With Maple, you can create powerful interactive documents. The Maple environment lets you start solving problems right away by entering expressions in 2-D Math and solving these expressions using point-and-click interfaces. You can combine text and math in the same line, add tables to organize the content of your work, or insert images and sketch regions. You can visualize and animate problems in two and three dimensions, format text for academic papers or books, and insert hyperlinks to other Maple files, websites, or email addresses.  You can embed and program graphical user interface components, as well as devise custom solutions using the Maple programming language.

To start Maple on:

When the first Maple session opens, a Start Page displays shortcuts to useful tasks and topics.

To start a Maple session:

or

You can opt to start Maple with a blank document instead of the start page.  You can also replace the default start page with a custom start page.  For instructions, refer to the startpage help page.

To invoke the Start Page at any time, click the home button ( ) on the worksheet toolbar.

Document and Worksheet Modes

Maple offers two modes, Document Mode and Worksheet Mode. Using either mode, you can create high quality interactive mathematical documents. Each mode offers the same features and functionality; the only difference is the default input region of each mode. Document Mode Document mode uses Document Blocks as the default input region to hide Maple syntax. A Document Block region is indicated by two triangles located in the vertical Markers column along the left pane of the Maple Document, .  If the Markers column is not visible, open the View menu and select Markers. This allows you to focus on the problem instead of the commands used to solve the problem.  For example, when using the context-sensitive operations from the Context Panel on Maple input in Document mode (invoked by moving your mouse cursor over your input expression, then selecting the appropriate operation from the displayed context panel), input and output are connected using an arrow or equal sign with self-documenting text indicating the calculation that had taken place.  The command used to solve this expression is hidden.       To create a new document, select File → New → Document Mode. $$ Worksheet Mode Worksheet mode uses a Maple prompt as the default input region. The Maple input prompt is a red angle bracket, . When using context-sensitive operations on input in Worksheet mode, all commands are displayed.   To create a new worksheet, select File → New → Worksheet Mode. Full Flexibility in Either Mode Regardless of which mode you begin working in, you have the opportunity to use both document blocks and command prompts.   For example, you can hide commands in Worksheet Mode by adding a document block from the Edit menu, Edit → Document Blocks → Create Document Block (see Document Blocks), or you can show commands in Document mode by adding a Maple prompt from the Insert menu, Insert → Execution Group → Before / After Cursor (see Input Prompt).   This chapter discusses features common to both modes. Specific aspects of Document mode are explained in Document Mode, and aspects of Worksheet mode are explained in Worksheet Mode.

The Maple Workbook

The Maple Workbook acts as a container that lets you collect Maple worksheets, library archives and language files, data (such as images or spreadsheets), and other items into a single file, stored in the .maple file format. This lets you better organize your Maple-based projects. For more information, refer to the Workbook Overview help page.   Navigation of Workbook files is accomplished through the workbook Navigator palette, available in the Workbook tab.  For more information, refer to The Workbook Navigator help page.

In documents, the default format for entering mathematical expressions is 2-D Math. This results in mathematical expressions that are equivalent to the quality of math found in textbooks. Entering 2-D Math in Maple is done using common key strokes or palette items.  For more information on palettes, see Palettes. An example of entering an expression using common key strokes is presented in the following section.  An example of entering an expression using palette items is presented in Example 3 - Enter an Expression Using Palettes.  

