Chapter 19 - Numbers in Different Bases, 19-1
Definitions, 19-1 The BASE menu, 19-1 Functions HEC, DEC, OCT and BIN, 19-2

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Conversion between number systems, 19-3 Wordsize, 19-4 Operations with binary integers, 19-4 The LOGIC menu, 19-5 The BIT menu, 19-6 The BYTE menu, 19-6 Hexadecimal numbers for pixel references, 19-7
Chapter 20 - Customizing menus and keyboard, 20-1
Customizing menus, 20-1 The PRG/MODES/MENU, 20-1 Menu numbers (RCLMENU and MENU functions), 20-2 Custom menus (MENU and TMENU functions), 20-2 Menu specification and CST variable, 20-4 Customizing the keyboard, 20-5 The PRG/MODES/KEYS sub-menu, 20-5 Recall current user-defined key list, 20-6 Assign an object to a user-defined key, 20-6 Operating user-defined keys, 20-6 Un-assigning a user-defined key, 20-7 Assigning multiple user-defined key, 20-7
Chapter 21 - Programming in User RPL language, 21-1
An example of programming, 21-1 Global and local variables and subprograms, 21-2 Global Variable Scope, 21-4 Local Variable Scope, 21-5 The PRG menu, 21-5 Navigating through RPN sub-menus, 21-6 Functions listed by sub-menu, 21-6 Shortcuts in the PRG menu, 21-9 Keystroke sequence for commonly used commands, 21-10 Programs for generating lists of numbers, 21-13 Examples of sequential programming, 21-15 Programs generated by defining a function, 21-15

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Programs that simulate a sequence of stack operations, 21-17 Interactive input in programs, 21-19 Prompt with an input string, 21-21 A function with an input string, 21-22 Input string for two or three input values, 21-24 Input through input forms, 21-27 Creating a choose box, 21-31 Identifying output in programs, 21-33 Tagging a numerical result, 21- 33 Decomposing a tagged numerical result into number and tag, 21-33 De-tagging a tagged quantity, 21-33 Examples of tagged output, 21-34 Using a message box, 21-37 Relational and logical operators, 21-43 Relational operators, 21-43 Logical operators, 21-44 Program branching, 21-46 Branching with IF, 21-46 The CASE construct, 21-51 Program loops, 21-53 The START construct, 21-53 The FOR construct, 21-59 The DO construct, 21-61 The WHILE construct, 21-62 Errors and error trapping, 21-64 DOERR, 21-64 ERRN, 21-64 ERRM, 21-65 ERR0, 21-65 LASTARG, 21-65 Sub-menu IFERR, 21-65 User RPL programming in algebraic mode, 21-66
Chapter 22 - Programs for graphics manipulation, 22-1
The PLOT menu, 22-1 User-defined key for the PLOT menu, 22-1

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Description of the PLOT menu, 22-2 Generating plots with programs, 22-14 Two-dimensional graphics, 22-14 Three-dimensional graphics, 22-15 The variable EQ, 22-15 Examples of interactive plots using the PLOT menu, 22-15 Examples of program-generated plots, 22-17 Drawing commands for use in programming, 22-19 PICT, 22-20 PDIM, 22-20 LINE, 22-20 TLINE, 22-20 BOX, 22-21 ARC, 22-21 PIX?, PIXON, and PIXOFF, 22-22 PVIEW, 22-22 PX C, 22-22 C PX, 22-22 Programming examples using drawing functions, 22-22 Pixel coordinates, 22-25 Animating graphics, 22-26 Animating a collection of graphics, 22-27 More information on the ANIMATE function, 22-29 Graphic objects (GROBs), 22-30 The GROB menu, 22-31 A program with plotting and drawing functions, 22-33 Modular programming, 22-36 Running the program, 22-36 A program to calculate principal stresses, 22-38 Ordering the variables in the sub-directory, 22-39 A second example of Mohrs circle calculations, 22-39 An input form for the Mohrs circle program, 22-40

Editing expressions in the screen
In this section we present examples of expression editing directly into the calculator display (algebraic history or RPN stack).
Creating arithmetic expressions
For this example, we select the Algebraic operating mode and select a Fix format with 3 decimals for the display. We are going to enter the arithmetic expression:

1.0 7.5 5.0 3.0 2.1.0 +

To enter this expression use the following keystrokes:

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5.*1.+1./7.5/ R3.-2.Q3 The resulting expression is: 5.*(1.+1./7.5)/(3.-2.^3). Press ` to get the expression in the display as follows:
Notice that, if your CAS is set to EXACT (see Appendix C) and you enter your expression using integer numbers for integer values, the result is a symbolic quantity, e.g., 5*1+1/7.5/ R3-2Q3 Before producing a result, you will be asked to change to Approximate mode. Accept the change to get the following result (shown in Fix decimal mode with three decimal places see Chapter 1):
In this case, when the expression is entered directly into the stack, as soon as you press `, the calculator will attempt to calculate a value for the expression. If the expression is entered between quotes, however, the calculator will reproduce the expression as entered. In the following example, we enter the same expression as above, but using quotes. For this case we set the operating mode to Algebraic, the CAS mode to Exact (deselect _Approx), and the display setting to Textbook. The keystrokes to enter the expression are the following: 5*1+1/7.5/ R3-2Q3`

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The result will be shown as follows:
To evaluate the expression we can use the EVAL function, as follows: ` As in the previous example, you will be asked to approve changing the CAS setting to Approx. Once this is done, you will get the same result as before. An alternative way to evaluate the expression entered earlier between quotes is by using the option. To recover the expression from the existing stack, use the following keystrokes: We will now enter the expression used above when the calculator is set to the RPN operating mode. We also set the CAS to Exact and the display to Textbook. The keystrokes to enter the expression between quotes are the same used earlier, i.e., 5*1+1/7.5/ R3-2Q3` Resulting in the output
Press ` once more to keep two copies of the expression available in the stack for evaluation. We first evaluate the expression using the function EVAL, and next using the function NUM. First, evaluate the expression using function EVAL. The resulting expression is semi-symbolic in the sense that there are floating-point components to the result, as well as a 3. Next, we switch stack locations and evaluate using function NUM: Exchange stack levels 1 and 2 (the SWAP command) Evaluate using function NUM

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Use the down arrow key () to select the option 2. MEMORY , or just press 2. Then, press @@OK@@. This will produce the following pull-down menu:
Use the down arrow key () to select the 5. DIRECTORY option, or just press 5. Then, press @@OK@@. This will produce the following pull-down menu:
Use the down arrow key () to select the 5. CRDIR option, and press @@OK@@. Command CRDIR in Algebraic mode Once you have selected the CRDIR through one of the means shown above, the command will be available in your stack as follows: At this point, you need to type a directory name, say chap1 : ~~~chap1~` The name of the new directory will be shown in the soft menu keys, e.g.,

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Command CRDIR in RPN mode To use the CRDIR in RPN mode you need to have the name of the directory already available in the stack before accessing the command. For example: ~~~chap2~` Then access the CRDIR command by either of the means shown above, e.g., through the N key:
Press the @@OK@ soft menu key to activate the command, to create the subdirectory:
Moving among subdirectories
To move down the directory tree, you need to press the soft menu key corresponding to the sub-directory you want to move to. The list of variables in a sub-directory can be produced by pressing the J (VARiables) key. To move up in the directory tree, use the function UPDIR, i.e., enter. Alternatively, you can use the FILES menu, i.e., press. Use the up and down arrow keys () to select the sub-directory you want to move to, and then press the !CHDIR (CHange DIRectory) or A soft menu key. This will show the contents of the sub-directory you moved to in the soft menu key labels.

