5. Highlight the f function variable, and view its contents. Notice that the function was assigned using f(x) but is listed as f on the screen. Press D 2 6. Close the Contents window. Press N 7. With the f variable still highlighted, close VAR-LINK to paste the contents of the variable to the entry line. Notice that ( is pasted. Press 8. Complete the operation. Press 2 d

5f(2) 5f(

Archiving a variable
1. Redisplay VAR-LINK, and highlight the variable you want to archive. The previous change in view is no longer in effect. The screen lists all defined variables. Press 2 (use D to highlight x1) 2. Use the , Manage toolbar menu to archive the variable. indicates the variable is archived. Press , 8
3. Return to the Home screen and use the archived variable in a calculation. Press " 6 p X1
4. Attempt to store a different value to the archived variable. Press X1 5. Cancel the error message. Press N 6. Use VAR-LINK to unarchive the variable.

x1) , 9

Press 2 (use D to highlight
7. Return to the Home screen and store a different value to the unarchived variable. Press "

Deleting variables

1. Display VAR-LINK, and use the All toolbar menu to select all variables. A mark indicates items that are selected. Notice that this also selected the MAIN folder.
Note: Instead of using (if you dont
want to delete all your variables), you can select individual variables. Highlight each variable to delete and press. Press 1 2. Use , to delete.
Note: You can press 0 (instead of , 1) to delete the marked variables.
Press , 1 3. Confirm the deletion. Press
4. Because 1 also selected the MAIN folder, an error message states that you cannot delete the MAIN folder. Acknowledge the message. When VAR-LINK is redisplayed, the deleted variables are not listed. Press 5. Close VAR-LINK and return to the current application (Home screen in this example). When you use N (instead of ) to close VAR-LINK, the highlighted name is not pasted to the entry line. Press N

Operating the Calculator

Turning the Calculator On and Off
You can turn your graphing calculator on and off manually by using the and 2 (or 8 ) keys. To prolong battery life, the APD (Automatic Power Down) feature lets the calculator turn itself off automatically. Turning the Calculator On Press. If you turned the unit off by pressing 2 , the unit returns to either the Apps desktop or the Home screen. If you turned the unit off by pressing 8 or if the unit turned itself off through APD, the unit returns to whichever application you used last.

Turning the Calculator Off You can use either of the following keys to turn off your graphing calculator.
Press: Description Settings and memory contents are retained by the Constant Memory feature. However:
You cannot use 2 if an error message is displayed. When you turn the calculator on again, it displays either the Home screen or the Apps desktop (regardless of the last application you used).
2 (press 2 and then press )
Similar to 2 except: 8 (press 8 and then You can use 8 if an error message is press ) displayed.
When you turn the calculator on again, it will be exactly as you left it.
APD (Automatic Power Down) After several minutes without any activity, the calculator turns itself off automatically. This feature is called APD. When you press , the calculator will be exactly as you left it. The display, cursor, and any error conditions are exactly as you left them. All settings and memory contents are retained.
APD does not occur if a calculation or program is in progress, unless the program is paused. If a program is running, but waiting for a key press, APD will occur after several minutes of inactivity.
Setting the Display Contrast
The brightness and contrast of the display depend on room lighting, battery freshness, viewing angle, and the adjustment of the display contrast. The contrast setting is retained in memory when the graphing calculator is turned off. Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions.
To: Decrease (lighten) the contrast Increase (darken) the contrast

V A R -L IN K O

Press and hold both:

8 and | 8 and

Contrast keys If you press and hold 8 | or 8 too long, the display may go completely black or blank. To make finer adjustments, hold 8 and then tap | or.
When to Replace Batteries As the batteries get low, the display begins to dim (especially during calculations) and you must increase the contrast. If you have to increase the contrast frequently, replace the four alkaline batteries.
Note: The display may be very dark after you change batteries. Use 8 | to lighten the
display. The status line along the bottom of the display also gives battery information.

Toolbar

Lets you display menus for selecting operations applicable to the calculator Home screen. To display a toolbar menu, press , , etc.

Pretty Print Display

Shows exponents, roots, fractions, etc., in traditional form.

Last Entry

Your last entry.

Entry Line

Where you enter expressions or instructions.

Status Line

Shows the current state of the calculator, including several important mode settings.
Result of your last entry. Note that results are not displayed on the entry line. Note: 8 (Approx) was used in this example.

Last Answer

The following example shows an answer that is not on the same line as the expression. Note that the answer is longer than the screen width. An arrow (8) indicates the answer is continued. The entry line contains ellipsis (). Ellipsis indicates the entry is longer than the screen width.

Last Entry

"Pretty print" is ON. Exponents, roots, fractions, etc., are displayed in the same form in which they are traditionally written.

History Area

Lists entry/answer pairs you have entered. Pairs scroll up the screen as you make new entries.

Answer Continues

Highlight the answer and press B to scroll right and view the rest of it. Note that the answer is not on the same line as the expression.
Expression Continues () Press B to scroll right and view the rest of the entry. Press 2 A or 2 B to go to the beginning
or end of the entry line.
History Area The history area shows up to eight previous entry/answer pairs (depending on the complexity and height of the displayed expressions). When the display is filled, information scrolls off the top of the screen. You can use the history area to: Review previous entries and answers. You can use the cursor to view entries and answers that have scrolled off the screen. Recall or auto-paste a previous entry or answer onto the entry line so that you can re-use or edit it.
Scrolling through the History Area Normally, the cursor is in the entry line. However, you can move the cursor into the history area.
To: View entries or answers that have scrolled off the screen Do this:
From the entry line, press C to highlight the last answer. Continue using C to move the cursor from answer to entry, up through the history area.
Go to the oldest or newest history pair View an entry or answer that is too long for one line (8 is at end of line)
If the cursor is in the history area, press 8 C or 8 D, respectively.
A and B to scroll left and right (or 2 A and 2 B to go to the beginning or end),

respectively.

Move the cursor to the entry or answer. Use

Trace

Only 1:Value, 6:Derivatives, 9:Distance, A:Tangent, and B:Arc are available for polar graphs. These tools are based on q values. For example:
1:Value displays an r value (or x and y, depending on the
graph format) for a specified q value.
6:Derivatives finds dy/dx or dr/dq at a point defined for a specified q value.
During a trace, you can also evaluate r(q) by typing the q value and pressing.
Note: You can use QuickCenter at any time during a trace, even if the cursor is still on the screen.
Overview of Steps in Graphing Parametric Equations
To graph parametric equations, use the same general steps used for y(x) functions as described in Basic Function Graphing. Any differences that apply to parametric equations are described on the following pages. Graping Parametic Equations 1. Set Graph mode (3) to PARAMETRIC. Also set Angle mode, if necessary.
2. Define x and y components on Y= Editor (8 #). 3. Select (), which defined equations to graph. Select the x or y component, or both.
Exploring the Graph From the Graph screen, you can: Display the coordinates of any pixel by using the free-moving cursor, or of a plotted point by tracing a parametric equation.
Use the Zoom toolbar menu to zoom in or out on a portion of the graph. Use the Math toolbar menu to find derivatives, tangents, etc. Some menu items are not available for parametric graphs.
Differences in Parametric and Function Graphing
This module assumes that you already know how to graph y(x) functions as described in Basic Function Graphing. This section describes the differences that apply to parametric equations. Setting the Graph Mode Use 3 to set Graph = PARAMETRIC before you define equations or set Window variables. The Y= Editor and the Window Editor let you enter information for the current Graph mode setting only. Defining Parametric Equations on the Y= Editor To graph a parametric equation, you must define both its x and y components. If you define only one component, the equation cannot be graphed. (However, you can use single components to generate an automatic table as described in Tables.)