Common Operations

Entering mathematical expressions, such as $\frac{35}{99}+\frac{1}{9}$, $x^2+x$, and $x\cdot y$ is natural in 2-D Math. To enter a fraction starting with the numerator: 1.  Enter the numerator. 2.  Press the forward slash (/) key. 3.  Enter the denominator. 4.  To leave the denominator, press the right arrow key.   To enter a fraction starting with the denominator: 1.  Enter the denominator. 2.  Press // (two forward slashes). 3.  Enter the numerator. 4.  To leave the numerator, press the right arrow key.   To enter a power: 1.  Enter the base. 2.  Press the caret (^) key. 3.  Enter the exponent, which displays in math as a superscript. 4.  To leave the exponent, press the right arrow key.   To enter a product: 1.  Enter the first factor. 2.  Press the asterisk (*) key, which displays in 2-D Math as a dot, $\cdot$. 3.  Enter the second factor.   Implied Multiplication: In general, the best practice is to enter a multiplication symbol (*) for multiplication in any calculation.  In some cases, you can instead insert a space character between two quantities to multiply them.  This is called implicit multiplication.  For example, in the expression $$$\frac{-b\+\sqrt{b^2-4 a c}}{2 a}$ a space is used for the multiplication 4*a*c and 2*a. In the case of a number followed by a variable, Maple interprets the expression as meaning multiplication even without the presence of * or a space character. However, it's easier to identify and correct mistakes in your formulas if you use the multiplication symbol (*) regularly. Important: Maple interprets a sequence of letters, for example, $\mathrm{xy}$, as a single variable. To specify the product of two variables, you must insert a space character (or multiplication operator), for example, $xy$ or $x\cdot y$. For more information, refer to the 2DMathDetails help page.

Shortcuts for Entering Mathematical Expressions

Table 1.1: Common Keystrokes for Entering Symbols and Formats Symbol/Formats Key Example implicit multiplication   Space key $\left(x^2-7 x y\+3 y^2\right) x y$   explicit multiplication${}^1$ Shift + * $2\cdot 3$ fraction${}^2$ / (forward slash) // (two forward slashes) $\frac{1}{4}$ exponent (superscript)${}^2$ Shift + ^ $x^2$$$ indexed subscript${}^2$ Ctrl + Shift + _ (Command + Shift + _ in Mac) $x_a$ literal subscript (subscripted variable name) __ (two underscores) $\mathrm{x\_\_max}$ navigating expressions >    Arrow keys   command / symbol completion${}^3$${}^{}$     •  Esc in Mac, Windows, and Linux •  Ctrl + Space in Windows •  Ctrl + Shift + Space in Linux square root sqrt and then command completion $\sqrt{25}$ exponential function${}^2$ exp and then command completion ${\ⅇ}^x$ enter / exit 2-D Math •  F5 key •  Math and Text icons in the toolbar $\frac{1}{4}$  versus$$ 1/4 ${}^1$ required for products of numbers ${}^2$ use the right arrow key to leave a denominator, numerator, superscript, or subscript region ${}^3$ for more information, see Command Completion. For a complete list of shortcut keys, refer to the 2-D Math Shortcut Keys and Hints help page.  For information on the Maple Help System, see The Maple Help System.

Example 1 - Enter and Evaluate an Expression Using Keystrokes

Review the following example: $\frac{x^2\+y^2}{2}$  In this example, you will enter $\frac{x^2\+y^2}{2}$ and evaluate the expression. Action Result in Document To enter the expression: 1.  Enter x. 2.  Press Shift + ^ . The cursor moves to the superscript position. 3.  Enter 2. 4.  Press the right arrow key. The cursor moves right and out of the superscript position. 5.  Enter the + symbol.   6.  Enter y. 7.  Press Shift + ^ to move to the superscript position.   8.  Enter 2 and press the right arrow key. 9.  With the mouse, select the expression that will be the numerator of the fraction.   10.  Enter the / symbol.  The cursor moves to the denominator, with the entire expression in the numerator. 11.  Enter 2. 12.  Press the right arrow key to move right and out of the denominator position. To evaluate the expression and display the result inline: 13.  Press Ctrl + = (Command + = in Mac). $\frac{x^2\+y^2}{2}$ = $\frac{x^2}{2}+\frac{y^2}{2}$$$ To execute 2-D Math, you can use any of the following methods. •  Pressing Ctrl + =  (Command + = in Mac). That is, press and hold the Ctrl (or Command) key, and then press the equal sign (=) key.  This evaluates and displays results inline. •  Pressing the Enter key. This evaluates and displays results on the next line and centered. •  Select the input and from the context panel, select Evaluate and Display Inline.  See The Context Panel for more details. •  Using the Evaluate menu items Evaluate and Evaluate and Display Inline.

