How do I...
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Maple's Tutorials are designed to help you get started with Maple, learn about the key tools available in Maple, and lead you through a series of problems.
The How do I... topics cover essentials for doing mathematics in Maple. Learn more about Maple's tools and features, such as palettes and contextsensitive menus.
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How do I...


This section explains how to perform basic tasks in Maple, including entering mathematical objects (such as simple expressions, functions, matrices, and complex numbers), evaluating expressions, and plotting functions.

...enter a simple expression?


In Maple, mathematical expressions, such as , can be entered in a natural, textbooklike notation. In Maple, this is called 2D Math notation. The following examples demonstrate the process of entering expressions.
To begin, create a new document in Document mode. To begin entering a 2D mathematical expression, ensure that you are in Math mode. In this mode, the cursor is inside a box with a dotted outline that indicates the boundaries of the mathematical expression. By default, all new documents created in Document mode start in Math mode so that you can begin entering mathematical expressions immediately. To switch between Math mode and Text mode, press [F5].
A video demonstration of the following examples is available online.

Example:


Ensure that you are in Math mode, and follow the steps below to enter the expression .
Step

Description

Illustration

1

Type , then . Maple's Math mode treats the juxtaposition of a constant and a variable as an implicit multiplication.


2

Type the division [/] character.


3

Type .


4

To bring the cursor back onto the base line, press the right arrow [→] key on your keyboard.


5

Type [+]. There is no need to type a space, as Maple automatically adjusts the spacing for you.


6

Repeat steps 1 through 4 to type .


(7)

If you wish to continue typing nonmathematical text, press [F5] to switch to Text mode.






Example:


Ensure that you are in Math mode, and follow the steps below to enter the expression .
Step

Description

Illustration

1

Click the template in the Expression palette. The green placeholder is selected automatically.


2

Type , overwriting the .


3

To enter an exponent, type the common power character [^] using the key combination [Shift][6]. The cursor is now in the exponent position. Type .


4

To bring the cursor back onto the base line, press the right arrow [→] key on your keyboard.


5

Type [+]. There is no need to type a space, as Maple automatically adjusts spacing for you.


6

Type the word pi, and press [Esc]. The command completion list appears, listing every available symbol and command whose name begins with . For the Greek symbol for pi, Select .


(7)

If you wish to continue typing nonmathematical text, press [F5] to switch to Text mode.





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...enter a function?


Mathematical functions are represented in Maple as operators. There are various methods for entering a function: by using a template from the Expression palette, by using Maple's operator syntax directly, or by converting an existing expression into an operator.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions. (See the subsection above.) Open a new worksheet in Document mode, and ensure that you are in Math mode.

Using a template from the Expression palette


Follow the steps below to enter the operator and assign it to a variable whose name is .
Step

Description

Illustration

1

Select the template from the Expression palette. The green placeholder is selected automatically.


2

Type , overwriting the green .


3

Move the cursor among placeholders by pressing [Tab]. The is selected as you do so. Type .


4

Press [Tab] to select the final placeholder . To type , first type . Use the common power character [^] ([Shift][6]) to bring the cursor into the exponent position and type .


5

To bring the cursor back onto the base line, press the right arrow [→] key on your keyboard.


6

Type []. There is no need to type a space, as Maple automatically adjusts spacing for you. Type .


7

Press [Enter] to execute the statement. Maple displays and labels the result of an executed statement on a new line. (For more information, see the How do I subsection on evaluating expressions.)


8

To see what does, enter and press [Ctrl][=] to evaluate it inline. As you can see, Maple evaluates the expression at , which yields .




When working with templates from the palettes, keep these tips in mind.
•

If you accidentally move the cursor outside a template, simply move the cursor back into the template and press [Tab] to move to the next placeholder.

•

Use [Shift][Tab] to move back to the previous placeholder, if you have not overwritten it yet.