For more accurate estimates, increase the xgrid and ygrid Window variables. However, this increases the graph evaluation time. When you animate the graph, the screen changes to normal view. Use p to toggle between normal and expanded views.

Implicit Plots

An implicit plot is used primarily as a way to graph 2D implicit forms that cannot be graphed in function graphing mode. Technically, an implicit plot is a 3D contour plot with a single contour drawn for z=0 only. Explicit and Implicit Forms In 2D function graphing mode, equations have an explicit form y=f(x), where y is unique for each value of x. Many equations, however, have an implicit form f(x,y)=g(x,y), where you cannot explicitly solve for y in terms of x or for x in terms of y.
y is not unique for each x, so you cannot graph this in function graphing mode.
By using implicit plots in 3D graphing mode, you can graph these implicit forms without solving for y or x. Rearrange the implicit form as an equation set to zero. In the Y= Editor, enter the non-zero side of the equation. This is valid because an implicit plot automatically sets the equation equal to zero. For example, given the ellipse equation shown to the right, enter the implicit form in the Y= Editor.
f(x,y)g(x,y)=0 z1(x,y)=f(x,y)g(x,y)
If x2+.5y2=30, then z1(x,y)=x2+.5y230.
Notes: You can also graph many implicit forms if you either:
Express them as parametric equations. Break them into separate, explicit functions.
Selecting the Graph Format Style In 3D graphing mode, define an appropriate equation and graph it as you would any 3D equation, with the following exception. Display the GRAPH FORMATS dialog box from the Y= Editor, Window editor, or Graph screen: 8
Note: From the Graph screen, you can switch to the other graph format styles by
and then set Style = IMPLICIT PLOT.
pressing: However, to return to IMPLICIT PLOT press: 8 The viewing angle is set initially so that you are viewing the plot by looking down the z axis. You can change the viewing angle as necessary. The plot is shown in expanded view. To switch between expanded and normal view, press p. The Labels format is set to OFF automatically.

2. Define equations and, optionally, initial conditions on Y= Editor (8 #). 3. Select () which defined functions to graph.
4. Set the display style for a function. @ 2
5. Set the graph format. Solution Method and Fields are unique to differential equations. ,9 or @ 8
Note: The Fields format is critical, depending on the order of the equation.
6. Set the axes as applicable, depending on the Fields format. @ 2
Note: Valid Axes settings depend on the Fields format.
7. Define the viewing window (8 $).
Note: Depending on the Solution Method and Fields formats, different Window variables are displayed. Zoom also
changes the viewing window.
8. Graph the selected functions (8 %).
Differences in Diff Equations and Function Graphing
This module assumes that you already know how to graph y(x) functions as described in Basic Function Graphing. This section describes the differences. Setting the Graph Mode Use 3 to set Graph = DIFF EQUATIONS before you define differential equations or set Window variables. The Y= Editor and the Window Editor let you enter information for the current Graph mode setting only. Defining Differential Equations on the Y= Editor
Use t0 to specify when initial conditions occur. You can also set t0 in the Window Editor. Use yi to specify one or more initial conditions for the corresponding differential equation. You can define differential equations y1'(t) through y99'(t).
Note: You can use the Define command from the Home screen to define functions and
equations. When entering equations in the Y= Editor, do not use y(t) formats to refer to results. For example:
Do not use implied multiplication between a variable and parenthetical expression. If you do, it is treated as a function call.
Enter: y1' =.001y1(100Ny1) Not: y1' =.001y1(t)(100Ny1(t)) Only 1st-order equations can be entered in the Y= Editor. To graph 2nd- or higher-order equations, you must enter them as a system of 1st-order equations. Detailed information is available on setting initial conditions. Selecting Differential Equations

Sorting All Columns Based on a Key Column Consider a database structure in which each column along the same row contains related information (such as a students first name, last name, and test scores). In such a case, sorting only a single column would destroy the relationship between the columns. In the Data/Matrix Editor: 1. Move the cursor to any cell in the key column. 2. In this example, move the cursor to the second column (c2) to sort by last name.
Note: For a list variable, this is the same
as sorting a single column. 3. Press: 2 and select 4:Sort Col, adjust all.
Note: This menu item is not available if
any column is locked. When using this procedure for a data variable: All columns must have the same length. None of the columns can be locked (defined by a function in the column header). When the cursor is in a locked column, is shown at the beginning of the entry line.
Saving a Copy of a List, Data, or Matrix Variable
You can save a copy of a list, data, or matrix variable. You can also copy a list to a data variable, or you can select a column from a data variable and copy that column to a list. Valid Copy Types
You can copy a: List Data Data column Matrix To a: List or data Data List Matrix
Note: A list is automatically converted to a data variable if you enter more than one
column of information. Procedure From the Data/Matrix Editor: 1. Display the variable that you want to copy.
2. Press and select 2:Save Copy As. 3. In the dialog box: Select the Type and Folder for the copy. Type a variable name for the copy. When available, select the column to copy from.
Note: If you type the name of an existing
variable, its contents will be replaced. Column is dimmed unless you copy a data column to a list. The
column information is not used for other types of copies.
4. Press (after typing in an input box such as Variable, you must press twice). To Copy a Data Column to a List A data variable can have multiple columns, but a list variable can have only one column. Therefore, when copying from a data variable to a list, you must select the column that you want to copy. List variable to copy to. Data column that will be copied to the
list. By default, this shows the column that contains the cursor.
Overview of Steps in Statistical Analysis
This section gives an overview of the steps used to perform a statistical calculation or graph a statistical plot. For detailed descriptions, refer to the following pages. 1. Set Graph mode (3) to FUNCTION. 2. Enter stat data in the Data/Matrix Editor.

Press: To: Paste the highlighted variable or folder name to the cursor location in the current application.
To: Return to the current application without pasting the highlighted name.
Displaying Information about Variables on the Home Screen
From the Home screen, you can display information about variables without opening the VAR-LINK screen. To determine if a variable with a given name exists in the system table, Enter the IsVar() function on the Home screen.
IsVar (var_name) IsVar is a function, which requires you to enclose the variable name in parentheses.
To determine if a variable is archived, use the IsArchiv() function.

IsArchiv (var_name)

To determine if a variable is locked, use the IsLocked() function.