The Maple toolbar offers easy access to a number of actions. See Table 1.2.

The Context Bar shows icons that are relevant to the location of the cursor in the document.  For example, place the cursor at an input region and the Text and Math tools are accessible. See Table 1.3 for a list of the tools available in each icon.

The Text and Math icons allow you to enter text and math in the same line by choosing the appropriate input style at each stage when entering the sentence, such as the following sentence:

The graph of $y\={\left(x-2\right)}^2-1$ is a parabola that opens up with vertex at $\left(2\,1\right)$.

For a step-by-step example of creating a sentence with text and math, see Example 6 - Enter Text and 2-D Math in the Same Line Using Toolbar Icons.

The meaning of the Text and Math icons differs while at a Maple input prompt.  The Math icon displays input as 2-D Math, whereas the Text icon displays Maple input. For details, refer to Math Mode vs. Text Mode.

To access the tools available in the Plot and Drawing icons, click a plot region.  These tools allow you to manipulate the plot or draw shapes and enter text on the plot region. By clicking an animation region, you have the same features available for a plot region, in addition to tools for playing the animation in the Animation icon. For details on plots and animations, refer to Plots and Animations.

For the description of any icon, hover the mouse over the icon to display at tooltip.

To save these examples you created, from the File menu, select Save.  Maple documents are saved as .mw files.  

To save these examples you created as part of a new Maple workbook, from the Workbook tab, click Save As Workbook. For more information about saving Maple content refer to the worksheet,managing,saving help page.

An execution group is a grouping of Maple input with its corresponding Maple output. It is distinguished by a large square bracket, called a group boundary, at the left. An execution group may also contain any or all of the following: a plot, text, embedded components, and a drawing canvas.

Execution groups are the fundamental computation and documentation elements in the document. If you place the cursor in an input command and press the Enter or Return key, Maple executes all of the input commands in the current execution group.

The default mode of entry in Document or Worksheet mode is Math Mode, which displays input in 2-D Math. In Worksheet Mode or at a prompt, you can opt to use Maple Input (1-D Math).  This is 1-D math input:

$1$

$\frac{a\sqrt{2}{\ⅇ}^{\sqrt{2}x}}{2}$

$\underset{x\to \mathrm{\infty }}{lim}f\left(x\right)$

$\sum _{k=0}^m{a}_k{x}^k=\prod _{j=0}^n{b}_j{x}^j$

In Document Mode, to enter input using Maple Input mode, insert a Maple prompt by clicking  in the toolbar, and then click the Text button in the context bar. In Worksheet Mode, simply click the Text button. See Figure 1.2.

If you prefer 1-D Math input in Worksheet mode, you can change the default math input notation.

To change math input notation for a session or globally across all documents:

This changes the default input math notation at the prompt ( ).

Important: The new input display becomes the default setting after pressing the Enter key.

Palettes are collections of related items that you can insert into a document by clicking or drag-and-dropping. The Maple environment provides access to over 30 palettes containing items such as symbols $\left(\infty \right)$, layouts $\left(A^b\right)\,$mathematical operations $\left({\int }_a^{b}f\ⅆx\right)\,$and much more.

By default, palettes are displayed in the left pane of the Maple environment when you launch Maple.  If the palettes are not displayed,

Alternatively, select View → Palettes → Show All Palettes.

You can create a Favorites palette of the expressions and entities you use often by right-clicking (Control-click, Mac) the palette template you want to add and selecting Add To Favorites Palette from the context menu.  