Using Maple's operator syntax


Follow the steps below to enter and assign it to a variable whose name is .
Step

Description

Illustration

1

Type , followed by a colon [:] and an equal sign [=]. The colonequals notation assigns the content on the righthand side to a variable name on the lefthand side.


2

Type . This is the name of the independent variable. To type the arrow, first type a minus sign [], then the right angular bracket [>]. Maple automatically converts these characters to an arrow.
Tip: ">" looks like a right arrow.


3

Type . For detailed instructions, see the above example, steps 4 to 6.


4

Press [Enter] to execute the statement. Maple displays and labels the result of an executed statement in a new line. (For more information, see the How do I subsection on evaluating expressions.)


5

To see what does, enter and press [Ctrl][=] to evaluate it inline. As you can see, Maple evaluates the expression at , which yields .






Converting an existing expression into an operator


Suppose the expression has already been typed. Follow the steps below to convert it to the operator and assign the result to a variable whose name is .
Step

Description

Illustration

1

Rightclick any part of the expression (within the dotted outline). A contextsensitive menu is displayed. For more information, see the ContextSensitive Menus subsection under the Tools and Features section of this document.


2

Select Conversions → Operator → . Maple will convert the expression to an operator of .


3

Rightclick any part of the blue output; in the contextsensitive menu that appears, select Assign to a Name.


4

A dialogue box appears; enter the name . Click OK.


5

To see what does, enter and press [Ctrl][=] to evaluate it inline. As you can see, Maple evaluates the expression at , which yields .





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...enter a matrix?


Entering matrices in Maple is very simple. This section demonstrates two methods for entering a matrix: by inserting a template from the Matrix palette and by using the Matrixconstructor shortcut syntax.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions (see the subsection above). Open a new worksheet in Document mode, and ensure that you are in Math mode.
A video demonstration showing how to enter a matrix using the Matrix palette is available online.

Using the Matrix palette to create a template


Follow the steps below to enter the threebyfour matrix and assign it to a variable whose name is .
Step

Description

Illustration

1

Type , followed by a colon [:] and an equal sign [=]. The colonequals notation assigns the content on the righthand side to a variable on the lefthand side.


2

In the Matrix palette, either
•

Click and hold the Choose... button and drag a threebyfour rectangle in the box that pops up, or

•

Type into the Rows field and into the Columns field.



3

Click Insert Matrix.


4

Type over the highlighted placeholder. To move to and highlight the next placeholder, press the [Tab] key.


5

Continue to navigate through the placeholders using the [Tab] key and enter values for the entire matrix.


6

Press [Enter]. Maple displays and labels the result of an executed statement in a new line. (For more information, see the How do I subsection on evaluating expressions and the Tools and Features subsection
Equation Labels.)




When working with templates from the palettes, keep these tips in mind.
•

If you accidentally move the cursor outside a template, simply move the cursor back into the template and press [Tab] to move to the next placeholder.

•

Use [Shift][Tab] to move back to the previous placeholder, if you have not overwritten it yet.



Using Maple's Matrixconstructor shortcut syntax


Follow the steps below to enter the threebyfour matrix and assign it to a variable whose name is . For details about the special syntax used in these steps, see the associated help topic.
Step

Description

Illustration

1

Type , followed by a colon [:] and an equal sign [=]. The colonequals notation assigns the content on the righthand side to a variable name on the lefthand side.


2

Type two left angular brackets [<] [<], followed by (separated by commas), and a right angular bracket [>]. The expression represents the first column of the final matrix.


3

Type the pipe character []. This character is usually typed by pressing [Shift][\], the backslash key. The pipe character separates the four columns in the final matrix.


4

As before, type the columns , , and , separated by pipe characters []. Type a final right angular bracket [>]. The angular brackets are automatically formatted by Maple.


5

Press [Enter]. Maple displays and labels the result of an executed statement in a new line. (For more information, see the How do I subsection on evaluating expressions and the Tools and Features subsection
Equation Labels.)




When working with this shortcut syntax, keep these tips in mind.
•

The comma [,] is used to separate elements in different rows, while the pipe symbol [] is used to separate elements in different columns.