IsLocked (var_name)

Manipulating Variables and Folders with VAR-LINK On the VAR-LINK screen, you can show the contents of a variable. You can also select one or more listed items and manipulate them by using the operations in this section.
Showing the Contents of a Variable You can show all variable types except ASM, DATA, GDB, and variables created by Flash Apps. For example, you must open a DATA variable in the Data/Matrix Editor. 1. On VAR-LINK, move the cursor to highlight the variable. 2. Press: 2 If you highlight a folder, the screen shows the number of variables in that folder. 3. To return to VAR-LINK, press any key.
Note: You cannot edit the contents from this screen.
Selecting Items from the List For other operations, select one or more variables and/or folders.
To select: A single variable or folder A group of variables or folders Do this: Move the cursor to highlight the item, then press. Highlight each item and press. A is displayed to the left of each selected item. (If you select a folder, all variables in that folder are selected.) Use to select or deselect an item.
To select: All folders and all variables
Do this: Press B to expand the folder, then press All and select 1:Select All. Choosing 3:Select Current selects the last set of items transmitted to your unit during the current VAR-LINK session. Choosing 4:Expand All or 5:Collapse All expands or collapses your folders or Flash applications.
Note: Press either A or B to toggle between expanded or collapsed view when you have

2. Copy and paste the last answer to the entry line and store it in the function f(x).
area to highlight the last answer and press , to copy it to the entry line.
3. Use the abs( ) function to find the absolute value of f(x+yi). (This calculation may take about 2 minutes.)
Note: The absolute value of a function
forces any roots to visually just touch rather than cross the x axis. Likewise, the absolute value of a function of two variables will force any roots to visually just touch the xy plane. 4. Copy and paste the last answer to the entry line and store it in the function z1(x,y).
Note: The graph of z1(x,y) will be the
modulus surface. 5. Set the unit to 3D graph mode, turn on the axes for graph format, and set the Window variables to:
eye= [20,70,0] x= [L2,2,20] y= [ L2,2,20] z= [ L1,2] ncontour= [5]
6. In the Y=Editor, press: 8 and set the Graph Format variables to:
Axes= ON Labels= ON Style= HIDDEN SURFACE Note: Calculating and drawing the graph
takes about three minutes. 7. Graph the modulus surface. The 3D graph is used to visually display a picture of the roots where the surface touches the xy plane. 8. Use the Trace tool to explore the function values at x=1 and y=0.
9. Use the Trace tool to explore the function values at x=0 and y=1.
10. Use the Trace tool to explore the function values at x=0 and y=L1.
Summary Note that zc is zero for each of the function values in steps 79. Thus, the complex zeros 1,Li, i of the polynomial x3Nx2+xN1 can be visualized with the three points where the graph of the modulus surface touches the xy plane.
Solving a Standard Annuity Problem
This activity can be used to find the interest rate, starting principal, number of compounding periods, and future value of an annuity.
Finding the Interest Rate of an Annuity Perform the following steps to find the interest rate (i) of an annuity where the starting principal (p) is 1,000, number of compounding periods (n) is 6, and the future value (s) is 2,000. 1. On the Home screen, enter the equation to solve for p.
2. Enter the equation to solve for n.
3. Enter the equation to solve for i using the with operator.

Operations whose names are not alphabetic (such as +, !, and >) are listed at the end of this appendix, starting on page 900. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined. Additionally, due to formatting restraints, approximate results are truncated at three decimal places (3.14159265359 is shown as 3.141.).

MATH/Number menu

abs(expression1) expression abs(list1) list abs(matrix1) matrix
abs({p/2,p/3}) abs(23i) abs(z) abs(x+yi)

p } |z|

Returns the absolute value of the argument. If the argument is a complex number, returns the numbers modulus. Note: All undefined variables are treated as real variables.
MATH/Test and MATH/Base menus
Boolean expression1 and expression2 Boolean expression Boolean list1 and list2 Boolean list Boolean matrix1 and matrix2 Boolean matrix

x3 and x4

{x3,x0} and {x4,x2} {x 4 x 2}
Returns true or false or a simplified form of the original entry.
integer1 and integer2 integer

In Hex base mode:

Compares two real integers bit-by-bit using an 0h7AC36 and 0h3D5F 0h2C16 and operation. Internally, both integers are Important: Zero, not the letter O. converted to signed, 32-bit binary numbers. When corresponding bits are compared, the result In Bin base mode: is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and 0b100101 and 0b100 0b100 is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). If you enter a decimal integer that is too large for a signed, 32-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. In Dec base mode:

37 and 0b100 4

Note: A binary entry can have up to 32 digits (not counting the 0b prefix). A hexadecimal entry can have up to 8 digits.

AndPic

:clearerr() :Prgm :PlotsOff:FnOff:ZoomStd :For i,0,238 :@x i+xmin! xcord : Try : PtOn xcord,ln(xcord) : Else : If errornum=800 or errornum=260 Then : ClrErr clear the error : Else : PassErr pass on any other error : EndIf : EndTry :EndFor :EndPrgm

ClrGraph

Clears any functions or expressions that were graphed with the Graph command or were created with the Table command. (See Graph or Table.) Any previously selected Y= functions will be graphed the next time that the graph is displayed.

ClrHome

Clears all items stored in the entry() and ans() Home screen history area. Does not clear the current entry line. While viewing the Home screen, you can clear the history area by pressing and selecting 8:Clear Home. For functions such as solve() that return arbitrary constants or integers (@1, @ 2, etc.), ClrHome resets the suffix to 1.
Clears the Program I/O screen.

ClrTable

Clears all table values. Applies only to the ASK setting on the Table Setup dialog box. While viewing the Table screen in Ask mode, you can clear the values by pressing and selecting 8:Clear Table.

colDim()

MATH/Matrix/Dimensions menu

colDim(matrix)

colDim([0,1,2;3,4,5])
Returns the number of columns contained in matrix. Note: See also rowDim().
colNorm() MATH/Matrix/Norms menu
colNorm(matrix) expression
[1, 2,3;4,5, 6]! mat colNorm(mat)
Returns the maximum of the sums of the absolute values of the elements in the columns in matrix. Note: Undefined matrix elements are not allowed. See also rowNorm().
comDenom() MATH/Algebra menu
comDenom(expression1[,var]) expression comDenom(list1[,var]) list comDenom(matrix1[,var]) matrix comDenom(expression1) returns a reduced ratio of
comDenom((y^2+y)/(x+1)^2+y^2+y)
a fully expanded numerator over a fully expanded denominator.
comDenom(expression1,var) returns a reduced
ratio of numerator and denominator expanded with respect to var. The terms and their factors are sorted with var as the main variable. Similar powers of var are collected. There might be some incidental factoring of the collected coefficients. Compared to omitting var, this often saves time, memory, and screen space, while making the expression more comprehensible. It also makes subsequent operations on the result faster and less likely to exhaust memory.
comDenom((y^2+y)/(x+1) ^2+y^2+y,x)
comDenom((y^2+y)/(x+1) ^2+y^2+y,y)
If var does not occur in expression1, comDenom(expression1,var) returns a reduced ratio of an unexpanded numerator over an unexpanded denominator. Such results usually save even more time, memory, and screen space. Such partially factored results also make subsequent operations on the result much faster and much less likely to exhaust memory.
comDenom(exprn,abc)!comden (exprn) comden((y^2+y)/(x+1)^2+y^2+y)

lMatName uMatName = pMatName matrix
LU m1,lower,upper,perm lower

Done 1/0 1

Optionally, any matrix element is treated as zero if its absolute value is less than tol. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, tol is ignored. If you use or set the mode to Exact/Approx=APPROXIMATE, computations are done using floating-point arithmetic. If tol is omitted or not used, the default tolerance is calculated as:
5E 14 max(dim(matrix)) rowNorm(matrix)