Viewing and Arranging Palettes

By default, palettes display in palette dock in the left pane of the Maple window.  To view and manage palettes and palette docks, see Table 1.7. Table 1.7: Managing Palettes To view the palette dock: •  From the View menu, select Palettes, and then Expand Dock. The dock is in the left pant of the window.   To add a palette: 1.  Right-click the palette dock.  Maple displays a context menu near the palette. 2.  From the context menu, select Show Palette and then select the palette. To expand or collapse a palette in the palette dock: •  Click the triangle at the left of the palette title.   To move a palette in the palette dock: •  Move the palette by clicking the title and dragging the palette to the new location.   To expand or collapse the pane containing the palette dock: •  Select the appropriate triangle at the top right side of the palette region.

Example 3 - Enter an Expression Using Palettes

Review the following example: $\sum _{i\=1}^{10}\left(7 i^2-5 i\right)$ = $2420$  In this example, we will enter $\sum _{i\=0}^{10}\left(7 i^2-5 i\right)$ and evaluate the expression. Action Result in Document 1.  Place the cursor in a new document block. In the Expression palette, click the summation template . Maple inserts the summation symbol with the range variable placeholder highlighted. 2.  Enter i and then press Tab. The left endpoint placeholder is selected.  Notice that the color of the range placeholder has changed to black. Each placeholder must have an assigned value before you execute the expression. The Tab key advances you through the placeholders of an inserted palette item. 3.  Enter 1 and then press Tab. The right endpoint placeholder is selected. 4.  Enter 10 and then press Tab. The expression placeholder is selected. 5.  Enter $\left(\mathbf{7}\mathbf{ }{\mathbf{i}}^{\mathbf{2}}\mathbf{-}\mathbf{5}\mathbf{ }\mathbf{i}\right)\.$ For instructions on entering this type of expression, see Example 1 - Enter and Evaluate an Expression Using Keystrokes. 6.  Press Ctrl + = (Command + = for Mac) to evaluate the summation. $\sum _{i\=1}^{10}\left(7 i^2-5 i\right)$ = $2420$

	Favorites Palette
	You can add to the Favorites palette any expressions that you use most often. •  To add an entry from another palette to the Favorites palette, simply drag the entry to the Favorites palette. •  To add a custom expression, select the expression in the worksheet and select Add Selection to Favorites Palette from the Context Panel.

Each symbol has a name and some have aliases. By entering its name (or an alias) in Math mode, you can insert the symbol in your document. All common mathematical symbols, including all Greek characters, $\mathrm{\π}$, and $$the square root symbol ($\sqrt{}$), are recognized by Maple.  

Note: If you hover the mouse pointer over a palette item, a tooltip displays the symbol's name.

To insert a symbol, enter the first few characters of a symbol name using a keyword that is familiar to you and then press the completion shortcut key, Esc (see Shortcut Keys by Platform). Symbol completion works in the same way as command completion (see Command Completion).

Example 4 - Square Root

To find the square root of $603729$: Action Result in Document 1.  In a new document block, enter sqrt. 2.  Press the symbol completion shortcut key, Esc. Maple displays a popup list of exact matches. 3.  In the completion list, select . Maple inserts the symbol with the $x$ placeholder selected. 4.  Enter $603729$ into the placeholder. $\sqrt{603729}$ 5.  Press Ctrl + = (Command + =, Mac). $\sqrt{603729}$ = $777$