•

As a result, the matrix could also be entered as .


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...evaluate an expression?


Maple can evaluate any mathematical expression and display the results inline or on a new line. Maple can also evaluate an expression at a point.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions. (See the subsection above.) Open a new worksheet in Document mode, and ensure that you are in Math mode.

Evaluating an expression inline


Follow the steps below to evaluate and display the result inline.
Step

Description

Illustration

1

Type . For instructions on entering this expression, see the subsection entering an expression above.


2

Press [Ctrl][=] to evaluate the expression inline.




The inline evaluation mechanism, when used with Maple's ContextSensitive Menus, is one of the fastest methods to perform a string of successive computations.


Evaluating an expression on a new line


Follow the steps below to evaluate and display the result on a new line.
Step

Description

Illustration

1

Type . For instructions on entering this expression, see the subsection entering an expression above.


2

Press [Enter]. Maple displays and labels the result of an executed statement on a new line. By default, if this result is the first label in the document, it will be shown as (1). For more information on labels, see the Equation Labels subsection of the Tools and Features section.




Equation labels organize the flow of computations. Keep these tips in mind when working with labels.
•

References can be made to any labeled result.

•

Labels are automatically numbered in sequence; if any labeled result is removed, Maple automatically renumbers all equation labels and updates all equation label references.



Evaluating at a point


Follow the steps to evaluate at .
Step

Description

Illustration

1

Type . For instructions on entering this expression, see the subsection entering an expression above.


2

Rightclick on the expression. In the contextsensitive menu that appears, select Evaluate at a Point.


3

A dialog box appears; enter .
The substitution is made.


(4)

Note that the result was calculated in symbolic form. If you prefer an approximation, rightclick on the result and choose Approximate and the desired number of digits.




You can also use the "evaluate at a point" template
from the Expression palette.
For example,

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...plot a function?


Maple has extensive plotting functionality to help you visualize the behavior of mathematical functions. The examples below show how to construct a graph of the function by using two different methods: by using Maple's Context Menu system and by using the interactive Plot Builder.
The generated plot can be manipulated; it can be scaled, zoomed, panned, and resized. For more details on plotting, refer to the comprehensive Maple Plotting Guide. For information about Maple commands used in plotting, see the help pages on plot, plot3d, and plottools.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions (see the subsection above). Open a new worksheet in Document mode, and ensure that you are in Math mode.
A video demonstration of the first method (and of plotting in general) is available online.

Using Maple's context menu system


Follow the steps below to plot the function .
Step

Description

Illustration

1

Type .


2

Rightclick the equation, and from the Context Menu, select Plots → 2D Plot of Right Side.






Using the interactive Plot Builder


Follow the steps below to plot the function .
Step

Description

Illustration

1

Type the expression . Do not type an equation, since the Plot Builder interprets equations as implicit plots.


2

Rightclick the expression, and from the Context Menu, select Plots → Plot Builder. The Plot Builder dialog opens. Note that if the Plot Builder is accessed from the main menu (Tools → Assistants → Plot Builder...), then the expression must be entered manually.


3

The plot type and plot ranges for independent variables can be set here. The Options button opens a window where the settings for this plot can be changed. For this example, the default settings suffice.


4

Click Plot. The plot is displayed.





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...enter a complex number


In Maple, the default representation of the imaginary unit is I. Thus, is a complex number in Maple. The example below demonstrates two ways to enter a complex number in Maple.
Maple provides a way to customize the way complex numbers are displayed. For instance, you may want to use i or j as the imaginary unit instead of I.

Example: Multiply two complex numbers


Maple uses I for the constant . Multiply by and display the result inline.
Step

Description

Illustration

1

Type . Put a space between 2 and to signify multiplication. (Alternatively, use [*] for multiplication.)


2

Enter a space (or *) and then type .


3

Press [Ctrl][=] to evaluate the expression inline.