1 5/6 1/0 0

upper
[m,n;o,p]!m1 LU m1,lower,upper,perm lower

[m n] o p

The LU factorization algorithm uses partial pivoting with row interchanges.

1 m o o 0

mp n o

[0 1] 1 0

mat4data 4
mat4data mat,data[,row1][,col1][,row2][,col2] 4
Converts a matrix to data. Each argument [,row1][,col1][,row2][,col2] can be individually omitted. If row1 is omitted the default is 1. If col1 is omitted the default is 1. If row2 is omitted, the default is max row. If col2 is omitted, the default is max column.
mat4data,m1,d1,1,,,1 Done

mat4list() 4

mat4list(matrix) 4
mat4list([1,2,3]) [1,2,3;4,5,6]! M1 mat4list(M1)
Returns a list filled with the elements in matrix. The elements are copied from matrix row by row.
max(expression1, expression2) expression max(list1, list2) list max(matrix1, matrix2) matrix
max(2.3,1.4) max({1,2},{ 4,3})

2.3 {1 3}

Returns the maximum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the maximum value of each pair of corresponding elements.

max(list) expression

max({0,1, 7,1.3,.5})
Returns the maximum element in list.

max(matrix1)

max([1, 3,7; 4,0,.3])
Returns a row vector containing the maximum element of each column in matrix1. Note: See also fMax() and min().

mean()

MATH/Statistics menu

mean(list[, freqlist])

mean({.2,0,1,.3,.4})
Returns the mean of the elements in list. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list.
mean(matrix1[, freqmatrix]) matrix

mean({1,2,3},{3,2,1})

In vector format rectangular mode: mean([.2,0;L1,3;.4,L.5]) [L.133.833.] mean([1/5,0;L1,3;2/5,L1/2]) [ 2/15 5/6] mean([1,2;3,4;5,6],[5,3;4,1; 6,2]) [47/15, 11/3]
Returns a row vector of the means of all the columns in matrix1. Each freqmatrix element counts the number of consecutive occurrences of the corresponding element in matrix1.

median()

median(list)

10!arctest Archive arctest 5arctest 15!arctest

10 Done 50

unitV()

vector

unitV(vector1)

unitV([a,b,c]) [

a a +b +c b a +b +c c a +b +c
Returns either a row- or column-unit vector, depending on the form of vector1.
vector1 must be either a single-row matrix or a single-column matrix.

unitV([1,2,1])

unitV([1;2;3])

Unlock

Unlock var1[, var2][, var3].
Unlocks the specified variables. Note: The variables can be locked using the Lock command.
variance() MATH/Statistics menu
variance(list[, freqlist]) expression
Returns the variance of list. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Note: list must contain at least two elements.
variance(matrix1[, freqmatrix])
variance({a,b,c}) a -a (b+c)+b -b c+c 3 variance({1,2,5, 6,3, 2}) variance({1,3,5},{4,6,2}) 31/2 68/33
Returns a row vector containing the variance of each column in matrix1. Each freqmatrix element counts the number of consecutive occurrences of the corresponding element in matrix1. Note: matrix1 must contain at least two rows.
variance([1,2,5; 3,0,1; [4.75 1.03 4].5,.7,3]) variance([L1.1,2.2;3.4,5.1; L2.3,4.3],[6,3;2,4;5,1]) [3.91731,2.08411]

when()

when(condition, trueResult [, falseResult] [, unknownResult]) expression
Returns trueResult, falseResult, or unknownResult, depending on whether condition is true, false, or unknown. Returns the input if there are too few arguments to specify the appropriate result. Omit both falseResult and unknownResult to make an expression defined only in the region where condition is true. Use an undef falseResult to define an expression that graphs only on an interval.
when(x<0,x+3)|x=5 when(x<0,3+x)
ClrGraph Graph when(xp and x<0,x+3,undef)
Omit only the unknownResult to define a two-piece expression.
Graph when(x<0,x+3,5 x^2)
Nest when() to define expressions that have more than two pieces.
" ClrGraph Graph when(x<0,when(x<p, 4 sin(x),2x+3),5 x^2)
when() is helpful for defining recursive functions.
when(n>0,n factoral(n 1),1) ! factoral(n) factoral(3) 3!

Done 6 6

:1! i :0! temp :While i<=20 : temp+1/i! temp : i+1! i :EndWhile :Disp "sum of reciprocals up to 20",te

EndWhile

Executes the statements in block as long as condition is true.

With xor

See |, page 912.
Boolean expression1 xor Boolean expression2 expression Boolean
true xor true (5>3) xor (3>5)

false true

Returns true if Boolean expression1 is true and Boolean expression2 is false, or vice versa. Returns false if Boolean expression1 and Boolean expression2 are both true or both false. Returns a simplified Boolean expression if either of the original Boolean expressions cannot be resolved to true or false. Note: See or.

In this example, eyeq=20 and eyef=70
Note: During rotation, the axes expand or contract to fit the screens width and height. This causes some distortion as shown in the example.
z1(x,y)=(x 3y y 3x) / 390
When eye=0, the z axis runs the height of the screen.

eye=45

When eye=90, the z axis runs the width of the screen.

z=10 z=10 eye=90

As the z axis rotates 90, its range ( 10 to 10 in this example) expands to almost twice its original length. Likewise, the x and y axes expand or contract.
The eye values are stored in the system variables eyeq, eyef, and eye. You can access or store to these variables as necessary.
TI-89: To type f or , press c j [F] or c , respectively. You can also press 2 and use the Greek menu. TI-92 Plus: To type f or , press 2 G F or 2 G Y respectively. You can also press 2 and use the Greek menu. Chapter 10: 3D Graphing 163
10_3D.DOC TI-89/TI-92 Plus: 3D Graphing (English) Susan Gullord Revised: 02/23/01 11:00 AM Printed: 02/23/01 4:22 PM Page 163 of 22
Animating a 3D Graph Interactively
After plotting any 3D graph, you can change the viewing angle interactively by using the cursor. Refer to the preview example on page 154.