Example 5 - Complex Numbers

In Maple, the default display for imaginary i is a capital $\mathrm{I}$. When you simply type the letter $i$ in Math mode, it is in italics. This letter is just a variable, and is not the same as the imaginary unit $\sqrt{-1}\,$denoted by $\mathrm{I}$ or $\mathrm{i}$ in Maple. Because of this, i can be used as a variable, for instance $\mathrm{sum}\left(i\,i\=1..4\right)$ = $10$  .     Multiply two complex numbers, $-0.123\+0.745 \mathrm{i}$ and $4.2-\mathrm{i}$:   We will compute the result two ways, using $\mathrm{I}$ and then using $\mathrm{i}$.  The first way is the quickest to enter. Action Result in Document 1.  In a new document block, enter $\left(-0.123\+0.745 \mathrm{I}\right)\cdot \left(4.2-\mathrm{I}\right)$  Use * to enter multiplication between the two complex numbers. $\left(-0.123\+0.745 \mathrm{I}\right)\cdot \left(4.2-\mathrm{I}\right)$ 2.  Press Ctrl + = (Command + =, Mac) to evaluate the product. $\left(-0.123\+0.745 \mathrm{I}\right)\cdot \left(4.2-\mathrm{I}\right)$ = $0.2284+3.2520\mathrm{I}$    Table 1.8: Complex Numbers using I   The next method, while not as quick to enter, displays the computation using lowercase i. Action Result in Document 1.  In a new document block, enter $\(-0.123\+0.745 i$. 2.  Press the symbol completion shortcut key, Esc. Maple displays a popup list of partial and exact matches, including symbols and commands. 3.  Select the imaginary unit, . 4.  Close the parentheses, enter * (for multiplication), and type the second expression in parentheses, using symbol completion for the second imaginary number. $\left(-0.123\+0.745 \mathrm{i}\right)\cdot \left(4.2-\mathrm{i}\right)$ 5.  Press Ctrl + = (Command + =, Mac) to evaluate the product. $\left(-0.123\+0.745 \mathrm{i}\right)\cdot \left(4.2-\mathrm{i}\right)$ = $0.2284\+3.2520\mathrm{I}$  Table 1.9: Complex Numbers using i For more information on entering complex numbers, refer to the HowDoI/EnterAComplexNumber help page.

In the introduction section, you learned about the toolbar icons and context toolbars available in Maple (see Toolbar Options). The toolbar can be used to format your document, alter plots and animations, draw in a canvas, write in both Math and Text modes in one line and much more. The last of these is demonstrated in the next example.

Example 6 - Enter Text and 2-D Math in the Same Line Using Toolbar Icons

Enter the following sentence: Evaluate ${\int }_1^5\left(3 x^2\+2 \sqrt{x}\+3\sqrt[3]{x}\right) \ⅆx$ and write in simplest terms.    Action Result in Document To enter this sentence: 1.  Select the Text icon and enter "Evaluate ". 2.  Select the Nonexecutable Math icon. 3.  From the Calculus palette, select the definite integration template, .  The expression is displayed with the first placeholder highlighted. 4.  With the first placeholder highlighted, enter 1, then press Tab. 5.  Enter 5 and press Tab to highlight the integrand region. 6.  Enter (3x^2 and press the right arrow to leave the superscript position. 7.  Enter + 2. 8.  Press the Space bar for implicit multiplication. Enter sqrt and press Esc to show the command completion options.  Maple displays a popup list of exact matches.  Select the square root symbol, $\sqrt{x}$.   Maple inserts the symbol with the x placeholder selected.  (Alternatively, select the square root symbol from the Expression palette.) 9.  Enter x, then press the right arrow to leave the square root region. 10.  Enter + 3, and then press the Space bar. 11.  Select the n-th root symbol from the Expression palette, .   12.  Enter 3, then press Tab. 13.  Enter x, then press the right arrow to leave the root region. 14.  Enter ), then press Tab. 15.  Enter x for the integration variable.   16.  Put the cursor after the expression and click the Text icon in the toolbar, then enter the rest of the sentence: " and write in simplest terms." Note: When an expression is intended for display purposes only, as in this example, it can be displayed in nonexecutable math.  This is indicated by the gray background.  For more information on executable and nonexecutable math, refer to the 2DMathDetails help page.

Maple offers a set of assistants in the form of graphical user interfaces to perform many tasks without the need to use any syntax.

Using the Tools → Assistants menu, you can access tools to help you accomplish various tasks.  See Figure 1.3.  In some cases, you can launch an assistant by entering an expression and selecting the assistant from the options in the Context Panel.

