description: Composite out command: This is equivalent to the RPL LIST→ command, but it also works on Program and Symbolic objects.
Input/Output: Level 1/Argument 1 Example: “string” "8BA207CA93B2130" H→ returns π. Level 1/Item 1 → obj →H Description: Object to hex command: Returns the hex representation of a object. Input/Output: Level 1/Argument 1 Example: H→ →A Description: obj π →H returns "8BA207CA93B2130". Level 1/Item 1 → “string” String to address command: Returns the address represented by a 5 character hex string. The hex representation of an address is a 5 character string where the address is written backwards.
Example: 32.5 LR~R returns 3.25E1. →LST Description: Create symbolic command: This is equivalent to the RPL →LIST command, but it can also convert a program or symbolic to a list. Input/Output: Example: Leveln+1/Argument1 7Level2/Argumentn Level1/Argumentn+1 obj1 … objn n → {obj1, ...,objn} obj1, ...,objn → {obj1, ...,objn} Level 1/Item 1 « 3 2 + » →LST returns { « 3 2 + » }. MAKESTR Description: String creation command: Creates a test string of the given size.
POKEARM Description: Memory write command: Writes bytes to a specified address in the ARM memory address space. You can not write data in the Flash ROM using this command. Writing data in memory randomly can cause all memory to be lost. Input/Output: Level 2/Argument 1 Example: Level 1/Argument 2 Level 1/Item 1 → #n “string” #7300000h "00804421" POKEARM writes the given four bytes to ARM memory address 0x7300000.
Input/Output: Level 1/Argument 1 #n Example: SERIAL Description: ¤n #EC2Ah SB~B returns ¤ EC2Ah. Level 1/Item 1 → ¤n → #n Serial number command: Retrieves the calculator serial number. This is the software serial number and does not match the hardware serial number printed on the back of the calculator, but it is typically similar. Input/Output: Level 1/Argument 1 Level 1/Item 1 → Example: “string” SERIAL may return "HP50 Serial Number: CNA6110007".
Example: « » →S2 returns "!NO CODE !RPL :: x« x» ; @". XLIB~ Description: XLIB conversion command: Convert reals to an XLIB and vice versa. Input/Output: Level 2/Argument 1 Level 1/Argument 2 n m → Xlib #n n → Xlib n #n → Xlib #n #m → Xlib Level 1/Argument 1 Example 1: Example 2: Example 3: Level 1/Item 1 Level 2/Item 1 → Xlib n #314h #40h XLIB~ returns ZEROS. 1648 2 XLIB~ returns XLIB 1648 2. { SYLVESTER } OBJ→ DROP XLIB~ returns 788. 78..
Extension program It is possible to enhance some of the statistics menus using a user library. The calculator does not provide every possible function in every area, but they let you customize the built in menu in order to add your functions as if they were built in. Example: Customize the main statistic menu. Ensure you are in RPL mode (H, W, `) and attach the development library (256 ATTACH).
MASD – The Machine Language and System RPL Compiler MASD is used for compiling assembly language and System RPL. Introduction Warnings The operating system can not control what a low level program is doing. Therefore, any programming error is likely to cause the calculator to crash (with potential memory loss). A careful developer will always save source code in the internal flash ROM or port 1 for protection before trying low level programs.
Directives change the way MASD interprets your source. Theses directives begin with a ! and will be explained later. Errors If MASD detects one or more syntax error, it will push a list describing all errors on the stack. The ER command can help you make sense of that list, point you on the errors and let you correct them. MASD will report a maximum of 16 errors before stopping compilation.
Define Error ARM register expected ARM invalid imediate You can not do this operation in a DEFINE No comments. In ARM mode, constants must be representable on 8 bit with an even number of rotation Links Links are secondary source files that MASD can be directed to compile (equivalent to the {$I} directive in Pascal and #include in C). As there is no linking phase with MASD (like in C), a multi source project will usually have the form of a main source file that contains a certain number of links.
• A Local label is a label that is only accessible in a local section like local variables in Pascal or C. A local section starts at the beginning of a source, after a global label or after a link (see link section). A local section finishes at the end of a source, before a link or before a global label. A local label is identified by a ‘.’ as the first character. Link labels A link label is a label that exists only in the link where it is declared, like a private clause in Object Pascal.
3. A constant value is stored in 16 nibbles. 4. Having constants starting with something that can be interpreted as a hex number, or an ARM register is not a good idea as the compiler might get confused. For example: DC SPFOO 4 MOV R4 SPFOO will generate an error on FOO as the compiler will interpret the mov as a mov from SP to R4. MASD introduces a ‘constant pointer’ called CP which helps to define constants.
• • • • • • • • Entries from the EXTABLE may be used. As the EXTABLE does not have the label names limitations with operators, in ambiguous case (DUP+#5 may either be an addition DUP + 5, or an entry ‘DUP+#5’), add "" around the word: "DUP"+#5. Calculations are done with 64 bits. X divide by 0 = $FFFFFFFFFFFFFFFF. In order to avoid wasting memory, MASD tries to compile expressions as soon as it sees them. If MASD is not able to compile an expression directly, it’s compiled at the end of the compilation.
- In case of a list, only the first object of the list will be included following the previous rules The syntax in ASM or ARM mode is: /FileName Note: To know how MASD looks for the FileName file, see the following section. You can also include a complete object (prologue included) using INCLUDE or INCLOB. In ASM or ARM mode, use INCLUDE or INCLOB followed by a filename to include an object, in RPL mode, use INCLOB. Filename conventions MASD sometimes needs to find a file in the calculator’s memory.
!EVEN !ADR !COMPEXP !STAT !DBGINF !JAZZ !MASD In absolute mode, cause an error if the directive is not on an even address. MASD will generate a source defining all constants and labels used in the program instead of the program. Cause MASD to calculate all previous expressions.
Saturn ASM mode This section is only applicable to the Saturn ASM mode. CPU architecture This section’s purpose is to make experienced ASM programmers familiar with the Saturn architecture, not to teach anyone to program in Saturn ASM. The Saturn CPU has 12 main registers: A, B, C, D, R0, R1, R2, R3 and R4 are 64 bits register (see description below), D0 and D1 are 20 bits pointers (you can only access memory through them, the Saturn is a little endian), PC, 20 bit program counter.
Other notes You should read documentation on the internal structure of RPL objects (www.hpcalc.org has good documentation) D0, D1, Ba and Da are used by the system (next RPL instruction pointer, RPL stack pointer (@@object on level 1 of the stack), start of free memory and free memory in 5 nibble blocks). The SAVE instruction will save these registers in dedicated memory areas, the LOADRPL instruction will restore them and continue the execution in the system.
The foundation of Skips is the Block structure. A block is enclosed in { and }, and can be nested within another block. The following instructions deal with blocks. SKIPS instructions { ... } SKIP { ... } SKIPL { ... } SKIPC { ... } SKC {... } SKIPNC {... } SKNC { ... } Test SKIPYES {... } Test { ... } Test { ... } Test -> { ... } SKUB { ... } SKUBL { ... } STRING { ... } CODE { ... } STROBJ $PROLOG { ... } Equivalents Defines a block (generates no code) GOTO .S ... *.S GOTOL .S ... *.S GOC .S ... *.
These instructions Are equivalent to { *.Beg3 *.Beg2 *.Beg1 GOTO.Beg2 GOTO.Beg3 GOTO.End1 GOTO.End3 *.End1 *.End2 *.End3 { { UP2 UP3 EXIT1 EXIT3 } } } Notes: 1. EXIT1 is equivalent to EXIT, and UP1 is equivalent to UP. 2. The same rules apply in ARM mode: EXITGE3 for example is a BGE for the exit label 3 blocks down Using SKELSE, SKEC, SKENC, SKLSE instructions, two blocks create an IFNOT-THEN-ELSE structure. These instructions Are equivalent to Or in high-level language ?A=0.
Saturn instructions syntax In this section: x is a decimal number between 1 and 16. An expression can be used if its value can be determined at the first encounter. h is a hexadecimal digit. a is a decimal number ranging from 1 to 16 or a 0 to 15 number depending of the current mode (0-15 or 1-16). An expression can be used, if its value can be determined at the first encounter. f is a field A, B, X, XS, P, WP, M, S, F1, F2, F3, F4, F5, F6 or F7. Reg is a working register A, B, C or D.
Syntax Reg=Reg+Cst.f Reg+Cst.f Reg=Reg-Cst.f Reg-Cst.f Example A=A+10.A A+10.A A=A-10.A A-FOO.A RegSR.f ASR.W RegSL.f ASL.W Reg1=Reg1Reg2.f Reg1>Reg2.f RegSRB.f RegSRC RegSLC Reg1=Reg1&Reg2.f Reg1&Reg2.f Reg1=Reg1!Reg2.f Reg1!Reg2.f A=A
Syntax DReg=hh DReg=hhhh DReg=hhhhh DReg=(2)Exp DReg=(4)Exp DReg=(5)Exp Dreg=Reg Dreg=RegS Example D0=AD D0=0100 D0=80100 D0=(2)label D0=(4)lab+$10 D1=(5)Variable Notes Change the first 2, 4 or all nibbles of the Data register with the given value Reg can only be A or C Sets the first 4 nibbles of Dreg with the 4 first nibbles of Reg Reg can only be A or C RegDRegEX Reg can only be A or C AD0EX RegDRexXS Exchange the first 4 nibbles of Dreg with the 4 first nibbles of Reg AD1XS Reg can only be A or C DRe
Syntax Example SB=1 XM=1 SR=1 MP=1 HST=a ?SB=1 ?XM=1 ?SR=1 ?MP=1 ?HST=1.a P=a P=P+1 P+1 P=P-1 P-1 ?P=a ?P#a P=C.a C=P.a CPEX.a C=C+P+1 C+P+1 GOTO label GOTOL label GOLONG Lab GOVLNG hex GOVLNG =Label GOVLNG ="COMND" GOSUB label GOSUBL label GOSBVL hex GOSBVL =Label GOSBVL ="COMND" GOC label GONC label GOTOC label GOTONC label RTN RTNSXM RTNCC RTNSC RTNC RTNNC RTI RTNYES RTY C=RSTK RSTK=C OUT=CS OUT=C A=IN C=IN SETDEC SETHEX UNCNGF CONFIG RESET SHUTDN INTON INTOFF RSI GOINC label GOINA label $hhh...
Syntax Example $(x)Exp CON(x)Exp EXP(x)Exp ¢Ascii "Ascii" GOIN5 lab G5 lab GOIN4 lab G4 lab GOIN3 lab G3 lab GOIN2 lab G2 lab SAVE LOAD RPL or LOOP LOADRPL INTOFF2 INTON2 ERROR_C A=IN2 C=IN2 OUT=C=IN RES.STR RES.ROOM RESRAM SHRINK$ COPY<- COPY← COPYDN COPY-> COPY→ COPYUP DISP DISPKEY SRKLST SCREEN MENU ZEROMEM MULT.A MULT DIV.A DIV BEEP NATIVE? $hex HST=1.x ?HST=1.x { } SETFLD(1-7) OFF Notes Places the value of Exp in the code, on x nibbles. Includes ASCII data.
Syntax Example RPL2 KEYDN CRTMP BEEP2 REMON SERIAL OUTBYT MOVEUP MOVEDN ARMSYS ARMSAT REMOFF GOSLOW WSCREEN SETTIME SETLNED 6-28 The Development Library Notes Simulates a LOOP (A=DAT0.A D0+5 PC=(A)). (C[A]) kbd peeks with immediate rtn CS if keydn. Also - Sets DOUSEALARM flag if [ON][9] sequence. Entry: P=0, HEX Mode, C[A]: #kbd peeks (loop count) Abstract: Creates a hole in the tempob area of the specified size + 6 (5 for the link field and 1 for marker nibble).
Syntax Example SETOFFD HSCREEN UNCNFGD GETTIME MIDAPP? CONFIGD BIGAPP? RESETOS REFRESHD AUTOTEST ACCESSSD PORTTAG? Notes Set offset of display inside disp0 in bytes from C[X]&7FF. Return how many lines the screen contains to Ca. Unconfigure the 4KB block containing the top 16-line header. This will refresh the header on the display. Emulates gettime function in ROM, and also updates the 8192Hz timer accordingly. Purpose: Get current time: (=NEXTIRQ)-Timer2 Return CS iff time appears corrupt.