The Viewing Orbit

Note: The viewing orbit affects the eye Window variables in differing amounts.
When using A and B to animate a graph, think of it as moving the viewing angle along its viewing orbit around the graph. Moving along this orbit can cause the z axis to wobble slightly during the animation (as you can see in the preview example on page 154).

Animating the Graph

Note: If the graph is shown in expanded view, it returns to normal view automatically when you press a cursor key. Tip: After animating the graph, you can stop and then re-start the animation in the same direction by pressing:
TI-89: or j TI-92 Plus: or space
Animate the graph incrementally
Press and release the cursor quickly.
Move along the viewing orbit: A or B Change the viewing orbits: C or D elevation (primarily increases or decreases eyef) Animate the graph continuously Press and hold the cursor for about 1 second, and then release it. TI-89: To stop, press N, , , or (space).
TI-92 Plus: To stop, press N,

Copying from the Home Screen to the Y= Editor
Tip: Instead of using 5 or 6 to copy and paste, use:
TI-89: 6 or 7. TI-92 Plus: C (copy) or V(paste).
If you have an expression on the Home screen, you can use any of the following methods to copy it to the Y= Editor.

Copy and paste

1. Highlight the expression on the Home screen. Press and select 5:Copy. 2. Display the Y= Editor, highlight the desired function, and press. 3. Press and select 6:Paste. Then press.
Tip: To copy an expression from the Home screens history area to the entry line, use the auto-paste feature or copy and paste. Tip: Define is available from the Home screens toolbar menu. Tip: 2 is useful if an expression is stored to a variable or function that does not correspond to the Y= Editor, such as a1 or f1(x).
Store the expression to a Y= function name.

2x^3+3x^24x+12!y1(x)

Use the complete function name: y1(x), not just y1.

Define

Define the expression as a user-defined Y= function.
Define y1(x)=2x^3+3x^24x+12

command

If the expression is already stored to a variable: 1. Display the Y= Editor, highlight the desired function, and press. 2. Press 2. Type the variable name that contains the expression, and press twice. Important: To recall a function variable such as f1(x), type only f1, not the full function name. 3. Press to save the recalled expression in the Y= Editors function list.
12ADDLGR.DOC TI-89/TI-92 Plus: Additional Graphing Tools (English) Susan Gullord Revised: 02/23/01 1:03 PM Printed: 02/23/01 2:15 PM Page 204 of 20
Graphing Directly from the Home Screen
The Graph command lets you graph an expression from the Home screen without using the Y= Editor. Unlike the Y= Editor, Graph lets you specify an expression in terms of any independent variable, regardless of the current graphing mode.
If the expression is in terms of: Use the Graph command as shown in this example: graph 1.25xcos(x)
For function graphing, x is the native variable.
Tip: Graph is available from the Home screens toolbar menu.

For Pictures Saved from a Portion of the Graph Screen
When you press and select 1:Open, the picture is superimposed starting at the upper-left corner of the Graph screen. If the picture was saved from a portion of the Graph screen (page 217), it may appear shifted from the underlying graph. To specify which screen pixel to use as the upper-left corner, you can use the commands listed in From a Program or the Home Screen below.

Deleting a Graph Picture

Unwanted Picture variables take up calculator memory. To delete a variable, use the VAR-LINK screen ( 2 ) as described in Chapter 21. To save (store) and open (recall) a graph picture, use the StoPic, RclPic, AndPic, XorPic, and RplcPic commands as described in Appendix A. To display a series of graph pictures as an animation, use the CyclePic command. For an example, refer to page 219.
From a Program or the Home Screen
12ADDLGR.DOC TI-89/TI-92 Plus: Additional Graphing Tools (English) Susan Gullord Revised: 02/23/01 1:03 PM Printed: 02/23/01 2:15 PM Page 218 of 20
As described earlier in this chapter, you can save a picture of a graph. By using the CyclePic command, you can flip through a series of graph pictures to create an animation.

CyclePic Command

Before using CyclePic, you must have a series of graph pictures that have the same base name and are sequentially numbered starting with 1 (such as pic1, pic2, pic3,. ). To cycle the pictures, use the syntax:
CyclePic picNameString, n [,wait] [,cycles] [,direction]
1 = forward/circular cycle 1= forward/backward # of times to repeat cycle seconds between pictures # of pictures to cycle base name of pictures in quotes, such as "pic"
This example program (named cyc) generates 10 views of a 3D graph, with each view rotated 10 further around the Z axis. For information about each command, refer to Appendix A. For information about using the Program Editor, refer to Chapter 17.

Program Listing

:cyc() :Prgm :local i :Set mode and Window variables :setMode(graph,3d) :70! eyef : 10! xmin :10! xmax :14! xgrid : 10! ymin :10! ymax :14! ygrid : 10! zmin :10! zmax :1! zscl :Define the function :(x^3 y y^3 x)/390! z1(x,y) :Generate pics and rotate :For i,1,10,1 : i 10! eyeq : DispG : StoPic #("pic" & string(i)) :EndFor :Display animation :CyclePic "pic",10,.5,5, 1 :EndPrgm

The Data/Matrix Editor serves two main purposes.
This chapter describes how to use the Data/Matrix Editor to create and maintain a list, matrix, or data variable.
Chapter 16 describes how to use the Data/Matrix Editor to perform statistical calculations and graph statistical plots.
15DATAMA.DOC TI-89/TI-92 Plus: Data/Matrix Editor (English) Susan Gullord Revised: 02/23/01 1:10 PM Printed: 02/23/01 2:17 PM Page 237 of 16
Preview of the Data/Matrix Editor
Use the Data/Matrix Editor to create a one-column list variable. Then add a second column of information. Notice that the list variable (which can have only one column) is automatically converted into a data variable (which can have multiple columns).
TI-92 Plus Keystrokes O63 B3 DD TEMP C
1. Start the Data/Matrix Editor and O create a new list variable named B 3 TEMP. DD
2. Enter a column of numbers. Then move the cursor up one cell (just to see that a highlighted cells value is shown on the entry line).
You can use D instead of to enter information in a cell.
5 LIST is shown in the upper-left corner 6 to indicate a list variable. C
3. Move to column 2, and define its B column header so that it is twice the value of column 1. 2pjC1
DATA is shown in the upper-left corner to indicate that the list variable was converted to a data variable.

B 2pC1

means the cell is in a defined column.
4. Move to the column 2 header cell to show its definition in the entry line.
When the cursor is on the header cell, you do not need to press to define it. Simply begin typing the expression.
5. Go to the Home screen, and then " return to the current variable. O61 6. Clear the contents of the variable.
Simply clearing the data does not convert the data variable back into a list variable.

" O61 8

Tip: If you dont need to save the current variable, use it as a scratchpad. The next time you need a variable for temporary data, clear the current variable and re-use it. This lets you enter temporary data without creating a new variable each time, which uses up memory.

Variable Type After , the cursor moves:
Note: To enter a value from the entry line, you can also use D or C.