Using the Palette

You can also enter complex numbers using the Common Symbols palette. From the palette, the symbols , , and can all be used to enter a complex number.
Note that simply typing will not produce the imaginary unit, but typing will.




When you type the letter i or j in Maple, it is understood as the name `i` or `j`. Only I is an initially known constant. This means:
•

You can use i or j as variables. For instance, as the index in expressions such as = .

•

Typing I results in the imaginary constant. Thus, = .



Using a different symbol for the imaginary unit


You can customize the setting that specifies which symbol represents the imaginary unit. This will enable you to simply type this symbol to get . Furthermore, ordinarily in output the imaginary unit is displayed with a capital I, no matter which symbol was used for input. By changing this setting, you change the output display.
Step

Description

Illustration

1

To change the symbol used for the imaginary unit, (both for input and output), use the interface command. The calling sequence is interface(imaginaryunit=symbol);
Here, we set to be the symbol for the imaginary unit.


2

Thereafter, clicking on , , or in the Common Symbols palette, or typing the letter will produce the imaginary unit, and its symbol as displayed in any output will be .

From the palette:
By typing:
In computations:




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Tools and Features


This section details the pointandclick tools and core features available in Maple to help you accomplish tasks quickly and easily. These features include palettes, context sensitive menus, and assistants.

Palettes


Maple has over thirty palettes containing an extensive collection of symbols, templates, and other features. These palettes are located beside the Maple workspace.
A template is an editable expression containing placeholders that can be easily overwritten. Use the [Tab] key to move to and highlight the next placeholder in a template, and [Shift][Tab] to move back to the previous placeholder. The How do I... section contains many examples where a template from a palette is used.
•

The Expression palette contains many common mathematical expressions—such as integrals, derivatives, exponents, subscripts, th roots, elementary functions, operators, and piecewise functions—as easily editable templates. See the How do I... subsection on entering a simple expression for an example of its use.

•

The Matrix palette is a tool used to insert a matrix template of a specified size, type, shape, and data type for entering a matrix quickly. See the How do I... subsection on entering a matrix for an example of its use.

By default, not all palettes are shown; to show a hidden palette, navigate to View → Palettes → Show Palette, and select a palette. Alternatively, navigate to View → Palettes → Arrange Palettes... to show, hide, and rearrange palettes interactively. Note that as more palettes are enabled, you may want to display some palettes to the right of the Maple workspace.
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ContextSensitive Menus


One of the most useful features in Maple is the ContextSensitive Menu, or Context Menu. Together with inline evaluation, the use of Context Menus is one of the fastest ways to perform a string of successive computations.
To access the Context Menu menu for a specific Maple object, rightclick the object. The Menu will contain common operations associated with the object; for example, the Context Menu for a matrix will include the inverse operation, and for an expression, the Menu will contain the simplify operation.
Before you proceed with the example below, be sure to familiarize yourself with entering simple mathematical expressions (see the How do I... subsection on entering a simple expression). Open a new worksheet in Document mode, and ensure that you are in Math mode.

Example: simplify and factor


Follow the steps below to simplify and factor the expression .
Step

Description

Illustration

1

Rightclick any part of the expression (within the dotted outline) and a Context Menu is displayed. Select Collect → Name → x.


2

Rightclick on the resulting expression and select Simplify>Simplify.


3

Rightclick on the resulting expression and select Factor.


Note

If you were working with an equation, some of these functionalities would not be available. Equations cannot be simplified or explicitly differentiated and must therefore first be converted into an expression. To do this, rightclick the equation and select Righthand side.