Deleting subdirectories

To delete a sub-directory, use one of the following procedures: Using the FILES menu Press the key to trigger the FILES menu. Select the directory containing the sub-directory you want to delete, and press the !CHDIR if needed. This will close the FILES menu and display the contents of the directory you selected. In this case you will need to press `. Press the @@OK@@ soft menu

The display shows what is called a tagged value, Vm:359.0394. In here, Vm, is the tag of this result. Any arithmetic operation with this number will ignore the tag. Try, for example: 2*`, which produces:
The same operation in RPN mode will require the following keystrokes (after the value of Vm was extracted from the constants library): 2`*
Special physical functions
Menu 117, triggered by using MENU(117) in ALG mode, or 117 ` MENU in RPN mode, produces the following menu (labels listed in the display by using ):
The functions include: ZFACTOR: gas compressibility Z factor function FANNING: Fanning friction factor for fluid flow DARCY: Darcy-Weisbach friction factor for fluid flow F0: Black body emissive power function SIDENS: Silicon intrinsic density TDELTA: Temperature delta function

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In the second page of this menu (press L) we find the following items:
In this menu page, there is one function (TINC) and a number of units described in an earlier section on units (see above). The function of interest is: TINC: temperature increment command
Out of all the functions available in this MENU (UTILITY menu), namely, ZFACTOR, FANNING, DARCY, F0, SIDENS, TDELTA, and TINC, functions FANNING and DARCY are described in Chapter 6 in the context of solving equations for pipeline flow. The remaining functions are described following.

Function ZFACTOR

Function ZFACTOR calculates the gas compressibility correction factor for nonideal behavior of hydrocarbon gas. The function is called by using ZFACTOR(xT, yP), where xT is the reduced temperature, i.e., the ratio of actual temperature to pseudo-critical temperature, and yP is the reduced pressure, i.e., the ratio of the actual pressure to the pseudo-critical pressure. The value of xT must be between 1.05 and 3.0, while the value of yP must be between 0 and 30. Example, in ALG mode:

Function F0

Function F0 (T, ) calculates the fraction (dimensionless) of total black-body emissive power at temperature T between wavelengths 0 and. If no units are attached to T and , it is implied that T is in K and in m. Example, in ALG mode:

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Function SIDENS
Function SIDENS(T) calculates the intrinsic density of silicon (in units of 1/cm3) as a function of temperature T (T in K), for T between 0 and 1685 K. For example,

Function TDELTA

Function TDELTA(T0,Tf) yields the temperature increment Tf T0. The result is returned with the same units as T0, if any. Otherwise, it returns simply the difference in numbers. For example,
The purpose of this function is to facilitate the calculation of temperature differences given temperatures in different units. Otherwise, its simply calculates a subtraction, e.g.,

Function TINC

Also, you will see in your soft-menu key labels variables corresponding to those variables in the equation stored in EQ (press L to see all variables in your directory), i.e., variables ex, T, , z, y, n, x, and E. Example 2 Specific energy in open channel flow Specific energy in an open channel is defined as the energy per unit weight measured with respect to the channel bottom. Let E = specific energy, y = channel depth, V = flow velocity, g = acceleration of gravity, then we write

E = y+

V2. 2g
The flow velocity, in turn, is given by V = Q/A, where Q = water discharge, A = cross-sectional area. The area depends on the cross-section used, for example, for a trapezoidal cross-section, as shown in the figure below, A = (b+my) y, where b = bottom width, and m = side slope of cross section.

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We can type in the equation for E as shown above and use auxiliary variables for A and V, so that the resulting input form will have fields for the fundamental variables y, Q, g, m, and b, as follows: First, create a sub-directory called SPEN (SPecific ENergy) and work within that sub-directory. Next, define the following variables:
Launch the numerical solver for solving equations: @@OK@@. Notice that the input form contains entries for the variables y, Q, b, m, and g:
Try the following input data: E = 10 ft, Q = 10 cfs (cubic feet per second), b = 2.5 ft, m = 1.0, g = 32.2 ft/s2:

Solve for y.

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The result is 0.149836., i.e., y = 0.149836. It is known, however, that there are actually two solutions available for y in the specific energy equation. The solution we just found corresponds to a numerical solution with an initial value of 0 (the default value for y, i.e., whenever the solution field is empty, the initial value is zero). To find the other solution, we need to enter a larger value of y, say 15, highlight the y input field and solve for y once more:
The result is now 9.99990, i.e., y = 9.99990 ft. This example illustrates the use of auxiliary variables to write complicated equations. When NUM.SLV is activated, the substitutions implied by the auxiliary variables are implemented, and the input screen for the equation provides input field for the primitive or fundamental variables resulting from the substitutions. The example also illustrates an equation that has more than one solution, and how choosing the initial guess for the solution may produce those different solutions. In the next example we will use the DARCY function for finding friction factors in pipelines. Thus, we define the function in the following frame. Special function for pipe flow: DARCY (/D,Re) The Darcy-Weisbach equation is used to calculate the energy loss (per unit weight), hf, in a pipe flow through a pipe of diameter D, absolute roughness , and length L, when the flow velocity in the pipe is V. The equation is

To solve the linear system Ax = b, enter the matrix A, in the format [[ a11, a12, ], [.]] in the A: field. Also, enter the vector b in the B: field. When the X: field is highlighted, press [SOLVE]. If a solution is available, the solution vector x will be shown in the X: field. The solution is also copied to stack level 1. Some examples follow. A square system The system of linear equations 2x1 + 3x2 5x3 = 13, x1 3x2 + 8x3 = -13, 2x1 2x2 + 4x3 = -6, can be written as the matrix equation Ax = b, if
x1 , x = x , and A= 2 x

13 b = 13. 6

This system has the same number of equations as of unknowns, and will be referred to as a square system. In general, there should be a unique solution to the system. The solution will be the point of intersection of the three planes in the coordinate system (x1, x2, x3) represented by the three equations.

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To enter matrix A you can activate the Matrix Writer while the A: field is selected. The following screen shows the Matrix Writer used for entering matrix A, as well as the input form for the numerical solver after entering matrix A (press ` in the Matrix Writer):
Press to select the B: field. The vector b can be entered as a row vector with a single set of brackets, i.e., [13,-13,-6] @@@OK@@@. After entering matrix A and vector b, and with the X: field highlighted, we can press @SOLVE! to attempt a solution to this system of equations:
A solution was found as shown next.
To see the solution in the stack press `. The solution is x = [1,2,-1].
To check that the solution is correct, enter the matrix A and multiply times this solution vector (example in algebraic mode):

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Under-determined system The system of linear equations 2x1 + 3x2 5x3 = -10, x1 3x2 + 8x3 = 85, can be written as the matrix equation Ax = b, if
x A= , x = x2 , and 8 x3

10 b=. 85

This system has more unknowns than equations, therefore, it is not uniquely determined. We can visualize the meaning of this statement by realizing that each of the linear equations represents a plane in the three-dimensional Cartesian coordinate system (x1, x2, x3). The solution to the system of equations shown above will be the intersection of two planes in space. We know, however, that the intersection of two (non-parallel) planes is a straight line, and not a single point. Therefore, there is more than one point that satisfy the system. In that sense, the system is not uniquely determined. Lets use the numerical solver to attempt a solution to this system of equations: @@OK@@. Enter matrix A and vector b as illustrated in the previous example, and press @SOLVE when the X: field is highlighted:

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centered at the origin (0,0), will extend from -2 to 2 in x, and from -3 to 3 in y. Notice that for the circle and the ellipse the region corresponding to the left and right extremes of the curves are not plotted. This is the case with all circles or ellipses plotted using Conic as the TYPE. To see labels: @EDIT L@)LABEL @MENU To recover the menu: LL@)PICT To estimate the coordinates of the point of intersection, press the @(X,Y)@ menu key and move the cursor as close as possible to those points using the arrow keys. The coordinates of the cursor are shown in the display. For example, the left point of intersection is close to (-0.692, 1.67), while the right intersection is near (1.89,0.5).
To recover the menu and return to the PLOT environment, press L@CANCL. To return to normal calculator display, press L@@@OK@@@.