List or data Matrix

Down to the cell in the next row. Right to the cell in the next column. From the last cell in a row, the cursor automatically moves to the first cell in the next row. This lets you enter values for row1, row2, etc.
15DATAMA.DOC TI-89/TI-92 Plus: Data/Matrix Editor (English) Susan Gullord Revised: 02/23/01 1:10 PM Printed: 02/23/01 2:17 PM Page 243 of 16
Scrolling through the Editor
C or Go to row 1 in the current D column or to the last row that contains data for any column on the screen, respectively. If the cursor is in or past that last row, D goes to row 999. Go to column 1 or to the last column that contains data, respectively. If the cursor is in or past that last column, B goes to column 99. A or B
When you scroll down/up, the header row remains at the top of the screen so that the column numbers are always visible. When you scroll right/left, the row numbers remain on the left side of the screen so that they are always visible.
How Rows and Columns Are Filled Automatically
When you enter a value in a cell, the cursor moves to the next cell. However, you can move the cursor to any cell and enter a value. If you leave gaps between cells, the TI-89 / TI-92 Plus handles the gaps automatically.
In a list variable, a cell in the gap is undefined until you enter a value for the cell.
In a data variable, gaps in a column are handled the same as a list. However, if you leave a gap between columns, that column is blank.
15DATAMA.DOC TI-89/TI-92 Plus: Data/Matrix Editor (English) Susan Gullord Revised: 02/23/01 1:10 PM Printed: 02/23/01 2:17 PM Page 244 of 16
In a matrix variable, when you enter a value in a cell outside the current boundaries, additional rows and/or columns are added automatically to the matrix to include the new cell. Other cells in the new rows and/or columns are filled with zeros.
Note: Although you specify the size of a matrix when you create it, you can easily add additional rows and/or columns.
The cell width affects how many characters are displayed in any cell. To change the cell width in the Data/Matrix Editor: 1. To display the FORMATS dialog box, press 9 or TI-89: TI-92 Plus: F
Cell width is the maximum number of characters that can be displayed in a cell. All cells have the same cell width.
Tip: Remember, to see a number in full precision, you can always highlight the cell and look at the entry line.
2. With the current Cell Width setting highlighted, press B or A to display a menu of digits (3 through 12). 3. Move the cursor to highlight a number and press. (For single-digit numbers, you can type the number and press.) 4. Press to close the dialog box.
Clearing a Column or all Columns
Note: For a list or data variable, a clear column is empty. For a matrix, a clear column contains zeros.

This procedure erases the contents of a column. It does not delete the column.

To clear: Do this:

A column
1. Move the cursor to any cell in the column. 2. TI-89: 2 TI-92 Plus: and select 5:Clear Column. (This item is not available for a matrix.)

All columns

Press and select 8:Clear Editor. When prompted for confirmation, press (or N to cancel).
15DATAMA.DOC TI-89/TI-92 Plus: Data/Matrix Editor (English) Susan Gullord Revised: 02/23/01 1:10 PM Printed: 02/23/01 2:17 PM Page 245 of 16
Inserting and Deleting a Row, Column, or Cell
The general procedures for inserting and deleting a cell, row, or column are simple and straightforward. You can have up to 99 columns with up to 999 elements in each column.
Note About Column Titles and Headers
You cannot delete the rows or cells that contain column titles or headers. Also, you cannot insert a row or cell before a column title or header. The new row or column is inserted before the row or column that contains the highlighted cell. In the Data/Matrix Editor: 1. Move the cursor to any cell in the applicable row or column. 2. TI-89: 2 TI-92 Plus: and select 1:Insert. 3. Select either 2:row or 3:column.
Inserting a Row or Column
Note: For a list variable, inserting a row is the same as inserting a cell.

When you insert a row:

In a list or data variable, the row is undefined. In a matrix variable, the row is filled with zeros.
Note: For a list variable, you cannot insert a column because a list has only one column.
When you insert a column:
In a data variable, the column is blank. In a matrix variable, the column is filled with zeros.
You can then enter values in the undefined or blank cells.
15DATAMA.DOC TI-89/TI-92 Plus: Data/Matrix Editor (English) Susan Gullord Revised: 02/23/01 1:10 PM Printed: 02/23/01 2:17 PM Page 246 of 16

Inserting a Cell

The new cell is inserted before the highlighted cell in the same column. (You cannot insert a cell into a locked column, which is defined by a function in the column header. Refer to page 248.) In the Data/Matrix Editor: 1. Move the cursor to the applicable cell. 2. TI-89: 2 TI-92 Plus: and select 1:Insert. 3. Select 1:cell.

After the program stops, the TI-89 / TI-92 Plus shows the last screen that was displayed.

The Program I/O Screen

On the Program I/O screen, new output is displayed below any previous output (which may have been displayed earlier in the same program or a different program). After a full page of output, the previous output scrolls off the top of the screen.
Tip: To clear any previous output, enter the Clr[O command in your program. You can also execute Clr[O from the Home screen.

Last output

On the Program I/O screen: toolbar is available; all others are dimmed. There is no entry line.
Tip: If Home screen calculations dont work after you run a program, you may be on the Program I/O screen.
When a program stops on the Program I/O screen, you need to recognize that it is not the Home screen (although the two screens are similar). The Program I/O screen is used only to display output or to prompt the user for input. You cannot perform calculations on this screen. From the Program I/O screen:
Leaving the Program I/O Screen
Press to toggle between the Home screen and the Program I/O screen. or Press N, 2 K , or TI.89: " TI.92 Plus: " to display the Home screen. or Display any other application screen (with O, #, etc.).
17PROGRM.DOC TI-89/TI-92 Plus: Programming (English) Susan Gullord Revised: 02/23/01 1:14 PM Printed: 02/23/01 2:18 PM Page 279 of 40
Starting a Program Editor Session
Each time you start the Program Editor, you can resume the current program or function (that was displayed the last time you used the Program Editor), open an existing program or function, or start a new program or function.
Starting a New Program or Function
1. Press O and then select 7:Program Editor. 2. Select 3:New.
3. Specify the applicable information for the new program or function.

Item Type Folder

Select whether to create a new program or function. Select the folder in which the new program or function will be stored. For information about folders, refer to Chapter 5. Type a variable name for the program or function. If you specify a variable that already exists, an error message will be displayed when you press. When you press N or to acknowledge the error, the NEW dialog box is redisplayed.