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Command Completion


Command and symbol completion is a feature that automatically suggests a command to use as you enter a phrase in Maple. To access the command completion menu, press [Esc] after typing the phrase. A popup list displays commands that begin with the phrase typed. Maple lists symbols, commands, functions, and package names that match the entered text. To insert an item from this list, select it with the mouse or navigate to it by using the arrow keys and press Enter.
For example, to get the Greek letter (rho), type rho and press [Esc]. Select
This command completion list can include command completion templates. These provide the full syntax of common Maple commands including arguments, so that these commands can be easily entered. Simply choose the desired command completion template and replace the placeholders with the desired values.
For example, to get an integral, type int and press [Esc]. Select int(definite)
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Equation Labels


Equation Labels are automatically generated after executing a Maple command on a new line. The result returned is labeled so that you can refer to it later in the document. As an example, compute the reduced row echelon form of a matrix using equation labels. Maple's equation labels are automatically renumbered in sequential order if any labeled result is deleted or moved.
Before you proceed with the example below, be sure to familiarize yourself with entering simple mathematical expressions (see the How do I... subsection on entering a simple expression). Open a new worksheet in Document mode, and ensure that you are in Math mode.

Computing the reduced row echelon form of a matrix


Follow the steps below to find the reduced row echelon form of the threebyfour matrix .
Step

Description

Illustration

1

Follow the instructions in either of the two examples given in the How do I subsection on entering matrices. Press [Enter], and the resulting Matrix is labeled.


2

Type
.


3

Now pass the Matrix as an argument to this procedure by typing a left parenthesis [(], followed by the equation label. To enter the equation label, either press [Ctrl][l] or select Insert → Label.... Type the label value into the dialogue box; in this case, since it is the first labeled result, the label value is . Click OK. Now type a right parenthesis [)].


4

Press [Enter]. The reduced row echelon form of this Matrix is displayed and labeled.





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Assistants


Maple has many interactive assistants that provide graphical user interfaces to various Maple packages and functionalities. Here are some of the assistants available in Maple.
BackSolver

Solve for an unknown parameter in an equation whose other parameters are known


Curve Fitting

Compute regressions and fit curves on a collection of data


Data Analysis

Display textual and graphical information about data sets, traverse data sets, and generate new data sets via standard operations on existing ones


Equation Manipulator

Perform a series of operations on an equation


Import Data

Import data from an external file into Maple as an rtable


Installer Builder

Build installers for your own toolboxes, or return a Build command which you can store and execute later


Library Browser

Manipulate the libraries in a specified directory


ODE Analyzer

Investigate and solve ordinary differential equations and ordinary differential equation systems


Optimization

Graphically minimize or maximize an objective function under given constraints


Plot Builder

Build a Maple plot interactively


Scientific Constants

Browse an extensive collection of physical constants and properties of chemical elements


Special Functions

View properties of over 200 special mathematical functions


Units Calculator

Convert between over 500 units of measurement




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Maple Help


Maple's help system provides extensive help on topics and commands in Maple. Access the help system from the Help>Maple Help menu item. To find help on a particular topic, you can enter ?Topic in Math mode and then press [Enter].
This will open the help page on the Statistics package.
You can also put your cursor in a word and press [F2] to get help on that word.


Plotting Guide


The Plotting Guide provides a visual guide to Maple's plots and a summary of plotting features.


Applications


The sample application worksheets provide demonstrations of solutions to specific problems.
To see a list of applications, from the Help menu, choose Manuals, Resources, and more>Applications and Examples.


Example Worksheets


Maple provides a number of example worksheets to supplement the examples in the help pages. Example worksheets demonstrate the syntax of popular commands and packages, such as solve, Calculus, and Linear Algebra, as well as more sophisticated topics such as lexical scoping. You can execute all the commands in the example worksheets.
To view a list of example and application worksheets, see the examples index.


Manuals


Access the Maple User Manual and Maple Programming Guide within Maple.
1.

From the Help menu, select Manuals, Resources, and more.

2.

Select Manuals and then the desired manual.

The manual opens with the Table of Contents displayed.

Other Resources
Maple's Application Center offers over 1,500 Maple applications, Maplet applications, tutorials, Maple PowerTools, MapleSim models, and Maple packages for free download.
Maple Primes is a web community dedicated to sharing experiences, techniques, and opinions about Maple and related products, as well as general interest topics in math and computing.
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