Parametric plots

Parametric plots in the plane are those plots whose coordinates are generated through the system of equations x = x(t) and y = y(t), where t is known as the parameter. An example of such graph is the trajectory of a projectile, x(t) = x0 + v0COS 0t, y(t) = y0 + v0sin 0t gt2. To plot equations like these, which involve constant values x0, y0, v0, and 0, we need to store the values of those parameters in variables. To develop this example, create a subdirectory called PROJM for PROJectile Motion, and within that sub-directory store the following variables: X0 = 0, Y0 = 10, V0 = 10 , 0 = 30, and g = 9.806. Make sure that the calculators angle measure is set to DEG. Next, define the functions (use ):

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X(t) = X0 + V0*COS(0)*t Y(t) = Y0 + V0*SIN(0)*t 0.5*g*t^2 which will add the variables @@@Y@@@ and @@@X@@@ to the soft menu key labels.
To produce the graph itself, follow these steps: Press , simultaneously if in RPN mode, to access to the PLOT SETUP window. Change TYPE to Parametric, by pressing @CHOOS @@@OK@@@. Press and type X(t) + i*Y(t) @@@OK@@@ to define the parametric plot as that of a complex variable. (The real and imaginary parts of the complex variable correspond to the x- and y-coordinates of the curve.) The cursor is now in the Indep field. Press ~t @@@OK@@@ to change the independent variable to t. Press L@@@OK@@@ to return to normal calculator display. Press , simultaneously if in RPN mode, to access the PLOT window (in this case it will be called PLOT PARAMETRIC window). Instead of modifying the horizontal and vertical views first, as done for other types of plot, we will set the lower and upper values of the independent variable first as follows: Select the Indep Low field by pressing. Change this value to 0@@@OK@@@. Then, change the value of High to 2@@@OK@@@. Enter 0. 1@@@OK@@@ for the Step value (i.e., step = 0.1). Note: Through these settings we are indicating that the parameter t will take values of t = 0, 0.1, 0.2, , etc., until reaching the value of 2.0. Press @AUTO. This will generate automatic values of the H-View and V-View ranges based on the values of the independent variable t and the definitions of X(t) and Y(t) used. The result will be:

Press @HELP to obtain a screen explaining the meaning of the confidence interval in terms of random numbers generated by a calculator. To scroll down the resulting screen use the down-arrow key. Press @@@OK@@@ when done with the help screen. This will return you to the screen shown above. To calculate the confidence interval, press @@@OK@@@. calculator is: The result shown in the

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The result indicates that a 95% confidence interval has been calculated. The Critical z value shown in the screen above corresponds to the values z/2 in the confidence interval formula (Xz/2/n , X+z/2/n ). The values Min and Max are the lower and upper limits of this interval, i.e., Min = Xz/2/n, and Max = X+z/2/n. Press @GRAPH to see a graphical display of the confidence interval information:
The graph shows the standard normal distribution pdf (probability density function), the location of the critical points z/2, the mean value (23.2) and the corresponding interval limits (21.88424 and 24.51576). Press @TEXT to return to the previous results screen, and/or press @@@OK@@@ to exit the confidence interval environment. The results will be listed in the calculators display. Example 2 -- Data from two samples (samples 1 and 2) indicate that x1 = 57.8 and x2 = 60.0. The sample sizes are n1 = 45 and n2 = 75. If it is known that the populations standard deviations are 1 = 3.2, and 2 = 4.5, determine the 90% confidence interval for the difference of the population means, i.e., 1- 2. Press @@@OK@@@to access the confidence interval feature in the calculator. Press @@@OK@@@ to select option 2. Z-INT: 1 2. Enter the following values:
When done, press @@@OK@@@. The results, as text and graph, are shown below:

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The variable represents 1 2. Example 3 A survey of public opinion indicates that in a sample of 150 people 60 favor increasing property taxes to finance some public projects. Determine the 99% confidence interval for the population proportion that would favor increasing taxes. Press @@@OK@@@to access the confidence interval feature in the calculator. Press @@@OK@@@ to select option 3. Z-INT: 1 2. Enter the following values:
Example 4 -- Determine a 90% confidence interval for the difference between two proportions if sample 1 shows 20 successes out of 120 trials, and sample 2 shows 15 successes out of 100 trials.

Through the use of the many calculator menus you have become familiar with the operation of menus for a variety of applications. Also, you are familiar with the many functions available by using the keys in the keyboard, whether through their main function, or by combining them with the left-shift (), right-shift () or ALPHA (~) keys. In this Chapter we provide examples of customized menus and keyboard keys that you may find useful in your own applications.

Customizing menus

A custom menu is a menu created by the user. The specifications for the menu are stored into the reserved variables CST. Thus, to create a menu you must put together this variable with the features that you want to display in your menu and the actions required by the soft menu keys. To show examples of customizing menus we need to set system flag 117 to SOFT menu. Make sure you do this before continuing (See Chapter 2 for instructions on setting system flags).

The PRG/MODES/MENU menu

Commands useful in customizing menus are provided by the MENU menu, accessible through the PRG menu (). Setting system flag 117 to SOFT menu, the sequence L @)MODES @)MENU produces the following MENU soft menu:
The functions available are: MENU: Activates a menu given its number CST: Reference to the CST variable, e.g., @@CST@@ shows CST contents. TMENU: Use instead of MENU to create a temporary menu without overwriting the contents of CST RCLMENU: Returns menu number of current menu

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Menu numbers (RCLMENU and MENU functions)
Each pre-defined menu has a number attached to it. For example, suppose that you activate the MTH menu (). Then, using the function catalog (N) find function RCLMENU and activate it. In ALG mode simple press ` after RCLMENU() shows up in the screen. The result is the number 3.01. Thus, you can activate the MTH menu by using MENU(3.01), in ALG, or 3.01 MENU, in RPN. Most menus can be activated without knowing their numbers by using the keyboard. There are, however, some menus not accessible through the keyboard. For example, the soft menu STATS is only accessible by using function MENU. Its number is 96.01. Use MENU(96.01) in ALG mode, or 96.01 MENU in RPN mode to obtain the STAT soft menu. Note: The number 96.01 in this example means the first (01) sub-menu of menu 96.