ARM mode ARM architecture For all user intents and purposes the ARM CPU has sixteen 32 bit registers noted R0 to R15 (R15 is also the program counter, R14 is the link register (ie: a BL (GOSUB) instruction copies the return address in R14 before jumping, a Return From Subroutine is performed by doing MOV PC, LR), and R13 is the Stack pointer). Each instruction can be conditionally executed depending on the value of 5 flags.
Instruction set Note: For instruction names, the case does not matter. Register names are: R0, R1, R2, R3, R4, R5, R6, R7, R8, R9, R10, R11, R12, R13 (or SP), R14 (or LP or LR) and R15 (or PC). Setting the S flag on an instruction causes the instruction to modify the flags. Every instruction is evaluated ONLY if the attached condition is true. By default, the instruction is always evaluated. Separation between arguments can be either ‘,’ or spaces.
Operation Copy and shift Not Add Add with carry Sub Sub with carry Reverse Sub Rev sub with carry Multiply Multiply Add Compare Cmp Negative Test Test equivalence And Xor Or BitClear (~And) Branch Gosub Load Int Load Byte Multiple load Inc Before Inc After Dec Before Dec After Store Int Store Byte Multiple Store Inc Before Inc After Dec Before Dec After Multiplication Assembler MOV{cond}{S} Rd, MVN{cond}{S} Rd, ADD{cond}{S} Rd, Rn, ADC{cond}{S} Rd, Rn, SUB{cond}{S} Rd, R
In all cases, Cte must be a decimal value or an expression that can be evaluated immediately.
2332 2340 2348 2356 2364 2372 2380 2388 2392 2396 2408 2412 2416 3420 REG C; REG D; REG R0; REG R1; REG R2; REG R3; REG R4; U32 D0 U32 D1; U32 P, P4, P4_32; // P4 = 4*P, P4_32 = 4*P-32, use setP() to modify P. U32 ST; U32 HST; U32 carry; // 0 or !0 BOOL dec; // 0→hex or 1→dec U32 RSTK[NB_RSTK]; U32 RSTK_i; // Index for next push. REG FIELD[32]; // Field masks. U32 FIELD_START[32]; // Lowest nibble of the field. U32 FIELD_LENGTH[32]; // Length of the field.
System RPL mode MASD can also compile System RPL programs (you should read the book “An Introduction to System RPL” before trying to write System RPL programs). The !RPL directive will switch MASD in RPL mode. Note: if the Flag –92 is set, MASD starts in !RPL and !NO CODE mode. Instructions In RPL mode, MASD interprets instructions/tokens in the following order.
Defines If the instruction matches a define, the correct code is inserted (see the DEFINE instruction) Labels If the instruction matches the name of a constant or a label, the value of the said constant or label is inserted (if you insert a label, be sure to know what you are doing and to be in absolute mode). extable If the instruction matches an entry in the extable (see appropriate section at the end of this document) the value associated with this entry is used.
XxlibName HXS Size Data GROB Size Data LIBDAT Size Data BAK Size Data LIB Size Data EXT3 Size Data ARRAY Size Data LNKARRAY Size Data MINIFON Size Data ARRY2 Size Data ARRY [ ... ] ARRY [ [ . ] [ . ] ] xRplName CHR character LABEL labelname EXTERNAL name xlibname FEXTERNAL name fptrname CODE Size Data CODE Assembly stuff ENDCODE NIBB Size Data or NIBHEX Data or NIBBHEX Data or CON(Size) Expr INCLOB FileName INCLUDE FileName LABEL label EQU CstName ExpHex EQUCP Interleave CstName DEFINE name ...
Example of a Saturn assembly language program using the MASD compiler "!NO CODE !RPL * This program display a 131*64 graphic in a pretty way :-) * DO LCD->, run it, and enjoy! * This program has been created by Philippe Pamart :: * remove the menu and test for a grob CK1&Dispatch grob :: TURNMENUOFF CODE % R0a: X % R1a: Y % R2a: @ grob SAVE GOSBVL DisableIntr % No interrupts A=DAT1.A D0=A LC 00014 A+C.A R2=A.A % adr 1st pixels of the grob D0+10 A=0.W A=DAT0.10 C=0.W LC 8300040 ?A=C.W % test the size { *.
Example of an ARM assembly language program using the MASD compiler "!NO CODE !RPL :: TURNMENUOFF ( turn into RPL mode) ( open a RPL program ) ( remove the menu line ) CODE % open an assembly program % % % % % % % % % % this program takes control of the screen and displays a Mandelbrot set using the standard algorithm ie: for each point from x=-1.5 to 0.
LDRB R6 [R1 2408] ORR R6 R6 1 STRB R6 [R1 2408] LDMIA sp! {R4 R5 R6 R7 R8 PC} !ASM *end } C=RSTK D0=C D1=80100 % set the flag ST0 % restore all registers and return % back in ASM mode LC(5) end-start MOVEDN % % % % D0 points to ARM instruction D1 points at a place where I can copy the program copy n nibbles C=0.B SETLNED % hide the header D1=8229E % point on 2Kb free memory LC A9 A=0.W A-1.W { DAT1=A.W D1+16 C-1.B UPNC } % paint it in black D0=00120 LC 8229E DAT0=C.
Disassemblers ASM→ → The ASM→ disassembler converts Saturn assembly into a source string. The syntax used is MASD syntax, in mode 0-15. Each line contains an address and an instruction. If the system flag –71 is set (with -71 SF), addresses are not shown, except for the destinations of jumps. In this case, the resulting source may be then reassembled if needed. ASM→ can either disassemble a CODE object or the memory area between 2 given addresses (as binary integers).
The Entry Point Library: Extable The entry point library is an external library (you can get it from the HP web site) that contains a table of entry point names and addresses. This is used by the MASD compiler to get the value of System RPL entry points or assembler constants (like TURNMENUOFF for example). This library should be stored in port 0, 1 or 2. If you want to program in System RPL, you must install this library.
A A. Error and Status Messages The following table lists the most frequently encountered error and status messages on the calculator. They are arranged alphabetically by name. The second table lists all the built-in messages numerically by message number. Trailing spaces are indicated with a character. Messages Listed Alphabetically Message Meaning Acknowledged Alarm acknowledged. All Variables known No unknowns to solve for. Autoscaling Calculator is autoscaling x- and/or y- axis.
Messages Listed Alphabetically (continued) Message Meaning copied selected equation to stack. # (hex) Copied to stack %²STK% Current equation: Identifies current equation. 608 Deleting Column Matrix Writer application is deleting a row. 504 Deleting Row Name of existing directory variable used as argument. 503 Directory Not Allowed Name of existing directory variable used as argument. 12A Directory Recursion Attempted to store a directory into itself.
Messages Listed Alphabetically (continued) Message Meaning # (hex) Implicit ( ) off Implicit parentheses off. 207 Implicit ( ) on Implicit parentheses on. 208 or ` pressed before all function arguments supplied. Attempted unit conversion with incompatible units. B02 Infinite Result Math exception: Calculation such as 1/0 infinite result. 305 Inserting Column Matrix Writer application is inserting a column. 506 Inserting Row Matrix Writer application is inserting a row.
Messages Listed Alphabetically (continued) Message Meaning # (hex) Invalid N Attempted to calculate I%YR with N < 1 or N ≥ 1010. E604 Invalid Name Received illegal filename, or server asked to send illegal filename. C17 Invalid PPAR PPAR not a list, or one or more objects in list missing or invalid. 12E Invalid PRTPAR PRTPAR not a list, or one or more objects in list missing or invalid. C13 Invalid PTYPE Plot type invalid for current equation.
Messages Listed Alphabetically (continued) Message Meaning LAST CMD Disabled „® disabled. pressed while that recovery feature LAST STACK Disabled …¯pressed while that recovery feature LASTARG Disabled …Ëpressed while that recovery feature disabled. disabled. # (hex) 125 124 205 Low Battery System batteries too low to safely print or perform I/O. C14 Many or No Solutions A value for I%YR cannot be calculated. Check the values stored in PV, PMT, and FV. Check for correct signs.
Messages Listed Alphabetically (continued) Message Meaning Non-Empty Directory Attempted to purge non-empty directory. # (hex) 12B Execution of HP Solve application, ROOT, DRAW, or ∫ returned result other than real number or unit. Execution of HP Solve application, ROOT, DRAW, or ∫ returned result other than real number or unit. Alarm list did not contain alarm specified by alarm command. D04 Nonexistent ΣDAT Statistics command executed when ΣDAT did not exist.
Messages Listed Alphabetically (continued) Message Meaning Received a packet whose length was shorter than a null packet. Protocol Error Maximum packet length parameter from other machine is illegal. Kermit: More than 255 bytes of retries sent before calculator received another packet. Receive Buffer Overrun SRECV: Incoming data overflowed the buffer. # (hex) C07 C04 Receive Error UART overrun of framing error. C03 Receiving Identifies object name while receiving.
Messages Listed Alphabetically (continued) Message Meaning Undefined Constant Undefined Element The name supplied to CONST isn’t in the Constants Library. The element supplied to PTPROP doesn’t exist. # (hex) E129 E502 Undefined FPTR Name Executed a Flash Pointer that did not exist. 011 Undefined Local Name Executed or recalled local name for which corresponding local variable did not exist. 003 Undefined Name Executed or recalled global name for which corresponding variable did not exist.
Messages Listed Numerically # (hex) Message General Messages 001 002 003 004 005 006 007 008 009 00A 00B 00C 00D 00E 00F 010 011 012 013 014 015 016 017 018 019 01A 01B 01C 01D 01E 01F 020 021 022 023 024 025 Insufficient Memory Directory Recursion Undefined Local Name Undefined XLIB Name Memory Clear Power Lost Warning: Invalid Card Data Object In use Port Not Available No Room in Port Object Not in Port Recovering Memory Try To Recover Memory? Replace RAM, Press ON No Mem To Config All Undefined FPTR
Messages Listed Numerically (continued) # (hex) 026 027 028 029 02A 02B 02C 02D 02E 101 102 103 104 106 107 108 109 10A 10B 10C 10D 10E 10F 110 111 112 113 114 115 116 117 118 119 11A 11B 11C Message Invalid File Mode Disk Full Disk Format Error Disk Change No SD card inserted Not enough ARM memory DOS call unsupported DOS unknown error Disk Protected No Room to Save Stack Can't Edit Null Char.
Messages Listed Numerically (continued) # (hex) 11D 11E 11F 120 121 122 123 124 125 126 127 128 129 12A 12B 12C 12D 12E 12F 130 131 132 133 Message Long Complex Linked Array Character Code Library Data External (#123h DOERR is equivalent to KILL) LAST STACK Disabled LAST CMD Disabled HALT Not Allowed Array Wrong Argument Count Circular Reference Directory Not Allowed Non-Empty Directory Invalid Definition Missing Library Invalid PPAR Non-Real Result Unable to Isolate No Room to Show Stack Warning: Error:
Messages Listed Numerically (continued) # (hex) 141 142 143 144 145 146 147 148 149 14A 14B 14C 14D 14E 14F 150 151 Message Symbolic Matrix Font Aplet Extended Real Extended Complex FlashPtr Extended Ptr MiniFont Extended 1 Extended 2 Extended 3 YES NO TRUE FALSE Are you sure? Low Memory Condition Please Wait...
Messages Listed Numerically (continued) # (hex) Message Floating-Point Errors 301 302 303 304 305 Positive Underflow Negative Underflow Overflow Undefined Result Infinite Result Array Messages 501 502 503 504 505 506 Invalid Dimension 601 602 603 604 605 606 Invalid Σ Data Invalid Array Element Deleting Row Deleting Column Inserting Row Inserting Column Statistics Messages Nonexistent ΣDAT Insufficient Σ Data Invalid ΣPAR Invalid Σ Data LN(Neg) Invalid Σ Data LN(0) Plot, I/O, Time and HP Solve Ap
Messages Listed Numerically (continued) # (hex) 61A 61B 61C 61D 61E 61F 620 621 622 623 624 625 626 627 628 629 62A 62B 62C 62D 62E 62F Message Enter alarm, press SET Select repeat interval I/O setup menu Plot type: "" (OFF SCREEN) Invalid PTYPE Name the stat data, press ENTER Enter value (zoom out if>1), press ENTER Copied to stack x axis zoom w/AUTO. x axis zoom. y axis zoom. x and y axis zoom.