Descriptions of Assistants

The available assistants are described below.  Some of the assistants are interfaces to package commands.  For more information on package commands, see Package Commands. •  Code Generation - an interface to automatically transform Maple expressions and programs to other languages. •  eBook Publisher - an interface to the eBook Publisher tools. •  Import Data - an interface to read data from an external file into Maple. •  Installer Builder - an interface to the InstallerBuilder package in which you can create installers for your Maple toolboxes. •  Library Browser - an interface to manipulate the libraries in a specified directory. •  Maplet Builder - an interface to the Maplets package. The Maplets package contains commands for creating and displaying Maplet applications (point-and-click interfaces). Using the Maplet Builder, you can define the layout of a Maplet, drag-and-drop elements (visual and functional components of Maplets), set actions associated with elements, and directly run a Maplet application. The Maplet Builder is available in the Standard interface only. •  Plot Builder - an interface for creating two and three-dimensional plots, animations, and interactive plots. •  Scientific Constants - an interface to over 20 000 values of physical constants and properties of chemical elements. All of these constants come with the corresponding unit and, if applicable, with the uncertainty or error, that is, how precisely the value of this constant is known. •  Special Functions - an interface to the properties of over 200 special functions, including the Hypergeometric, Bessel, Mathieu, Heun and Legendre families of functions. •  Thermophysical Properties Calculator - Calculate state-dependent and independent thermophysical properties. •  Units Converter - an interface to convert between 500 units of measurement. •  Worksheet Migration - an interface to convert worksheets from Classic Maple (.mws files) to Standard Maple (.mw files).

Maple provides over 50 interactive tutors and assistants to aid in the learning of

These tutors are easily accessible in the Tools menu by selecting Tutors.  See Figure 1.4.

Some of the tutors can also be accessed through the Student package. The Differential Equations tutor, DE Plots, is accessible through the DEtools package.  For a definition of the term package, see Package Commands.

The Student package is a collection of subpackages designed to assist with the teaching and learning of standard undergraduate mathematics. The subpackages contain many commands for displaying functions, computations, and theorems in various ways, and include support for stepping through important computations.

The interactive commands help you explore concepts and solve problems using a point-and-click interface. These commands launch tutors that provide a graphical interface to some of the visualization and computation commands described above.  See Figure 1.5 for an example of one of the tutors.

 The Practice Sheets Assistant, found under Tools → Tutors→ Basics, lets you construct a practice sheet of math problems.  It's easy to interactively construct a randomized set of problems arithmetic, algebra, calculus, factorization and more.  Students can then do the problems, check their solutions, and even generate another set of problems.

For more information on the tutors and related resources for mathematics education, see Teaching and Learning with Maple.

Maple provides Math Apps that offer interactive, entertaining ways to explore mathematical concepts, ranging from Precalculus to Physics to Economics.  A guide to these demonstrations is accessible in the Tools menu by selecting Math Apps.

The context panel is a dynamically generated list of tools and actions that are applicable for the region on which it is invoked. These tools and actions are further organized into menus. Use the context panel to perform calculations and manipulations on expressions without using Maple syntax. To display the context panel, select an object, expression, or region. Context panel options are available for many input regions, including:

When performing calculations or manipulations on an expression, a self-documenting arrow or equal sign connects the input and output, indicating the action that took place.  See Figures 1.8 and 1.9 for two examples of context-sensitive operations.

Task templates help you perform specific tasks in Maple, such as:

Each task contains a description along with a collection of content that you can insert directly into your document. Content consists of 2-D mathematics, commands, embedded components (for example, buttons), and plots. You specify the parameters of your problem and then execute the commands in the document. See Figure 1.8 for an example of a Task Template.

	Previewing Tasks
	To preview Maple tasks, •  From the Tools menu, select Tasks, and then Browse. The Browse Tasks dialog opens and displays the list of tasks. The tasks are sorted by subject to help you quickly find the desired task. In the Browse Tasks dialog, you can view tasks without inserting them into your document.