On the sending unit, select 4:Send Product SW. A warning message displays. Press N to halt the process, or press to start the transmission.
22LINK.DOC TI-89/TI-92 Plus: Linking and Upgrading (English) Susan Gullord Revised: 02/23/01 1:23 PM Printed: 02/23/01 2:20 PM Page 375 of 18
Transferring Product Software (continued)
During the transfer, the receiving unit shows how the transfer is progressing. When the transfer is complete:
The sending unit returns to the VAR-LINK screen. The receiving unit returns to the Home screen. You may need to use | (lighten) or (darken) to adjust the contrast.
Do Not Attempt to Cancel a Product Software (Base Code) Transfer
After the transfer starts, the receiving units existing base code is effectively deleted. If you interrupt the transfer before it is complete, the receiving unit will not operate properly. You will then need to reinstall the base code (maintenance or feature) upgrade via a computer. To perform a maintenance upgrade on multiple units, you can transfer an upgrade from one unit to another instead of installing it on each unit via a computer. Maintenance upgrades are released free of charge and you do not need to obtain a certificate before you download or install them. Before installing a purchased feature upgrade, each TI-89 or TI-92 Plus must have its own unique certificate. During download and installation, you can choose both the certificate and feature upgrade or only the certificate. The illustration below shows the most efficient way to prepare multiple units for a purchased feature upgrade.
From the computer, download and install the certificate and feature upgrade for one unit. From the computer, download and install only the unique certificate for each of the other units.
If Youre Upgrading Product Software (Base Code) on Multiple Units
Note: Group certificates are also available. See page 378.
Tip: Generally, transmitting a base code upgrade from unit-to-unit is much quicker than installing it via a computer.
Starting with the first unit, transfer the feature upgrade from one unit to another as described below.
Preparing multiple TI-92 Plus units for a purchased feature upgrade works the same as illustrated above.
22LINK.DOC TI-89/TI-92 Plus: Linking and Upgrading (English) Susan Gullord Revised: 02/23/01 1:23 PM Printed: 02/23/01 2:20 PM Page 376 of 18

Error Messages

Most error messages are displayed on the sending unit. Depending on when the error occurs during the transfer process, you may see an error message on the receiving unit.

diag()
diag(list) matrix diag(rowMatrix) matrix diag(columnMatrix) matrix

diag({2,4,6})

Returns a matrix with the values in the argument list or matrix in its main diagonal.
diag(squareMatrix) rowMatrix
Returns a row matrix containing the elements from the main diagonal of squareMatrix.
squareMatrix must be square.
8 [4,6,8;1,2,3;5,7,9] diag(ans(1)) [9]
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 436 of 132

Dialog

CATALOG Program listing: :Dlogtest() :Prgm :Dialog :Title "This is a dialog box" :Request "Your name",Str1 :Dropdown "Month you were born", seq(string(i),i,1,12),Var1 :EndDlog :EndPrgm

Dialog block EndDlog

Generates a dialog box when the program is executed.
block can be either a single statement or a series of statements separated with the : character. Valid block options in the I/O, 1:Dialog menu item in the Program Editor are 1:Text, 2:Request, 4:DropDown, and 7:Title.
The variables in a dialog box can be given values that will be displayed as the default (or initial) value. If is pressed, the variables are updated from the dialog box and variable ok is set to 1. If N is pressed, its variables are not updated, and system variable ok is set to zero.

dim(list) integer

dim({0,1,2})
Returns the dimension of list.

dim(matrix) list

dim([1, 1,2; 2,3,5]) {2 3}
Returns the dimensions of matrix as a twoelement list {rows, columns}.

dim(string) integer

dim("Hello") dim("Hello"&" there")
Returns the number of characters contained in character string string.
Disp [exprOrString1] [, exprOrString2].
Disp "Hello" Disp cos(2.3) {1,2,3,4}! L1 Disp L1

Hello.666

Displays the current contents of the Program I/O screen. If one or more exprOrString is specified, each expression or character string is displayed on a separate line of the Program I/O screen. An expression can include conversion operations such as 4DD and 4Rect. You can also use the 4 operator to perform unit and number base conversions. If Pretty Print = ON, expressions are displayed in pretty print. From the Program I/O screen, you can press to display the Home screen, or a program can use DispHome.

Disp 180_min 4 _hr

Note: To type an underscore ( _ ), press: TI-89: TI-92 Plus: 2 To type 4, press 2.
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 437 of 132
CATALOG In function graphing mode: Displays the current contents of the Graph screen. Program segment: :5 cos(x)! y1(x) : 10! xmin :10! xmax : 5! ymin :5! ymax :DispG

part(cos(p x+3)) 1 part(cos(p x+3),0) "cos" part(cos(p x+3),1)! temp 3+px temp px+3 part(temp,0) "+" part(temp) 2 part(temp,2) 3 part(temp,1)! temp px part(temp,0) " " part(temp) 2 part(temp,1) p part(temp,2) x part(x+y+z) part(x+y+z,2) part(x+y+z,1) 2 z y+x
Expressions such as (x+y+z) and (x y z) are represented internally as (x+y)+z and (x y) z. This affects the values returned for the first and second argument. There are technical reasons why part(x+y+z,1) returns y+x instead of x+y. Similarly, x y z is represented internally as (x y) z. Again, there are technical reasons why the first argument is returned as yx instead of xy. When you extract sub-expressions from a matrix, remember that matrices are stored as lists of lists, as illustrated in the example to the right.
part(x y z) part(x y z,2) part(x y z,1) part([a,b,c;x,y,z],0) part([a,b,c;x,y,z]) part([a,b,c;x,y,z],2)! temp {x part(temp,0) part(temp) part(temp,3) delVar temp y

2 z yx "{" 2

z} "{" 3 z
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 478 of 132
The example Program Editor function to the right uses getType() and part() to partially implement symbolic differentiation. Studying and completing this function can help teach you how to differentiate manually. You could even include functions that the TI-89 / TI-92 Plus cannot differentiate, such as Bessel functions.
:d(y,x) :Func :Local f :If getType(y)="VAR" : Return when(y=x,1,0,0) :If part(y)=0 : Return 0 y=p,,i,numbers :part(y,0)! f :If f="L" if negate : Return d(part(y,1),x) :If f="" if minus : Return d(part(y,1),x) d(part(y,2),x) :If f="+" : Return d(part(y,1),x) +d(part(y,2),x) :If f=" " : Return part(y,1) d(part(y,2),x) +part(y,2) d(part(y,1),x) :If f="{" : Return seq(d(part(y,k),x), k,1,part(y)) :Return undef :EndFunc

PassErr

CATALOG See ClrErr program listing example.
Passes an error to the next level. If errornum is zero, PassErr does not do anything. The Else clause in the program should use ClrErr or PassErr. If the error is to be processed or ignored, use ClrErr. If what to do with the error is not known, use PassErr to send it to the next error handler. (See also ClrErr.)

rotate(list1[,#ofRotations])
In Dec base mode: rotate({1,2,3,4}) {2 3} rotate({1,2,3,4}, 2) {1 2} rotate({1,2,3,4},1) {4 1} rotate("abcd") rotate("abcd", 2) rotate("abcd",1) "dabc" "cdab" "bcda"
Returns a copy of list1 rotated right or left by #of Rotations elements. Does not alter list1. If #of Rotations is positive, the rotation is to the left. If #of Rotations is negative, the rotation is to the right. The default is 1 (rotate right one element).
rotate(string1[,#ofRotations]) string
Returns a copy of string1 rotated right or left by #of Rotations characters. Does not alter string1. If #of Rotations is positive, the rotation is to the left. If #of Rotations is negative, the rotation is to the right. The default is 1 (rotate right one character).