Messages Listed Numerically (continued) # (hex) 70F 710 711 712 713 714 715 716 717 718 719 71A 71B 71C 71D 71E 71F 720 721 722 723 724 725 726 727 728 729 72A 72B 72C 72D 72E 72F 730 731 732 733 734 Message Polar Spherical Operating Mode… Number Format…… Angle Measure…… Coord System……… FM, Beep Key Click Last Stack Choose calculator operating mode Choose number display format Choose decimal places to display Choose angle measure Choose coordinate system Use comma as fraction mark? Enable standard beep? E
Messages Listed Numerically (continued) # (hex) 735 736 737 738 739 73A 73B 73C 73D 73E 73F 740 741 742 743 744 745 746 747 748 749 74A 74B 74C 74D 74E 74F 750 751 752 753 754 755 756 757 758 759 75A Message Edit in full page? Automatically indent new lines? Edit in EQW using small font? Display EQW using small font? Choose header height Display ticking clock? Analog clock? DISPLAY MODES Indep var: Modulo: Verbose Step/Step Complex Approx Incr Pow Simp Non-Rational Rigorous Numeric Enter independent varia
Messages Listed Numerically (continued) # (hex) 75B 75C 75D 75E 75F 760 761 762 763 764 765 766 767 768 769 76A 76B 76C 76D 76E 76F 770 771 772 773 774 775 776 777 778 779 77A 77B 77C 77D 77E 77F 780 Message Zoom: Small Font File: Enter starting value Enter increment value Choose table format Enter zoom factor Display table using small font? Enter a filename to save data TABLE SETUP Automatic Build Your Own Function Polar Parametric Diff Eq Conic Truth Histogram Bar Scatter Slopefield Fast3D Wireframe Ps-
Messages Listed Numerically (continued) # (hex) 781 782 783 784 785 786 787 788 789 78A 78B 78C 78D 78E 78F 790 791 792 793 794 795 796 797 798 799 79A 79B 79C 79D 79E 79F 7A0 7A1 7A2 7A3 7A4 7A5 7A6 7A7 Message V-Tick: Pixels Depnd: Save Animation ΣDAT: Col: Cols: F: H-Var: V-Var: Stiff ˆFˆY: ˆFˆT: Choose type of plot Choose angle measure Enter function(s) to plot Enter independent variable name Connect plot points? Plot functions simultaneously? Enter horizontal tick spacing Enter vertical tick spacing
Messages Listed Numerically (continued) # (hex) 7A8 7A9 7AA 7AB 7AC 7AD 7AE 7AF 7B0 7B1 7B2 7B3 7B4 7B5 7B6 7B7 7B8 7B9 7BA 7BB 7BC 7BD 7BE 7BF 7C0 7C1 7C2 7C3 7C4 7C5 7C6 7C7 7C8 7C9 7CA 7CB 7CC Message Depnd Low: High: X-Left: X-Right: Y-Near: Y-Far: Step Indep: Depnd: Bar Width: Z-Low: Z-High: XE: YE: ZE: Init: Final: Init-Soln: Tol: XXLeft: XXRight: YYNear: YYFar: Enter minimum horizontal value Enter maximum horizontal value Enter minimum vertical value Enter maximum vertical value Enter minimum indep
Messages Listed Numerically (continued) # (hex) 7CD 7CE 7CF 7D0 7D1 7D2 7D3 7D4 7D5 7D6 7D7 7D8 7D9 7DA 7DB 7DC 7DD 7DE 7DF 7E0 7E1 7E2 7E3 7E4 7E5 7E6 7E7 7E8 7E9 7EA 7EB 7EC 7ED 7EE Message Enter Z eyepoint coordinate Enter absolute error tolerance Enter minimum XX range value Enter maximum XX range value Enter minimum YY range value Enter maximum YY range value PLOT WINDOW Default FUNCTION POLAR PARAMETRIC DIFF EQ CONIC TRUTH HISTOGRAM BAR SCATTER SLOPEFIELD FAST3D WIREFRAME PS-CONTOUR Y-SLICE GRIDMAP
Messages Listed Numerically (continued) # (hex) 804 805 806 807 808 809 80A 80B 80C 80D 80E 80F 810 811 812 813 814 815 816 817 818 819 81A 81B 81C 81D 81E 81F 820 821 822 823 824 825 826 827 828 829 Message : N: Œ: ˜: Null hypothesis population mean Sample mean Sample Size Significance level Population standard deviation Z-TEST: 1 µ, KNOWN ˜ Alternative Hypothesis 1: ˜1: N1: Œ: 2: ˜2: N2: Sample mean for population 1 Std deviation for population 1 Sample size for population 1 Significance level Sample
Messages Listed Numerically (continued) # (hex) 82A 82B 82C 82D 82E 82F 830 831 832 833 834 835 836 837 838 839 83A 83B 83C 83D 83E 83F 840 841 842 843 844 845 846 847 848 849 84A 84B 84C 84D 84E 84F Message X2: N2: Success count for sample 1 Size of sample 1 Significance level Success count for sample 2 Size of sample 2 Z-TEST: 2 P : Sx: µ0: Œ: N: Null hypothesis population mean Sample Standard deviation Sample Mean Significance level Sample size T-TEST: 1 µ, UNKNOWN ˜ 1: S1: N1: Œ: 2: S2: N2: Pooled?
Messages Listed Numerically (continued) # (hex) 850 851 852 853 854 855 856 857 858 859 85A 85B 85C 85D 85E 85F 860 861 862 863 864 865 866 867 868 869 86A 86B 86C 86D 86E 86F 870 871 872 873 874 875 Message N: C: Sample mean Population standard deviation Sample size Confidence level CONF. INT.: 1 µ, KNOWN ˜ 1: ˜1: N1: C: 2: ˜2: N2: Sample mean for population 1 Std deviation for sample 1 Size of sample 1 Sample mean for population 2 Std deviation for sample 2 Size of sample 2 Confidence level CONF. INT.
Messages Listed Numerically (continued) # (hex) 876 877 878 879 87A 87B 87C 87D 87E 87F 880 881 882 883 884 885 886 887 888 889 88A 88B 88C 88D 88E 88F 890 891 Message Confidence level CONF. INT.: 2 P : Sx: N: C: Sample mean Sample standard deviation Sample size Confidence level CONF. INT.: 1 µ, UNKNOWN ˜ 1: S1: N1: C: 2: S2: N2: Pooled Sample 1 mean Std deviation for sample 1 Sample 1 size Sample 2 mean Std deviation for sample 2 Sample 2 size Confidence level Pooled if checked CONF. INT.
Messages Listed Numerically (continued) # (hex) 89A 89B 89C 89D 89E 89F 8A0 8A1 8A2 8A3 8A4 8A5 8A6 8A7 8A8 8A9 8AA 8AB 8AC 8AD 8AE 8AF 8B0 901-90C 90D Message FIND REPLACE FIND Goto Line: Specify a line to go to GOTO LINE Goto Position: Specify a position to go to GOTO POSITION H-Factor: V-Factor: Recenter on cursor Enter horizontal zoom factor Enter vertical zoom factor Recenter plot on cursor? ZOOM FACTOR Object: Name: Directory Enter New Object Enter variable name Create a new directory? NEW VARIABLE
Messages Listed Numerically (continued) # (hex) Message Unit Management B01 B02 Invalid Unit C01 C02 C03 C04 C05 C06 C07 C08 C09 C0A C0B C0C C0D C0E C0F C10 C11 C12 C13 C14 C15 C16 C17 Bad Packet Block check Inconsistent Units I/O and Printing Timeout Receive Error Receive Buffer Overrun Parity Error Transfer Failed Protocol Error Invalid Server Cmd. Port Closed Connecting Retry # Awaiting Server Cmd.
Messages Listed Numerically (continued) # (hex) B905 B906 B907 B908 B909 B90A B90B B90C B90D B90E B90F B910 B911 B912 B913 B914 B915 B916 B917 B918 B919 B91A B91B B91C B91D B91E B91F B920 B921 B922 B923 B924 B925 B926 B927 B928 B929 B92A B92B Message Reset all Valid object types: Valid object type: Any object Real number (Complex num) "String" [ Real array ] [(Cmpl array)] { List } Name « Program » 'Algebraic' # Binary int _Unit object Invalid object type Invalid object value Calculator Modes Number Forma
Messages Listed Numerically (continued) # (hex) B92C B92D B92E B92F B930 B931 B932 B933 B934 Message Degrees Deg Radians Rad Grads Grad Rectangular Polar Spherical System Flags Choose Box Prompts B935 B936 B937 B938 B939 B93A B93B B93C B93D B93E B93F B940 B941 B942 B943 B944 B945 B946 B947 B948 B949 B94A B94B B94C B94D B94E B94F B950 SYSTEM FLAGS 01 General solutions 02 Constant → symb 03 Function → symb 14 Payment at end 19 →V2 → vector 20 Underflow → 0 21 Overflow → ±9E499 22 Infinite → error 27 'X+Y*
Messages Listed Numerically (continued) # (hex) B951 B952 B953 B954 B955 B956 B957 B958 B959 B95A B95B B95C B95D B95E B95F B960 B961 B962 B963 B964 B965 B966 B967 B968 B969 B96A B96B B96C B96D B96E B96F B970 B971 B972 B973 B974 B975 Message 53 No extra parens 54 Tiny element → 0 55 Save last args 56 Standard beep on 57 Alarm beep on 58 Show INFO 59 Show variables 60 [Œ][Œ] locks 61 [USR][USR] locks 62 User keys off 63 Custom ENTER off 65 All multiline 66 Stack:x lines str 67 Digital clock 68 No AutoIndent
Messages Listed Numerically (continued) # (hex) B976 B977 B978 B979 B97A B97B B97C B97D B97E B97F B980 B981 B982 B983 B984 B985 B986 B987 B988 B989 B98A B98B B98C B98D B98E B98F B990 B991 B992 B993 B994 B995 B996 B997 B998 B999 B99A Message 100 Step by step off 103 Complex off 105 Exact mode on 106 Simp. in series 109 Sym. factorize 110 Normal matrices 111 Simp non rat.
Messages Listed Numerically (continued) # (hex) B99B B99C B99D B99E B99F B9A0 B9A1 B9A2 B9A3 B9A4 B9A5 B9A6 B9A7 B9A8 B9A9 B9AA B9AB B9AC B9AD B9AE B9AF B9B0 B9B1 B9B2 B9B3 B9B4 B9B5 B9B6 B9B7 B9B8 B9B9 B9BA B9BB B9BC B9BD B9BE Message 37 Double-space prnt 38 No linefeeds 39 No I/O messages 40 Show clock 41 24-hour clock 42 dd.mm.
Messages Listed Numerically (continued) # (hex) B9BF B9C0 B9C1 B9C2 B9C3 B9C4 B9C5 B9C6 B9C7 B9C8 B9C9 B9CA B9CB B9CC B9CD B9CE B9CF B9D0 B9D1 B9D2 B9D3 B9D4 B9D5 B9D6 B9D7 B9D8 B9D9 B9DA B9DB B9DC B9DD Message 82 EQW edit mini fnt 83 Display grobs off 85 SysRPL stk disp 90 CHOOSE:mini font 91 MTRW:list of list 92 MASD SysRPL mode 94 Result <> LASTCMD 95 Algebraic mode 97 List:vert disp 98 Vector:vert disp 99 CAS:verbose 100 Step by step on 103 Complex on 105 Approx. mode on 106 !Simp. in series 109 Num.
Messages Listed Numerically (continued) # (hex) BA03 BA04 BA05 BA06 BA07 BA08 BA09 BA0A BA0B BA0C BA0D BA0E BA0F BA10 BA11 BA12 BA13 BA14 BA15 BA16 BA17 BA18 BA19 BA1A BA1B BA1C BA1D BA1E BA1F BA20 BA21 BA22 BA23 BA24 BA25 BA26 BA27 Message 3.Print display 4.Print… 5.Transfer… 6.