Inserting a Task into the Document

To insert a task into your document, 1.  Select the Insert into New Worksheet check box to insert the task into a new document. 2.  Click one of the insert buttons. •  Click the Insert Default Content button. Maple inserts the default content. The default content level is set using the Options dialog. For instructions, refer to the usingtasks help page. •  Click the Insert Minimal Content button. Maple inserts only the commands and embedded components, for example, a button to launch the related assistant or tutor. •  Click the Copy Task to Clipboard button. Place the cursor where you want to insert the task, and then paste the task. Maple inserts the default content. Use this method to quickly insert a task multiple times. Note: You can view the history of previously inserted tasks. From the Tools menu, select Tasks.  Previously selected task names are displayed below the Browse menu item. Before inserting a task, Maple checks whether the task variables have assigned values in your document. If any task variable is assigned, the Task Variables dialog opens to allow you to modify the names. Maple uses the edited variable names for all variable instances in the inserted task. By default, the Task Variables dialog is displayed only if there is a naming conflict. You can set it to display every time you insert a task.   To specify that the Task Variables dialog be displayed every time you insert a task: 1.  From the Tools menu, select Options. 2.  Click the Display tab. 3.  In the Show task variables on insert drop-down list, select Always. 4.  Click Apply to Session or Apply Globally, as necessary.

Updating Parameters and Executing the Commands

In inserted Task Templates, parameters are marked as placeholders (in purple text) or specified using sliders or other embedded components. 1.  Specify values for the parameters in placeholders or using graphical interface components. You can move to the next placeholder by pressing Tab. 2.  Execute all commands in the task by: •  Placing the cursor in the first task command, and then pressing Enter repeatedly to execute each command. •  Selecting all the template commands, and then clicking the execute toolbar icon . 3.  If the template contains a button that computes the result, click it.   For more information on task templates, refer to the tasks help page.

The Exploration Assistant allows you to interactively make parameter changes to expressions and view the result. The assistant can be used with almost any Maple expression or command that has at least one variable or parameter.

To launch the Exploration Assistant:

If you enter integer ranges, only integer values are allowed for parameters. To allow floating-point values, enter floating-point ranges.

Select skip for any of the parameters to leave that parameter as a variable.

Example 7 - Use the Exploration Assistant to Explore a Plot

In this example, we will explore how the plot of $\frac{\sin \left(a x\right)-b \cos \left(x\right)}{x}$ changes as we vary the parameters $a$ and $b$. Action Result in Document 1.  Enter the plot command shown. $\mathrm{plot}\left(\frac{\sin \left(a x\right)-b \cos \left(x\right)}{x}\,x\=1..10\right)$ 2.  Click the expression and select Explore from the context panel. 3.  In the Explore parameter selection dialog, set the ranges a = 0..10.0 and b = -5..5.0.   4.  Click Explore.  The Exploration Assistant creates a table in the document.  Move the sliders to see the plot as the parameters change.     Tip: Since decimal numbers were used for the ranges in step 3, the slider uses decimal numbers.  If you use integers for the ranges, the slider uses integer numbers.

Commands are contained in the Maple library, which is divided into two groups: the main library and packages.

The main library contains the most frequently used Maple commands.  

Packages contain related commands for performing tasks from disciplines such as Student Calculus, Statistics, or Differential Geometry.  For example, the Optimization package contains commands for numerically solving optimization problems.

For details on top-level and package commands, see Commands.

If you want to interact with Maple using commands, simply enter the command using 2-D math.  Notice that commands and variable names display in italics. Maple commands are constructed in a format similar to command(arguments), based on the command you are using.

For example, to factor an expression, enter:

$\mathrm{factor}\left(x^2\+2 x\+1\right)$

${\left(x\+1\right)}^2$

To differentiate an expression, enter:

$\mathrm{diff}\left(\sin \left(x\right)\, x\right)$

$\cos \left(x\right)$

To integrate an expression on the interval $\left[0\, 2 \mathrm{\π}\right]$, enter:

$\mathrm{int}\left(2 x\+\cos \left(x\right)\, x\=0..2 \mathrm{\π}\right)$

$4{\mathrm{\π}}^2$

To plot an expression, enter:

$\mathrm{plot}\left(\sin \left(x\right) x^2\, x\=-10..10\right)$

For a list of the top commands in Maple, see Top Commands.