round()

round(expression1[, digits])

round(1.234567,3)

Returns the argument rounded to the specified number of digits after the decimal point.
digits must be an integer in the range 012. If digits is not included, returns the argument
rounded to 12 significant digits. Note: Display digits mode may affect how this is displayed.
round(list1[, digits]) list
Returns a list of the elements rounded to the specified number of digits.
round(matrix1[, digits]) matrix
round({p,(2),ln(2)},4) {3.1416 1.4142.6931}
Returns a matrix of the elements rounded to the specified number of digits.
round([ln(5),ln(3);p,e^(1)],1)

1.1 2.7]

rowAdd()
rowAdd(matrix1, rIndex1, rIndex2)
Returns a copy of matrix1 with row rIndex2 replaced by the sum of rows rIndex1 and rIndex2.
rowAdd([3,4; 3, 2],1,2) [ 0 2] rowAdd([a,b;c,d],1,2) a b [a+c b+d]

rowDim()

rowDim(matrix)
[1,2;3,4;5,6]! M1 rowdim(M1)
Returns the number of rows in matrix. Note: See also colDim().
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 492 of 132

rowNorm()

rowNorm(matrix)
Returns the maximum of the sums of the absolute values of the elements in the rows in matrix. Note: All matrix elements must simplify to numbers. See also colNorm().
rowNorm([-5,6,-7;3,4,9;9,-9,-7]) 25

rowSwap()

rowSwap(matrix1, rIndex1, rIndex2)

[1,2;3,4;5,6]! Mat

Returns matrix1 with rows rIndex1 and rIndex2 exchanged. rowSwap(Mat,1,3)

RplcPic

RplcPic picVar[, row][, column]
Clears the Graph screen and places picture picVar at pixel coordinates (row, column). If you do not want to clear the screen, use RclPic.
picVar must be a picture data type variable. row and column, if included, specify the pixel

( b-4ac-+b) 2a

b-4ac-b 2a
a x^2+b x+c|x=ans(1)[2] exact(zeros(a (e^(x)+x) (sign (x) 1),x))
exact(solve(a (e^(x)+x) (sign (x) 1)=0,x)) e x + x = 0 or x>0 or a = 0
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 519 of 132
zeros({expression1, expression2}, {varOrGuess1, varOrGuess2 [, ]}) matrix
Returns candidate real zeros of the simultaneous algebraic expressions, where each varOrGuess specifies an unknown whose value you seek. Optionally, you can specify an initial guess for a variable. Each varOrGuess must have the form:
For example, x is valid and so is x=3. If all of the expressions are polynomials and if you do NOT specify any initial guesses, zeros() uses the lexical Grbner/Buchberger elimination method to attempt to determine all real zeros. For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use zeros() to find the intersections. As illustrated by r in the example to the right, simultaneous polynomial expressions can have extra variables that have no values, but represent given numeric values that could be substituted later. Each row of the resulting matrix represents an alternate zero, with the components ordered the same as the varOrGuess list. To extract a row, index the matrix by [row]. zeros({x^2+y^2 r^2, (x r)^2+y^2 r^2},{x,y})

r 2 r 2

You can also (or instead) include unknowns that do not appear in the expressions. For example, you can include z as an unknown to extend the previous example to two parallel intersecting cylinders of radius r. The cylinder zeros illustrate how families of zeros might contain arbitrary constants in the form @k, where k is an integer suffix from 1 through 255. The suffix resets to 1 when you use ClrHome or 8:Clear Home.
zeros({x^2+y^2 r^2, (x r)^2+y^2 r^2},{x,y,z})
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 520 of 132
For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list unknowns. If your initial choice exhausts memory or your patience, try rearranging the variables in the expressions and/or varOrGuess list. If you do not include any guesses and if any expression is non-polynomial in any variable but all expressions are linear in the unknowns, zeros() uses Gaussian elimination to attempt to determine all real zeros. If a system is neither polynomial in all of its variables nor linear in its unknowns, zeros() determines at most one zero using an approximate iterative method. To do so, the number of unknowns must equal the number of expressions, and all other variables in the expressions must simplify to numbers. Each unknown starts at its guessed value if there is one; otherwise, it starts at 0.0. Use guesses to seek additional zeros one by one. For convergence, a guess may have to be rather close to a zero. zeros({e^(z) y 1, y sin(z)}, {y,z=2p}) zeros({x+e^(z) y 1,x y sin(z)} ,{x,y}) ezsin(z)+1 (sin(z) 1)

All Other Customers

For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor.
8992APPC.DOC 8992APPC DOC TI-89 / TI-92 Plus: Appendix C (US English) Susan Gullord Revised: 02/23/01 1:56 PM Printed: 02/23/01 4:30 PM Page 582 of 8
Appendix D: Programmers Guide
setMode( ) and getMode( ).. 584 setGraph( ).... 587 setTable( ).... 589
The parameter/mode strings used in the setMode( ), getMode( ), setGraph( ), and setTable( ) functions do not translate into other languages when used in a program. For example, when you write a program in the French Language mode then switch to the Italian Language mode, the program will produce an error. To avoid this error, you must substitute digits for the alpha characters. These digits operate in all languages. This appendix contains the digit substitutions for these strings. The following examples show how to substitute digits in the setMode( ) function. Example 1: A program using alpha parameter/mode strings:
setMode("Graph","Sequence")
Example 2: The same program, substituting digits for those strings:
setMode("1","4")
8992APPD.DOC Appendix D Susan Gullord Revised: 02/23/01 1:57 PM Printed: 02/23/01 2:25 PM Page 583 of 8
setMode( ) and getMode( )
Parameter/Mode Setting ALL Graph FUNCTION PARAMETRIC POLAR SEQUENCE 3D DIFF EQUATIONS DisplayDigits FIX 0 FIX 1 FIX 2 FIX 3 FIX 4 FIX 5 FIX 6 FIX 7 FIX 8 FIX 9 FIX 10 FIX 11 FIX 12 FLOAT FLOAT 1 FLOAT 2 FLOAT 3 FLOAT 4 FLOAT 5 FLOAT 6 FLOAT 7 FLOAT 8 FLOAT 9 Strings 22 23
8992APPD.DOC Appendix D Susan Gullord Revised: 02/23/01 1:57 PM Printed: 02/23/01 2:25 PM Page 584 of 8
Parameter/Mode Setting FLOAT 10 FLOAT 11 FLOAT 12 Angle RADIAN DEGREE Exponential Format NORMAL SCIENTIFIC ENGINEERING Complex Format REAL RECTANGULAR POLAR Vector Format RECTANGULAR CYLINDRICAL SPHERICAL Pretty Print OFF ON SplitScreen FULL TOP-BOTTOM LEFT-RIGHT Split1App (applications are not numbered) Split2App (applications are not numbered) Number of Graphs 1 2