Messages Listed Numerically (continued) # (hex) BA28 BA29 BA2A BA2B BA2C BA2D BA2E BA2F BA30 BA31 BA32 BA33 BA34 BA35 BA36 BA37 BA38 BA39 BA3A BA3B BA3C BA3D BA3E BA3F BA40 BA41 BA42 BA43 BA44 BA45 BA46 BA47 BA48 BA49 BA4A BA4B BA4C Message Remote PC files Files in Enter name of dir to change to Choose Remote Directory Infrared IR Wire Kermit XModem Odd Even Mark Space Spc ASCII ASC Binary Bin None Newline (Ch 10) Newl Chr 128-159 →159 →255 Chr 128-255 One-digit arith Two-digit arith Three-digit CRC HP-I
Messages Listed Numerically (continued) # (hex) BA4D BA4E BA4F BA50 BA51 Message 2400 4800 9600 USB Serial Statistics Prompts BB01 BB02 BB03 BB04 BB05 BB06 BB07 BB08 BB09 BB0A BB0B BB0C BB0D BB0E BB0F BB10 BB11 BB12 BB13 BB14 BB15 BB16 BB17 BB18 BB19 BB1A BB1B BB1C BB1D BB1E BB1F BB20 BB21 1.Single-var… 2.Frequencies… 3.Fit data… 4.
Messages Listed Numerically (continued) # (hex) BB22 BB23 BB24 BB25 BB26 BB27 BB28 BB29 BB2A BB2B BB2C BB2D BB2E BB2F BB30 BB31 BB32 BB33 BB34 BB35 BB36 BB37 BB38 BB39 BB3A BB3B BB3C BB3D BB3E BB3F BB40 BB41 Message Y-Col: Model: Enter indep column number Enter dependent column number Choose statistical model Correlation Covariance PREDICT VALUES Y: Enter indep value or press PRED Enter dep value or press PRED SUMMARY STATISTICS Calculate: ΣX ΣY ΣX2 ΣY2 ΣXY NΣ Calculate sum of X column? Calculate sum of Y
Messages Listed Numerically (continued) # (hex) BC05 BC06 BC07 BC08 BC09 BC0A BC0B BC0C BC0D BC0E BC0F BC10 BC11 BC12 BC13 BC14 BC15 BC16 BC17 BC18 BC19 BC1A BC1B BC1C BC1D BC1E BC1F BC20 BC21 BC22 BC23 BC24 BC25 BC26 BC27 BC28 BC29 Message Message: Time: Date: Repeat: Enter "message" or « action » Enter hour Enter minute Enter second Choose AM, PM, or 24-hour time Enter month Enter day Enter year Enter alarm repeat multiple Enter alarm repeat unit SET TIME AND DATE Choose date display format Monday Tuesd
Messages Listed Numerically (continued) # (hex) BC2A BC2B BC2C BC2D BC2E BC2F BC30 BC31 BC32 BC33 BC34 BC35 BC36 BC37 BC38 BC39 BC3A BC3B Message 10 October 11 November 12 December Week Day Hour Minute Second Weeks Days Hours Minutes Seconds Month/Day/Year M/D/Y Day.Month.Year D.M.Y ALARMS Symbolic Application Prompts BD01 BD02 BD03 BD04 BD05 BD06 BD07 BD08 BD09 BD0A BD0B BD0C BD0D BD0E BD0F BD10 BD11 BD12 1.Integrate… 2.Differentiate… 3.Taylor poly… 4.Isolate var… 5.Solve quad… 6.
Messages Listed Numerically (continued) # (hex) BD13 BD14 BD15 BD16 BD17 BD18 BD19 BD1A BD1B BD1C BD1D BD1E BD1F BD20 BD21 BD22 BD23 BD24 BD25 BD26 BD27 Message Enter variable value Expression TAYLOR POLYNOMIAL Order: Enter Taylor polynomial order ISOLATE A VARIABLE Principal Get principal solution only? SOLVE QUADRATIC MANIPULATE EXPRESSION MATCH EXPRESSION Pattern: Replacement: Subexpr First Cond: Enter pattern to search for Enter replacement object Search subexpressions first? Enter conditional express
Messages Listed Numerically (continued) # (hex) BE10 BE11 BE12 BE13 BE14 BE15 BE16 BE17 BE18 BE19 BE1A BE1B BE1C BE1D BE1E BE1F BE20 BE21 BE22 BE23 BE24 BE25 BE26 BE27 BE28 BE29 BE2A BE2B BE2C BE2D BE2E BE2F BE30 BE31 BE32 BE33 BE34 Message Enter complex-valued func(s) Plot y'(t)=f(t,y) Enter function of INDEP and SOLN Enter derivative w.r.t. SOLN Enter derivative w.r.t.
Messages Listed Numerically (continued) # (hex) BE35 BE36 BE37 BE38 BE39 BE3A BE3B BE3C BE3D BE3E BE3F BE40 BE41 BE42 BE43 BE44 BE45 BE46 BE47 BE48 BE49 BE4A BE4B BE4C BE4D BE4E BE4F BE50 BE51 BE52 BE53 BE54 BE55 BE56 BE57 BE58 BE59 Message Tick spacing units are pixels? Depnd: Enter dependent var name Enter minimum dep var value Enter maximum dep var value H-Var: V-Var: Enter max indep var increment Choose horizontal variable Choose vertical variable 0 INDEP 1 SOLN SOLN( X-Left: X-Right: Y-Near: Y-Far: Z
Messages Listed Numerically (continued) # (hex) BE5A BE5B BE5C BE5D BE5E BE5F BE60 BE61 BE62 BE63 BE64 BE65 BE66 BE67 BE68 BE69 BE6A BE6B BE6C BE6D BE6E BE6F BE70 BE71 BE72 BE73 BE74 BE75 BE76 BE77 Message Enter minimum XX range value Enter maximum XX range value Enter minimum YY range value Enter maximum YY range value XX and YY Plot Options Zoom Factors H-Factor: V-Factor: Recenter at Crosshairs Enter horizontal zoom factor Enter vertical zoom factor Recenter plot at crosshairs? Reset plot Dflt Auto Fun
Messages Listed Numerically (continued) # (hex) BF07 BF08 BF09 BF0A BF0B BF0C BF0D BF0E BF0F BF10 BF11 BF12 BF13 BF14 BF15 BF16 BF17 BF18 BF19 BF1A BF1B BF1C BF1D BF1E BF1F BF20 BF21 BF22 BF23 BF24 BF25 BF26 BF27 BF28 BF29 BF2A BF2B Message Enter value or press SOLVE Eq: Enter function to solve Funcs in Solver Variable Order Variables: Enter order of vars to display SOLVE Y'(T)=F(T,Y) f: ˆfˆy: ˆfˆt: Indep: Init: Final: Soln: Tol: Step: Stiff Enter function of INDEP and SOLN Enter derivative w.r.t.
Messages Listed Numerically (continued) # (hex) BF2C BF2D BF2E BF2F BF30 BF31 BF32 BF33 BF34 BF35 BF36 BF37 BF38 BF39 BF3A BF3B BF3C BF3D BF3E BF3F BF40 BF41 BF42 BF43 BF44 BF45 BF46 BF47 BF48 BF49 BF4A BF4B BF4C BF4D BF4E BF4F BF50 Message Enter roots or press SOLVE Coefficients Roots SOLVE SYSTEM A·X=B A: B: X: Enter coefficients matrix A Enter constants or press SOLVE Enter solutions or press SOLVE Constants Solutions N: I%YR: PV: PMT: P/YR: FV: Enter no.
Messages Listed Numerically (continued) # (hex) BF51 BF52 BF53 BF54 BF55 BF56 C001 Message Interest: Balance: Enter no.
Messages Listed Numerically (continued) # (hex) DE1E DE1F DE20 DE21 DE22 DE23 DE24 DE25 DE26 DE27 DE28 DE29 DE2A DE2B DE2C DE2D DE2E DE2F DE30 DE31 DE32 DE33 DE34 DE35 DE36 DE37 DE38 DE39 DE3A DE3B DE3C DE3D DE3E DE3F DE40 DE41 DE42 Message Z is not prime Empty {} of equations Not reducible to a rational expression Non unary operator User function Non isolable operator Not exact system Parameters not allowed CAS internal error Invalid ^ for SERIES Operator not implemented (SERIES) No variable in expr.
Messages Listed Numerically (continued) # (hex) DE43 DE44 DE45 DE46 DE47 DE48 DE49 DE4A DE4B DE4C DE4D DE4E DE4F DE50 DE51 DE52 DE53 DE54 DE55 DE56 DE57 DE58 DE59 DE5A DE5B DE5C DE5D DE5E DE5F DE60 DE61 DE62 DE63 DE64 DE65 DE66 Message Numeric input Singularity! Continue? Cancelled Negative integer Parameter is cur. var. dependent Unsimplified sqrt Non polynomial system Unable to solve ODE Array dimension too large Unable to reduce system Complex number not allowed Polyn.
Messages Listed Numerically (continued) # (hex) Message DE67 DE68 Replacing strict with large inequality DF01 DF02 DF03 DF04 DF05 DF06 DF07 DF08 DF09 DF0A DF0B DF0C DF0D DF0E DF0F DF10 DF11 DF12 DF13 DF14 DF15 DF16 DF17 DF18 DF19 DF1A DF1B DF1C DF1D DF1E DF1F DF20 DF21 DF22 File Manager No valid environment stored Filer Application Messages NO ABORT ALL YES REN Already Exists Overwrite ? Rename PICK DESTINATION Are You Sure? Search Mode OFF Search Mode ON New DIR? Sort by: Original Type Name Size I
Messages Listed Numerically (continued) # (hex) DF23 DF24 DF25 DF26 DF27 DF28 DF29 DF2A DF2B DF2C DF2D DF2E DF2F DF30 DF31 DF32 Message RECV HALT VIEW EDITB HEADER LIST SORT XSEND CHDIR CANCL OK CHECK WARNING: Formatting will erase the SD card Do you want to continue? FORMAT Please Wait...
Messages Listed Numerically (continued) # (hex) E117 E118 E119 E11A E11B E11C E11D E11E E11F E120 E121 E122 E123 E124 E125 E126 E127 E128 E129 Message Rydberg Bohr radius Bohr magneton nuclear magneton photon wavelength photon frequency Compton wavelen 1 radian 2π radians in trig mode Wien's k/q “0/q q*“0 dielectric const SiO2 dielec cons ref intensity CONSTANTS LIBRARY Undefined Constant Equation Library Messages E301 E302 E303 E304 Starting Solver E305 E306 E307 E308 E309 E30A NEAR OF Keyword C
Messages Listed Numerically (continued) # (hex) E408 Message Searching Periodic Table Messages E501 E502 E503 Bad Molecular Formula E601 E602 E603 E604 E605 E606 E607 E608 E609 E60A E60B E60C E60D No Solution Undefined Element Undefined Property Financial Solver Messages Many or No Solutions I%YR/PYR ‰ -100 Invalid N Invalid PYR Invalid #Periods Undefined TVM Variable END mode BEGIN mode payments/year Principal Interest Balance Development Library and Miscellaneous Messages 10001 10002 10003 10004
Messages Listed Numerically (continued) # (hex) 1010F 10110 10111 10112 10113 10114 10115 10116 10117 10118 31401 70000 Message Forbidden Bad Expression Jump too Long Val betw 1-8 expected Insuffisant Memory Matrix Error Define Error [ or ] expected ARM register expected ARM invalid imediate No Message here (user-defined message created with DOERR) A-52 Error and Status Messages
B B. Tables of Units and Constants Units Unit (Full Name) Value in SI Units a (are) 100 m2 A (ampere) 1A acre (acre) 4046.87260987 m2 arcmin (minute of arc) 2.90888208666 x 10-4 r arcs (second of arc) 4.8481368111 x 10-6 r atm (atmosphere) 101325 kg / m•s2 au (astronomical unit) 1.495979 x 1011 m Å (Angstrom) 1 x 10-10 m b (barn) 1 x 10-28 m2 bar (bar) 100000 kg / m•s2 bbl (barrel) .158987294928 m3 Bq (becquerel) 11/s Btu (international table Btu) 1055.
Units (continued) Unit (Full Name) oF (degrees Fahrenheit) Value in SI Units 0.555555555556 K or 255.927777778 K fath (fathom) 1.82880365761 m fbm (board foot) .002359737216 m3 fc (footcandle) 10.7639104167 cd•sr / m2 Fdy (faraday) 96487 A•s fermi (fermi) 1 x 10-15 m flam (footlambert) 3.42625909964 cd / m2 ft (international foot) .3048 m ftUS (survey foot)) .304800609601 m g (gram) .001 kg ga (standard freefall) 9.80665 m / s2 gal (US gallon) .