Package Commands

There are two ways to access commands within a package, using the long form of the package command or the short form.     Long Form of Accessing Package Commands: The long form specifies both the package and command names using the syntax package[command](arguments).     $\mathrm{LinearAlgebra}\left[\mathrm{RandomMatrix}\right]\left(2\right)$ Short Form of Accessing Package Commands: The short form makes all of the commands in the package available using the with command, with(package).  If you are using a number of commands in a package, loading the entire package is recommended.  When you execute the with command, a list of all commands in the package displays.  To suppress the display of all command names, end the with(package) command with a colon.  Alternatively, you can load packages through the Tools menu, by selecting Load Package, and then the package name. $\mathrm{with}\left(\mathrm{Optimization}\right)$ $\left[\mathrm{ImportMPS}\,\mathrm{Interactive}\,\mathrm{LPSolve}\,\mathrm{LSSolve}\,\mathrm{Maximize}\,\mathrm{Minimize}\,\mathrm{NLPSolve}\,\mathrm{QPSolve}\right]$ After loading a package, you can use the short-form names, that is, the command names, without the package name. $\mathrm{LSSolve}\left(\left[x-2\, x-6\, x-9\right]\right)$ $\left[12.3333333333333321\,\left[x\=5.66666666666667\right]\right]$   For a list of the top packages in Maple, see Top Packages.

Command Completion

To help with syntax and reduce the amount of typing when entering Maple commands, you can use command completion. Command completion displays a list of all Maple packages, commands, and functions that match the entered text. If there are multiple ways to call a command, then the command completion list contains each one, with appropriate placeholders.   To use command completion: 1.  Begin entering a command or package name. 2.  Select Tools → Complete Command or use the shortcut key Esc (see Shortcut Keys by Platform). If there is a unique completion, it is inserted. Otherwise, a list of possible matches is displayed. 3.  Select the correct completion from the list. 4.  Some inserted commands have placeholders, denoted by purple text. The first placeholder is highlighted after you insert it into the document. Replace it with your parameter, then move to the next placeholder by pressing the Tab key.

Equation Labels

Equation labels help to save time entering expressions by referencing Maple output. See Figure 1.9. By default, equation labels are displayed. If equation labels are not displayed, 1.  From the Tools menu, select Options, and click the Display tab. Ensure that the Show equation labels check box is selected. 2.  From the Format menu, select Equation Labels. Ensure that both Execution Group and Worksheet are selected. Figure 1.9: Equation Label   To apply equation labels: 1.  Enter an expression and press Enter. Note that the equation label is displayed to the right of the answer in the document. 2.  In a new execution group, enter another expression that will reference the output of the previous execution group. 3.  From the Insert menu, select Label. Alternatively, press Ctrl+L (Command+L, for Mac) to open the Insert Label dialog.  Enter the label number in the Insert Label dialog and click OK. The item is now a label. See Figure 1.10. Figure 1.10: Inserting an Equation Label   4.  Press Enter to obtain the result.   To change the format of equation labels: •  Select Format → Equation Labels → Label Display. In the Format Labels dialog, select one of the numbering schemes.  Numbering can be flat numbers for the entire worksheet, or by section, so that equations in section 1 are labeled (1.1), (1.2), and so on. •  Optionally, enter an appropriate numbering prefix. Figure 1.11: Controlling Equation Label Format   The Label Reference menu item allows you to switch between the label name and its reference content. Place the cursor on the referenced equation label and select Format → Equation Labels → Label Reference. Figure 1.12: Label Reference   The label is associated with the last output within an execution group. You cannot apply equation labels to the following: •  Error, warning, and information messages •  Tables, images, plots, or sketches