Programs generated by defining a function
These are programs generated by using function DEFINE () with an argument of the form: 'function_name(x1, x2, ) = expression containing variables x1, x2, ' The program is stored in a variable called function_name. When the program is recalled to the stack, by using function_name. The program shows up as follows: x1, x2, 'expression containing variables x1, x2, '.
To evaluate the function for a set of input variables x1, x2, , in RPN mode, enter the variables into the stack in the appropriate order (i.e., x1 first, followed by x2, then x3, etc.), and press the soft menu key labeled function_name. The calculator will return the value of the function function_name(x1, x2, ). Example: Mannings equation for wide rectangular channel. As an example, consider the following equation that calculates the unit discharge (discharge per unit width), q, in a wide rectangular open channel using Mannings equation:

Cu 5 / 3 y0 S0 n

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where Cu is a constant that depends on the system of units used [Cu = 1.0 for units of the International System (S.I.), and Cu = 1.486 for units of the English System (E.S.)], n is the Mannings resistance coefficient, which depends on the type of channel lining and other factors, y0 is the flow depth, and S0 is the channel bed slope given as a dimensionless fraction. Note: Values of the Mannings coefficient, n, are available in tables as dimensionless numbers, typically between 0.001 to 0.5. The value of Cu is also used without dimensions. However, care should be taken to ensure that the value of y0 has the proper units, i.e., m in S.I. and ft in E.S. The result for q is returned in the proper units of the corresponding system in use, i.e., m2/s in S.I. and ft2/s in E.S. Mannings equation is, therefore, not dimensionally consistent. Suppose that we want to create a function q(Cu, n, y0, S0) to calculate the unit discharge q for this case. Use the expression q(Cu,n,y0,S0)=Cu/n*y0^(5./3.)*S0, as the argument of function DEFINE. Notice that the exponent 5./3., in the equation, represents a ratio of real numbers due to the decimal points. Press J, if needed, to recover the variable list. At this point there will be a variable called @@@q@@@ in your soft menu key labels. To see the contents of q, use @@@q@@@. The program generated by defining the function q(Cu,n,y0,S0)is shown as: Cu n y0 S0 Cu/n*y0^(5./3.)*S0. This is to be interpreted as enter Cu, n, y0, S0, in that order, then calculate the expression between quotes. For example, to calculate q for Cu = 1.0, n = 0.012, y0 = 2 m, and S0 = 0.0001, use, in RPN mode: 1 ` 0.012 ` 2 ` 0.0001 ` @@@q@@@ The result is 2.6456684 (or, q = 2.6456684 m2/s).

Press @)PLOT to return to the PLOT menu.
Generating plots with programs
Depending on whether we are dealing with a two-dimensional graph defined by a function, by data from DAT, or by a three-dimensional function, you need to set up the variables PPAR, PAR, and /or VPAR before generating a plot in a program. The commands shown in the previous section help you in setting up such variables. Following we describe the general format for the variables necessary to produce the different types of plots available in the calculator.

Two-dimensional graphics

The two-dimensional graphics generated by functions, namely, Function, Conic, Parametric, Polar, Truth and Differential Equation, use PPAR with the format: { (xmin, ymin) (xmax, ymax) indep res axes ptype depend } The two-dimensional graphics generated from data in the statistical matrix DAT, namely, Bar, Histogram, and Scatter, use the PAR variable with the following format: { x-column y-column slope intercept model } while at the same time using PPAR with the format shown above. The meaning of the different parameters in PPAR and PAR were presented in the previous section.

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Three-dimensional graphics
The three-dimensional graphics available, namely, options Slopefield, Wireframe, Y-Slice, Ps-Contour, Gridmap and Pr-Surface, use the VPAR variable with the following format: {xleft, xright, ynear, yfar, zlow, zhigh, xmin, xmax, ymin, ymax, xeye, yeye, zeye, xstep, ystep} These pairs of values of x, y, and z, represent the following: Dimensions of the view parallelepiped (xleft, xright, ynear, yfar, zlow, zhigh) Range of x and y independent variables (xmin, xmax, ymin, ymax) Location of viewpoint (xeye, yeye, zeye) Number of steps in the x- and y-directions (xstep, ystep) Three-dimensional graphics also require the PPAR variable with the parameters shown above.

The variable EQ

All plots, except those based on DAT, also require that you define the function or functions to be plotted by storing the expressions or references to those functions in the variable EQ. In summary, to produce a plot in a program you need to load EQ, if required. Then load PPAR, PPAR and PAR, or PPAR and VPAR. Finally, use the name of the proper plot type: FUNCTION, CONIC, POLAR, PARAMETRIC, TRUTH, DIFFEQ, BAR, HISTOGRAM, SCATTER, SLOPE, WIREFRAME, YSLICE, PCONTOUR, GRIDMAP, or PARSURFACE, to produce your plot.
Examples of interactive plots using the PLOT menu
To better understand the way a program works with the PLOT commands and variables, try the following examples of interactive plots using the PLOT menu. Example 1 A function plot: C Get PLOT menu (*) @)PTYPE @FUNCT Select FUNCTION as the plot type r ` @@EQ@@ Store function r into EQ

In this particular case we can give values to all but one of the variables, say, n = 10, I%YR = 8.5, PV = 10000, FV = 1000, and solve for variable PMT (the meaning of these variables will be presented later). Try the following: 10 @@OK@@ 8.5 @@OK@@ 10000 @@OK@@ 1000 @@OK@@ @SOLVE! The resulting screen is: Enter n = 10 Enter I%YR = 8.5 Enter PV = 10000 Enter FV = 1000 Select and solve for PMT
In this input form you will notice the following soft menu key labels: @EDIT !)AMOR @SOLVE Press to edit highlighted field Amortization menu - option specific to this application Press to solve for highlighted field
Pressing L we see the following soft menu key labels:

!RESET

Reset fields to default values

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!CALC !TYPES !CANCL @@OK@@
Press to access the stack for calculations Press to determine the type of object in highlighted field Cancel operation Accept entry
If you press !RESET you will be asked to select between the two options:
If you select Reset value only the highlighted value will be reset to the default value. If, instead, you select Rest all, all the fields will be reset to their default values (typically, 0). At this point you can accept your choice (press @@OK@@), or cancel the operation (press !CANCL). Press !CANCL in this instance. Press !CALC to access the stack. The resulting screen is the following:
At this point, you have access to the stack, and the value last highlighted in the input form is provided for you. Suppose that you want to halve this value. The following screen follows in ALG mode after entering 1136.22/2:

Page A-3

(In RPN mode, we would have used 1136.22 ` 2 `/). Press @@OK@@ to enter this new value. The input form will now look like this:
Press !TYPES to see the type of data in the PMT field (the highlighted field). As a result, you get the following specification:
This indicates that the value in the PMT field must be a real number. Press @@OK@@ to return to the input form, and press L to recover the first menu. Next, press the ` key or the $ key to return to the stack. In this instance, the following values will be shown:
The top result is the value that was solved for PMT in the first part of the exercise. The second value is the calculation we made to redefine the value of PMT.

Page H-1

You can type two or more letters of the command of interest, by locking the alphabetic keyboard. This will take you to the command of interest, or to its neighborhood. Afterwards, you need to unlock the alpha keyboard, and use the vertical arrow keys to locate the command, if needed. Press @@OK@@ to locate the to activate the command. For example, to locate the command PROPFRAC, you can use, one of the following keystroke sequences: I L@HELP ` ~~pr ~ @@OK@@ I L@HELP ` ~~pro ~ @@OK@@ I L@HELP ` ~~prop ~ @@OK@@
See Appendix C for more information on the CAS (Computer Algebraic System). Appendix C includes other examples of application of the CAS help facility.

Page H-2

Appendix I Command catalog list
This is a list of all commands in the command catalog (N). Those commands that belong to the CAS (Computer Algebraic System) are listed also in Appendix H. CAS help facility entries are available for a given command if the soft menu key @HELP shows up when you highlight that particular command. Press this soft menu key to get the CAS help facility entry for the command. The first few screens of the catalog are shown below:
User-installed library commands would also appear on the command catalog list, using italic font. If the library includes a help item, then the soft menu key @HELP shows up when you highlight those user-created commands.