Units (continued) Unit (Full Name) Value in SI Units lbmol (pound-mole) 453.59237 mol lbt (troy pound) .3732417216 kg lm (lumen) 1 cd•sr lx (lux) 1 cd•sr / m2 lyr (light year) 9.46052840488 x 1015 m m (meter) 1m µ (micron) 1 x 10-6 m mho (mho) 1 A2•s3 / kg•m2 mi (international mile) 1609.344 m mil (mil) .0000254 m min (minute) 60 s miUS (US statute mile) mmHg (millimeter of mercury (torr), 0 1609.34721869 m oC) 133.322368421 kg / m•s2 mol (mole) 1 mol mph (miles per hour) .
Units (continued) Unit (Full Name) Value in SI Units rd (rod) 5.02921005842 m rem (rem) .01 m2 / s2 rpm (revolutions per minute) 60 1 / s s (second) 1s S (siemens) 1 A2•s3 / kg•m2 sb (stilb) 10000 cd / m2 slug (slug) 14.5939029372 kg sr (steradian) 1 sr st (stere) 1 m3 St (stokes) .0001 m2 / s Sv (sievert) 1 m2 / s2 t (metric ton) 1000 kg T (tesla) 1 kg / A•s2 tbsp (tablespoon) 1.47867647813 x 10-5 m3 therm (EEC therm) 105506000 kg•m2 / s2 ton (short ton) 907.
Constants Constant (Full Name) Value in SI Units NA (Avogadro’s number) 6.0221367 x 1023 1 / gmol k (Boltzmann) 1.380658 x 10-23 J / K Vm (molar volume) 22.4141 l / gmol R (universal gas) 8.31451 J / (gmol•K) StdT (standard temperature) 273.15 K StdP (standard pressure) 101.325 kPa σ (Stefan-Boltzmann) 5.67051 x 10-8 W / (m2•K4) c (speed of light) 299792458 m/s ε0 (permittivity) 8.85418781761 x 10-12 F / m µ0 (permeability) 1.25663706144 x 10-6 H / m g (acceleration of gravity) 9.
Properties of Elements Property Type of Object * Property Number Atomic Number Real 1 Mass Number † Real 2 Atomic Weight Unit 3 Density † Unit 4 Oxidation States † String 5 Electron Configuration String 6 State String 7 Melting Point Unit 8 Boiling Point Unit 9 Heat of Vaporization Unit 10 Heat of Fusion Unit 11 Specific Heat Unit 12 Group (U.S.
C C. System Flags This appendix lists the calculator’s system flags. You can set, clear, and test all flags, although certain flags are used for specific purposes by the CAS and should not be altered. The default state of the flags is clear — except for flags –17, –27, –34, –90, –95 and –128 and the Binary Integer Math flags (flags –5 through –12). Flag –1 –2 System Flags Description Principal Solution. Clear: Symbolic commands return a result representing all possible solutions.
Flag –20 –21 System Flags (continued) Description Underflow Exception. Clear: Underflow exception returns 0, sets flag –23 or –24. Set: Underflow exception treated as an error. Overflow Exception. Clear: Overflow exception returns ± 9.99999999999E499 and sets flag –25. Set: Overflow exception treated as an error. –22 Infinite Result Exception. Clear: Infinite result exception treated as an error. Set: Infinite result exception returns ± 9.99999999999E499 and sets flag –26.
Flag –36 –37 –38 –39 –40 –41 –42 –43 –44 –45 through –48 –49 thru –50 –51 –52 System Flags (continued) Description I/O Receive Overwrite. Clear: If file name received by the calculator matches existing variable name, new variable name with number extension is created to prevent overwrite. Set: If file name received by the calculator matches existing variable name, existing variable is overwritten. Double-Spaced Printing. Clear: Single-spaced printing. Set: Double-spaced printing. Line Feed.
Flag –53 –54 System Flags (continued) Description Precedence. Clear: Certain parentheses in algebraic expressions suppressed to improve legibility. Set: All parentheses in algebraic expressions displayed. Tiny Array Elements. Clear: Singular values computed by RANK (and other commands that compute the rank of a matrix) that are more than 1 × 10-14 times smaller than the largest computed singular value in the matrix are converted to zero. Automatic rounding for DET is enabled.
Flag –65 –66 –67 –68 –69 –70 –71 –72 –73 –74 –75 –76 –77 –78 System Flags (continued) Description Multi-line Mode. Clear: Displays all levels over multiple lines. Set: Displays only the first level over multiple lines. Depends on flag –52. Multi-line Strings. Clear: Displays long strings in multiple lines. Set: Displays long strings in single lines. Depends on flags –52 and –65. Digital Clock. Clear: When the clock is displayed (see flag –40), it is digital-style.
Flag –79 –80 –81 –82 –83 –84 –85 –86 –87 –88 –89 –90 –91 –92 –93 C-6 System Flags System Flags (continued) Description Pretty Print Mode. Clear: Algebraic objects appear on the stack in textbook (EQW) form. (Only in multi-line levels, see flag –65). Set: Algebraic objects appear on the stack in linear form. Font used to show algebraics on stack if flag –79 is clear. Clear: Textbook stack display uses the current system font. Set: Textbook stack display uses mini-font. Font used by →GROB on algebraics.
Flag –94 –95 –96 –97 –98 –99 –100 –101 –102 –103 –104 –105 –106 –107 –108 –109 –110 –111 System Flags (continued) Description Auto-saving. Clear: In RPN mode, results are stored in LASTCMD. Set: In RPN mode, results are not stored in LASTCMD. Entry Mode. Clear: RPN mode Set (default): Algebraic mode. Not used. (Originally intended to toggle the softmenu in the editor in the HP 49G, though it was never implemented.) Vertical Lists. Clear: Lists on stack are displayed horizontally only, like the HP 48GX.
Flag –112 –113 –114 –115 –116 –117 –118 –119 –120 –121 –122 –123 –124 –125 –126 –127 –128 C-8 System Flags System Flags (continued) Description Simplifying ‘i’. Clear: ‘i’ can be simplified (i.e. i2 = –1) Set: ‘i’ cannot be simplified. Linear Simplification Mode. Clear: Apply linearity simplification when using integration CAS commands. Set: Do not apply linearity simplification when using integration CAS commands. Polynomial Term Order. Clear: Polynomial expressed in decreasing power order.
Four user flags are also used by the system: Flag 60 61 62 63 User Flags Description Units Type. Clear: The Equation Library and Constants Library use SI units. Set: The Equation Library and Constants Library use English units. Units Usage. Clear: The Equation Library and Constants Library display units. Set: The Equation Library and Constants Library do not display units. Payment Mode. Clear: The Time Value of Money solver uses End payment mode.
D D. Reserved Variables The calculator uses the following reserved variables. These have specific purposes, and their names are used as implicit arguments for certain commands. Avoid using these variables’ names for other purposes, or you may interfere with the execution of the commands that use these variables. You can change some of the values in these variables with programmable commands, while others require you to store new values into the appropriate place.
Reserved Variable What It Contains Used By PPAR Plotting parameters. DRAW PRTPAR Printing parameters. PRINT commands PTPAR Periodic Table parameters. PERTBL STARTED Program run on EDIT. EDIT STARTEQW CST commands list for EQW. Equation Writer STARTERR Program run on error. Error processing STARTOFF Program run at turnoff. OFF STARTRECV Program run at RECV. Filer, RECV STARTSEND Program run at SEND. Filer, SEND STARTUP Program run at reset. Reset s1, s2,… Arbitrary signs.
Parameter (Command) date (→DATE) Time (→TIME) action Repeat Description A real number specifying the date of the alarm: MM.DDYYYY (or DD. MMYYYY if flag –42 is set). If YYYY is not included, the current year is used. A real number specifying the time of the alarm: HH. MMSS.
You can specify menu labels and key actions independently by replacing a single object within the custom-menu list with a list of the form {“label-object” action-object }. To provide different shifted actions for custom menu keys, action-object can be a list containing three action objects in this order: The unshifted action (required if you want to specify the shifted actions). The left-shifted action. The right-shifted action.
Parameter (Command) Description Default Value baud (BAUD) The baud rate: 2400, 4800, 9600, 14400, 19200, 38400 or 115200. 115200 parity (PARITY) The parity used: 0=none, 1=odd, 2=even, 0 3=mark, 4=space. The value can be positive or negative: a positive parity is used upon both transmit and receive; a negative parity is used only upon transmit. receive pacing Controls whether receive pacing is used: a nonzero real value enables pacing, while zero disables it.
MASD.INI MASD.INI must contain valid MASD source code. This source code will be parsed/compiled before the source on the stack. It is useful to always include a basic set of commands or definitions in all compiled source. MHpar MHpar stores the status of an interrupted Minehunt game. MHpar is created when you exit Minehunt by pressing K. If MHpar still exists when you restart Minehunt, the interrupted game resumes and MHpar is purged.
Parameter (Command) Description Default Value (xmin, ymin) (XRNG, YRNG) A complex number specifying the lower left corner of PICT (the lower left corner of the display range). (xmax, ymax) (XRNG, YRNG) A complex number specifying the upper right corner of PICT (the upper right corner of the display range).
The $RESET$ operation („&ôL %RESET% ) resets the PPAR parameters (except ptype) to their default values, and erases PICT. (Note: the & means to press and hold the „key while pressing ô). Note that res behaves differently for the statistical plot types BAR, HISTOGRAM, and SCATTER than for other plot types. For BAR, res specifies bar width; for HISTOGRAM, res specifies bin width; res does not affect SCATTER. PRTPAR PRTPAR is a variable in the HOME directory that contains a list of printing parameters.
STARTEQW If it exists, the STARTEQW variable is evaluated whenver an element in the Equation Writer is selected. STARTERR If it exists, the STARTERR variable is evaluated whenever an error message is displayed. STARTOFF If it exists, the STARTOFF variable is evaluated when the calculator turnsoff automatically. STARTRECV If it exists, the STARTRECV variable is evaluated when the user presses RECV from inside the Filer. It takes as an argument, the selected argument’s name.
TPAR TPAR is a variable in the current directory. It contains a list of parameters used by the table of values plotting operation. Parameter (Command) starting-value step table-format zoom-factor font-size filename Description Real number that specifies the first value to show in the table. Real number that specifies the amount to increment from starting-value for each row in the table.
ZPAR ZPAR is a variable in the current directory. It contains a list of zooming parameters used by the DRAW command for all 2-D mathematical and statistical plots. Parameter (Command) Description Default Value h-factor Real number that specifies the horizontal zoom factor. 4 v-factor Real number that specifies the vertical zoom factor. 4 recenter flag 0 or 1 depending on whether the recenter at crosshairs option was selected in the set zoom factors input form.
ΣPAR ΣPAR is a variable in the current directory that contains either the current statistical parameter list or the name of the variable containing this list. Parameter (Command) Description Default Value columnindep (XCOL) A real number specifying the independent-variable’s column number. 1 columndep (YCOL) A real number specifying the dependent-variable’s column number. 2 intercept (LR) A real number specifying the coefficient of intercept as determined by the current regression.
CASDIR Reserved Variables The Computer Algebra System stored its reserved variables in a special directory called CASDIR. Reserved Variable What It Contains Used By CASINFO Graphic display temporary storage. Step-by-step operations ENVSTACK Flags and current path. PUSH, POP EPS Maximum coefficient to round to zero. EPSX0 IERR Error of integration Numerical integration operations MODULO The current modulus. MOD functions PERIOD Period for periodic operations.
MODULO The variable MODULO contains a real prime number for use with the modular operations. The default value is 13. It is used by ADDTMOD, DIV2MOD, DIVMOD, EXPANDMOD, FACTORMOD, GCDMOD, INVMOD, MODSTO, MULTMOD, POWMOD, RREFMOD, and SUBTMOD. PERIOD Contains the period for CAS periodic operations. The default value is 2π. PRIMIT Contains a primitive (subexpression) used temporarily for anti-derivitive expression during CAS operations.
E E. Technical Reference This appendix contains the following information: Object sizes. Symbolic integration patterns used by the calculator. Trigonometric expansions used by the calculator. Precedence of operations. References and as sources for constants and equations in the calculator (other than those in the Equation Library). Object Sizes The following table lists object types and their size in bytes. (Note that characters in names, strings, and tags use 1 byte each.
