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A computer algebra system or CAS is a representational toolkit that allows one to manipulate symbolic expressions and equations, to compute results in approximate and exact forms, and to create, move between, and transform linked graphic and numeric representations of functions.
Type into the Command line and press Enter to execute a command. Each entry will be recorded above in the History. Click on a result in the History and press Enter to re-enter it into the Command line.
Note: Some equations defined as explicit or implicit functions in the Command line (e.g., those involving function notation, or the variables x and y among others) will also be recorded in the Y= menu.
See also Algebra & Functions Commands.
The Algebra and Functions menus, and Options | Math Toolbar entries from the Home tab give common commands to use for CAS. Click here for explanations and examples of these commands in use.
Type +, -, *, /, ^ to substitute the last expression into an additional expression in the Command line.
Example. Keystrokes used in Command line: 3x+11=5x+7 [Enter] -3x [Enter] -7 [Enter] /2 [Enter]. Recorded in History: 3*x+11=5*x+7; 11=2*x+7; 4=2*x; 2=x.
A common error displayed in the History is "Syntax error," which indicates that the symbols used in the previously entered command may be out of order, missing, or inappropriately used. Check for correct spelling and use of parentheses.
Setting the mode and default display of computations is done using the Home | Options menu.
See also Settings for Graphs and Tables.
Note: The mode must be set in the Home tab; this setting applies to the entire CAS (Home, Y=, Settings, Table and Graphs).
For example, in Auto Numeric mode type 2/3 to yield .6667. Otherwise, 2/3 will be displayed.
Note: Another way to express numeric expressions in decimal form is to contaminate an expression with a period ".". For example, compare the results of expressions (4./5)^2 (a period after the 4) and (4/5)^2 (no period).
Use the Home tab Matrices menu to define new matrices, edit existing matrices, perform matrix computations, and view matrices as vertex-edge graphs.
There are several ways to define new matrices:
matrixName:=[[column 1],[column 2],...[column n]]
where [column 1] is a list of the entries of the first column in the form [a11, a21, ..., an1] such that a11 is the first entry of the first column, a21 is the second entry of the first column, and so on.
|m:=matrix(2,3)||Let the character m reference a 2x3 zero matrix. Type m Enter in the Command line to call this matrix.|
|m:=matrix(2,2,a,b,c,d)||Let the character m reference a 2x2 matrix with row entries a, b, and c, d. Type m Enter in the Command line to call this matrix.|
|m:=[[1,2],[3,4]]||Let the character m reference a 2x2 matrix that is defined by its first and second columns: [1,2] and [3,4]. Note: Be sure to include a comma (",") between the two column matrices.|
To edit a matrix:
Note: The Matrix Editor | Edit menu offers options to Add Row, Add Column Delete Row, and Delete Column. Click in the desired cell then choose an Edit menu option.
To compute with matrices type into the Command line or use the Matrix | Functions menu. Click below to view an explanation of a command and see examples of its use:
matrix(), inv(), det(), id(), tr(), size(), row(), col().
View a matrix as a Directed or Undirected Vertex Edge Graph by choosing the desired entry from Home | Matrices | View Matrix As. The selected matrix will be treated as an adjacency matrix and will be represented as a vertex-edge graph in a new window.
See also Advanced Apps | Vertex-Edge Graphs.
The Y= tab is used to define, select, and edit equations and functions that can later be viewed in the Table or Graph tabs.
Define Equations and Functions
In general, any explicit or implicit equality or inequality that relates variables is an allowable function that may be defined in either the Y= tab or the Home tab. Some Help Tips are included below:
See also Algebra and Functions Commands, Matrices.
See also Save & Print.
Select and Edit Equations and Functions
Type into the Y= Command line end press Enter; it will be listed below. Options to box and select equations/functions include:
Press Enter to re-execute a boxed equation in the Command line to edit it (or choose Edit | Edit Boxed Equation). Choose Edit | Delete Boxed equation to remove it from the Y= list.
Choose Edit | Clear All to erase all currently defined equations listed in the Y= tab.
If there is no check mark to its left, the equation is not selected and the settings, graph, and table cannot be viewed.
Choose Edit | Select All or (Edit | Deselect All) to check (or uncheck) all listed equations/functions at once.
Settings and Plot Options
When an equation has been defined, a pull down options menu becomes available to its left. Use this menu to select from Rectangular, Polar, Parametric, or 3D plot options.
See also Home | Settings, Settings tab.
The Settings tab allows you to modify the window options and plot styles that pertain to the Graph tab and Table tab. The Settings tab applies to all functions defined and selected in the Y= tab. Available options depend upon whether a function is 2D (explicit or implicit) or 3D.
Note: A check mark must be next to at least one equation/function within the Y= tab for the Settings tab to be available.
See also Home tab Settings.
Quickly modify settings for graphs and tables with the Options menu.
Note: The Mode (Degree/Radian) should be set prior to executing trigonometric commands and adjusting settings.
See also Home tab Settings.
The 2D Functions tab within the Settings tab pertains to all selected functions that are defined explicitly from within the Y= tab (e.g., the dependent variable is written as a function of the independent variable such as y=x+2).
Note: If Options | Simultaneous is not checked, then each explicitly defined function will have its own sub tab to adjust settings individually.
The Implicit sub tab within the Settings tab pertains to all selected functions that are defined implicitly from within the Y= tab (e.g., 4x+y=8). Minimum and maximum x and y values can be set for this type of 2D Function.
Settings for 3D Plots can be changed for each plot that is defined. Values for minimum and maximum X, Y, and Z coordinates can be changed for both the View Bounds and Graph Bounds.
Note: When simultaneously graphing multiple 3D functions it may be helpful to make one of the plots Transparent and to Color By: Z to better view the intersection.
The Table tab becomes available once an explicitly defined 2D Function or a 3D Plot is selected within the Y= tab. The settings that were determined within the Settings tab apply to the Table tab. Some Help Tips are include below:
See also Settings | Options.
For example, using y1(x):=8cos(x-30)+2 and y2(x):=6sin(x-60)+3 will give y1 and y2 as headers in the table, helping to distinguish between the two.
See also Save & Print.
The Graph tab becomes available once a function is defined and selected within the Y= tab. The window settings that are chosen from within the Settings tab determine the initial graphical display. Also use the Zoom and View Options to customize the display.
Note: To trace (i.e., view the coordinates of points) a graph move the cursor over the graph.
See also Save & Print.
Determine the Window in the Settings tab or use the Graph tab Zoom menu:
Note: Set the mode in the Home | Options menu before adjusting the window or zoom settings.
Graph View Options
Note: Choose Options | Polar Grid to show (or hide) a polar grid. It may be useful to hide the (Cartesian) grid when this options is selected.
Note: This option pertains to plotted functions that include parameters. For example, define and select y=a*x+b in the Y= tab. Notice the slider bars for a and b within the Graph tab.
Slice 3D Plots
The Slice menu of the Graph tab is only available when viewing 3D Plots. It allows you to position a slicing plane, parallel to either the x-y plane, y-z plane, or x-z plane, and examine how the slicing plane intersects the 3D plot(s).
To view a data tab, choose File | Data in the Home or Y= tab.
Help topics on Data sheets are available in the Data Analysis Help. Note however that Data tab functionality is slightly different than the Data Analysis tool:
Note: If you choose to plot a scatterplot from data within the Data tab of CAS, the scatterplot will be available within the Graph tab. Choose to plot functions over the scatterplot by selecting them in the Y= tab. Also plot multiple scatterplots in the same window by enabling more than one from within the Y= tab and adjusting the window Settings as needed.