Page I-1

Appendix J The MATHS menu
The MATHS menu, accessible through the command MATHS (available in the catalog N), contains the following sub-menus:

The CMPLX sub-menu

The CMPLX sub-menu contains functions pertinent to operations with complex numbers:
These functions are described in Chapter 4.

The CONSTANTS sub-menu

The CONSTANTS sub-menu provides access to the calculator mathematical constants. These are described in Chapter 3:

Page J-1

The HYPERBOLIC sub-menu
The HYPERBOLIC sub-menu contains the hyperbolic functions and their inverses. These functions are described in Chapter 3.

The INTEGER sub-menu

The INTEGER sub-menu provides functions for manipulating integer numbers and some polynomials. These functions are presented in Chapter 5:

Understanding Programming
An hp49g+/hp48gII program is an object with delimiters containing a sequence of numbers, commands, and other objects you want to execute automatically to perform a task. For example, a program that takes a number from the stack, finds its factorial, and divides the result by 2 would look like this: ! 2 / or ! 2 /
The Contents of a Program
As mentioned above, a program contains a sequence of objects. As each object is processed in a program, the action depends on the type of object, as summarized below. Actions for Certain Objects in Programs Object Command Number Algebraic or `Algebraic` String List Program Global name (quoted) Global name (unquoted) Action Executed. Put on the stack. Algebraic put on the stack. Put on the stack. Put on the stack. Put on the stack. Put on the stack.

! ! ! !

Program executed. Name evaluated. Directory becomes current. Other object put on the stack.
Local name (quoted) Local name (unquoted)
Put on the stack. Contents put on the stack
As you can see from this table, most types of objects are simply put on the stack but built-in commands and programs called by name cause execution. The following examples show the results of executing programs containing different sequences of objects.

RPL Programming 1-1

Examples of Program Actions Program "Hello" {A B} '1+2' '1+2' NUM + + EVAL Results 2: 1: 2: 1: 1: 1: 1: 1: "Hello" { A B } '1+2' 2 + 3
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. The command defines local variable names and a corresponding algebraic or program object that's evaluated using those variables. ! Branching structures. Structure words (like DO UNTILEND) define conditional or loop structures to control the order of execution within a program.
A local variable structure has one of the following organizations inside a program: name1 namen ' algebraic ' name1 namen program The " command removes n objects from the stack and stores them in the named local variables. The algebraic or program object in the structure is automatically evaluated because its an element of the structure even though algebraic and program objects are put on the stack in other situations. Each time a local variable name appears in the algebraic or program object, the variables contents are substituted. So the following program takes two numbers from the stack and returns a numeric result: a b 'ABS(a-b)'

Program: "Key in S.S. #" { " - " -1}
Comments: 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.
INPUT DUP SUB SWAP SUB 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. Program that contain input forms or choose boxes wait until you acknowledge them (%OK% or ) before they continue execution. If OK is pressed, CHOOSE returns the selected item (or its designated returned value) to level 2 and a 1 to level 1. INFORM returns a list of field values to level 2 and 1 to level 1. Both the INFORM and CHOOSE commands return 0 if CANCEL is pressed.

1-42 RPL Programming

To set up an input form: 1. Enter a title string for the input for the input form (use @). 2. Enter a list of field specifications. 3. Enter a list of format options. 4. Enter a list of reset values (values that appear when RESET is pressed). 5. Enter a list of default values. 6. Execute the INFORM command. Example: Enter a title "FIRST ONE" `. Specify a field { "Name:" } `. Enter format options (one column, tabs stop width five) { } `. Enter reset value for the field {"THERESA"} `. Enter default value for the field {"WENDY"} `. Execute INFORM (!L%IN% %INFOR%). The screen on the left appears. Press L%RESET% %OK% and the screen on the right appears.
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. If this is a list of two-element lists, the first element is displayed in the choose box, and the second element is returned to level 2 when OK is pressed. 3. Enter a position number for the default highlighted item. (0 makes a view-only choose box.) 4. Execute the CHOOSE command. Example: Enter a title "FIRST ONE" `. Enter a list of items {ONE TWO THREE } `. Enter a position number for default highlighted value 3 `. Execute CHOOSE (!L%IN% %CHOOS%). Example: The following choose box appears:
Example: The following program uses input forms, choose boxes, and message boxes to create a simple phone list database.

RPL Programming 1-43

Program: 'NAMES' VTYPE IF -1 == THEN{ } 'NAMES' STO END WHILE "PHONELIST OPTIONS:" { { "ADD A NAME" 1} { "VIEW A NUMBER" 2 } } 1 CHOOSE

10 RND IP n 0

i m k "" DO 'm' EVAL b i 'k' EVAL - ^ DUP2 MOD
IF DUP 0 == 'm' EVAL b AND THEN 1 SF END 'm' STO / IP
IF DUP 10 THEN 55 ELSE 48 END + CHR + 'k' 1 STO+
RPL Programming Examples 2-23
Program: UNTIL 'm' EVAL 0 == END IF 1 FS?C THEN "0" + WHILE i 'k' EVAL - 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. Begin WHILE.REPEAT loop to determine if additional placeholding zeros are needed. Loop repeats as long as i k. Add an additional placeholding zero and increment k before repeating the testclause. End the WHILE.REPEAT.END loop, the IF.THEN.END structure, and the inner local variable structure. End the outermost IF.THEN.ELSE.END structure and create the label string and tag the result string using the original arguments. Also restore original flag settings.
REPEAT "0" + 1 'k' STO+ END END " base" b + n SWAP + TAG f STOF
`OnBASE K Checksum: # 54850d Bytes: 433 Example: Convert 100010 to base 23. 1000 `23 J %NBASE% Stores the program in nBASE.
Verifying Program Arguments
The two utility programs in this section verify that the argument to a program is the correct object type.
NAMES verifies that a list argument contains exactly two names. VFY verifies that the argument is either a name or a list containing exactly two names. It calls NAMES if the argument is a list.
You can modify these utilities to verify other object types and object content.
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.
2-24 RPL Programming Examples
{ valid list } { invalid list }
(error message in status area)

Techniques used in NAMES

Nested conditionals. The outer conditional verifies that there are two objects in the list. If so, the inner conditional verifies that both objects are names. Logical functions. NAMES uses the AND command in the inner conditional to determine if both objects are names, and the NOT command to display the error message if they are not both names.
NAMES program listing Program: IF OBJ Comments: Starts the outer conditional structure. Returns the n objects in the list to levels 2 through (n + 1), and returns the list size n to level 1. Copies the list size and tests if it's 2. If the size is 2, moves the objects to level 1 and 2, and starts the inner conditional structure. Tests if the object is a name: returns 1 if so, otherwise 0. Moves the second object to level 1, then tests if it is a name (returns 1 or 0). Combines test results: Returns 1 if both tests were true, otherwise returns 0.