Object Size, continued Object Type Size (bytes) Unit object real magnitude each prefix each unit name each ×, ^, or / each exponent Unquoted global or local name Vector XLIB name 7.5 + 2.5 or 10.5 6 5 + number of characters 2.5 2.5 or 10.5 3.5 + number of characters 12.5 + 8 × number of elements 5.5 Symbolic Integration Patterns This table lists the symbolic integration patterns used by the calculator. These are the integrands that the calculator can integrate symbolically.
Symbolic Integration (continued) Pattern Antiderivative 1/(SIN(φ)×TAN(φ)) –INV(SIN(φ)) 1/(SIN(φ)2) –INV(TAN(φ)) SINH(φ) 1/(SINH(φ)×COSH(φ)) COSH(φ) LN(TANH(φ)) 1/(SINH(φ)×TANH(φ)) –INV(SINH(φ)) SQ(φ) φ 3/3 TAN(φ)2 TAN(φ)–φ TAN(φ) –LN(COS(φ)) INV(COS(φ)) LN(SIN(φ)) –INV(SIN(φ)) LN(COSH(φ)) INV(COSH(φ)) LN(SINH(φ)) –INV(SINH(φ)) TAN(φ)/COS(φ) 1/TAN(φ) 1/TAN(φ)×SIN(φ)) TANH(φ) TANH(φ)/COSH(φ) 1/TANH(φ) 1/TANH(φ)×SINH(φ)) φ 2×φ 1.5/3 1/ φ 1/(2× (φ)) 2× φ 2× (φ)×.
Trigonometric Expansions The following tables list expansions for trigonometric functions in Radians mode when using the →DEF, TRG*, and →TRG operations. These operations appear in the Equation Writer RULES menu.
Precedence of Operations Evaluation of an algebraic object is carried according to the order of precedence of the operators — those with higher precedence are executed first. Operations with the same order of precedence are executed from left to right. From highest precedence to lowest, the order of precedence is: Order Operation 1. 1.1 1.2 1.3 Unit attachment: Parenthesized expressions from innermost to outermost Power (^) from bottom to top (i.e.
Source References The following references were used as sources for many of the constants and equations used in the calculator. (See “References” in chapter 5, “Equation Reference,” for the references used as sources for the Equation Library.) 1. E.A. Mechtly. The International System of Units, Physical Constants and Conversion Factors, Second Revision. National Aeronautics and Space Administration, Washington DC, 1973. 2. The American Heritage Dictionary. Houghton Mifflin Company, Boston, MA, 1979. 3.
F F. Parallel Processing with Lists Parallel processing is the idea that, generally, if a command can be applied to one or more individual arguments, then it can also be extended to be applied to one or more sets of arguments. (Note: some examples assume approximate mode.) Some examples: 5 INV returns .2, so { 4 5 8 } INV returns { .25 .2 .125 }. 4 5 * returns 20, so { 4 5 6 } { 5 6 7 } * returns { 20 30 42 }, and { 4 5 6 } 5 * returns { 20 25 30 }.
integer matrix having 3 rows and 4 columns. Since these commands can normally use lists as arguments, they cannot perform parallel processing, except by using DOLIST. Program control commands. Program control structures and commands do no perform parallel processing and cannot be forced to do so. However, programs containing these structures can be made to parallel process by using DOLIST. For example, { 1 2 3 4 5 6 } 4 « IF DUP 3 ‰ THEN DROP END » DOLIST returns { 3 4 5 6 }.
Group 7: Two -argument, one result commands Two-argument commands can operate in parallel in any of three different ways: {list } {list } {list } object object {list } In the first form, parallel elements are combined by the command: { 1 2 3 } { 4 5 6 } returns { .04 .1 .18 }. In the second form, the level 1 object is combined with each element in the level 2 list in succession: { 1 2 3 } 30 %CH returns { 2900 1400 900 }.
_ (Attach Unit). This command will create unit objects in parallel only if level 1 contains a list. Thus 1 { ft in m } _ produces { 1_ft 1_in 1_m } while { 1 2 3 } 'm' _ produces an error. STO+. STO+ performs parallel list addition only if both arguments are lists. If one argument is a list and the other is not, STO+ appends the non-list argument to each element in the list. STO-, STO*, STO/. These commands perform parallel processing if both arguments are lists, but fail otherwise.
G G. Keyboard Shortcuts Each key on the calculator performs so many different functions that only the most fundamental ones are actually shown on the keyboard (on the keys themselves or on the space around the keys). The following is the complete list of the “hidden” functions of the calculator’s keyboard. Notation: In this appendix, there are two ways of showing key presses: @` means: press Right Shift, release it, then press `. @&` means: while holding Right Shift, press `.
Other keyboard shortcuts Keycode Keystroke Definition 11.21 through 22.21 ! & A through F Accesses the graphing input forms !&£ (!& H) MODES menu (menu 63) 23.21 !&¥ (!&I) Toggles real/complex mode (flag –103) 25.1 — 31.21 !& § (!& J) HOME 33.21 !&« (!& L) Last Menu 34.1 š PICTURE 35.1 ˜ EDITB 35.2 !˜ VISIT for variables, EDIT for everything else. 35.21 !& ˜ VISITB for variables, EDITB for everything else. 35.
Keycode Keystroke Definition 93.61 ~@& 2 ¡ (upside down exclamation point) 94.61 ~@& 3 ¿ (upside down question mark) 104.31 @ & í (@& †) ; or . (depends on flag –51) 104.61 ~@&í(@&†) ; or . (depends on flag –51) 105.31 @ & ï(@& `) Toggles exact/approximate mode (flag –105) Shifted softkeys This section describes the effect of using the shift keys and menu labels displayed above the A through F keys. @%VARNAME% = 'varname' !©.
In the first page of the PRG BRCH menu, pressing the shift keys before pressing any menu key provides a handy typing shortcut for programmers. In all these cases, the cursor is placed at the end of the first command. Thus these shifted keys can be thought of as “program structure delimiters”.
H H. The Menu-Number Table Menu Numbers “*” in the first column means the menu is not one of the keyboard menus and is therefore only available through the MENU command. Menus are identified by keyboard path (used when flag –117 is clear) followed by choose-box path (used when flag –117 is set) followed by its displayed name. RS-9 means “press right-shift, let go, then press 9”. RS&9 means “press right-shift, hold it down, and press 9”.
Menus 0 through 117 These menus are mostly compatible with the menus in the HP 48G series.
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 * 81 * 82 * 83 * 84 * 85 * 86 * 87 * 88 * 89 * 90 * 91 * 92 * 93 94 95 * 96 * 97 * 98 * 99 *100 *101 *102 *103 [CONVERT] UNITS NXT POWR (CONVERT 1 10 or UNITS 10: "POWER") [CONVERT] UNITS NXT PRESS (CONVERT 1 11 or UNITS 11: "PRESSURE") [CONVERT] UNITS NXT TEMP (CONVERT 1 12 or UNITS 12: "TEMPERATURE") [CONVERT] UNITS NXT NXT ELEC (CONVERT 1 13 or UNITS 13: "ELECTRIC CURRENT") [CONVERT] UNITS NXT NXT ANGL (CONVERT 1 1
*104 *105 *106 *107 *108 *109 *110 111 112 113 114 115 116 117 old soft-menu I/O (105 MENU I/O: "INPUT/OUTPUT") old soft-menu I/O SRVR (104 MENU SRVR: "SERVER") old soft-menu I/O IOPAR (no choose-box version available) old soft-menu I/O PRINT (104 MENU PRINT: "PRINT") old soft-menu I/O PRINT PRTPAR (no choose-box version available) old soft-menu I/O SERIAL (104.
154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 SYMB SOLVE (SYMB 5: "SYMBOLIC SOLVER") SYMB NXT EXPLN (SYMB 7: "SYMBOLIC EXP & LN") MATRICES OPER (MATRICES 2: "MATRIX OPERATIONS") MATRICES QUADF (MATRICES 4: "MATRIX QUAD. FORM") MATRICES LIN-S (MATRICES 5: "MATRIX LINEAR SYS.") MATRICES NXT EIGEN (MATRICES 7: "MATRIX EIGENVECT.") MATRICES NXT VECT (MATRICES 8: "MATRIX VECTOR") TRIG HYP (TRIG 1: "TRIG HYPERBOLIC") CALC DERIV (CALC 1: "DERIV. & INTEG.
I I. The Command Menu-Path Table This lists the calculator’s programmable commands in CAT order. Of the 818 commands, 808 are shown by CAT. This list assumes that library 256 is attached, flag –95 is off, and flag –117 is set. “Keys” column: Each command identifies its menu path or key sequence (if any) with alternatives on additional lines. “/” means “either”. The most efficient key sequence is shown first if several exist, assuming that NXT NXT is better than PREV, etc. “[]” = optional.
Command ! Type Library F 2-99 % F 2-124 %CH %T ' F F F * *H *W + A C C A / A A 2-126 2-125 1792-20 1792-21 2-71 2-189 2-190 2-68 2-69 2-70 2-72 ; C 2-388 < F 2-235 = == A F 2-59 2-233 > F 2-236 ? ABCUV ABS F C F 788-137 788-48 2-61 ACK C 2-21 ACKALL C 2-20 ACOS ACOS2S A C 2-88 788-37 ACOSH A 2-91 Size Keys 2.5 key ALPHA-RS-2 MTH NXT PROB 2.5 key ALPHA-LS-1 MTH REAL 2.5 MTH REAL 2.5 MTH REAL 2.5 key 43.1 2.5 2.5 2.5 2.5 ? First 28C 28C 14 14 key 75.
Command ADD Type Library C 171-92 Size Keys 5.5 MTH LIST Menu 11 2219.16 128 ADDTMOD F 788-110 5.5 ARITH MODUL «MODULAR» 5.5 CAT 5.5 «MAIN» 2.5 key 61.2: 10^x 5.5 RS&NUM.
Command ATAN2S Type Library C 788-34 Size Keys 5.5 TRIG CONVERT TRIG «TRIGO» 2.5 MTH HYP TRIG HYP «HYPERBOLIC» 5.5 83.02 MENU ATANH A 2-92 ATICK C 171-16 ATTACH AUGMENT AUTO AXES AXL C C C C C 2-358 222-19 2-192 2-186 788-74 2.5 5.5 2.5 2.5 5.5 AXM C 788-73 5.5 AXQ C 788-76 5.5 A→ A→H BAR BARPLOT BASIS BAUD BEEP BESTFIT C C C C C C C C 256-3 256-4 2-227 2-316 222-17 2-371 2-52 2-323 5.5 5.5 2.5 2.5 5.5 2.5 2.5 2.5 BIN C 2-144 2.
Command CF Type Library C 2-132 Size Keys 2.5 LS&MODE FLAG PRG TEST NXT NXT PRG NXT MODES FLAG 5.5 ARITH POLY 5.5 MATRICES QUADF 5.5 PRG NXT IN CHINREM CHOLESKY CHOOSE C C C 788-58 222-11 171-77 CHR C 2-165 CIRC CKSM CLEAR CLKADJ C C C C 222-29 2-370 2-282 2-24 CLLCD CLOSEIO CLUSR CLVAR CLΣ C C C C C 2-56 2-363 2-347 2-347 2-284 CMPLX C 788-129 CNRM C 2-119 COL+ C 171-63 5.5 MTH MATRX COL MATRICES CREAT COL COL- C 171-62 5.
Command COND Type Library C 171-38 Size Keys 5.5 MATRICES OPER MTH MATRX NORM CONIC CONJ C F 2-221 2-62 2.5 82 MENU 2.5 CMPLX MTH NXT CMPLX NXT «CMPLX» 5.5 APPS 3 APPS 12 COLIB 115 MENU 5.5 APPS 12 COLIB 115 MENU 5.5 «MATHS» 2.5 key 101.02 2.5 [CONVERT] UNITS TOOLS CONLIB C 171-24 CONST C 171-25 CONSTANTS CONT CONVERT C C C 222-42 2-58 2-11 CORR COS COSH C A A 2-289 2-82 2-85 COV CR CRC CRDIR CRLIB CROSS C C C C C C 2-290 2-243 256-27 2-32 256-26 2-122 CSWP C 171-65 5.
Command DATE+ Type Library C 2-31 Size Keys 2.5 RS&TIME NXT PRG NXT NXT TIME NXT APPS 5 4 NXT 5.5 CAT DBUG C 221-21 DDAYS C 2-30 DEC C 2-145 2.5 RS&TIME NXT PRG NXT NXT TIME NXT APPS 5 4 NXT 2.5 [MTH/CONVERT] BASE DECR DEDICACE DEF DEFINE C C F C 2-332 222-55 222-37 2-343 2.5 5.5 5.5 2.5 DEG C 2-135 2.5 DEGREE DELALARM F C 222-54 39872 5.5 2.5 DELAY DELKEYS C C 2-245 2-382 2.5 2.5 DEPND DEPTH DERIV C C F 2-196 2-276 788-14 2.5 2.5 5.5 DERVX F 788-3 5.
Command DIR DISP DISPXY DISTRIB Type C C C F Library 1792-27 2-50 221-22 222-25 Size 2.5 2.5 5.5 5.5 DIV C 788-86 Keys CAT PRG NXT OUT CAT CONVERT REWRITE «REWRITE» 5.5 CALC DERIV DIV2 DIV2MOD C C 788-38 788-114 5.5 ARITH POLY 5.5 ARITH MODUL DIVIS C 788-68 DIVMOD F 788-113 DIVPC F 788-98 DO C 1792-7 5.5 ARITH SYMB ARITH «INTEGER» 5.5 ARITH MODUL «MODULAR» 5.5 CALC LIMIT «DIFF» 2.5 PRG BRCH [DO] DOERR DOLIST C C 2-42 171-91 2.5 PRG NXT NXT ERROR 5.
Command EGCD Type Library C 788-46 Size Keys 5.5 ARITH POLY «POLYNOMIAL» 5.5 MATRICES NXT EIGEN MTH MATRX NXT EGV C 171-44 EGVL C 171-45 5.5 MATRICES NXT EIGEN MTH MATRX NXT ELSE C 1792-2 2.5 PRG BRCH IF PRG NXT NXT ERROR IFERR END C 1792-23 1792-3 1792-22 2.5 PRG BRCH IF/CASE/DO/WHILE PRG NXT NXT ERROR IFERR ENDSUB F 171-87 5.
Command EXPAN Type Library C 2-334 Size Keys 2.5 93/142 MENU EXPAND C 788-0 5.5 ALG SYMB ALG «ALGB» 5.5 ARITH MODUL «MODULAR» 2.5 90/99 MENU EXPANDMOD F 788-118 EXPFIT C 2-321 EXPLN C 788-23 EXPM A 2-98 EYEPT C 171-5 5.5 86.02 MENU F0λ F 171-98 FACT FACTOR F C 2-100 788-1 FACTORMOD F 788-119 FACTORS FANNING C F 788-67 171-96 FAST3D FC? C C 2-400 2-134 FC?C C 2-143 FCOEF C 788-65 FDISTRIB F 222-24 FFT C 171-26 5.5 APPS 12 UTILS 117 MENU 2.5 CAT 5.
Command FINDALARM Type Library C 2-27 FINISH FIX C C 2-368 2-138 FLASHEVAL FLOOR F F 171-23 2-103 FONT6 FONT7 FONT8 FONT→ FOR C C C C C 221-15 221-14 221-13 221-3 1792-10 FOURIER F 788-94 FP FREE FREEZE FROOTS F C C C 2-102 2-356 2-51 788-66 FS? C 2-133 FS?C C 2-142 FUNCTION FXND GAMMA GAUSS C C F C 2-220 788-107 222-7 788-77 GBASIS GCD C F 222-58 788-44 GCDMOD F 788-117 GET C 2-178 GETI C 2-179 GOR GRAD C C 2-211 2-137 GRAMSCHMIDT C 222-9 Size Keys 2.
Command GRAPH GREDUCE GREY GRIDMAP Type C C C C Library 2-200 222-59 1792-29 171-10 Size 2.5 5.5 2.5 5.5 GROB GROBADD C C 1792-29 788-124 GXOR HADAMARD C C 2-212 788-70 HALFTAN C 788-32 HALT HEAD C C 1792-14 171-81 HEADER→ HELP HERMITE C C F 221-5 222-50 788-92 HESS C 788-89 2.5 CAT 5.5 SYMB GRAPH CALC GRAPH 2.5 PRG NXT GROB 5.5 MATRICES OPER NXT «MATR» 5.5 TRIG SYMB TRIG CONVERT TRIG «TRIGO» 2.5 PRG NXT NXT RUN 5.5 RS&CHARS NXT PRG LIST ELEM NXT PRG NXT CHARS NXT 5.5 CAT 5.
Command IBASIS IBERNOULLI IBP Type C F C Library 222-18 222-6 788-11 Size 5.5 5.5 5.5 Keys MATRICES NXT VECT ARITH INTEG SYMB CALC CALC DERIV NXT «DIFF» 5.5 ARITH INTEG 5.5 ARITH INTEG 2.5 MATRICES CREAT MTH MATRX MAKE ICHINREM IDIV2 IDN C C C 788-59 788-39 2-174 IEGCD C 788-47 IF C 1792-0 5.5 SYMB ARITH ARITH INTEG «INTEGER» 2.5 PRG BRCH [IF] IFERR IFFT C C 1792-13 171-27 2.5 PRG NXT NXT ERROR [IFERR] 5.5 MTH NXT FFT IFT C 2-48 2.
Command IREMAINDER Type Library F 788-43 ISOL C 2-336 ISOM ISPRIME? C F 222-13 788-60 I→R JORDAN F C 2-390 788-80 KER KERRM KEY KEYEVAL KEYTIME→ KGET KILL LABEL LAGRANGE C C C C C C C C C 222-15 2-374 2-57 788-123 171-109 2-365 2-40 2-201 788-93 LANGUAGE→ LAP C F 221-1 788-16 LAPL C 788-88 LAST LASTARG C C 2-54 2-54 LCD→ LCM C F 2-213 788-45 LCXM C 788-85 LC~C LDEC C C 256-23 788-18 LEGENDRE F 788-90 LGCD LIBEVAL LIBS LIMIT C C C F 788-50 171-22 2-357 788-5 Size Keys 5.
Command LIN Type Library C 788-20 Size Keys 5.5 ALG EXP&LN SYMB ALG CONVERT REWRITE SYMB NXT EXPLN «EXP&LN» «REWRITE» 2.5 PRG NXT PICT 2.5 90/99 MENU Menu 121 124 135 151 155 172 LINE LINFIT C C 2-206 2-319 LININ F 171-21 5.5 PRG TEST PREV LINSOLVE C 788-82 LIST→ LN C A 2-158 2-94 LNAME LNCOLLECT C C 788-109 788-22 LNP1 A 2-97 5.5 S.SLV SYMB SOLVE MATRICES LIN-S «SOLVER» «MATR» NXT NXT 2.5 CAT 2.5 key 51.3 141 MENU 5.5 109 DUP MENUXY 5.
Command MAD Type Library C 788-81 MAIN MAKESTR MANT MAP MATHS MATR MAX MAXR MAXΣ MCALC C C F C C C F F C C 788-127 256-28 2-111 788-102 222-47 788-131 2-106 2-64 2-296 171-118 MEAN MEM MENU C C C 2-297 2-345 2-349 MENUXY MERGE MIN MINEHUNT C C F C 788-122 2-355 2-107 227-3 MINIFONT→ MINIT C C 221-18 171-115 MINR MINΣ MITM F C C 2-65 2-298 171-116 MKISOM MOD C F 222-14 2-110 MODSTO C 788-121 MODULAR C 222-44 MOLWT MROOT F C 229-2 171-119 MSGBOX C 171-78 MSLV C 222-32 MSOLVR
Command MULTMOD Type Library F 788-112 Size Keys 5.5 ARITH MODUL NXT «MODULAR» NXT 5.5 APPS 12 MES 116 MENU 5.5 MTH NXT PROB NXT 2.5 PRG/TOOL STACK PREV 2.5 key 62.1: +/CMPLX MTH NXT CMPLX NXT «CMPLX» NXT 2.5 PRG MEM 2.5 PRG BRCH START/FOR MUSER C 171-117 NDIST NDUPN NEG C C A 171-28 2-399 2-60 NEWOB NEXT C C 2-39 1792-11 NEXTPRIME F 788-61 NIP NOT C F 2-396 2-231 NOVAL NSUB C F 2-391 171-86 NUM C 2-164 NUMX C 171-6 2.5 RS&CHARS PRG TYPE NXT PRG NXT CHARS 5.5 86.
Command PARSURFACE Type Library C 171-9 Size Keys 5.5 85 MENU PARTFRAC C 788-52 5.5 ALG ARITH POLY NXT NXT «ALGB» «POLYNOMIAL» NXT 2.5 PRG MEM DIR 5.5 MATRICES NXT EIGEN «MATR» NXT 5.5 RS&NUM.SLV POLY ARITH POLY NXT NXT PATH PCAR C C 2-33 788-79 PCOEF C 171-69 PCONTOUR C 171-13 5.5 85 MENU PCOV C 171-31 5.5 102.02 MENU PDIM PEEK PEEKARM PERINFO PERM PERTBL PEVAL C C C C F C C 2-195 256-17 256-36 229-3 2-130 229-0 171-70 2.5 5.5 5.5 5.5 2.5 5.5 5.
Command POP POS Type Library C 222-53 C 2-161 Size Keys 5.5 CAT 2.5 RS&CHARS PRG LIST ELEM PRG NXT CHARS 5.5 CAT 5.5 CONVERT REWRITE NXT «REWRITE» 5.5 ARITH MODUL NXT «MODULAR» NXT 2.5 104/107 MENU POTENTIAL POWEXPAND C F 222-56 222-27 POWMOD F 788-115 PR1 C 2-240 PREDV PREDX PREDY PREVAL C C C F 2-303 2-305 2-304 788-12 2.5 2.5 2.5 5.5 PREVPRIME F 788-62 5.5 PRLCD PROMPT PROMPTSTO PROOT C C C C 2-246 1792-28 788-139 171-68 2.5 2.5 5.5 5.
Command PVIEW Type Library C 2-202 Size Keys 2.5 PRG NXT OUT PRG NXT PICT NXT 2.5 90/99 MENU PWRFIT C 2-322 PX→C Psi QR C F C 2-198 222-3 171-49 2.5 PRG NXT PICT NXT 5.5 MTH NXT SPECIAL 5.5 MATRICES FACT MTH MATRX FACTR QUAD QUOT C F 2-337 788-40 QUOTE F 2-257 QXA C 788-75 RAD C 2-136 RAND RANK C C 2-127 171-42 2.5 93 MENU 5.5 ARITH POLY PREV «POLYNOMIAL» NXT 2.5 «ALGB» 93.03 MENU 5.5 MATRICES QUADF CONVERT MATRX «MATR» NXT 2.5 LS&MODE ANGLE PRG NXT MODES ANGLE 2.5 MTH NXT PROB 5.
Command RCLΣ Type Library C 2-286 Size Keys 2.5 91/97 MENU RS-ΣDAT RCWS C 2-149 2.5 [MTH/CONVERT] BASE NXT RDM C 2-172 RDZ RE C F 2-128 2-154 RECN RECT C C 2-366 171-17 RECV REF C C 2-367 788-72 REMAINDER F 788-42 RENAME REORDER REPEAT C F C 221-19 788-105 1792-6 2.5 MTH MATRX MAKE MATRICES CREAT NXT NXT 2.5 MTH NXT PROB 2.5 CMPLX NXT MTH NXT CMPLX «CMPLX» NXT 2.5 104.02 MENU 5.5 LS&MODE ANGLE MTH VECTR NXT PRG NXT MODES ANGLE 2.5 104 MENU 5.5 MATRICES LIN-S «MATR» 5.
Command RNRM Type Library C 2-118 Size Keys 2.5 MTH MATRX NORM MATRICES OPER NXT ROLL ROLLD ROMUPLOAD ROOT ROT ROW+ C C C C C C 2-280 2-281 171-111 2-251 2-274 171-61 2.5 2.5 5.5 2.5 2.5 5.5 ROW- C 171-60 5.5 MTH MATRX ROW MATRICES CREAT ROW ROW→ C 171-55 5.5 MTH MATRX ROW MATRICES CREAT ROW RPL> RR C C 2-393 2-3 2.5 CAT 2.5 [MTH/CONVERT] BASE NXT BIT RRB C 2-4 2.5 [MTH/CONVERT] BASE NXT BYTE RREF C 171-52 5.5 MATRICES LIN-S MTH MATRX FACTR RREFMOD RRK C C 788-120 171-35 5.