objsymb

NUM Type: Command Description: Character Number Command: Returns the character code n for the first character in the string. The character codes are an extension of ISO 8859/1. 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. Access: !TYPE LNUM ( is the left-shift of the Nkey). ! LCHARS NUM ( is the left-shift of the Nkey). &N NUM Input/Output:
string CHR, POS, REPL, SIZE, SUB
NUMX Type: Command Description: Number of X-Steps Command: Sets the number of x-steps for each y-step in 3D perspective plots. The number of x-steps is the number of independent variable points plotted for each dependent variable point plotted. This number must be 2 or more. This value is stored in the reserved variable VPAR. YSLICE is the only 3D plot type that does not use this value. Access: NUMX Input/Output:
NUMY Type: Command Description: Number of Y-Steps Command: Sets the number of y-steps across the view volume in 3D perspective plots. The number of y-steps is the number of dependent variable points plotted across the view volume. This number must be 2 or more. This value is stored in the reserved variable VPAR. Access: NUMY Input/Output:
3-112 Full Command and Function Reference
OBJ Type: Command Description: Object to Stack Command: Separates an object into its components. For some object types, the number of components is returned as item n+1 (stack level 1). If the argument is a complex number, list, array, or string, OBJ provides the same functions as CR, LIST, ARRY, and STR, respectively. For lists, OBJ also returns the number of list elements. If the argument is an array, OBJ also returns the dimensions { m n } of the array, where m is the number of rows and n is the number of columns. For algebraic objects, OBJ returns the arguments of the top-level (least-nested) function (arg1 argn), the number of arguments of the top-level function (n), and the name of the top-level function (function). If the argument is a string, the object sequence defined by the string is executed. Access: !TYPE OBJ ( is the left-shift of the Nkey). !LIST OBJ ( is the left-shift of the Nkey). &NL OBJ !LCHARS LOBJ ( is the left-shift of the Nkey). Input/Output:

Full Command and Function Reference 3-159

[[ matrix ]]T

LQ, LU, QR, SVD, SVL, TRN
SCI Type: Command Description: Scientific Mode Command: Sets the number display format to scientific mode, which displays one digit to the left of the fraction mark and n significant digits to the right. Scientific mode is equivalent to scientific notation using n + 1 significant digits, where 0 n 11. (Values for n outside this range are rounded to the nearest integer.) In scientific mode, numbers are displayed and printed like this: (sign) mantissa E (sign) exponent where the mantissa has the form n.(n ) and has zero to 11 decimal places, and the exponent has one to three digits. Access: & H FMT SCI L MODES FMT SCI ( is the left-shift of the Nkey). Input/Output:

ENG, FIX, STD

SCL Type: Command Description: Scale Sigma Command: Adjusts (xmin, y min) and (xmax, ymax) in PPAR so that a subsequent scatter plot exactly fills PICT. When the plot type is SCATTER, the command AUTO incorporates the functions of SCL. In addition, the command SCATRPLOT automatically executes AUTO to achieve the same result. Access: SCL Input/Output: None See also: AUTO, SCATRPLOT SCONJ Type: Command Description: 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. Access: !MEMORY ARITHMETIC LSCONJ ( is the left-shift of the Nkey). Input/Output:

CONJ, SINV, SNEG

SCROLL Type: Command Description: Displays any object. This is the programmable equivalent of pressing I%VIEW% and is the best way to view any object larger than the screen, such as complicated algebraic expressions. Access: SCROLL
3-160 Full Command and Function Reference
SDEV Type: Command Description: Standard Deviation Command: Calculates the sample standard deviation of each of the m columns of coordinate values in the current statistics matrix (reserved variable DAT). SDEV returns a vector of m real numbers, or a single real number if m = 1. The standard deviation (the square root of the variances) is computed using this formula:
----------- ( x i x ) n 1i = 1 n
where xi is the ith coordinate value in a column, the number of data points. Access: SDEV Input/Output:
is the mean of the data in this column, and n is
xsdev [ xsdev 1 xsdev 2. xsdev m ]
MAX, MEAN, MIN, PSDEV, PVAR, TOT, VAR
SEND Type: Command Description: Send Object Command: Sends a copy of the named objects to a Kermit device. 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. Access: SEND Flags: I/O Device flag (-33), I/O Data Format (-35), I/O Messages (-39) Input/Output:

xT x_unit 'symb'

xdensity x_1/cm3 'SIDENS(symb)'

SIGMA CAS:

For given variable y, calculate discrete antiderivative G of given function f : G(y + 1) G(y) = f(y).
SIGMAVX CAS: For current variable x, calculate discrete antiderivative G of function f : G(x + 1) G(x) = f(x). SIGN Type: Function Description: Sign Function: Returns the sign of a real number argument, the sign of the numerical part of a unit object argument, or the unit vector in the direction of a complex number argument. For real number and unit object arguments, the sign is defined as +1 for positive arguments, 1 for negative arguments. In exact mode, the sign for argument 0 is undefined (?). In approximate mode, the sign for argument 0 is 0. SIGN in the !menu returns the sign of a number, while SIGN in the menu returns returns the unit vector of a complex number. For a complex argument:
iy x SIGN ( x + iy ) = -------------------- + -------------------x +y x +y
! REAL LSIGN L SIGN Numerical Results (-3)
( is the left-shift of the Pkey). ( is the right-shift of the 1key).
Full Command and Function Reference 3-163

z1 x_unit 'symb'

z2 xsign 'SIGN(symb)'

ABS, MANT, XPON

SIGNTAB CAS: Tabulate the sign of a rational function of the current CAS variable. SIMP2 CAS: SIMPLIFY
Simplify two objects by dividing them by their greatest common divisor. Simplify an expression.
SIN Type: Analytic function Description: Sine Analytic Function: Returns the sine of the argument. For real arguments, the current angle mode determines the number's units, unless angular units are specified. For complex arguments, sin(x + iy) = sinx coshy + i cosx sinhy. If the argument for SIN 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. Therefore, to correctly integrate or differentiate expressions containing SIN with a unit object, the angle mode must be set to radians (since this is a neutral mode). S Access: Flags: Numerical Results (-3), Angle Mode (-17, -18) Input/Output:

z x_unitangular 'symb'

sin z sin(x_unitangular) 'SIN(symb)'
ASIN, COS, TAN Convert logarithmic and exponential expressions to expressions with trigonometric terms.

SINCOS

SINH Type: Analytic function Description: Hyperbolic Sine Analytic Function: Returns the hyperbolic sine of the argument. For complex arguments, sinh(x + iy) = sinhx cosy + i coshx siny. Access: HYPERBOLIC SINH ( is the right-shift of the 8key). ! HYPERBOLIC SINH ( is the left-shift of the Pkey). Flags: Numerical Results (-3)

ASR, SL, SLB, SR

SRECV Type: Command Description: Serial Receive Command: Reads up to n characters from the serial input buffer and returns them as a string, along with a digit indicating whether errors occurred. SRECV does not use Kermit protocol. If n characters are not received within the time specified by STIME (default is 10 seconds), SRECV times out, returning a 0 to level 1 and as many characters as were received to level 2.
Full Command and Function Reference 3-169
If the level 2 output from BUFLEN is used as the input for SRECV, SRECV will not have to wait for more characters to be received. Instead, it returns the characters already in the input buffer. If you want to accumulate bytes in the input buffer before executing SRECV, you must first open the port using OPENIO (if the port isn't already open). SRECV can detect three types of error when reading the input buffer: Framing errors and UART overruns (both causing "Receive Error" in ERRM). Input-buffer overflows (causing "Receive Buffer Overflow" in ERRM). Parity errors (causing "Parity Error" in ERRM). SRECV returns 0 if an error is detected when reading the input buffer, or 1 if no error is detected. Parity errors do not stop data flow into the input buffer. However, if a parity error occurs, SRECV stops reading data after encountering a character with an error. Framing, overrun, and overflow errors cause all subsequently received characters to be ignored until the error is cleared. SRECV does not detect and clear any of these types of errors until it tries to read the byte where the error occurred. Since these three errors cause the byte where the error occurred and all subsequent bytes to be ignored, the input buffer will be empty after all previously received good bytes have been read. Therefore, SRECV detects and clears these errors when it tries to read a byte from an empty input buffer. 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. To find where the data error occurred, save the number of characters returned by BUFLEN (which gives the number of good characters received), because as soon as the error is cleared, new characters can enter the input buffer. Access: SRECV Flags: I/O Device (-33) Input/Output:

DROITE Type: Description:
Example 1: Find an equation for the straight line through the points (1, 2), (3, 4). Command: DROITE((1, 2), (3, 4)) Result: Y=X-1.+2. Example 2: Find a symbolic equation for the straight line through the points (, e), (e, ). Command: With constants to symbolic mode selected and exact mode set, type:

DROITE(+e*i, e+*i)

Y=(-e)/(e-)*(X-)+e
LAGRANGE Function Differential of a function with respect to its argument n. For example d1f(x,y) is the differential of f(x,y) with respect to x and d3g(y,z,t) is the differential of g(y,z,t) with respect to t. The second-order derivative of f(x,y) with respect to x is written d1d1f(x,y). The dn function is an alternative to the function; d1f(x,y) is the same as x(f(x,y)). dn does not require brackets after it, it must be followed immediately by the function name, with no spaces. dn differentiates with respect to the whole of argument n, see the example. dn is mainly used for formal arguments, see the example in DESOLVE, but can be used to differentiate expressions, as in the example.

dn Type: Description:

4-26 Computer Algebra Commands

Access: Output: Flags:

Access is by typing the letter d from the alpha keyboard, followed by the number n, before the function whose differential is required. dn does not change its argument, it works like the negative sign placed before a number or an expression. If the argument can be differentiated, N will carry out the differentiation. 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: Differentiate the function sin(2x) with respect to its argument: Command: EVAL(d1SIN(2*X)) Result: COS(2*X) (Note that the function was differentiated with respect to its argument 2x, not with respect to the variable x.) See also: DERIV, DERVX, DESOLVE, Command Given two polynomials, a and b, returns polynomials u, v, and c where: au+bv=c In the equation, c is the greatest common divisor of a and b. Arithmetic, !POLYNOMIAL Level 2/Argument 1: The expression corresponding to a in the equation. Level 1/Argument 2: The expression corresponding to b in the equation. Level 3/Item 1: The result corresponding to c in the equation. Level 2/Item 2: The result corresponding to u in the equation. Level 1/Item 3: The result corresponding to v in the equation. 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). Find the polynomials for u, v, and c, where c is the greatest common divisor of a and b such that:

Example: Express eix in trigonometric terms. Command: SINCOS(EXP(i*X)) Result: COS(X)+iSIN(X) See also: EXPLN Command Finds zeros of an expression equated to 0, or solves an equation. Symbolic solve, !, P SOLVE, L 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. A zero or solution, or a list of zeros or solutions. Radians mode must be set (flag 17 set). If exact mode is set (flag 105 clear) and there are no exact solutions, the command returns a null list even when there are approximate solutions. Radians mode must be set (flag 17 set). If complex mode is set (flag 103 set) then SOLVE will search for complex roots as well as real ones. Complex roots are displayed according to the coordinate system selected. Find the zeros of the following expression:

SOLVE Type: Description:

Command: SOLVE(X^3-X-9,X) Result: X=2.24004098747 Example 2: Find the real and complex roots of the two equations: x 1=3 , x A= 0 Command: Clear numeric mode, clear approximate mode, set complex mode, set rectangular mode, enter:
SOLVE({X^4-1=3,X^2-A=0},X)
{{X=2i,X=2-1,X=-(2i),X=2}, {X=A-1,X=A}} Note that in this case, imaginary solutions for X are returned, even if X is in

REALASSUME.

DESOLVE, LDEC, LINSOLVE, MSLV, QUAD, SOLVEVX
Computer Algebra Commands 4-67
SOLVEVX Type: Description:
Command Finds zeros of an expression with respect to the current variable, or solves an equation with respect to the current variable. (You use the CAS modes input form to set the current variable.) Symbolic solve, !, P SOLVE An expression or equation in the current variable. A list of equations and expressions can be given too, each will be solved for the current variable. A zero or solution, or a list of zeros or solutions. Radians mode must be set (flag 17 set). For a symbolic result, clear the CAS modes numeric option (flag -3 clear). If Exact mode is set (flag 105 clear) and there are no exact solutions, the command returns a null list even when there are approximate solutions. If complex mode is set (flag 103 set) then SOLVE will search for complex roots as well as real ones. Complex roots are displayed according to the coordinate system selected. Solve the following expression for 0, where X is the default variable on the calculator:
Command: SOLVEVX(X^3-X-9) Result: X=2.24004098747 Note that if exact mode is set, this example returns a null list as there are no exact solutions to the equation. See also: LINSOLVE, SOLVE 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. Catalog, Level 2/Argument 1: A number or an expression that evaluates to a numeric value. Level 1/Argument 2: The name of the variable in which the number is to be stored. If this variable does not already exist in the current directory path then it is created. Level 1/Item 1: The number to which the first argument is evaluated, and which is stored in the variable. Exact mode must be set (flag 105 clear). Numeric mode must not be set (flag -3 clear). Store in variable Z the result of calculating 17*Y. Assume that Y contains the integer number 2.

Bernoulli Equation (3, 2)
These equations represent the streamlined flow of an incompressible fluid.

Equation Reference 5-19

P v 2 v 1 ------ + ----------------------- + g y = 2 Av 2 1 ------ A1 P ------ + -------------------------------------------- + g y = 2 Av 1 ------ 1 A1 P ------ + -------------------------------------------- + g y = P = P 2 P 1 y = y2 y 1
Q = A2 v2 D1 A 1 = ----------------4
Q = A1 v1 D2 A 2 = ----------------4
Example: Given: P2=25_psi, P1=75_psi, y2=35_ft, y1=0_fr, D1=18_in, =64_lb/ft^3, v1=100_ft/s. Solution: Q=10602.8752_ft^3/min, M=678584.0132_lb/min, v2=122.4213_ft/s, A2=207.8633_in^2, D2=16.2684_in, A1=254.4690_in^2, P= -50_psi, y=35_ft.

Flow with Losses (3, 3)

These equations extend Bernoulli's equation to include power input (or output) and head loss.
P v 2 v 1 M ------ + ----------------------- + g y + h L = W 2 A2 v 2 1 ------ A1 P M ------ + -------------------------------------------- + g y + h L = W 2
2 A v 1 ------- 1 A2 P M ------ + -------------------------------------------- + g y + h L = W 2 2 2

P = P 2 P 1

y = y 2 y 1
Q = A 1 v1 D2 A 2 = ----------------4

5-20 Equation Reference

Example: Given: P2=30_psi, P1=65_psi, y2=100_ft, y1=0_ft, =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.)
P L ----D-- v a v g --- + g y + v a v g 2 2 f --- + K = W --- - --- -------- 4 D 2 P = P 2 P 1 Q = A vavg y = y 2 y 1

D A = -------------4

D vavg R e = ----------------------------

n = -

Example: Given: =62.4_lb/ft^3, D=12_in, vavg= 8_ft/s, P2=15_psi, P1=20_psi, y2=40_ft, y1=0_ft, =0.00002_lbfs/ft^2, K=2.25, =0.02_in, L=250_ft. Solution: P=-5_psi, y=40_ft, A=113.0973_in^2, n=1.0312_ft^2/s, Q=376.9911_ft^3/min, M=23524.2358_lb/min, W=25.8897_hp, Re=775780.5.