Command R→I SAME SBRK SB~B SCALE SCALEH SCALEW SCATRPLOT SCATTER SCHUR Type F C C C C C C C C C Library 2-389 2-228 2-377 256-20 2-194 2-189 2-190 2-318 2-225 171-51 SCI C 2-139 SCLΣ SCONJ SCROLL C C C 2-313 2-326 788-125 SDEV SEND SEQ C C C 2-299 2-364 171-83 SERIAL SERIES C C 256-29 788-7 SERVER SEVAL SF C F C 2-369 788-100 2-131 SHOW SIDENS C F 2-338 171-99 SIGMA SIGMAVX SIGN F F F 222-2 222-1 2-78 SIGNTAB C 788-95 SIMP2 SIMPLIFY C F 788-51 222-34 Size 2.5 2.5 2.5 5.5 2.5 2.
Command SIN SINCOS Type Library A 2-81 C 788-24 Size Keys 2.5 key 53 5.5 TRIG NXT CONVERT TRIG SYMB NXT EXPLN «TRIGO» «REWRITE» 2.5 MTH HYP TRIG HYP «HYPERBOLIC» 2.5 PRG MEM ARITH NXT 2.5 RS&CHARS MTH MATRX MAKE PRG LIST ELEM PRG NXT CHARS PRG NXT GROB NXT MATRICES OPER NXT NXT 2.5 [MTH/CONVERT] BASE NXT BIT SINH A 2-84 SINV SIZE C C 2-324 2-160 SL C 2-5 SLB C 2-6 2.5 [MTH/CONVERT] BASE NXT BYTE SLOPEFIELD C 171-12 5.5 85 MENU SNEG SNRM C C 2-325 171-41 2.5 PRG MEM ARITH NXT 5.
Command SRB Type Library C 2-8 Size Keys 2.5 [MTH/CONVERT] BASE NXT BYTE SRECV SREPL C C 2-361 221-16 2.5 109 MENU 5.5 RS&CHARS NXT PRG NXT CHARS NXT 5.5 256.03 MENU 2.5 PRG BRCH [START] SREV START C C 256-15 1792-9 STD C 2-141 STEP C 1792-12 2.5 LS&MODE FMT PRG NXT MODES FMT 2.5 PRG BRCH START/FOR STEQ C 2-250 2.5 RS&NUM.
Command SUBTMOD Type Library F 788-111 Size Keys 5.5 ARITH MODUL NXT «MODULAR» NXT 5.5 MATRICES FACT MTH MATRX FACTR SVD C 171-46 SVL C 171-47 5.5 MATRICES FACT NXT MTH MATRX FACTR NXT SWAP SYLVESTER C C 2-271 788-78 SYSEVAL SYST2MAT C C 2-49 222-10 S~N S→H TABVAL C C C 256-22 256-8 788-97 2.5 PRG/TOOL STACK 5.5 MATRICES QUADF «MATR» NXT 2.5 CAT 5.5 CONVERT MATRX MATRICES LIN-S 5.5 256.04 MENU 5.5 256.02 MENU 5.
Command TESTS TEVAL TEXPAND Type C C C Library 222-46 788-101 788-19 Size 5.5 5.5 5.5 Keys «MATHS» NXT 101 DUP MENUXY EXP&LN SYMB ALG SYMB TRIG ALG NXT TRIG NXT SYMB NXT EXPLN «EXP&LN» «TRIGO» NXT «ALGB» NXT 2.5 PRG NXT OUT 2.5 PRG BRCH IF/CASE PRG NXT NXT ERROR IFERR TEXT THEN C C 2-217 1792-26 1792-1 1792-24 TICKS C 2-18 TIME C 2-16 TINC F 171-101 TLIN C 788-25 TLINE TMENU C C 2-207 2-348 TOT TRACE C C 2-300 171-39 TRAN C 788-69 5.
Command TRIGSIN Type Library C 788-29 Size Keys 5.5 TRIG NXT NXT CONVERT TRIG NXT «TRIGO» NXT NXT 5.5 TRIG NXT NXT «TRIGO» NXT NXT 2.5 MTH MATRX MAKE 2.5 MTH REAL NXT NXT 5.5 «DIFF» NXT NXT 99 DUP MENUXY 2.5 82 MENU 5.5 EXP&LN NXT TRIG NXT NXT CONVERT TRIG NXT NXT «EXP&LN» 2.5 RS&TIME NXT NXT PRG NXT NXT TIME NXT NXT APPS 5 4 NXT NXT 2.5 PRG MEM DIR NXT 5.5 RS&NUM.
Command Type Library VANDERMONDE C 788-83 Size Keys 5.5 MATRICES CREAT NXT NXT MTH MATRX MAKE NXT NXT «MATR» NXT NXT 2.5 100.02 MENU 2.5 PRG MEM DIR NXT 5.5 140 DUP MENUXY 5.5 CAT 5.5 key LS-downarrow 5.5 CAT 5.5 CAT 2.5 PRG TYPE NXT NXT 2.5 MTH VECTR 2.5 PRG NXT IN 2.5 PRG BRCH [WHILE] VAR VARS VER VERSION VISIT VISITB VPOTENTIAL VTYPE V→ WAIT WHILE C C F C C C C C C C C 2-301 2-36 788-140 171-15 221-8 221-10 222-57 2-167 2-180 2-55 1792-5 WIREFRAME C 171-8 5.
Command YSLICE Type Library C 171-11 Size Keys 5.5 85 MENU YVOL C 171-1 5.5 86 MENU YYRNG C 171-4 5.5 86 MENU ZEROS C 788-64 ZFACTOR F 171-95 ZVOL C 171-2 5.5 SYMB SOLVE S.SLV NXT «SOLVER» 5.5 APPS 12 UTILS 117 MENU 5.5 86 MENU ^ _ dB A F F 2-73 2-267 171-105 e F 2-66 gmol F 171-102 i F 2-67 lbmol F 171-103 lim F 788-5 qr rpm C F 222-8 171-104 rref C 788-71 | F 2-255 2-256 √ ∫ A F Σ Σ+ F C 2-79 2-252 2-253 2-254 2-286 Σ- C 2-287 2.5 key 51.1: y^x 2.
Command ΣLINE ΣLIST Type Library C 2-314 C 171-89 ΣX ΣX^2 ΣX2 ΣX*Y ΣXY ΣY ΣY^2 ΣY2 ► π C C C C C C C C F F 2-291 2-295 2-293 2-295 2-293 2-292 2-294 2-294 2-342 2-63 ∂ F ≤ F 2-247 2-248 2-237 ≥ F 2-238 ≠ F 2-234 → C →A →ALG →ARRY →CD →COL C C C C C 1792-4 1792-16 256-2 256-11 2-170 256-6 171-56 →DATE C 2-22 →DIAG C 171-58 →FONT →GROB →H →HEADER C C C C 221-2 2-215 256-0 221-4 Size Keys 2.5 102 MENU 5.5 MTH LIST Menu 102 11 2219.15 103 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.
Command →HMS Type Library C 2-114 →KEYTIME →LANGUAGE →LCD →LIST C C C C 171-108 221-0 2-214 2-154 →LST →MINIFONT →NDISP →NUM C C C C 256-10 221-17 221-6 2-53 →PRG →Q C C 256-12 2-263 Size Keys 2.5 RS&TIME NXT PRG NXT NXT TIME NXT APPS 5 4 NXT 5.5 CAT 5.5 CAT 2.5 PRG NXT GROB NXT 2.5 PRG TYPE PRG LIST 5.5 256.02 MENU 5.5 CAT 5.5 CAT 2.5 key 105.3 CONVERT REWRITE NXT 5.5 256.03 MENU 2.5 CONVERT REWRITE NXT →Qп C 2-264 2.5 CONVERT REWRITE NXT →RAM →ROW C C 256-14 171-54 5.5 256.03 MENU 5.
J J. ASCII Character Codes and Translations The following table shows the relation between character codes (results of NUM, arguments to CHR) and characters (results of CHR, arguments to NUM) for the lower half of the character set.
The following table shows the relation between character codes (results of NUM, arguments to CHR) and characters (results of CHR, arguments to NUM), as well as the translation codes to be used to transmit characters between the calculator and a remote device, for the upper half of the character set. Character Codes 128-255 With ASCII Character Translations Code 128 129 130 131 132 133 134 135 136 137 138 Trans. \<) \x‚ \.V ƒ \v/ „ \.S Σ \GS ► \|> π \pi ˆ \.
K. Index ! ! (Factorial) .....................................................................3-291 !Directives ........................................................................6-17 !PATH...............................................................................6-17 !RPL ..................................................................................6-35 % % (Percent) ....................................................................3-292 %CH .................................................
alpha keyboard automatically locking..................................................1-42 ALRMDAT.......................................................................D-2 alternant..........................................................................3-269 AMORT ...........................................................................3-11 AND .................................................................................3-11 angular motion............................................................
calculator turning off ....................................................................1-55 calculator clock.................................................................. 2-4 cantilevers........................................................................... 5-3 capacitor .................................................................5-14, 5-16 CASCFG ..........................................................................3-31 CASCMD ...........................................................
CROSS..............................................................................3-47 CST.....................................................................................D-3 CSWP................................................................................3-47 CURL................................................................................3-48 current.............................................................5-9, 5-31, 5-50 cursor (command line) ................................................
energy......................................................................5-13, 5-24 ENG .................................................................................3-74 ENVSTACK ..................................................................D-13 EPS...................................................................................D-13 EPSX0 ..............................................................................3-74 EQ ........................................................................
Fibonacci numbers ........................................................... 2-1 FIBT.................................................................................... 2-4 Filename conventions ....................................................6-17 FILER...............................................................................3-87 FINDALARM.................................................................3-87 FINISH ............................................................................
H H→ ..................................................................................... 6-4 H→A .................................................................................. 6-5 H→S ................................................................................... 6-5 HADAMARD...............................................................3-102 HALFTAN ....................................................................3-102 HALT ......................................................................
L LABEL ...........................................................................3-126 Labels ................................................................................6-13 LAGRANGE ................................................................3-126 LANGUAGE→ ...........................................................3-126 LAP .................................................................................3-127 LAPL...............................................................................
MAIN .............................................................................3-141 MAKESTR ........................................................................ 6-6 MANT ............................................................................3-141 MAP ................................................................................3-142 MASD...............................................................................6-11 MASD syntax...............................................................
N P names action in programs ........................................................ 1-1 NAMES............................................................................2-25 nBASE ..............................................................................2-22 NDIST............................................................................3-154 NDUPN .........................................................................3-155 NEG .....................................................................
differential equations..................................................3-59 draw graph ...................................................................3-68 fast 3D ..........................................................................3-84 function ........................................................................3-93 histogram....................................................................3-105 label axes ....................................................................3-126 parametric.
using arrays...................................................................2-12 using calculator clock ................................................... 2-4 using flags.....................................................................2-20 using other programs ....................... 2-4, 2-8, 2-15, 2-26 using statistics commands .........................................2-34 utility programs ...........................................................2-26 vectored enter...............................
R→C ...............................................................................3-215 R→D...............................................................................3-215 R→I ................................................................................3-215 RAD ................................................................................3-190 RAND ............................................................................3-190 random number.......................................................
SCROLL.........................................................................3-219 SDEV..............................................................................3-219 SEND .............................................................................3-219 SEQ.................................................................................3-220 SERIAL .............................................................................. 6-8 serial communications bitrate..........................................
SSEC .................................................................................1-44 ß ßENTER .................................................................2-37, D-3 S SST ..................................................................................3-233 SST↓................................................................................3-233 stack calculations on............................................................... 1-2 stack operations depth .......................................
SYST2MAT ...................................................................3-245 System RPL......................................................................6-35 T TABVAL........................................................................3-246 TABVAR........................................................................3-247 TAG→ ...........................................................................3-247 tagged objects as program output.......................................................
UNTIL............................................................................3-265 UPDIR............................................................................3-265 UPs ..........................................................................6-21, 6-30 user input reading key .................................................................3-123 waiting.........................................................................3-272 user-defined errors..................................................