Forces and Energy (4)

Variable
Description Angular acceleration Angular acceleration Initial and final angular velocities Fluid density Torque Angular displacement Acceleration

EQUCP 5 Foo

Defines a Foo constant with a value of $10 and then change the value of CP to $15. Several constants can be defined at once using CP.
The Development Library 6-11
: Inc CstName0 CstName1. CstNameN-1 : Defines N constants CstNamex with a value of CP+x*Inc and then changes the CP value to CP+N*Inc.
By default, Inc is a decimal number or an expression that can be immediately evaluated. These features are extremely useful to define area of memory for storage of ASM program variables. Note 1: If the entry point library (see related section) is installed on your calculator, all the values in the constant library will be available in your programs the same way than constants are. Note 2: You can define a constant in your program to override the value of an entry in the equation library.

4.1.10

Expressions
An expression is a mathematical operation that is calculated at compilation time. Terms of this operation are hexadecimal or decimal values, constants or labels. An expression stops on a separation character or a ].
DCCP 5 @Data. D1=(5)@Data+$10/#2 D0=(5)$5+DUP LC(5)"DUP"+#5
are correct expressions (provided that the entry point library is installed). Notes: A hexadecimal value must begin with a $. A decimal value may begin with a # or a number directly. A & or (*) equals the offset of the current instruction in the program (This value has no meaning in itself, but may be used to calculate the distance between a label and the current instruction). In absolute mode, this represents the final address of the instruction. The value of a label is the offset of the label in the program (This value has no meaning in itself, but may be used to calculate the distance between a label and the current instruction). In absolute mode, this represents the final address of the instruction. 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, its compiled at the end of the compilation. In order to use less memory, its a good idea to define your constants at the beginning of the sources so MASD can compile expression using the constants directly. The only operator symbols not allowed in labels are +, -, * and /; therefore, if you want to use a symbol operator after a label, you must put the symbol between " in order to limit the symbol. Meaningless Example: "DUP"<<5. A label/constant with strange char may be protected between " chars. The evaluation stack of MASD allows you to have around 10 pending computations (parenthesis, operator priority). MASD only works with integers. You can represent signed values using standard 2s complement, but be careful as all operators are unsigned.

The Development Library 6-19
Syntax Reg1=Reg1^Reg2.f Reg1^Reg2.f Reg1=-Reg1.f Reg1=-Reg1-1.f Reg1=~Reg1.f RReg=Reg.f Reg=RReg.f RegRRegEX.f Data=Reg.f Data=Reg.x Reg= Data.f Reg Data.x DReg=hh DReg=hhhh DReg=hhhhh DReg=(2)Exp DReg=(4)Exp DReg=(5)Exp Dreg=Reg Dreg=RegS
Example A=A^B.X A^C.B C=-C.A C=-C-1.A C=~C.A R0=A.W A=R0.A AR0EX.A DAT1=C.A DAT0=A.10 C=DAT1.A A=DAT0.10 D0=AD D0=0100 D0=80100 D0=(2)label D0=(4)lab+$10 D1=(5)Variable D0=A D0=CS
Notes Logical xor on the specified field Mathematical not on the specified field Logical not on the specified field Sets the specified field of RReg to the value of the specified field of Reg Only A and C are valid for Reg. If f is W, the shorter encoding of the instruction is used Sets the specified field of Reg to the value of the specified field of RReg Only A and C are valid for Reg. If f is W, the shorter encoding of the instruction is used Exchanged the value of the specified field of RReg with the value of the specified field of Reg Only A and C are valid for Reg. If f is W, the shorter encoding of the instruction is used Write the content of the specified field of the specified register in the memory location pointed by Data register (POKE) Reg can only be A or C Read the content of the memory location pointed by Data register in the specified field of the REG register (PEEK) Reg can only be A or C 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 nibble 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 nibble of Reg AD1XS Reg can only be A or C Note 1: The Saturn processor is not able to add a constant greater than 16 DReg=DReg+Cst D0=D0+12 D1+25 to a register but if cst is greater than 16, MASD will generate as many DReg+Cst D1=D1-12 instructions as needed. DReg=DReg-Cst D1-5 DReg-Cst Note 2: Even if adding constants to a register is very useful, big constants should be avoided because this will slow down execution, and generate a big program. Note 3: After adding a constant greater than 16, the carry should not be tested. Note 4: You can put an expression instead of the constant (MASD must be able to evaluate the expression strait away). If the expression is negative, MASD will invert the addition in a subtraction and vice versa. Note 5: Be careful when using subtraction; its easy to be misled. D0-5-6.A is equivalent to D0+1.A, not D0-11.A Please read the section on test above for information on what MUST follow a test instruction. f can NOT be a Fn field. ?Reg1=Reg2.f ?A=C.B ?Reg1#Reg2.f The HP special character can also be used ?A#C.A ?Reg=0.f ?A=0.B ?Reg#0.f The HP special character can also be used ?A#0.A ?Reg1<Reg2.f ?A<B.X ?Reg1>Reg2.f ?C>D.W ?Reg1<=Reg2.f The HP <= character can be used ?A<=B.X ?Reg1>=Reg2.f The HP >= character can be used ?C>=D.W Test if a specific bit of A or C register is 0 or 1 ?RegBIT=0.a ?ABIT=0.5 ?ABIT=1.number Reg must be A or C ?RegBIT=1.a

Default Value Current date.

Time ("TIME)

00.0000

action

Empty string (appointment alarm).

Repeat

A real number specifying the 0 interval between automatic recurrences of the alarm, given in ticks ( a tick is 1/8192 of a second ).
Parameters without commands can be modified with a program by storing new values in the list contained in ALRMDAT ( use the PUT command ).
This is the vectored ENTER post-processor. If flags -62 and -63 are set and ENTER is pressed, the command that triggered the command-line processing is put on the stack as a string and ENTER is evaluated.
CST contains a list ( or a name specifying a list ) of the objects that define the CST ( custom ) menu. Objects in the custom menu behave as do objects in built-in menus. For example:
Names behave like the VAR menu keys. Thus, if ABC is a variable name, %ABC% evaluates ABC, %ABC% recalls its contents, and %ABC% stores new contents in ABC. The menu label for the name of a directory has a bar over the left side of the label; pressing the menu key switches to that directory. Unit objects act like unit catalog entries ( and have left-shifted conversion capabilities, for example ). String keys echo the string. You can include backup objects in the list defining a custom menu by tagging the name of the backup object with its port location.

Reserved Variables D - 3

You can specify menu labels and key actions independently by replacing a single object within the custommenu 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.

ENVSTACK

ENVSTACK is a variable stored in the CAS directory. It is used by PUSH and POP to save the status of flags and the current directory. (PUSH saves the data in ENVSTACK; POP restores it.)
EQ contains the current equation or the name of the variable containing the current equation, EQ supplies the equation for ROOT, as well as for the plotting command DRAW. (DAT supplies the information when the plot type is HISTOGRAM, BAR, or SCATTER.) The object in EQ can be an algebraic object, a number, a name, or a program. How DRAW interprets EQ depends on the plot type. For graphics use, EQ can also be a list of equations or other objects. If EQ contains a list, then DRAW treats each object in turn as the current equation, and plots them successively. However, ROOT in the HP Solve application cannot solve an EQ containing al list. To alter the contents of EQ, use the command STEQ.